,a ,,system ,,of ,,logic1 ,,ratiocinative ,,and ,,inductive1 ,,being ,a ,,connected ,,view ,,of ,,the ,,principles ,,of ,,evidence1 ,,and ,,the ,,methods ,,of ,,scientific ,,investigation4 by ,,john ,,stuart ,,mill4 ,eighth ,edition4 ,new ,york3 ,harper ,brothers1 ,publishers1 ,franklin ,square4 #ahhb4 ,,contents ,preface ,to ,the ,first ,edition4 ,preface ,to ,the ,third ,and ,fourth ,editions4 ,introduction4 ,book ,i4 ,of ,names ,and ,propositions4 ,chapter ,i4 ,of ,the ,necessity ,of ,commencing ,with ,an ,analysis ,of ,language4 ,chapter ,,ii4 ,of ,names4 ,chapter ,,iii4 ,of ,the ,things ,denoted ,by ,names4 ,chapter ,,iv4 ,of ,propositions4 ,chapter ,v4 ,of ,the ,import ,of ,propositions4 ,chapter ,,vi4 ,of ,propositions ,merely ,verbal4 ,chapter ,,vii4 ,of ,the ,nature ,of ,classification1 ,and ,the ,five ,predicables4 ,chapter ,,viii4 ,of ,definition4 ,book ,,ii4 ,on ,reasoning4 ,chapter ,i4 ,of ,inference1 ,or ,reasoning1 ,in ,general4 ,chapter ,,ii4 ,of ,ratiocination1 ,or ,syllogism4 ,chapter ,,iii4 ,of ,the ,functions ,and ,logical ,value ,of ,the ,syllogism4 ,chapter ,,iv4 ,of ,trains ,of ,reasoning1 ,and ,deductive ,sciences4 ,chapter ,v4 ,of ,demonstration1 ,and ,necessary ,truths4 ,chapter ,,vi4 ,the ,same ,subject ,continued4 ,chapter ,,vii4 ,examination ,of ,some ,opinions ,opposed ,to ,the ,preceding ,doctrines4 ,book ,,iii4 ,of ,induction4 ,chapter ,i4 ,preliminary ,observations ,on ,induction ,in ,general4 ,chapter ,,ii4 ,of ,inductions ,improperly ,so ,called4 ,chapter ,,iii4 ,of ,the ,ground ,of ,induction4 ,chapter ,,iv4 ,of ,laws ,of ,nature4 ,chapter ,v4 ,of ,the ,law ,of ,universal ,causation4 ,chapter ,,vi4 ,on ,the ,composition ,of ,causes4 ,chapter ,,vii4 ,on ,observation ,and ,experiment4 ,chapter ,,viii4 ,of ,the ,four ,methods ,of ,experimental ,inquiry4 ,chapter ,,ix4 ,miscellaneous ,examples ,of ,the ,four ,methods4 ,chapter ,x4 ,of ,plurality ,of ,causes1 ,and ,of ,the ,intermixture ,of ,effects4 ,chapter ,,xi4 ,of ,the ,deductive ,method4 ,chapter ,,xii4 ,of ,the ,explanation ,of ,laws ,of ,nature4 ,chapter ,,xiii4 ,miscellaneous ,examples ,of ,the ,explanation ,of ,laws ,of ,nature4 ,chapter ,,xiv4 ,of ,the ,limits ,to ,the ,explanation ,of ,laws ,of ,nature2 ,and ,of ,hypotheses4 ,chapter ,,xv4 ,of ,progressive ,effects2 ,and ,of ,the ,continued ,action ,of ,causes4 ,chapter ,,xvi4 ,of ,empirical ,laws4 ,chapter ,,xvii4 ,of ,chance ,and ,its ,elimination4 ,chapter ,,xviii4 ,of ,the ,calculation ,of ,chances4 ,chapter ,,xix4 ,of ,the ,extension ,of ,derivative ,laws ,to ,adjacent ,cases4 ,chapter ,,xx4 ,of ,analogy4 ,chapter ,,xxi4 ,of ,the ,evidence ,of ,the ,law ,of ,universal ,causation4 ,chapter ,,xxii4 ,of ,uniformities ,of ,co-,existence ,not ,dependent ,on ,causation4 ,chapter ,,xxiii4 ,of ,approximate ,generalizations1 ,and ,probable ,evidence4 ,chapter ,,xxiv4 ,of ,the ,remaining ,laws ,of ,nature4 ,chapter ,,xxv4 ,of ,the ,grounds ,of ,disbelief4 ,book ,,iv4 ,of ,operations ,subsidiary ,to ,induction4 ,chapter ,i4 ,of ,observation ,and ,description4 ,chapter ,,ii4 ,of ,abstraction1 ,or ,the ,formation ,of ,conceptions4 ,chapter ,,iii4 ,of ,naming1 ,as ,subsidiary ,to ,induction4 ,chapter ,,iv4 ,of ,the ,requisites ,of ,a ,philosophical ,language1 ,and ,the ,principles ,of ,definition4 ,chapter ,v4 ,on ,the ,natural ,history ,of ,the ,variations ,in ,the ,meaning ,of ,terms4 ,chapter ,,vi4 ,the ,principles ,of ,a ,philosophical ,language ,further ,considered4 ,chapter ,,vii4 ,of ,classification1 ,as ,subsidiary ,to ,induction4 ,chapter ,,viii4 ,of ,classification ,by ,series4 ,book ,v4 ,on ,fallacies4 ,chapter ,i4 ,of ,fallacies ,in ,general4 ,chapter ,,ii4 ,classification ,of ,fallacies4 ,chapter ,,iii4 ,fallacies ,of ,simple ,inspection2 ,or ,a ,priori ,fallacies4 ,chapter ,,iv4 ,fallacies ,of ,observation4 ,chapter ,v4 ,fallacies ,of ,generalization4 ,chapter ,,vi4 ,fallacies ,of ,ratiocination4 ,chapter ,,vii4 ,fallacies ,of ,confusion4 ,book ,,vi4 ,on ,the ,logic ,of ,the ,moral ,sciences4 ,chapter ,i4 ,introductory ,remarks4 ,chapter ,,ii4 ,of ,liberty ,and ,necessity4 ,chapter ,,iii4 ,that ,there ,is1 ,or ,may ,be1 ,a ,science ,of ,human ,nature4 ,chapter ,,iv4 ,of ,the ,laws ,of ,mind4 ,chapter ,v4 ,of ,ethology1 ,or ,the ,science ,of ,the ,formation ,of ,character4 ,chapter ,,vi4 ,general ,considerations ,on ,the ,social ,science4 ,chapter ,,vii4 ,of ,the ,chemical1 ,or ,experimental1 ,method ,in ,the ,social ,science4 ,chapter ,,viii4 ,of ,the ,geometrical1 ,or ,abstract1 ,method4 ,chapter ,,ix4 ,of ,the ,physical1 ,or ,concrete ,deductive1 ,method4 ,chapter ,x4 ,of ,the ,inverse ,deductive1 ,or ,historical1 ,method4 ,chapter ,,xi4 ,additional ,elucidations ,of ,the ,science ,of ,history4 ,chapter ,,xii4 ,of ,the ,logic ,of ,practice1 ,or ,art2 ,including ,morality ,and ,policy4 ,footnotes ,,preface ,,to ,,the ,,first ,,edition4 ,this book makes no pretense of giving to the world a new theory of the intellectual operations4 ,its claim to attention1 if it possess any1 is grounded on the fact that it is an attempt1 not to supersede1 but to embody and systematize1 the best ideas which have been either promulgated on its subject by speculative writers1 or conformed to by accurate thinkers in their scientific inquiries4 ,to cement together the detached fragments of a subject1 never yet treated as a whole2 to harmonize the true portions of discordant theories1 by supplying the links of thought necessary to connect them1 and by disentangling them from the errors with which they are always more or less interwoven1 must necessarily require a considerable amount of original speculation4 ,to other originality than this1 the present work lays no claim4 ,in the existing state of the cultivation of the sciences1 there would be a very strong presumption against any one who should imagine that he had effected a revolution in the theory of the investigation of truth1 or added any fundamentally new process to the practice of it4 ,the improvement which remains to be effected in the methods of philosophizing 7and the author believes that they have much need of improvement7 can only consist in performing more systematically and accurately operations with which1 at least in their elementary form1 the human intellect1 in some one or other of its employments1 is already familiar4 ,in the portion of the work which treats of ,ratiocination1 the author has not deemed it necessary to enter into technical details which may be obtained in so perfect a shape from the existing treatises on what is termed the ,logic of the ,schools4 ,in the contempt entertained by many modern philosophers for the syllogistic art1 it will be seen that he by no means participates2 though the scientific theory on which its defense is usually rested appears to him erroneous3 and the view which he has suggested of the nature and functions of the ,syllogism may1 perhaps1 afford the means of conciliating the principles of the art with as much as is well grounded in the doctrines and objections of its assailants4 ,the same abstinence from details could not be observed in the ,first ,book1 on ,names and ,propositions2 because many useful principles and distinctions which were contained in the old ,logic have been gradually omitted from the writings of its later teachers2 and it appeared desirable both to revive these1 and to reform and rationalize the philosophical foundation on which they stood4 ,the earlier chapters of this preliminary ,book will consequently appear1 to some readers1 needlessly elementary and scholastic4 ,but those who know in what darkness the nature of our knowledge1 and of the processes by which it is obtained1 is often involved by a confused apprehension of the import of the different classes of ,words and ,assertions1 will not regard these discussions as either frivolous1 or irrelevant to the topics considered in the later ,books4 ,on the subject of ,induction1 the task to be performed was that of generalizing the modes of investigating truth and estimating evidence1 by which so many important and recondite laws of nature have1 in the various sciences1 been aggregated to the stock of human knowledge4 ,that this is not a task free from difficulty may be presumed from the fact that even at a very recent period1 eminent writers 7among whom it is sufficient to name ,archbishop ,whately1 and the author of a celebrated article on ,bacon in the ,edinburgh ,review7 have not scrupled to pronounce it impossible47#a7 ,the author has endeavored to combat their theory in the manner in which ,diogenes confuted the skeptical reasonings against the possibility of motion2 remembering that ,diogenes's argument would have been equally conclusive1 though his individual perambulations might not have extended beyond the circuit of his own tub4 ,whatever may be the value of what the author has succeeded in effecting on this branch of his subject1 it is a duty to acknowledge that for much of it he has been indebted to several important treatises1 partly historical and partly philosophical1 on the generalities and processes of physical science1 which have been published within the last few years4 ,to these treatises1 and to their authors1 he has endeavored to do justice in the body of the work4 ,but as with one of these writers1 ,dr4 ,whewell1 he has occasion frequently to express differences of opinion1 it is more particularly incumbent on him in this place to declare1 that without the aid derived from the facts and ideas contained in that gentleman's 8,history of the ,inductive ,sciences10 the corresponding portion of this work would probably not have been written4 ,the concluding ,book is an attempt to contribute toward the solution of a question which the decay of old opinions1 and the agitation that disturbs ,european society to its inmost depths1 render as important in the present day to the practical interests of human life1 as it must at all times be to the completeness of our speculative knowledge--viz43 ,whether moral and social phenomena are really exceptions to the general certainty and uniformity of the course of nature2 and how far the methods by which so many of the laws of the physical world have been numbered among truths irrevocably acquired and universally assented to1 can be made instrumental to the formation of a similar body of received doctrine in moral and political science4 ,,preface ,,to ,,the ,,third ,,and ,,fourth ,,editions4 ,several criticisms1 of a more or less controversial character1 on this work1 have appeared since the publication of the second edition2 and ,dr4 ,whewell has lately published a reply to those parts of it in which some of his opinions were controverted47#b7 ,i have carefully reconsidered all the points on which my conclusions have been assailed4 ,but ,i have not to announce a change of opinion on any matter of importance4 ,such minor oversights as have been detected1 either by myself or by my critics1 ,i have1 in general silently1 corrected3 but it is not to be inferred that ,i agree with the objections which have been made to a passage1 in every instance in which ,i have altered or canceled it4 ,i have often done so1 merely that it might not remain a stumbling-block1 when the amount of discussion necessary to place the matter in its true light would have exceeded what was suitable to the occasion4 ,to several of the arguments which have been urged against me1 ,i have thought it useful to reply with some degree of minuteness2 not from any taste for controversy1 but because the opportunity was favorable for placing my own conclusions1 and the grounds of them1 more clearly and completely before the reader4 ,truth on these subjects is militant1 and can only establish itself by means of conflict4 ,the most opposite opinions can make a plausible show of evidence while each has the statement of its own case2 and it is only possible to ascertain which of them is in the right1 after hearing and comparing what each can say against the other1 and what the other can urge in its defense4 ,even the criticisms from which ,i most dissent have been of great service to me1 by showing in what places the exposition most needed to be improved1 or the argument strengthened4 ,and ,i should have been well pleased if the book had undergone a much greater amount of attack2 as in that case ,i should probably have been enabled to improve it still more than ,i believe ,i have now done4 ------------------------------------ ,in the subsequent editions1 the attempt to improve the work by additions and corrections1 suggested by criticism or by thought1 has been continued4 ,the additions and corrections in the present 7eighth7 edition1 which are not very considerable1 are chiefly such as have been suggested by ,professor ,bain's 8,logic10 a book of great merit and value4 ,mr4 ,bain's view of the science is essentially the same with that taken in the present treatise1 the differences of opinion being few and unimportant compared with the agreements2 and he has not only enriched the exposition by many applications and illustrative details1 but has appended to it a minute and very valuable discussion of the logical principles specially applicable to each of the sciences--a task for which the encyclopedical character of his knowledge peculiarly qualified him4 ,i have in several instances made use of his exposition to improve my own1 by adopting1 and occasionally by controverting1 matter contained in his treatise4 ,the longest of the additions belongs to the chapter on ,causation1 and is a discussion of the question how far1 if at all1 the ordinary mode of stating the law of ,cause and ,effect requires modification to adapt it to the new doctrine of the ,conservation of ,force--a point still more fully and elaborately treated in ,mr4 ,bain's work4 ,,introduction4 #a4 ,there is as great diversity among authors in the modes which they have adopted of defining logic1 as in their treatment of the details of it4 ,this is what might naturally be expected on any subject on which writers have availed themselves of the same language as a means of delivering different ideas4 ,ethics and jurisprudence are liable to the remark in common with logic4 ,almost every writer having taken a different view of some of the particulars which these branches of knowledge are usually understood to include2 each has so framed his definition as to indicate beforehand his own peculiar tenets1 and sometimes to beg the question in their favor4 ,this diversity is not so much an evil to be complained of1 as an inevitable and in some degree a proper result of the imperfect state of those sciences4 ,it is not to be expected that there should be agreement about the definition of any thing1 until there is agreement about the thing itself4 ,to define1 is to select from among all the properties of a thing1 those which shall be understood to be designated and declared by its name2 and the properties must be well known to us before we can be competent to determine which of them are fittest to be chosen for this purpose4 ,accordingly1 in the case of so complex an aggregation of particulars as are comprehended in any thing which can be called a science1 the definition we set out with is seldom that which a more extensive knowledge of the subject shows to be the most appropriate4 ,until we know the particulars themselves1 we can not fix upon the most correct and compact mode of circumscribing them by a general description4 ,it was not until after an extensive and accurate acquaintance with the details of chemical phenomena1 that it was found possible to frame a rational definition of chemistry2 and the definition of the science of life and organization is still a matter of dispute4 ,so long as the sciences are imperfect1 the definitions must partake of their imperfection2 and if the former are progressive1 the latter ought to be so too4 ,as much1 therefore1 as is to be expected from a definition placed at the commencement of a subject1 is that it should define the scope of our inquiries3 and the definition which ,i am about to offer of the science of logic1 pretends to nothing more than to be a statement of the question which ,i have put to myself1 and which this book is an attempt to resolve4 ,the reader is at liberty to object to it as a definition of logic2 but it is at all events a correct definition of the subject of this volume4 #b4 ,logic has often been called the ,art of ,reasoning4 ,a writer7#c7 who has done more than any other person to restore this study to the rank from which it had fallen in the estimation of the cultivated class in our own country1 has adopted the above definition with an amendment2 he has defined ,logic to be the ,science1 as well as the ,art1 of reasoning2 meaning by the former term1 the analysis of the mental process which takes place whenever we reason1 and by the latter1 the rules1 grounded on that analysis1 for conducting the process correctly4 ,there can be no doubt as to the propriety of the emendation4 ,a right understanding of the mental process itself1 of the conditions it depends on1 and the steps of which it consists1 is the only basis on which a system of rules1 fitted for the direction of the process1 can possibly be founded4 ,art necessarily presupposes knowledge2 art1 in any but its infant state1 presupposes scientific knowledge3 and if every art does not bear the name of a science1 it is only because several sciences are often necessary to form the groundwork of a single art4 ,so complicated are the conditions which govern our practical agency1 that to enable one thing to be done1 it is often requisite to know the nature and properties of many things4 ,logic1 then1 comprises the science of reasoning1 as well as an art1 founded on that science4 ,but the word ,reasoning1 again1 like most other scientific terms in popular use1 abounds in ambiguities4 ,in one of its acceptations1 it means syllogizing2 or the mode of inference which may be called 7with sufficient accuracy for the present purpose7 concluding from generals to particulars4 ,in another of its senses1 to reason is simply to infer any assertion1 from assertions already admitted3 and in this sense induction is as much entitled to be called reasoning as the demonstrations of geometry4 ,writers on logic have generally preferred the former acceptation of the term3 the latter1 and more extensive signification is that in which ,i mean to use it4 ,i do this by virtue of the right ,i claim for every author1 to give whatever provisional definition he pleases of his own subject4 ,but sufficient reasons will1 ,i believe1 unfold themselves as we advance1 why this should be not only the provisional but the final definition4 ,it involves1 at all events1 no arbitrary change in the meaning of the word2 for1 with the general usage of the ,english language1 the wider signification1 ,i believe1 accords better than the more restricted one4 #c4 ,but reasoning1 even in the widest sense of which the word is susceptible1 does not seem to comprehend all that is included1 either in the best1 or even in the most current1 conception of the scope and province of our science4 ,the employment of the word ,logic to denote the theory of ,argumentation1 is derived from the ,aristotelian1 or1 as they are commonly termed1 the scholastic1 logicians4 ,yet even with them1 in their systematic treatises1 ,argumentation was the subject only of the third part3 the two former treated of ,terms1 and of ,propositions2 under one or other of which heads were also included ,definition and ,division4 ,by some1 indeed1 these previous topics were professedly introduced only on account of their connection with reasoning1 and as a preparation for the doctrine and rules of the syllogism4 ,yet they were treated with greater minuteness1 and dwelt on at greater length1 than was required for that purpose alone4 ,more recent writers on logic have generally understood the term as it was employed by the able author of the ,port ,royal ,logic2 viz41 as equivalent to the ,art of ,thinking4 ,nor is this acceptation confined to books1 and scientific inquiries4 ,even in ordinary conversation1 the ideas connected with the word ,logic include at least precision of language1 and accuracy of classification3 and we perhaps oftener hear persons speak of a logical arrangement1 or of expressions logically defined1 than of conclusions logically deduced from premises4 ,again1 a man is often called a great logician1 or a man of powerful logic1 not for the accuracy of his deductions1 but for the extent of his command over premises2 because the general propositions required for explaining a difficulty or refuting a sophism1 copiously and promptly occur to him3 because1 in short1 his knowledge1 besides being ample1 is well under his command for argumentative use4 ,whether1 therefore1 we conform to the practice of those who have made the subject their particular study1 or to that of popular writers and common discourse1 the province of logic will include several operations of the intellect not usually considered to fall within the meaning of the terms ,reasoning and ,argumentation4 ,these various operations might be brought within the compass of the science1 and the additional advantage be obtained of a very simple definition1 if1 by an extension of the term1 sanctioned by high authorities1 we were to define logic as the science which treats of the operations of the human understanding in the pursuit of truth4 ,for to this ultimate end1 naming1 classification1 definition1 and all other operations over which logic has ever claimed jurisdiction1 are essentially subsidiary4 ,they may all be regarded as contrivances for enabling a person to know the truths which are needful to him1 and to know them at the precise moment at which they are needful4 ,other purposes1 indeed1 are also served by these operations2 for instance1 that of imparting our knowledge to others4 ,but1 viewed with regard to this purpose1 they have never been considered as within the province of the logician4 ,the sole object of ,logic is the guidance of one's own thoughts3 the communication of those thoughts to others falls under the consideration of ,rhetoric1 in the large sense in which that art was conceived by the ancients2 or of the still more extensive art of ,education4 ,logic takes cognizance of our intellectual operations only as they conduce to our own knowledge1 and to our command over that knowledge for our own uses4 ,if there were but one rational being in the universe1 that being might be a perfect logician2 and the science and art of logic would be the same for that one person as for the whole human race4 #d4 ,but1 if the definition which we formerly examined included too little1 that which is now suggested has the opposite fault of including too much4 ,truths are known to us in two ways3 some are known directly1 and of themselves2 some through the medium of other truths4 ,the former are the subject of ,intuition1 or ,consciousness27#d7 the latter1 of ,inference4 ,the truths known by intuition are the original premises from which all others are inferred4 ,our assent to the conclusion being grounded on the truth of the premises1 we never could arrive at any knowledge by reasoning1 unless something could be known antecedently to all reasoning4 ,examples of truths known to us by immediate consciousness1 are our own bodily sensations and mental feelings4 ,i know directly1 and of my own knowledge1 that ,i was vexed yesterday1 or that ,i am hungry to-day4 ,examples of truths which we know only by way of inference1 are occurrences which took place while we were absent1 the events recorded in history1 or the theorems of mathematics4 ,the two former we infer from the testimony adduced1 or from the traces of those past occurrences which still exist2 the latter1 from the premises laid down in books of geometry1 under the title of definitions and axioms4 ,whatever we are capable of knowing must belong to the one class or to the other2 must be in the number of the primitive data1 or of the conclusions which can be drawn from these4 ,with the original data1 or ultimate premises of our knowledge2 with their number or nature1 the mode in which they are obtained1 or the tests by which they may be distinguished2 logic1 in a direct way at least1 has1 in the sense in which ,i conceive the science1 nothing to do4 ,these questions are partly not a subject of science at all1 partly that of a very different science4 ,whatever is known to us by consciousness is known beyond possibility of question4 ,what one sees or feels1 whether bodily or mentally1 one can not but be sure that one sees or feels4 ,no science is required for the purpose of establishing such truths2 no rules of art can render our knowledge of them more certain than it is in itself4 ,there is no logic for this portion of our knowledge4 ,but we may fancy that we see or feel what we in reality infer4 ,a truth1 or supposed truth1 which is really the result of a very rapid inference1 may seem to be apprehended intuitively4 ,it has long been agreed by thinkers of the most opposite schools1 that this mistake is actually made in so familiar an instance as that of the eyesight4 ,there is nothing of which we appear to ourselves to be more directly conscious than the distance of an object from us4 ,yet it has long been ascertained1 that what is perceived by the eye1 is at most nothing more than a variously colored surface2 that when we fancy we see distance1 all we really see is certain variations of apparent size1 and degrees of faintness of color2 that our estimate of the object's distance from us is the result partly of a rapid inference from the muscular sensations accompanying the adjustment of the focal distance of the eye to objects unequally remote from us1 and partly of a comparison 7made with so much rapidity that we are unconscious of making it7 between the size and color of the object as they appear at the time1 and the size and color of the same or of similar objects as they appeared when close at hand1 or when their degree of remoteness was known by other evidence4 ,the perception of distance by the eye1 which seems so like intuition1 is thus1 in reality1 an inference grounded on experience2 an inference1 too1 which we learn to make2 and which we make with more and more correctness as our experience increases2 though in familiar cases it takes place so rapidly as to appear exactly on a par with those perceptions of sight which are really intuitive1 our perceptions of color47#e7 ,of the science1 therefore1 which expounds the operations of the human understanding in the pursuit of truth1 one essential part is the inquiry3 ,what are the facts which are the objects of intuition or consciousness1 and what are those which we merely infer8 ,but this inquiry has never been considered a portion of logic4 ,its place is in another and a perfectly distinct department of science1 to which the name metaphysics more particularly belongs3 that portion of mental philosophy which attempts to determine what part of the furniture of the mind belongs to it originally1 and what part is constructed out of materials furnished to it from without4 ,to this science appertain the great and much debated questions of the existence of matter2 the existence of spirit1 and of a distinction between it and matter2 the reality of time and space1 as things without the mind1 and distinguishable from the objects which are said to exist in them4 ,for in the present state of the discussion on these topics1 it is almost universally allowed that the existence of matter or of spirit1 of space or of time1 is in its nature unsusceptible of being proved2 and that if any thing is known of them1 it must be by immediate intuition4 ,to the same science belong the inquiries into the nature of ,conception1 ,perception1 ,memory1 and ,belief2 all of which are operations of the understanding in the pursuit of truth2 but with which1 as phenomena of the mind1 or with the possibility which may or may not exist of analyzing any of them into simpler phenomena1 the logician as such has no concern4 ,to this science must also be referred the following1 and all analogous questions3 ,to what extent our intellectual faculties and our emotions are innate--to what extent the result of association3 ,whether ,god and duty are realities1 the existence of which is manifest to us a priori by the constitution of our rational faculty2 or whether our ideas of them are acquired notions1 the origin of which we are able to trace and explain2 and the reality of the objects themselves a question not of consciousness or intuition1 but of evidence and reasoning4 ,the province of logic must be restricted to that portion of our knowledge which consists of inferences from truths previously known2 whether those antecedent data be general propositions1 or particular observations and perceptions4 ,logic is not the science of ,belief1 but the science of ,proof1 or ,evidence4 ,in so far as belief professes to be founded on proof1 the office of logic is to supply a test for ascertaining whether or not the belief is well grounded4 ,with the claims which any proposition has to belief on the evidence of consciousness--that is1 without evidence in the proper sense of the word--logic has nothing to do4 #e4 ,by far the greatest portion of our knowledge1 whether of general truths or of particular facts1 being avowedly matter of inference1 nearly the whole1 not only of science1 but of human conduct1 is amenable to the authority of logic4 ,to draw inferences has been said to be the great business of life4 ,every one has daily1 hourly1 and momentary need of ascertaining facts which he has not directly observed2 not from any general purpose of adding to his stock of knowledge1 but because the facts themselves are of importance to his interests or to his occupations4 ,the business of the magistrate1 of the military commander1 of the navigator1 of the physician1 of the agriculturist1 is merely to judge of evidence1 and to act accordingly4 ,they all have to ascertain certain facts1 in order that they may afterward apply certain rules1 either devised by themselves or prescribed for their guidance by others2 and as they do this well or ill1 so they discharge well or ill the duties of their several callings4 ,it is the only occupation in which the mind never ceases to be engaged2 and is the subject1 not of logic1 but of knowledge in general4 ,logic1 however1 is not the same thing with knowledge1 though the field of logic is co-extensive with the field of knowledge4 ,logic is the common judge and arbiter of all particular investigations4 ,it does not undertake to find evidence1 but to determine whether it has been found4 ,logic neither observes1 nor invents1 nor discovers2 but judges4 ,it is no part of the business of logic to inform the surgeon what appearances are found to accompany a violent death4 ,this he must learn from his own experience and observation1 or from that of others1 his predecessors in his peculiar pursuit4 ,but logic sits in judgment on the sufficiency of that observation and experience to justify his rules1 and on the sufficiency of his rules to justify his conduct4 ,it does not give him proofs1 but teaches him what makes them proofs1 and how he is to judge of them4 ,it does not teach that any particular fact proves any other1 but points out to what conditions all facts must conform1 in order that they may prove other facts4 ,to decide whether any given fact fulfills these conditions1 or whether facts can be found which fulfill them in a given case1 belongs exclusively to the particular art or science1 or to our knowledge of the particular subject4 ,it is in this sense that logic is1 what it was so expressively called by the schoolmen and by ,bacon1 ars artium2 the science of science itself4 ,all science consists of data and conclusions from those data1 of proofs and what they prove3 now logic points out what relations must subsist between data and whatever can be concluded from them1 between proof and every thing which it can prove4 ,if there be any such indispensable relations1 and if these can be precisely determined1 every particular branch of science1 as well as every individual in the guidance of his conduct1 is bound to conform to those relations1 under the penalty of making false inferences--of drawing conclusions which are not grounded in the realities of things4 ,whatever has at any time been concluded justly1 whatever knowledge has been acquired otherwise than by immediate intuition1 depended on the observance of the laws which it is the province of logic to investigate4 ,if the conclusions are just1 and the knowledge real1 those laws1 whether known or not1 have been observed4 #f4 ,we need not1 therefore1 seek any further for a solution of the question1 so often agitated1 respecting the utility of logic4 ,if a science of logic exists1 or is capable of existing1 it must be useful4 ,if there be rules to which every mind consciously or unconsciously conforms in every instance in which it infers rightly1 there seems little necessity for discussing whether a person is more likely to observe those rules1 when he knows the rules1 than when he is unacquainted with them4 ,a science may undoubtedly be brought to a certain1 not inconsiderable1 stage of advancement1 without the application of any other logic to it than what all persons1 who are said to have a sound understanding1 acquire empirically in the course of their studies4 ,mankind judged of evidence1 and often correctly1 before logic was a science1 or they never could have made it one4 ,and they executed great mechanical works before they understood the laws of mechanics4 ,but there are limits both to what mechanicians can do without principles of mechanics1 and to what thinkers can do without principles of logic4 ,a few individuals1 by extraordinary genius1 or by the accidental acquisition of a good set of intellectual habits1 may work without principles in the same way1 or nearly the same way1 in which they would have worked if they had been in possession of principles4 ,but the bulk of mankind require either to understand the theory of what they are doing1 or to have rules laid down for them by those who have understood the theory4 ,in the progress of science from its easiest to its more difficult problems1 each great step in advance has usually had either as its precursor1 or as its accompaniment and necessary condition1 a corresponding improvement in the notions and principles of logic received among the most advanced thinkers4 ,and if several of the more difficult sciences are still in so defective a state2 if not only so little is proved1 but disputation has not terminated even about the little which seemed to be so2 the reason perhaps is1 that men's logical notions have not yet acquired the degree of extension1 or of accuracy1 requisite for the estimation of the evidence proper to those particular departments of knowledge4 #g4 ,logic1 then1 is the science of the operations of the understanding which are subservient to the estimation of evidence3 both the process itself of advancing from known truths to unknown1 and all other intellectual operations in so far as auxiliary to this4 ,it includes1 therefore1 the operation of ,naming2 for language is an instrument of thought1 as well as a means of communicating our thoughts4 ,it includes1 also1 ,definition1 and ,classification4 ,for1 the use of these operations 7putting all other minds than one's own out of consideration7 is to serve not only for keeping our evidences and the conclusions from them permanent and readily accessible in the memory1 but for so marshaling the facts which we may at any time be engaged in investigating1 as to enable us to perceive more clearly what evidence there is1 and to judge with fewer chances of error whether it be sufficient4 ,these1 therefore1 are operations specially instrumental to the estimation of evidence1 and1 as such1 are within the province of ,logic4 ,there are other more elementary processes1 concerned in all thinking1 such as ,conception1 ,memory1 and the like2 but of these it is not necessary that ,logic should take any peculiar cognizance1 since they have no special connection with the problem of ,evidence1 further than that1 like all other problems addressed to the understanding1 it presupposes them4 ,our object1 then1 will be1 to attempt a correct analysis of the intellectual process called ,reasoning or ,inference1 and of such other mental operations as are intended to facilitate this3 as well as1 on the foundation of this analysis1 and pari passu with it1 to bring together or frame a set of rules or canons for testing the sufficiency of any given evidence to prove any given proposition4 ,with respect to the first part of this undertaking1 ,i do not attempt to decompose the mental operations in question into their ultimate elements4 ,it is enough if the analysis as far as it goes is correct1 and if it goes far enough for the practical purposes of logic considered as an art4 ,the separation of a complicated phenomenon into its component parts is not like a connected and interdependent chain of proof4 ,if one link of an argument breaks1 the whole drops to the ground2 but one step toward an analysis holds good and has an independent value1 though we should never be able to make a second4 ,the results which have been obtained by analytical chemistry are not the less valuable1 though it should be discovered that all which we now call simple substances are really compounds4 ,all other things are at any rate compounded of those elements3 whether the elements themselves admit of decomposition1 is an important inquiry1 but does not affect the certainty of the science up to that point4 ,i shall1 accordingly1 attempt to analyze the process of inference1 and the processes subordinate to inference1 so far only as may be requisite for ascertaining the difference between a correct and an incorrect performance of those processes4 ,the reason for thus limiting our design1 is evident4 ,it has been said by objectors to logic1 that we do not learn to use our muscles by studying their anatomy4 ,the fact is not quite fairly stated2 for if the action of any of our muscles were vitiated by local weakness1 or other physical defect1 a knowledge of their anatomy might be very necessary for effecting a cure4 ,but we should be justly liable to the criticism involved in this objection1 were we1 in a treatise on logic1 to carry the analysis of the reasoning process beyond the point at which any inaccuracy which may have crept into it must become visible4 ,in learning bodily exercises 7to carry on the same illustration7 we do1 and must1 analyze the bodily motions so far as is necessary for distinguishing those which ought to be performed from those which ought not4 ,to a similar extent1 and no further1 it is necessary that the logician should analyze the mental processes with which ,logic is concerned4 ,logic has no interest in carrying the analysis beyond the point at which it becomes apparent whether the operations have in any individual case been rightly or wrongly performed3 in the same manner as the science of music teaches us to discriminate between musical notes1 and to know the combinations of which they are susceptible1 but not what number of vibrations in a second correspond to each2 which1 though useful to be known1 is useful for totally different purposes4 ,the extension of ,logic as a ,science is determined by its necessities as an ,art3 whatever it does not need for its practical ends1 it leaves to the larger science which may be said to correspond1 not to any particular art1 but to art in general2 the science which deals with the constitution of the human faculties2 and to which1 in the part of our mental nature which concerns ,logic1 as well as in all other parts1 it belongs to decide what are ultimate facts1 and what are resolvable into other facts4 ,and ,i believe it will be found that most of the conclusions arrived at in this work have no necessary connection with any particular views respecting the ulterior analysis4 ,logic is common ground on which the partisans of ,hartley and of ,reid1 of ,locke and of ,kant1 may meet and join hands4 ,particular and detached opinions of all these thinkers will no doubt occasionally be controverted1 since all of them were logicians as well as metaphysicians2 but the field on which their principal battles have been fought1 lies beyond the boundaries of our science4 ,it can not1 indeed1 be pretended that logical principles can be altogether irrelevant to those more abstruse discussions2 nor is it possible but that the view we are led to take of the problem which logic proposes1 must have a tendency favorable to the adoption of some one opinion1 on these controverted subjects1 rather than another4 ,for metaphysics1 in endeavoring to solve its own peculiar problem1 must employ means1 the validity of which falls under the cognizance of logic4 ,it proceeds1 no doubt1 as far as possible1 merely by a closer and more attentive interrogation of our consciousness1 or more properly speaking1 of our memory2 and so far is not amenable to logic4 ,but wherever this method is insufficient to attain the end of its inquiries1 it must proceed1 like other sciences1 by means of evidence4 ,now1 the moment this science begins to draw inferences from evidence1 logic becomes the sovereign judge whether its inferences are well grounded1 or what other inferences would be so4 ,this1 however1 constitutes no nearer or other relation between logic and metaphysics1 than that which exists between logic and every other science4 ,and ,i can conscientiously affirm that no one proposition laid down in this work has been adopted for the sake of establishing1 or with any reference to its fitness for being employed in establishing1 preconceived opinions in any department of knowledge or of inquiry on which the speculative world is still undecided47#f7 ,book ,i4 ,,of ,,names ,,and ,,propositions4 8,la scolastique1 qui produisit dans la logique1 comme dans la morale1 et dans une partie de la mtaphysique1 une subtilit1 une prcision d'ides1 dont l'habitude inconnue aux anciens1 a contribu plus qu'on ne croit au progrs de la bonne philosophie40--,,condorcet1 ,vie de ,turgot4 8,to the schoolmen the vulgar languages are principally indebted for what precision and analytic subtlety they possess40--,,sir ,w4 ,,hamilton1 ,discussions in ,philosophy4 ,chapter ,i4 ,of ,the ,necessity ,of ,commencing ,with ,an ,analysis ,of ,language4 #a4 ,it is so much the established practice of writers on logic to commence their treatises by a few general observations 7in most cases1 it is true1 rather meagre7 on ,terms and their varieties1 that it will1 perhaps1 scarcely be required from me1 in merely following the common usage1 to be as particular in assigning my reasons1 as it is usually expected that those should be who deviate from it4 ,the practice1 indeed1 is recommended by considerations far too obvious to require a formal justification4 ,logic is a portion of the ,art of ,thinking3 ,language is evidently1 and by the admission of all philosophers1 one of the principal instruments or helps of thought2 and any imperfection in the instrument1 or in the mode of employing it1 is confessedly liable1 still more than in almost any other art1 to confuse and impede the process1 and destroy all ground of confidence in the result4 ,for a mind not previously versed in the meaning and right use of the various kinds of words1 to attempt the study of methods of philosophizing1 would be as if some one should attempt to become an astronomical observer1 having never learned to adjust the focal distance of his optical instruments so as to see distinctly4 ,since ,reasoning1 or ,inference1 the principal subject of logic1 is an operation which usually takes place by means of words1 and in complicated cases can take place in no other way2 those who have not a thorough insight into the signification and purposes of words1 will be under chances1 amounting almost to certainty1 of reasoning or inferring incorrectly4 ,and logicians have generally felt that unless1 in the very first stage1 they removed this source of error2 unless they taught their pupil to put away the glasses which distort the object1 and to use those which are adapted to his purpose in such a manner as to assist1 not perplex1 his vision2 he would not be in a condition to practice the remaining part of their discipline with any prospect of advantage4 ,therefore it is that an inquiry into language1 so far as is needful to guard against the errors to which it gives rise1 has at all times been deemed a necessary preliminary to the study of logic4 ,but there is another reason1 of a still more fundamental nature1 why the import of words should be the earliest subject of the logician's consideration3 because without it he can not examine into the import of ,propositions4 ,now this is a subject which stands on the very threshold of the science of logic4 ,the object of logic1 as defined in the ,introductory ,chapter1 is to ascertain how we come by that portion of our knowledge 7much the greatest portion7 which is not intuitive3 and by what criterion we can1 in matters not self-evident1 distinguish between things proved and things not proved1 between what is worthy and what is unworthy of belief4 ,of the various questions which present themselves to our inquiring faculties1 some receive an answer from direct consciousness1 others1 if resolved at all1 can only be resolved by means of evidence4 ,logic is concerned with these last4 ,but before inquiring into the mode of resolving questions1 it is necessary to inquire what are those which offer themselves2 what questions are conceivable2 what inquiries are there1 to which mankind have either obtained1 or been able to imagine it possible that they should obtain1 an answer4 ,this point is best ascertained by a survey and analysis of ,propositions4 #b4 ,the answer to every question which it is possible to frame1 must be contained in a ,proposition1 or ,assertion4 ,whatever can be an object of belief1 or even of disbelief1 must1 when put into words1 assume the form of a proposition4 ,all truth and all error lie in propositions4 ,what1 by a convenient misapplication of an abstract term1 we call a ,truth1 means simply a ,true ,proposition2 and errors are false propositions4 ,to know the import of all possible propositions would be to know all questions which can be raised1 all matters which are susceptible of being either believed or disbelieved4 ,how many kinds of inquiries can be propounded2 how many kinds of judgments can be made2 and how many kinds of propositions it is possible to frame with a meaning1 are but different forms of one and the same question4 ,since1 then1 the objects of all ,belief and of all ,inquiry express themselves in propositions1 a sufficient scrutiny of ,propositions and of their varieties will apprise us what questions mankind have actually asked of themselves1 and what1 in the nature of answers to those questions1 they have actually thought they had grounds to believe4 ,now the first glance at a proposition shows that it is formed by putting together two names4 ,a proposition1 according to the common simple definition1 which is sufficient for our purpose is1 discourse1 in which something is affirmed or denied of something4 ,thus1 in the proposition1 ,gold is yellow1 the quality yellow is affirmed of the substance gold4 ,in the proposition1 ,franklin was not born in ,england1 the fact expressed by the words born in ,england is denied of the man ,franklin4 ,every proposition consists of three parts3 the ,subject1 the ,predicate1 and the ,copula4 ,the predicate is the name denoting that which is affirmed or denied4 ,the subject is the name denoting the person or thing which something is affirmed or denied of4 ,the copula is the sign denoting that there is an affirmation or denial1 and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse4 ,thus1 in the proposition1 ,the earth is round1 the ,predicate is the word round1 which denotes the quality affirmed1 or 7as the phrase is7 predicated3 the earth1 words denoting the object which that quality is affirmed of1 compose the ,subject2 the word is1 which serves as the connecting mark between the subject and predicate1 to show that one of them is affirmed of the other1 is called the ,copula4 ,dismissing1 for the present1 the copula1 of which more will be said hereafter1 every proposition1 then1 consists of at least two names--brings together two names1 in a particular manner4 ,this is already a first step toward what we are in quest of4 ,it appears from this1 that for an act of belief1 one object is not sufficient2 the simplest act of belief supposes1 and has something to do with1 two objects--two names1 to say the least2 and 7since the names must be names of something7 two namable things4 ,a large class of thinkers would cut the matter short by saying1 two ideas4 ,they would say1 that the subject and predicate are both of them names of ideas2 the idea of gold1 for instance1 and the idea of yellow2 and that what takes place 7or part of what takes place7 in the act of belief consists in bringing 7as it is often expressed7 one of these ideas under the other4 ,but this we are not yet in a condition to say3 whether such be the correct mode of describing the phenomenon1 is an after consideration4 ,the result with which for the present we must be contented1 is1 that in every act of belief two objects are in some manner taken cognizance of2 that there can be no belief claimed1 or question propounded1 which does not embrace two distinct 7either material or intellectual7 subjects of thought2 each of them capable1 or not1 of being conceived by itself1 but incapable of being believed by itself4 ,i may say1 for instance1 8the sun40 ,the word has a meaning1 and suggests that meaning to the mind of any one who is listening to me4 ,but suppose ,i ask him1 ,whether it is true3 whether he believes it8 ,he can give no answer4 ,there is as yet nothing to believe1 or to disbelieve4 ,now1 however1 let me make1 of all possible assertions respecting the sun1 the one which involves the least of reference to any object besides itself2 let me say1 8the sun exists40 ,here1 at once1 is something which a person can say he believes4 ,but here1 instead of only one1 we find two distinct objects of conception3 the sun is one object2 existence is another4 ,let it not be said that this second conception1 existence1 is involved in the first2 for the sun may be conceived as no longer existing4 8,the sun0 does not convey all the meaning that is conveyed by 8the sun exists30 8my father0 does not include all the meaning of 8my father exists10 for he may be dead2 8a round square0 does not include the meaning of 8a round square exists10 for it does not and can not exist4 ,when ,i say 8the sun10 8my father10 or a 8round square10 ,i do not call upon the hearer for any belief or disbelief1 nor can either the one or the other be afforded me2 but if ,i say1 8the sun exists10 8my father exists10 or 8a round square exists10 ,i call for belief2 and should1 in the first of the three instances1 meet with it2 in the second1 with belief or disbelief1 as the case might be2 in the third1 with disbelief4 #c4 ,this first step in the analysis of the object of belief1 which1 though so obvious1 will be found to be not unimportant1 is the only one which we shall find it practicable to make without a preliminary survey of language4 ,if we attempt to proceed further in the same path1 that is1 to analyze any further the import of ,propositions2 we find forced upon us1 as a subject of previous consideration1 the import of ,names4 ,for every proposition consists of two names2 and every proposition affirms or denies one of these names1 of the other4 ,now what we do1 what passes in our mind1 when we affirm or deny two names of one another1 must depend on what they are names of2 since it is with reference to that1 and not to the mere names themselves1 that we make the affirmation or denial4 ,here1 therefore1 we find a new reason why the signification of names1 and the relation generally between names and the things signified by them1 must occupy the preliminary stage of the inquiry we are engaged in4 ,it may be objected that the meaning of names can guide us at most only to the opinions1 possibly the foolish and groundless opinions1 which mankind have formed concerning things1 and that as the object of philosophy is truth1 not opinion1 the philosopher should dismiss words and look into things themselves1 to ascertain what questions can be asked and answered in regard to them4 ,this advice 7which no one has it in his power to follow7 is in reality an exhortation to discard the whole fruits of the labors of his predecessors1 and conduct himself as if he were the first person who had ever turned an inquiring eye upon nature4 ,what does any one's personal knowledge of ,things amount to1 after subtracting all which he has acquired by means of the words of other people8 ,even after he has learned as much as people usually do learn from others1 will the notions of things contained in his individual mind afford as sufficient a basis for a catalogue raisonn as the notions which are in the minds of all mankind8 ,in any enumeration and classification of ,things1 which does not set out from their names1 no varieties of things will of course be comprehended but those recognized by the particular inquirer2 and it will still remain to be established1 by a subsequent examination of names1 that the enumeration has omitted nothing which ought to have been included4 ,but if we begin with names1 and use them as our clue to the things1 we bring at once before us all the distinctions which have been recognized1 not by a single inquirer1 but by all inquirers taken together4 ,it doubtless may1 and ,i believe it will1 be found1 that mankind have multiplied the varieties unnecessarily1 and have imagined distinctions among things1 where there were only distinctions in the manner of naming them4 ,but we are not entitled to assume this in the commencement4 ,we must begin by recognizing the distinctions made by ordinary language4 ,if some of these appear1 on a close examination1 not to be fundamental1 the enumeration of the different kinds of realities may be abridged accordingly4 ,but to impose upon the facts in the first instance the yoke of a theory1 while the grounds of the theory are reserved for discussion in a subsequent stage1 is not a course which a logician can reasonably adopt4 ,chapter ,,ii4 ,of ,names4 #a4 8,a name10 says ,hobbes17#g7 8is a word taken at pleasure to serve for a mark which may raise in our mind a thought like to some thought we had before1 and which being pronounced to others1 may be to them a sign of what thought the speaker had7#h7 before in his mind40 ,this simple definition of a name1 as a word 7or set of words7 serving the double purpose of a mark to recall to ourselves the likeness of a former thought1 and a sign to make it known to others1 appears unexceptionable4 ,names1 indeed1 do much more than this2 but whatever else they do1 grows out of1 and is the result of this3 as will appear in its proper place4 ,are names more properly said to be the names of things1 or of our ideas of things8 ,the first is the expression in common use2 the last is that of some metaphysicians1 who conceived that in adopting it they were introducing a highly important distinction4 ,the eminent thinker1 just quoted1 seems to countenance the latter opinion4 8,but seeing10 he continues1 8names ordered in speech 7as is defined7 are signs of our conceptions1 it is manifest they are not signs of the things themselves2 for that the sound of this word stone should be the sign of a stone1 can not be understood in any sense but this1 that he that hears it collects that he that pronounces it thinks of a stone40 ,if it be merely meant that the conception alone1 and not the thing itself1 is recalled by the name1 or imparted to the hearer1 this of course can not be denied4 ,nevertheless1 there seems good reason for adhering to the common usage1 and calling 7as indeed ,hobbes himself does in other places7 the word sun the name of the sun1 and not the name of our idea of the sun4 ,for names are not intended only to make the hearer conceive what we conceive1 but also to inform him what we believe4 ,now1 when ,i use a name for the purpose of expressing a belief1 it is a belief concerning the thing itself1 not concerning my idea of it4 ,when ,i say1 8the sun is the cause of day10 ,i do not mean that my idea of the sun causes or excites in me the idea of day2 or in other words1 that thinking of the sun makes me think of day4 ,i mean1 that a certain physical fact1 which is called the sun's presence 7and which1 in the ultimate analysis1 resolves itself into sensations1 not ideas7 causes another physical fact1 which is called day4 ,it seems proper to consider a word as the name of that which we intend to be understood by it when we use it2 of that which any fact that we assert of it is to be understood of2 that1 in short1 concerning which1 when we employ the word1 we intend to give information4 ,names1 therefore1 shall always be spoken of in this work as the names of things themselves1 and not merely of our ideas of things4 ,but the question now arises1 of what things8 and to answer this it is necessary to take into consideration the different kinds of names4 #b4 ,it is usual1 before examining the various classes into which names are commonly divided1 to begin by distinguishing from names of every description1 those words which are not names1 but only parts of names4 ,among such are reckoned particles1 as of1 to1 truly1 often2 the inflected cases of nouns substantive1 as me1 him1 ,john's2 and even adjectives1 as large1 heavy4 ,these words do not express things of which any thing can be affirmed or denied4 ,we can not say1 ,heavy fell1 or ,a heavy fell2 ,truly1 or ,a truly1 was asserted2 ,of1 or ,an of1 was in the room4 ,unless1 indeed1 we are speaking of the mere words themselves1 as when we say1 ,truly is an ,english word1 or1 ,heavy is an adjective4 ,in that case they are complete names--viz41 names of those particular sounds1 or of those particular collections of written characters4 ,this employment of a word to denote the mere letters and syllables of which it is composed1 was termed by the schoolmen the suppositio materialis of the word4 ,in any other sense we can not introduce one of these words into the subject of a proposition1 unless in combination with other words2 as1 ,a heavy body fell1 ,a truly important fact was asserted1 ,a member of parliament was in the room4 ,an adjective1 however1 is capable of standing by itself as the predicate of a proposition2 as when we say1 ,snow is white2 and occasionally even as the subject1 for we may say1 ,white is an agreeable color4 ,the adjective is often said to be so used by a grammatical ellipsis3 ,snow is white1 instead of ,snow is a white object2 ,white is an agreeable color1 instead of1 ,a white color1 or1 ,the color white1 is agreeable4 ,the ,greeks and ,romans were allowed1 by the rules of their language1 to employ this ellipsis universally in the subject as well as in the predicate of a proposition4 ,in ,english this can not1 generally speaking1 be done4 ,we may say1 ,the earth is round2 but we can not say1 ,round is easily moved2 we must say1 ,a round object4 ,this distinction1 however1 is rather grammatical than logical4 ,since there is no difference of meaning between round1 and a round object1 it is only custom which prescribes that on any given occasion one shall be used1 and not the other4 ,we shall1 therefore1 without scruple1 speak of adjectives as names1 whether in their own right1 or as representative of the more circuitous forms of expression above exemplified4 ,the other classes of subsidiary words have no title whatever to be considered as names4 ,an adverb1 or an accusative case1 can not under any circumstances 7except when their mere letters and syllables are spoken of7 figure as one of the terms of a proposition4 ,words which are not capable of being used as names1 but only as parts of names1 were called by some of the schoolmen ,syncategorematic terms3 from 1 with1 and 1 to predicate1 because it was only with some other word that they could be predicated4 ,a word which could be used either as the subject or predicate of a proposition without being accompanied by any other word1 was termed by the same authorities a ,categorematic term4 ,a combination of one or more ,categorematic1 and one or more ,syncategorematic words1 as ,a heavy body1 or ,a court of justice1 they sometimes called a mixed term2 but this seems a needless multiplication of technical expressions4 ,a mixed term is1 in the only useful sense of the word1 ,categorematic4 ,it belongs to the class of what have been called many-worded names4 ,for1 as one word is frequently not a name1 but only part of a name1 so a number of words often compose one single name1 and no more4 ,these words1 8,the place which the wisdom or policy of antiquity had destined for the residence of the ,abyssinian princes10 form in the estimation of the logician only one name2 one ,categorematic term4 ,a mode of determining whether any set of words makes only one name1 or more than one1 is by predicating something of it1 and observing whether1 by this predication1 we make only one assertion or several4 ,thus1 when we say1 ,john ,nokes1 who was the mayor of the town1 died yesterday--by this predication we make but one assertion2 whence it appears that 8,john ,nokes1 who was the mayor of the town10 is no more than one name4 ,it is true that in this proposition1 besides the assertion that ,john ,nokes died yesterday1 there is included another assertion1 namely1 that ,john ,nokes was mayor of the town4 ,but this last assertion was already made3 we did not make it by adding the predicate1 8died yesterday40 ,suppose1 however1 that the words had been1 ,john ,nokes and the mayor of the town1 they would have formed two names instead of one4 ,for when we say1 ,john ,nokes and the mayor of the town died yesterday1 we make two assertions3 one1 that ,john ,nokes died yesterday2 the other1 that the mayor of the town died yesterday4 ,it being needless to illustrate at any greater length the subject of many-worded names1 we proceed to the distinctions which have been established among names1 not according to the words they are composed of1 but according to their signification4 #c4 ,all names are names of something1 real or imaginary2 but all things have not names appropriated to them individually4 ,for some individual objects we require1 and consequently have1 separate distinguishing names2 there is a name for every person1 and for every remarkable place4 ,other objects1 of which we have not occasion to speak so frequently1 we do not designate by a name of their own2 but when the necessity arises for naming them1 we do so by putting together several words1 each of which1 by itself1 might be and is used for an indefinite number of other objects2 as when ,i say1 this stone3 8this0 and 8stone0 being1 each of them1 names that may be used of many other objects besides the particular one meant1 though the only object of which they can both be used at the given moment1 consistently with their signification1 may be the one of which ,i wish to speak4 ,were this the sole purpose for which names1 that are common to more things than one1 could be employed2 if they only served1 by mutually limiting each other1 to afford a designation for such individual objects as have no names of their own3 they could only be ranked among contrivances for economizing the use of language4 ,but it is evident that this is not their sole function4 ,it is by their means that we are enabled to assert general propositions2 to affirm or deny any predicate of an indefinite number of things at once4 ,the distinction1 therefore1 between general names1 and individual or singular names1 is fundamental2 and may be considered as the first grand division of names4 ,a general name is familiarly defined1 a name which is capable of being truly affirmed1 in the same sense1 of each of an indefinite number of things4 ,an individual or singular name is a name which is only capable of being truly affirmed1 in the same sense1 of one thing4 ,thus1 man is capable of being truly affirmed of ,john1 ,george1 ,mary1 and other persons without assignable limit2 and it is affirmed of all of them in the same sense2 for the word man expresses certain qualities1 and when we predicate it of those persons1 we assert that they all possess those qualities4 ,but ,john is only capable of being truly affirmed of one single person1 at least in the same sense4 ,for1 though there are many persons who bear that name1 it is not conferred upon them to indicate any qualities1 or any thing which belongs to them in common2 and can not be said to be affirmed of them in any sense at all1 consequently not in the same sense4 8,the king who succeeded ,william the ,conqueror10 is also an individual name4 ,for1 that there can not be more than one person of whom it can be truly affirmed1 is implied in the meaning of the words4 ,even 8the king10 when the occasion or the context defines the individual of whom it is to be understood1 may justly be regarded as an individual name4 ,it is not unusual1 by way of explaining what is meant by a general name1 to say that it is the name of a class4 ,but this1 though a convenient mode of expression for some purposes1 is objectionable as a definition1 since it explains the clearer of two things by the more obscure4 ,it would be more logical to reverse the proposition1 and turn it into a definition of the word class3 8,a class is the indefinite multitude of individuals denoted by a general name40 ,it is necessary to distinguish general from collective names4 ,a general name is one which can be predicated of each individual of a multitude2 a collective name can not be predicated of each separately1 but only of all taken together4 8,the #gfth regiment of foot in the ,british army10 which is a collective name1 is not a general but an individual name2 for though it can be predicated of a multitude of individual soldiers taken jointly1 it can not be predicated of them severally4 ,we may say1 ,jones is a soldier1 and ,thompson is a soldier1 and ,smith is a soldier1 but we can not say1 ,jones is the #gfth regiment1 and ,thompson is the #gfth regiment1 and ,smith is the #gfth regiment4 ,we can only say1 ,jones1 and ,thompson1 and ,smith1 and ,brown1 and so forth 7enumerating all the soldiers71 are the #gfth regiment4 8,the #gfth regiment0 is a collective name1 but not a general one3 8a regiment0 is both a collective and a general name4 ,general with respect to all individual regiments1 of each of which separately it can be affirmed3 collective with respect to the individual soldiers of whom any regiment is composed4 #d4 ,the second general division of names is into concrete and abstract4 ,a concrete name is a name which stands for a thing2 an abstract name is a name which stands for an attribute of a thing4 ,thus ,john1 the sea1 this table1 are names of things4 ,white1 also1 is a name of a thing1 or rather of things4 ,whiteness1 again1 is the name of a quality or attribute of those things4 ,man is a name of many things2 humanity is a name of an attribute of those things4 ,old is a name of things3 old age is a name of one of their attributes4 ,i have used the words concrete and abstract in the sense annexed to them by the schoolmen1 who1 notwithstanding the imperfections of their philosophy1 were unrivaled in the construction of technical language1 and whose definitions1 in logic at least1 though they never went more than a little way into the subject1 have seldom1 ,i think1 been altered but to be spoiled4 ,a practice1 however1 has grown up in more modern times1 which1 if not introduced by ,locke1 has gained currency chiefly from his example1 of applying the expression 8abstract name0 to all names which are the result of abstraction or generalization1 and consequently to all general names1 instead of confining it to the names of attributes4 ,the metaphysicians of the ,condillac school--whose admiration of ,locke1 passing over the profoundest speculations of that truly original genius1 usually fastens with peculiar eagerness upon his weakest points--have gone on imitating him in this abuse of language1 until there is now some difficulty in restoring the word to its original signification4 ,a more wanton alteration in the meaning of a word is rarely to be met with2 for the expression general name1 the exact equivalent of which exists in all languages ,i am acquainted with1 was already available for the purpose to which abstract has been misappropriated1 while the misappropriation leaves that important class of words1 the names of attributes1 without any compact distinctive appellation4 ,the old acceptation1 however1 has not gone so completely out of use as to deprive those who still adhere to it of all chance of being understood4 ,by abstract1 then1 ,i shall always1 in ,logic proper1 mean the opposite of concrete2 by an abstract name1 the name of an attribute2 by a concrete name1 the name of an object4 ,do abstract names belong to the class of general1 or to that of singular names8 ,some of them are certainly general4 ,i mean those which are names not of one single and definite attribute1 but of a class of attributes4 ,such is the word color1 which is a name common to whiteness1 redness1 etc4 ,such is even the word whiteness1 in respect of the different shades of whiteness to which it is applied in common3 the word magnitude1 in respect of the various degrees of magnitude and the various dimensions of space2 the word weight1 in respect of the various degrees of weight4 ,such also is the word attribute itself1 the common name of all particular attributes4 ,but when only one attribute1 neither variable in degree nor in kind1 is designated by the name2 as visibleness2 tangibleness2 equality2 squareness2 milk-whiteness2 then the name can hardly be considered general2 for though it denotes an attribute of many different objects1 the attribute itself is always conceived as one1 not many47#i7 ,to avoid needless logomachies1 the best course would probably be to consider these names as neither general nor individual1 and to place them in a class apart4 ,it may be objected to our definition of an abstract name1 that not only the names which we have called abstract1 but adjectives1 which we have placed in the concrete class1 are names of attributes2 that white1 for example1 is as much the name of the color as whiteness is4 ,but 7as before remarked7 a word ought to be considered as the name of that which we intend to be understood by it when we put it to its principal use1 that is1 when we employ it in predication4 ,when we say snow is white1 milk is white1 linen is white1 we do not mean it to be understood that snow1 or linen1 or milk1 is a color4 ,we mean that they are things having the color4 ,the reverse is the case with the word whiteness2 what we affirm to be whiteness is not snow1 but the color of snow4 ,whiteness1 therefore1 is the name of the color exclusively3 white is a name of all things whatever having the color2 a name1 not of the quality whiteness1 but of every white object4 ,it is true1 this name was given to all those various objects on account of the quality2 and we may therefore say1 without impropriety1 that the quality forms part of its signification2 but a name can only be said to stand for1 or to be a name of1 the things of which it can be predicated4 ,we shall presently see that all names which can be said to have any signification1 all names by applying which to an individual we give any information respecting that individual1 may be said to imply an attribute of some sort2 but they are not names of the attribute2 it has its own proper abstract name4 #e4 ,this leads to the consideration of a third great division of names1 into connotative and non-connotative1 the latter sometimes1 but improperly1 called absolute4 ,this is one of the most important distinctions which we shall have occasion to point out1 and one of those which go deepest into the nature of language4 ,a non-connotative term is one which signifies a subject only1 or an attribute only4 ,a connotative term is one which denotes a subject1 and implies an attribute4 ,by a subject is here meant any thing which possesses attributes4 ,thus ,john1 or ,london1 or ,england1 are names which signify a subject only4 ,whiteness1 length1 virtue1 signify an attribute only4 ,none of these names1 therefore1 are connotative4 ,but white1 long1 virtuous1 are connotative4 ,the word white1 denotes all white things1 as snow1 paper1 the foam of the sea1 etc41 and implies1 or in the language of the schoolmen1 connotes17#aj7 the attribute whiteness4 ,the word white is not predicated of the attribute1 but of the subjects1 snow1 etc42 but when we predicate it of them1 we convey the meaning that the attribute whiteness belongs to them4 ,the same may be said of the other words above cited4 ,virtuous1 for example1 is the name of a class1 which includes ,socrates1 ,howard1 the ,man of ,ross1 and an undefinable number of other individuals1 past1 present1 and to come4 ,these individuals1 collectively and severally1 can alone be said with propriety to be denoted by the word3 of them alone can it properly be said to be a name4 ,but it is a name applied to all of them in consequence of an attribute which they are supposed to possess in common1 the attribute which has received the name of virtue4 ,it is applied to all beings that are considered to possess this attribute2 and to none which are not so considered4 ,all concrete general names are connotative4 ,the word man1 for example1 denotes ,peter1 ,jane1 ,john1 and an indefinite number of other individuals1 of whom1 taken as a class1 it is the name4 ,but it is applied to them1 because they possess1 and to signify that they possess1 certain attributes4 ,these seem to be1 corporeity1 animal life1 rationality1 and a certain external form1 which for distinction we call the human4 ,every existing thing1 which possessed all these attributes1 would be called a man2 and any thing which possessed none of them1 or only one1 or two1 or even three of them without the fourth1 would not be so called4 ,for example1 if in the interior of ,africa there were to be discovered a race of animals possessing reason equal to that of human beings1 but with the form of an elephant1 they would not be called men4 ,swift's ,houyhnhnms would not be so called4 ,or if such newly-discovered beings possessed the form of man without any vestige of reason1 it is probable that some other name than that of man would be found for them4 ,how it happens that there can be any doubt about the matter1 will appear hereafter4 ,the word man1 therefore1 signifies all these attributes1 and all subjects which possess these attributes4 ,but it can be predicated only of the subjects4 ,what we call men1 are the subjects1 the individual ,stiles and ,nokes2 not the qualities by which their humanity is constituted4 ,the name1 therefore1 is said to signify the subjects directly1 the attributes indirectly2 it denotes the subjects1 and implies1 or involves1 or indicates1 or as we shall say henceforth connotes1 the attributes4 ,it is a connotative name4 ,connotative names have hence been also called denominative1 because the subject which they denote is denominated by1 or receives a name from the attribute which they connote4 ,snow1 and other objects1 receive the name white1 because they possess the attribute which is called whiteness2 ,peter1 ,james1 and others receive the name man because they possess the attributes which are considered to constitute humanity4 ,the attribute1 or attributes1 may therefore be said to denominate those objects1 or to give them a common name47#aa7 ,it has been seen that all concrete general names are connotative4 ,even abstract names1 though the names only of attributes1 may in some instances be justly considered as connotative2 for attributes themselves may have attributes ascribed to them2 and a word which denotes attributes may connote an attribute of those attributes4 ,of this description1 for example1 is such a word as fault2 equivalent to bad or hurtful quality4 ,this word is a name common to many attributes1 and connotes hurtfulness1 an attribute of those various attributes4 ,when1 for example1 we say that slowness1 in a horse1 is a fault1 we do not mean that the slow movement1 the actual change of pace of the slow horse1 is a bad thing1 but that the property or peculiarity of the horse1 from which it derives that name1 the quality of being a slow mover1 is an undesirable peculiarity4 ,in regard to those concrete names which are not general but individual1 a distinction must be made4 ,proper names are not connotative3 they denote the individuals who are called by them2 but they do not indicate or imply any attributes as belonging to those individuals4 ,when we name a child by the name ,paul1 or a dog by the name ,csar1 these names are simply marks used to enable those individuals to be made subjects of discourse4 ,it may be said1 indeed1 that we must have had some reason for giving them those names rather than any others2 and this is true2 but the name1 once given1 is independent of the reason4 ,a man may have been named ,john1 because that was the name of his father2 a town may have been named ,dartmouth1 because it is situated at the mouth of the ,dart4 ,but it is no part of the signification of the word ,john1 that the father of the person so called bore the same name2 nor even of the word ,dartmouth1 to be situated at the mouth of the ,dart4 ,if sand should choke up the mouth of the river1 or an earthquake change its course1 and remove it to a distance from the town1 the name of the town would not necessarily be changed4 ,that fact1 therefore1 can form no part of the signification of the word2 for otherwise1 when the fact confessedly ceased to be true1 no one would any longer think of applying the name4 ,proper names are attached to the objects themselves1 and are not dependent on the continuance of any attribute of the object4 ,but there is another kind of names1 which1 although they are individual names--that is1 predicable only of one object--are really connotative4 ,for1 though we may give to an individual a name utterly unmeaning1 which we call a proper name--a word which answers the purpose of showing what thing it is we are talking about1 but not of telling any thing about it2 yet a name peculiar to an individual is not necessarily of this description4 ,it may be significant of some attribute1 or some union of attributes1 which1 being possessed by no object but one1 determines the name exclusively to that individual4 8,the sun0 is a name of this description2 8,god10 when used by a monotheist1 is another4 ,these1 however1 are scarcely examples of what we are now attempting to illustrate1 being1 in strictness of language1 general1 not individual names3 for1 however they may be in fact predicable only of one object1 there is nothing in the meaning of the words themselves which implies this3 and1 accordingly1 when we are imagining and not affirming1 we may speak of many suns2 and the majority of mankind have believed1 and still believe1 that there are many gods4 ,but it is easy to produce words which are real instances of connotative individual names4 ,it may be part of the meaning of the connotative name itself1 that there can exist but one individual possessing the attribute which it connotes3 as1 for instance1 8the only son of ,john ,stiles20 8the first emperor of ,rome40 ,or the attribute connoted may be a connection with some determinate event1 and the connection may be of such a kind as only one individual could have2 or may at least be such as only one individual actually had2 and this may be implied in the form of the expression4 8,the father of ,socrates0 is an example of the one kind 7since ,socrates could not have had two fathers72 8the author of the ,iliad10 8the murderer of ,henri ,quatre10 of the second4 ,for1 though it is conceivable that more persons than one might have participated in the authorship of the ,iliad1 or in the murder of ,henri ,quatre1 the employment of the article the implies that1 in fact1 this was not the case4 ,what is here done by the word the1 is done in other cases by the context3 thus1 8,csar's army0 is an individual name1 if it appears from the context that the army meant is that which ,csar commanded in a particular battle4 ,the still more general expressions1 8the ,roman army10 or 8the ,christian army10 may be individualized in a similar manner4 ,another case of frequent occurrence has already been noticed2 it is the following3 ,the name1 being a many-worded one1 may consist1 in the first place1 of a general name1 capable therefore in itself of being affirmed of more things than one1 but which is1 in the second place1 so limited by other words joined with it1 that the entire expression can only be predicated of one object1 consistently with the meaning of the general term4 ,this is exemplified in such an instance as the following3 8the present prime minister of ,england40 ,prime ,minister of ,england is a general name2 the attributes which it connotes may be possessed by an indefinite number of persons3 in succession however1 not simultaneously2 since the meaning of the name itself imports 7among other things7 that there can be only one such person at a time4 ,this being the case1 and the application of the name being afterward limited by the article and the word present1 to such individuals as possess the attributes at one indivisible point of time1 it becomes applicable only to one individual4 ,and as this appears from the meaning of the name1 without any extrinsic proof1 it is strictly an individual name4 ,from the preceding observations it will easily be collected1 that whenever the names given to objects convey any information--that is1 whenever they have properly any meaning--the meaning resides not in what they denote1 but in what they connote4 ,the only names of objects which connote nothing are proper names2 and these have1 strictly speaking1 no signification47#ab7 ,if1 like the robber in the ,arabian ,nights1 we make a mark with chalk on a house to enable us to know it again1 the mark has a purpose1 but it has not properly any meaning4 ,the chalk does not declare any thing about the house2 it does not mean1 ,this is such a person's house1 or ,this is a house which contains booty4 ,the object of making the mark is merely distinction4 ,i say to myself1 ,all these houses are so nearly alike that if ,i lose sight of them ,i shall not again be able to distinguish that which ,i am now looking at1 from any of the others2 ,i must therefore contrive to make the appearance of this one house unlike that of the others1 that ,i may hereafter know when ,i see the mark--not indeed any attribute of the house--but simply that it is the same house which ,i am now looking at4 ,morgiana chalked all the other houses in a similar manner1 and defeated the scheme3 how8 simply by obliterating the difference of appearance between that house and the others4 ,the chalk was still there1 but it no longer served the purpose of a distinctive mark4 ,when we impose a proper name1 we perform an operation in some degree analogous to what the robber intended in chalking the house4 ,we put a mark1 not indeed upon the object itself1 but1 so to speak1 upon the idea of the object4 ,a proper name is but an unmeaning mark which we connect in our minds with the idea of the object1 in order that whenever the mark meets our eyes or occurs to our thoughts1 we may think of that individual object4 ,not being attached to the thing itself1 it does not1 like the chalk1 enable us to distinguish the object when we see it2 but it enables us to distinguish it when it is spoken of1 either in the records of our own experience1 or in the discourse of others2 to know that what we find asserted in any proposition of which it is the subject1 is asserted of the individual thing with which we were previously acquainted4 ,when we predicate of any thing its proper name2 when we say1 pointing to a man1 this is ,brown or ,smith1 or pointing to a city1 that it is ,york1 we do not1 merely by so doing1 convey to the reader any information about them1 except that those are their names4 ,by enabling him to identify the individuals1 we may connect them with information previously possessed by him2 by saying1 ,this is ,york1 we may tell him that it contains the ,minster4 ,but this is in virtue of what he has previously heard concerning ,york2 not by any thing implied in the name4 ,it is otherwise when objects are spoken of by connotative names4 ,when we say1 ,the town is built of marble1 we give the hearer what may be entirely new information1 and this merely by the signification of the many-worded connotative name1 8built of marble40 ,such names are not signs of the mere objects1 invented because we have occasion to think and speak of those objects individually2 but signs which accompany an attribute2 a kind of livery in which the attribute clothes all objects which are recognized as possessing it4 ,they are not mere marks1 but more1 that is to say1 significant marks2 and the connotation is what constitutes their significance4 ,as a proper name is said to be the name of the one individual which it is predicated of1 so 7as well from the importance of adhering to analogy1 as for the other reasons formerly assigned7 a connotative name ought to be considered a name of all the various individuals which it is predicable of1 or in other words denotes1 and not of what it connotes4 ,but by learning what things it is a name of1 we do not learn the meaning of the name3 for to the same thing we may1 with equal propriety1 apply many names1 not equivalent in meaning4 ,thus1 ,i call a certain man by the name ,sophroniscus3 ,i call him by another name1 ,the father of ,socrates4 ,both these are names of the same individual1 but their meaning is altogether different2 they are applied to that individual for two different purposes3 the one1 merely to distinguish him from other persons who are spoken of2 the other to indicate a fact relating to him1 the fact that ,socrates was his son4 ,i further apply to him these other expressions3 a man1 a ,greek1 an ,athenian1 a sculptor1 an old man1 an honest man1 a brave man4 ,all these are1 or may be1 names of ,sophroniscus1 not indeed of him alone1 but of him and each of an indefinite number of other human beings4 ,each of these names is applied to ,sophroniscus for a different reason1 and by each whoever understands its meaning is apprised of a distinct fact or number of facts concerning him2 but those who knew nothing about the names except that they were applicable to ,sophroniscus1 would be altogether ignorant of their meaning4 ,it is even possible that ,i might know every single individual of whom a given name could be with truth affirmed1 and yet could not be said to know the meaning of the name4 ,a child knows who are its brothers and sisters1 long before it has any definite conception of the nature of the facts which are involved in the signification of those words4 ,in some cases it is not easy to decide precisely how much a particular word does or does not connote2 that is1 we do not exactly know 7the case not having arisen7 what degree of difference in the object would occasion a difference in the name4 ,thus1 it is clear that the word man1 besides animal life and rationality1 connotes also a certain external form2 but it would be impossible to say precisely what form2 that is1 to decide how great a deviation from the form ordinarily found in the beings whom we are accustomed to call men1 would suffice in a newly-discovered race to make us refuse them the name of man4 ,rationality1 also1 being a quality which admits of degrees1 it has never been settled what is the lowest degree of that quality which would entitle any creature to be considered a human being4 ,in all such cases1 the meaning of the general name is so far unsettled and vague2 mankind have not come to any positive agreement about the matter4 ,when we come to treat of ,classification1 we shall have occasion to show under what conditions this vagueness may exist without practical inconvenience2 and cases will appear in which the ends of language are better promoted by it than by complete precision2 in order that1 in natural history for instance1 individuals or species of no very marked character may be ranged with those more strongly characterized individuals or species to which1 in all their properties taken together1 they bear the nearest resemblance4 ,but this partial uncertainty in the connotation of names can only be free from mischief when guarded by strict precautions4 ,one of the chief sources1 indeed1 of lax habits of thought1 is the custom of using connotative terms without a distinctly ascertained connotation1 and with no more precise notion of their meaning than can be loosely collected from observing what objects they are used to denote4 ,it is in this manner that we all acquire1 and inevitably so1 our first knowledge of our vernacular language4 ,a child learns the meaning of the words man1 or white1 by hearing them applied to a variety of individual objects1 and finding out1 by a process of generalization and analysis which he could not himself describe1 what those different objects have in common4 ,in the case of these two words the process is so easy as to require no assistance from culture2 the objects called human beings1 and the objects called white1 differing from all others by qualities of a peculiarly definite and obvious character4 ,but in many other cases1 objects bear a general resemblance to one another1 which leads to their being familiarly classed together under a common name1 while1 without more analytic habits than the generality of mankind possess1 it is not immediately apparent what are the particular attributes1 upon the possession of which in common by them all1 their general resemblance depends4 ,when this is the case1 people use the name without any recognized connotation1 that is1 without any precise meaning2 they talk1 and consequently think1 vaguely1 and remain contented to attach only the same degree of significance to their own words1 which a child three years old attaches to the words brother and sister4 ,the child at least is seldom puzzled by the starting up of new individuals1 on whom he is ignorant whether or not to confer the title2 because there is usually an authority close at hand competent to solve all doubts4 ,but a similar resource does not exist in the generality of cases2 and new objects are continually presenting themselves to men1 women1 and children1 which they are called upon to class proprio motu4 ,they1 accordingly1 do this on no other principle than that of superficial similarity1 giving to each new object the name of that familiar object1 the idea of which it most readily recalls1 or which1 on a cursory inspection1 it seems to them most to resemble3 as an unknown substance found in the ground will be called1 according to its texture1 earth1 sand1 or a stone4 ,in this manner1 names creep on from subject to subject1 until all traces of a common meaning sometimes disappear1 and the word comes to denote a number of things not only independently of any common attribute1 but which have actually no attribute in common2 or none but what is shared by other things to which the name is capriciously refused47#ac7 ,even scientific writers have aided in this perversion of general language from its purpose2 sometimes because1 like the vulgar1 they knew no better2 and sometimes in deference to that aversion to admit new words1 which induces mankind1 on all subjects not considered technical1 to attempt to make the original stock of names serve with but little augmentation to express a constantly increasing number of objects and distinctions1 and1 consequently1 to express them in a manner progressively more and more imperfect4 ,to what a degree this loose mode of classing and denominating objects has rendered the vocabulary of mental and moral philosophy unfit for the purposes of accurate thinking1 is best known to whoever has most meditated on the present condition of those branches of knowledge4 ,since1 however1 the introduction of a new technical language as the vehicle of speculations on subjects belonging to the domain of daily discussion1 is extremely difficult to effect1 and would not be free from inconvenience even if effected1 the problem for the philosopher1 and one of the most difficult which he has to resolve1 is1 in retaining the existing phraseology1 how best to alleviate its imperfections4 ,this can only be accomplished by giving to every general concrete name which there is frequent occasion to predicate1 a definite and fixed connotation2 in order that it may be known what attributes1 when we call an object by that name1 we really mean to predicate of the object4 ,and the question of most nicety is1 how to give this fixed connotation to a name1 with the least possible change in the objects which the name is habitually employed to denote2 with the least possible disarrangement1 either by adding or subtraction1 of the group of objects which1 in however imperfect a manner1 it serves to circumscribe and hold together2 and with the least vitiation of the truth of any propositions which are commonly received as true4 ,this desirable purpose1 of giving a fixed connotation where it is wanting1 is the end aimed at whenever any one attempts to give a definition of a general name already in use2 every definition of a connotative name being an attempt either merely to declare1 or to declare and analyze1 the connotation of the name4 ,and the fact1 that no questions which have arisen in the moral sciences have been subjects of keener controversy than the definitions of almost all the leading expressions1 is a proof how great an extent the evil to which we have adverted has attained4 ,names with indeterminate connotation are not to be confounded with names which have more than one connotation1 that is to say1 ambiguous words4 ,a word may have several meanings1 but all of them fixed and recognized ones2 as the word post1 for example1 or the word box1 the various senses of which it would be endless to enumerate4 ,and the paucity of existing names1 in comparison with the demand for them1 may often render it advisable and even necessary to retain a name in this multiplicity of acceptations1 distinguishing these so clearly as to prevent their being confounded with one another4 ,such a word may be considered as two or more names1 accidentally written and spoken alike47#ad7 #f4 ,the fourth principal division of names1 is into positive and negative4 ,positive1 as man1 tree1 good2 negative1 as not-man1 not-tree1 not-good4 ,to every positive concrete name1 a corresponding negative one might be framed4 ,after giving a name to any one thing1 or to any plurality of things1 we might create a second name which should be a name of all things whatever1 except that particular thing or things4 ,these negative names are employed whenever we have occasion to speak collectively of all things other than some thing or class of things4 ,when the positive name is connotative1 the corresponding negative name is connotative likewise2 but in a peculiar way1 connoting not the presence but the absence of an attribute4 ,thus1 not-white denotes all things whatever except white things2 and connotes the attribute of not possessing whiteness4 ,for the non-possession of any given attribute is also an attribute1 and may receive a name as such2 and thus negative concrete names may obtain negative abstract names to correspond to them47#ae7 ,names which are positive in form are often negative in reality1 and others are really positive though their form is negative4 ,the word inconvenient1 for example1 does not express the mere absence of convenience2 it expresses a positive attribute--that of being the cause of discomfort or annoyance4 ,so the word unpleasant1 notwithstanding its negative form1 does not connote the mere absence of pleasantness1 but a less degree of what is signified by the word painful1 which1 it is hardly necessary to say1 is positive4 ,idle1 on the other hand1 is a word which1 though positive in form1 expresses nothing but what would be signified either by the phrase not working1 or by the phrase not disposed to work2 and sober1 either by not drunk or by not drunken4 ,there is a class of names called privative4 ,a privative name is equivalent in its signification to a positive and a negative name taken together2 being the name of something which has once had a particular attribute1 or for some other reason might have been expected to have it1 but which has it not4 ,such is the word blind1 which is not equivalent to not seeing1 or to not capable of seeing1 for it would not1 except by a poetical or rhetorical figure1 be applied to stocks and stones4 ,a thing is not usually said to be blind1 unless the class to which it is most familiarly referred1 or to which it is referred on the particular occasion1 be chiefly composed of things which can see1 as in the case of a blind man1 or a blind horse2 or unless it is supposed for any reason that it ought to see2 as in saying of a man1 that he rushed blindly into an abyss1 or of philosophers or the clergy that the greater part of them are blind guides4 ,the names called privative1 therefore1 connote two things2 the absence of certain attributes1 and the presence of others1 from which the presence also of the former might naturally have been expected4 #g4 ,the fifth leading division of names is into relative and absolute1 or let us rather say1 relative and non-relative2 for the word absolute is put upon much too hard duty in metaphysics1 not to be willingly spared when its services can be dispensed with4 ,it resembles the word civil in the language of jurisprudence1 which stands for the opposite of criminal1 the opposite of ecclesiastical1 the opposite of military1 the opposite of political--in short1 the opposite of any positive word which wants a negative4 ,relative names are such as father1 son2 ruler1 subject2 like2 equal2 unlike2 unequal2 longer1 shorter2 cause1 effect4 ,their characteristic property is1 that they are always given in pairs4 ,every relative name which is predicated of an object1 supposes another object 7or objects71 of which we may predicate either that same name or another relative name which is said to be the correlative of the former4 ,thus1 when we call any person a son1 we suppose other persons who must be called parents4 ,when we call any event a cause1 we suppose another event which is an effect4 ,when we say of any distance that it is longer1 we suppose another distance which is shorter4 ,when we say of any object that it is like1 we mean that it is like some other object1 which is also said to be like the first4 ,in this last case both objects receive the same name2 the relative term is its own correlative4 ,it is evident that these words1 when concrete1 are1 like other concrete general names1 connotative2 they denote a subject1 and connote an attribute2 and each of them has1 or might have1 a corresponding abstract name1 to denote the attribute connoted by the concrete4 ,thus the concrete like has its abstract likeness2 the concretes1 father and son1 have1 or might have1 the abstracts1 paternity1 and filiety1 or sonship4 ,the concrete name connotes an attribute1 and the abstract name which answers to it denotes that attribute4 ,but of what nature is the attribute8 ,wherein consists the peculiarity in the connotation of a relative name8 ,the attribute signified by a relative name1 say some1 is a relation2 and this they give1 if not as a sufficient explanation1 at least as the only one attainable4 ,if they are asked1 ,what then is a relation8 they do not profess to be able to tell4 ,it is generally regarded as something peculiarly recondite and mysterious4 ,i can not1 however1 perceive in what respect it is more so than any other attribute2 indeed1 it appears to me to be so in a somewhat less degree4 ,i conceive rather1 that it is by examining into the signification of relative names1 or1 in other words1 into the nature of the attribute which they connote1 that a clear insight may best be obtained into the nature of all attributes3 of all that is meant by an attribute4 ,it is obvious1 in fact1 that if we take any two correlative names1 father and son for instance1 though the objects denoted by the names are different1 they both1 in a certain sense1 connote the same thing4 ,they can not1 indeed1 be said to connote the same attribute3 to be a father1 is not the same thing as to be a son4 ,but when we call one man a father1 another a son1 what we mean to affirm is a set of facts1 which are exactly the same in both cases4 ,to predicate of ,a that he is the father of ,b1 and of ,b that he is the son of ,a1 is to assert one and the same fact in different words4 ,the two propositions are exactly equivalent3 neither of them asserts more or asserts less than the other4 ,the paternity of ,a and the filiety of ,b are not two facts1 but two modes of expressing the same fact4 ,that fact1 when analysed1 consists of a series of physical events or phenomena1 in which both ,a and ,b are parties concerned1 and from which they both derive names4 ,what those names really connote1 is this series of events3 that is the meaning1 and the whole meaning1 which either of them is intended to convey4 ,the series of events may be said to constitute the relation2 the schoolmen called it the foundation of the relation1 fundamentum relationis4 ,in this manner any fact1 or series of facts1 in which two different objects are implicated1 and which is therefore predicable of both of them1 may be either considered as constituting an attribute of the one1 or an attribute of the other4 ,according as we consider it in the former1 or in the latter aspect1 it is connoted by the one or the other of the two correlative names4 ,father connotes the fact1 regarded as constituting an attribute of ,a2 son connotes the same fact1 as constituting an attribute of ,b4 ,it may evidently be regarded with equal propriety in either light4 ,and all that appears necessary to account for the existence of relative names1 is1 that whenever there is a fact in which two individuals are concerned1 an attribute grounded on that fact may be ascribed to either of these individuals4 ,a name1 therefore1 is said to be relative1 when1 over and above the object which it denotes1 it implies in its signification the existence of another object1 also deriving a denomination from the same fact which is the ground of the first name4 ,or 7to express the same meaning in other words7 a name is relative1 when1 being the name of one thing1 its signification can not be explained but by mentioning another4 ,or we may state it thus--when the name can not be employed in discourse so as to have a meaning1 unless the name of some other thing than what it is itself the name of1 be either expressed or understood4 ,these definitions are all1 at bottom1 equivalent1 being modes of variously expressing this one distinctive circumstance--that every other attribute of an object might1 without any contradiction1 be conceived still to exist if no object besides that one had ever existed27#af7 but those of its attributes which are expressed by relative names1 would on that supposition be swept away4 #h4 ,names have been further distinguished into univocal and quivocal3 these1 however1 are not two kinds of names1 but two different modes of employing names4 ,a name is univocal1 or applied univocally1 with respect to all things of which it can be predicated in the same sense2 it is quivocal1 or applied quivocally1 as respects those things of which it is predicated in different senses4 ,it is scarcely necessary to give instances of a fact so familiar as the double meaning of a word4 ,in reality1 as has been already observed1 an quivocal or ambiguous word is not one name1 but two names1 accidentally coinciding in sound4 ,file meaning a steel instrument1 and file meaning a line of soldiers1 have no more title to be considered one word1 because written alike1 than grease and ,greece have1 because they are pronounced alike4 ,they are one sound1 appropriated to form two different words4 ,an intermediate case is that of a name used analogically or metaphorically2 that is1 a name which is predicated of two things1 not univocally1 or exactly in the same signification1 but in significations somewhat similar1 and which being derived one from the other1 one of them may be considered the primary1 and the other a secondary signification4 ,as when we speak of a brilliant light and a brilliant achievement4 ,the word is not applied in the same sense to the light and to the achievement2 but having been applied to the light in its original sense1 that of brightness to the eye1 it is transferred to the achievement in a derivative signification1 supposed to be somewhat like the primitive one4 ,the word1 however1 is just as properly two names instead of one1 in this case1 as in that of the most perfect ambiguity4 ,and one of the commonest forms of fallacious reasoning arising from ambiguity1 is that of arguing from a metaphorical expression as if it were literal2 that is1 as if a word1 when applied metaphorically1 were the same name as when taken in its original sense3 which will be seen more particularly in its place4 ,chapter ,,iii4 ,of ,the ,things ,denoted ,by ,names4 #a4 ,looking back now to the commencement of our inquiry1 let us attempt to measure how far it has advanced4 ,logic1 we found1 is the ,theory of ,proof4 ,but proof supposes something provable1 which must be a ,proposition or ,assertion2 since nothing but a ,proposition can be an object of belief1 or therefore of proof4 ,a ,proposition is1 discourse which affirms or denies something of some other thing4 ,this is one step3 there must1 it seems1 be two things concerned in every act of belief4 ,but what are these ,things8 ,they can be no other than those signified by the two names1 which being joined together by a copula constitute the ,proposition4 ,if1 therefore1 we knew what all names signify1 we should know every thing which1 in the existing state of human knowledge1 is capable either of being made a subject of affirmation or denial1 or of being itself affirmed or denied of a subject4 ,we have accordingly1 in the preceding chapter1 reviewed the various kinds of ,names1 in order to ascertain what is signified by each of them4 ,and we have now carried this survey far enough to be able to take an account of its results1 and to exhibit an enumeration of all kinds of ,things which are capable of being made predicates1 or of having any thing predicated of them3 after which to determine the import of ,predication1 that is1 of ,propositions1 can be no arduous task4 ,the necessity of an enumeration of ,existences1 as the basis of ,logic1 did not escape the attention of the schoolmen1 and of their master ,aristotle1 the most comprehensive1 if not also the most sagacious1 of the ancient philosophers4 ,the ,categories1 or ,predicaments--the former a ,greek word1 the latter its literal translation in the ,latin language--were believed to be an enumeration of all things capable of being named2 an enumeration by the summa genera1 i4e41 the most extensive classes into which things could be distributed2 which1 therefore1 were so many highest ,predicates1 one or other of which was supposed capable of being affirmed with truth of every namable thing whatsoever4 ,the following are the classes into which1 according to this school of philosophy1 ,things in general might be reduced3 1 ,substantia4 1 ,quantitas4 1 ,qualitas4 1 ,relatio4 1 ,actio4 1 ,passio4 1 ,ubi4 1 ,quando4 1 ,situs4 1 ,habitus4 ,the imperfections of this classification are too obvious to require1 and its merits are not sufficient to reward1 a minute examination4 ,it is a mere catalogue of the distinctions rudely marked out by the language of familiar life1 with little or no attempt to penetrate1 by philosophic analysis1 to the rationale even of those common distinctions4 ,such an analysis1 however superficially conducted1 would have shown the enumeration to be both redundant and defective4 ,some objects are omitted1 and others repeated several times under different heads4 ,it is like a division of animals into men1 quadrupeds1 horses1 asses1 and ponies4 ,that1 for instance1 could not be a very comprehensive view of the nature of ,relation which could exclude action1 passivity1 and local situation from that category4 ,the same observation applies to the categories ,quando 7or position in time71 and ,ubi 7or position in space72 while the distinction between the latter and ,situs is merely verbal4 ,the incongruity of erecting into a summum genus the class which forms the tenth category is manifest4 ,on the other hand1 the enumeration takes no notice of any thing besides substances and attributes4 ,in what category are we to place sensations1 or any other feelings and states of mind2 as hope1 joy1 fear2 sound1 smell1 taste2 pain1 pleasure2 thought1 judgment1 conception1 and the like8 ,probably all these would have been placed by the ,aristotelian school in the categories of actio and passio2 and the relation of such of them as are active1 to their objects1 and of such of them as are passive1 to their causes1 would rightly be so placed2 but the things themselves1 the feelings or states of mind1 wrongly4 ,feelings1 or states of consciousness1 are assuredly to be accounted among realities1 but they can not be reckoned either among substances or attributes47#ag7 #b4 ,before recommencing1 under better auspices1 the attempt made with such imperfect success by the early logicians1 we must take notice of an unfortunate ambiguity in all the concrete names which correspond to the most general of all abstract terms1 the word ,existence4 ,when we have occasion for a name which shall be capable of denoting whatever exists1 as contradistinguished from non-entity or ,nothing1 there is hardly a word applicable to the purpose which is not also1 and even more familiarly1 taken in a sense in which it denotes only substances4 ,but substances are not all that exists2 attributes1 if such things are to be spoken of1 must be said to exist2 feelings certainly exist4 ,yet when we speak of an object1 or of a thing1 we are almost always supposed to mean a substance4 ,there seems a kind of contradiction in using such an expression as that one thing is merely an attribute of another thing4 ,and the announcement of a ,classification of ,things would1 ,i believe1 prepare most readers for an enumeration like those in natural history1 beginning with the great divisions of animal1 vegetable1 and mineral1 and subdividing them into classes and orders4 ,if1 rejecting the word ,thing1 we endeavor to find another of a more general import1 or at least more exclusively confined to that general import1 a word denoting all that exists1 and connoting only simple existence2 no word might be presumed fitter for such a purpose than being3 originally the present participle of a verb which in one of its meanings is exactly equivalent to the verb exists2 and therefore suitable1 even by its grammatical formation1 to be the concrete of the abstract existence4 ,but this word1 strange as the fact may appear1 is still more completely spoiled for the purpose which it seemed expressly made for1 than the word ,thing4 ,being is1 by custom1 exactly synonymous with substance2 except that it is free from a slight taint of a second ambiguity2 being implied impartially to matter and to mind1 while substance1 though originally and in strictness applicable to both1 is apt to suggest in preference the idea of matter4 ,attributes are never called ,beings2 nor are feelings4 ,a ,being is that which excites feelings1 and which possesses attributes4 ,the soul is called a ,being2 ,god and angels are called ,beings2 but if we were to say1 extension1 color1 wisdom1 virtue1 are beings1 we should perhaps be suspected of thinking with some of the ancients1 that the cardinal virtues are animals2 or1 at the least1 of holding with the ,platonic school the doctrine of self-existent ,ideas1 or with the followers of ,epicurus that of ,sensible ,forms1 which detach themselves in every direction from bodies1 and by coming in contact with our organs1 cause our perceptions4 ,we should be supposed1 in short1 to believe that ,attributes are ,substances4 ,in consequence of this perversion of the word ,being1 philosophers looking about for something to supply its place1 laid their hands upon the word ,entity1 a piece of barbarous ,latin1 invented by the schoolmen to be used as an abstract name1 in which class its grammatical form would seem to place it3 but being seized by logicians in distress to stop a leak in their terminology1 it has ever since been used as a concrete name4 ,the kindred word essence1 born at the same time and of the same parents1 scarcely underwent a more complete transformation when1 from being the abstract of the verb to be1 it came to denote something sufficiently concrete to be inclosed in a glass bottle4 ,the word ,entity1 since it settled down into a concrete name1 has retained its universality of signification somewhat less impaired than any of the names before mentioned4 ,yet the same gradual decay to which1 after a certain age1 all the language of psychology seems liable1 has been at work even here4 ,if you call virtue an entity1 you are indeed somewhat less strongly suspected of believing it to be a substance than if you called it a being2 but you are by no means free from the suspicion4 ,every word which was originally intended to connote mere existence1 seems1 after a time1 to enlarge its connotation to separate existence1 or existence freed from the condition of belonging to a substance2 which condition being precisely what constitutes an attribute1 attributes are gradually shut out2 and along with them feelings1 which in ninety-nine cases out of a hundred have no other name than that of the attribute which is grounded on them4 ,strange that when the greatest embarrassment felt by all who have any considerable number of thoughts to express1 is to find a sufficient variety of precise words fitted to express them1 there should be no practice to which even scientific thinkers are more addicted than that of taking valuable words to express ideas which are sufficiently expressed by other words already appropriated to them4 ,when it is impossible to obtain good tools1 the next best thing is to understand thoroughly the defects of those we have4 ,i have therefore warned the reader of the ambiguity of the names which1 for want of better1 ,i am necessitated to employ4 ,it must now be the writer's endeavor so to employ them as in no case to leave the meaning doubtful or obscure4 ,no one of the above terms being altogether unambiguous1 ,i shall not confine myself to any one1 but shall employ on each occasion the word which seems least likely in the particular case to lead to misunderstanding2 nor do ,i pretend to use either these or any other words with a rigorous adherence to one single sense4 ,to do so would often leave us without a word to express what is signified by a known word in some one or other of its senses3 unless authors had an unlimited license to coin new words1 together with 7what it would be more difficult to assume7 unlimited power of making readers understand them4 ,nor would it be wise in a writer1 on a subject involving so much of abstraction1 to deny himself the advantage derived from even an improper use of a term1 when1 by means of it1 some familiar association is called up which brings the meaning home to the mind1 as it were by a flash4 ,the difficulty both to the writer and reader1 of the attempt which must be made to use vague words so as to convey a precise meaning1 is not wholly a matter of regret4 ,it is not unfitting that logical treatises should afford an example of that1 to facilitate which is among the most important uses of logic4 ,philosophical language will for a long time1 and popular language still longer1 retain so much of vagueness and ambiguity1 that logic would be of little value if it did not1 among its other advantages1 exercise the understanding in doing its work neatly and correctly with these imperfect tools4 ,after this preamble it is time to proceed to our enumeration4 ,we shall commence with ,feelings1 the simplest class of namable things2 the term ,feeling being of course understood in its most enlarged sense4 ,i4 ,feelings1 ,or ,states of ,consciousness4 #c4 ,a ,feeling and a ,state of consciousness are1 in the language of philosophy1 equivalent expressions3 every thing is a feeling of which the mind is conscious2 every thing which it feels1 or1 in other words1 which forms a part of its own sentient existence4 ,in popular language ,feeling is not always synonymous with ,state of ,consciousness2 being often taken more peculiarly for those states which are conceived as belonging to the sensitive1 or to the emotional1 phasis of our nature1 and sometimes1 with a still narrower restriction1 to the emotional alone1 as distinguished from what are conceived as belonging to the percipient or to the intellectual phasis4 ,but this is an admitted departure from correctness of language2 just as1 by a popular perversion the exact converse of this1 the word ,mind is withdrawn from its rightful generality of signification1 and restricted to the intellect4 ,the still greater perversion by which ,feeling is sometimes confined not only to bodily sensations1 but to the sensations of a single sense1 that of touch1 needs not be more particularly adverted to4 ,feeling1 in the proper sense of the term1 is a genus1 of which ,sensation1 ,emotion1 and ,thought1 are subordinate species4 ,under the word ,thought is here to be included whatever we are internally conscious of when we are said to think2 from the consciousness we have when we think of a red color without having it before our eyes1 to the most recondite thoughts of a philosopher or poet4 ,be it remembered1 however1 that by a thought is to be understood what passes in the mind itself1 and not any object external to the mind1 which the person is commonly said to be thinking of4 ,he may be thinking of the sun1 or of ,god1 but the sun and ,god are not thoughts2 his mental image1 however1 of the sun1 and his idea of ,god1 are thoughts2 states of his mind1 not of the objects themselves2 and so also is his belief of the existence of the sun1 or of ,god2 or his disbelief1 if the case be so4 ,even imaginary objects 7which are said to exist only in our ideas7 are to be distinguished from our ideas of them4 ,i may think of a hobgoblin1 as ,i may think of the loaf which was eaten yesterday1 or of the flower which will bloom to-morrow4 ,but the hobgoblin which never existed is not the same thing with my idea of a hobgoblin1 any more than the loaf which once existed is the same thing with my idea of a loaf1 or the flower which does not yet exist1 but which will exist1 is the same with my idea of a flower4 ,they are all1 not thoughts1 but objects of thought2 though at the present time all the objects are alike non-existent4 ,in like manner1 a ,sensation is to be carefully distinguished from the object which causes the sensation2 our sensation of white from a white object3 nor is it less to be distinguished from the attribute whiteness1 which we ascribe to the object in consequence of its exciting the sensation4 ,unfortunately for clearness and due discrimination in considering these subjects1 our sensations seldom receive separate names4 ,we have a name for the objects which produce in us a certain sensation3 the word white4 ,we have a name for the quality in those objects1 to which we ascribe the sensation3 the name whiteness4 ,but when we speak of the sensation itself 7as we have not occasion to do this often except in our scientific speculations71 language1 which adapts itself for the most part only to the common uses of life1 has provided us with no single-worded or immediate designation2 we must employ a circumlocution1 and say1 ,the sensation of white1 or ,the sensation of whiteness2 we must denominate the sensation either from the object1 or from the attribute1 by which it is excited4 ,yet the sensation1 though it never does1 might very well be conceived to exist1 without any thing whatever to excite it4 ,we can conceive it as arising spontaneously in the mind4 ,but if it so arose1 we should have no name to denote it which would not be a misnomer4 ,in the case of our sensations of hearing we are better provided2 we have the word ,sound1 and a whole vocabulary of words to denote the various kinds of sounds4 ,for as we are often conscious of these sensations in the absence of any perceptible object1 we can more easily conceive having them in the absence of any object whatever4 ,we need only shut our eyes and listen to music1 to have a conception of a universe with nothing in it except sounds1 and ourselves hearing them3 and what is easily conceived separately1 easily obtains a separate name4 ,but in general our names of sensations denote indiscriminately the sensation and the attribute4 ,thus1 color stands for the sensations of white1 red1 etc41 but also for the quality in the colored object4 ,we talk of the colors of things as among their properties4 #d4 ,in the case of sensations1 another distinction has also to be kept in view1 which is often confounded1 and never without mischievous consequences4 ,this is1 the distinction between the sensation itself1 and the state of the bodily organs which precedes the sensation1 and which constitutes the physical agency by which it is produced4 ,one of the sources of confusion on this subject is the division commonly made of feelings into ,bodily and ,mental4 ,philosophically speaking1 there is no foundation at all for this distinction3 even sensations are states of the sentient mind1 not states of the body1 as distinguished from it4 ,what ,i am conscious of when ,i see the color blue1 is a feeling of blue color1 which is one thing2 the picture on my retina1 or the phenomenon of hitherto mysterious nature which takes place in my optic nerve or in my brain1 is another thing1 of which ,i am not at all conscious1 and which scientific investigation alone could have apprised me of4 ,these are states of my body2 but the sensation of blue1 which is the consequence of these states of body1 is not a state of body3 that which perceives and is conscious is called ,mind4 ,when sensations are called bodily feelings1 it is only as being the class of feelings which are immediately occasioned by bodily states2 whereas the other kinds of feelings1 thoughts1 for instance1 or emotions1 are immediately excited not by any thing acting upon the bodily organs1 but by sensations1 or by previous thoughts4 ,this1 however1 is a distinction not in our feelings1 but in the agency which produces our feelings3 all of them when actually produced are states of mind4 ,besides the affection of our bodily organs from without1 and the sensation thereby produced in our minds1 many writers admit a third link in the chain of phenomena1 which they call a ,perception1 and which consists in the recognition of an external object as the exciting cause of the sensation4 ,this perception1 they say1 is an act of the mind1 proceeding from its own spontaneous activity2 while in a sensation the mind is passive1 being merely acted upon by the outward object4 ,and according to some metaphysicians1 it is by an act of the mind1 similar to perception1 except in not being preceded by any sensation1 that the existence of ,god1 the soul1 and other hyperphysical objects1 is recognized4 ,these acts of what is termed perception1 whatever be the conclusion ultimately come to respecting their nature1 must1 ,i conceive1 take their place among the varieties of feelings or states of mind4 ,in so classing them1 ,i have not the smallest intention of declaring or insinuating any theory as to the law of mind in which these mental processes may be supposed to originate1 or the conditions under which they may be legitimate or the reverse4 ,far less do ,i mean 7as ,dr4 ,whewell seems to suppose must be meant in an analogous case7#ah77 to indicate that as they are 8merely states of mind10 it is superfluous to inquire into their distinguishing peculiarities4 ,i abstain from the inquiry as irrelevant to the science of logic4 ,in these so-called perceptions1 or direct recognitions by the mind1 of objects1 whether physical or spiritual1 which are external to itself1 ,i can see only cases of belief2 but of belief which claims to be intuitive1 or independent of external evidence4 ,when a stone lies before me1 ,i am conscious of certain sensations which ,i receive from it2 but if ,i say that these sensations come to me from an external object which ,i perceive1 the meaning of these words is1 that receiving the sensations1 ,i intuitively believe that an external cause of those sensations exists4 ,the laws of intuitive belief1 and the conditions under which it is legitimate1 are a subject which1 as we have already so often remarked1 belongs not to logic1 but to the science of the ultimate laws of the human mind4 ,to the same region of speculation belongs all that can be said respecting the distinction which the ,german metaphysicians and their ,french and ,english followers so elaborately draw between the acts of the mind and its merely passive states2 between what it receives from1 and what it gives to1 the crude materials of its experience4 ,i am aware that with reference to the view which those writers take of the primary elements of thought and knowledge1 this distinction is fundamental4 ,but for the present purpose1 which is to examine1 not the original groundwork of our knowledge1 but how we come by that portion of it which is not original2 the difference between active and passive states of mind is of secondary importance4 ,for us1 they all are states of mind1 they all are feelings2 by which1 let it be said once more1 ,i mean to imply nothing of passivity1 but simply that they are psychological facts1 facts which take place in the mind1 and are to be carefully distinguished from the external or physical facts with which they may be connected either as effects or as causes4 #e4 ,among active states of mind1 there is1 however1 one species which merits particular attention1 because it forms a principal part of the connotation of some important classes of names4 ,i mean volitions1 or acts of the will4 ,when we speak of sentient beings by relative names1 a large portion of the connotation of the name usually consists of the actions of those beings2 actions past1 present1 and possible or probable future4 ,take1 for instance1 the words ,sovereign and ,subject4 ,what meaning do these words convey1 but that of innumerable actions1 done or to be done by the sovereign and the subjects1 to or in regard to one another reciprocally8 ,so with the words physician and patient1 leader and follower1 tutor and pupil4 ,in many cases the words also connote actions which would be done under certain contingencies by persons other than those denoted3 as the words mortgagor and mortgagee1 obligor and obligee1 and many other words expressive of legal relation1 which connote what a court of justice would do to enforce the legal obligation if not fulfilled4 ,there are also words which connote actions previously done by persons other than those denoted either by the name itself or by its correlative2 as the word brother4 ,from these instances1 it may be seen how large a portion of the connotation of names consists of actions4 ,now what is an action8 ,not one thing1 but a series of two things3 the state of mind called a volition1 followed by an effect4 ,the volition or intention to produce the effect1 is one thing2 the effect produced in consequence of the intention1 is another thing2 the two together constitute the action4 ,i form the purpose of instantly moving my arm2 that is a state of my mind3 my arm 7not being tied or paralytic7 moves in obedience to my purpose2 that is a physical fact1 consequent on a state of mind4 ,the intention1 followed by the fact1 or 7if we prefer the expression7 the fact when preceded and caused by the intention1 is called the action of moving my arm4 #f4 ,of the first leading division of namable things1 viz41 ,feelings or ,states of ,consciousness1 we began by recognizing three subdivisions2 ,sensations1 ,thoughts1 and ,emotions4 ,the first two of these we have illustrated at considerable length2 the third1 ,emotions1 not being perplexed by similar ambiguities1 does not require similar exemplification4 ,and1 finally1 we have found it necessary to add to these three a fourth species1 commonly known by the name ,volitions4 ,we shall now proceed to the two remaining classes of namable things2 all things which are regarded as external to the mind being considered as belonging either to the class of ,substances or to that of ,attributes4 ,,ii4 ,substances4 ,logicians have endeavored to define ,substance and ,attribute2 but their definitions are not so much attempts to draw a distinction between the things themselves1 as instructions what difference it is customary to make in the grammatical structure of the sentence1 according as we are speaking of substances or of attributes4 ,such definitions are rather lessons of ,english1 or of ,greek1 ,latin1 or ,german1 than of mental philosophy4 ,an attribute1 say the school logicians1 must be the attribute of something2 color1 for example1 must be the color of something2 goodness must be the goodness of something2 and if this something should cease to exist1 or should cease to be connected with the attribute1 the existence of the attribute would be at an end4 ,a substance1 on the contrary1 is self-existent2 in speaking about it1 we need not put of after its name4 ,a stone is not the stone of any thing2 the moon is not the moon of any thing1 but simply the moon4 ,unless1 indeed1 the name which we choose to give to the substance be a relative name2 if so1 it must be followed either by of1 or by some other particle1 implying1 as that preposition does1 a reference to something else3 but then the other characteristic peculiarity of an attribute would fail2 the something might be destroyed1 and the substance might still subsist4 ,thus1 a father must be the father of something1 and so far resembles an attribute1 in being referred to something besides himself3 if there were no child1 there would be no father3 but this1 when we look into the matter1 only means that we should not call him father4 ,the man called father might still exist though there were no child1 as he existed before there was a child2 and there would be no contradiction in supposing him to exist1 though the whole universe except himself were destroyed4 ,but destroy all white substances1 and where would be the attribute whiteness8 ,whiteness1 without any white thing1 is a contradiction in terms4 ,this is the nearest approach to a solution of the difficulty1 that will be found in the common treatises on logic4 ,it will scarcely be thought to be a satisfactory one4 ,if an attribute is distinguished from a substance by being the attribute of something1 it seems highly necessary to understand what is meant by of2 a particle which needs explanation too much itself1 to be placed in front of the explanation of any thing else4 ,and as for the self-existence of substance1 it is very true that a substance may be conceived to exist without any other substance1 but so also may an attribute without any other attribute3 and we can no more imagine a substance without attributes than we can imagine attributes without a substance4 ,metaphysicians1 however1 have probed the question deeper1 and given an account of ,substance considerably more satisfactory than this4 ,substances are usually distinguished as ,bodies or ,minds4 ,of each of these1 philosophers have at length provided us with a definition which seems unexceptionable4 #g4 ,a body1 according to the received doctrine of modern metaphysicians1 may be defined1 the external cause to which we ascribe our sensations4 ,when ,i see and touch a piece of gold1 ,i am conscious of a sensation of yellow color1 and sensations of hardness and weight2 and by varying the mode of handling1 ,i may add to these sensations many others completely distinct from them4 ,the sensations are all of which ,i am directly conscious2 but ,i consider them as produced by something not only existing independently of my will1 but external to my bodily organs and to my mind4 ,this external something ,i call a body4 ,it may be asked1 how come we to ascribe our sensations to any external cause8 ,and is there sufficient ground for so ascribing them8 ,it is known1 that there are metaphysicians who have raised a controversy on the point2 maintaining that we are not warranted in referring our sensations to a cause such as we understand by the word ,body1 or to any external cause whatever4 ,though we have no concern here with this controversy1 nor with the metaphysical niceties on which it turns1 one of the best ways of showing what is meant by ,substance is1 to consider what position it is necessary to take up1 in order to maintain its existence against opponents4 ,it is certain1 then1 that a part of our notion of a body consists of the notion of a number of sensations of our own1 or of other sentient beings1 habitually occurring simultaneously4 ,my conception of the table at which ,i am writing is compounded of its visible form and size1 which are complex sensations of sight2 its tangible form and size1 which are complex sensations of our organs of touch and of our muscles2 its weight1 which is also a sensation of touch and of the muscles2 its color1 which is a sensation of sight2 its hardness1 which is a sensation of the muscles2 its composition1 which is another word for all the varieties of sensation which we receive under various circumstances from the wood of which it is made1 and so forth4 ,all or most of these various sensations frequently are1 and1 as we learn by experience1 always might be1 experienced simultaneously1 or in many different orders of succession at our own choice3 and hence the thought of any one of them makes us think of the others1 and the whole becomes mentally amalgamated into one mixed state of consciousness1 which1 in the language of the school of ,locke and ,hartley1 is termed a ,complex ,idea4 ,now1 there are philosophers who have argued as follows3 ,if we conceive an orange to be divested of its natural color without acquiring any new one2 to lose its softness without becoming hard1 its roundness without becoming square or pentagonal1 or of any other regular or irregular figure whatever2 to be deprived of size1 of weight1 of taste1 of smell2 to lose all its mechanical and all its chemical properties1 and acquire no new ones2 to become1 in short1 invisible1 intangible1 imperceptible not only by all our senses1 but by the senses of all other sentient beings1 real or possible2 nothing1 say these thinkers1 would remain4 ,for of what nature1 they ask1 could be the residuum8 and by what token could it manifest its presence8 ,to the unreflecting its existence seems to rest on the evidence of the senses4 ,but to the senses nothing is apparent except the sensations4 ,we know1 indeed1 that these sensations are bound together by some law2 they do not come together at random1 but according to a systematic order1 which is part of the order established in the universe4 ,when we experience one of these sensations1 we usually experience the others also1 or know that we have it in our power to experience them4 ,but a fixed law of connection1 making the sensations occur together1 does not1 say these philosophers1 necessarily require what is called a substratum to support them4 ,the conception of a substratum is but one of many possible forms in which that connection presents itself to our imagination2 a mode of1 as it were1 realizing the idea4 ,if there be such a substratum1 suppose it at this instant miraculously annihilated1 and let the sensations continue to occur in the same order1 and how would the substratum be missed8 ,by what signs should we be able to discover that its existence had terminated8 ,should we not have as much reason to believe that it still existed as we now have8 ,and if we should not then be warranted in believing it1 how can we be so now8 ,a body1 therefore1 according to these metaphysicians1 is not any thing intrinsically different from the sensations which the body is said to produce in us2 it is1 in short1 a set of sensations1 or rather1 of possibilities of sensation1 joined together according to a fixed law4 ,the controversies to which these speculations have given rise1 and the doctrines which have been developed in the attempt to find a conclusive answer to them1 have been fruitful of important consequences to the ,science of ,mind4 ,the sensations 7it was answered7 which we are conscious of1 and which we receive1 not at random1 but joined together in a certain uniform manner1 imply not only a law or laws of connection1 but a cause external to our mind1 which cause1 by its own laws1 determines the laws according to which the sensations are connected and experienced4 ,the schoolmen used to call this external cause by the name we have already employed1 a substratum2 and its attributes 7as they expressed themselves7 inhered1 literally stuck1 in it4 ,to this substratum the name ,matter is usually given in philosophical discussions4 ,it was soon1 however1 acknowledged by all who reflected on the subject1 that the existence of matter can not be proved by extrinsic evidence4 ,the answer1 therefore1 now usually made to ,berkeley and his followers1 is1 that the belief is intuitive2 that mankind1 in all ages1 have felt themselves compelled1 by a necessity of their nature1 to refer their sensations to an external cause3 that even those who deny it in theory1 yield to the necessity in practice1 and both in speech1 thought1 and feeling1 do1 equally with the vulgar1 acknowledge their sensations to be the effects of something external to them3 this knowledge1 therefore1 it is affirmed1 is as evidently intuitive as our knowledge of our sensations themselves is intuitive4 ,and here the question merges in the fundamental problem of metaphysics properly so called3 to which science we leave it4 ,but although the extreme doctrine of the ,idealist metaphysicians1 that objects are nothing but our sensations and the laws which connect them1 has not been generally adopted by subsequent thinkers2 the point of most real importance is one on which those metaphysicians are now very generally considered to have made out their case3 viz41 that all we know of objects is the sensations which they give us1 and the order of the occurrence of those sensations4 ,kant himself1 on this point1 is as explicit as ,berkeley or ,locke4 ,however firmly convinced that there exists a universe of 8,things in themselves10 totally distinct from the universe of phenomena1 or of things as they appear to our senses2 and even when bringing into use a technical expression 7,noumenon7 to denote what the thing is in itself1 as contrasted with the representation of it in our minds2 he allows that this representation 7the matter of which1 he says1 consists of our sensations1 though the form is given by the laws of the mind itself7 is all we know of the object3 and that the real nature of the ,thing is1 and by the constitution of our faculties ever must remain1 at least in the present state of existence1 an impenetrable mystery to us4 8,of things absolutely or in themselves10 says ,sir ,william ,hamilton17#ai7 8be they external1 be they internal1 we know nothing1 or know them only as incognizable2 and become aware of their incomprehensible existence1 only as this is indirectly and accidentally revealed to us1 through certain qualities related to our faculties of knowledge1 and which qualities1 again1 we can not think as unconditional1 irrelative1 existent in and of ourselves4 ,all that we know is therefore phenomenal--phenomenal of the unknown407#bj7 ,the same doctrine is laid down in the clearest and strongest terms by ,m4 ,cousin1 whose observations on the subject are the more worthy of attention1 as1 in consequence of the ultra-,german and ontological character of his philosophy in other respects1 they may be regarded as the admissions of an opponent47#ba7 ,there is not the slightest reason for believing that what we call the sensible qualities of the object are a type of any thing inherent in itself1 or bear any affinity to its own nature4 ,a cause does not1 as such1 resemble its effects2 an east wind is not like the feeling of cold1 nor heat like the steam of boiling water4 ,why then should matter resemble our sensations8 ,why should the inmost nature of fire or water resemble the impressions made by those objects upon our senses87#bb7 ,or on what principle are we authorized to deduce from the effects1 any thing concerning the cause1 except that it is a cause adequate to produce those effects8 ,it may1 therefore1 safely be laid down as a truth both obvious in itself1 and admitted by all whom it is at present necessary to take into consideration1 that1 of the outward world1 we know and can know absolutely nothing1 except the sensations which we experience from it47#bc7 #h4 ,body having now been defined the external cause1 and 7according to the more reasonable opinion7 the unknown external cause1 to which we refer our sensations2 it remains to frame a definition of ,mind4 ,nor1 after the preceding observations1 will this be difficult4 ,for1 as our conception of a body is that of an unknown exciting cause of sensations1 so our conception of a mind is that of an unknown recipient or percipient1 of them2 and not of them alone1 but of all our other feelings4 ,as body is understood to be the mysterious something which excites the mind to feel1 so mind is the mysterious something which feels and thinks4 ,it is unnecessary to give in the case of mind1 as we gave in the case of matter1 a particular statement of the skeptical system by which its existence as a ,thing in itself1 distinct from the series of what are denominated its states1 is called in question4 ,but it is necessary to remark1 that on the inmost nature 7whatever be meant by inmost nature7 of the thinking principle1 as well as on the inmost nature of matter1 we are1 and with our faculties must always remain1 entirely in the dark4 ,all which we are aware of1 even in our own minds1 is 7in the words of ,james ,mill7 a certain 8thread of consciousness20 a series of feelings1 that is1 of sensations1 thoughts1 emotions1 and volitions1 more or less numerous and complicated4 ,there is a something ,i call ,myself1 or1 by another form of expression1 my mind1 which ,i consider as distinct from these sensations1 thoughts1 etc42 a something which ,i conceive to be not the thoughts1 but the being that has the thoughts1 and which ,i can conceive as existing forever in a state of quiescence1 without any thoughts at all4 ,but what this being is1 though it is myself1 ,i have no knowledge1 other than the series of its states of consciousness4 ,as bodies manifest themselves to me only through the sensations of which ,i regard them as the causes1 so the thinking principle1 or mind1 in my own nature1 makes itself known to me only by the feelings of which it is conscious4 ,i know nothing about myself1 save my capacities of feeling or being conscious 7including1 of course1 thinking and willing73 and were ,i to learn any thing new concerning my own nature1 ,i can not with my present faculties conceive this new information to be any thing else1 than that ,i have some additional capacities1 as yet unknown to me1 of feeling1 thinking1 or willing4 ,thus1 then1 as body is the unsentient cause to which we are naturally prompted to refer a certain portion of our feelings1 so mind may be described as the sentient subject 7in the scholastic sense of the term7 of all feelings2 that which has or feels them4 ,but of the nature of either body or mind1 further than the feelings which the former excites1 and which the latter experiences1 we do not1 according to the best existing doctrine1 know any thing2 and if any thing1 logic has nothing to do with it1 or with the manner in which the knowledge is acquired4 ,with this result we may conclude this portion of our subject1 and pass to the third and only remaining class or division of ,namable ,things4 ,,iii4 ,attributes3 and1 first1 ,qualities4 #i4 ,from what has already been said of ,substance1 what is to be said of ,attribute is easily deducible4 ,for if we know not1 and can not know1 any thing of bodies but the sensations which they excite in us or in others1 those sensations must be all that we can1 at bottom1 mean by their attributes2 and the distinction which we verbally make between the properties of things and the sensations we receive from them1 must originate in the convenience of discourse rather than in the nature of what is signified by the terms4 ,attributes are usually distributed under the three heads of ,quality1 ,quantity1 and ,relation4 ,we shall come to the two latter presently3 in the first place we shall confine ourselves to the former4 ,let us take1 then1 as our example1 one of what are termed the sensible qualities of objects1 and let that example be whiteness4 ,when we ascribe whiteness to any substance1 as1 for instance1 snow2 when we say that snow has the quality whiteness1 what do we really assert8 ,simply1 that when snow is present to our organs1 we have a particular sensation1 which we are accustomed to call the sensation of white4 ,but how do ,i know that snow is present8 ,obviously by the sensations which ,i derive from it1 and not otherwise4 ,i infer that the object is present1 because it gives me a certain assemblage or series of sensations4 ,and when ,i ascribe to it the attribute whiteness1 my meaning is only1 that1 of the sensations composing this group or series1 that which ,i call the sensation of white color is one4 ,this is one view which may be taken of the subject4 ,but there is also another and a different view4 ,it may be said1 that it is true we know nothing of sensible objects1 except the sensations they excite in us2 that the fact of our receiving from snow the particular sensation which is called a sensation of white1 is the ground on which we ascribe to that substance the quality whiteness2 the sole proof of its possessing that quality4 ,but because one thing may be the sole evidence of the existence of another thing1 it does not follow that the two are one and the same4 ,the attribute whiteness 7it may be said7 is not the fact of receiving the sensation1 but something in the object itself2 a power inherent in it2 something in virtue of which the object produces the sensation4 ,and when we affirm that snow possesses the attribute whiteness1 we do not merely assert that the presence of snow produces in us that sensation1 but that it does so through1 and by reason of1 that power or quality4 ,for the purposes of logic it is not of material importance which of these opinions we adopt4 ,the full discussion of the subject belongs to the other department of scientific inquiry1 so often alluded to under the name of metaphysics2 but it may be said here1 that for the doctrine of the existence of a peculiar species of entities called qualities1 ,i can see no foundation except in a tendency of the human mind which is the cause of many delusions4 ,i mean1 the disposition1 wherever we meet with two names which are not precisely synonymous1 to suppose that they must be the names of two different things2 whereas in reality they may be names of the same thing viewed in two different lights1 or under different suppositions as to surrounding circumstances4 ,because quality and sensation can not be put indiscriminately one for the other1 it is supposed that they can not both signify the same thing1 namely1 the impression or feeling with which we are affected through our senses by the presence of an object2 though there is at least no absurdity in supposing that this identical impression or feeling may be called a sensation when considered merely in itself1 and a quality when looked at in relation to any one of the numerous objects1 the presence of which to our organs excites in our minds that among various other sensations or feelings4 ,and if this be admissible as a supposition1 it rests with those who contend for an entity per se called a quality1 to show that their opinion is preferable1 or is any thing in fact but a lingering remnant of the old doctrine of occult causes2 the very absurdity which ,molire so happily ridiculed when he made one of his pedantic physicians account for the fact that opium produces sleep by the maxim1 ,because it has a soporific virtue4 ,it is evident that when the physician stated that opium has a soporific virtue1 he did not account for1 but merely asserted over again1 the fact that it produces sleep4 ,in like manner1 when we say that snow is white because it has the quality of whiteness1 we are only re-asserting in more technical language the fact that it excites in us the sensation of white4 ,if it be said that the sensation must have some cause1 ,i answer1 its cause is the presence of the assemblage of phenomena which is termed the object4 ,when we have asserted that as often as the object is present1 and our organs in their normal state1 the sensation takes place1 we have stated all that we know about the matter4 ,there is no need1 after assigning a certain and intelligible cause1 to suppose an occult cause besides1 for the purpose of enabling the real cause to produce its effect4 ,if ,i am asked1 why does the presence of the object cause this sensation in me1 ,i can not tell3 ,i can only say that such is my nature1 and the nature of the object2 that the fact forms a part of the constitution of things4 ,and to this we must at last come1 even after interpolating the imaginary entity4 ,whatever number of links the chain of causes and effects may consist of1 how any one link produces the one which is next to it1 remains equally inexplicable to us4 ,it is as easy to comprehend that the object should produce the sensation directly and at once1 as that it should produce the same sensation by the aid of something else called the power of producing it4 ,but1 as the difficulties which may be felt in adopting this view of the subject can not be removed without discussions transcending the bounds of our science1 ,i content myself with a passing indication1 and shall1 for the purposes of logic1 adopt a language compatible with either view of the nature of qualities4 ,i shall say--what at least admits of no dispute--that the quality of whiteness ascribed to the object snow1 is grounded on its exciting in us the sensation of white2 and adopting the language already used by the school logicians in the case of the kind of attributes called ,relations1 ,i shall term the sensation of white the foundation of the quality whiteness4 ,for logical purposes the sensation is the only essential part of what is meant by the word2 the only part which we ever can be concerned in proving4 ,when that is proved1 the quality is proved2 if an object excites a sensation1 it has1 of course1 the power of exciting it4 ,,iv4 ,relations4 #aj4 ,the qualities of a body1 we have said1 are the attributes grounded on the sensations which the presence of that particular body to our organs excites in our minds4 ,but when we ascribe to any object the kind of attribute called a ,relation1 the foundation of the attribute must be something in which other objects are concerned besides itself and the percipient4 ,as there may with propriety be said to be a relation between any two things to which two correlative names are or may be given1 we may expect to discover what constitutes a relation in general1 if we enumerate the principal cases in which mankind have imposed correlative names1 and observe what these cases have in common4 ,what1 then1 is the character which is possessed in common by states of circumstances so heterogeneous and discordant as these3 one thing like another2 one thing unlike another2 one thing near another2 one thing far from another2 one thing before1 after1 along with another2 one thing greater1 equal1 less1 than another2 one thing the cause of another1 the effect of another2 one person the master1 servant1 child1 parent1 debtor1 creditor1 sovereign1 subject1 attorney1 client1 of another1 and so on8 ,omitting1 for the present1 the case of ,resemblance1 7a relation which requires to be considered separately17 there seems to be one thing common to all these cases1 and only one2 that in each of them there exists or occurs1 or has existed or occurred1 or may be expected to exist or occur1 some fact or phenomenon1 into which the two things which are said to be related to each other1 both enter as parties concerned4 ,this fact1 or phenomenon1 is what the ,aristotelian logicians called the fundamentum relationis4 ,thus in the relation of greater and less between two magnitudes1 the fundamentum relationis is the fact that one of the two magnitudes could1 under certain conditions1 be included in1 without entirely filling1 the space occupied by the other magnitude4 ,in the relation of master and servant1 the fundamentum relationis is the fact that the one has undertaken1 or is compelled1 to perform certain services for the benefit and at the bidding of the other4 ,examples might be indefinitely multiplied2 but it is already obvious that whenever two things are said to be related1 there is some fact1 or series of facts1 into which they both enter2 and that whenever any two things are involved in some one fact1 or series of facts1 we may ascribe to those two things a mutual relation grounded on the fact4 ,even if they have nothing in common but what is common to all things1 that they are members of the universe1 we call that a relation1 and denominate them fellow-creatures1 fellow-beings1 or fellow-denizens of the universe4 ,but in proportion as the fact into which the two objects enter as parts is of a more special and peculiar1 or of a more complicated nature1 so also is the relation grounded upon it4 ,and there are as many conceivable relations as there are conceivable kinds of fact in which two things can be jointly concerned4 ,in the same manner1 therefore1 as a quality is an attribute grounded on the fact that a certain sensation or sensations are produced in us by the object1 so an attribute grounded on some fact into which the object enters jointly with another object1 is a relation between it and that other object4 ,but the fact in the latter case consists of the very same kind of elements as the fact in the former2 namely1 states of consciousness4 ,in the case1 for example1 of any legal relation1 as debtor and creditor1 principal and agent1 guardian and ward1 the fundamentum relationis consists entirely of thoughts1 feelings1 and volitions 7actual or contingent71 either of the persons themselves or of other persons concerned in the same series of transactions2 as1 for instance1 the intentions which would be formed by a judge1 in case a complaint were made to his tribunal of the infringement of any of the legal obligations imposed by the relation2 and the acts which the judge would perform in consequence2 acts being 7as we have already seen7 another word for intentions followed by an effect1 and that effect being but another word for sensations1 or some other feelings1 occasioned either to the agent himself or to somebody else4 ,there is no part of what the names expressive of the relation imply1 that is not resolvable into states of consciousness2 outward objects being1 no doubt1 supposed throughout as the causes by which some of those states of consciousness are excited1 and minds as the subjects by which all of them are experienced1 but neither the external objects nor the minds making their existence known otherwise than by the states of consciousness4 ,cases of relation are not always so complicated as those to which we last alluded4 ,the simplest of all cases of relation are those expressed by the words antecedent and consequent1 and by the word simultaneous4 ,if we say1 for instance1 that dawn preceded sunrise1 the fact in which the two things1 dawn and sunrise1 were jointly concerned1 consisted only of the two things themselves2 no third thing entered into the fact or phenomenon at all4 ,unless1 indeed1 we choose to call the succession of the two objects a third thing2 but their succession is not something added to the things themselves2 it is something involved in them4 ,dawn and sunrise announce themselves to our consciousness by two successive sensations4 ,our consciousness of the succession of these sensations is not a third sensation or feeling added to them2 we have not first the two feelings1 and then a feeling of their succession4 ,to have two feelings at all1 implies having them either successively1 or else simultaneously4 ,sensations1 or other feelings1 being given1 succession and simultaneousness are the two conditions1 to the alternative of which they are subjected by the nature of our faculties2 and no one has been able1 or needs expect1 to analyze the matter any further4 #aa4 ,in a somewhat similar position are two other sorts of relations1 ,likeness and ,unlikeness4 ,i have two sensations2 we will suppose them to be simple ones2 two sensations of white1 or one sensation of white and another of black4 ,i call the first two sensations like2 the last two unlike4 ,what is the fact or phenomenon constituting the fundamentum of this relation8 ,the two sensations first1 and then what we call a feeling of resemblance1 or of want of resemblance4 ,let us confine ourselves to the former case4 ,resemblance is evidently a feeling2 a state of the consciousness of the observer4 ,whether the feeling of the resemblance of the two colors be a third state of consciousness1 which ,i have after having the two sensations of color1 or whether 7like the feeling of their succession7 it is involved in the sensations themselves1 may be a matter of discussion4 ,but in either case1 these feelings of resemblance1 and of its opposite dissimilarity1 are parts of our nature2 and parts so far from being capable of analysis1 that they are presupposed in every attempt to analyze any of our other feelings4 ,likeness and unlikeness1 therefore1 as well as antecedence1 sequence1 and simultaneousness1 must stand apart among relations1 as things sui generis4 ,they are attributes grounded on facts1 that is1 on states of consciousness1 but on states which are peculiar1 unresolvable1 and inexplicable4 ,but1 though likeness or unlikeness can not be resolved into any thing else1 complex cases of likeness or unlikeness can be resolved into simpler ones4 ,when we say of two things which consist of parts1 that they are like one another1 the likeness of the wholes does admit of analysis2 it is compounded of likenesses between the various parts respectively1 and of likeness in their arrangement4 ,of how vast a variety of resemblances of parts must that resemblance be composed1 which induces us to say that a portrait1 or a landscape1 is like its original4 ,if one person mimics another with any success1 of how many simple likenesses must the general or complex likeness be compounded3 likeness in a succession of bodily postures2 likeness in voice1 or in the accents and intonations of the voice2 likeness in the choice of words1 and in the thoughts or sentiments expressed1 whether by word1 countenance1 or gesture4 ,all likeness and unlikeness of which we have any cognizance1 resolve themselves into likeness and unlikeness between states of our own1 or some other1 mind4 ,when we say that one body is like another1 7since we know nothing of bodies but the sensations which they excite17 we mean really that there is a resemblance between the sensations excited by the two bodies1 or between some portions at least of those sensations4 ,if we say that two attributes are like one another 7since we know nothing of attributes except the sensations or states of feeling on which they are grounded71 we mean really that those sensations1 or states of feeling1 resemble each other4 ,we may also say that two relations are alike4 ,the fact of resemblance between relations is sometimes called analogy1 forming one of the numerous meanings of that word4 ,the relation in which ,priam stood to ,hector1 namely1 that of father and son1 resembles the relation in which ,philip stood to ,alexander2 resembles it so closely that they are called the same relation4 ,the relation in which ,cromwell stood to ,england resembles the relation in which ,napoleon stood to ,france1 though not so closely as to be called the same relation4 ,the meaning in both these instances must be1 that a resemblance existed between the facts which constituted the fundamentum relationis4 ,this resemblance may exist in all conceivable gradations1 from perfect undistinguishableness to something extremely slight4 ,when we say1 that a thought suggested to the mind of a person of genius is like a seed cast into the ground1 because the former produces a multitude of other thoughts1 and the latter a multitude of other seeds1 this is saying that between the relation of an inventive mind to a thought contained in it1 and the relation of a fertile soil to a seed contained in it1 there exists a resemblance3 the real resemblance being in the two fundamenta relationis1 in each of which there occurs a germ1 producing by its development a multitude of other things similar to itself4 ,and as1 whenever two objects are jointly concerned in a phenomenon1 this constitutes a relation between those objects1 so1 if we suppose a second pair of objects concerned in a second phenomenon1 the slightest resemblance between the two phenomena is sufficient to admit of its being said that the two relations resemble2 provided1 of course1 the points of resemblance are found in those portions of the two phenomena respectively which are connoted by the relative names4 ,while speaking of resemblance1 it is necessary to take notice of an ambiguity of language1 against which scarcely any one is sufficiently on his guard4 ,resemblance1 when it exists in the highest degree of all1 amounting to undistinguishableness1 is often called identity1 and the two similar things are said to be the same4 ,i say often1 not always2 for we do not say that two visible objects1 two persons1 for instance1 are the same1 because they are so much alike that one might be mistaken for the other3 but we constantly use this mode of expression when speaking of feelings2 as when ,i say that the sight of any object gives me the same sensation or emotion to-day that it did yesterday1 or the same which it gives to some other person4 ,this is evidently an incorrect application of the word same2 for the feeling which ,i had yesterday is gone1 never to return2 what ,i have to-day is another feeling1 exactly like the former1 perhaps1 but distinct from it2 and it is evident that two different persons can not be experiencing the same feeling1 in the sense in which we say that they are both sitting at the same table4 ,by a similar ambiguity we say1 that two persons are ill of the same disease2 that two persons hold the same office2 not in the sense in which we say that they are engaged in the same adventure1 or sailing in the same ship1 but in the sense that they fill offices exactly similar1 though1 perhaps1 in distant places4 ,great confusion of ideas is often produced1 and many fallacies engendered1 in otherwise enlightened understandings1 by not being sufficiently alive to the fact 7in itself not always to be avoided71 that they use the same name to express ideas so different as those of identity and undistinguishable resemblance4 ,among modern writers1 ,archbishop ,whately stands almost alone in having drawn attention to this distinction1 and to the ambiguity connected with it4 ,several relations1 generally called by other names1 are really cases of resemblance4 ,as1 for example1 equality2 which is but another word for the exact resemblance commonly called identity1 considered as subsisting between things in respect of their quantity4 ,and this example forms a suitable transition to the third and last of the three heads under which1 as already remarked1 ,attributes are commonly arranged4 ,v4 ,quantity4 #ab4 ,let us imagine two things1 between which there is no difference 7that is1 no dissimilarity71 except in quantity alone2 for instance1 a gallon of water1 and more than a gallon of water4 ,a gallon of water1 like any other external object1 makes its presence known to us by a set of sensations which it excites4 ,ten gallons of water are also an external object1 making its presence known to us in a similar manner2 and as we do not mistake ten gallons of water for a gallon of water1 it is plain that the set of sensations is more or less different in the two cases4 ,in like manner1 a gallon of water1 and a gallon of wine1 are two external objects1 making their presence known by two sets of sensations1 which sensations are different from each other4 ,in the first case1 however1 we say that the difference is in quantity2 in the last there is a difference in quality1 while the quantity of the water and of the wine is the same4 ,what is the real distinction between the two cases8 ,it is not within the province of ,logic to analyze it2 nor to decide whether it is susceptible of analysis or not4 ,for us the following considerations are sufficient3 ,it is evident that the sensations ,i receive from the gallon of water1 and those ,i receive from the gallon of wine1 are not the same1 that is1 not precisely alike2 neither are they altogether unlike3 they are partly similar1 partly dissimilar2 and that in which they resemble is precisely that in which alone the gallon of water and the ten gallons do not resemble4 ,that in which the gallon of water and the gallon of wine are like each other1 and in which the gallon and the ten gallons of water are unlike each other1 is called their quantity4 ,this likeness and unlikeness ,i do not pretend to explain1 no more than any other kind of likeness or unlikeness4 ,but my object is to show1 that when we say of two things that they differ in quantity1 just as when we say that they differ in quality1 the assertion is always grounded on a difference in the sensations which they excite4 ,nobody1 ,i presume1 will say1 that to see1 or to lift1 or to drink1 ten gallons of water1 does not include in itself a different set of sensations from those of seeing1 lifting1 or drinking one gallon2 or that to see or handle a foot-rule1 and to see or handle a yard-measure made exactly like it1 are the same sensations4 ,i do not undertake to say what the difference in the sensations is4 ,every body knows1 and nobody can tell2 no more than any one could tell what white is to a person who had never had the sensation4 ,but the difference1 so far as cognizable by our faculties1 lies in the sensations4 ,whatever difference we say there is in the things themselves1 is1 in this as in all other cases1 grounded1 and grounded exclusively1 on a difference in the sensations excited by them4 ,,vi4 ,attributes ,concluded4 #ac4 ,thus1 then1 all the attributes of bodies which are classed under ,quality or ,quantity1 are grounded on the sensations which we receive from those bodies1 and may be defined1 the powers which the bodies have of exciting those sensations4 ,and the same general explanation has been found to apply to most of the attributes usually classed under the head of ,relation4 ,they1 too1 are grounded on some fact or phenomenon into which the related objects enter as parts2 that fact or phenomenon having no meaning and no existence to us1 except the series of sensations or other states of consciousness by which it makes itself known2 and the relation being simply the power or capacity which the object possesses of taking part along with the correlated object in the production of that series of sensations or states of consciousness4 ,we have been obliged1 indeed1 to recognize a somewhat different character in certain peculiar relations1 those of succession and simultaneity1 of likeness and unlikeness4 ,these1 not being grounded on any fact or phenomenon distinct from the related objects themselves1 do not admit of the same kind of analysis4 ,but these relations1 though not1 like other relations1 grounded on states of consciousness1 are themselves states of consciousness3 resemblance is nothing but our feeling of resemblance2 succession is nothing but our feeling of succession4 ,or1 if this be disputed 7and we can not1 without transgressing the bounds of our science1 discuss it here71 at least our knowledge of these relations1 and even our possibility of knowledge1 is confined to those which subsist between sensations1 or other states of consciousness2 for1 though we ascribe resemblance1 or succession1 or simultaneity1 to objects and to attributes1 it is always in virtue of resemblance or succession or simultaneity in the sensations or states of consciousness which those objects excite1 and on which those attributes are grounded4 #ad4 ,in the preceding investigation we have1 for the sake of simplicity1 considered bodies only1 and omitted minds4 ,but what we have said1 is applicable1 mutatis mutandis1 to the latter4 ,the attributes of minds1 as well as those of bodies1 are grounded on states of feeling or consciousness4 ,but in the case of a mind1 we have to consider its own states1 as well as those which it produces in other minds4 ,every attribute of a mind consists either in being itself affected in a certain way1 or affecting other minds in a certain way4 ,considered in itself1 we can predicate nothing of it but the series of its own feelings4 ,when we say of any mind1 that it is devout1 or superstitious1 or meditative1 or cheerful1 we mean that the ideas1 emotions1 or volitions implied in those words1 form a frequently recurring part of the series of feelings1 or states of consciousness1 which fill up the sentient existence of that mind4 ,in addition1 however1 to those attributes of a mind which are grounded on its own states of feeling1 attributes may also be ascribed to it1 in the same manner as to a body1 grounded on the feelings which it excites in other minds4 ,a mind does not1 indeed1 like a body1 excite sensations1 but it may excite thoughts or emotions4 ,the most important example of attributes ascribed on this ground1 is the employment of terms expressive of approbation or blame4 ,when1 for example1 we say of any character1 or 7in other words7 of any mind1 that it is admirable1 we mean that the contemplation of it excites the sentiment of admiration2 and indeed somewhat more1 for the word implies that we not only feel admiration1 but approve that sentiment in ourselves4 ,in some cases1 under the semblance of a single attribute1 two are really predicated3 one of them1 a state of the mind itself2 the other1 a state with which other minds are affected by thinking of it4 ,as when we say of any one that he is generous4 ,the word generosity expresses a certain state of mind1 but being a term of praise1 it also expresses that this state of mind excites in us another mental state1 called approbation4 ,the assertion made1 therefore1 is twofold1 and of the following purport3 ,certain feelings form habitually a part of this person's sentient existence2 and the idea of those feelings of his1 excites the sentiment of approbation in ourselves or others4 ,as we thus ascribe attributes to minds on the ground of ideas and emotions1 so may we to bodies on similar grounds1 and not solely on the ground of sensations3 as in speaking of the beauty of a statue2 since this attribute is grounded on the peculiar feeling of pleasure which the statue produces in our minds2 which is not a sensation1 but an emotion4 ,,vii4 ,general ,results4 #ae4 ,our survey of the varieties of ,things which have been1 or which are capable of being1 named--which have been1 or are capable of being1 either predicated of other ,things1 or themselves made the subject of predications--is now concluded4 ,our enumeration commenced with ,feelings4 ,these we scrupulously distinguished from the objects which excite them1 and from the organs by which they are1 or may be supposed to be1 conveyed4 ,feelings are of four sorts3 ,sensations1 ,thoughts1 ,emotions1 and ,volitions4 ,what are called ,perceptions are merely a particular case of ,belief1 and ,belief is a kind of thought4 ,actions are merely volitions followed by an effect4 ,after ,feelings we proceeded to ,substances4 ,these are either ,bodies or ,minds4 ,without entering into the grounds of the metaphysical doubts which have been raised concerning the existence of ,matter and ,mind as objective realities1 we stated as sufficient for us the conclusion in which the best thinkers are now for the most part agreed1 that all we can know of ,matter is the sensations which it gives us1 and the order of occurrence of those sensations2 and that while the substance ,body is the unknown cause of our sensations1 the substance ,mind is the unknown recipient4 ,the only remaining class of ,namable ,things is ,attributes2 and these are of three kinds1 ,quality1 ,relation1 and ,quantity4 ,qualities1 like substances1 are known to us no otherwise than by the sensations or other states of consciousness which they excite3 and while1 in compliance with common usage1 we have continued to speak of them as a distinct class of ,things1 we showed that in predicating them no one means to predicate any thing but those sensations or states of consciousness1 on which they may be said to be grounded1 and by which alone they can be defined or described4 ,relations1 except the simple cases of likeness and unlikeness1 succession and simultaneity1 are similarly grounded on some fact or phenomenon1 that is1 on some series of sensations or states of consciousness1 more or less complicated4 ,the third species of ,attribute1 ,quantity1 is also manifestly grounded on something in our sensations or states of feeling1 since there is an indubitable difference in the sensations excited by a larger and a smaller bulk1 or by a greater or a less degree of intensity1 in any object of sense or of consciousness4 ,all attributes1 therefore1 are to us nothing but either our sensations and other states of feeling1 or something inextricably involved therein2 and to this even the peculiar and simple relations just adverted to are not exceptions4 ,those peculiar relations1 however1 are so important1 and1 even if they might in strictness be classed among states of consciousness1 are so fundamentally distinct from any other of those states1 that it would be a vain subtlety to bring them under that common description1 and it is necessary that they should be classed apart47#bd7 ,as the result1 therefore1 of our analysis1 we obtain the following as an enumeration and classification of all ,namable ,things3 #ast4 ,feelings1 or ,states of ,consciousness4 #b;d4 ,the ,minds which experience those feelings4 #c;d4 ,the ,bodies1 or external objects which excite certain of those feelings1 together with the powers or properties whereby they excite them2 these latter 7at least7 being included rather in compliance with common opinion1 and because their existence is taken for granted in the common language from which ,i can not prudently deviate1 than because the recognition of such powers or properties as real existences appears to be warranted by a sound philosophy4 #dth1 and last4 ,the ,successions and ,co-existences1 the ,likenesses and ,unlikenesses1 between feelings or states of consciousness4 ,those relations1 when considered as subsisting between other things1 exist in reality only between the states of consciousness which those things1 if bodies1 excite1 if minds1 either excite or experience4 ,this1 until a better can be suggested1 may serve as a substitute for the ,categories of ,aristotle considered as a classification of ,existences4 ,the practical application of it will appear when we commence the inquiry into the ,import of ,propositions2 in other words1 when we inquire what it is which the mind actually believes1 when it gives what is called its assent to a proposition4 ,these four classes comprising1 if the classification be correct1 all ,namable ,things1 these or some of them must of course compose the signification of all names3 and of these1 or some of them1 is made up whatever we call a fact4 ,for distinction's sake1 every fact which is solely composed of feelings or states of consciousness considered as such1 is often called a ,psychological or ,subjective fact2 while every fact which is composed1 either wholly or in part1 of something different from these1 that is1 of substances and attributes1 is called an ,objective fact4 ,we may say1 then1 that every objective fact is grounded on a corresponding subjective one2 and has no meaning to us 7apart from the subjective fact which corresponds to it71 except as a name for the unknown and inscrutable process by which that subjective or psychological fact is brought to pass4 ,chapter ,,iv4 ,of ,propositions4 #a4 ,in treating of ,propositions1 as already in treating of ,names1 some considerations of a comparatively elementary nature respecting their form and varieties must be premised1 before entering upon that analysis of the import conveyed by them1 which is the real subject and purpose of this preliminary book4 ,a proposition1 we have before said1 is a portion of discourse in which a predicate is affirmed or denied of a subject4 ,a predicate and a subject are all that is necessarily required to make up a proposition3 but as we can not conclude from merely seeing two names put together1 that they are a predicate and a subject1 that is1 that one of them is intended to be affirmed or denied of the other1 it is necessary that there should be some mode or form of indicating that such is the intention2 some sign to distinguish a predication from any other kind of discourse4 ,this is sometimes done by a slight alteration of one of the words1 called an inflection2 as when we say1 ,fire burns2 the change of the second word from burn to burns showing that we mean to affirm the predicate burn of the subject fire4 ,but this function is more commonly fulfilled by the word is1 when an affirmation is intended1 is not1 when a negation2 or by some other part of the verb to be4 ,the word which thus serves the purpose of a sign of predication is called1 as we formerly observed1 the copula4 ,it is important that there should be no indistinctness in our conception of the nature and office of the copula2 for confused notions respecting it are among the causes which have spread mysticism over the field of logic1 and perverted its speculations into logomachies4 ,it is apt to be supposed that the copula is something more than a mere sign of predication2 that it also signifies existence4 ,in the proposition1 ,socrates is just1 it may seem to be implied not only that the quality just can be affirmed of ,socrates1 but moreover that ,socrates is1 that is to say1 exists4 ,this1 however1 only shows that there is an ambiguity in the word is2 a word which not only performs the function of the copula in affirmations1 but has also a meaning of its own1 in virtue of which it may itself be made the predicate of a proposition4 ,that the employment of it as a copula does not necessarily include the affirmation of existence1 appears from such a proposition as this1 ,a centaur is a fiction of the poets2 where it can not possibly be implied that a centaur exists1 since the proposition itself expressly asserts that the thing has no real existence4 ,many volumes might be filled with the frivolous speculations concerning the nature of ,being 7 1 1 ,ens1 ,entitas1 ,essentia1 and the like71 which have arisen from overlooking this double meaning of the word to be2 from supposing that when it signifies to exist1 and when it signifies to be some specified thing1 as to be a man1 to be ,socrates1 to be seen or spoken of1 to be a phantom1 even to be a nonentity1 it must still1 at bottom1 answer to the same idea2 and that a meaning must be found for it which shall suit all these cases4 ,the fog which rose from this narrow spot diffused itself at an early period over the whole surface of metaphysics4 ,yet it becomes us not to triumph over the great intellects of ,plato and ,aristotle because we are now able to preserve ourselves from many errors into which they1 perhaps inevitably1 fell4 ,the fire-teazer of a modern steam-engine produces by his exertions far greater effects than ,milo of ,crotona could1 but he is not therefore a stronger man4 ,the ,greeks seldom knew any language but their own4 ,this rendered it far more difficult for them than it is for us1 to acquire a readiness in detecting ambiguities4 ,one of the advantages of having accurately studied a plurality of languages1 especially of those languages which eminent thinkers have used as the vehicle of their thoughts1 is the practical lesson we learn respecting the ambiguities of words1 by finding that the same word in one language corresponds1 on different occasions1 to different words in another4 ,when not thus exercised1 even the strongest understandings find it difficult to believe that things which have a common name1 have not in some respect or other a common nature2 and often expend much labor very unprofitably 7as was frequently done by the two philosophers just mentioned7 in vain attempts to discover in what this common nature consists4 ,but1 the habit once formed1 intellects much inferior are capable of detecting even ambiguities which are common to many languages3 and it is surprising that the one now under consideration1 though it exists in the modern languages as well as in the ancient1 should have been overlooked by almost all authors4 ,the quantity of futile speculation which had been caused by a misapprehension of the nature of the copula1 was hinted at by ,hobbes2 but ,mr4 ,james ,mill7#be7 was1 ,i believe1 the first who distinctly characterized the ambiguity1 and pointed out how many errors in the received systems of philosophy it has had to answer for4 ,it has1 indeed1 misled the moderns scarcely less than the ancients1 though their mistakes1 because our understandings are not yet so completely emancipated from their influence1 do not appear equally irrational4 ,we shall now briefly review the principal distinctions which exist among propositions1 and the technical terms most commonly in use to express those distinctions4 #b4 ,a proposition being a portion of discourse in which something is affirmed or denied of something1 the first division of propositions is into affirmative and negative4 ,an affirmative proposition is that in which the predicate is affirmed of the subject2 as1 ,csar is dead4 ,a negative proposition is that in which the predicate is denied of the subject2 as1 ,csar is not dead4 ,the copula1 in this last species of proposition1 consists of the words is not1 which are the sign of negation2 is being the sign of affirmation4 ,some logicians1 among whom may be mentioned ,hobbes1 state this distinction differently2 they recognize only one form of copula1 is1 and attach the negative sign to the predicate4 8,csar is dead10 and 8,csar is not dead10 according to these writers1 are propositions agreeing not in the subject and predicate1 but in the subject only4 ,they do not consider 8dead10 but 8not dead10 to be the predicate of the second proposition1 and they accordingly define a negative proposition to be one in which the predicate is a negative name4 ,the point1 though not of much practical moment1 deserves notice as an example 7not unfrequent in logic7 where by means of an apparent simplification1 but which is merely verbal1 matters are made more complex than before4 ,the notion of these writers was1 that they could get rid of the distinction between affirming and denying1 by treating every case of denying as the affirming of a negative name4 ,but what is meant by a negative name8 ,a name expressive of the absence of an attribute4 ,so that when we affirm a negative name1 what we are really predicating is absence and not presence2 we are asserting not that any thing is1 but that something is not2 to express which operation no word seems so proper as the word denying4 ,the fundamental distinction is between a fact and the non-existence of that fact2 between seeing something and not seeing it1 between ,csar's being dead and his not being dead2 and if this were a merely verbal distinction1 the generalization which brings both within the same form of assertion would be a real simplification3 the distinction1 however1 being real1 and in the facts1 it is the generalization confounding the distinction that is merely verbal2 and tends to obscure the subject1 by treating the difference between two kinds of truths as if it were only a difference between two kinds of words4 ,to put things together1 and to put them or keep them asunder1 will remain different operations1 whatever tricks we may play with language4 ,a remark of a similar nature may be applied to most of those distinctions among propositions which are said to have reference to their modality2 as1 difference of tense or time2 the sun did rise1 the sun is rising1 the sun will rise4 ,these differences1 like that between affirmation and negation1 might be glossed over by considering the incident of time as a mere modification of the predicate3 thus1 ,the sun is an object having risen1 ,the sun is an object now rising1 ,the sun is an object to rise hereafter4 ,but the simplification would be merely verbal4 ,past1 present1 and future1 do not constitute so many different kinds of rising2 they are designations belonging to the event asserted1 to the sun's rising to-day4 ,they affect1 not the predicate1 but the applicability of the predicate to the particular subject4 ,that which we affirm to be past1 present1 or future1 is not what the subject signifies1 nor what the predicate signifies1 but specifically and expressly what the predication signifies2 what is expressed only by the proposition as such1 and not by either or both of the terms4 ,therefore the circumstance of time is properly considered as attaching to the copula1 which is the sign of predication1 and not to the predicate4 ,if the same can not be said of such modifications as these1 ,csar may be dead2 ,csar is perhaps dead2 it is possible that ,csar is dead2 it is only because these fall altogether under another head1 being properly assertions not of any thing relating to the fact itself1 but of the state of our own mind in regard to it2 namely1 our absence of disbelief of it4 ,thus 8,csar may be dead0 means 8,i am not sure that ,csar is alive40 #c4 ,the next division of propositions is into ,simple and ,complex2 more aptly 7by ,professor ,bain7#bf77 termed ,compound4 ,a simple proposition is that in which one predicate is affirmed or denied of one subject4 ,a compound proposition is that in which there is more than one predicate1 or more than one subject1 or both4 ,at first sight this division has the air of an absurdity2 a solemn distinction of things into one and more than one2 as if we were to divide horses into single horses and teams of horses4 ,and it is true that what is called a complex 7or compound7 proposition is often not a proposition at all1 but several propositions1 held together by a conjunction4 ,such1 for example1 is this3 ,csar is dead1 and ,brutus is alive3 or even this1 ,csar is dead1 but ,brutus is alive4 ,there are here two distinct assertions2 and we might as well call a street a complex house1 as these two propositions a complex proposition4 ,it is true that the syncategorematic words and and but have a meaning2 but that meaning is so far from making the two propositions one1 that it adds a third proposition to them4 ,all particles are abbreviations1 and generally abbreviations of propositions2 a kind of short-hand1 whereby something which1 to be expressed fully1 would have required a proposition or a series of propositions1 is suggested to the mind at once4 ,thus the words1 ,csar is dead and ,brutus is alive1 are equivalent to these3 ,csar is dead2 ,brutus is alive2 it is desired that the two preceding propositions should be thought of together4 ,if the words were1 ,csar is dead1 but ,brutus is alive1 the sense would be equivalent to the same three propositions together with a fourth2 8between the two preceding propositions there exists a contrast30 viz41 either between the two facts themselves1 or between the feelings with which it is desired that they should be regarded4 ,in the instances cited the two propositions are kept visibly distinct1 each subject having its separate predicate1 and each predicate its separate subject4 ,for brevity1 however1 and to avoid repetition1 the propositions are often blended together3 as in this1 8,peter and ,james preached at ,jerusalem and in ,galilee10 which contains four propositions3 ,peter preached at ,jerusalem1 ,peter preached in ,galilee1 ,james preached at ,jerusalem1 ,james preached in ,galilee4 ,we have seen that when the two or more propositions comprised in what is called a complex proposition are stated absolutely1 and not under any condition or proviso1 it is not a proposition at all1 but a plurality of propositions2 since what it expresses is not a single assertion1 but several assertions1 which1 if true when joined1 are true also when separated4 ,but there is a kind of proposition which1 though it contains a plurality of subjects and of predicates1 and may be said in one sense of the word to consist of several propositions1 contains but one assertion2 and its truth does not at all imply that of the simple propositions which compose it4 ,an example of this is1 when the simple propositions are connected by the particle or2 as1 either ,a is ,b or ,c is ,d2 or by the particle if2 as1 ,a is ,b if ,c is ,d4 ,in the former case1 the proposition is called disjunctive1 in the latter1 conditional3 the name hypothetical was originally common to both4 ,as has been well remarked by ,archbishop ,whately and others1 the disjunctive form is resolvable into the conditional2 every disjunctive proposition being equivalent to two or more conditional ones4 8,either ,a is ,b or ,c is ,d10 means1 8if ,a is not ,b1 ,c is ,d2 and if ,c is not ,d1 ,a is ,b40 ,all hypothetical propositions1 therefore1 though disjunctive in form1 are conditional in meaning2 and the words hypothetical and conditional may be1 as indeed they generally are1 used synonymously4 ,propositions in which the assertion is not dependent on a condition1 are said1 in the language of logicians1 to be categorical4 ,a hypothetical proposition is not1 like the pretended complex propositions which we previously considered1 a mere aggregation of simple propositions4 ,the simple propositions which form part of the words in which it is couched1 form no part of the assertion which it conveys4 ,when we say1 ,if the ,koran comes from ,god1 ,mohammed is the prophet of ,god1 we do not intend to affirm either that the ,koran does come from ,god1 or that ,mohammed is really his prophet4 ,neither of these simple propositions may be true1 and yet the truth of the hypothetical proposition may be indisputable4 ,what is asserted is not the truth of either of the propositions1 but the inferribility of the one from the other4 ,what1 then1 is the subject1 and what the predicate of the hypothetical proposition8 8,the ,koran0 is not the subject of it1 nor is 8,mohammed30 for nothing is affirmed or denied either of the ,koran or of ,mohammed4 ,the real subject of the predication is the entire proposition1 8,mohammed is the prophet of ,god20 and the affirmation is1 that this is a legitimate inference from the proposition1 8,the ,koran comes from ,god40 ,the subject and predicate1 therefore1 of a hypothetical proposition are names of propositions4 ,the subject is some one proposition4 ,the predicate is a general relative name applicable to propositions2 of this form--8an inference from so and so40 ,a fresh instance is here afforded of the remark1 that particles are abbreviations2 since 8,if ,a is ,b1 ,c is ,d10 is found to be an abbreviation of the following3 8,the proposition ,c is ,d1 is a legitimate inference from the proposition ,a is ,b40 ,the distinction1 therefore1 between hypothetical and categorical propositions is not so great as it at first appears4 ,in the conditional1 as well as in the categorical form1 one predicate is affirmed of one subject1 and no more3 but a conditional proposition is a proposition concerning a proposition2 the subject of the assertion is itself an assertion4 ,nor is this a property peculiar to hypothetical propositions4 ,there are other classes of assertions concerning propositions4 ,like other things1 a proposition has attributes which may be predicated of it4 ,the attribute predicated of it in a hypothetical proposition1 is that of being an inference from a certain other proposition4 ,but this is only one of many attributes that might be predicated4 ,we may say1 ,that the whole is greater than its part1 is an axiom in mathematics3 ,that the ,holy ,ghost proceeds from the ,father alone1 is a tenet of the ,greek ,church3 ,the doctrine of the divine right of kings was renounced by ,parliament at the ,revolution3 ,the infallibility of the ,pope has no countenance from ,scripture4 ,in all these cases the subject of the predication is an entire proposition4 ,that which these different predicates are affirmed of1 is the proposition1 8the whole is greater than its part20 the proposition1 8the ,holy ,ghost proceeds from the ,father alone20 the proposition1 8kings have a divine right20 the proposition1 8the ,pope is infallible40 ,seeing1 then1 that there is much less difference between hypothetical propositions and any others1 than one might be led to imagine from their form1 we should be at a loss to account for the conspicuous position which they have been selected to fill in treatises on logic1 if we did not remember that what they predicate of a proposition1 namely1 its being an inference from something else1 is precisely that one of its attributes with which most of all a logician is concerned4 #d4 ,the next of the common divisions of ,propositions is into ,universal1 ,particular1 ,indefinite1 and ,singular3 a distinction founded on the degree of generality in which the name1 which is the subject of the proposition1 is to be understood4 ,the following are examples3 ,all men are mortal--,universal4 ,some men are mortal--,particular4 ,man is mortal--,indefinite4 ,julius ,csar is mortal--,singular4 ,the proposition is ,singular1 when the subject is an individual name4 ,the individual name needs not be a proper name4 8,the ,founder of ,christianity was crucified10 is as much a singular proposition as 8,christ was crucified40 ,when the name which is the subject of the proposition is a general name1 we may intend to affirm or deny the predicate1 either of all the things that the subject denotes1 or only of some4 ,when the predicate is affirmed or denied of all and each of the things denoted by the subject1 the proposition is universal2 when of some undefined portion of them only1 it is particular4 ,thus1 ,all men are mortal2 ,every man is mortal2 are universal propositions4 ,no man is immortal1 is also a universal proposition1 since the predicate1 immortal1 is denied of each and every individual denoted by the term man2 the negative proposition being exactly equivalent to the following1 ,every man is not-immortal4 ,but 8some men are wise10 8some men are not wise10 are particular propositions2 the predicate wise being in the one case affirmed and in the other denied not of each and every individual denoted by the term man1 but only of each and every one of some portion of those individuals1 without specifying what portion2 for if this were specified1 the proposition would be changed either into a singular proposition1 or into a universal proposition with a different subject2 as1 for instance1 8all properly instructed men are wise40 ,there are other forms of particular propositions2 as1 8,most men are imperfectly educated30 it being immaterial how large a portion of the subject the predicate is asserted of1 as long as it is left uncertain how that portion is to be distinguished from the rest47#bg7 ,when the form of the expression does not clearly show whether the general name which is the subject of the proposition is meant to stand for all the individuals denoted by it1 or only for some of them1 the proposition is1 by some logicians1 called ,indefinite2 but this1 as ,archbishop ,whately observes1 is a solecism1 of the same nature as that committed by some grammarians when in their list of genders they enumerate the doubtful gender4 ,the speaker must mean to assert the proposition either as a universal or as a particular proposition1 though he has failed to declare which3 and it often happens that though the words do not show which of the two he intends1 the context1 or the custom of speech1 supplies the deficiency4 ,thus1 when it is affirmed that 8,man is mortal10 nobody doubts that the assertion is intended of all human beings2 and the word indicative of universality is commonly omitted1 only because the meaning is evident without it4 ,in the proposition1 8,wine is good10 it is understood with equal readiness1 though for somewhat different reasons1 that the assertion is not intended to be universal1 but particular47#bh7 ,as is observed by ,professor ,bain17#bi7 the chief examples of ,indefinite propositions occur 8with names of material1 which are the subjects sometimes of universal1 and at other times of particular predication4 #8,food is chemically constituted by carbon1 oxygen1 etc41' is a proposition of universal quantity2 the meaning is all food--all kinds of food4 #8,food is necessary to animal life' is a case of particular quantity2 the meaning is some sort of food1 not necessarily all sorts4 #8,metal is requisite in order to strength' does not mean all kinds of metal4 #8,gold will make a way1' means a portion of gold40 ,when a general name stands for each and every individual which it is a name of1 or in other words1 which it denotes1 it is said by logicians to be distributed1 or taken distributively4 ,thus1 in the proposition1 ,all men are mortal1 the subject1 ,man1 is distributed1 because mortality is affirmed of each and every man4 ,the predicate1 ,mortal1 is not distributed1 because the only mortals who are spoken of in the proposition are those who happen to be men2 while the word may1 for aught that appears1 and in fact does1 comprehend within it an indefinite number of objects besides men4 ,in the proposition1 ,some men are mortal1 both the predicate and the subject are undistributed4 ,in the following1 ,no men have wings1 both the predicate and the subject are distributed4 ,not only is the attribute of having wings denied of the entire class ,man1 but that class is severed and cast out from the whole of the class ,winged1 and not merely from some part of that class4 ,this phraseology1 which is of great service in stating and demonstrating the rules of the syllogism1 enables us to express very concisely the definitions of a universal and a particular proposition4 ,a universal proposition is that of which the subject is distributed2 a particular proposition is that of which the subject is undistributed4 ,there are many more distinctions among propositions than those we have here stated1 some of them of considerable importance4 ,but1 for explaining and illustrating these1 more suitable opportunities will occur in the sequel4 ,chapter ,v4 ,of ,the ,import ,of ,propositions4 #a4 ,an inquiry into the nature of propositions must have one of two objects3 to analyze the state of mind called ,belief1 or to analyze what is believed4 ,all language recognizes a difference between a doctrine or opinion1 and the fact of entertaining the opinion2 between assent1 and what is assented to4 ,logic1 according to the conception here formed of it1 has no concern with the nature of the act of judging or believing2 the consideration of that act1 as a phenomenon of the mind1 belongs to another science4 ,philosophers1 however1 from ,descartes downward1 and especially from the era of ,leibnitz and ,locke1 have by no means observed this distinction2 and would have treated with great disrespect any attempt to analyze the import of ,propositions1 unless founded on an analysis of the act of ,judgment4 ,a proposition1 they would have said1 is but the expression in words of a ,judgment4 ,the thing expressed1 not the mere verbal expression1 is the important matter4 ,when the mind assents to a proposition1 it judges4 ,let us find out what the mind does when it judges1 and we shall know what propositions mean1 and not otherwise4 ,conformably to these views1 almost all the writers on ,logic in the last two centuries1 whether ,english1 ,german1 or ,french1 have made their theory of ,propositions1 from one end to the other1 a theory of ,judgments4 ,they considered a ,proposition1 or a ,judgment1 for they used the two words indiscriminately1 to consist in affirming or denying one idea of another4 ,to judge1 was to put two ideas together1 or to bring one idea under another1 or to compare two ideas1 or to perceive the agreement or disagreement between two ideas3 and the whole doctrine of ,propositions1 together with the theory of ,reasoning 7always necessarily founded on the theory of ,propositions71 was stated as if ,ideas1 or ,conceptions1 or whatever other term the writer preferred as a name for mental representations generally1 constituted essentially the subject-matter and substance of those operations4 ,it is1 of course1 true1 that in any case of judgment1 as for instance when we judge that gold is yellow1 a process takes place in our minds1 of which some one or other of these theories is a partially correct account4 ,we must have the idea of gold and the idea of yellow1 and these two ideas must be brought together in our mind4 ,but in the first place1 it is evident that this is only a part of what takes place2 for we may put two ideas together without any act of belief2 as when we merely imagine something1 such as a golden mountain2 or when we actually disbelieve3 for in order even to disbelieve that ,mohammed was an apostle of ,god1 we must put the idea of ,mohammed and that of an apostle of ,god together4 ,to determine what it is that happens in the case of assent or dissent besides putting two ideas together1 is one of the most intricate of metaphysical problems4 ,but whatever the solution may be1 we may venture to assert that it can have nothing whatever to do with the import of propositions2 for this reason1 that propositions 7except sometimes when the mind itself is the subject treated of7 are not assertions respecting our ideas of things1 but assertions respecting the things themselves4 ,in order to believe that gold is yellow1 ,i must1 indeed1 have the idea of gold1 and the idea of yellow1 and something having reference to those ideas must take place in my mind2 but my belief has not reference to the ideas1 it has reference to the things4 ,what ,i believe1 is a fact relating to the outward thing1 gold1 and to the impression made by that outward thing upon the human organs2 not a fact relating to my conception of gold1 which would be a fact in my mental history1 not a fact of external nature4 ,it is true1 that in order to believe this fact in external nature1 another fact must take place in my mind1 a process must be performed upon my ideas2 but so it must in every thing else that ,i do4 ,i can not dig the ground unless ,i have the idea of the ground1 and of a spade1 and of all the other things ,i am operating upon1 and unless ,i put those ideas together47#cj7 ,but it would be a very ridiculous description of digging the ground to say that it is putting one idea into another4 ,digging is an operation which is performed upon the things themselves1 though it can not be performed unless ,i have in my mind the ideas of them4 ,and in like manner1 believing is an act which has for its subject the facts themselves1 though a previous mental conception of the facts is an indispensable condition4 ,when ,i say that fire causes heat1 do ,i mean that my idea of fire causes my idea of heat8 ,no3 ,i mean that the natural phenomenon1 fire1 causes the natural phenomenon1 heat4 ,when ,i mean to assert any thing respecting the ideas1 ,i give them their proper name1 ,i call them ideas3 as when ,i say1 that a child's idea of a battle is unlike the reality1 or that the ideas entertained of the ,deity have a great effect on the characters of mankind4 ,the notion that what is of primary importance to the logician in a proposition1 is the relation between the two ideas corresponding to the subject and predicate 7instead of the relation between the two phenomena which they respectively express71 seems to me one of the most fatal errors ever introduced into the philosophy of ,logic2 and the principal cause why the theory of the science has made such inconsiderable progress during the last two centuries4 ,the treatises on ,logic1 and on the branches of ,mental ,philosophy connected with ,logic1 which have been produced since the intrusion of this cardinal error1 though sometimes written by men of extraordinary abilities and attainments1 almost always tacitly imply a theory that the investigation of truth consists in contemplating and handling our ideas1 or conceptions of things1 instead of the things themselves3 a doctrine tantamount to the assertion1 that the only mode of acquiring knowledge of nature is to study it at second hand1 as represented in our own minds4 ,meanwhile1 inquiries into every kind of natural phenomena were incessantly establishing great and fruitful truths on most important subjects1 by processes upon which these views of the nature of ,judgment and ,reasoning threw no light1 and in which they afforded no assistance whatever4 ,no wonder that those who knew by practical experience how truths are arrived at1 should deem a science futile1 which consisted chiefly of such speculations4 ,what has been done for the advancement of ,logic since these doctrines came into vogue1 has been done not by professed logicians1 but by discoverers in the other sciences2 in whose methods of investigation many principles of logic1 not previously thought of1 have successively come forth into light1 but who have generally committed the error of supposing that nothing whatever was known of the art of philosophizing by the old logicians1 because their modern interpreters have written to so little purpose respecting it4 ,we have to inquire1 then1 on the present occasion1 not into ,judgment1 but judgments2 not into the act of believing1 but into the thing believed4 ,what is the immediate object of belief in a ,proposition8 ,what is the matter of fact signified by it8 ,what is it to which1 when ,i assert the proposition1 ,i give my assent1 and call upon others to give theirs8 ,what is that which is expressed by the form of discourse called a ,proposition1 and the conformity of which to fact constitutes the truth of the proposition8 #b4 ,one of the clearest and most consecutive thinkers whom this country or the world has produced1 ,i mean ,hobbes1 has given the following answer to this question4 ,in every proposition 7says he7 what is signified is1 the belief of the speaker that the predicate is a name of the same thing of which the subject is a name2 and if it really is so1 the proposition is true4 ,thus the proposition1 ,all men are living beings 7he would say7 is true1 because living being is a name of every thing of which man is a name4 ,all men are six feet high1 is not true1 because six feet high is not a name of every thing 7though it is of some things7 of which man is a name4 ,what is stated in this theory as the definition of a true proposition1 must be allowed to be a property which all true propositions possess4 ,the subject and predicate being both of them names of things1 if they were names of quite different things the one name could not1 consistently with its signification1 be predicated of the other4 ,if it be true that some men are copper-colored1 it must be true--and the proposition does really assert--that among the individuals denoted by the name man1 there are some who are also among those denoted by the name copper-colored4 ,if it be true that all oxen ruminate1 it must be true that all the individuals denoted by the name ox are also among those denoted by the name ruminating2 and whoever asserts that all oxen ruminate1 undoubtedly does assert that this relation subsists between the two names4 ,the assertion1 therefore1 which1 according to ,hobbes1 is the only one made in any proposition1 really is made in every proposition3 and his analysis has consequently one of the requisites for being the true one4 ,we may go a step further2 it is the only analysis that is rigorously true of all propositions without exception4 ,what he gives as the meaning of propositions1 is part of the meaning of all propositions1 and the whole meaning of some4 ,this1 however1 only shows what an extremely minute fragment of meaning it is quite possible to include within the logical formula of a proposition4 ,it does not show that no proposition means more4 ,to warrant us in putting together two words with a copula between them1 it is really enough that the thing or things denoted by one of the names should be capable1 without violation of usage1 of being called by the other name also4 ,if1 then1 this be all the meaning necessarily implied in the form of discourse called a ,proposition1 why do ,i object to it as the scientific definition of what a proposition means8 ,because1 though the mere collocation which makes the proposition a proposition1 conveys no more than this scanty amount of meaning1 that same collocation combined with other circumstances1 that form combined with other matter1 does convey more1 and the proposition in those other circumstances does assert more1 than merely that relation between the two names4 ,the only propositions of which ,hobbes's principle is a sufficient account1 are that limited and unimportant class in which both the predicate and the subject are proper names4 ,for1 as has already been remarked1 proper names have strictly no meaning2 they are mere marks for individual objects3 and when a proper name is predicated of another proper name1 all the signification conveyed is1 that both the names are marks for the same object4 ,but this is precisely what ,hobbes produces as a theory of predication in general4 ,his doctrine is a full explanation of such predications as these3 ,hyde was ,clarendon1 or1 ,tully is ,cicero4 ,it exhausts the meaning of those propositions4 ,but it is a sadly inadequate theory of any others4 ,that it should ever have been thought of as such1 can be accounted for only by the fact1 that ,hobbes1 in common with the other ,nominalists1 bestowed little or no attention upon the connotation of words2 and sought for their meaning exclusively in what they denote3 as if all names had been 7what none but proper names really are7 marks put upon individuals2 and as if there were no difference between a proper and a general name1 except that the first denotes only one individual1 and the last a greater number4 ,it has been seen1 however1 that the meaning of all names1 except proper names and that portion of the class of abstract names which are not connotative1 resides in the connotation4 ,when1 therefore1 we are analyzing the meaning of any proposition in which the predicate and the subject1 or either of them1 are connotative names1 it is to the connotation of those terms that we must exclusively look1 and not to what they denote1 or in the language of ,hobbes 7language so far correct7 are names of4 ,in asserting that the truth of a proposition depends on the conformity of import between its terms1 as1 for instance1 that the proposition1 ,socrates is wise1 is a true proposition1 because ,socrates and wise are names applicable to1 or1 as he expresses it1 names of1 the same person2 it is very remarkable that so powerful a thinker should not have asked himself the question1 ,but how came they to be names of the same person8 ,surely not because such was the intention of those who invented the words4 ,when mankind fixed the meaning of the word wise1 they were not thinking of ,socrates1 nor1 when his parents gave him the name of ,socrates1 were they thinking of wisdom4 ,the names happen to fit the same person because of a certain fact1 which fact was not known1 nor in being1 when the names were invented4 ,if we want to know what the fact is1 we shall find the clue to it in the connotation of the names4 ,a bird or a stone1 a man1 or a wise man1 means simply1 an object having such and such attributes4 ,the real meaning of the word man1 is those attributes1 and not ,smith1 ,brown1 and the remainder of the individuals4 ,the word mortal1 in like manner connotes a certain attribute or attributes2 and when we say1 ,all men are mortal1 the meaning of the proposition is1 that all beings which possess the one set of attributes1 possess also the other4 ,if1 in our experience1 the attributes connoted by man are always accompanied by the attribute connoted by mortal1 it will follow as a consequence1 that the class man will be wholly included in the class mortal1 and that mortal will be a name of all things of which man is a name3 but why8 ,those objects are brought under the name1 by possessing the attributes connoted by it3 but their possession of the attributes is the real condition on which the truth of the proposition depends2 not their being called by the name4 ,connotative names do not precede1 but follow1 the attributes which they connote4 ,if one attribute happens to be always found in conjunction with another attribute1 the concrete names which answer to those attributes will of course be predicable of the same subjects1 and may be said1 in ,hobbes's language 7in the propriety of which on this occasion ,i fully concur71 to be two names for the same things4 ,but the possibility of a concurrent application of the two names1 is a mere consequence of the conjunction between the two attributes1 and was1 in most cases1 never thought of when the names were introduced and their signification fixed4 ,that the diamond is combustible1 was a proposition certainly not dreamed of when the words ,diamond and ,combustible first received their meaning2 and could not have been discovered by the most ingenious and refined analysis of the signification of those words4 ,it was found out by a very different process1 namely1 by exerting the senses1 and learning from them1 that the attribute of combustibility existed in the diamonds upon which the experiment was tried2 the number or character of the experiments being such1 that what was true of those individuals might be concluded to be true of all substances 8called by the name10 that is1 of all substances possessing the attributes which the name connotes4 ,the assertion1 therefore1 when analyzed1 is1 that wherever we find certain attributes1 there will be found a certain other attribute3 which is not a question of the signification of names1 but of laws of nature2 the order existing among phenomena4 #c4 ,although ,hobbes's theory of ,predication has not1 in the terms in which he stated it1 met with a very favorable reception from subsequent thinkers1 a theory virtually identical with it1 and not by any means so perspicuously expressed1 may almost be said to have taken the rank of an established opinion4 ,the most generally received notion of ,predication decidedly is that it consists in referring something to a class1 i4e41 either placing an individual under a class1 or placing one class under another class4 ,thus1 the proposition1 ,man is mortal1 asserts1 according to this view of it1 that the class man is included in the class mortal4 8,plato is a philosopher10 asserts that the individual ,plato is one of those who compose the class philosopher4 ,if the proposition is negative1 then instead of placing something in a class1 it is said to exclude something from a class4 ,thus1 if the following be the proposition1 ,the elephant is not carnivorous2 what is asserted 7according to this theory7 is1 that the elephant is excluded from the class carnivorous1 or is not numbered among the things comprising that class4 ,there is no real difference1 except in language1 between this theory of ,predication and the theory of ,hobbes4 ,for a class is absolutely nothing but an indefinite number of individuals denoted by a general name4 ,the name given to them in common1 is what makes them a class4 ,to refer any thing to a class1 therefore1 is to look upon it as one of the things which are to be called by that common name4 ,to exclude it from a class1 is to say that the common name is not applicable to it4 ,how widely these views of predication have prevailed1 is evident from this1 that they are the basis of the celebrated dictum de omni et nullo4 ,when the syllogism is resolved1 by all who treat of it1 into an inference that what is true of a class is true of all things whatever that belong to the class2 and when this is laid down by almost all professed logicians as the ultimate principle to which all reasoning owes its validity2 it is clear that in the general estimation of logicians1 the propositions of which reasonings are composed can be the expression of nothing but the process of dividing things into classes1 and referring every thing to its proper class4 ,this theory appears to me a signal example of a logical error very often committed in logic1 that of 1 or explaining a thing by something which presupposes it4 ,when ,i say that snow is white1 ,i may and ought to be thinking of snow as a class1 because ,i am asserting a proposition as true of all snow3 but ,i am certainly not thinking of white objects as a class2 ,i am thinking of no white object whatever except snow1 but only of that1 and of the sensation of white which it gives me4 ,when1 indeed1 ,i have judged1 or assented to the propositions1 that snow is white1 and that several other things are also white1 ,i gradually begin to think of white objects as a class1 including snow and those other things4 ,but this is a conception which followed1 not preceded1 those judgments1 and therefore can not be given as an explanation of them4 ,instead of explaining the effect by the cause1 this doctrine explains the cause by the effect1 and is1 ,i conceive1 founded on a latent misconception of the nature of classification4 ,there is a sort of language very generally prevalent in these discussions1 which seems to suppose that classification is an arrangement and grouping of definite and known individuals3 that when names were imposed1 mankind took into consideration all the individual objects in the universe1 distributed them into parcels or lists1 and gave to the objects of each list a common name1 repeating this operation toties quoties until they had invented all the general names of which language consists2 which having been once done1 if a question subsequently arises whether a certain general name can be truly predicated of a certain particular object1 we have only 7as it were7 to read the roll of the objects upon which that name was conferred1 and see whether the object about which the question arises is to be found among them4 ,the framers of language 7it would seem to be supposed7 have predetermined all the objects that are to compose each class1 and we have only to refer to the record of an antecedent decision4 ,so absurd a doctrine will be owned by nobody when thus nakedly stated2 but if the commonly received explanations of classification and naming do not imply this theory1 it requires to be shown how they admit of being reconciled with any other4 ,general names are not marks put upon definite objects2 classes are not made by drawing a line round a given number of assignable individuals4 ,the objects which compose any given class are perpetually fluctuating4 ,we may frame a class without knowing the individuals1 or even any of the individuals1 of which it may be composed2 we may do so while believing that no such individuals exist4 ,if by the meaning of a general name are to be understood the things which it is the name of1 no general name1 except by accident1 has a fixed meaning at all1 or ever long retains the same meaning4 ,the only mode in which any general name has a definite meaning1 is by being a name of an indefinite variety of things2 namely1 of all things1 known or unknown1 past1 present1 or future1 which possess certain definite attributes4 ,when1 by studying not the meaning of words1 but the phenomena of nature1 we discover that these attributes are possessed by some object not previously known to possess them 7as when chemists found that the diamond was combustible71 we include this new object in the class2 but it did not already belong to the class4 ,we place the individual in the class because the proposition is true2 the proposition is not true because the object is placed in the class47#ca7 ,it will appear hereafter1 in treating of reasoning1 how much the theory of that intellectual process has been vitiated by the influence of these erroneous notions1 and by the habit which they exemplify of assimilating all the operations of the human understanding which have truth for their object1 to processes of mere classification and naming4 ,unfortunately1 the minds which have been entangled in this net are precisely those which have escaped the other cardinal error commented upon in the beginning of the present chapter4 ,since the revolution which dislodged ,aristotle from the schools1 logicians may almost be divided into those who have looked upon reasoning as essentially an affair of ,ideas1 and those who have looked upon it as essentially an affair of ,names4 ,although1 however1 ,hobbes's theory of ,predication1 according to the well-known remark of ,leibnitz1 and the avowal of ,hobbes himself17#cb7 renders truth and falsity completely arbitrary1 with no standard but the will of men1 it must not be concluded that either ,hobbes1 or any of the other thinkers who have in the main agreed with him1 did in fact consider the distinction between truth and error as less real1 or attached less importance to it1 than other people4 ,to suppose that they did so would argue total unacquaintance with their other speculations4 ,but this shows how little hold their doctrine possessed over their own minds4 ,no person1 at bottom1 ever imagined that there was nothing more in truth than propriety of expression2 than using language in conformity to a previous convention4 ,when the inquiry was brought down from generals to a particular case1 it has always been acknowledged that there is a distinction between verbal and real questions2 that some false propositions are uttered from ignorance of the meaning of words1 but that in others the source of the error is a misapprehension of things2 that a person who has not the use of language at all may form propositions mentally1 and that they may be untrue--that is1 he may believe as matters of fact what are not really so4 ,this last admission can not be made in stronger terms than it is by ,hobbes himself17#cc7 though he will not allow such erroneous belief to be called falsity1 but only error4 ,and he has himself laid down1 in other places1 doctrines in which the true theory of predication is by implication contained4 ,he distinctly says that general names are given to things on account of their attributes1 and that abstract names are the names of those attributes4 8,abstract is that which in any subject denotes the cause of the concrete name4444 ,and these causes of names are the same with the causes of our conceptions1 namely1 some power of action1 or affection1 of the thing conceived1 which some call the manner by which any thing works upon our senses1 but by most men they are called accidents407#cd7 ,it is strange that having gone so far1 he should not have gone one step further1 and seen that what he calls the cause of the concrete name1 is in reality the meaning of it2 and that when we predicate of any subject a name which is given because of an attribute 7or1 as he calls it1 an accident71 our object is not to affirm the name1 but1 by means of the name1 to affirm the attribute4 #d4 ,let the predicate be1 as we have said1 a connotative term2 and to take the simplest case first1 let the subject be a proper name3 8,the summit of ,chimborazo is white40 ,the word white connotes an attribute which is possessed by the individual object designated by the words 8summit of ,chimborazo20 which attribute consists in the physical fact1 of its exciting in human beings the sensation which we call a sensation of white4 ,it will be admitted that1 by asserting the proposition1 we wish to communicate information of that physical fact1 and are not thinking of the names1 except as the necessary means of making that communication4 ,the meaning of the proposition1 therefore1 is1 that the individual thing denoted by the subject1 has the attributes connoted by the predicate4 ,if we now suppose the subject also to be a connotative name1 the meaning expressed by the proposition has advanced a step further in complication4 ,let us first suppose the proposition to be universal1 as well as affirmative3 8,all men are mortal40 ,in this case1 as in the last1 what the proposition asserts 7or expresses a belief of7 is1 of course1 that the objects denoted by the subject 7man7 possess the attributes connoted by the predicate 7mortal74 ,but the characteristic of this case is1 that the objects are no longer individually designated4 ,they are pointed out only by some of their attributes3 they are the objects called men1 that is1 possessing the attributes connoted by the name man2 and the only thing known of them may be those attributes3 indeed1 as the proposition is general1 and the objects denoted by the subject are therefore indefinite in number1 most of them are not known individually at all4 ,the assertion1 therefore1 is not1 as before1 that the attributes which the predicate connotes are possessed by any given individual1 or by any number of individuals previously known as ,john1 ,thomas1 etc41 but that those attributes are possessed by each and every individual possessing certain other attributes2 that whatever has the attributes connoted by the subject1 has also those connoted by the predicate2 that the latter set of attributes constantly accompany the former set4 ,whatever has the attributes of man has the attribute of mortality2 mortality constantly accompanies the attributes of man47#ce7 ,if it be remembered that every attribute is grounded on some fact or phenomenon1 either of outward sense or of inward consciousness1 and that to possess an attribute is another phrase for being the cause of1 or forming part of1 the fact or phenomenon upon which the attribute is grounded2 we may add one more step to complete the analysis4 ,the proposition which asserts that one attribute always accompanies another attribute1 really asserts thereby no other thing than this1 that one phenomenon always accompanies another phenomenon2 insomuch that where we find the latter1 we have assurance of the existence of the former4 ,thus1 in the proposition1 ,all men are mortal1 the word man connotes the attributes which we ascribe to a certain kind of living creatures1 on the ground of certain phenomena which they exhibit1 and which are partly physical phenomena1 namely the impressions made on our senses by their bodily form and structure1 and partly mental phenomena1 namely the sentient and intellectual life which they have of their own4 ,all this is understood when we utter the word man1 by any one to whom the meaning of the word is known4 ,now1 when we say1 ,man is mortal1 we mean that wherever these various physical and mental phenomena are all found1 there we have assurance that the other physical and mental phenomenon1 called death1 will not fail to take place4 ,the proposition does not affirm when2 for the connotation of the word mortal goes no further than to the occurrence of the phenomenon at some time or other1 leaving the particular time undecided4 #e4 ,we have already proceeded far enough1 not only to demonstrate the error of ,hobbes1 but to ascertain the real import of by far the most numerous class of propositions4 ,the object of belief in a proposition1 when it asserts any thing more than the meaning of words1 is generally1 as in the cases which we have examined1 either the co-existence or the sequence of two phenomena4 ,at the very commencement of our inquiry1 we found that every act of belief implied two ,things3 we have now ascertained what1 in the most frequent case1 these two things are1 namely1 two ,phenomena2 in other words1 two states of consciousness2 and what it is which the proposition affirms 7or denies7 to subsist between them1 namely1 either succession or co-existence4 ,and this case includes innumerable instances which no one1 previous to reflection1 would think of referring to it4 ,take the following example3 ,a generous person is worthy of honor4 ,who would expect to recognize here a case of co-existence between phenomena8 ,but so it is4 ,the attribute which causes a person to be termed generous1 is ascribed to him on the ground of states of his mind1 and particulars of his conduct3 both are phenomena3 the former are facts of internal consciousness2 the latter1 so far as distinct from the former1 are physical facts1 or perceptions of the senses4 ,worthy of honor admits of a similar analysis4 ,honor1 as here used1 means a state of approving and admiring emotion1 followed on occasion by corresponding outward acts4 8,worthy of honor0 connotes all this1 together with our approval of the act of showing honor4 ,all these are phenomena2 states of internal consciousness1 accompanied or followed by physical facts4 ,when we say1 ,a generous person is worthy of honor1 we affirm co-existence between the two complicated phenomena connoted by the two terms respectively4 ,we affirm1 that wherever and whenever the inward feelings and outward facts implied in the word generosity have place1 then and there the existence and manifestation of an inward feeling1 honor1 would be followed in our minds by another inward feeling1 approval4 ,after the analysis1 in a former chapter1 of the import of names1 many examples are not needed to illustrate the import of propositions4 ,when there is any obscurity1 or difficulty1 it does not lie in the meaning of the proposition1 but in the meaning of the names which compose it2 in the extremely complicated connotation of many words2 the immense multitude and prolonged series of facts which often constitute the phenomenon connoted by a name4 ,but where it is seen what the phenomenon is1 there is seldom any difficulty in seeing that the assertion conveyed by the proposition is1 the co-existence of one such phenomenon with another2 or the succession of one such phenomenon to another3 so that where the one is found1 we may calculate on finding the other1 though perhaps not conversely4 ,this1 however1 though the most common1 is not the only meaning which propositions are ever intended to convey4 ,in the first place1 sequences and co-existences are not only asserted respecting ,phenomena2 we make propositions also respecting those hidden causes of phenomena1 which are named substances and attributes4 ,a substance1 however1 being to us nothing but either that which causes1 or that which is conscious of1 phenomena2 and the same being true1 mutatis mutandis1 of attributes2 no assertion can be made1 at least with a meaning1 concerning these unknown and unknowable entities1 except in virtue of the ,phenomena by which alone they manifest themselves to our faculties4 ,when we say ,socrates was contemporary with the ,peloponnesian war1 the foundation of this assertion1 as of all assertions concerning substances1 is an assertion concerning the phenomena which they exhibit--namely1 that the series of facts by which ,socrates manifested himself to mankind1 and the series of mental states which constituted his sentient existence1 went on simultaneously with the series of facts known by the name of the ,peloponnesian war4 ,still1 the proposition as commonly understood does not assert that alone2 it asserts that the ,thing in itself1 the noumenon ,socrates1 was existing1 and doing or experiencing those various facts during the same time4 ,co-existence and sequence1 therefore1 may be affirmed or denied not only between phenomena1 but between noumena1 or between a noumenon and phenomena4 ,and both of noumena and of phenomena we may affirm simple existence4 ,but what is a noumenon8 ,an unknown cause4 ,in affirming1 therefore1 the existence of a noumenon1 we affirm causation4 ,here1 therefore1 are two additional kinds of fact1 capable of being asserted in a proposition4 ,besides the propositions which assert ,sequence or ,co-existence1 there are some which assert simple ,existence27#cf7 and others assert ,causation1 which1 subject to the explanations which will follow in the ,third ,book1 must be considered provisionally as a distinct and peculiar kind of assertion4 #f4 ,to these four kinds of matter-of-fact or assertion1 must be added a fifth1 ,resemblance4 ,this was a species of attribute which we found it impossible to analyze2 for which no fundamentum1 distinct from the objects themselves1 could be assigned4 ,besides propositions which assert a sequence or co-existence between two phenomena1 there are therefore also propositions which assert resemblance between them2 as1 ,this color is like that color2 ,the heat of to-day is equal to the heat of yesterday4 ,it is true that such an assertion might with some plausibility be brought within the description of an affirmation of sequence1 by considering it as an assertion that the simultaneous contemplation of the two colors is followed by a specific feeling termed the feeling of resemblance4 ,but there would be nothing gained by incumbering ourselves1 especially in this place1 with a generalization which may be looked upon as strained4 ,logic does not undertake to analyze mental facts into their ultimate elements4 ,resemblance between two phenomena is more intelligible in itself than any explanation could make it1 and under any classification must remain specifically distinct from the ordinary cases of sequence and co-existence4 ,it is sometimes said1 that all propositions whatever1 of which the predicate is a general name1 do1 in point of fact1 affirm or deny resemblance4 ,all such propositions affirm that a thing belongs to a class2 but things being classed together according to their resemblance1 every thing is of course classed with the things which it is supposed to resemble most2 and thence1 it may be said1 when we affirm that ,gold is a metal1 or that ,socrates is a man1 the affirmation intended is1 that gold resembles other metals1 and ,socrates other men1 more nearly than they resemble the objects contained in any other of the classes co-ordinate with these4 ,there is some slight degree of foundation for this remark1 but no more than a slight degree4 ,the arrangement of things into classes1 such as the class metal1 or the class man1 is grounded indeed on a resemblance among the things which are placed in the same class1 but not on a mere general resemblance3 the resemblance it is grounded on consists in the possession by all those things1 of certain common peculiarities2 and those peculiarities it is which the terms connote1 and which the propositions consequently assert2 not the resemblance4 ,for though when ,i say1 ,gold is a metal1 ,i say by implication that if there be any other metals it must resemble them1 yet if there were no other metals ,i might still assert the proposition with the same meaning as at present1 namely1 that gold has the various properties implied in the word metal2 just as it might be said1 ,christians are men1 even if there were no men who were not ,christians4 ,propositions1 therefore1 in which objects are referred to a class because they possess the attributes constituting the class1 are so far from asserting nothing but resemblance1 that they do not1 properly speaking1 assert resemblance at all4 ,but we remarked some time ago 7and the reasons of the remark will be more fully entered into in a subsequent ,book7#cg77 that there is sometimes a convenience in extending the boundaries of a class so as to include things which possess in a very inferior degree1 if in any1 some of the characteristic properties of the class--provided they resemble that class more than any other1 insomuch that the general propositions which are true of the class1 will be nearer to being true of those things than any other equally general propositions4 ,for instance1 there are substances called metals which have very few of the properties by which metals are commonly recognized2 and almost every great family of plants or animals has a few anomalous genera or species on its borders1 which are admitted into it by a sort of courtesy1 and concerning which it has been matter of discussion to what family they properly belonged4 ,now when the class-name is predicated of any object of this description1 we do1 by so predicating it1 affirm resemblance and nothing more4 ,and in order to be scrupulously correct it ought to be said1 that in every case in which we predicate a general name1 we affirm1 not absolutely that the object possesses the properties designated by the name1 but that it either possesses those properties1 or if it does not1 at any rate resembles the things which do so1 more than it resembles any other things4 ,in most cases1 however1 it is unnecessary to suppose any such alternative1 the latter of the two grounds being very seldom that on which the assertion is made3 and when it is1 there is generally some slight difference in the form of the expression1 as1 ,this species 7or genus7 is considered1 or may be ranked1 as belonging to such and such a family3 we should hardly say positively that it does belong to it1 unless it possessed unequivocally the properties of which the class-name is scientifically significant4 ,there is still another exceptional case1 in which1 though the predicate is the name of a class1 yet in predicating it we affirm nothing but resemblance1 the class being founded not on resemblance in any given particular1 but on general unanalyzable resemblance4 ,the classes in question are those into which our simple sensations1 or other simple feelings1 are divided4 ,sensations of white1 for instance1 are classed together1 not because we can take them to pieces1 and say they are alike in this1 and not alike in that1 but because we feel them to be alike altogether1 though in different degrees4 ,when1 therefore1 ,i say1 ,the color ,i saw yesterday was a white color1 or1 ,the sensation ,i feel is one of tightness1 in both cases the attribute ,i affirm of the color or of the other sensation is mere resemblance--simple likeness to sensations which ,i have had before1 and which have had those names bestowed upon them4 ,the names of feelings1 like other concrete general names1 are connotative2 but they connote a mere resemblance4 ,when predicated of any individual feeling1 the information they convey is that of its likeness to the other feelings which we have been accustomed to call by the same name4 ,thus much may suffice in illustration of the kind of propositions in which the matter-of-fact asserted 7or denied7 is simple ,resemblance4 ,existence1 ,co-existence1 ,sequence1 ,causation1 ,resemblance3 one or other of these is asserted 7or denied7 in every proposition which is not merely verbal4 ,this five-fold division is an exhaustive classification of matters-of-fact2 of all things that can be believed1 or tendered for belief2 of all questions that can be propounded1 and all answers that can be returned to them4 ,professor ,bain7#ch7 distinguishes two kinds of ,propositions of ,co-existence4 8,in the one kind1 account is taken of ,place2 they may be described as propositions of ,order in ,place40 ,in the other kind1 the co-existence which is predicated is termed by ,mr4 ,bain ,co-inherence of ,attributes4 8,this is a distinct variety of ,propositions of ,co-existence4 ,instead of an arrangement in place with numerical intervals1 we have the concurrence of two or more attributes or powers in the same part or locality4 ,a mass of gold contains1 in every atom1 the concurring attributes that mark the substance--weight1 hardness1 color1 lustre1 incorrosibility1 etc4 ,an animal1 besides having parts situated in place1 has co-inhering functions in the same parts1 exerted by the very same masses and molecules of its substance4444 ,the ,mind1 which affords no ,propositions of ,order in ,place1 has co-inhering functions4 ,we affirm mind to contain ,feeling1 ,will1 and ,thought1 not in local separation1 but in commingling exercise4 ,the concurring properties of minerals1 of plants1 and of the bodily and the mental structure of animals1 are united in affirmations of co-inherence40 ,the distinction is real and important4 ,but1 as has been seen1 an ,attribute1 when it is any thing but a simple unanalyzable ,resemblance between the subject and some other things1 consists in causing impressions of some sort on consciousness4 ,consequently1 the co-inherence of two attributes is but the co-existence of the two states of consciousness implied in their meaning3 with the difference1 however1 that this co-existence is sometimes potential only1 the attribute being considered as in existence1 though the fact on which it is grounded may not be actually1 but only potentially present4 ,snow1 for instance1 is1 with great convenience1 said to be white even in a state of total darkness1 because1 though we are not now conscious of the color1 we shall be conscious of it as soon as morning breaks4 ,co-inherence of attributes is therefore still a case1 though a complex one1 of co-existence of states of consciousness2 a totally different thing1 however1 from ,order in ,place4 ,being a part of simultaneity1 it belongs not to ,place but to ,time4 ,we may therefore 7and we shall sometimes find it a convenience7 instead of ,co-existence and ,sequence1 say1 for greater particularity1 ,order in ,place and ,order in ,time3 ,order in ,place being a specific mode of co-existence1 not necessary to be more particularly analyzed here2 while the mere fact of co-existence1 whether between actual sensations1 or between the potentialities of causing them1 known by the name of attributes1 may be classed1 together with ,sequence1 under the head of ,order in ,time4 #g4 ,in the foregoing inquiry into the import of propositions1 we have thought it necessary to analyze directly those alone1 in which the terms of the proposition 7or the predicate at least7 are concrete terms4 ,but1 in doing so1 we have indirectly analyzed those in which the terms are abstract4 ,the distinction between an abstract term and its corresponding concrete1 does not turn upon any difference in what they are appointed to signify2 for the real signification of a concrete general name is1 as we have so often said1 its connotation2 and what the concrete term connotes1 forms the entire meaning of the abstract name4 ,since there is nothing in the import of an abstract name which is not in the import of the corresponding concrete1 it is natural to suppose that neither can there be any thing in the import of a proposition of which the terms are abstract1 but what there is in some proposition which can be framed of concrete terms4 ,and this presumption a closer examination will confirm4 ,an abstract name is the name of an attribute1 or combination of attributes4 ,the corresponding concrete is a name given to things1 because of1 and in order to express1 their possessing that attribute1 or that combination of attributes4 ,when1 therefore1 we predicate of any thing a concrete name1 the attribute is what we in reality predicate of it4 ,but it has now been shown that in all propositions of which the predicate is a concrete name1 what is really predicated is one of five things3 ,existence1 ,co-existence1 ,causation1 ,sequence1 or ,resemblance4 ,an attribute1 therefore1 is necessarily either an existence1 a co-existence1 a causation1 a sequence1 or a resemblance4 ,when a proposition consists of a subject and predicate which are abstract terms1 it consists of terms which must necessarily signify one or other of these things4 ,when we predicate of any thing an abstract name1 we affirm of the thing that it is one or other of these five things2 that it is a case of ,existence1 or of ,co-existence1 or of ,causation1 or of ,sequence1 or of ,resemblance4 ,it is impossible to imagine any proposition expressed in abstract terms1 which can not be transformed into a precisely equivalent proposition in which the terms are concrete2 namely1 either the concrete names which connote the attributes themselves1 or the names of the fundamenta of those attributes2 the facts or phenomena on which they are grounded4 ,to illustrate the latter case1 let us take this proposition1 of which the subject only is an abstract name1 8,thoughtlessness is dangerous40 ,thoughtlessness is an attribute1 grounded on the facts which we call thoughtless actions2 and the proposition is equivalent to this1 ,thoughtless actions are dangerous4 ,in the next example the predicate as well as the subject are abstract names3 8,whiteness is a color20 or 8,the color of snow is a whiteness40 ,these attributes being grounded on sensations1 the equivalent propositions in the concrete would be1 ,the sensation of white is one of the sensations called those of color--,the sensation of sight1 caused by looking at snow1 is one of the sensations called sensations of white4 ,in these propositions1 as we have before seen1 the matter-of-fact asserted is a ,resemblance4 ,in the following examples1 the concrete terms are those which directly correspond to the abstract names2 connoting the attribute which these denote4 8,prudence is a virtue30 this may be rendered1 8,all prudent persons1 in so far as prudent1 are virtuous30 8,courage is deserving of honor20 thus1 8,all courageous persons are deserving of honor in so far as they are courageous30 which is equivalent to this--8,all courageous persons deserve an addition to the honor1 or a diminution of the disgrace1 which would attach to them on other grounds40 ,in order to throw still further light upon the import of propositions of which the terms are abstract1 we will subject one of the examples given above to a minuter analysis4 ,the proposition we shall select is the following3 8,prudence is a virtue40 ,let us substitute for the word virtue an equivalent but more definite expression1 such as 8a mental quality beneficial to society10 or 8a mental quality pleasing to ,god10 or whatever else we adopt as the definition of virtue4 ,what the proposition asserts is a sequence1 accompanied with causation2 namely1 that benefit to society1 or that the approval of ,god1 is consequent on1 and caused by1 prudence4 ,here is a sequence2 but between what8 ,we understand the consequent of the sequence1 but we have yet to analyze the antecedent4 ,prudence is an attribute2 and1 in connection with it1 two things besides itself are to be considered2 prudent persons1 who are the subjects of the attribute1 and prudential conduct1 which may be called the foundation of it4 ,now is either of these the antecedent8 and1 first1 is it meant1 that the approval of ,god1 or benefit to society1 is attendant upon all prudent persons8 ,no2 except in so far as they are prudent2 for prudent persons who are scoundrels can seldom1 on the whole1 be beneficial to society1 nor can they be acceptable to a good being4 ,is it upon prudential conduct1 then1 that divine approbation and benefit to mankind are supposed to be invariably consequent8 ,neither is this the assertion meant1 when it is said that prudence is a virtue2 except with the same reservation as before1 and for the same reason1 namely1 that prudential conduct1 although in so far as it is prudential it is beneficial to society1 may yet1 by reason of some other of its qualities1 be productive of an injury outweighing the benefit1 and deserve a displeasure exceeding the approbation which would be due to the prudence4 ,neither the substance1 therefore 7viz41 the person71 nor the phenomenon 7the conduct71 is an antecedent on which the other term of the sequence is universally consequent4 ,but the proposition1 8,prudence is a virtue10 is a universal proposition4 ,what is it1 then1 upon which the proposition affirms the effects in question to be universally consequent8 ,upon that in the person1 and in the conduct1 which causes them to be called prudent1 and which is equally in them when the action1 though prudent1 is wicked2 namely1 a correct foresight of consequences1 a just estimation of their importance to the object in view1 and repression of any unreflecting impulse at variance with the deliberate purpose4 ,these1 which are states of the person's mind1 are the real antecedent in the sequence1 the real cause in the causation1 asserted by the proposition4 ,but these are also the real ground1 or foundation1 of the attribute ,prudence2 since wherever these states of mind exist we may predicate prudence1 even before we know whether any conduct has followed4 ,and in this manner every assertion respecting an attribute1 may be transformed into an assertion exactly equivalent respecting the fact or phenomenon which is the ground of the attribute4 ,and no case can be assigned1 where that which is predicated of the fact or phenomenon1 does not belong to one or other of the five species formerly enumerated3 it is either simple ,existence1 or it is some ,sequence1 ,co-existence1 ,causation1 or ,resemblance4 ,and as these five are the only things which can be affirmed1 so are they the only things which can be denied4 8,no horses are web-footed0 denies that the attributes of a horse ever co-exist with web-feet4 ,it is scarcely necessary to apply the same analysis to ,particular affirmations and negations4 8,some birds are web-footed10 affirms that1 with the attributes connoted by bird1 the phenomenon web-feet is sometimes co-existent3 8,some birds are not web-footed10 asserts that there are other instances in which this co-existence does not have place4 ,any further explanation of a thing which1 if the previous exposition has been assented to1 is so obvious1 may here be spared4 ,chapter ,,vi4 ,of ,propositions ,merely ,verbal4 #a4 ,as a preparation for the inquiry which is the proper object of ,logic1 namely1 in what manner propositions are to be proved1 we have found it necessary to inquire what they contain which requires1 or is susceptible of1 proof2 or 7which is the same thing7 what they assert4 ,in the course of this preliminary investigation into the import of ,propositions1 we examined the opinion of the ,conceptualists1 that a proposition is the expression of a relation between two ideas2 and the doctrine of the extreme ,nominalists1 that it is the expression of an agreement or disagreement between the meanings of two names4 ,we decided that1 as general theories1 both of these are erroneous2 and that1 though propositions may be made both respecting names and respecting ideas1 neither the one nor the other are the subject-matter of ,propositions considered generally4 ,we then examined the different kinds of ,propositions1 and found that1 with the exception of those which are merely verbal1 they assert five different kinds of matters of fact1 namely1 ,existence1 ,order in ,place1 ,order in ,time1 ,causation1 and ,resemblance2 that in every proposition one of these five is either affirmed1 or denied1 of some fact or phenomenon1 or of some object the unknown source of a fact or phenomenon4 ,in distinguishing1 however1 the different kinds of matters of fact asserted in propositions1 we reserved one class of propositions1 which do not relate to any matter of fact1 in the proper sense of the term at all1 but to the meaning of names4 ,since names and their signification are entirely arbitrary1 such propositions are not1 strictly speaking1 susceptible of truth or falsity1 but only of conformity or disconformity to usage or convention2 and all the proof they are capable of1 is proof of usage2 proof that the words have been employed by others in the acceptation in which the speaker or writer desires to use them4 ,these propositions occupy1 however1 a conspicuous place in philosophy2 and their nature and characteristics are of as much importance in logic1 as those of any of the other classes of propositions previously adverted to4 ,if all propositions respecting the signification of words were as simple and unimportant as those which served us for examples when examining ,hobbes's theory of predication1 viz41 those of which the subject and predicate are proper names1 and which assert only that those names have1 or that they have not1 been conventionally assigned to the same individual1 there would be little to attract to such propositions the attention of philosophers4 ,but the class of merely verbal propositions embraces not only much more than these1 but much more than any propositions which at first sight present themselves as verbal2 comprehending a kind of assertions which have been regarded not only as relating to things1 but as having actually a more intimate relation with them than any other propositions whatever4 ,the student in philosophy will perceive that ,i allude to the distinction on which so much stress was laid by the schoolmen1 and which has been retained either under the same or under other names by most metaphysicians to the present day1 viz41 between what were called essential1 and what were called accidental1 propositions1 and between essential and accidental properties or attributes4 #b4 ,almost all metaphysicians prior to ,locke1 as well as many since his time1 have made a great mystery of ,essential ,predication1 and of predicates which are said to be of the essence of the subject4 ,the essence of a thing1 they said1 was that without which the thing could neither be1 nor be conceived to be4 ,thus1 rationality was of the essence of man1 because without rationality1 man could not be conceived to exist4 ,the different attributes which made up the essence of the thing were called its essential properties2 and a proposition in which any of these were predicated of it was called an ,essential ,proposition1 and was considered to go deeper into the nature of the thing1 and to convey more important information respecting it1 than any other proposition could do4 ,all properties1 not of the essence of the thing1 were called its accidents2 were supposed to have nothing at all1 or nothing comparatively1 to do with its inmost nature2 and the propositions in which any of these were predicated of it were called ,accidental ,propositions4 ,a connection may be traced between this distinction1 which originated with the schoolmen1 and the well-known dogmas of substanti secund or general substances1 and substantial forms1 doctrines which under varieties of language pervaded alike the ,aristotelian and the ,platonic schools1 and of which more of the spirit has come down to modern times than might be conjectured from the disuse of the phraseology4 ,the false views of the nature of classification and generalization which prevailed among the schoolmen1 and of which these dogmas were the technical expression1 afford the only explanation which can be given of their having misunderstood the real nature of those ,essences which held so conspicuous a place in their philosophy4 ,they said1 truly1 that man can not be conceived without rationality4 ,but though man can not1 a being may be conceived exactly like a man in all points except that one quality1 and those others which are the conditions or consequences of it4 ,all1 therefore1 which is really true in the assertion that man can not be conceived without rationality1 is only1 that if he had not rationality1 he would not be reputed a man4 ,there is no impossibility in conceiving the thing1 nor1 for aught we know1 in its existing3 the impossibility is in the conventions of language1 which will not allow the thing1 even if it exist1 to be called by the name which is reserved for rational beings4 ,rationality1 in short1 is involved in the meaning of the word man3 is one of the attributes connoted by the name4 ,the essence of man1 simply means the whole of the attributes connoted by the word2 and any one of those attributes taken singly1 is an essential property of man4 ,but these reflections1 so easy to us1 would have been difficult to persons who thought1 as most of the later ,aristotelians did1 that objects were made what they were called1 that gold 7for instance7 was made gold1 not by the possession of certain properties to which mankind have chosen to attach that name1 but by participation in the nature of a general substance1 called gold in general1 which substance1 together with all the properties that belonged to it1 inhered in every individual piece of gold47#ci7 ,as they did not consider these universal substances to be attached to all general names1 but only to some1 they thought that an object borrowed only a part of its properties from a universal substance1 and that the rest belonged to it individually3 the former they called its essence1 and the latter its accidents4 ,the scholastic doctrine of essences long survived the theory on which it rested1 that of the existence of real entities corresponding to general terms2 and it was reserved for ,locke1 at the end of the seventeenth century1 to convince philosophers that the supposed essences of classes were merely the signification of their names2 nor1 among the signal services which his writings rendered to philosophy1 was there one more needful or more valuable4 ,now1 as the most familiar of the general names by which an object is designated usually connotes not one only1 but several attributes of the object1 each of which attributes separately forms also the bond of union of some class1 and the meaning of some general name2 we may predicate of a name which connotes a variety of attributes1 another name which connotes only one of these attributes1 or some smaller number of them than all4 ,in such cases1 the universal affirmative proposition will be true2 since whatever possesses the whole of any set of attributes1 must possess any part of that same set4 ,a proposition of this sort1 however1 conveys no information to any one who previously understood the whole meaning of the terms4 ,the propositions1 ,every man is a corporeal being1 ,every man is a living creature1 ,every man is rational1 convey no knowledge to any one who was already aware of the entire meaning of the word man1 for the meaning of the word includes all this3 and that every man has the attributes connoted by all these predicates1 is already asserted when he is called a man4 ,now1 of this nature are all the propositions which have been called essential4 ,they are1 in fact1 identical propositions4 ,it is true that a proposition which predicates any attribute1 even though it be one implied in the name1 is in most cases understood to involve a tacit assertion that there exists a thing corresponding to the name1 and possessing the attributes connoted by it2 and this implied assertion may convey information1 even to those who understood the meaning of the name4 ,but all information of this sort1 conveyed by all the essential propositions of which man can be made the subject1 is included in the assertion1 ,men exist4 ,and this assumption of real existence is1 after all1 the result of an imperfection of language4 ,it arises from the ambiguity of the copula1 which1 in addition to its proper office of a mark to show that an assertion is made1 is also1 as formerly remarked1 a concrete word connoting existence4 ,the actual existence of the subject of the proposition is therefore only apparently1 not really1 implied in the predication1 if an essential one3 we may say1 ,a ghost is a disembodied spirit1 without believing in ghosts4 ,but an accidental1 or non-essential1 affirmation1 does imply the real existence of the subject1 because in the case of a non-existent subject there is nothing for the proposition to assert4 ,such a proposition as1 ,the ghost of a murdered person haunts the couch of the murderer1 can only have a meaning if understood as implying a belief in ghosts2 for since the signification of the word ghost implies nothing of the kind1 the speaker either means nothing1 or means to assert a thing which he wishes to be believed to have really taken place4 ,it will be hereafter seen that when any important consequences seem to follow1 as in mathematics1 from an essential proposition1 or1 in other words1 from a proposition involved in the meaning of a name1 what they really flow from is the tacit assumption of the real existence of the objects so named4 ,apart from this assumption of real existence1 the class of propositions in which the predicate is of the essence of the subject 7that is1 in which the predicate connotes the whole or part of what the subject connotes1 but nothing besides7 answer no purpose but that of unfolding the whole or some part of the meaning of the name1 to those who did not previously know it4 ,accordingly1 the most useful1 and in strictness the only useful kind of essential propositions1 are ,definitions3 which1 to be complete1 should unfold the whole of what is involved in the meaning of the word defined2 that is 7when it is a connotative word71 the whole of what it connotes4 ,in defining a name1 however1 it is not usual to specify its entire connotation1 but so much only as is sufficient to mark out the objects usually denoted by it from all other known objects4 ,and sometimes a merely accidental property1 not involved in the meaning of the name1 answers this purpose equally well4 ,the various kinds of definition which these distinctions give rise to1 and the purposes to which they are respectively subservient1 will be minutely considered in the proper place4 #c4 ,according to the above view of essential propositions1 no proposition can be reckoned such which relates to an individual by name1 that is1 in which the subject is a proper name4 ,individuals have no essences4 ,when the schoolmen talked of the essence of an individual1 they did not mean the properties implied in its name1 for the names of individuals imply no properties4 ,they regarded as of the essence of an individual1 whatever was of the essence of the species in which they were accustomed to place that individual2 i4e41 of the class to which it was most familiarly referred1 and to which1 therefore1 they conceived that it by nature belonged4 ,thus1 because the proposition ,man is a rational being1 was an essential proposition1 they affirmed the same thing of the proposition1 ,julius ,csar is a rational being4 ,this followed very naturally if genera and species were to be considered as entities1 distinct from1 but inhering in1 the individuals composing them4 ,if man was a substance inhering in each individual man1 the essence of man 7whatever that might mean7 was naturally supposed to accompany it2 to inhere in ,john ,thompson1 and to form the common essence of ,thompson and ,julius ,csar4 ,it might then be fairly said1 that rationality1 being of the essence of ,man1 was of the essence also of ,thompson4 ,but if ,man altogether be only the individual men and a name bestowed upon them in consequence of certain common properties1 what becomes of ,john ,thompson's essence8 ,a fundamental error is seldom expelled from philosophy by a single victory4 ,it retreats slowly1 defends every inch of ground1 and often1 after it has been driven from the open country1 retains a footing in some remote fastness4 ,the essences of individuals were an unmeaning figment arising from a misapprehension of the essences of classes1 yet even ,locke1 when he extirpated the parent error1 could not shake himself free from that which was its fruit4 ,he distinguished two sorts of essences1 ,real and ,nominal4 ,his nominal essences were the essences of classes1 explained nearly as we have now explained them4 ,nor is any thing wanting to render the third book of ,locke's ,essay a nearly unexceptional treatise on the connotation of names1 except to free its language from the assumption of what are called ,abstract ,ideas1 which unfortunately is involved in the phraseology1 though not necessarily connected with the thoughts contained in that immortal ,third ,book47#dj7 ,but besides nominal essences1 he admitted real essences1 or essences of individual objects1 which he supposed to be the causes of the sensible properties of those objects4 ,we know not 7said he7 what these are 7and this acknowledgment rendered the fiction comparatively innocuous72 but if we did1 we could1 from them alone1 demonstrate the sensible properties of the object1 as the properties of the triangle are demonstrated from the definition of the triangle4 ,i shall have occasion to revert to this theory in treating of ,demonstration1 and of the conditions under which one property of a thing admits of being demonstrated from another property4 ,it is enough here to remark that1 according to this definition1 the real essence of an object has1 in the progress of physics1 come to be conceived as nearly equivalent1 in the case of bodies1 to their corpuscular structure3 what it is now supposed to mean in the case of any other entities1 ,i would not take upon myself to define4 #d4 ,an essential proposition1 then1 is one which is purely verbal2 which asserts of a thing under a particular name1 only what is asserted of it in the fact of calling it by that name2 and which1 therefore1 either gives no information1 or gives it respecting the name1 not the thing4 ,non-essential1 or accidental propositions1 on the contrary1 may be called ,real ,propositions1 in opposition to ,verbal4 ,they predicate of a thing some fact not involved in the signification of the name by which the proposition speaks of it2 some attribute not connoted by that name4 ,such are all propositions concerning things individually designated1 and all general or particular propositions in which the predicate connotes any attribute not connoted by the subject4 ,all these1 if true1 add to our knowledge3 they convey information1 not already involved in the names employed4 ,when ,i am told that all1 or even that some objects1 which have certain qualities1 or which stand in certain relations1 have also certain other qualities1 or stand in certain other relations1 ,i learn from this proposition a new fact2 a fact not included in my knowledge of the meaning of the words1 nor even of the existence of ,things answering to the signification of those words4 ,it is this class of propositions only which are in themselves instructive1 or from which any instructive propositions can be inferred47#da7 ,nothing has probably contributed more to the opinion so long prevalent of the futility of the school logic1 than the circumstance that almost all the examples used in the common school books to illustrate the doctrine of predication and that of the syllogism1 consist of essential propositions4 ,they were usually taken either from the branches or from the main trunk of the ,predicamental ,tree1 which included nothing but what was of the essence of the species3 ,omne corpus est substantia1 ,omne animal est corpus1 ,omnis homo est corpus1 ,omnis homo est animal1 ,omnis homo est rationalis1 and so forth4 ,it is far from wonderful that the syllogistic art should have been thought to be of no use in assisting correct reasoning1 when almost the only propositions which1 in the hands of its professed teachers1 it was employed to prove1 were such as every one assented to without proof the moment he comprehended the meaning of the words2 and stood exactly on a level1 in point of evidence1 with the premises from which they were drawn4 ,i have1 therefore1 throughout this work1 avoided the employment of essential propositions as examples1 except where the nature of the principle to be illustrated specifically required them4 #e4 ,with respect to propositions which do convey information--which assert something of a ,thing1 under a name that does not already presuppose what is about to be asserted2 there are two different aspects in which these1 or rather such of them as are general propositions1 may be considered3 we may either look at them as portions of speculative truth1 or as memoranda for practical use4 ,according as we consider propositions in one or the other of these lights1 their import may be conveniently expressed in one or in the other of two formulas4 ,according to the formula which we have hitherto employed1 and which is best adapted to express the import of the proposition as a portion of our theoretical knowledge1 ,all men are mortal1 means that the attributes of man are always accompanied by the attribute mortality3 ,no men are gods1 means that the attributes of man are never accompanied by the attributes1 or at least never by all the attributes1 signified by the word god4 ,but when the proposition is considered as a memorandum for practical use1 we shall find a different mode of expressing the same meaning better adapted to indicate the office which the proposition performs4 ,the practical use of a proposition is1 to apprise or remind us what we have to expect1 in any individual case which comes within the assertion contained in the proposition4 ,in reference to this purpose1 the proposition1 ,all men are mortal1 means that the attributes of man are evidence of1 are a mark of1 mortality2 an indication by which the presence of that attribute is made manifest4 ,no men are gods1 means that the attributes of man are a mark or evidence that some or all of the attributes understood to belong to a god are not there2 that where the former are1 we need not expect to find the latter4 ,these two forms of expression are at bottom equivalent2 but the one points the attention more directly to what a proposition means1 the latter to the manner in which it is to be used4 ,now it is to be observed that ,reasoning 7the subject to which we are next to proceed7 is a process into which propositions enter not as ultimate results1 but as means to the establishment of other propositions4 ,we may expect1 therefore1 that the mode of exhibiting the import of a general proposition which shows it in its application to practical use1 will best express the function which propositions perform in ,reasoning4 ,and accordingly1 in the theory of ,reasoning1 the mode of viewing the subject which considers a ,proposition as asserting that one fact or phenomenon is a mark or evidence of another fact or phenomenon1 will be found almost indispensable4 ,for the purposes of that ,theory1 the best mode of defining the import of a proposition is not the mode which shows most clearly what it is in itself1 but that which most distinctly suggests the manner in which it may be made available for advancing from it to other propositions4 ,chapter ,,vii4 ,of ,the ,nature ,of ,classification1 ,and ,the ,five ,predicables4 #a4 ,in examining into the nature of general propositions1 we have adverted much less than is usual with logicians to the ideas of a ,class1 and ,classification2 ideas which1 since the ,realist doctrine of ,general ,substances went out of vogue1 have formed the basis of almost every attempt at a philosophical theory of general terms and general propositions4 ,we have considered general names as having a meaning1 quite independently of their being the names of classes4 ,that circumstance is in truth accidental1 it being wholly immaterial to the signification of the name whether there are many objects1 or only one1 to which it happens to be applicable1 or whether there be any at all4 ,god is as much a general term to the ,christian or ,jew as to the ,polytheist2 and dragon1 hippogriff1 chimera1 mermaid1 ghost1 are as much so as if real objects existed1 corresponding to those names4 ,every name the signification of which is constituted by attributes1 is potentially a name of an indefinite number of objects2 but it needs not be actually the name of any2 and if of any1 it may be the name of only one4 ,as soon as we employ a name to connote attributes1 the things1 be they more or fewer1 which happen to possess those attributes1 are constituted ipso facto a class4 ,but in predicating the name we predicate only the attributes2 and the fact of belonging to a class does not1 in many cases1 come into view at all4 ,although1 however1 ,predication does not presuppose ,classification1 and though the theory of ,names and of ,propositions is not cleared up1 but only encumbered1 by intruding the idea of classification into it1 there is nevertheless a close connection between ,classification and the employment of ,general ,names4 ,by every general name which we introduce1 we create a class1 if there be any things1 real or imaginary1 to compose it2 that is1 any ,things corresponding to the signification of the name4 ,classes1 therefore1 mostly owe their existence to general language4 ,but general language1 also1 though that is not the most common case1 sometimes owes its existence to classes4 ,a general1 which is as much as to say a significant1 name1 is indeed mostly introduced because we have a signification to express by it2 because we need a word by means of which to predicate the attributes which it connotes4 ,but it is also true that a name is sometimes introduced because we have found it convenient to create a class2 because we have thought it useful for the regulation of our mental operations1 that a certain group of objects should be thought of together4 ,a naturalist1 for purposes connected with his particular science1 sees reason to distribute the animal or vegetable creation into certain groups rather than into any others1 and he requires a name to bind1 as it were1 each of his groups together4 ,it must not1 however1 be supposed that such names1 when introduced1 differ in any respect1 as to their mode of signification1 from other connotative names4 ,the classes which they denote are1 as much as any other classes1 constituted by certain common attributes1 and their names are significant of those attributes1 and of nothing else4 ,the names of ,cuvier's classes and orders1 ,plantigrades1 ,digitigrades1 etc41 are as much the expression of attributes as if those names had preceded1 instead of grown out of1 his classification of animals4 ,the only peculiarity of the case is1 that the convenience of classification was here the primary motive for introducing the names2 while in other cases the name is introduced as a means of predication1 and the formation of a class denoted by it is only an indirect consequence4 ,the principles which ought to regulate ,classification1 as a logical process subservient to the investigation of truth1 can not be discussed to any purpose until a much later stage of our inquiry4 ,but1 of ,classification as resulting from1 and implied in1 the fact of employing general language1 we can not forbear to treat here1 without leaving the theory of general names1 and of their employment in predication1 mutilated and formless4 #b4 ,this portion of the theory of general language is the subject of what is termed the doctrine of the ,predicables2 a set of distinctions handed down from ,aristotle1 and his follower ,porphyry1 many of which have taken a firm root in scientific1 and some of them even in popular1 phraseology4 ,the predicables are a fivefold division of ,general ,names1 not grounded as usual on a difference in their meaning1 that is1 in the attribute which they connote1 but on a difference in the kind of class which they denote4 ,we may predicate of a thing five different varieties of class-name3 ,a genus of the thing3 774 ,a species3 774 ,a differentia3 774 ,a proprium3 774 ,an accidens3 774 ,it is to be remarked of these distinctions1 that they express1 not what the predicate is in its own meaning1 but what relation it bears to the subject of which it happens on the particular occasion to be predicated4 ,there are not some names which are exclusively genera1 and others which are exclusively species1 or differenti2 but the same name is referred to one or another predicable1 according to the subject of which it is predicated on the particular occasion4 ,animal1 for instance1 is a genus with respect to man1 or ,john2 a species with respect to ,substance1 or ,being4 ,rectangular is one of the ,differenti of a geometrical square2 it is merely one of the ,accidentia of the table at which ,i am writing4 ,the words genus1 species1 etc41 are therefore relative terms2 they are names applied to certain predicates1 to express the relation between them and some given subject3 a relation grounded1 as we shall see1 not on what the predicate connotes1 but on the class which it denotes1 and on the place which1 in some given classification1 that class occupies relatively to the particular subject4 #c4 ,of these five names1 two1 ,genus and ,species1 are not only used by naturalists in a technical acceptation not precisely agreeing with their philosophical meaning1 but have also acquired a popular acceptation1 much more general than either4 ,in this popular sense any two classes1 one of which includes the whole of the other and more1 may be called a ,genus and a ,species4 ,such1 for instance1 are ,animal and ,man2 ,man and ,mathematician4 ,animal is a ,genus2 ,man and ,brute are its two species2 or we may divide it into a greater number of species1 as man1 horse1 dog1 etc4 ,biped1 or two-footed animal1 may also be considered a genus1 of which man and bird are two species4 ,taste is a genus1 of which sweet taste1 sour taste1 salt taste1 etc41 are species4 ,virtue is a genus2 justice1 prudence1 courage1 fortitude1 generosity1 etc41 are its species4 ,the same class which is a genus with reference to the sub-classes or species included in it1 may be itself a species with reference to a more comprehensive1 or1 as it is often called1 a superior genus4 ,man is a species with reference to animal1 but a genus with reference to the species ,mathematician4 ,animal is a genus1 divided into two species1 man and brute2 but animal is also a species1 which1 with another species1 vegetable1 makes up the genus1 organized being4 ,biped is a genus with reference to man and bird1 but a species with respect to the superior genus1 animal4 ,taste is a genus divided into species1 but also a species of the genus sensation4 ,virtue1 a genus with reference to justice1 temperance1 etc41 is one of the species of the genus1 mental quality4 ,in this popular sense the words ,genus and ,species have passed into common discourse4 ,and it should be observed that in ordinary parlance1 not the name of the class1 but the class itself1 is said to be the genus or species2 not1 of course1 the class in the sense of each individual of the class1 but the individuals collectively1 considered as an aggregate whole2 the name by which the class is designated being then called not the genus or species1 but the generic or specific name4 ,and this is an admissible form of expression2 nor is it of any importance which of the two modes of speaking we adopt1 provided the rest of our language is consistent with it2 but1 if we call the class itself the genus1 we must not talk of predicating the genus4 ,we predicate of man the name mortal2 and by predicating the name1 we may be said1 in an intelligible sense1 to predicate what the name expresses1 the attribute mortality2 but in no allowable sense of the word predication do we predicate of man the class mortal4 ,we predicate of him the fact of belonging to the class4 ,by the ,aristotelian logicians1 the terms genus and species were used in a more restricted sense4 ,they did not admit every class which could be divided into other classes to be a genus1 or every class which could be included in a larger class to be a species4 ,animal was by them considered a genus2 man and brute co-ordinate species under that genus3 biped1 however1 would not have been admitted to be a genus with reference to man1 but a proprium or accidens only4 ,it was requisite1 according to their theory1 that genus and species should be of the essence of the subject4 ,animal was of the essence of man2 biped was not4 ,and in every classification they considered some one class as the lowest or infima species4 ,man1 for instance1 was a lowest species4 ,any further divisions into which the class might be capable of being broken down1 as man into white1 black1 and red man1 or into priest and layman1 they did not admit to be species4 ,it has been seen1 however1 in the preceding chapter1 that the distinction between the essence of a class1 and the attributes or properties which are not of its essence--a distinction which has given occasion to so much abstruse speculation1 and to which so mysterious a character was formerly1 and by many writers is still1 attached--amounts to nothing more than the difference between those attributes of the class which are1 and those which are not1 involved in the signification of the class-name4 ,as applied to individuals1 the word ,essence1 we found1 has no meaning1 except in connection with the exploded tenets of the ,realists2 and what the schoolmen chose to call the essence of an individual1 was simply the essence of the class to which that individual was most familiarly referred4 ,is there no difference1 then1 save this merely verbal one1 between the classes which the schoolmen admitted to be genera or species1 and those to which they refused the title8 ,is it an error to regard some of the differences which exist among objects as differences in kind 7genere or specie71 and others only as differences in the accidents8 ,were the schoolmen right or wrong in giving to some of the classes into which things may be divided1 the name of kinds1 and considering others as secondary divisions1 grounded on differences of a comparatively superficial nature8 ,examination will show that the ,aristotelians did mean something by this distinction1 and something important2 but which1 being but indistinctly conceived1 was inadequately expressed by the phraseology of essences1 and the various other modes of speech to which they had recourse4 #d4 ,it is a fundamental principle in logic1 that the power of framing classes is unlimited1 as long as there is any 7even the smallest7 difference to found a distinction upon4 ,take any attribute whatever1 and if some things have it1 and others have not1 we may ground on the attribute a division of all things into two classes2 and we actually do so1 the moment we create a name which connotes the attribute4 ,the number of possible classes1 therefore1 is boundless2 and there are as many actual classes 7either of real or of imaginary things7 as there are general names1 positive and negative together4 ,but if we contemplate any one of the classes so formed1 such as the class animal or plant1 or the class sulphur or phosphorus1 or the class white or red1 and consider in what particulars the individuals included in the class differ from those which do not come within it1 we find a very remarkable diversity in this respect between some classes and others4 ,there are some classes1 the things contained in which differ from other things only in certain particulars which may be numbered1 while others differ in more than can be numbered1 more even than we need ever expect to know4 ,some classes have little or nothing in common to characterize them by1 except precisely what is connoted by the name3 white things1 for example1 are not distinguished by any common properties except whiteness2 or if they are1 it is only by such as are in some way dependent on1 or connected with1 whiteness4 ,but a hundred generations have not exhausted the common properties of animals or of plants1 of sulphur or of phosphorus2 nor do we suppose them to be exhaustible1 but proceed to new observations and experiments1 in the full confidence of discovering new properties which were by no means implied in those we previously knew4 ,while1 if any one were to propose for investigation the common properties of all things which are of the same color1 the same shape1 or the same specific gravity1 the absurdity would be palpable4 ,we have no ground to believe that any such common properties exist1 except such as may be shown to be involved in the supposition itself1 or to be derivable from it by some law of causation4 ,it appears1 therefore1 that the properties1 on which we ground our classes1 sometimes exhaust all that the class has in common1 or contain it all by some mode of implication2 but in other instances we make a selection of a few properties from among not only a greater number1 but a number inexhaustible by us1 and to which as we know no bounds1 they may1 so far as we are concerned1 be regarded as infinite4 ,there is no impropriety in saying that1 of these two classifications1 the one answers to a much more radical distinction in the things themselves1 than the other does4 ,and if any one even chooses to say that the one classification is made by nature1 the other by us for our convenience1 he will be right2 provided he means no more than this3 ,where a certain apparent difference between things 7though perhaps in itself of little moment7 answers to we know not what number of other differences1 pervading not only their known properties1 but properties yet undiscovered1 it is not optional but imperative to recognize this difference as the foundation of a specific distinction2 while1 on the contrary1 differences that are merely finite and determinate1 like those designated by the words white1 black1 or red1 may be disregarded if the purpose for which the classification is made does not require attention to those particular properties4 ,the differences1 however1 are made by nature1 in both cases2 while the recognition of those differences as grounds of classification and of naming1 is1 equally in both cases1 the act of man3 only in the one case1 the ends of language and of classification would be subverted if no notice were taken of the difference1 while in the other case1 the necessity of taking notice of it depends on the importance or unimportance of the particular qualities in which the difference happens to consist4 ,now1 these classes1 distinguished by unknown multitudes of properties1 and not solely by a few determinate ones--which are parted off from one another by an unfathomable chasm1 instead of a mere ordinary ditch with a visible bottom--are the only classes which1 by the ,aristotelian logicians1 were considered as genera or species4 ,differences which extended only to a certain property or properties1 and there terminated1 they considered as differences only in the accidents of things2 but where any class differed from other things by an infinite series of differences1 known and unknown1 they considered the distinction as one of kind1 and spoke of it as being an essential difference1 which is also one of the current meanings of that vague expression at the present day4 ,conceiving the schoolmen to have been justified in drawing a broad line of separation between these two kinds of classes and of class-distinctions1 ,i shall not only retain the division itself1 but continue to express it in their language4 ,according to that language1 the proximate 7or lowest7 ,kind to which any individual is referrible1 is called its species4 ,conformably to this1 ,isaac ,newton would be said to be of the species man4 ,there are indeed numerous sub-classes included in the class man1 to which ,newton also belongs2 for example1 ,christian1 and ,englishman1 and ,mathematician4 ,but these1 though distinct classes1 are not1 in our sense of the term1 distinct ,kinds of men4 ,a ,christian1 for example1 differs from other human beings2 but he differs only in the attribute which the word expresses1 namely1 belief in ,christianity1 and whatever else that implies1 either as involved in the fact itself1 or connected with it through some law of cause and effect4 ,we should never think of inquiring what properties1 unconnected with ,christianity1 either as cause or effect1 are common to all ,christians and peculiar to them2 while in regard to all ,men1 physiologists are perpetually carrying on such an inquiry2 nor is the answer ever likely to be completed4 ,man1 therefore1 we may call a species2 ,christian1 or ,mathematician1 we can not4 ,note here1 that it is by no means intended to imply that there may not be different ,kinds1 or logical species1 of man4 ,the various races and temperaments1 the two sexes1 and even the various ages1 may be differences of kind1 within our meaning of the term4 ,i do not say that they are so4 ,for in the progress of physiology it may almost be said to be made out1 that the differences which really exist between different races1 sexes1 etc41 follow as consequences1 under laws of nature1 from a small number of primary differences which can be precisely determined1 and which1 as the phrase is1 account for all the rest4 ,if this be so1 these are not distinctions in kind2 no more than ,christian1 ,jew1 ,mussulman1 and ,pagan1 a difference which also carries many consequences along with it4 ,and in this way classes are often mistaken for real ,kinds1 which are afterward proved not to be so4 ,but if it turned out that the differences were not capable of being thus accounted for1 then ,caucasian1 ,mongolian1 ,negro1 etc41 would be really different ,kinds of human beings1 and entitled to be ranked as species by the logician2 though not by the naturalist4 ,for 7as already noticed7 the word species is used in a different signification in logic and in natural history4 ,by the naturalist1 organized beings are not usually said to be of different species1 if it is supposed that they have descended from the same stock4 ,that1 however1 is a sense artificially given to the word1 for the technical purposes of a particular science4 ,to the logician1 if a negro and a white man differ in the same manner 7however less in degree7 as a horse and a camel do1 that is1 if their differences are inexhaustible1 and not referrible to any common cause1 they are different species1 whether they are descended from common ancestors or not4 ,but if their differences can all be traced to climate and habits1 or to some one or a few special differences in structure1 they are not1 in the logician's view1 specifically distinct4 ,when the infima species1 or proximate ,kind1 to which an individual belongs1 has been ascertained1 the properties common to that ,kind include necessarily the whole of the common properties of every other real ,kind to which the individual can be referrible4 ,let the individual1 for example1 be ,socrates1 and the proximate ,kind1 man4 ,animal1 or living creature1 is also a real kind1 and includes ,socrates2 but1 since it likewise includes man1 or in other words1 since all men are animals1 the properties common to animals form a portion of the common properties of the sub-class1 man4 ,and if there be any class which includes ,socrates without including man1 that class is not a real ,kind4 ,let the class1 for example1 be flat-nosed2 that being a class which includes ,socrates1 without including all men4 ,to determine whether it is a real ,kind1 we must ask ourselves this question3 ,have all flat-nosed animals1 in addition to whatever is implied in their flat noses1 any common properties1 other than those which are common to all animals whatever8 ,if they had2 if a flat nose were a mark or index to an indefinite number of other peculiarities1 not deducible from the former by an ascertainable law1 then out of the class man we might cut another class1 flat-nosed man1 which1 according to our definition1 would be a ,kind4 ,but if we could do this1 man would not be1 as it was assumed to be1 the proximate ,kind4 ,therefore1 the properties of the proximate ,kind do comprehend those 7whether known or unknown7 of all other ,kinds to which the individual belongs2 which was the point we undertook to prove4 ,and hence1 every other ,kind which is predicable of the individual1 will be to the proximate ,kind in the relation of a genus1 according to even the popular acceptation of the terms genus and species2 that is1 it will be a larger class1 including it and more4 ,we are now able to fix the logical meaning of these terms4 ,every class which is a real ,kind1 that is1 which is distinguished from all other classes by an indeterminate multitude of properties not derivable from one another1 is either a genus or a species4 ,a ,kind which is not divisible into other ,kinds1 can not be a genus1 because it has no species under it2 but it is itself a species1 both with reference to the individuals below and to the genera above 7,species ,prdicabilis and ,species ,subjicibilis74 ,but every ,kind which admits of division into real ,kinds 7as animal into mammal1 bird1 fish1 etc41 or bird into various species of birds7 is a genus to all below it1 a species to all genera in which it is itself included4 ,and here we may close this part of the discussion1 and pass to the three remaining predicables1 ,differentia1 ,proprium1 and ,accidens4 #e4 ,to begin with ,differentia4 ,this word is correlative with the words genus and species1 and as all admit1 it signifies the attribute which distinguishes a given species from every other species of the same genus4 ,this is so far clear3 but we may still ask1 which of the distinguishing attributes it signifies4 ,for we have seen that every ,kind 7and a species must be a ,kind7 is distinguished from other ,kinds1 not by any one attribute1 but by an indefinite number4 ,man1 for instance1 is a species of the genus animal3 ,rational 7or rationality1 for it is of no consequence here whether we use the concrete or the abstract form7 is generally assigned by logicians as the ,differentia2 and doubtless this attribute serves the purpose of distinction3 but it has also been remarked of man1 that he is a cooking animal2 the only animal that dresses its food4 ,this1 therefore1 is another of the attributes by which the species man is distinguished from other species of the same genus3 would this attribute serve equally well for a differentia8 ,the ,aristotelians say ,no2 having laid it down that the differentia must1 like the genus and species1 be of the essence of the subject4 ,and here we lose even that vestige of a meaning grounded in the nature of the things themselves1 which may be supposed to be attached to the word essence when it is said that genus and species must be of the essence of the thing4 ,there can be no doubt that when the schoolmen talked of the essences of things as opposed to their accidents1 they had confusedly in view the distinction between differences of kind1 and the differences which are not of kind2 they meant to intimate that genera and species must be ,kinds4 ,their notion of the essence of a thing was a vague notion of a something which makes it what it is1 i4e41 which makes it the ,kind of thing that it is--which causes it to have all that variety of properties which distinguish its ,kind4 ,but when the matter came to be looked at more closely1 nobody could discover what caused the thing to have all those properties1 nor even that there was any thing which caused it to have them4 ,logicians1 however1 not liking to admit this1 and being unable to detect what made the thing to be what it was1 satisfied themselves with what made it to be what it was called4 ,of the innumerable properties1 known and unknown1 that are common to the class man1 a portion only1 and of course a very small portion1 are connoted by its name2 these few1 however1 will naturally have been thus distinguished from the rest either for their greater obviousness1 or for greater supposed importance4 ,these properties1 then1 which were connoted by the name1 logicians seized upon1 and called them the essence of the species2 and not stopping there1 they affirmed them1 in the case of the infima species1 to be the essence of the individual too2 for it was their maxim1 that the species contained the 8whole essence0 of the thing4 ,metaphysics1 that fertile field of delusion propagated by language1 does not afford a more signal instance of such delusion4 ,on this account it was that rationality1 being connoted by the name man1 was allowed to be a differentia of the class2 but the peculiarity of cooking their food1 not being connoted1 was relegated to the class of accidental properties4 ,the distinction1 therefore1 between ,differentia1 ,proprium1 and ,accidens1 is not grounded in the nature of things1 but in the connotation of names2 and we must seek it there1 if we wish to find what it is4 ,from the fact that the genus includes the species1 in other words denotes more than the species1 or is predicable of a greater number of individuals1 it follows that the species must connote more than the genus4 ,it must connote all the attributes which the genus connotes1 or there would be nothing to prevent it from denoting individuals not included in the genus4 ,and it must connote something besides1 otherwise it would include the whole genus4 ,animal denotes all the individuals denoted by man1 and many more4 ,man1 therefore1 must connote all that animal connotes1 otherwise there might be men who are not animals2 and it must connote something more than animal connotes1 otherwise all animals would be men4 ,this surplus of connotation--this which the species connotes over and above the connotation of the genus--is the ,differentia1 or specific difference2 or1 to state the same proposition in other words1 the ,differentia is that which must be added to the connotation of the genus1 to complete the connotation of the species4 ,the word man1 for instance1 exclusively of what it connotes in common with animal1 also connotes rationality1 and at least some approximation to that external form which we all know1 but which as we have no name for it considered in itself1 we are content to call the human4 ,the ,differentia1 or specific difference1 therefore1 of man1 as referred to the genus animal1 is that outward form and the possession of reason4 ,the ,aristotelians said1 the possession of reason1 without the outward form4 ,but if they adhered to this1 they would have been obliged to call the ,houyhnhnms men4 ,the question never arose1 and they were never called upon to decide how such a case would have affected their notion of essentiality4 ,however this may be1 they were satisfied with taking such a portion of the differentia as sufficed to distinguish the species from all other existing things1 though by so doing they might not exhaust the connotation of the name4 #f4 ,and here1 to prevent the notion of differentia from being restricted within too narrow limits1 it is necessary to remark1 that a species1 even as referred to the same genus1 will not always have the same differentia1 but a different one1 according to the principle and purpose which preside over the particular classification4 ,for example1 a naturalist surveys the various kinds of animals1 and looks out for the classification of them most in accordance with the order in which1 for zoological purposes1 he considers it desirable that we should think of them4 ,with this view he finds it advisable that one of his fundamental divisions should be into warm-blooded and cold-blooded animals2 or into animals which breathe with lungs and those which breathe with gills2 or into carnivorous1 and frugivorous or graminivorous2 or into those which walk on the flat part and those which walk on the extremity of the foot1 a distinction on which two of ,cuvier's families are founded4 ,in doing this1 the naturalist creates as many new classes2 which are by no means those to which the individual animal is familiarly and spontaneously referred2 nor should we ever think of assigning to them so prominent a position in our arrangement of the animal kingdom1 unless for a preconceived purpose of scientific convenience4 ,and to the liberty of doing this there is no limit4 ,in the examples we have given1 most of the classes are real ,kinds1 since each of the peculiarities is an index to a multitude of properties belonging to the class which it characterizes3 but even if the case were otherwise--if the other properties of those classes could all be derived1 by any process known to us1 from the one peculiarity on which the class is founded--even then1 if these derivative properties were of primary importance for the purposes of the naturalist1 he would be warranted in founding his primary divisions on them4 ,if1 however1 practical convenience is a sufficient warrant for making the main demarcations in our arrangement of objects run in lines not coinciding with any distinction of ,kind1 and so creating genera and species in the popular sense which are not genera or species in the rigorous sense at all2 fortiori must we be warranted1 when our genera and species are real genera and species1 in marking the distinction between them by those of their properties which considerations of practical convenience most strongly recommend4 ,if we cut a species out of a given genus--the species man1 for instance1 out of the genus animal--with an intention on our part that the peculiarity by which we are to be guided in the application of the name man should be rationality1 then rationality is the differentia of the species man4 ,suppose1 however1 that being naturalists1 we1 for the purposes of our particular study1 cut out of the genus animal the same species man1 but with an intention that the distinction between man and all other species of animal should be1 not rationality1 but the possession of 8four incisors in each jaw1 tusks solitary1 and erect posture40 ,it is evident that the word man1 when used by us as naturalists1 no longer connotes rationality1 but connotes the three other properties specified2 for that which we have expressly in view when we impose a name1 assuredly forms part of the meaning of that name4 ,we may1 therefore1 lay it down as a maxim1 that wherever there is a ,genus1 and a ,species marked out from that genus by an assignable differentia1 the name of the species must be connotative1 and must connote the differentia2 but the connotation may be special--not involved in the signification of the term as ordinarily used1 but given to it when employed as a term of art or science4 ,the word ,man in common use1 connotes rationality and a certain form1 but does not connote the number or character of the teeth2 in the ,linnan system it connotes the number of incisor and canine teeth1 but does not connote rationality nor any particular form4 ,the word man has1 therefore1 two different meanings2 though not commonly considered as ambiguous1 because it happens in both cases to denote the same individual objects4 ,but a case is conceivable in which the ambiguity would become evident3 we have only to imagine that some new kind of animal were discovered1 having ,linnus's three characteristics of humanity1 but not rational1 or not of the human form4 ,in ordinary parlance1 these animals would not be called men2 but in natural history they must still be called so by those1 if any there should be1 who adhere to the ,linnan classification2 and the question would arise1 whether the word should continue to be used in two senses1 or the classification be given up1 and the technical sense of the term be abandoned along with it4 ,words not otherwise connotative may1 in the mode just adverted to1 acquire a special or technical connotation4 ,thus the word whiteness1 as we have so often remarked1 connotes nothing2 it merely denotes the attribute corresponding to a certain sensation3 but if we are making a classification of colors1 and desire to justify1 or even merely to point out1 the particular place assigned to whiteness in our arrangement1 we may define it 8the color produced by the mixture of all the simple rays20 and this fact1 though by no means implied in the meaning of the word whiteness as ordinarily used1 but only known by subsequent scientific investigation1 is part of its meaning in the particular essay or treatise1 and becomes the differentia of the species47#db7 ,the differentia1 therefore1 of a species may be defined to be1 that part of the connotation of the specific name1 whether ordinary or special and technical1 which distinguishes the species in question from all other species of the genus to which on the particular occasion we are referring it4 #g4 ,having disposed of ,genus1 ,species1 and ,differentia1 we shall not find much difficulty in attaining a clear conception of the distinction between the other two predicables1 as well as between them and the first three4 ,in the ,aristotelian phraseology1 ,genus and ,differentia are of the essence of the subject2 by which1 as we have seen1 is really meant that the properties signified by the genus and those signified by the differentia1 form part of the connotation of the name denoting the species4 ,proprium and ,accidens1 on the other hand1 form no part of the essence1 but are predicated of the species only accidentally4 ,both are ,accidents1 in the wider sense in which the accidents of a thing are opposed to its essence2 though1 in the doctrine of the ,predicables1 ,accidens is used for one sort of accident only1 ,proprium being another sort4 ,proprium1 continue the schoolmen1 is predicated accidentally1 indeed1 but necessarily2 or1 as they further explain it1 signifies an attribute which is not indeed part of the essence1 but which flows from1 or is a consequence of1 the essence1 and is1 therefore1 inseparably attached to the species2 e4g41 the various properties of a triangle1 which1 though no part of its definition1 must necessarily be possessed by whatever comes under that definition4 ,accidens1 on the contrary1 has no connection whatever with the essence1 but may come and go1 and the species still remain what it was before4 ,if a species could exist without its ,propria1 it must be capable of existing without that on which its ,propria are necessarily consequent1 and therefore without its essence1 without that which constitutes it a species4 ,but an ,accidens1 whether separable or inseparable from the species in actual experience1 may be supposed separated1 without the necessity of supposing any other alteration2 or at least1 without supposing any of the essential properties of the species to be altered1 since with them an ,accidens has no connection4 ,a ,proprium1 therefore1 of the species1 may be defined1 any attribute which belongs to all the individuals included in the species1 and which1 though not connoted by the specific name 7either ordinarily if the classification we are considering be for ordinary purposes1 or specially if it be for a special purpose71 yet follows from some attribute which the name either ordinarily or specially connotes4 ,one attribute may follow from another in two ways2 and there are consequently two kinds of ,proprium4 ,it may follow as a conclusion follows premises1 or it may follow as an effect follows a cause4 ,thus1 the attribute of having the opposite sides equal1 which is not one of those connoted by the word ,parallelogram1 nevertheless follows from those connoted by it1 namely1 from having the opposite sides straight lines and parallel1 and the number of sides four4 ,the attribute1 therefore1 of having the opposite sides equal1 is a ,proprium of the class parallelogram2 and a ,proprium of the first kind1 which follows from the connoted attributes by way of demonstration4 ,the attribute of being capable of understanding language1 is a ,proprium of the species man1 since without being connoted by the word1 it follows from an attribute which the word does connote1 viz41 from the attribute of rationality4 ,but this is a ,proprium of the second kind1 which follows by way of causation4 ,how it is that one property of a thing follows1 or can be inferred1 from another2 under what conditions this is possible1 and what is the exact meaning of the phrase2 are among the questions which will occupy us in the two succeeding ,books4 ,at present it needs only be said1 that whether a ,proprium follows by demonstration or by causation1 it follows necessarily2 that is to say1 its not following would be inconsistent with some law which we regard as a part of the constitution either of our thinking faculty or of the universe4 #h4 ,under the remaining predicable1 ,accidens1 are included all attributes of a thing which are neither involved in the signification of the name 7whether ordinarily or as a term of art71 nor have1 so far as we know1 any necessary connection with attributes which are so involved4 ,they are commonly divided into ,separable and ,inseparable ,accidents4 ,inseparable accidents are those which--although we know of no connection between them and the attributes constitutive of the species1 and although1 therefore1 so far as we are aware1 they might be absent without making the name inapplicable and the species a different species--are yet never in fact known to be absent4 ,a concise mode of expressing the same meaning is1 that inseparable accidents are properties which are universal to the species1 but not necessary to it4 ,thus1 blackness is an attribute of a crow1 and1 as far as we know1 a universal one4 ,but if we were to discover a race of white birds1 in other respects resembling crows1 we should not say1 ,these are not crows2 we should say1 ,these are white crows4 ,crow1 therefore1 does not connote blackness2 nor1 from any of the attributes which it does connote1 whether as a word in popular use or as a term of art1 could blackness be inferred4 ,not only1 therefore1 can we conceive a white crow1 but we know of no reason why such an animal should not exist4 ,since1 however1 none but black crows are known to exist1 blackness1 in the present state of our knowledge1 ranks as an accident1 but an inseparable accident1 of the species crow4 ,separable ,accidents are those which are found1 in point of fact1 to be sometimes absent from the species2 which are not only not necessary1 but not even universal4 ,they are such as do not belong to every individual of the species1 but only to some individuals2 or if to all1 not at all times4 ,thus the color of a ,european is one of the separable accidents of the species man1 because it is not an attribute of all human creatures4 ,being born1 is also 7speaking in the logical sense7 a separable accident of the species man1 because1 though an attribute of all human beings1 it is so only at one particular time4 ,a fortiori those attributes which are not constant even in the same individual1 as1 to be in one or in another place1 to be hot or cold1 sitting or walking1 must be ranked as separable accidents4 ,chapter ,,viii4 ,of ,definition4 #a4 ,one necessary part of the theory of ,names and of ,propositions remains to be treated of in this place3 the theory of ,definitions4 ,as being the most important of the class of propositions which we have characterized as purely verbal1 they have already received some notice in the chapter preceding the last4 ,but their fuller treatment was at that time postponed1 because definition is so closely connected with classification1 that1 until the nature of the latter process is in some measure understood1 the former can not be discussed to much purpose4 ,the simplest and most correct notion of a ,definition is1 a proposition declaratory of the meaning of a word2 namely1 either the meaning which it bears in common acceptation1 or that which the speaker or writer1 for the particular purposes of his discourse1 intends to annex to it4 ,the definition of a word being the proposition which enunciates its meaning1 words which have no meaning are unsusceptible of definition4 ,proper names1 therefore1 can not be defined4 ,a proper name being a mere mark put upon an individual1 and of which it is the characteristic property to be destitute of meaning1 its meaning can not of course be declared2 though we may indicate by language1 as we might indicate still more conveniently by pointing with the finger1 upon what individual that particular mark has been1 or is intended to be1 put4 ,it is no definition of 8,john ,thomson0 to say he is 8the son of ,general ,thomson20 for the name ,john ,thomson does not express this4 ,neither is it any definition of 8,john ,thomson0 to say he is 8the man now crossing the street40 ,these propositions may serve to make known who is the particular man to whom the name belongs1 but that may be done still more unambiguously by pointing to him1 which1 however1 has not been esteemed one of the modes of definition4 ,in the case of connotative names1 the meaning1 as has been so often observed1 is the connotation2 and the definition of a connotative name1 is the proposition which declares its connotation4 ,this might be done either directly or indirectly4 ,the direct mode would be by a proposition in this form3 8,man0 7or whatsoever the word may be7 8is a name connoting such and such attributes10 or 8is a name which1 when predicated of any thing1 signifies the possession of such and such attributes by that thing40 ,or thus3 ,man is every thing which possesses such and such attributes3 ,man is every thing which possesses corporeity1 organization1 life1 rationality1 and certain peculiarities of external form4 ,this form of definition is the most precise and least equivocal of any2 but it is not brief enough1 and is besides too technical for common discourse4 ,the more usual mode of declaring the connotation of a name1 is to predicate of it another name or names of known signification1 which connote the same aggregation of attributes4 ,this may be done either by predicating of the name intended to be defined1 another connotative name exactly synonymous1 as1 8,man is a human being10 which is not commonly accounted a definition at all2 or by predicating two or more connotative names1 which make up among them the whole connotation of the name to be defined4 ,in this last case1 again1 we may either compose our definition of as many connotative names as there are attributes1 each attribute being connoted by one1 as1 ,man is a corporeal1 organized1 animated1 rational being1 shaped so and so2 or we employ names which connote several of the attributes at once1 as1 ,man is a rational animal1 shaped so and so4 ,the definition of a name1 according to this view of it1 is the sum total of all the essential propositions which can be framed with that name for their subject4 ,all propositions the truth of which is implied in the name1 all those which we are made aware of by merely hearing the name1 are included in the definition1 if complete1 and may be evolved from it without the aid of any other premises2 whether the definition expresses them in two or three words1 or in a larger number4 ,it is1 therefore1 not without reason that ,condillac and other writers have affirmed a definition to be an analysis4 ,to resolve any complex whole into the elements of which it is compounded1 is the meaning of analysis3 and this we do when we replace one word which connotes a set of attributes collectively1 by two or more which connote the same attributes singly1 or in smaller groups4 #b4 ,from this1 however1 the question naturally arises1 in what manner are we to define a name which connotes only a single attribute3 for instance1 8white10 which connotes nothing but whiteness2 8rational10 which connotes nothing but the possession of reason4 ,it might seem that the meaning of such names could only be declared in two ways2 by a synonymous term1 if any such can be found2 or in the direct way already alluded to3 8,white is a name connoting the attribute whiteness40 ,let us see1 however1 whether the analysis of the meaning of the name1 that is1 the breaking down of that meaning into several parts1 admits of being carried farther4 ,without at present deciding this question as to the word white1 it is obvious that in the case of rational some further explanation may be given of its meaning than is contained in the proposition1 8,rational is that which possesses the attribute of reason20 since the attribute reason itself admits of being defined4 ,and here we must turn our attention to the definitions of attributes1 or rather of the names of attributes1 that is1 of abstract names4 ,in regard to such names of attributes as are connotative1 and express attributes of those attributes1 there is no difficulty3 like other connotative names1 they are defined by declaring their connotation4 ,thus the word fault may be defined1 8a quality productive of evil or inconvenience40 ,sometimes1 again1 the attribute to be defined is not one attribute1 but a union of several3 we have only1 therefore1 to put together the names of all the attributes taken separately1 and we obtain the definition of the name which belongs to them all taken together2 a definition which will correspond exactly to that of the corresponding concrete name4 ,for1 as we define a concrete name by enumerating the attributes which it connotes1 and as the attributes connoted by a concrete name form the entire signification of the corresponding abstract name1 the same enumeration will serve for the definition of both4 ,thus1 if the definition of a human being be this1 8a being1 corporeal1 animated1 rational1 shaped so and so10 the definition of humanity will be corporeity and animal life1 combined with rationality1 and with such and such a shape4 ,when1 on the other hand1 the abstract name does not express a complication of attributes1 but a single attribute1 we must remember that every attribute is grounded on some fact or phenomenon1 from which1 and which alone1 it derives its meaning4 ,to that fact or phenomenon1 called in a former chapter the foundation of the attribute1 we must1 therefore1 have recourse for its definition4 ,now1 the foundation of the attribute may be a phenomenon of any degree of complexity1 consisting of many different parts1 either co-existent or in succession4 ,to obtain a definition of the attribute1 we must analyze the phenomenon into these parts4 ,eloquence1 for example1 is the name of one attribute only2 but this attribute is grounded on external effects of a complicated nature1 flowing from acts of the person to whom we ascribe the attribute2 and by resolving this phenomenon of causation into its two parts1 the cause and the effect1 we obtain a definition of eloquence1 viz4 the power of influencing the feelings by speech or writing4 ,a name1 therefore1 whether concrete or abstract1 admits of definition1 provided we are able to analyze1 that is1 to distinguish into parts1 the attribute or set of attributes which constitute the meaning both of the concrete name and of the corresponding abstract3 if a set of attributes1 by enumerating them2 if a single attribute1 by dissecting the fact or phenomenon 7whether of perception or of internal consciousness7 which is the foundation of the attribute4 ,but1 further1 even when the fact is one of our simple feelings or states of consciousness1 and therefore unsusceptible of analysis1 the names both of the object and of the attribute still admit of definition2 or rather1 would do so if all our simple feelings had names4 ,whiteness may be defined1 the property or power of exciting the sensation of white4 ,a white object may be defined1 an object which excites the sensation of white4 ,the only names which are unsusceptible of definition1 because their meaning is unsusceptible of analysis1 are the names of the simple feelings themselves4 ,these are in the same condition as proper names4 ,they are not indeed1 like proper names1 unmeaning2 for the words sensation of white signify1 that the sensation which ,i so denominate resembles other sensations which ,i remember to have had before1 and to have called by that name4 ,but as we have no words by which to recall those former sensations1 except the very word which we seek to define1 or some other which1 being exactly synonymous with it1 requires definition as much1 words can not unfold the signification of this class of names2 and we are obliged to make a direct appeal to the personal experience of the individual whom we address4 #c4 ,having stated what seems to be the true idea of a ,definition1 ,i proceed to examine some opinions of philosophers1 and some popular conceptions on the subject1 which conflict more or less with that idea4 ,the only adequate definition of a name is1 as already remarked1 one which declares the facts1 and the whole of the facts1 which the name involves in its signification4 ,but with most persons the object of a definition does not embrace so much2 they look for nothing more1 in a definition1 than a guide to the correct use of the term--a protection against applying it in a manner inconsistent with custom and convention4 ,any thing1 therefore1 is to them a sufficient definition of a term1 which will serve as a correct index to what the term denotes2 though not embracing the whole1 and sometimes1 perhaps1 not even any part1 of what it connotes4 ,this gives rise to two sorts of imperfect1 or unscientific definition2 ,essential but incomplete ,definitions1 and ,accidental ,definitions1 or ,descriptions4 ,in the former1 a connotative name is defined by a part only of its connotation2 in the latter1 by something which forms no part of the connotation at all4 ,an example of the first kind of imperfect definitions is the following3 ,man is a rational animal4 ,it is impossible to consider this as a complete definition of the word ,man1 since 7as before remarked7 if we adhered to it we should be obliged to call the ,houyhnhnms men2 but as there happen to be no ,houyhnhnms1 this imperfect definition is sufficient to mark out and distinguish from all other things1 the objects at present denoted by 8man20 all the beings actually known to exist1 of whom the name is predicable4 ,though the word is defined by some only among the attributes which it connotes1 not by all1 it happens that all known objects which possess the enumerated attributes1 possess also those which are omitted2 so that the field of predication which the word covers1 and the employment of it which is conformable to usage1 are as well indicated by the inadequate definition as by an adequate one4 ,such definitions1 however1 are always liable to be overthrown by the discovery of new objects in nature4 ,definitions of this kind are what logicians have had in view1 when they laid down the rule1 that the definition of a species should be per genus et differentiam4 ,differentia being seldom taken to mean the whole of the peculiarities constitutive of the species1 but some one of those peculiarities only1 a complete definition would be per genus et differentias1 rather than differentiam4 ,it would include1 with the name of the superior genus1 not merely some attribute which distinguishes the species intended to be defined from all other species of the same genus1 but all the attributes implied in the name of the species1 which the name of the superior genus has not already implied4 ,the assertion1 however1 that a definition must of necessity consist of a genus and differenti1 is not tenable4 ,it was early remarked by logicians1 that the summum genus in any classification1 having no genus superior to itself1 could not be defined in this manner4 ,yet we have seen that all names1 except those of our elementary feelings1 are susceptible of definition in the strictest sense2 by setting forth in words the constituent parts of the fact or phenomenon1 of which the connotation of every word is ultimately composed4 #d4 ,although the first kind of imperfect definition 7which defines a connotative term by a part only of what it connotes1 but a part sufficient to mark out correctly the boundaries of its denotation71 has been considered by the ancients1 and by logicians in general1 as a complete definition2 it has always been deemed necessary that the attributes employed should really form part of the connotation2 for the rule was that the definition must be drawn from the essence of the class2 and this would not have been the case if it had been in any degree made up of attributes not connoted by the name4 ,the second kind of imperfect definition1 therefore1 in which the name of a class is defined by any of its accidents--that is1 by attributes which are not included in its connotation--has been rejected from the rank of genuine ,definition by all logicians1 and has been termed ,description4 ,this kind of imperfect definition1 however1 takes its rise from the same cause as the other1 namely1 the willingness to accept as a definition any thing which1 whether it expounds the meaning of the name or not1 enables us to discriminate the things denoted by the name from all other things1 and consequently to employ the term in predication without deviating from established usage4 ,this purpose is duly answered by stating any 7no matter what7 of the attributes which are common to the whole of the class1 and peculiar to it2 or any combination of attributes which happens to be peculiar to it1 though separately each of those attributes may be common to it with some other things4 ,it is only necessary that the definition 7or description7 thus formed1 should be convertible with the name which it professes to define2 that is1 should be exactly co-extensive with it1 being predicable of every thing of which it is predicable1 and of nothing of which it is not predicable2 though the attributes specified may have no connection with those which mankind had in view when they formed or recognized the class1 and gave it a name4 ,the following are correct definitions of ,man1 according to this test3 ,man is a mammiferous animal1 having 7by nature7 two hands 7for the human species answers to this description1 and no other animal does73 ,man is an animal who cooks his food3 ,man is a featherless biped4 ,what would otherwise be a mere description1 may be raised to the rank of a real definition by the peculiar purpose which the speaker or writer has in view4 ,as was seen in the preceding chapter1 it may1 for the ends of a particular art or science1 or for the more convenient statement of an author's particular doctrines1 be advisable to give to some general name1 without altering its denotation1 a special connotation1 different from its ordinary one4 ,when this is done1 a definition of the name by means of the attributes which make up the special connotation1 though in general a mere accidental definition or description1 becomes on the particular occasion and for the particular purpose a complete and genuine definition4 ,this actually occurs with respect to one of the preceding examples1 8,man is a mammiferous animal having two hands10 which is the scientific definition of man1 considered as one of the species in ,cuvier's distribution of the animal kingdom4 ,in cases of this sort1 though the definition is still a declaration of the meaning which in the particular instance the name is appointed to convey1 it can not be said that to state the meaning of the word is the purpose of the definition4 ,the purpose is not to expound a name1 but a classification4 ,the special meaning which ,cuvier assigned to the word ,man 7quite foreign to its ordinary meaning1 though involving no change in the denotation of the word71 was incidental to a plan of arranging animals into classes on a certain principle1 that is1 according to a certain set of distinctions4 ,and since the definition of ,man according to the ordinary connotation of the word1 though it would have answered every other purpose of a definition1 would not have pointed out the place which the species ought to occupy in that particular classification2 he gave the word a special connotation1 that he might be able to define it by the kind of attributes on which1 for reasons of scientific convenience1 he had resolved to found his division of animated nature4 ,scientific definitions1 whether they are definitions of scientific terms1 or of common terms used in a scientific sense1 are almost always of the kind last spoken of3 their main purpose is to serve as the landmarks of scientific classification4 ,and since the classifications in any science are continually modified as scientific knowledge advances1 the definitions in the sciences are also constantly varying4 ,a striking instance is afforded by the words ,acid and ,alkali1 especially the former4 ,as experimental discovery advanced1 the substances classed with acids have been constantly multiplying1 and by a natural consequence the attributes connoted by the word have receded and become fewer4 ,at first it connoted the attributes1 of combining with an alkali to form a neutral substance 7called a salt72 being compounded of a base and oxygen2 causticity to the taste and touch2 fluidity1 etc4 ,the true analysis of muriatic acid1 into chlorine and hydrogen1 caused the second property1 composition from a base and oxygen1 to be excluded from the connotation4 ,the same discovery fixed the attention of chemists upon hydrogen as an important element in acids2 and more recent discoveries having led to the recognition of its presence in sulphuric1 nitric1 and many other acids1 where its existence was not previously suspected1 there is now a tendency to include the presence of this element in the connotation of the word4 ,but carbonic acid1 silica1 sulphurous acid1 have no hydrogen in their composition2 that property can not1 therefore1 be connoted by the term1 unless those substances are no longer to be considered acids4 ,causticity and fluidity have long since been excluded from the characteristics of the class1 by the inclusion of silica and many other substances in it2 and the formation of neutral bodies by combination with alkalis1 together with such electro-chemical peculiarities as this is supposed to imply1 are now the only differenti which form the fixed connotation of the word ,acid1 as a term of chemical science4 ,what is true of the definition of any term of science1 is of course true of the definition of a science itself2 and accordingly 7as observed in the ,introductory ,chapter of this work71 the definition of a science must necessarily be progressive and provisional4 ,any extension of knowledge or alteration in the current opinions respecting the subject-matter1 may lead to a change more or less extensive in the particulars included in the science2 and its composition being thus altered1 it may easily happen that a different set of characteristics will be found better adapted as differenti for defining its name4 ,in the same manner in which a special or technical definition has for its object to expound the artificial classification out of which it grows2 the ,aristotelian logicians seem to have imagined that it was also the business of ordinary definition to expound the ordinary1 and what they deemed the natural1 classification of things1 namely1 the division of them into ,kinds2 and to show the place which each ,kind occupies1 as superior1 collateral1 or subordinate1 among other ,kinds4 ,this notion would account for the rule that all definition must necessarily be per genus et differentiam1 and would also explain why a single differentia was deemed sufficient4 ,but to expound1 or express in words1 a distinction of ,kind1 has already been shown to be an impossibility3 the very meaning of a ,kind is1 that the properties which distinguish it do not grow out of one another1 and can not therefore be set forth in words1 even by implication1 otherwise than by enumerating them all3 and all are not known1 nor are ever likely to be so4 ,it is idle1 therefore1 to look to this as one of the purposes of a definition3 while1 if it be only required that the definition of a ,kind should indicate what kinds include it or are included by it1 any definitions which expound the connotation of the names will do this3 for the name of each class must necessarily connote enough of its properties to fix the boundaries of the class4 ,if the definition1 therefore1 be a full statement of the connotation1 it is all that a definition can be required to be47#dc7 #e4 ,of the two incomplete and popular modes of definition1 and in what they differ from the complete or philosophical mode1 enough has now been said4 ,we shall next examine an ancient doctrine1 once generally prevalent and still by no means exploded1 which ,i regard as the source of a great part of the obscurity hanging over some of the most important processes of the understanding in the pursuit of truth4 ,according to this1 the definitions of which we have now treated are only one of two sorts into which definitions may be divided1 viz41 definitions of names1 and definitions of things4 ,the former are intended to explain the meaning of a term2 the latter1 the nature of a thing2 the last being incomparably the most important4 ,this opinion was held by the ancient philosophers1 and by their followers1 with the exception of the ,nominalists2 but as the spirit of modern metaphysics1 until a recent period1 has been on the whole a ,nominalist spirit1 the notion of definitions of things has been to a certain extent in abeyance1 still continuing1 however1 to breed confusion in logic1 by its consequences indeed rather than by itself4 ,yet the doctrine in its own proper form now and then breaks out1 and has appeared 7among other places7 where it was scarcely to be expected1 in a justly admired word1 ,archbishop ,whately's ,logic47#dd7 ,in a review of that work published by me in the ,westminster ,review for ,january1 #ahbh1 and containing some opinions which ,i no longer entertain1 ,i find the following observations on the question now before us2 observations with which my present view of that question is still sufficiently in accordance4 8,the distinction between nominal and real definitions1 between definitions of words and what are called definitions of things1 though conformable to the ideas of most of the ,aristotelian logicians1 can not1 as it appears to us1 be maintained4 ,we apprehend that no definition is ever intended to #8explain and unfold the nature of a thing4' ,it is some confirmation of our opinion1 that none of those writers who have thought that there were definitions of things1 have ever succeeded in discovering any criterion by which the definition of a thing can be distinguished from any other proposition relating to the thing4 ,the definition1 they say1 unfolds the nature of the thing3 but no definition can unfold its whole nature2 and every proposition in which any quality whatever is predicated of the thing1 unfolds some part of its nature4 ,the true state of the case we take to be this4 ,all definitions are of names1 and of names only2 but1 in some definitions1 it is clearly apparent1 that nothing is intended except to explain the meaning of the word2 while in others1 besides explaining the meaning of the word1 it is intended to be implied that there exists a thing1 corresponding to the word4 ,whether this be or be not implied in any given case1 can not be collected from the mere form of the expression4 #8,a centaur is an animal with the upper parts of a man and the lower parts of a horse1' and #8,a triangle is a rectilineal figure with three sides1' are1 in form1 expressions precisely similar2 although in the former it is not implied that any thing1 conformable to the term1 really exists1 while in the latter it is2 as may be seen by substituting in both definitions1 the word means for is4 ,in the first expression1 #8,a centaur means an animal1' etc41 the sense would remain unchanged3 in the second1 #8,a triangle means1' etc41 the meaning would be altered1 since it would be obviously impossible to deduce any of the truths of geometry from a proposition expressive only of the manner in which we intend to employ a particular sign4 8,there are1 therefore1 expressions1 commonly passing for definitions1 which include in themselves more than the mere explanation of the meaning of a term4 ,but it is not correct to call an expression of this sort a peculiar kind of definition4 ,its difference from the other kind consists in this1 that it is not a definition1 but a definition and something more4 ,the definition above given of a triangle1 obviously comprises not one1 but two propositions1 perfectly distinguishable4 ,the one is1 #8,there may exist a figure1 bounded by three straight lines2' the other1 #8,and this figure may be termed a triangle4' ,the former of these propositions is not a definition at all3 the latter is a mere nominal definition1 or explanation of the use and application of a term4 ,the first is susceptible of truth or falsehood1 and may therefore be made the foundation of a train of reasoning4 ,the latter can neither be true nor false2 the only character it is susceptible of is that of conformity or disconformity to the ordinary usage of language40 ,there is a real distinction1 then1 between definitions of names1 and what are erroneously called definitions of things2 but it is1 that the latter1 along with the meaning of a name1 covertly asserts a matter of fact4 ,this covert assertion is not a definition1 but a postulate4 ,the definition is a mere identical proposition1 which gives information only about the use of language1 and from which no conclusions affecting matters of fact can possibly be drawn4 ,the accompanying postulate1 on the other hand1 affirms a fact1 which may lead to consequences of every degree of importance4 ,it affirms the actual or possible existence of ,things possessing the combination of attributes set forth in the definition2 and this1 if true1 may be foundation sufficient on which to build a whole fabric of scientific truth4 ,we have already made1 and shall often have to repeat1 the remark1 that the philosophers who overthrew ,realism by no means got rid of the consequences of ,realism1 but retained long afterward1 in their own philosophy1 numerous propositions which could only have a rational meaning as part of a ,realistic system4 ,it had been handed down from ,aristotle1 and probably from earlier times1 as an obvious truth1 that the science of ,geometry is deduced from definitions4 ,this1 so long as a definition was considered to be a proposition 8unfolding the nature of the thing10 did well enough4 ,but ,hobbes followed1 and rejected utterly the notion that a definition declares the nature of the thing1 or does any thing but state the meaning of a name2 yet he continued to affirm as broadly as any of his predecessors1 that the 1 principia1 or original premises of mathematics1 and even of all science1 are definitions2 producing the singular paradox1 that systems of scientific truth1 nay1 all truths whatever at which we arrive by reasoning1 are deduced from the arbitrary conventions of mankind concerning the signification of words4 ,to save the credit of the doctrine that definitions are the premises of scientific knowledge1 the proviso is sometimes added1 that they are so only under a certain condition1 namely1 that they be framed conformably to the phenomena of nature2 that is1 that they ascribe such meanings to terms as shall suit objects actually existing4 ,but this is only an instance of the attempt so often made1 to escape from the necessity of abandoning old language after the ideas which it expresses have been exchanged for contrary ones4 ,from the meaning of a name 7we are told7 it is possible to infer physical facts1 provided the name has corresponding to it an existing thing4 ,but if this proviso be necessary1 from which of the two is the inference really drawn8 ,from the existence of a thing having the properties1 or from the existence of a name meaning them8 ,take1 for instance1 any of the definitions laid down as premises in ,euclid's ,elements2 the definition1 let us say1 of a circle4 ,this1 being analyzed1 consists of two propositions2 the one an assumption with respect to a matter of fact1 the other a genuine definition4 8,a figure may exist1 having all the points in the line which bounds it equally distant from a single point within it30 8,any figure possessing this property is called a circle40 ,let us look at one of the demonstrations which are said to depend on this definition1 and observe to which of the two propositions contained in it the demonstration really appeals4 8,about the centre ,a1 describe the circle ,b ,c ,d40 ,here is an assumption that a figure1 such as the definition expresses1 may be described2 which is no other than the postulate1 or covert assumption1 involved in the so-called definition4 ,but whether that figure be called a circle or not is quite immaterial4 ,the purpose would be as well answered1 in all respects except brevity1 were we to say1 8,through the point ,b1 draw a line returning into itself1 of which every point shall be at an equal distance from the point ,a40 ,by this the definition of a circle would be got rid of1 and rendered needless2 but not the postulate implied in it2 without that the demonstration could not stand4 ,the circle being now described1 let us proceed to the consequence4 8,since ,b ,c ,d is a circle1 the radius ,b ,a is equal to the radius ,c ,a40 ,b ,a is equal to ,c ,a1 not because ,b ,c ,d is a circle1 but because ,b ,c ,d is a figure with the radii equal4 ,our warrant for assuming that such a figure about the centre ,a1 with the radius ,b ,a1 may be made to exist1 is the postulate4 ,whether the admissibility of these postulates rests on intuition1 or on proof1 may be a matter of dispute2 but in either case they are the premises on which the theorems depend2 and while these are retained it would make no difference in the certainty of geometrical truths1 though every definition in ,euclid1 and every technical term therein defined1 were laid aside4 ,it is1 perhaps1 superfluous to dwell at so much length on what is so nearly self-evident2 but when a distinction1 obvious as it may appear1 has been confounded1 and by powerful intellects1 it is better to say too much than too little for the purpose of rendering such mistakes impossible in future4 ,i will1 therefore detain the reader while ,i point out one of the absurd consequences flowing from the supposition that definitions1 as such1 are the premises in any of our reasonings1 except such as relate to words only4 ,if this supposition were true1 we might argue correctly from true premises1 and arrive at a false conclusion4 ,we should only have to assume as a premise the definition of a nonentity2 or rather of a name which has no entity corresponding to it4 ,let this1 for instance1 be our definition3 ,a dragon is a serpent breathing flame4 ,this proposition1 considered only as a definition1 is indisputably correct4 ,a dragon is a serpent breathing flame3 the word means that4 ,the tacit assumption1 indeed 7if there were any such understood assertion71 of the existence of an object with properties corresponding to the definition1 would1 in the present instance1 be false4 ,out of this definition we may carve the premises of the following syllogism3 ,a dragon is a thing which breathes flame3 ,a dragon is a serpent3 ,from which the conclusion is1 ,therefore some serpent or serpents breathe flame3 an unexceptionable syllogism in the first mode of the third figure1 in which both premises are true and yet the conclusion false2 which every logician knows to be an absurdity4 ,the conclusion being false and the syllogism correct1 the premises can not be true4 ,but the premises1 considered as parts of a definition1 are true4 ,therefore1 the premises considered as parts of a definition can not be the real ones4 ,the real premises must be-- ,a dragon is a really existing thing which breathes flame3 ,a dragon is a really existing serpent3 which implied premises being false1 the falsity of the conclusion presents no absurdity4 ,if we would determine what conclusion follows from the same ostensible premises when the tacit assumption of real existence is left out1 let us1 according to the recommendation in a previous page1 substitute means for is4 ,we then have-- ,dragon is a word meaning a thing which breathes flame3 ,dragon is a word meaning a serpent3 ,from which the conclusion is1 ,some word or words which mean a serpent1 also mean a thing which breathes flame3 where the conclusion 7as well as the premises7 is true1 and is the only kind of conclusion which can ever follow from a definition1 namely1 a proposition relating to the meaning of words4 ,there is still another shape into which we may transform this syllogism4 ,we may suppose the middle term to be the designation neither of a thing nor of a name1 but of an idea4 ,we then have-- ,the idea of a dragon is an idea of a thing which breathes flame3 ,the idea of a dragon is an idea of a serpent3 ,therefore1 there is an idea of a serpent1 which is an idea of a thing breathing flame4 ,here the conclusion is true1 and also the premises2 but the premises are not definitions4 ,they are propositions affirming that an idea existing in the mind1 includes certain ideal elements4 ,the truth of the conclusion follows from the existence of the psychological phenomenon called the idea of a dragon2 and therefore still from the tacit assumption of a matter of fact47#de7 ,when1 as in this last syllogism1 the conclusion is a proposition respecting an idea1 the assumption on which it depends may be merely that of the existence of an idea4 ,but when the conclusion is a proposition concerning a ,thing1 the postulate involved in the definition which stands as the apparent premise1 is the existence of a thing conformable to the definition1 and not merely of an idea conformable to it4 ,this assumption of real existence we always convey the impression that we intend to make1 when we profess to define any name which is already known to be a name of really existing objects4 ,on this account it is1 that the assumption was not necessarily implied in the definition of a dragon1 while there was no doubt of its being included in the definition of a circle4 #f4 ,one of the circumstances which have contributed to keep up the notion1 that demonstrative truths follow from definitions rather than from the postulates implied in those definitions1 is1 that the postulates1 even in those sciences which are considered to surpass all others in demonstrative certainty1 are not always exactly true4 ,it is not true that a circle exists1 or can be described1 which has all its radii exactly equal4 ,such accuracy is ideal only2 it is not found in nature1 still less can it be realized by art4 ,people had a difficulty1 therefore1 in conceiving that the most certain of all conclusions could rest on premises which1 instead of being certainly true1 are certainly not true to the full extent asserted4 ,this apparent paradox will be examined when we come to treat of ,demonstration2 where we shall be able to show that as much of the postulate is true1 as is required to support as much as is true of the conclusion4 ,philosophers1 however1 to whom this view had not occurred1 or whom it did not satisfy1 have thought it indispensable that there should be found in definitions something more certain1 or at least more accurately true1 than the implied postulate of the real existence of a corresponding object4 ,and this something they flattered themselves they had found1 when they laid it down that a definition is a statement and analysis not of the mere meaning of a word1 nor yet of the nature of a thing1 but of an idea4 ,thus1 the proposition1 8,a circle is a plane figure bounded by a line all the points of which are at an equal distance from a given point within it10 was considered by them1 not as an assertion that any real circle has that property 7which would not be exactly true71 but that we conceive a circle as having it2 that our abstract idea of a circle is an idea of a figure with its radii exactly equal4 ,conformably to this it is said1 that the subject-matter of mathematics1 and of every other demonstrative science1 is not things as they really exist1 but abstractions of the mind4 ,a geometrical line is a line without breadth2 but no such line exists in nature2 it is a notion merely suggested to the mind by its experience of nature4 ,the definition 7it is said7 is a definition of this mental line1 not of any actual line3 and it is only of the mental line1 not of any line existing in nature1 that the theorems of geometry are accurately true4 ,allowing this doctrine respecting the nature of demonstrative truth to be correct 7which1 in a subsequent place1 ,i shall endeavor to prove that it is not72 even on that supposition1 the conclusions which seem to follow from a definition1 do not follow from the definition as such1 but from an implied postulate4 ,even if it be true that there is no object in nature answering to the definition of a line1 and that the geometrical properties of lines are not true of any lines in nature1 but only of the idea of a line2 the definition1 at all events1 postulates the real existence of such an idea3 it assumes that the mind can frame1 or rather has framed1 the notion of length without breadth1 and without any other sensible property whatever4 ,to me1 indeed1 it appears that the mind can not form any such notion2 it can not conceive length without breadth2 it can only1 in contemplating objects1 attend to their length1 exclusively of their other sensible qualities1 and so determine what properties may be predicated of them in virtue of their length alone4 ,if this be true1 the postulate involved in the geometrical definition of a line1 is the real existence1 not of length without breadth1 but merely of length1 that is1 of long objects4 ,this is quite enough to support all the truths of geometry1 since every property of a geometrical line is really a property of all physical objects in so far as possessing length4 ,but even what ,i hold to be the false doctrine on the subject1 leaves the conclusion that our reasonings are grounded on the matters of fact postulated in definitions1 and not on the definitions themselves1 entirely unaffected2 and accordingly this conclusion is one which ,i have in common with ,dr4 ,whewell1 in his ,philosophy of the ,inductive ,sciences3 though1 on the nature of demonstrative truth1 ,dr4 ,whewell's opinions are greatly at variance with mine4 ,and here1 as in many other instances1 ,i gladly acknowledge that his writings are eminently serviceable in clearing from confusion the initial steps in the analysis of the mental processes1 even where his views respecting the ultimate analysis are such as 7though with unfeigned respect7 ,i can not but regard as fundamentally erroneous4 #g4 ,although1 according to the opinion here presented1 ,definitions are properly of names only1 and not of things1 it does not follow from this that definitions are arbitrary4 ,how to define a name1 may not only be an inquiry of considerable difficulty and intricacy1 but may involve considerations going deep into the nature of the things which are denoted by the name4 ,such1 for instance1 are the inquiries which form the subjects of the most important of ,plato's ,dialogues2 as1 8,what is rhetoric80 the topic of the ,gorgias1 or1 8,what is justice80 that of the ,republic4 ,such1 also1 is the question scornfully asked by ,pilate1 8,what is truth80 and the fundamental question with speculative moralists in all ages1 8,what is virtue80 ,it would be a mistake to represent these difficult and noble inquiries as having nothing in view beyond ascertaining the conventional meaning of a name4 ,they are inquiries not so much to determine what is1 as what should be1 the meaning of a name2 which1 like other practical questions of terminology1 requires for its solution that we should enter1 and sometimes enter very deeply1 into the properties not merely of names but of the things named4 ,although the meaning of every concrete general name resides in the attributes which it connotes1 the objects were named before the attributes2 as appears from the fact that in all languages1 abstract names are mostly compounds or other derivatives of the concrete names which correspond to them4 ,connotative names1 therefore1 were1 after proper names1 the first which were used3 and in the simpler cases1 no doubt1 a distinct connotation was present to the minds of those who first used the name1 and was distinctly intended by them to be conveyed by it4 ,the first person who used the word white1 as applied to snow or to any other object1 knew1 no doubt1 very well what quality he intended to predicate1 and had a perfectly distinct conception in his mind of the attribute signified by the name4 ,but where the resemblances and differences on which our classifications are founded are not of this palpable and easily determinable kind2 especially where they consist not in any one quality but in a number of qualities1 the effects of which1 being blended together1 are not very easily discriminated1 and referred each to its true source2 it often happens that names are applied to namable objects1 with no distinct connotation present to the minds of those who apply them4 ,they are only influenced by a general resemblance between the new object and all or some of the old familiar objects which they have been accustomed to call by that name4 ,this1 as we have seen1 is the law which even the mind of the philosopher must follow1 in giving names to the simple elementary feelings of our nature3 but1 where the things to be named are complex wholes1 a philosopher is not content with noticing a general resemblance2 he examines what the resemblance consists in3 and he only gives the same name to things which resemble one another in the same definite particulars4 ,the philosopher1 therefore1 habitually employs his general names with a definite connotation4 ,but language was not made1 and can only in some small degree be mended1 by philosophers4 ,in the minds of the real arbiters of language1 general names1 especially where the classes they denote can not be brought before the tribunal of the outward senses to be identified and discriminated1 connote little more than a vague gross resemblance to the things which they were earliest1 or have been most1 accustomed to call by those names4 ,when1 for instance1 ordinary persons predicate the words just or unjust of any action1 noble or mean of any sentiment1 expression1 or demeanor1 statesman or charlatan of any personage figuring in politics1 do they mean to affirm of those various subjects any determinate attributes1 of whatever kind8 ,no3 they merely recognize1 as they think1 some likeness1 more or less vague and loose1 between these and some other things which they have been accustomed to denominate or to hear denominated by those appellations4 ,language1 as ,sir ,james ,mackintosh used to say of governments1 8is not made1 but grows40 ,a name is not imposed at once and by previous purpose upon a class of objects1 but is first applied to one thing1 and then extended by a series of transitions to another and another4 ,by this process 7as has been remarked by several writers1 and illustrated with great force and clearness by ,dugald ,stewart in his ,philosophical ,essays7 a name not unfrequently passes by successive links of resemblance from one object to another1 until it becomes applied to things having nothing in common with the first things to which the name was given2 which1 however1 do not1 for that reason1 drop the name2 so that it at last denotes a confused huddle of objects1 having nothing whatever in common2 and connotes nothing1 not even a vague and general resemblance4 ,when a name has fallen into this state1 in which by predicating it of any object we assert literally nothing about the object1 it has become unfit for the purposes either of thought or of the communication of thought2 and can only be made serviceable by stripping it of some part of its multifarious denotation1 and confining it to objects possessed of some attributes in common1 which it may be made to connote4 ,such are the inconveniences of a language which 8is not made1 but grows40 ,like the governments which are in a similar case1 it may be compared to a road which is not made but has made itself3 it requires continual mending in order to be passable4 ,from this it is already evident1 why the question respecting the definition of an abstract name is often one of so much difficulty4 ,the question1 ,what is justice8 is1 in other words1 ,what is the attribute which mankind mean to predicate when they call an action just8 ,to which the first answer is1 that having come to no precise agreement on the point1 they do not mean to predicate distinctly any attribute at all4 ,nevertheless1 all believe that there is some common attribute belonging to all the actions which they are in the habit of calling just4 ,the question then must be1 whether there is any such common attribute8 and1 in the first place1 whether mankind agree sufficiently with one another as to the particular actions which they do or do not call just1 to render the inquiry1 what quality those actions have in common1 a possible one3 if so1 whether the actions really have any quality in common2 and if they have1 what it is4 ,of these three1 the first alone is an inquiry into usage and convention2 the other two are inquiries into matters of fact4 ,and if the second question 7whether the actions form a class at all7 has been answered negatively1 there remains a fourth1 often more arduous than all the rest1 namely1 how best to form a class artificially1 which the name may denote4 ,and here it is fitting to remark1 that the study of the spontaneous growth of languages is of the utmost importance to those who would logically remodel them4 ,the classifications rudely made by established language1 when retouched1 as they almost all require to be1 by the hands of the logician1 are often themselves excellently suited to his purposes4 ,as compared with the classifications of a philosopher1 they are like the customary law of a country1 which has grown up as it were spontaneously1 compared with laws methodized and digested into a code3 the former are a far less perfect instrument than the latter2 but being the result of a long1 though unscientific1 course of experience1 they contain a mass of materials which may be made very usefully available in the formation of the systematic body of written law4 ,in like manner1 the established grouping of objects under a common name1 even when founded only on a gross and general resemblance1 is evidence1 in the first place1 that the resemblance is obvious1 and therefore considerable2 and1 in the next place1 that it is a resemblance which has struck great numbers of persons during a series of years and ages4 ,even when a name1 by successive extensions1 has come to be applied to things among which there does not exist this gross resemblance common to them all1 still at every step in its progress we shall find such a resemblance4 ,and these transitions of the meaning of words are often an index to real connections between the things denoted by them1 which might otherwise escape the notice of thinkers2 of those at least who1 from using a different language1 or from any difference in their habitual associations1 have fixed their attention in preference on some other aspect of the things4 ,the history of philosophy abounds in examples of such oversights1 committed for want of perceiving the hidden link that connected together the seemingly disparate meanings of some ambiguous word47#df7 ,whenever the inquiry into the definition of the name of any real object consists of any thing else than a mere comparison of authorities1 we tacitly assume that a meaning must be found for the name1 compatible with its continuing to denote1 if possible all1 but at any rate the greater or the more important part1 of the things of which it is commonly predicated4 ,the inquiry1 therefore1 into the definition1 is an inquiry into the resemblances and differences among those things3 whether there be any resemblance running through them all2 if not1 through what portion of them such a general resemblance can be traced3 and finally1 what are the common attributes1 the possession of which gives to them all1 or to that portion of them1 the character of resemblance which has led to their being classed together4 ,when these common attributes have been ascertained and specified1 the name which belongs in common to the resembling objects acquires a distinct instead of a vague connotation2 and by possessing this distinct connotation1 becomes susceptible of definition4 ,in giving a distinct connotation to the general name1 the philosopher will endeavor to fix upon such attributes as1 while they are common to all the things usually denoted by the name1 are also of greatest importance in themselves2 either directly1 or from the number1 the conspicuousness1 or the interesting character1 of the consequences to which they lead4 ,he will select1 as far as possible1 such differenti as lead to the greatest number of interesting propria4 ,for these1 rather than the more obscure and recondite qualities on which they often depend1 give that general character and aspect to a set of objects1 which determine the groups into which they naturally fall4 ,but to penetrate to the more hidden agreement on which these obvious and superficial agreements depend1 is often one of the most difficult of scientific problems4 ,as it is among the most difficult1 so it seldom fails to be among the most important4 ,and since upon the result of this inquiry respecting the causes of the properties of a class of things1 there incidentally depends the question what shall be the meaning of a word2 some of the most profound and most valuable investigations which philosophy presents to us1 have been introduced by1 and have offered themselves under the guise of1 inquiries into the definition of a name4 ,book ,,ii4 ,,of ,,reasoning4 1 1 1 4 1 1 4 1 2 1 4--,,arist41 ,analyt4 ,prior41 l4 i41 cap4 #d4 ,chapter ,i4 ,of ,inference1 ,or ,reasoning1 ,in ,general4 #a4 ,in the preceding ,book1 we have been occupied not with the nature of ,proof1 but with the nature of ,assertion3 the import conveyed by a ,proposition1 whether that ,proposition be true or false2 not the means by which to discriminate true from false ,propositions4 ,the proper subject1 however1 of ,logic is ,proof4 ,before we could understand what ,proof is1 it was necessary to understand what that is to which proof is applicable2 what that is which can be a subject of belief or disbelief1 of affirmation or denial2 what1 in short1 the different kinds of ,propositions assert4 ,this preliminary inquiry we have prosecuted to a definite result4 ,assertion1 in the first place1 relates either to the meaning of words1 or to some property of the things which words signify4 ,assertions respecting the meaning of words1 among which definitions are the most important1 hold a place1 and an indispensable one1 in philosophy2 but as the meaning of words is essentially arbitrary1 this class of assertions are not susceptible of truth or falsity1 nor therefore of proof or disproof4 ,assertions respecting ,things1 or what may be called ,real ,propositions1 in contradistinction to verbal ones1 are of various sorts4 ,we have analyzed the import of each sort1 and have ascertained the nature of the things they relate to1 and the nature of what they severally assert respecting those things4 ,we found that whatever be the form of the proposition1 and whatever its nominal subject or predicate1 the real subject of every proposition is some one or more facts or phenomena of consciousness1 or some one or more of the hidden causes or powers to which we ascribe those facts2 and that what is predicated or asserted1 either in the affirmative or negative1 of those phenomena or those powers1 is always either ,existence1 ,order in ,place1 ,order in ,time1 ,causation1 or ,resemblance4 ,this1 then1 is the theory of the ,import of ,propositions1 reduced to its ultimate elements3 but there is another and a less abstruse expression for it1 which1 though stopping short in an earlier stage of the analysis1 is sufficiently scientific for many of the purposes for which such a general expression is required4 ,this expression recognizes the commonly received distinction between ,subject and ,attribute1 and gives the following as the analysis of the meaning of propositions3--,every ,proposition asserts1 that some given subject does or does not possess some attribute2 or that some attribute is or is not 7either in all or in some portion of the subjects in which it is met with7 conjoined with some other attribute4 ,we shall now for the present take our leave of this portion of our inquiry1 and proceed to the peculiar problem of the ,science of ,logic1 namely1 how the assertions1 of which we have analyzed the import1 are proved or disproved2 such of them1 at least1 as1 not being amenable to direct consciousness or intuition1 are appropriate subjects of proof4 ,we say of a fact or statement1 that it is proved1 when we believe its truth by reason of some other fact or statement from which it is said to follow4 ,most of the propositions1 whether affirmative or negative1 universal1 particular1 or singular1 which we believe1 are not believed on their own evidence1 but on the ground of something previously assented to1 from which they are said to be inferred4 ,to infer a proposition from a previous proposition or propositions2 to give credence to it1 or claim credence for it1 as a conclusion from something else2 is to reason1 in the most extensive sense of the term4 ,there is a narrower sense1 in which the name reasoning is confined to the form of inference which is termed ratiocination1 and of which the syllogism is the general type4 ,the reasons for not conforming to this restricted use of the term were stated in an earlier stage of our inquiry1 and additional motives will be suggested by the considerations on which we are now about to enter4 #b4 ,in proceeding to take into consideration the cases in which inferences can legitimately be drawn1 we shall first mention some cases in which the inference is apparent1 not real2 and which require notice chiefly that they may not be confounded with cases of inference properly so called4 ,this occurs when the proposition ostensibly inferred from another1 appears on analysis to be merely a repetition of the same1 or part of the same1 assertion1 which was contained in the first4 ,all the cases mentioned in books of ,logic as examples of equipollency or equivalence of propositions1 are of this nature4 ,thus1 if we were to argue1 ,no man is incapable of reason1 for every man is rational2 or1 ,all men are mortal1 for no man is exempt from death2 it would be plain that we were not proving the proposition1 but only appealing to another mode of wording it1 which may or may not be more readily comprehensible by the hearer1 or better adapted to suggest the real proof1 but which contains in itself no shadow of proof4 ,another case is where1 from a universal proposition1 we affect to infer another which differs from it only in being particular3 as ,all ,a is ,b1 therefore ,some ,a is ,b3 ,no ,a is ,b1 therefore ,some ,a is not ,b4 ,this1 too1 is not to conclude one proposition from another1 but to repeat a second time something which had been asserted at first2 with the difference1 that we do not here repeat the whole of the previous assertion1 but only an indefinite part of it4 ,a third case is where1 the antecedent having affirmed a predicate of a given subject1 the consequent affirms of the same subject something already connoted by the former predicate3 as1 ,socrates is a man1 therefore ,socrates is a living creature2 where all that is connoted by living creature was affirmed of ,socrates when he was asserted to be a man4 ,if the propositions are negative1 we must invert their order1 thus3 ,socrates is not a living creature1 therefore he is not a man2 for if we deny the less1 the greater1 which includes it1 is already denied by implication4 ,these1 therefore1 are not really cases of inference2 and yet the trivial examples by which1 in manuals of ,logic1 the rules of the syllogism are illustrated1 are often of this ill-chosen kind2 formal demonstrations of conclusions to which whoever understands the terms used in the statement of the data1 has already1 and consciously1 assented47#dg7 ,the most complex case of this sort of apparent inference is what is called the ,conversion of propositions2 which consists in turning the predicate into a subject1 and the subject into a predicate1 and framing out of the same terms thus reversed1 another proposition1 which must be true if the former is true4 ,thus1 from the particular affirmative proposition1 ,some ,a is ,b1 we may infer that ,some ,b is ,a4 ,from the universal negative1 ,no ,a is ,b1 we may conclude that ,no ,b is ,a4 ,from the universal affirmative proposition1 ,all ,a is ,b1 it can not be inferred that all ,b is ,a2 though all water is liquid1 it is not implied that all liquid is water2 but it is implied that some liquid is so2 and hence the proposition1 ,all ,a is ,b1 is legitimately convertible into ,some ,b is ,a4 ,this process1 which converts a universal proposition into a particular1 is termed conversion per accidens4 ,from the proposition1 ,some ,a is not ,b1 we can not even infer that some ,b is not ,a2 though some men are not ,englishmen1 it does not follow that some ,englishmen are not men4 ,the only mode usually recognized of converting a particular negative proposition1 is in the form1 ,some ,a is not ,b1 therefore something which is not ,b is ,a2 and this is termed conversion by contraposition4 ,in this case1 however1 the predicate and subject are not merely reversed1 but one of them is changed4 ,instead of ,a and ,b1 the terms of the new proposition are a thing which is not ,b1 and ,a4 ,the original proposition1 ,some ,a is not ,b1 is first changed into a proposition equipollent with it1 ,some ,a is 8a thing which is not ,b20 and the proposition1 being now no longer a particular negative1 but a particular affirmative1 admits of conversion in the first mode1 or as it is called1 simple conversion47#dh7 ,in all these cases there is not really any inference2 there is in the conclusion no new truth1 nothing but what was already asserted in the premises1 and obvious to whoever apprehends them4 ,the fact asserted in the conclusion is either the very same fact1 or part of the fact1 asserted in the original proposition4 ,this follows from our previous analysis of the ,import of ,propositions4 ,when we say1 for example1 that some lawful sovereigns are tyrants1 what is the meaning of the assertion8 ,that the attributes connoted by the term 8lawful sovereign10 and the attributes connoted by the term 8tyrant10 sometimes co-exist in the same individual4 ,now this is also precisely what we mean1 when we say that some tyrants are lawful sovereigns2 which1 therefore1 is not a second proposition inferred from the first1 any more than the ,english translation of ,euclid's ,elements is a collection of theorems different from and consequences of1 those contained in the ,greek original4 ,again1 if we assert that no great general is a rash man1 we mean that the attributes connoted by 8great general10 and those connoted by 8rash10 never co-exist in the same subject2 which is also the exact meaning which would be expressed by saying1 that no rash man is a great general4 ,when we say that all quadrupeds are warm-blooded1 we assert1 not only that the attributes connoted by 8quadruped0 and those connoted by 8warm-blooded0 sometimes co-exist1 but that the former never exist without the latter3 now the proposition1 ,some warm-blooded creatures are quadrupeds1 expresses the first half of this meaning1 dropping the latter half2 and therefore has been already affirmed in the antecedent proposition1 ,all quadrupeds are warm-blooded4 ,but that all warm-blooded creatures are quadrupeds1 or1 in other words1 that the attributes connoted by 8warm-blooded0 never exist without those connoted by 8quadruped10 has not been asserted1 and can not be inferred4 ,in order to re-assert1 in an inverted form1 the whole of what was affirmed in the proposition1 ,all quadrupeds are warm-blooded1 we must convert it by contraposition1 thus1 ,nothing which is not warm-blooded is a quadruped4 ,this proposition1 and the one from which it is derived1 are exactly equivalent1 and either of them may be substituted for the other2 for1 to say that when the attributes of a quadruped are present1 those of a warm-blooded creature are present1 is to say that when the latter are absent the former are absent4 ,in a manual for young students1 it would be proper to dwell at greater length on the conversion and equipollency of propositions4 ,for though that can not be called reasoning or inference which is a mere re-assertion in different words of what had been asserted before1 there is no more important intellectual habit1 nor any the cultivation of which falls more strictly within the province of the art of logic1 than that of discerning rapidly and surely the identity of an assertion when disguised under diversity of language4 ,that important chapter in logical treatises which relates to the ,opposition of ,propositions1 and the excellent technical language which logic provides for distinguishing the different kinds or modes of opposition1 are of use chiefly for this purpose4 ,such considerations as these1 that contrary propositions may both be false1 but can not both be true2 that subcontrary propositions may both be true1 but can not both be false2 that of two contradictory propositions one must be true and the other false2 that of two subalternate propositions the truth of the universal proves the truth of the particular1 and the falsity of the particular proves the falsity of the universal1 but not vic versa27#di7 are apt to appear1 at first sight1 very technical and mysterious1 but when explained1 seem almost too obvious to require so formal a statement1 since the same amount of explanation which is necessary to make the principles intelligible1 would enable the truths which they convey to be apprehended in any particular case which can occur4 ,in this respect1 however1 these axioms of logic are on a level with those of mathematics4 ,that things which are equal to the same thing are equal to one another1 is as obvious in any particular case as it is in the general statement3 and if no such general maxim had ever been laid down1 the demonstrations in ,euclid would never have halted for any difficulty in stepping across the gap which this axiom at present serves to bridge over4 ,yet no one has ever censured writers on geometry1 for placing a list of these elementary generalizations at the head of their treatises1 as a first exercise to the learner of the faculty which will be required in him at every step1 that of apprehending a general truth4 ,and the student of logic1 in the discussion even of such truths as we have cited above1 acquires habits of circumspect interpretation of words1 and of exactly measuring the length and breadth of his assertions1 which are among the most indispensable conditions of any considerable mental attainment1 and which it is one of the primary objects of logical discipline to cultivate4 #c4 ,having noticed1 in order to exclude from the province of ,reasoning or ,inference properly so called1 the cases in which the progression from one truth to another is only apparent1 the logical consequent being a mere repetition of the logical antecedent2 we now pass to those which are cases of inference in the proper acceptation of the term1 those in which we set out from known truths1 to arrive at others really distinct from them4 ,reasoning1 in the extended sense in which ,i use the term1 and in which it is synonymous with ,inference1 is popularly said to be of two kinds3 reasoning from particulars to generals1 and reasoning from generals to particulars2 the former being called ,induction1 the latter ,ratiocination or ,syllogism4 ,it will presently be shown that there is a third species of reasoning1 which falls under neither of these descriptions1 and which1 nevertheless1 is not only valid1 but is the foundation of both the others4 ,it is necessary to observe1 that the expressions1 reasoning from particulars to generals1 and reasoning from generals to particulars1 are recommended by brevity rather than by precision1 and do not adequately mark1 without the aid of a commentary1 the distinction between ,induction 7in the sense now adverted to7 and ,ratiocination4 ,the meaning intended by these expressions is1 that ,induction is inferring a proposition from propositions less general than itself1 and ,ratiocination is inferring a proposition from propositions equally or more general4 ,when1 from the observation of a number of individual instances1 we ascend to a general proposition1 or when1 by combining a number of general propositions1 we conclude from them another proposition still more general1 the process1 which is substantially the same in both instances1 is called ,induction4 ,when from a general proposition1 not alone 7for from a single proposition nothing can be concluded which is not involved in the terms71 but by combining it with other propositions1 we infer a proposition of the same degree of generality with itself1 or a less general proposition1 or a proposition merely individual1 the process is ,ratiocination4 ,when1 in short1 the conclusion is more general than the largest of the premises1 the argument is commonly called ,induction2 when less general1 or equally general1 it is ,ratiocination4 ,as all experience begins with individual cases1 and proceeds from them to generals1 it might seem most conformable to the natural order of thought that ,induction should be treated of before we touch upon ,ratiocination4 ,it will1 however1 be advantageous1 in a science which aims at tracing our acquired knowledge to its sources1 that the inquirer should commence with the latter rather than with the earlier stages of the process of constructing our knowledge2 and should trace derivative truths backward to the truths from which they are deduced1 and on which they depend for their evidence1 before attempting to point out the original spring from which both ultimately take their rise4 ,the advantages of this order of proceeding in the present instance will manifest themselves as we advance1 in a manner superseding the necessity of any further justification or explanation4 ,of ,induction1 therefore1 we shall say no more at present1 than that it at least is1 without doubt1 a process of real inference4 ,the conclusion in an induction embraces more than is contained in the premises4 ,the principle or law collected from particular instances1 the general proposition in which we embody the result of our experience1 covers a much larger extent of ground than the individual experiments which form its basis4 ,a principle ascertained by experience1 is more than a mere summing up of what has been specifically observed in the individual cases which have been examined2 it is a generalization grounded on those cases1 and expressive of our belief1 that what we there found true is true in an indefinite number of cases which we have not examined1 and are never likely to examine4 ,the nature and grounds of this inference1 and the conditions necessary to make it legitimate1 will be the subject of discussion in the ,third ,book3 but that such inference really takes place is not susceptible of question4 ,in every induction we proceed from truths which we knew1 to truths which we did not know2 from facts certified by observation1 to facts which we have not observed1 and even to facts not capable of being now observed2 future facts1 for example2 but which we do not hesitate to believe on the sole evidence of the induction itself4 ,induction1 then1 is a real process of ,reasoning or ,inference4 ,whether1 and in what sense1 as much can be said of the ,syllogism1 remains to be determined by the examination into which we are about to enter4 ,chapter ,,ii4 ,of ,ratiocination1 ,or ,syllogism4 #a4 ,the analysis of the ,syllogism has been so accurately and fully performed in the common manuals of ,logic1 that in the present work1 which is not designed as a manual1 it is sufficient to recapitulate1 memori caus1 the leading results of that analysis1 as a foundation for the remarks to be afterward made on the functions of the ,syllogism1 and the place which it holds in science4 ,to a legitimate syllogism it is essential that there should be three1 and no more than three1 propositions1 namely1 the conclusion1 or proposition to be proved1 and two other propositions which together prove it1 and which are called the premises4 ,it is essential that there should be three1 and no more than three1 terms1 namely1 the subject and predicate of the conclusion1 and another called the middle term1 which must be found in both premises1 since it is by means of it that the other two terms are to be connected together4 ,the predicate of the conclusion is called the major term of the syllogism2 the subject of the conclusion is called the minor term4 ,as there can be but three terms1 the major and minor terms must each be found in one1 and only one1 of the premises1 together with the middle term which is in them both4 ,the premise which contains the middle term and the major term is called the major premise2 that which contains the middle term and the minor term is called the minor premise4 ,syllogisms are divided by some logicians into three figures1 by others into four1 according to the position of the middle term1 which may either be the subject in both premises1 the predicate in both1 or the subject in one and the predicate in the other4 ,the most common case is that in which the middle term is the subject of the major premise and the predicate of the minor4 ,this is reckoned as the first figure4 ,when the middle term is the predicate in both premises1 the syllogism belongs to the second figure2 when it is the subject in both1 to the third4 ,in the fourth figure the middle term is the subject of the minor premise and the predicate of the major4 ,those writers who reckon no more than three figures1 include this case in the first4 ,each figure is divided into moods1 according to what are called the quantity and quality of the propositions1 that is1 according as they are universal or particular1 affirmative or negative4 ,the following are examples of all the legitimate moods1 that is1 all those in which the conclusion correctly follows from the premises4 ,a is the minor term1 ,c the major1 ,b the middle term4 ,,first ,,figure4 ,all ,b is ,c ,no ,b is ,c ,all ,b is ,c ,no ,b is ,c ,all ,a is ,b ,all ,a is ,b ,some ,a is ,b ,some ,a is ,b therefore therefore therefore therefore ,all ,a is ,c ,no ,a is ,c ,some ,a is ,c ,some ,a is not ,c ,,second ,,figure4 ,no ,c is ,b ,all ,c is ,b ,no ,c is ,b ,all ,c is ,b ,all ,a is ,b ,no ,a is ,b ,some ,a is ,b ,some ,a is not ,b therefore therefore therefore therefore ,no ,a is ,c ,no ,a is ,c ,some ,a is not ,c ,some ,a is not ,c ,,third ,,figure4 ,all ,b is ,no ,b is ,c ,some ,b is ,all ,b is ,some ,b is ,no ,b is ,c ,c ,c ,c not ,c ,all ,b is ,all ,b is ,all ,b is ,some ,b is ,all ,b is ,some ,b is ,a ,a ,a ,a ,a ,a therefore therefore therefore therefore therefore therefore ,some ,a is ,some ,a is ,some ,a is ,some ,a is ,some ,a is ,some ,a is ,c not ,c ,c ,c not ,c not ,c ,,fourth ,,figure4 ,all ,c is ,b ,all ,c is ,b ,some ,c is ,b ,no ,c is ,b ,no ,c is ,b ,all ,b is ,a ,no ,b is ,a ,all ,b is ,a ,all ,b is ,a ,some ,b is ,a therefore therefore therefore therefore therefore ,some ,a is ,c ,some ,a is ,some ,a is ,c ,some ,a is ,some ,a is not ,c not ,c not ,c ,in these exemplars1 or blank forms for making syllogisms1 no place is assigned to singular propositions2 not1 of course1 because such propositions are not used in ratiocination1 but because1 their predicate being affirmed or denied of the whole of the subject1 they are ranked1 for the purposes of the syllogism1 with universal propositions4 ,thus1 these two syllogisms-- ,all men are mortal1 ,all men are mortal1 ,all kings are men1 ,socrates is a man1 therefore therefore ,all kings are mortal1 ,socrates is mortal1 are arguments precisely similar1 and are both ranked in the first mood of the first figure47#ej7 ,the reasons why syllogisms in any of the above forms are legitimate1 that is1 why1 if the premises are true1 the conclusion must inevitably be so1 and why this is not the case in any other possible mood 7that is1 in any other combination of universal and particular1 affirmative and negative propositions71 any person taking interest in these inquiries may be presumed to have either learned from the common-school books of the syllogistic logic1 or to be capable of discovering for himself4 ,the reader may1 however1 be referred1 for every needful explanation1 to ,archbishop ,whately's ,elements of ,logic1 where he will find stated with philosophical precision1 and explained with remarkable perspicuity1 the whole of the common doctrine of the syllogism4 ,all valid ratiocination2 all reasoning by which1 from general propositions previously admitted1 other propositions equally or less general are inferred2 may be exhibited in some of the above forms4 ,the whole of ,euclid1 for example1 might be thrown without difficulty into a series of syllogisms1 regular in mood and figure4 ,though a syllogism framed according to any of these formul is a valid argument1 all correct ratiocination admits of being stated in syllogisms of the first figure alone4 ,the rules for throwing an argument in any of the other figures into the first figure1 are called rules for the reduction of syllogisms4 ,it is done by the conversion of one or other1 or both1 of the premises4 ,thus an argument in the first mood of the second figure1 as-- ,no ,c is ,b ,all ,a is ,b therefore ,no ,a is ,c1 may be reduced as follows4 ,the proposition1 ,no ,c is ,b1 being a universal negative1 admits of simple conversion1 and may be changed into ,no ,b is ,c1 which1 as we showed1 is the very same assertion in other words--the same fact differently expressed4 ,this transformation having been effected1 the argument assumes the following form3 ,no ,b is ,c ,all ,a is ,b therefore ,no ,a is ,c1 which is a good syllogism in the second mood of the first figure4 ,again1 an argument in the first mood of the third figure must resemble the following3 ,all ,b is ,c ,all ,b is ,a therefore ,some ,a is ,c1 where the minor premise1 ,all ,b is ,a1 conformably to what was laid down in the last chapter respecting universal affirmatives1 does not admit of simple conversion1 but may be converted per accidens1 thus1 ,some ,a is ,b2 which1 though it does not express the whole of what is asserted in the proposition ,all ,b is ,a1 expresses1 as was formerly shown1 part of it1 and must therefore be true if the whole is true4 ,we have1 then1 as the result of the reduction1 the following syllogism in the third mood of the first figure3 ,all ,b is ,c ,some ,a is ,b1 from which it obviously follows1 that ,some ,a is ,c4 ,in the same manner1 or in a manner on which after these examples it is not necessary to enlarge1 every mood of the second1 third1 and fourth figures may be reduced to some one of the four moods of the first4 ,in other words1 every conclusion which can be proved in any of the last three figures1 may be proved in the first figure from the same premises1 with a slight alteration in the mere manner of expressing them4 ,every valid ratiocination1 therefore1 may be stated in the first figure1 that is1 in one of the following forms3 ,every ,b is ,c ,no ,b is ,c ,all ,a is ,b1 ,all ,a is ,b1 ,some ,a is ,b1 ,some ,a is ,b1 therefore therefore ,all ,a is ,c4 ,no ,a is ,c4 ,some ,a is ,c4 ,some ,a is not ,c4 ,or1 if more significant symbols are preferred3 ,to prove an affirmative1 the argument must admit of being stated in this form3 ,all animals are mortal2 ,all men_/,some men_/,socrates are animals2 therefore ,all men_/,some men_/,socrates are mortal4 ,to prove a negative1 the argument must be capable of being expressed in this form3 ,no one who is capable of self-control is necessarily vicious2 ,no one who is capable of self-control is necessarily vicious2 ,all negroes_/,some negroes_/,mr4 ,a's negro are capable of self-control2 therefore ,no negroes are_/,some negroes are not_/,mr4 ,a's negro is not necessarily vicious4 ,though all ratiocination admits of being thrown into one or the other of these forms1 and sometimes gains considerably by the transformation1 both in clearness and in the obviousness of its consequence2 there are1 no doubt1 cases in which the argument falls more naturally into one of the other three figures1 and in which its conclusiveness is more apparent at the first glance in those figures1 than when reduced to the first4 ,thus1 if the proposition were that pagans may be virtuous1 and the evidence to prove it were the example of ,aristides2 a syllogism in the third figure1 ,aristides was virtuous1 ,aristides was a pagan1 therefore ,some pagan was virtuous1 would be a more natural mode of stating the argument1 and would carry conviction more instantly home1 than the same ratiocination strained into the first figure1 thus-- ,aristides was virtuous1 ,some pagan was ,aristides1 therefore ,some pagan was virtuous4 ,a ,german philosopher1 ,lambert1 whose ,neues ,organon 7published in the year #agfd7 contains among other things one of the most elaborate and complete expositions which had ever been made of the syllogistic doctrine1 has expressly examined what sort of arguments fall most naturally and suitably into each of the four figures2 and his investigation is characterized by great ingenuity and clearness of thought47#ea7 ,the argument1 however1 is one and the same1 in whichever figure it is expressed2 since1 as we have already seen1 the premises of a syllogism in the second1 third1 or fourth figure1 and those of the syllogism in the first figure to which it may be reduced1 are the same premises in every thing except language1 or1 at least1 as much of them as contributes to the proof of the conclusion is the same4 ,we are therefore at liberty1 in conformity with the general opinion of logicians1 to consider the two elementary forms of the first figure as the universal types of all correct ratiocination2 the one1 when the conclusion to be proved is affirmative1 the other1 when it is negative2 even though certain arguments may have a tendency to clothe themselves in the forms of the second1 third1 and fourth figures2 which1 however1 can not possibly happen with the only class of arguments which are of first-rate scientific importance1 those in which the conclusion is a universal affirmative1 such conclusions being susceptible of proof in the first figure alone47#eb7 #b4 ,on examining1 then1 these two general formul1 we find that in both of them1 one premise1 the major1 is a universal proposition2 and according as this is affirmative or negative1 the conclusion is so too4 ,all ratiocination1 therefore1 starts from a general proposition1 principle1 or assumption3 a proposition in which a predicate is affirmed or denied of an entire class2 that is1 in which some attribute1 or the negation of some attribute1 is asserted of an indefinite number of objects distinguished by a common characteristic1 and designated1 in consequence1 by a common name4 ,the other premise is always affirmative1 and asserts that something 7which may be either an individual1 a class1 or part of a class7 belongs to1 or is included in1 the class respecting which something was affirmed or denied in the major premise4 ,it follows that the attribute affirmed or denied of the entire class may 7if that affirmation or denial was correct7 be affirmed or denied of the object or objects alleged to be included in the class3 and this is precisely the assertion made in the conclusion4 ,whether or not the foregoing is an adequate account of the constituent parts of the syllogism1 will be presently considered2 but as far as it goes it is a true account4 ,it has accordingly been generalized1 and erected into a logical maxim1 on which all ratiocination is said to be founded1 insomuch that to reason1 and to apply the maxim1 are supposed to be one and the same thing4 ,the maxim is1 ,that whatever can be affirmed 7or denied7 of a class1 may be affirmed 7or denied7 of every thing included in the class4 ,this axiom1 supposed to be the basis of the syllogistic theory1 is termed by logicians the dictum de omni et nullo4 ,this maxim1 however1 when considered as a principle of reasoning1 appears suited to a system of metaphysics once indeed generally received1 but which for the last two centuries has been considered as finally abandoned1 though there have not been wanting in our own day attempts at its revival4 ,so long as what are termed ,universals were regarded as a peculiar kind of substances1 having an objective existence distinct from the individual objects classed under them1 the dictum de omni conveyed an important meaning2 because it expressed the intercommunity of nature1 which it was necessary on that theory that we should suppose to exist between those general substances and the particular substances which were subordinated to them4 ,that every thing predicable of the universal was predicable of the various individuals contained under it1 was then no identical proposition1 but a statement of what was conceived as a fundamental law of the universe4 ,the assertion that the entire nature and properties of the substantia secunda formed part of the nature and properties of each of the individual substances called by the same name2 that the properties of ,man1 for example1 were properties of all men2 was a proposition of real significance when man did not mean all men1 but something inherent in men1 and vastly superior to them in dignity4 ,now1 however1 when it is known that a class1 a universal1 a genus or species1 is not an entity per se1 but neither more nor less than the individual substances themselves which are placed in the class1 and that there is nothing real in the matter except those objects1 a common name given to them1 and common attributes indicated by the name2 what1 ,i should be glad to know1 do we learn by being told1 that whatever can be affirmed of a class1 may be affirmed of every object contained in the class8 ,the class is nothing but the objects contained in it3 and the dictum de omni merely amounts to the identical proposition1 that whatever is true of certain objects1 is true of each of those objects4 ,if all ratiocination were no more than the application of this maxim to particular cases1 the syllogism would indeed be1 what it has so often been declared to be1 solemn trifling4 ,the dictum de omni is on a par with another truth1 which in its time was also reckoned of great importance1 8,whatever is1 is40 ,to give any real meaning to the dictum de omni1 we must consider it not as an axiom1 but as a definition2 we must look upon it as intended to explain1 in a circuitous and paraphrastic manner1 the meaning of the word class4 ,an error which seemed finally refuted and dislodged from thought1 often needs only put on a new suit of phrases1 to be welcomed back to its old quarters1 and allowed to repose unquestioned for another cycle of ages4 ,modern philosophers have not been sparing in their contempt for the scholastic dogma that genera and species are a peculiar kind of substances1 which general substances being the only permanent things1 while the individual substances comprehended under them are in a perpetual flux1 knowledge1 which necessarily imports stability1 can only have relation to those general substances or universals1 and not to the facts or particulars included under them4 ,yet1 though nominally rejected1 this very doctrine1 whether disguised under the ,abstract ,ideas of ,locke 7whose speculations1 however1 it has less vitiated than those of perhaps any other writer who has been infected with it71 under the ultra-nominalism of ,hobbes and ,condillac1 or the ontology of the later ,german schools1 has never ceased to poison philosophy4 ,once accustomed to consider scientific investigation as essentially consisting in the study of universals1 men did not drop this habit of thought when they ceased to regard universals as possessing an independent existence3 and even those who went the length of considering them as mere names1 could not free themselves from the notion that the investigation of truth consisted entirely or partly in some kind of conjuration or juggle with those names4 ,when a philosopher adopted fully the ,nominalist view of the signification of general language1 retaining along with it the dictum de omni as the foundation of all reasoning1 two such premises fairly put together were likely1 if he was a consistent thinker1 to land him in rather startling conclusions4 ,accordingly it has been seriously held1 by writers of deserved celebrity1 that the process of arriving at new truths by reasoning consists in the mere substitution of one set of arbitrary signs for another2 a doctrine which they suppose to derive irresistible confirmation from the example of algebra4 ,if there were any process in sorcery or necromancy more preternatural than this1 ,i should be much surprised4 ,the culminating point of this philosophy is the noted aphorism of ,condillac1 that a science is nothing1 or scarcely any thing1 but une langue bien faite2 in other words1 that the one sufficient rule for discovering the nature and properties of objects is to name them properly3 as if the reverse were not the truth1 that it is impossible to name them properly except in proportion as we are already acquainted with their nature and properties4 ,can it be necessary to say1 that none1 not even the most trivial knowledge with respect to ,things1 ever was or could be originally got at by any conceivable manipulation of mere names1 as such2 and that what can be learned from names1 is only what somebody who used the names knew before8 ,philosophical analysis confirms the indication of common sense1 that the function of names is but that of enabling us to remember and to communicate our thoughts4 ,that they also strengthen1 even to an incalculable extent1 the power of thought itself1 is most true3 but they do this by no intrinsic and peculiar virtue2 they do it by the power inherent in an artificial memory1 an instrument of which few have adequately considered the immense potency4 ,as an artificial memory1 language truly is1 what it has so often been called1 an instrument of thought2 but it is one thing to be the instrument1 and another to be the exclusive subject upon which the instrument is exercised4 ,we think1 indeed1 to a considerable extent1 by means of names1 but what we think of1 are the things called by those names2 and there can not be a greater error than to imagine that thought can be carried on with nothing in our mind but names1 or that we can make the names think for us4 #c4 ,those who considered the dictum de omni as the foundation of the syllogism1 looked upon arguments in a manner corresponding to the erroneous view which ,hobbes took of propositions4 ,because there are some propositions which are merely verbal1 ,hobbes1 in order apparently that his definition might be rigorously universal1 defined a proposition as if no propositions declared any thing except the meaning of words4 ,if ,hobbes was right2 if no further account than this could be given of the import of propositions2 no theory could be given but the commonly received one1 of the combination of propositions in a syllogism4 ,if the minor premise asserted nothing more than that something belongs to a class1 and if the major premise asserted nothing of that class except that it is included in another class1 the conclusion would only be that what was included in the lower class is included in the higher1 and the result1 therefore1 nothing except that the classification is consistent with itself4 ,but we have seen that it is no sufficient account of the meaning of a proposition1 to say that it refers something to1 or excludes something from1 a class4 ,every proposition which conveys real information asserts a matter of fact1 dependent on the laws of nature1 and not on classification4 ,it asserts that a given object does or does not possess a given attribute2 or it asserts that two attributes1 or sets of attributes1 do or do not 7constantly or occasionally7 co-exist4 ,since such is the purport of all propositions which convey any real knowledge1 and since ratiocination is a mode of acquiring real knowledge1 any theory of ratiocination which does not recognize this import of propositions1 can not1 we may be sure1 be the true one4 ,applying this view of propositions to the two premises of a syllogism1 we obtain the following results4 ,the major premise1 which1 as already remarked1 is always universal1 asserts1 that all things which have a certain attribute 7or attributes7 have or have not along with it1 a certain other attribute 7or attributes74 ,the minor premise asserts that the thing or set of things which are the subject of that premise1 have the first-mentioned attribute2 and the conclusion is1 that they have 7or that they have not71 the second4 ,thus in our former example1 ,all men are mortal1 ,socrates is a man1 therefore ,socrates is mortal1 the subject and predicate of the major premise are connotative terms1 denoting objects and connoting attributes4 ,the assertion in the major premise is1 that along with one of the two sets of attributes1 we always find the other3 that the attributes connoted by 8man0 never exist unless conjoined with the attribute called mortality4 ,the assertion in the minor premise is that the individual named ,socrates possesses the former attributes2 and it is concluded that he possesses also the attribute mortality4 ,or1 if both the premises are general propositions1 as ,all men are mortal1 ,all kings are men1 therefore ,all kings are mortal1 the minor premise asserts that the attributes denoted by kingship only exist in conjunction with those signified by the word man4 ,the major asserts as before1 that the last-mentioned attributes are never found without the attribute of mortality4 ,the conclusion is1 that wherever the attributes of kingship are found1 that of mortality is found also4 ,if the major premise were negative1 as1 ,no men are omnipotent1 it would assert1 not that the attributes connoted by 8man0 never exist without1 but that they never exist with1 those connoted by 8omnipotent30 from which1 together with the minor premise1 it is concluded1 that the same incompatibility exists between the attribute omnipotence and those constituting a king4 ,in a similar manner we might analyze any other example of the syllogism4 ,if we generalize this process1 and look out for the principle or law involved in every such inference1 and presupposed in every syllogism1 the propositions of which are any thing more than merely verbal2 we find1 not the unmeaning dictum de omni et nullo1 but a fundamental principle1 or rather two principles1 strikingly resembling the axioms of mathematics4 ,the first1 which is the principle of affirmative syllogisms1 is1 that things which co-exist with the same thing1 co-exist with one another3 or 7still more precisely7 a thing which co-exists with another thing1 which other co-exists with a third thing1 also co-exists with that third thing4 ,the second is the principle of negative syllogisms1 and is to this effect3 that a thing which co-exists with another thing1 with which other a third thing does not co-exist1 is not co-existent with that third thing4 ,these axioms manifestly relate to facts1 and not to conventions2 and one or other of them is the ground of the legitimacy of every argument in which facts and not conventions are the matter treated of47#ec7 #d4 ,it remains to translate this exposition of the syllogism from the one into the other of the two languages in which we formerly remarked7#ed7 that all propositions1 and of course therefore all combinations of propositions1 might be expressed4 ,we observed that a proposition might be considered in two different lights2 as a portion of our knowledge of nature1 or as a memorandum for our guidance4 ,under the former1 or speculative aspect1 an affirmative general proposition is an assertion of a speculative truth1 viz41 that whatever has a certain attribute has a certain other attribute4 ,under the other aspect1 it is to be regarded not as a part of our knowledge1 but as an aid for our practical exigencies1 by enabling us1 when we see or learn that an object possesses one of the two attributes1 to infer that it possesses the other2 thus employing the first attribute as a mark or evidence of the second4 ,thus regarded1 every syllogism comes within the following general formula3 ,attribute ,a is a mark of attribute ,b1 ,the given object has the mark ,a1 therefore ,the given object has the attribute ,b4 ,referred to this type1 the arguments which we have lately cited as specimens of the syllogism1 will express themselves in the following manner3 ,the attributes of man are a mark of the attribute mortality1 ,socrates has the attributes of man1 therefore ,socrates has the attribute mortality4 ,and again1 ,the attributes of man are a mark of the attribute mortality1 ,the attributes of a king are a mark of the attributes of man1 therefore ,the attributes of a king are a mark of the attribute mortality4 ,and1 lastly1 ,the attributes of man are a mark of the absence of the attribute omnipotence1 ,the attributes of a king are a mark of the attributes of man1 therefore ,the attributes of a king are a mark of the absence of the attribute signified by the word omnipotent 7or1 are evidence of the absence of that attribute74 ,to correspond with this alteration in the form of the syllogisms1 the axioms on which the syllogistic process is founded must undergo a corresponding transformation4 ,in this altered phraseology1 both those axioms may be brought under one general expression2 namely1 that whatever has any mark1 has that which it is a mark of4 ,or1 when the minor premise as well as the major is universal1 we may state it thus3 ,whatever is a mark of any mark1 is a mark of that which this last is a mark of4 ,to trace the identity of these axioms with those previously laid down1 may be left to the intelligent reader4 ,we shall find1 as we proceed1 the great convenience of the phraseology into which we have last thrown them1 and which is better adapted than any ,i am acquainted with1 to express with precision and force what is aimed at1 and actually accomplished1 in every case of the ascertainment of a truth by ratiocination47#ee7 ,chapter ,,iii4 ,of ,the ,functions ,and ,logical ,value ,of ,the ,syllogism4 #a4 ,we have shown what is the real nature of the truths with which the ,syllogism is conversant1 in contradistinction to the more superficial manner in which their import is conceived in the common theory2 and what are the fundamental axioms on which its probative force or conclusiveness depends4 ,we have now to inquire1 whether the syllogistic process1 that of reasoning from generals to particulars1 is1 or is not1 a process of inference2 a progress from the known to the unknown3 a means of coming to a knowledge of something which we did not know before4 ,logicians have been remarkably unanimous in their mode of answering this question4 ,it is universally allowed that a syllogism is vicious if there be any thing more in the conclusion than was assumed in the premises4 ,but this is1 in fact1 to say1 that nothing ever was1 or can be1 proved by syllogism1 which was not known1 or assumed to be known1 before4 ,is ratiocination1 then1 not a process of inference8 ,and is the syllogism1 to which the word reasoning has so often been represented to be exclusively appropriate1 not really entitled to be called reasoning at all8 ,this seems an inevitable consequence of the doctrine1 admitted by all writers on the subject1 that a syllogism can prove no more than is involved in the premises4 ,yet the acknowledgment so explicitly made1 has not prevented one set of writers from continuing to represent the syllogism as the correct analysis of what the mind actually performs in discovering and proving the larger half of the truths1 whether of science or of daily life1 which we believe2 while those who have avoided this inconsistency1 and followed out the general theorem respecting the logical value of the syllogism to its legitimate corollary1 have been led to impute uselessness and frivolity to the syllogistic theory itself1 on the ground of the petitio principii which they allege to be inherent in every syllogism4 ,as ,i believe both these opinions to be fundamentally erroneous1 ,i must request the attention of the reader to certain considerations1 without which any just appreciation of the true character of the syllogism1 and the functions it performs in philosophy1 appears to me impossible2 but which seem to have been either overlooked1 or insufficiently adverted to1 both by the defenders of the syllogistic theory and by its assailants4 #b4 ,it must be granted that in every syllogism1 considered as an argument to prove the conclusion1 there is a petitio principii4 ,when we say1 ,all men are mortal1 ,socrates is a man1 therefore ,socrates is mortal2 it is unanswerably urged by the adversaries of the syllogistic theory1 that the proposition1 ,socrates is mortal1 is presupposed in the more general assumption1 ,all men are mortal3 that we can not be assured of the mortality of all men1 unless we are already certain of the mortality of every individual man3 that if it be still doubtful whether ,socrates1 or any other individual we choose to name1 be mortal or not1 the same degree of uncertainty must hang over the assertion1 ,all men are mortal3 that the general principle1 instead of being given as evidence of the particular case1 can not itself be taken for true without exception1 until every shadow of doubt which could affect any case comprised with it1 is dispelled by evidence aliund2 and then what remains for the syllogism to prove8 ,that1 in short1 no reasoning from generals to particulars can1 as such1 prove any thing3 since from a general principle we can not infer any particulars1 but those which the principle itself assumes as known4 ,this doctrine appears to me irrefragable2 and if logicians1 though unable to dispute it1 have usually exhibited a strong disposition to explain it away1 this was not because they could discover any flaw in the argument itself1 but because the contrary opinion seemed to rest on arguments equally indisputable4 ,in the syllogism last referred to1 for example1 or in any of those which we previously constructed1 is it not evident that the conclusion may1 to the person to whom the syllogism is presented1 be actually and bona fide a new truth8 ,is it not matter of daily experience that truths previously unthought of1 facts which have not been1 and can not be1 directly observed1 are arrived at by way of general reasoning8 ,we believe that the ,duke of ,wellington is mortal4 ,we do not know this by direct observation1 so long as he is not yet dead4 ,if we were asked how1 this being the case1 we know the duke to be mortal1 we should probably answer1 ,because all men are so4 ,here1 therefore1 we arrive at the knowledge of a truth not 7as yet7 susceptible of observation1 by a reasoning which admits of being exhibited in the following syllogism3 ,all men are mortal1 ,the ,duke of ,wellington is a man1 therefore ,the ,duke of ,wellington is mortal4 ,and since a large portion of our knowledge is thus acquired1 logicians have persisted in representing the syllogism as a process of inference or proof2 though none of them has cleared up the difficulty which arises from the inconsistency between that assertion1 and the principle1 that if there be any thing in the conclusion which was not already asserted in the premises1 the argument is vicious4 ,for it is impossible to attach any serious scientific value to such a mere salvo1 as the distinction drawn between being involved by implication in the premises1 and being directly asserted in them4 ,when ,archbishop ,whately says7#ef7 that the object of reasoning is 8merely to expand and unfold the assertions wrapped up1 as it were1 and implied in those with which we set out1 and to bring a person to perceive and acknowledge the full force of that which he has admitted10 he does not1 ,i think1 meet the real difficulty requiring to be explained1 namely1 how it happens that a science1 like geometry1 can be all 8wrapped up0 in a few definitions and axioms4 ,nor does this defense of the syllogism differ much from what its assailants urge against it as an accusation1 when they charge it with being of no use except to those who seek to press the consequences of an admission into which a person has been entrapped without having considered and understood its full force4 ,when you admitted the major premise1 you asserted the conclusion2 but1 says ,archbishop ,whately1 you asserted it by implication merely3 this1 however1 can here only mean that you asserted it unconsciously2 that you did not know you were asserting it2 but1 if so1 the difficulty revives in this shape--,ought you not to have known8 ,were you warranted in asserting the general proposition without having satisfied yourself of the truth of every thing which it fairly includes8 ,and if not1 is not the syllogistic art prima facie what its assailants affirm it to be1 a contrivance for catching you in a trap1 and holding you fast in it87#eg7 #c4 ,from this difficulty there appears to be but one issue4 ,the proposition that the ,duke of ,wellington is mortal1 is evidently an inference2 it is got at as a conclusion from something else2 but do we1 in reality1 conclude it from the proposition1 ,all men are mortal8 ,i answer1 no4 ,the error committed is1 ,i conceive1 that of overlooking the distinction between two parts of the process of philosophizing1 the inferring part1 and the registering part2 and ascribing to the latter the functions of the former4 ,the mistake is that of referring a person to his own notes for the origin of his knowledge4 ,if a person is asked a question1 and is at the moment unable to answer it1 he may refresh his memory by turning to a memorandum which he carries about with him4 ,but if he were asked1 how the fact came to his knowledge1 he would scarcely answer1 because it was set down in his note-book3 unless the book was written1 like the ,koran1 with a quill from the wing of the angel ,gabriel4 ,assuming that the proposition1 ,the ,duke of ,wellington is mortal1 is immediately an inference from the proposition1 ,all men are mortal2 whence do we derive our knowledge of that general truth8 ,of course from observation4 ,now1 all which man can observe are individual cases4 ,from these all general truths must be drawn1 and into these they may be again resolved2 for a general truth is but an aggregate of particular truths2 a comprehensive expression1 by which an indefinite number of individual facts are affirmed or denied at once4 ,but a general proposition is not merely a compendious form for recording and preserving in the memory a number of particular facts1 all of which have been observed4 ,generalization is not a process of mere naming1 it is also a process of inference4 ,from instances which we have observed1 we feel warranted in concluding1 that what we found true in those instances1 holds in all similar ones1 past1 present1 and future1 however numerous they may be4 ,we then1 by that valuable contrivance of language which enables us to speak of many as if they were one1 record all that we have observed1 together with all that we infer from our observations1 in one concise expression2 and have thus only one proposition1 instead of an endless number1 to remember or to communicate4 ,the results of many observations and inferences1 and instructions for making innumerable inferences in unforeseen cases1 are compressed into one short sentence4 ,when1 therefore1 we conclude from the death of ,john and ,thomas1 and every other person we ever heard of in whose case the experiment had been fairly tried1 that the ,duke of ,wellington is mortal like the rest2 we may1 indeed1 pass through the generalization1 ,all men are mortal1 as an intermediate stage2 but it is not in the latter half of the process1 the descent from all men to the ,duke of ,wellington1 that the inference resides4 ,the inference is finished when we have asserted that all men are mortal4 ,what remains to be performed afterward is merely deciphering our own notes4 ,archbishop ,whately has contended that syllogizing1 or reasoning from generals to particulars1 is not1 agreeably to the vulgar idea1 a peculiar mode of reasoning1 but the philosophical analysis of the mode in which all men reason1 and must do so if they reason at all4 ,with the deference due to so high an authority1 ,i can not help thinking that the vulgar notion is1 in this case1 the more correct4 ,if1 from our experience of ,john1 ,thomas1 etc41 who once were living1 but are now dead1 we are entitled to conclude that all human beings are mortal1 we might surely without any logical inconsequence have concluded at once from those instances1 that the ,duke of ,wellington is mortal4 ,the mortality of ,john1 ,thomas1 and others is1 after all1 the whole evidence we have for the mortality of the ,duke of ,wellington4 ,not one iota is added to the proof by interpolating a general proposition4 ,since the individual cases are all the evidence we can possess1 evidence which no logical form into which we choose to throw it can make greater than it is2 and since that evidence is either sufficient in itself1 or1 if insufficient for the one purpose1 can not be sufficient for the other2 ,i am unable to see why we should be forbidden to take the shortest cut from these sufficient premises to the conclusion1 and constrained to travel the 8high priori road10 by the arbitrary fiat of logicians4 ,i can not perceive why it should be impossible to journey from one place to another unless we 8march up a hill1 and then march down again40 ,it may be the safest road1 and there may be a resting-place at the top of the hill1 affording a commanding view of the surrounding country2 but for the mere purpose of arriving at our journey's end1 our taking that road is perfectly optional2 it is a question of time1 trouble1 and danger4 ,not only may we reason from particulars to particulars without passing through generals1 but we perpetually do so reason4 ,all our earliest inferences are of this nature4 ,from the first dawn of intelligence we draw inferences1 but years elapse before we learn the use of general language4 ,the child1 who1 having burned his fingers1 avoids to thrust them again into the fire1 has reasoned or inferred1 though he has never thought of the general maxim1 ,fire burns4 ,he knows from memory that he has been burned1 and on this evidence believes1 when he sees a candle1 that if he puts his finger into the flame of it1 he will be burned again4 ,he believes this in every case which happens to arise2 but without looking1 in each instance1 beyond the present case4 ,he is not generalizing2 he is inferring a particular from particulars4 ,in the same way1 also1 brutes reason4 ,there is no ground for attributing to any of the lower animals the use of signs1 of such a nature as to render general propositions possible4 ,but those animals profit by experience1 and avoid what they have found to cause them pain1 in the same manner1 though not always with the same skill1 as a human creature4 ,not only the burned child1 but the burned dog1 dreads the fire4 ,i believe that1 in point of fact1 when drawing inferences from our personal experience1 and not from maxims handed down to us by books or tradition1 we much oftener conclude from particulars to particulars directly1 than through the intermediate agency of any general proposition4 ,we are constantly reasoning from ourselves to other people1 or from one person to another1 without giving ourselves the trouble to erect our observations into general maxims of human or external nature4 ,when we conclude that some person will1 on some given occasion1 feel or act so and so1 we sometimes judge from an enlarged consideration of the manner in which human beings in general1 or persons of some particular character1 are accustomed to feel and act2 but much oftener from merely recollecting the feelings and conduct of the same person in some previous instance1 or from considering how we should feel or act ourselves4 ,it is not only the village matron1 who1 when called to a consultation upon the case of a neighbor's child1 pronounces on the evil and its remedy simply on the recollection and authority of what she accounts the similar case of her ,lucy4 ,we all1 where we have no definite maxims to steer by1 guide ourselves in the same way3 and if we have an extensive experience1 and retain its impressions strongly1 we may acquire in this manner a very considerable power of accurate judgment1 which we may be utterly incapable of justifying or of communicating to others4 ,among the higher order of practical intellects there have been many of whom it was remarked how admirably they suited their means to their ends1 without being able to give any sufficient reasons for what they did2 and applied1 or seemed to apply1 recondite principles which they were wholly unable to state4 ,this is a natural consequence of having a mind stored with appropriate particulars1 and having been long accustomed to reason at once from these to fresh particulars1 without practicing the habit of stating to one's self or to others the corresponding general propositions4 ,an old warrior1 on a rapid glance at the outlines of the ground1 is able at once to give the necessary orders for a skillful arrangement of his troops2 though if he has received little theoretical instruction1 and has seldom been called upon to answer to other people for his conduct1 he may never have had in his mind a single general theorem respecting the relation between ground and array4 ,but his experience of encampments1 in circumstances more or less similar1 has left a number of vivid1 unexpressed1 ungeneralized analogies in his mind1 the most appropriate of which1 instantly suggesting itself1 determines him to a judicious arrangement4 ,the skill of an uneducated person in the use of weapons1 or of tools1 is of a precisely similar nature4 ,the savage who executes unerringly the exact throw which brings down his game1 or his enemy1 in the manner most suited to his purpose1 under the operation of all the conditions necessarily involved1 the weight and form of the weapon1 the direction and distance of the object1 the action of the wind1 etc41 owes this power to a long series of previous experiments1 the results of which he certainly never framed into any verbal theorems or rules4 ,the same thing may generally be said of any other extraordinary manual dexterity4 ,not long ago a ,scotch manufacturer procured from ,england1 at a high rate of wages1 a working dyer1 famous for producing very fine colors1 with the view of teaching to his other workmen the same skill4 ,the workman came2 but his mode of proportioning the ingredients1 in which lay the secret of the effects he produced1 was by taking them up in handfuls1 while the common method was to weigh them4 ,the manufacturer sought to make him turn his handling system into an equivalent weighing system1 that the general principle of his peculiar mode of proceeding might be ascertained4 ,this1 however1 the man found himself quite unable to do1 and therefore could impart his skill to nobody4 ,he had1 from the individual cases of his own experience1 established a connection in his mind between fine effects of color1 and tactual perceptions in handling his dyeing materials2 and from these perceptions he could1 in any particular case1 infer the means to be employed1 and the effects which would be produced1 but could not put others in possession of the grounds on which he proceeded1 from having never generalized them in his own mind1 or expressed them in language4 ,almost every one knows ,lord ,mansfield's advice to a man of practical good sense1 who1 being appointed governor of a colony1 had to preside in its courts of justice1 without previous judicial practice or legal education4 ,the advice was to give his decision boldly1 for it would probably be right2 but never to venture on assigning reasons1 for they would almost infallibly be wrong4 ,in cases like this1 which are of no uncommon occurrence1 it would be absurd to suppose that the bad reason was the source of the good decision4 ,lord ,mansfield knew that if any reason were assigned it would be necessarily an afterthought1 the judge being in fact guided by impressions from past experience1 without the circuitous process of framing general principles from them1 and that if he attempted to frame any such he would assuredly fail4 ,lord ,mansfield1 however1 would not have doubted that a man of equal experience who had also a mind stored with general propositions derived by legitimate induction from that experience1 would have been greatly preferable as a judge1 to one1 however sagacious1 who could not be trusted with the explanation and justification of his own judgments4 ,the cases of men of talent performing wonderful things they know not how1 are examples of the rudest and most spontaneous form of the operations of superior minds4 ,it is a defect in them1 and often a source of errors1 not to have generalized as they went on2 but generalization1 though a help1 the most important indeed of all helps1 is not an essential4 ,even the scientifically instructed1 who possess1 in the form of general propositions1 a systematic record of the results of the experience of mankind1 need not always revert to those general propositions in order to apply that experience to a new case4 ,it is justly remarked by ,dugald ,stewart1 that though the reasonings in mathematics depend entirely on the axioms1 it is by no means necessary to our seeing the conclusiveness of the proof1 that the axioms should be expressly adverted to4 ,when it is inferred that ,,ab is equal to ,,cd because each of them is equal to ,,ef1 the most uncultivated understanding1 as soon as the propositions were understood1 would assent to the inference1 without having ever heard of the general truth that 8things which are equal to the same thing are equal to one another40 ,this remark of ,stewart1 consistently followed out1 goes to the root1 as ,i conceive1 of the philosophy of ratiocination2 and it is to be regretted that he himself stopped short at a much more limited application of it4 ,he saw that the general propositions on which a reasoning is said to depend1 may1 in certain cases1 be altogether omitted1 without impairing its probative force4 ,but he imagined this to be a peculiarity belonging to axioms2 and argued from it1 that axioms are not the foundations or first principles of geometry1 from which all the other truths of the science are synthetically deduced 7as the laws of motion and of the composition of forces in dynamics1 the equal mobility of fluids in hydrostatics1 the laws of reflection and refraction in optics1 are the first principles of those sciences72 but are merely necessary assumptions1 self-evident indeed1 and the denial of which would annihilate all demonstration1 but from which1 as premises1 nothing can be demonstrated4 ,in the present1 as in many other instances1 this thoughtful and elegant writer has perceived an important truth1 but only by halves4 ,finding1 in the case of geometrical axioms1 that general names have not any talismanic virtue for conjuring new truths out of the well where they lie hid1 and not seeing that this is equally true in every other case of generalization1 he contended that axioms are in their nature barren of consequences1 and that the really fruitful truths1 the real first principles of geometry1 are the definitions2 that the definition1 for example1 of the circle is to the properties of the circle1 what the laws of equilibrium and of the pressure of the atmosphere are to the rise of the mercury in the ,torricellian tube4 ,yet all that he had asserted respecting the function to which the axioms are confined in the demonstrations of geometry1 holds equally true of the definitions4 ,every demonstration in ,euclid might be carried on without them4 ,this is apparent from the ordinary process of proving a proposition of geometry by means of a diagram4 ,what assumption1 in fact1 do we set out from1 to demonstrate by a diagram any of the properties of the circle8 ,not that in all circles the radii are equal1 but only that they are so in the circle ,,abc4 ,as our warrant for assuming this1 we appeal1 it is true1 to the definition of a circle in general2 but it is only necessary that the assumption be granted in the case of the particular circle supposed4 ,from this1 which is not a general but a singular proposition1 combined with other propositions of a similar kind1 some of which when generalized are called definitions1 and other axioms1 we prove that a certain conclusion is true1 not of all circles1 but of the particular circle ,,abc2 or at least would be so1 if the facts precisely accorded with our assumptions4 ,the enunciation1 as it is called1 that is1 the general theorem which stands at the head of the demonstration1 is not the proposition actually demonstrated4 ,one instance only is demonstrated3 but the process by which this is done1 is a process which1 when we consider its nature1 we perceive might be exactly copied in an indefinite number of other instances2 in every instance which conforms to certain conditions4 ,the contrivance of general language furnishing us with terms which connote these conditions1 we are able to assert this indefinite multitude of truths in a single expression1 and this expression is the general theorem4 ,by dropping the use of diagrams1 and substituting1 in the demonstrations1 general phrases for the letters of the alphabet1 we might prove the general theorem directly1 that is1 we might demonstrate all the cases at once2 and to do this we must1 of course1 employ as our premises1 the axioms and definitions in their general form4 ,but this only means1 that if we can prove an individual conclusion by assuming an individual fact1 then in whatever case we are warranted in making an exactly similar assumption1 we may draw an exactly similar conclusion4 ,the definition is a sort of notice to ourselves and others1 what assumptions we think ourselves entitled to make4 ,and so in all cases1 the general propositions1 whether called definitions1 axioms1 or laws of nature1 which we lay down at the beginning of our reasonings1 are merely abridged statements1 in a kind of short-hand1 of the particular facts1 which1 as occasion arises1 we either think we may proceed on as proved1 or intend to assume4 ,in any one demonstration it is enough if we assume for a particular case suitably selected1 what by the statement of the definition or principle we announce that we intend to assume in all cases which may arise4 ,the definition of the circle1 therefore1 is to one of ,euclid's demonstrations1 exactly what1 according to ,stewart1 the axioms are2 that is1 the demonstration does not depend on it1 but yet if we deny it the demonstration fails4 ,the proof does not rest on the general assumption1 but on a similar assumption confined to the particular case3 that case1 however1 being chosen as a specimen or paradigm of the whole class of cases included in the theorem1 there can be no ground for making the assumption in that case which does not exist in every other2 and to deny the assumption as a general truth1 is to deny the right of making it in the particular instance4 ,there are1 undoubtedly1 the most ample reasons for stating both the principles and the theorems in their general form1 and these will be explained presently1 so far as explanation is requisite4 ,but1 that unpracticed learners1 even in making use of one theorem to demonstrate another1 reason rather from particular to particular than from the general proposition1 is manifest from the difficulty they find in applying a theorem to a case in which the configuration of the diagram is extremely unlike that of the diagram by which the original theorem was demonstrated4 ,a difficulty which1 except in cases of unusual mental power1 long practice can alone remove1 and removes chiefly by rendering us familiar with all the configurations consistent with the general conditions of the theorem4 #d4 ,from the considerations now adduced1 the following conclusions seem to be established4 ,all inference is from particulars to particulars3 ,general propositions are merely registers of such inferences already made1 and short formul for making more3 ,the major premise of a syllogism1 consequently1 is a formula of this description3 and the conclusion is not an inference drawn from the formula1 but an inference drawn according to the formula3 the real logical antecedent1 or premise1 being the particular facts from which the general proposition was collected by induction4 ,those facts1 and the individual instances which supplied them1 may have been forgotten3 but a record remains1 not indeed descriptive of the facts themselves1 but showing how those cases may be distinguished1 respecting which1 the facts1 when known1 were considered to warrant a given inference4 ,according to the indications of this record we draw our conclusion3 which is1 to all intents and purposes1 a conclusion from the forgotten facts4 ,for this it is essential that we should read the record correctly3 and the rules of the syllogism are a set of precautions to insure our doing so4 ,this view of the functions of the syllogism is confirmed by the consideration of precisely those cases which might be expected to be least favorable to it1 namely1 those in which ratiocination is independent of any previous induction4 ,we have already observed that the syllogism1 in the ordinary course of our reasoning1 is only the latter half of the process of traveling from premises to a conclusion4 ,there are1 however1 some peculiar cases in which it is the whole process4 ,particulars alone are capable of being subjected to observation2 and all knowledge which is derived from observation1 begins1 therefore1 of necessity1 in particulars2 but our knowledge may1 in cases of certain descriptions1 be conceived as coming to us from other sources than observation4 ,it may present itself as coming from testimony1 which1 on the occasion and for the purpose in hand1 is accepted as of an authoritative character3 and the information thus communicated1 may be conceived to comprise not only particular facts but general propositions1 as when a scientific doctrine is accepted without examination on the authority of writers1 or a theological doctrine on that of ,scripture4 ,or the generalization may not be1 in the ordinary sense1 an assertion at all1 but a command2 a law1 not in the philosophical1 but in the moral and political sense of the term3 an expression of the desire of a superior1 that we1 or any number of other persons1 shall conform our conduct to certain general instructions4 ,so far as this asserts a fact1 namely1 a volition of the legislator1 that fact is an individual fact1 and the proposition1 therefore1 is not a general proposition4 ,but the description therein contained of the conduct which it is the will of the legislator that his subjects should observe1 is general4 ,the proposition asserts1 not that all men are any thing1 but that all men shall do something4 ,in both these cases the generalities are the original data1 and the particulars are elicited from them by a process which correctly resolves itself into a series of syllogisms4 ,the real nature1 however1 of the supposed deductive process1 is evident enough4 ,the only point to be determined is1 whether the authority which declared the general proposition1 intended to include this case in it2 and whether the legislator intended his command to apply to the present case among others1 or not4 ,this is ascertained by examining whether the case possesses the marks by which1 as those authorities have signified1 the cases which they meant to certify or to influence may be known4 ,the object of the inquiry is to make out the witness's or the legislator's intention1 through the indication given by their words4 ,this is a question1 as the ,germans express it1 of hermeneutics4 ,the operation is not a process of inference1 but a process of interpretation4 ,in this last phrase we have obtained an expression which appears to me to characterize1 more aptly than any other1 the functions of the syllogism in all cases4 ,when the premises are given by authority1 the function of ,reasoning is to ascertain the testimony of a witness1 or the will of a legislator1 by interpreting the signs in which the one has intimated his assertion and the other his command4 ,in like manner1 when the premises are derived from observation1 the function of ,reasoning is to ascertain what we 7or our predecessors7 formerly thought might be inferred from the observed facts1 and to do this by interpreting a memorandum of ours1 or of theirs4 ,the memorandum reminds us1 that from evidence1 more or less carefully weighed1 it formerly appeared that a certain attribute might be inferred wherever we perceive a certain mark4 ,the proposition1 ,all men are mortal 7for instance7 shows that we have had experience from which we thought it followed that the attributes connoted by the term man1 are a mark of mortality4 ,but when we conclude that the ,duke of ,wellington is mortal1 we do not infer this from the memorandum1 but from the former experience4 ,all that we infer from the memorandum is our own previous belief1 7or that of those who transmitted to us the proposition71 concerning the inferences which that former experience would warrant4 ,this view of the nature of the syllogism renders consistent and intelligible what otherwise remains obscure and confused in the theory of ,archbishop ,whately and other enlightened defenders of the syllogistic doctrine1 respecting the limits to which its functions are confined4 ,they affirm in as explicit terms as can be used1 that the sole office of general reasoning is to prevent inconsistency in our opinions2 to prevent us from assenting to any thing1 the truth of which would contradict something to which we had previously on good grounds given our assent4 ,and they tell us1 that the sole ground which a syllogism affords for assenting to the conclusion1 is that the supposition of its being false1 combined with the supposition that the premises are true1 would lead to a contradiction in terms4 ,now this would be but a lame account of the real grounds which we have for believing the facts which we learn from reasoning1 in contradistinction to observation4 ,the true reason why we believe that the ,duke of ,wellington will die1 is that his fathers1 and our fathers1 and all other persons who were contemporary with them1 have died4 ,those facts are the real premises of the reasoning4 ,but we are not led to infer the conclusion from those premises1 by the necessity of avoiding any verbal inconsistency4 ,there is no contradiction in supposing that all those persons have died1 and that the ,duke of ,wellington may1 notwithstanding1 live forever4 ,but there would be a contradiction if we first1 on the ground of those same premises1 made a general assertion including and covering the case of the ,duke of ,wellington1 and then refused to stand to it in the individual case4 ,there is an inconsistency to be avoided between the memorandum we make of the inferences which may be justly drawn in future cases1 and the inferences we actually draw in those cases when they arise4 ,with this view we interpret our own formula1 precisely as a judge interprets a law3 in order that we may avoid drawing any inferences not conformable to our former intention1 as a judge avoids giving any decision not conformable to the legislator's intention4 ,the rules for this interpretation are the rules of the syllogism3 and its sole purpose is to maintain consistency between the conclusions we draw in every particular case1 and the previous general directions for drawing them2 whether those general directions were framed by ourselves as the result of induction1 or were received by us from an authority competent to give them4 #e4 ,in the above observations it has1 ,i think1 been shown1 that1 though there is always a process of reasoning or inference where a syllogism is used1 the syllogism is not a correct analysis of that process of reasoning or inference2 which is1 on the contrary 7when not a mere inference from testimony71 an inference from particulars to particulars2 authorized by a previous inference from particulars to generals1 and substantially the same with it2 of the nature1 therefore1 of ,induction4 ,but while these conclusions appear to me undeniable1 ,i must yet enter a protest1 as strong as that of ,archbishop ,whately himself1 against the doctrine that the syllogistic art is useless for the purposes of reasoning4 ,the reasoning lies in the act of generalization1 not in interpreting the record of that act2 but the syllogistic form is an indispensable collateral security for the correctness of the generalization itself4 ,it has already been seen1 that if we have a collection of particulars sufficient for grounding an induction1 we need not frame a general proposition2 we may reason at once from those particulars to other particulars4 ,but it is to be remarked withal1 that whenever1 from a set of particular cases1 we can legitimately draw any inference1 we may legitimately make our inference a general one4 ,if1 from observation and experiment1 we can conclude to one new case1 so may we to an indefinite number4 ,if that which has held true in our past experience will therefore hold in time to come1 it will hold not merely in some individual case1 but in all cases of some given description4 ,every induction1 therefore1 which suffices to prove one fact1 proves an indefinite multitude of facts3 the experience which justifies a single prediction must be such as will suffice to bear out a general theorem4 ,this theorem it is extremely important to ascertain and declare1 in its broadest form of generality2 and thus to place before our minds1 in its full extent1 the whole of what our evidence must prove if it proves any thing4 ,this throwing of the whole body of possible inferences from a given set of particulars1 into one general expression1 operates as a security for their being just inferences1 in more ways than one4 ,first1 the general principle presents a larger object to the imagination than any of the singular propositions which it contains4 ,a process of thought which leads to a comprehensive generality1 is felt as of greater importance than one which terminates in an insulated fact2 and the mind is1 even unconsciously1 led to bestow greater attention upon the process1 and to weigh more carefully the sufficiency of the experience appealed to1 for supporting the inference grounded upon it4 ,there is another1 and a more important1 advantage4 ,in reasoning from a course of individual observations to some new and unobserved case1 which we are but imperfectly acquainted with 7or we should not be inquiring into it71 and in which1 since we are inquiring into it1 we probably feel a peculiar interest2 there is very little to prevent us from giving way to negligence1 or to any bias which may affect our wishes or our imagination1 and1 under that influence1 accepting insufficient evidence as sufficient4 ,but if1 instead of concluding straight to the particular case1 we place before ourselves an entire class of facts--the whole contents of a general proposition1 every tittle of which is legitimately inferable from our premises1 if that one particular conclusion is so2 there is then a considerable likelihood that if the premises are insufficient1 and the general inference therefore1 groundless1 it will comprise within it some fact or facts the reverse of which we already know to be true2 and we shall thus discover the error in our generalization by a reductio ad impossibile4 ,thus if1 during the reign of ,marcus ,aurelius1 a subject of the ,roman empire1 under the bias naturally given to the imagination and expectations by the lives and characters of the ,antonines1 had been disposed to expect that ,commodus would be a just ruler2 supposing him to stop there1 he might only have been undeceived by sad experience4 ,but if he reflected that this expectation could not be justifiable unless from the same evidence he was warranted in concluding some general proposition1 as1 for instance1 that all ,roman emperors are just rulers2 he would immediately have thought of ,nero1 ,domitian1 and other instances1 which1 showing the falsity of the general conclusion1 and therefore the insufficiency of the premises1 would have warned him that those premises could not prove in the instance of ,commodus1 what they were inadequate to prove in any collection of cases in which his was included4 ,the advantage1 in judging whether any controverted inference is legitimate1 of referring to a parallel case1 is universally acknowledged4 ,but by ascending to the general proposition1 we bring under our view not one parallel case only1 but all possible parallel cases at once2 all cases to which the same set of evidentiary considerations are applicable4 ,when1 therefore1 we argue from a number of known cases to another case supposed to be analogous1 it is always possible1 and generally advantageous1 to divert our argument into the circuitous channel of an induction from those known cases to a general proposition1 and a subsequent application of that general proposition to the unknown case4 ,this second part of the operation1 which1 as before observed1 is essentially a process of interpretation1 will be resolvable into a syllogism or a series of syllogisms1 the majors of which will be general propositions embracing whole classes of cases2 every one of which propositions must be true in all its extent1 if the argument is maintainable4 ,if1 therefore1 any fact fairly coming within the range of one of these general propositions1 and consequently asserted by it1 is known or suspected to be other than the proposition asserts it to be1 this mode of stating the argument causes us to know or to suspect that the original observations1 which are the real grounds of our conclusion1 are not sufficient to support it4 ,and in proportion to the greater chance of our detecting the inconclusiveness of our evidence1 will be the increased reliance we are entitled to place in it if no such evidence of defect shall appear4 ,the value1 therefore1 of the syllogistic form1 and of the rules for using it correctly1 does not consist in their being the form and the rules according to which our reasonings are necessarily1 or even usually1 made2 but in their furnishing us with a mode in which those reasonings may always be represented1 and which is admirably calculated1 if they are inconclusive1 to bring their inconclusiveness to light4 ,an induction from particulars to generals1 followed by a syllogistic process from those generals to other particulars1 is a form in which we may always state our reasonings if we please4 ,it is not a form in which we must reason1 but it is a form in which we may reason1 and into which it is indispensable to throw our reasoning1 when there is any doubt of its validity3 though when the case is familiar and little complicated1 and there is no suspicion of error1 we may1 and do1 reason at once from the known particular cases to unknown ones47#eh7 ,these are the uses of syllogism1 as a mode of verifying any given argument4 ,its ulterior uses1 as respects the general course of our intellectual operations1 hardly require illustration1 being in fact the acknowledged uses of general language4 ,they amount substantially to this1 that the inductions may be made once for all3 a single careful interrogation of experience may suffice1 and the result may be registered in the form of a general proposition1 which is committed to memory or to writing1 and from which afterward we have only to syllogize4 ,the particulars of our experiments may then be dismissed from the memory1 in which it would be impossible to retain so great a multitude of details2 while the knowledge which those details afforded for future use1 and which would otherwise be lost as soon as the observations were forgotten1 or as their record became too bulky for reference1 is retained in a commodious and immediately available shape by means of general language4 ,against this advantage is to be set the countervailing inconvenience1 that inferences originally made on insufficient evidence become consecrated1 and1 as it were1 hardened into general maxims2 and the mind cleaves to them from habit1 after it has outgrown any liability to be misled by similar fallacious appearances if they were now for the first time presented2 but having forgotten the particulars1 it does not think of revising its own former decision4 ,an inevitable drawback1 which1 however considerable in itself1 forms evidently but a small set-off against the immense benefits of general language4 ,the use of the syllogism is in truth no other than the use of general propositions in reasoning4 ,we can reason without them2 in simple and obvious cases we habitually do so2 minds of great sagacity can do it in cases not simple and obvious1 provided their experience supplies them with instances essentially similar to every combination of circumstances likely to arise4 ,but other minds1 and the same minds where they have not the same pre-eminent advantages of personal experience1 are quite helpless without the aid of general propositions1 wherever the case presents the smallest complication2 and if we made no general propositions1 few persons would get much beyond those simple inferences which are drawn by the more intelligent of the brutes4 ,though not necessary to reasoning1 general propositions are necessary to any considerable progress in reasoning4 ,it is1 therefore1 natural and indispensable to separate the process of investigation into two parts2 and obtain general formul for determining what inferences may be drawn1 before the occasion arises for drawing the inferences4 ,the work of drawing them is then that of applying the formul2 and the rules of syllogism are a system of securities for the correctness of the application4 #f4 ,to complete the series of considerations connected with the philosophical character of the syllogism1 it is requisite to consider1 since the syllogism is not the universal type of the reasoning process1 what is the real type4 ,this resolves itself into the question1 what is the nature of the minor premise1 and in what manner it contributes to establish the conclusion3 for as to the major1 we now fully understand1 that the place which it nominally occupies in our reasonings1 properly belongs to the individual facts or observations of which it expresses the general result2 the major itself being no real part of the argument1 but an intermediate halting-place for the mind1 interposed by an artifice of language between the real premises and the conclusion1 by way of a security1 which it is in a most material degree1 for the correctness of the process4 ,the minor1 however1 being an indispensable part of the syllogistic expression of an argument1 without doubt either is1 or corresponds to1 an equally indispensable part of the argument itself1 and we have only to inquire what part4 ,it is perhaps worth while to notice here a speculation of a philosopher to whom mental science is much indebted1 but who1 though a very penetrating1 was a very hasty thinker1 and whose want of due circumspection rendered him fully as remarkable for what he did not see1 as for what he saw4 ,i allude to ,dr4 ,thomas ,brown1 whose theory of ratiocination is peculiar4 ,he saw the petitio principii which is inherent in every syllogism1 if we consider the major to be itself the evidence by which the conclusion is proved1 instead of being1 what in fact it is1 an assertion of the existence of evidence sufficient to prove any conclusion of a given description4 ,seeing this1 ,dr4 ,brown not only failed to see the immense advantage1 in point of security for correctness1 which is gained by interposing this step between the real evidence and the conclusion2 but he thought it incumbent on him to strike out the major altogether from the reasoning process1 without substituting any thing else1 and maintained that our reasonings consist only of the minor premise and the conclusion1 ,socrates is a man1 therefore ,socrates is mortal3 thus actually suppressing1 as an unnecessary step in the argument1 the appeal to former experience4 ,the absurdity of this was disguised from him by the opinion he adopted1 that reasoning is merely analyzing our own general notions1 or abstract ideas2 and that the proposition1 ,socrates is mortal1 is evolved from the proposition1 ,socrates is a man1 simply by recognizing the notion of mortality as already contained in the notion we form of a man4 ,after the explanations so fully entered into on the subject of propositions1 much further discussion can not be necessary to make the radical error of this view of ratiocination apparent4 ,if the word man connoted mortality2 if the meaning of 8mortal0 were involved in the meaning of 8man20 we might1 undoubtedly1 evolve the conclusion from the minor alone1 because the minor would have already asserted it4 ,but if1 as is in fact the case1 the word man does not connote mortality1 how does it appear that in the mind of every person who admits ,socrates to be a man1 the idea of man must include the idea of mortality8 ,dr4 ,brown could not help seeing this difficulty1 and in order to avoid it1 was led1 contrary to his intention1 to re-establish1 under another name1 that step in the argument which corresponds to the major1 by affirming the necessity of previously perceiving the relation between the idea of man and the idea of mortal4 ,if the reasoner has not previously perceived this relation1 he will not1 says ,dr4 ,brown1 infer because ,socrates is a man1 that ,socrates is mortal4 ,but even this admission1 though amounting to a surrender of the doctrine that an argument consists of the minor and the conclusion alone1 will not save the remainder of ,dr4 ,brown's theory4 ,the failure of assent to the argument does not take place merely because the reasoner1 for want of due analysis1 does not perceive that his idea of man includes the idea of mortality2 it takes place1 much more commonly1 because in his mind that relation between the two ideas has never existed4 ,and in truth it never does exist1 except as the result of experience4 ,consenting1 for the sake of the argument1 to discuss the question on a supposition of which we have recognized the radical incorrectness1 namely1 that the meaning of a proposition relates to the ideas of the things spoken of1 and not to the things themselves2 ,i must yet observe1 that the idea of man1 as a universal idea1 the common property of all rational creatures1 can not involve any thing but what is strictly implied in the name4 ,if any one includes in his own private idea of man1 as no doubt is always the case1 some other attributes1 such for instance as mortality1 he does so only as the consequence of experience1 after having satisfied himself that all men possess that attribute3 so that whatever the idea contains1 in any person's mind1 beyond what is included in the conventional signification of the word1 has been added to it as the result of assent to a proposition2 while ,dr4 ,brown's theory requires us to suppose1 on the contrary1 that assent to the proposition is produced by evolving1 through an analytic process1 this very element out of the idea4 ,this theory1 therefore1 may be considered as sufficiently refuted2 and the minor premise must be regarded as totally insufficient to prove the conclusion1 except with the assistance of the major1 or of that which the major represents1 namely1 the various singular propositions expressive of the series of observations1 of which the generalization called the major premise is the result4 ,in the argument1 then1 which proves that ,socrates is mortal1 one indispensable part of the premises will be as follows3 8,my father1 and my father's father1 ,a1 ,b1 ,c1 and an indefinite number of other persons1 were mortal20 which is only an expression in different words of the observed fact that they have died4 ,this is the major premise divested of the petitio principii1 and cut down to as much as is really known by direct evidence4 ,in order to connect this proposition with the conclusion ,socrates is mortal1 the additional link necessary is such a proposition as the following3 8,socrates resembles my father1 and my father's father1 and the other individuals specified40 ,this proposition we assert when we say that ,socrates is a man4 ,by saying so we likewise assert in what respect he resembles them1 namely1 in the attributes connoted by the word man4 ,and we conclude that he further resembles them in the attribute mortality4 #g4 ,we have thus obtained what we were seeking1 a universal type of the reasoning process4 ,we find it resolvable in all cases into the following elements3 ,certain individuals have a given attribute2 an individual or individuals resemble the former in certain other attributes2 therefore they resemble them also in the given attribute4 ,this type of ratiocination does not claim1 like the syllogism1 to be conclusive from the mere form of the expression2 nor can it possibly be so4 ,that one proposition does or does not assert the very fact which was already asserted in another1 may appear from the form of the expression1 that is1 from a comparison of the language2 but when the two propositions assert facts which are bona fide different1 whether the one fact proves the other or not can never appear from the language1 but must depend on other considerations4 ,whether1 from the attributes in which ,socrates resembles those men who have heretofore died1 it is allowable to infer that he resembles them also in being mortal1 is a question of ,induction2 and is to be decided by the principles or canons which we shall hereafter recognize as tests of the correct performance of that great mental operation4 ,meanwhile1 however1 it is certain1 as before remarked1 that if this inference can be drawn as to ,socrates1 it can be drawn as to all others who resemble the observed individuals in the same attributes in which he resembles them2 that is 7to express the thing concisely7 of all mankind4 ,if1 therefore1 the argument be admissible in the case of ,socrates1 we are at liberty1 once for all1 to treat the possession of the attributes of man as a mark1 or satisfactory evidence1 of the attribute of mortality4 ,this we do by laying down the universal proposition1 ,all men are mortal1 and interpreting this1 as occasion arises1 in its application to ,socrates and others4 ,by this means we establish a very convenient division of the entire logical operation into two steps2 first1 that of ascertaining what attributes are marks of mortality2 and1 secondly1 whether any given individuals possess those marks4 ,and it will generally be advisable1 in our speculations on the reasoning process1 to consider this double operation as in fact taking place1 and all reasoning as carried on in the form into which it must necessarily be thrown to enable us to apply to it any test of its correct performance4 ,although1 therefore1 all processes of thought in which the ultimate premises are particulars1 whether we conclude from particulars to a general formula1 or from particulars to other particulars according to that formula1 are equally ,induction2 we shall yet1 conformably to usage1 consider the name ,induction as more peculiarly belonging to the process of establishing the general proposition1 and the remaining operation1 which is substantially that of interpreting the general proposition1 we shall call by its usual name1 ,deduction4 ,and we shall consider every process by which any thing is inferred respecting an unobserved case1 as consisting of an ,induction followed by a ,deduction2 because1 although the process needs not necessarily be carried on in this form1 it is always susceptible of the form1 and must be thrown into it when assurance of scientific accuracy is needed and desired4 #h4 ,the theory of the syllogism laid down in the preceding pages1 has obtained1 among other important adhesions1 three of peculiar value3 those of ,sir ,john ,herschel17#ei7 ,dr4 ,whewell17#fj7 and ,mr4 ,bailey27#fa7 ,sir ,john ,herschel considering the doctrine1 though not strictly 8a discovery10 having been anticipated by ,berkeley17#fb7 to be 8one of the greatest steps which have yet been made in the philosophy of ,logic40 8,when we consider0 7to quote the further words of the same authority7 8the inveteracy of the habits and prejudices which it has cast to the winds10 there is no cause for misgiving in the fact that other thinkers1 no less entitled to consideration1 have formed a very different estimate of it4 ,their principal objection can not be better or more succinctly stated than by borrowing a sentence from ,archbishop ,whately47#fc7 8,in every case where an inference is drawn from ,induction 7unless that name is to be given to a mere random guess without any grounds at all7 we must form a judgment that the instance or instances adduced are sufficient to authorize the conclusion2 that it is allowable to take these instances as a sample warranting an inference respecting the whole class20 and the expression of this judgment in words 7it has been said by several of my critics7 is the major premise4 ,i quite admit that the major is an affirmation of the sufficiency of the evidence on which the conclusion rests4 ,that it is so1 is the very essence of my own theory4 ,and whoever admits that the major premise is only this1 adopts the theory in its essentials4 ,but ,i can not concede that this recognition of the sufficiency of the evidence--that is1 of the correctness of the induction--is a part of the induction itself2 unless we ought to say that it is a part of every thing we do1 to satisfy ourselves that it has been done rightly4 ,we conclude from known instances to unknown by the impulse of the generalizing propensity2 and 7until after a considerable amount of practice and mental discipline7 the question of the sufficiency of the evidence is only raised by a retrospective act1 turning back upon our own footsteps1 and examining whether we were warranted in doing what we have provisionally done4 ,to speak of this reflex operation as part of the original one1 requiring to be expressed in words in order that the verbal formula may correctly represent the psychological process1 appears to me false psychology47#fd7 ,we review our syllogistic as well as our inductive processes1 and recognize that they have been correctly performed2 but logicians do not add a third premise to the syllogism1 to express this act of recognition4 ,a careful copyist verifies his transcript by collating it with the original2 and if no error appears1 he recognizes that the transcript has been correctly made4 ,but we do not call the examination of the copy a part of the act of copying4 ,the conclusion in an induction is inferred from the evidence itself1 and not from a recognition of the sufficiency of the evidence2 as ,i infer that my friend is walking toward me because ,i see him1 and not because ,i recognize that my eyes are open1 and that eyesight is a means of knowledge4 ,in all operations which require care1 it is good to assure ourselves that the process has been performed accurately2 but the testing of the process is not the process itself2 and1 besides1 may have been omitted altogether1 and yet the process be correct4 ,it is precisely because that operation is omitted in ordinary unscientific reasoning1 that there is any thing gained in certainty by throwing reasoning into the syllogistic form4 ,to make sure1 as far as possible1 that it shall not be omitted1 we make the testing operation a part of the reasoning process itself4 ,we insist that the inference from particulars to particulars shall pass through a general proposition4 ,but this is a security for good reasoning1 not a condition of all reasoning2 and in some cases not even a security4 ,our most familiar inferences are all made before we learn the use of general propositions2 and a person of untutored sagacity will skillfully apply his acquired experience to adjacent cases1 though he would bungle grievously in fixing the limits of the appropriate general theorem4 ,but though he may conclude rightly1 he never1 properly speaking1 knows whether he has done so or not2 he has not tested his reasoning4 ,now1 this is precisely what forms of reasoning do for us4 ,we do not need them to enable us to reason1 but to enable us to know whether we reason correctly4 ,in still further answer to the objection1 it may be added that--even when the test has been applied1 and the sufficiency of the evidence recognized--if it is sufficient to support the general proposition1 it is sufficient also to support an inference from particulars to particulars without passing through the general proposition4 ,the inquirer who has logically satisfied himself that the conditions of legitimate induction were realized in the cases ,a1 ,b1 ,c1 would be as much justified in concluding directly to the ,duke of ,wellington as in concluding to all men4 ,the general conclusion is never legitimate1 unless the particular one would be so too2 and in no sense1 intelligible to me1 can the particular conclusion be said to be drawn from the general one4 ,whenever there is ground for drawing any conclusion at all from particular instances1 there is ground for a general conclusion2 but that this general conclusion should be actually drawn1 however useful1 can not be an indispensable condition of the validity of the inference in the particular case4 ,a man gives away sixpence by the same power by which he disposes of his whole fortune2 but it is not necessary to the legality of the smaller act1 that he should make a formal assertion of his right to the greater one4 ,some additional remarks1 in reply to minor objections1 are appended47#fe7 #i4 ,the preceding considerations enable us to understand the true nature of what is termed1 by recent writers1 ,formal ,logic1 and the relation between it and ,logic in the widest sense4 ,logic1 as ,i conceive it1 is the entire theory of the ascertainment of reasoned or inferred truth4 ,formal ,logic1 therefore1 which ,sir ,william ,hamilton from his own point of view1 and ,archbishop ,whately from his1 have represented as the whole of ,logic properly so called1 is really a very subordinate part of it1 not being directly concerned with the process of ,reasoning or ,inference in the sense in which that process is a part of the ,investigation of ,truth4 ,what1 then1 is ,formal ,logic8 ,the name seems to be properly applied to all that portion of doctrine which relates to the equivalence of different modes of expression2 the rules for determining when assertions in a given form imply or suppose the truth or falsity of other assertions4 ,this includes the theory of the ,import of ,propositions1 and of their ,conversion1 quipollence1 and ,opposition2 of those falsely called ,inductions 7to be hereafter spoken of77#ff71 in which the apparent generalization is a mere abridged statement of cases known individually2 and finally1 of the syllogism3 while the theory of ,naming1 and of 7what is inseparably connected with it7 ,definition1 though belonging still more to the other and larger kind of logic than to this1 is a necessary preliminary to this4 ,the end aimed at by ,formal ,logic1 and attained by the observance of its precepts1 is not truth1 but consistency4 ,it has been seen that this is the only direct purpose of the rules of the syllogism2 the intention and effect of which is simply to keep our inferences or conclusions in complete consistency with our general formul or directions for drawing them4 ,the ,logic of ,consistency is a necessary auxiliary to the logic of truth1 not only because what is inconsistent with itself or with other truths can not be true1 but also because truth can only be successfully pursued by drawing inferences from experience1 which1 if warrantable at all1 admit of being generalized1 and1 to test their warrantableness1 require to be exhibited in a generalized form2 after which the correctness of their application to particular cases is a question which specially concerns the ,logic of ,consistency4 ,this ,logic1 not requiring any preliminary knowledge of the processes or conclusions of the various sciences1 may be studied with benefit in a much earlier stage of education than the ,logic of ,truth3 and the practice which has empirically obtained of teaching it apart1 through elementary treatises which do not attempt to include any thing else1 though the reasons assigned for the practice are in general very far from philosophical1 admits of philosophical justification4 ,chapter ,,iv4 ,of ,trains ,of ,reasoning1 ,and ,deductive ,sciences4 #a4 ,in our analysis of the syllogism1 it appeared that the minor premise always affirms a resemblance between a new case and some cases previously known2 while the major premise asserts something which1 having been found true of those known cases1 we consider ourselves warranted in holding true of any other case resembling the former in certain given particulars4 ,if all ratiocinations resembled1 as to the minor premise1 the examples which were exclusively employed in the preceding chapter2 if the resemblance1 which that premise asserts1 were obvious to the senses1 as in the proposition 8,socrates is a man10 or were at once ascertainable by direct observation2 there would be no necessity for trains of reasoning1 and ,deductive or ,ratiocinative ,sciences would not exist4 ,trains of reasoning exist only for the sake of extending an induction founded1 as all inductions must be1 on observed cases1 to other cases in which we not only can not directly observe the fact which is to be proved1 but can not directly observe even the mark which is to prove it4 #b4 ,suppose the syllogism to be1 ,all cows ruminate1 the animal which is before me is a cow1 therefore it ruminates4 ,the minor1 if true at all1 is obviously so3 the only premise the establishment of which requires any anterior process of inquiry1 is the major2 and provided the induction of which that premise is the expression was correctly performed1 the conclusion respecting the animal now present will be instantly drawn2 because1 as soon as she is compared with the formula1 she will be identified as being included in it4 ,but suppose the syllogism to be the following3 ,all arsenic is poisonous1 the substance which is before me is arsenic1 therefore it is poisonous4 ,the truth of the minor may not here be obvious at first sight2 it may not be intuitively evident1 but may itself be known only by inference4 ,it may be the conclusion of another argument1 which1 thrown into the syllogistic form1 would stand thus3 ,whatever when lighted produces a dark spot on a piece of white porcelain held in the flame1 which spot is soluble in hypochloride of calcium1 is arsenic2 the substance before me conforms to this condition2 therefore it is arsenic4 ,to establish1 therefore1 the ultimate conclusion1 ,the substance before me is poisonous1 requires a process1 which1 in order to be syllogistically expressed1 stands in need of two syllogisms2 and we have a ,train of ,reasoning4 ,when1 however1 we thus add syllogism to syllogism1 we are really adding induction to induction4 ,two separate inductions must have taken place to render this chain of inference possible2 inductions founded1 probably1 on different sets of individual instances1 but which converge in their results1 so that the instance which is the subject of inquiry comes within the range of them both4 ,the record of these inductions is contained in the majors of the two syllogisms4 ,first1 we1 or others for us1 have examined various objects which yielded under the given circumstances a dark spot with the given property1 and found that they possessed the properties connoted by the word arsenic2 they were metallic1 volatile1 their vapor had a smell of garlic1 and so forth4 ,next1 we1 or others for us1 have examined various specimens which possessed this metallic and volatile character1 whose vapor had this smell1 etc41 and have invariably found that they were poisonous4 ,the first observation we judge that we may extend to all substances whatever which yield that particular kind of dark spot2 the second1 to all metallic and volatile substances resembling those we examined2 and consequently1 not to those only which are seen to be such1 but to those which are concluded to be such by the prior induction4 ,the substance before us is only seen to come within one of these inductions2 but by means of this one1 it is brought within the other4 ,we are still1 as before1 concluding from particulars to particulars2 but we are now concluding from particulars observed1 to other particulars which are not1 as in the simple case1 seen to resemble them in material points1 but inferred to do so1 because resembling them in something else1 which we have been led by quite a different set of instances to consider as a mark of the former resemblance4 ,this first example of a train of reasoning is still extremely simple1 the series consisting of only two syllogisms4 ,the following is somewhat more complicated3 ,no government1 which earnestly seeks the good of its subjects1 is likely to be overthrown2 some particular government earnestly seeks the good of its subjects1 therefore it is not likely to be overthrown4 ,the major premise in this argument we shall suppose not to be derived from considerations a priori1 but to be a generalization from history1 which1 whether correct or erroneous1 must have been founded on observation of governments concerning whose desire of the good of their subjects there was no doubt4 ,it has been found1 or thought to be found1 that these were not easily overthrown1 and it has been deemed that those instances warranted an extension of the same predicate to any and every government which resembles them in the attribute of desiring earnestly the good of its subjects4 ,but does the government in question thus resemble them8 ,this may be debated pro and con by many arguments1 and must1 in any case1 be proved by another induction2 for we can not directly observe the sentiments and desires of the persons who carry on the government4 ,to prove the minor1 therefore1 we require an argument in this form3 ,every government which acts in a certain manner1 desires the good of its subjects2 the supposed government acts in that particular manner1 therefore it desires the good of its subjects4 ,but is it true that the government acts in the manner supposed8 ,this minor also may require proof2 still another induction1 as thus3 ,what is asserted by intelligent and disinterested witnesses1 may be believed to be true2 that the government acts in this manner1 is asserted by such witnesses1 therefore it may be believed to be true4 ,the argument hence consists of three steps4 ,having the evidence of our senses that the case of the government under consideration resembles a number of former cases1 in the circumstance of having something asserted respecting it by intelligent and disinterested witnesses1 we infer1 first1 that1 as in those former instances1 so in this instance1 the assertion is true4 ,secondly1 what was asserted of the government being that it acts in a particular manner1 and other governments or persons having been observed to act in the same manner1 the government in question is brought into known resemblance with those other governments or persons2 and since they were known to desire the good of the people1 it is thereupon1 by a second induction1 inferred that the particular government spoken of1 desires the good of the people4 ,this brings that government into known resemblance with the other governments which were thought likely to escape revolution1 and thence1 by a third induction1 it is concluded that this particular government is also likely to escape4 ,this is still reasoning from particulars to particulars1 but we now reason to the new instance from three distinct sets of former instances3 to one only of those sets of instances do we directly perceive the new one to be similar2 but from that similarity we inductively infer that it has the attribute by which it is assimilated to the next set1 and brought within the corresponding induction2 after which by a repetition of the same operation we infer it to be similar to the third set1 and hence a third induction conducts us to the ultimate conclusion4 #c4 ,notwithstanding the superior complication of these examples1 compared with those by which in the preceding chapter we illustrated the general theory of reasoning1 every doctrine which we then laid down holds equally true in these more intricate cases4 ,the successive general propositions are not steps in the reasoning1 are not intermediate links in the chain of inference1 between the particulars observed and those to which we apply the observation4 ,if we had sufficiently capacious memories1 and a sufficient power of maintaining order among a huge mass of details1 the reasoning could go on without any general propositions2 they are mere formul for inferring particulars from particulars4 ,the principle of general reasoning is 7as before explained71 that if1 from observation of certain known particulars1 what was seen to be true of them can be inferred to be true of any others1 it may be inferred of all others which are of a certain description4 ,and in order that we may never fail to draw this conclusion in a new case when it can be drawn correctly1 and may avoid drawing it when it can not1 we determine once for all what are the distinguishing marks by which such cases may be recognized4 ,the subsequent process is merely that of identifying an object1 and ascertaining it to have those marks2 whether we identify it by the very marks themselves1 or by others which we have ascertained 7through another and a similar process7 to be marks of those marks4 ,the real inference is always from particulars to particulars1 from the observed instances to an unobserved one3 but in drawing this inference1 we conform to a formula which we have adopted for our guidance in such operations1 and which is a record of the criteria by which we thought we had ascertained that we might distinguish when the inference could1 and when it could not1 be drawn4 ,the real premises are the individual observations1 even though they may have been forgotten1 or1 being the observations of others and not of ourselves1 may1 to us1 never have been known3 but we have before us proof that we or others once thought them sufficient for an induction1 and we have marks to show whether any new case is one of those to which1 if then known1 the induction would have been deemed to extend4 ,these marks we either recognize at once1 or by the aid of other marks1 which by another previous induction we collected to be marks of the first4 ,even these marks of marks may only be recognized through a third set of marks2 and we may have a train of reasoning1 of any length1 to bring a new case within the scope of an induction grounded on particulars its similarity to which is only ascertained in this indirect manner4 ,thus1 in the preceding example1 the ultimate inductive inference was1 that a certain government was not likely to be overthrown2 this inference was drawn according to a formula in which desire of the public good was set down as a mark of not being likely to be overthrown2 a mark of this mark was1 acting in a particular manner2 and a mark of acting in that manner was1 being asserted to do so by intelligent and disinterested witnesses3 this mark1 the government under discussion was recognized by the senses as possessing4 ,hence that government fell within the last induction1 and by it was brought within all the others4 ,the perceived resemblance of the case to one set of observed particular cases1 brought it into known resemblance with another set1 and that with a third4 ,in the more complex branches of knowledge1 the deductions seldom consist1 as in the examples hitherto exhibited1 of a single chain1 a a mark of b1 b of c1 c of d1 therefore a a mark of d4 ,they consist 7to carry on the same metaphor7 of several chains united at the extremity1 as thus3 a a mark of d1 b of e1 c of f1 d e f of n1 therefore a b c a mark of n4 ,suppose1 for example1 the following combination of circumstances3 #ast1 rays of light impinging on a reflecting surface2 #b;d1 that surface parabolic2 #c;d1 those rays parallel to each other and to the axis of the surface4 ,it is to be proved that the concourse of these three circumstances is a mark that the reflected rays will pass through the focus of the parabolic surface4 ,now1 each of the three circumstances is singly a mark of something material to the case4 ,rays of light impinging on a reflecting surface are a mark that those rays will be reflected at an angle equal to the angle of incidence4 ,the parabolic form of the surface1 is a mark that1 from any point of it1 a line drawn to the focus and a line parallel to the axis will make equal angles with the surface4 ,and finally1 the parallelism of the rays to the axis is a mark that their angle of incidence coincides with one of these equal angles4 ,the three marks taken together are therefore a mark of all these three things united4 ,but the three united are evidently a mark that the angle of reflection must coincide with the other of the two equal angles1 that formed by a line drawn to the focus2 and this again1 by the fundamental axiom concerning straight lines1 is a mark that the reflected rays pass through the focus4 ,most chains of physical deduction are of this more complicated type2 and even in mathematics such are abundant1 as in all propositions where the hypothesis includes numerous conditions3 8,if a circle be taken1 and if within that circle a point be taken1 not the centre1 and if straight lines be drawn from that point to the circumference1 then10 etc4 #d4 ,the considerations now stated remove a serious difficulty from the view we have taken of reasoning2 which view might otherwise have seemed not easily reconcilable with the fact that there are ,deductive or ,ratiocinative ,sciences4 ,it might seem to follow1 if all reasoning be induction1 that the difficulties of philosophical investigation must lie in the inductions exclusively1 and that when these were easy1 and susceptible of no doubt or hesitation1 there could be no science1 or1 at least1 no difficulties in science4 ,the existence1 for example1 of an extensive ,science of ,mathematics1 requiring the highest scientific genius in those who contributed to its creation1 and calling for a most continued and vigorous exertion of intellect in order to appropriate it when created1 may seem hard to be accounted for on the foregoing theory4 ,but the considerations more recently adduced remove the mystery1 by showing1 that even when the inductions themselves are obvious1 there may be much difficulty in finding whether the particular case which is the subject of inquiry comes within them2 and ample room for scientific ingenuity in so combining various inductions1 as1 by means of one within which the case evidently falls1 to bring it within others in which it can not be directly seen to be included4 ,when the more obvious of the inductions which can be made in any science from direct observations1 have been made1 and general formulas have been framed1 determining the limits within which these inductions are applicable2 as often as a new case can be at once seen to come within one of the formulas1 the induction is applied to the new case1 and the business is ended4 ,but new cases are continually arising1 which do not obviously come within any formula whereby the question we want solved in respect of them could be answered4 ,let us take an instance from geometry3 and as it is taken only for illustration1 let the reader concede to us for the present1 what we shall endeavor to prove in the next chapter1 that the first principles of geometry are results of induction4 ,our example shall be the fifth proposition of the first book of ,euclid4 ,the inquiry is1 ,are the angles at the base of an isosceles triangle equal or unequal8 ,the first thing to be considered is1 what inductions we have1 from which we can infer equality or inequality4 ,for inferring equality we have the following formul3 ,things which being applied to each other coincide1 are equals4 ,things which are equal to the same thing are equals4 ,a whole and the sum of its parts are equals4 ,the sums of equal things are equals4 ,the differences of equal things are equals4 ,there are no other original formul to prove equality4 ,for inferring inequality we have the following3 ,a whole and its parts are unequals4 ,the sums of equal things and unequal things are unequals4 ,the differences of equal things and unequal things are unequals4 ,in all1 eight formul4 ,the angles at the base of an isosceles triangle do not obviously come within any of these4 ,the formul specify certain marks of equality and of inequality1 but the angles can not be perceived intuitively to have any of those marks4 ,on examination it appears that they have2 and we ultimately succeed in bringing them within the formula1 8,the differences of equal things are equal40 ,whence comes the difficulty of recognizing these angles as the differences of equal things8 ,because each of them is the difference not of one pair only1 but of innumerable pairs of angles2 and out of these we had to imagine and select two1 which could either be intuitively perceived to be equals1 or possessed some of the marks of equality set down in the various formul4 ,by an exercise of ingenuity1 which1 on the part of the first inventor1 deserves to be regarded as considerable1 two pairs of angles were hit upon1 which united these requisites4 ,first1 it could be perceived intuitively that their differences were the angles at the base2 and1 secondly1 they possessed one of the marks of equality1 namely1 coincidence when applied to one another4 ,this coincidence1 however1 was not perceived intuitively1 but inferred1 in conformity to another formula4 ,for greater clearness1 ,i subjoin an analysis of the demonstration4 ,euclid1 it will be remembered1 demonstrates his fifth proposition by means of the fourth4 ,this it is not allowable for us to do1 because we are undertaking to trace deductive truths not to prior deductions1 but to their original inductive foundation4 ,we must1 therefore1 use the premises of the fourth proposition instead of its conclusion1 and prove the fifth directly from first principles4 ,to do so requires six formulas4 7,we presuppose an equilateral triangle1 whose vertices are ,a1 ,d1 ,e1 with point ,b on the side ,,ad1 and point ,c on the side ,,ae1 such that ,,bc is parallel to ,,de4 ,we must begin1 as in ,euclid1 by prolonging the equal sides ,,ab1 ,,ac1 to equal distances1 and joining the extremities ,,be1 ,,dc47 ,,first ,,formula4--,the sums of equals are equal4 ,,ad and ,,ae are sums of equals by the supposition4 ,having that mark of equality1 they are concluded by this formula to be equal4 ,,second ,,formula4--,equal straight lines or angles1 being applied to one another1 coincide4 ,,ac1 ,,ab1 are within this formula by supposition2 ,,ad1 ,,ae1 have been brought within it by the preceding step4 ,the angle at ,a considered as an angle of the triangle ,,abe1 and the same angle considered as an angle of the triangle ,,acd1 are of course within the formula4 ,all these pairs1 therefore1 possess the property which1 according to the second formula1 is a mark that when applied to one another they will coincide4 ,conceive them1 then1 applied to one another1 by turning over the triangle ,,abe1 and laying it on the triangle ,,acd in such a manner that ,,ab of the one shall lie upon ,,ac of the other4 ,then1 by the equality of the angles1 ,,ae will lie on ,,ad4 ,but ,,ab and ,,ac1 ,,ae and ,,ad are equals2 therefore they will coincide altogether1 and of course at their extremities1 ,d1 ,e1 and ,b1 ,c4 ,,third ,,formula4--,straight lines1 having their extremities coincident1 coincide4 ,,be and ,,cd have been brought within this formula by the preceding induction2 they will1 therefore1 coincide4 ,,fourth ,,formula4--,angles1 having their sides coincident1 coincide4 ,the third induction having shown that ,,be and ,,cd coincide1 and the second that ,,ab1 ,,ac1 coincide1 the angles ,,abe and ,,acd are thereby brought within the fourth formula1 and accordingly coincide4 ,,fifth ,,formula4--,things which coincide are equal4 ,the angles ,,abe and ,,acd are brought within this formula by the induction immediately preceding4 ,this train of reasoning being also applicable1 mutatis mutandis1 to the angles ,,ebc1 ,,dcb1 these also are brought within the fifth formula4 ,and1 finally1 ,,sixth ,,formula4--,the differences of equals are equal4 ,the angle ,,abc being the difference of ,,abe1 ,,cbe1 and the angle ,,acb being the difference of ,,acd1 ,,dcb2 which have been proved to be equals2 ,,abc and ,,acb are brought within the last formula by the whole of the previous process4 ,the difficulty here encountered is chiefly that of figuring to ourselves the two angles at the base of the triangle ,,abc as remainders made by cutting one pair of angles out of another1 while each pair shall be corresponding angles of triangles which have two sides and the intervening angle equal4 ,it is by this happy contrivance that so many different inductions are brought to bear upon the same particular case4 ,and this not being at all an obvious thought1 it may be seen from an example so near the threshold of mathematics1 how much scope there may well be for scientific dexterity in the higher branches of that and other sciences1 in order so to combine a few simple inductions1 as to bring within each of them innumerable cases which are not obviously included in it2 and how long1 and numerous1 and complicated may be the processes necessary for bringing the inductions together1 even when each induction may itself be very easy and simple4 ,all the inductions involved in all geometry are comprised in those simple ones1 the formul of which are the ,axioms1 and a few of the so-called ,definitions4 ,the remainder of the science is made up of the processes employed for bringing unforeseen cases within these inductions2 or 7in syllogistic language7 for proving the minors necessary to complete the syllogisms2 the majors being the definitions and axioms4 ,in those definitions and axioms are laid down the whole of the marks1 by an artful combination of which it has been found possible to discover and prove all that is proved in geometry4 ,the marks being so few1 and the inductions which furnish them being so obvious and familiar2 the connecting of several of them together1 which constitutes ,deductions1 or ,trains of ,reasoning1 forms the whole difficulty of the science1 and1 with a trifling exception1 its whole bulk2 and hence ,geometry is a ,deductive ,science4 #e4 ,it will be seen hereafter7#fg7 that there are weighty scientific reasons for giving to every science as much of the character of a ,deductive ,science as possible2 for endeavoring to construct the science from the fewest and the simplest possible inductions1 and to make these1 by any combinations however complicated1 suffice for proving even such truths1 relating to complex cases1 as could be proved1 if we chose1 by inductions from specific experience4 ,every branch of natural philosophy was originally experimental2 each generalization rested on a special induction1 and was derived from its own distinct set of observations and experiments4 ,from being sciences of pure experiment1 as the phrase is1 or1 to speak more correctly1 sciences in which the reasonings mostly consist of no more than one step1 and are expressed by single syllogisms1 all these sciences have become to some extent1 and some of them in nearly the whole of their extent1 sciences of pure reasoning2 whereby multitudes of truths1 already known by induction from as many different sets of experiments1 have come to be exhibited as deductions or corollaries from inductive propositions of a simpler and more universal character4 ,thus mechanics1 hydrostatics1 optics1 acoustics1 thermology1 have successively been rendered mathematical2 and astronomy was brought by ,newton within the laws of general mechanics4 ,why it is that the substitution of this circuitous mode of proceeding for a process apparently much easier and more natural1 is held1 and justly1 to be the greatest triumph of the investigation of nature1 we are not1 in this stage of our inquiry1 prepared to examine4 ,but it is necessary to remark1 that although1 by this progressive transformation1 all sciences tend to become more and more ,deductive1 they are not1 therefore1 the less ,inductive2 every step in the ,deduction is still an ,induction4 ,the opposition is not between the terms ,deductive and ,inductive1 but between ,deductive and ,experimental4 ,a science is experimental1 in proportion as every new case1 which presents any peculiar features1 stands in need of a new set of observations and experiments--a fresh induction4 ,it is deductive1 in proportion as it can draw conclusions1 respecting cases of a new kind1 by processes which bring those cases under old inductions2 by ascertaining that cases which can not be observed to have the requisite marks1 have1 however1 marks of those marks4 ,we can now1 therefore1 perceive what is the generic distinction between sciences which can be made ,deductive1 and those which must as yet remain ,experimental4 ,the difference consists in our having been able1 or not yet able1 to discover marks of marks4 ,if by our various inductions we have been able to proceed no further than to such propositions as these1 a a mark of b1 or a and b marks of one another1 c a mark of d1 or c and d marks of one another1 without any thing to connect a or b with c or d2 we have a science of detached and mutually independent generalizations1 such as these1 that acids redden vegetable blues1 and that alkalies color them green2 from neither of which propositions could we1 directly or indirectly1 infer the other3 and a science1 so far as it is composed of such propositions1 is purely experimental4 ,chemistry1 in the present state of our knowledge1 has not yet thrown off this character4 ,there are other sciences1 however1 of which the propositions are of this kind3 a a mark of b1 b a mark of c1 c of d1 d of e1 etc4 ,in these sciences we can mount the ladder from a to e by a process of ratiocination2 we can conclude that a is a mark of e1 and that every object which has the mark a has the property e1 although1 perhaps1 we never were able to observe a and e together1 and although even d1 our only direct mark of e1 may not be perceptible in those objects1 but only inferable4 ,or1 varying the first metaphor1 we may be said to get from a to e underground3 the marks b1 c1 d1 which indicate the route1 must all be possessed somewhere by the objects concerning which we are inquiring2 but they are below the surface3 a is the only mark that is visible1 and by it we are able to trace in succession all the rest4 #f4 ,we can now understand how an experimental may transform itself into a deductive science by the mere progress of experiment4 ,in an experimental science1 the inductions1 as we have said1 lie detached1 as1 a a mark of b1 c a mark of d1 e a mark of f1 and so on3 now1 a new set of instances1 and a consequent new induction1 may at any time bridge over the interval between two of these unconnected arches2 b1 for example1 may be ascertained to be a mark of c1 which enables us thenceforth to prove deductively that a is a mark of c4 ,or1 as sometimes happens1 some comprehensive induction may raise an arch high in the air1 which bridges over hosts of them at once2 b1 d1 f1 and all the rest1 turning out to be marks of some one thing1 or of things between which a connection has already been traced4 ,as when ,newton discovered that the motions1 whether regular or apparently anomalous1 of all the bodies of the solar system 7each of which motions had been inferred by a separate logical operation1 from separate marks71 were all marks of moving round a common centre1 with a centripetal force varying directly as the mass1 and inversely as the square of the distance from that centre4 ,this is the greatest example which has yet occurred of the transformation1 at one stroke1 of a science which was still to a great degree merely experimental1 into a deductive science4 ,transformations of the same nature1 but on a smaller scale1 continually take place in the less advanced branches of physical knowledge1 without enabling them to throw off the character of experimental sciences4 ,thus with regard to the two unconnected propositions before cited1 namely1 ,acids redden vegetable blues1 ,alkalies make them green2 it is remarked by ,liebig1 that all blue coloring matters which are reddened by acids 7as well as1 reciprocally1 all red coloring matters which are rendered blue by alkalies7 contain nitrogen3 and it is quite possible that this circumstance may one day furnish a bond of connection between the two propositions in question1 by showing that the antagonistic action of acids and alkalies in producing or destroying the color blue1 is the result of some one1 more general1 law4 ,although this connecting of detached generalizations is so much gain1 it tends but little to give a deductive character to any science as a whole2 because the new courses of observation and experiment1 which thus enable us to connect together a few general truths1 usually make known to us a still greater number of unconnected new ones4 ,hence chemistry1 though similar extensions and simplifications of its generalizations are continually taking place1 is still in the main an experimental science2 and is likely so to continue unless some comprehensive induction should be hereafter arrived at1 which1 like ,newton's1 shall connect a vast number of the smaller known inductions together1 and change the whole method of the science at once4 ,chemistry has already one great generalization1 which1 though relating to one of the subordinate aspects of chemical phenomena1 possesses within its limited sphere this comprehensive character2 the principle of ,dalton1 called the atomic theory1 or the doctrine of chemical equivalents3 which by enabling us to a certain extent to foresee the proportions in which two substances will combine1 before the experiment has been tried1 constitutes undoubtedly a source of new chemical truths obtainable by deduction1 as well as a connecting principle for all truths of the same description previously obtained by experiment4 #g4 ,the discoveries which change the method of a science from experimental to deductive1 mostly consist in establishing1 either by deduction or by direct experiment1 that the varieties of a particular phenomenon uniformly accompany the varieties of some other phenomenon better known4 ,thus the science of sound1 which previously stood in the lowest rank of merely experimental science1 became deductive when it was proved by experiment that every variety of sound was consequent on1 and therefore a mark of1 a distinct and definable variety of oscillatory motion among the particles of the transmitting medium4 ,when this was ascertained1 it followed that every relation of succession or co-existence which obtained between phenomena of the more known class1 obtained also between the phenomena which correspond to them in the other class4 ,every sound1 being a mark of a particular oscillatory motion1 became a mark of every thing which1 by the laws of dynamics1 was known to be inferable from that motion2 and every thing which by those same laws was a mark of any oscillatory motion among the particles of an elastic medium1 became a mark of the corresponding sound4 ,and thus many truths1 not before suspected1 concerning sound1 become deducible from the known laws of the propagation of motion through an elastic medium2 while facts already empirically known respecting sound1 become an indication of corresponding properties of vibrating bodies1 previously undiscovered4 ,but the grand agent for transforming experimental into deductive sciences1 is the science of number4 ,the properties of number1 alone among all known phenomena1 are1 in the most rigorous sense1 properties of all things whatever4 ,all things are not colored1 or ponderable1 or even extended2 but all things are numerable4 ,and if we consider this science in its whole extent1 from common arithmetic up to the calculus of variations1 the truths already ascertained seem all but infinite1 and admit of indefinite extension4 ,these truths1 though affirmable of all things whatever1 of course apply to them only in respect of their quantity4 ,but if it comes to be discovered that variations of quality in any class of phenomena1 correspond regularly to variations of quantity either in those same or in some other phenomena2 every formula of mathematics applicable to quantities which vary in that particular manner1 becomes a mark of a corresponding general truth1 respecting the variations in quality which accompany them3 and the science of quantity being 7as far as any science can be7 altogether deductive1 the theory of that particular kind of qualities becomes1 to this extent1 deductive likewise4 ,the most striking instance in point which history affords 7though not an example of an experimental science rendered deductive1 but of an unparalleled extension given to the deductive process in a science which was deductive already71 is the revolution in geometry which originated with ,descartes1 and was completed by ,clairaut4 ,these great mathematicians pointed out the importance of the fact1 that to every variety of position in points1 direction in lines1 or form in curves or surfaces 7all of which are ,qualities71 there corresponds a peculiar relation of quantity between either two or three rectilineal co-ordinates2 insomuch that if the law were known according to which those co-ordinates vary relatively to one another1 every other geometrical property of the line or surface in question1 whether relating to quantity or quality1 would be capable of being inferred4 ,hence it followed that every geometrical question could be solved1 if the corresponding algebraical one could2 and geometry received an accession 7actual or potential7 of new truths1 corresponding to every property of numbers which the progress of the calculus had brought1 or might in future bring1 to light4 ,in the same general manner1 mechanics1 astronomy1 and in a less degree1 every branch of natural philosophy commonly so called1 have been made algebraical4 ,the varieties of physical phenomena with which those sciences are conversant1 have been found to answer to determinable varieties in the quantity of some circumstance or other2 or at least to varieties of form or position1 for which corresponding equations of quantity had already been1 or were susceptible of being1 discovered by geometers4 ,in these various transformations1 the propositions of the science of number do but fulfill the function proper to all propositions forming a train of reasoning1 viz41 that of enabling us to arrive in an indirect method1 by marks of marks1 at such of the properties of objects as we can not directly ascertain 7or not so conveniently7 by experiment4 ,we travel from a given visible or tangible fact1 through the truths of numbers1 to the facts sought4 ,the given fact is a mark that a certain relation subsists between the quantities of some of the elements concerned2 while the fact sought presupposes a certain relation between the quantities of some other elements3 now1 if these last quantities are dependent in some known manner upon the former1 or vic versa1 we can argue from the numerical relation between the one set of quantities1 to determine that which subsists between the other set2 the theorems of the calculus affording the intermediate links4 ,and thus one of the two physical facts becomes a mark of the other1 by being a mark of a mark of a mark of it4 ,chapter ,v4 ,of ,demonstration1 ,and ,necessary ,truths4 #a4 ,if1 as laid down in the two preceding chapters1 the foundation of all sciences1 even deductive or demonstrative sciences1 is ,induction2 if every step in the ratiocinations even of geometry is an act of induction2 and if a train of reasoning is but bringing many inductions to bear upon the same subject of inquiry1 and drawing a case within one induction by means of another2 wherein lies the peculiar certainty always ascribed to the sciences which are entirely1 or almost entirely1 deductive8 ,why are they called the ,exact ,sciences8 ,why are mathematical certainty1 and the evidence of demonstration1 common phrases to express the very highest degree of assurance attainable by reason8 ,why are mathematics by almost all philosophers1 and 7by some7 even those branches of natural philosophy which1 through the medium of mathematics1 have been converted into deductive sciences1 considered to be independent of the evidence of experience and observation1 and characterized as systems of ,necessary ,truth8 ,the answer ,i conceive to be1 that this character of necessity1 ascribed to the truths of mathematics1 and 7even with some reservations to be hereafter made7 the peculiar certainty attributed to them1 is an illusion2 in order to sustain which1 it is necessary to suppose that those truths relate to1 and express the properties of1 purely imaginary objects4 ,it is acknowledged that the conclusions of geometry are deduced1 partly at least1 from the so-called ,definitions1 and that those definitions are assumed to be correct representations1 as far as they go1 of the objects with which geometry is conversant4 ,now we have pointed out that1 from a definition as such1 no proposition1 unless it be one concerning the meaning of a word1 can ever follow2 and that what apparently follows from a definition1 follows in reality from an implied assumption that there exists a real thing conformable thereto4 ,this assumption1 in the case of the definitions of geometry1 is not strictly true3 there exist no real things exactly conformable to the definitions4 ,there exist no points without magnitude2 no lines without breadth1 nor perfectly straight2 no circles with all their radii exactly equal1 nor squares with all their angles perfectly right4 ,it will perhaps be said that the assumption does not extend to the actual1 but only to the possible1 existence of such things4 ,i answer that1 according to any test we have of possibility1 they are not even possible4 ,their existence1 so far as we can form any judgment1 would seem to be inconsistent with the physical constitution of our planet at least1 if not of the universe4 ,to get rid of this difficulty1 and at the same time to save the credit of the supposed system of necessary truth1 it is customary to say that the points1 lines1 circles1 and squares which are the subject of geometry1 exist in our conceptions merely1 and are part of our minds2 which minds1 by working on their own materials1 construct an a priori science1 the evidence of which is purely mental1 and has nothing whatever to do with outward experience4 ,by howsoever high authorities this doctrine may have been sanctioned1 it appears to me psychologically incorrect4 ,the points1 lines1 circles1 and squares which any one has in his mind1 are 7,i apprehend7 simply copies of the points1 lines1 circles1 and squares which he has known in his experience4 ,our idea of a point1 ,i apprehend to be simply our idea of the minimum visibile1 the smallest portion of surface which we can see4 ,a line1 as defined by geometers1 is wholly inconceivable4 ,we can reason about a line as if it had no breadth2 because we have a power1 which is the foundation of all the control we can exercise over the operations of our minds2 the power1 when a perception is present to our senses1 or a conception to our intellects1 of attending to a part only of that perception or conception1 instead of the whole4 ,but we can not conceive a line without breadth2 we can form no mental picture of such a line3 all the lines which we have in our minds are lines possessing breadth4 ,if any one doubts this1 we may refer him to his own experience4 ,i much question if any one who fancies that he can conceive what is called a mathematical line1 thinks so from the evidence of his consciousness3 ,i suspect it is rather because he supposes that unless such a conception were possible1 mathematics could not exist as a science3 a supposition which there will be no difficulty in showing to be entirely groundless4 ,since1 then1 neither in nature1 nor in the human mind1 do there exist any objects exactly corresponding to the definitions of geometry1 while yet that science can not be supposed to be conversant about nonentities2 nothing remains but to consider geometry as conversant with such lines1 angles1 and figures1 as really exist2 and the definitions1 as they are called1 must be regarded as some of our first and most obvious generalizations concerning those natural objects4 ,the correctness of those generalizations1 as generalizations1 is without a flaw3 the equality of all the radii of a circle is true of all circles1 so far as it is true of any one3 but it is not exactly true of any circle2 it is only nearly true2 so nearly that no error of any importance in practice will be incurred by feigning it to be exactly true4 ,when we have occasion to extend these inductions1 or their consequences1 to cases in which the error would be appreciable--to lines of perceptible breadth or thickness1 parallels which deviate sensibly from equidistance1 and the like--we correct our conclusions1 by combining with them a fresh set of propositions relating to the aberration2 just as we also take in propositions relating to the physical or chemical properties of the material1 if those properties happen to introduce any modification into the result2 which they easily may1 even with respect to figure and magnitude1 as in the case1 for instance1 of expansion by heat4 ,so long1 however1 as there exists no practical necessity for attending to any of the properties of the object except its geometrical properties1 or to any of the natural irregularities in those1 it is convenient to neglect the consideration of the other properties and of the irregularities1 and to reason as if these did not exist3 accordingly1 we formally announce in the definitions1 that we intend to proceed on this plan4 ,but it is an error to suppose1 because we resolve to confine our attention to a certain number of the properties of an object1 that we therefore conceive1 or have an idea of1 the object1 denuded of its other properties4 ,we are thinking1 all the time1 of precisely such objects as we have seen and touched1 and with all the properties which naturally belong to them2 but1 for scientific convenience1 we feign them to be divested of all properties1 except those which are material to our purpose1 and in regard to which we design to consider them4 ,the peculiar accuracy1 supposed to be characteristic of the first principles of geometry1 thus appears to be fictitious4 ,the assertions on which the reasonings of the science are founded1 do not1 any more than in other sciences1 exactly correspond with the fact2 but we suppose that they do so1 for the sake of tracing the consequences which follow from the supposition4 ,the opinion of ,dugald ,stewart respecting the foundations of geometry1 is1 ,i conceive1 substantially correct2 that it is built on hypotheses2 that it owes to this alone the peculiar certainty supposed to distinguish it2 and that in any science whatever1 by reasoning from a set of hypotheses1 we may obtain a body of conclusions as certain as those of geometry1 that is1 as strictly in accordance with the hypotheses1 and as irresistibly compelling assent1 on condition that those hypotheses are true47#fh7 ,when1 therefore1 it is affirmed that the conclusions of geometry are necessary truths1 the necessity consists in reality only in this1 that they correctly follow from the suppositions from which they are deduced4 ,those suppositions are so far from being necessary1 that they are not even true2 they purposely depart1 more or less widely1 from the truth4 ,the only sense in which necessity can be ascribed to the conclusions of any scientific investigation1 is that of legitimately following from some assumption1 which1 by the conditions of the inquiry1 is not to be questioned4 ,in this relation1 of course1 the derivative truths of every deductive science must stand to the inductions1 or assumptions1 on which the science is founded1 and which1 whether true or untrue1 certain or doubtful in themselves1 are always supposed certain for the purposes of the particular science4 ,and therefore the conclusions of all deductive sciences were said by the ancients to be necessary propositions4 ,we have observed already that to be predicated necessarily was characteristic of the predicable ,proprium1 and that a proprium was any property of a thing which could be deduced from its essence1 that is1 from the properties included in its definition4 #b4 ,the important doctrine of ,dugald ,stewart1 which ,i have endeavored to enforce1 has been contested by ,dr4 ,whewell1 both in the dissertation appended to his excellent ,mechanical ,euclid1 and in his elaborate work on the ,philosophy of the ,inductive ,sciences2 in which last he also replies to an article in the ,edinburgh ,review 7ascribed to a writer of great scientific eminence71 in which ,stewart's opinion was defended against his former strictures4 ,the supposed refutation of ,stewart consists in proving against him 7as has also been done in this work7 that the premises of geometry are not definitions1 but assumptions of the real existence of things corresponding to those definitions4 ,this1 however1 is doing little for ,dr4 ,whewell's purpose2 for it is these very assumptions which are asserted to be hypotheses1 and which he1 if he denies that geometry is founded on hypotheses1 must show to be absolute truths4 ,all he does1 however1 is to observe1 that they1 at any rate1 are not arbitrary hypotheses2 that we should not be at liberty to substitute other hypotheses for them2 that not only 8a definition1 to be admissible1 must necessarily refer to and agree with some conception which we can distinctly frame in our thoughts10 but that the straight lines1 for instance1 which we define1 must be 8those by which angles are contained1 those by which triangles are bounded1 those of which parallelism may be predicated1 and the like407#fi7 ,and this is true2 but this has never been contradicted4 ,those who say that the premises of geometry are hypotheses1 are not bound to maintain them to be hypotheses which have no relation whatever to fact4 ,since an hypothesis framed for the purpose of scientific inquiry must relate to something which has real existence 7for there can be no science respecting nonentities71 it follows that any hypothesis we make respecting an object1 to facilitate our study of it1 must not involve any thing which is distinctly false1 and repugnant to its real nature3 we must not ascribe to the thing any property which it has not2 our liberty extends only to slightly exaggerating some of those which it has 7by assuming it to be completely what it really is very nearly71 and suppressing others1 under the indispensable obligation of restoring them whenever1 and in as far as1 their presence or absence would make any material difference in the truth of our conclusions4 ,of this nature1 accordingly1 are the first principles involved in the definitions of geometry4 ,that the hypotheses should be of this particular character1 is1 however1 no further necessary1 than inasmuch as no others could enable us to deduce conclusions which1 with due corrections1 would be true of real objects3 and in fact1 when our aim is only to illustrate truths1 and not to investigate them1 we are not under any such restriction4 ,we might suppose an imaginary animal1 and work out by deduction1 from the known laws of physiology1 its natural history2 or an imaginary commonwealth1 and from the elements composing it1 might argue what would be its fate4 ,and the conclusions which we might thus draw from purely arbitrary hypotheses1 might form a highly useful intellectual exercise3 but as they could only teach us what would be the properties of objects which do not really exist1 they would not constitute any addition to our knowledge of nature3 while1 on the contrary1 if the hypothesis merely divests a real object of some portion of its properties1 without clothing it in false ones1 the conclusions will always express1 under known liability to correction1 actual truth4 #c4 ,but though ,dr4 ,whewell has not shaken ,stewart's doctrine as to the hypothetical character of that portion of the first principles of geometry which are involved in the so-called definitions1 he has1 ,i conceive1 greatly the advantage of ,stewart on another important point in the theory of geometrical reasoning2 the necessity of admitting1 among those first principles1 axioms as well as definitions4 ,some of the axioms of ,euclid might1 no doubt1 be exhibited in the form of definitions1 or might be deduced1 by reasoning1 from propositions similar to what are so called4 ,thus1 if instead of the axiom1 ,magnitudes which can be made to coincide are equal1 we introduce a definition1 8,equal magnitudes are those which may be so applied to one another as to coincide20 the three axioms which follow 7,magnitudes which are equal to the same are equal to one another--,if equals are added to equals1 the sums are equal--,if equals are taken from equals1 the remainders are equal71 may be proved by an imaginary superposition1 resembling that by which the fourth proposition of the first book of ,euclid is demonstrated4 ,but though these and several others may be struck out of the list of first principles1 because1 though not requiring demonstration1 they are susceptible of it2 there will be found in the list of axioms two or three fundamental truths1 not capable of being demonstrated3 among which must be reckoned the proposition that two straight lines can not inclose a space 7or its equivalent1 ,straight lines which coincide in two points coincide altogether71 and some property of parallel lines1 other than that which constitutes their definition3 one of the most suitable for the purpose being that selected by ,professor ,playfair3 8,two straight lines which intersect each other can not both of them be parallel to a third straight line407#gj7 ,the axioms1 as well those which are indemonstrable as those which admit of being demonstrated1 differ from that other class of fundamental principles which are involved in the definitions1 in this1 that they are true without any mixture of hypothesis4 ,that things which are equal to the same thing are equal to one another1 is as true of the lines and figures in nature1 as it would be of the imaginary ones assumed in the definitions4 ,in this respect1 however1 mathematics are only on a par with most other sciences4 ,in almost all sciences there are some general propositions which are exactly true1 while the greater part are only more or less distant approximations to the truth4 ,thus in mechanics1 the first law of motion 7the continuance of a movement once impressed1 until stopped or slackened by some resisting force7 is true without qualification or error4 ,the rotation of the earth in twenty-four hours1 of the same length as in our time1 has gone on since the first accurate observations1 without the increase or diminution of one second in all that period4 ,these are inductions which require no fiction to make them be received as accurately true3 but along with them there are others1 as for instance the propositions respecting the figure of the earth1 which are but approximations to the truth2 and in order to use them for the further advancement of our knowledge1 we must feign that they are exactly true1 though they really want something of being so4 #d4 ,it remains to inquire1 what is the ground of our belief in axioms--what is the evidence on which they rest8 ,i answer1 they are experimental truths2 generalizations from observation4 ,the proposition1 ,two straight lines can not inclose a space--or1 in other words1 ,two straight lines which have once met1 do not meet again1 but continue to diverge--is an induction from the evidence of our senses4 ,this opinion runs counter to a scientific prejudice of long standing and great strength1 and there is probably no proposition enunciated in this work for which a more unfavorable reception is to be expected4 ,it is1 however1 no new opinion2 and even if it were so1 would be entitled to be judged1 not by its novelty1 but by the strength of the arguments by which it can be supported4 ,i consider it very fortunate that so eminent a champion of the contrary opinion as ,dr4 ,whewell has found occasion for a most elaborate treatment of the whole theory of axioms1 in attempting to construct the philosophy of the mathematical and physical sciences on the basis of the doctrine against which ,i now contend4 ,whoever is anxious that a discussion should go to the bottom of the subject1 must rejoice to see the opposite side of the question worthily represented4 ,if what is said by ,dr4 ,whewell1 in support of an opinion which he has made the foundation of a systematic work1 can be shown not to be conclusive1 enough will have been done1 without going elsewhere in quest of stronger arguments and a more powerful adversary4 ,it is not necessary to show that the truths which we call axioms are originally suggested by observation1 and that we should never have known that two straight lines can not inclose a space if we had never seen a straight line3 thus much being admitted by ,dr4 ,whewell1 and by all1 in recent times1 who have taken his view of the subject4 ,but they contend1 that it is not experience which proves the axiom2 but that its truth is perceived a priori1 by the constitution of the mind itself1 from the first moment when the meaning of the proposition is apprehended2 and without any necessity for verifying it by repeated trials1 as is requisite in the case of truths really ascertained by observation4 ,they can not1 however1 but allow that the truth of the axiom1 ,two straight lines can not inclose a space1 even if evident independently of experience1 is also evident from experience4 ,whether the axiom needs confirmation or not1 it receives confirmation in almost every instant of our lives2 since we can not look at any two straight lines which intersect one another1 without seeing that from that point they continue to diverge more and more4 ,experimental proof crowds in upon us in such endless profusion1 and without one instance in which there can be even a suspicion of an exception to the rule1 that we should soon have stronger ground for believing the axiom1 even as an experimental truth1 than we have for almost any of the general truths which we confessedly learn from the evidence of our senses4 ,independently of a priori evidence1 we should certainly believe it with an intensity of conviction far greater than we accord to any ordinary physical truth3 and this too at a time of life much earlier than that from which we date almost any part of our acquired knowledge1 and much too early to admit of our retaining any recollection of the history of our intellectual operations at that period4 ,where then is the necessity for assuming that our recognition of these truths has a different origin from the rest of our knowledge1 when its existence is perfectly accounted for by supposing its origin to be the same8 when the causes which produce belief in all other instances1 exist in this instance1 and in a degree of strength as much superior to what exists in other cases1 as the intensity of the belief itself is superior8 ,the burden of proof lies on the advocates of the contrary opinion3 it is for them to point out some fact1 inconsistent with the supposition that this part of our knowledge of nature is derived from the same sources as every other part47#ga7 ,this1 for instance1 they would be able to do1 if they could prove chronologically that we had the conviction 7at least practically7 so early in infancy as to be anterior to those impressions on the senses1 upon which1 on the other theory1 the conviction is founded4 ,this1 however1 can not be proved3 the point being too far back to be within the reach of memory1 and too obscure for external observation4 ,the advocates of the a priori theory are obliged to have recourse to other arguments4 ,these are reducible to two1 which ,i shall endeavor to state as clearly and as forcibly as possible4 #e4 ,in the first place it is said1 that if our assent to the proposition that two straight lines can not inclose a space1 were derived from the senses1 we could only be convinced of its truth by actual trial1 that is1 by seeing or feeling the straight lines2 whereas1 in fact1 it is seen to be true by merely thinking of them4 ,that a stone thrown into water goes to the bottom1 may be perceived by our senses1 but mere thinking of a stone thrown into the water would never have led us to that conclusion3 not so1 however1 with the axioms relating to straight lines3 if ,i could be made to conceive what a straight line is1 without having seen one1 ,i should at once recognize that two such lines can not inclose a space4 ,intuition is 8imaginary looking207#gb7 but experience must be real looking3 if we see a property of straight lines to be true by merely fancying ourselves to be looking at them1 the ground of our belief can not be the senses1 or experience2 it must be something mental4 ,to this argument it might be added in the case of this particular axiom 7for the assertion would not be true of all axioms71 that the evidence of it from actual ocular inspection is not only unnecessary1 but unattainable4 ,what says the axiom8 ,that two straight lines can not inclose a space2 that after having once intersected1 if they are prolonged to infinity they do not meet1 but continue to diverge from one another4 ,how can this1 in any single case1 be proved by actual observation8 ,we may follow the lines to any distance we please2 but we can not follow them to infinity3 for aught our senses can testify1 they may1 immediately beyond the farthest point to which we have traced them1 begin to approach1 and at last meet4 ,unless1 therefore1 we had some other proof of the impossibility than observation affords us1 we should have no ground for believing the axiom at all4 ,to these arguments1 which ,i trust ,i can not be accused of understating1 a satisfactory answer will1 ,i conceive1 be found1 if we advert to one of the characteristic properties of geometrical forms--their capacity of being painted in the imagination with a distinctness equal to reality3 in other words1 the exact resemblance of our ideas of form to the sensations which suggest them4 ,this1 in the first place1 enables us to make 7at least with a little practice7 mental pictures of all possible combinations of lines and angles1 which resemble the realities quite as well as any which we could make on paper2 and in the next place1 make those pictures just as fit subjects of geometrical experimentation as the realities themselves2 inasmuch as pictures1 if sufficiently accurate1 exhibit of course all the properties which would be manifested by the realities at one given instant1 and on simple inspection3 and in geometry we are concerned only with such properties1 and not with that which pictures could not exhibit1 the mutual action of bodies one upon another4 ,the foundations of geometry would therefore be laid in direct experience1 even if the experiments 7which in this case consist merely in attentive contemplation7 were practiced solely upon what we call our ideas1 that is1 upon the diagrams in our minds1 and not upon outward objects4 ,for in all systems of experimentation we take some objects to serve as representatives of all which resemble them2 and in the present case the conditions which qualify a real object to be the representative of its class1 are completely fulfilled by an object existing only in our fancy4 ,without denying1 therefore1 the possibility of satisfying ourselves that two straight lines can not inclose a space1 by merely thinking of straight lines without actually looking at them2 ,i contend1 that we do not believe this truth on the ground of the imaginary intuition simply1 but because we know that the imaginary lines exactly resemble real ones1 and that we may conclude from them to real ones with quite as much certainty as we could conclude from one real line to another4 ,the conclusion1 therefore1 is still an induction from observation4 ,and we should not be authorized to substitute observation of the image in our mind1 for observation of the reality1 if we had not learned by long-continued experience that the properties of the reality are faithfully represented in the image2 just as we should be scientifically warranted in describing an animal which we have never seen1 from a picture made of it with a daguerreotype2 but not until we had learned by ample experience1 that observation of such a picture is precisely equivalent to observation of the original4 ,these considerations also remove the objection arising from the impossibility of ocularly following the lines in their prolongation to infinity4 ,for though1 in order actually to see that two given lines never meet1 it would be necessary to follow them to infinity2 yet without doing so we may know that if they ever do meet1 or if1 after diverging from one another1 they begin again to approach1 this must take place not at an infinite1 but at a finite distance4 ,supposing1 therefore1 such to be the case1 we can transport ourselves thither in imagination1 and can frame a mental image of the appearance which one or both of the lines must present at that point1 which we may rely on as being precisely similar to the reality4 ,now1 whether we fix our contemplation upon this imaginary picture1 or call to mind the generalizations we have had occasion to make from former ocular observation1 we learn by the evidence of experience1 that a line which1 after diverging from another straight line1 begins to approach to it1 produces the impression on our senses which we describe by the expression1 8a bent line10 not by the expression1 8a straight line407#gc7 ,the preceding argument1 which is1 to my mind unanswerable1 merges1 however1 in a still more comprehensive one1 which is stated most clearly and conclusively by ,professor ,bain4 ,the psychological reason why axioms1 and indeed many propositions not ordinarily classed as such1 may be learned from the idea only without referring to the fact1 is that in the process of acquiring the idea we have learned the fact4 ,the proposition is assented to as soon as the terms are understood1 because in learning to understand the terms we have acquired the experience which proves the proposition to be true4 8,we required10 says ,mr4 ,bain17#gd7 8concrete experience in the first instance1 to attain to the notion of whole and part2 but the notion1 once arrived at1 implies that the whole is greater4 ,in fact1 we could not have the notion without an experience tantamount to this conclusion4444 ,when we have mastered the notion of straightness1 we have also mastered that aspect of it expressed by the affirmation that two straight lines can not inclose a space4 ,no intuitive or innate powers or perceptions are needed in such case4444 ,we can not have the full meaning of ,straightness1 without going through a comparison of straight objects among themselves1 and with their opposites1 bent or crooked objects4 ,the result of this comparison is1 inter alia1 that straightness in two lines is seen to be incompatible with inclosing a space2 the inclosure of space involves crookedness in at least one of the lines40 ,and similarly1 in the case of every first principle17#ge7 8the same knowledge that makes it understood1 suffices to verify it40 ,the more this observation is considered the more 7,i am convinced7 it will be felt to go to the very root of the controversy4 #f4 ,the first of the two arguments in support of the theory that axioms are a priori truths1 having1 ,i think1 been sufficiently answered2 ,i proceed to the second1 which is usually the most relied on4 ,axioms 7it is asserted7 are conceived by us not only as true1 but as universally and necessarily true4 ,now1 experience can not possibly give to any proposition this character4 ,i may have seen snow a hundred times1 and may have seen that it was white1 but this can not give me entire assurance even that all snow is white2 much less that snow must be white4 8,however many instances we may have observed of the truth of a proposition1 there is nothing to assure us that the next case shall not be an exception to the rule4 ,if it be strictly true that every ruminant animal yet known has cloven hoofs1 we still can not be sure that some creature will not hereafter be discovered which has the first of these attributes1 without having the other4444 ,experience must always consist of a limited number of observations2 and1 however numerous these may be1 they can show nothing with regard to the infinite number of cases in which the experiment has not been made40 ,besides1 ,axioms are not only universal1 they are also necessary4 ,now 8experience can not offer the smallest ground for the necessity of a proposition4 ,she can observe and record what has happened2 but she can not find1 in any case1 or in any accumulation of cases1 any reason for what must happen4 ,she may see objects side by side2 but she can not see a reason why they must ever be side by side4 ,she finds certain events to occur in succession2 but the succession supplies1 in its occurrence1 no reason for its recurrence4 ,she contemplates external objects2 but she can not detect any internal bond1 which indissolubly connects the future with the past1 the possible with the real4 ,to learn a proposition by experience1 and to see it to be necessarily true1 are two altogether different processes of thought407#gf7 ,and ,dr4 ,whewell adds1 8,if any one does not clearly comprehend this distinction of necessary and contingent truths1 he will not be able to go along with us in our researches into the foundations of human knowledge2 nor1 indeed1 to pursue with success any speculation on the subject407#gg7 ,in the following passage1 we are told what the distinction is1 the non-recognition of which incurs this denunciation4 8,necessary truths are those in which we not only learn that the proposition is true1 but see that it must be true2 in which the negation of the truth is not only false1 but impossible2 in which we can not1 even by an effort of imagination1 or in a supposition1 conceive the reverse of that which is asserted4 ,that there are such truths can not be doubted4 ,we may take1 for example1 all relations of number4 ,three and ,two added together make ,five4 ,we can not conceive it to be otherwise4 ,we can not1 by any freak of thought1 imagine ,three and ,two to make ,seven407#gh7 ,although ,dr4 ,whewell has naturally and properly employed a variety of phrases to bring his meaning more forcibly home1 he would1 ,i presume1 allow that they are all equivalent2 and that what he means by a necessary truth1 would be sufficiently defined1 a proposition the negation of which is not only false but inconceivable4 ,i am unable to find in any of his expressions1 turn them what way you will1 a meaning beyond this1 and ,i do not believe he would contend that they mean any thing more4 ,this1 therefore1 is the principle asserted3 that propositions1 the negation of which is inconceivable1 or in other words1 which we can not figure to ourselves as being false1 must rest on evidence of a higher and more cogent description than any which experience can afford4 ,now ,i can not but wonder that so much stress should be laid on the circumstance of inconceivableness1 when there is such ample experience to show1 that our capacity or incapacity of conceiving a thing has very little to do with the possibility of the thing in itself2 but is in truth very much an affair of accident1 and depends on the past history and habits of our own minds4 ,there is no more generally acknowledged fact in human nature1 than the extreme difficulty at first felt in conceiving any thing as possible1 which is in contradiction to long established and familiar experience2 or even to old familiar habits of thought4 ,and this difficulty is a necessary result of the fundamental laws of the human mind4 ,when we have often seen and thought of two things together1 and have never in any one instance either seen or thought of them separately1 there is by the primary law of association an increasing difficulty1 which may in the end become insuperable1 of conceiving the two things apart4 ,this is most of all conspicuous in uneducated persons1 who are in general utterly unable to separate any two ideas which have once become firmly associated in their minds2 and if persons of cultivated intellect have any advantage on the point1 it is only because1 having seen and heard and read more1 and being more accustomed to exercise their imagination1 they have experienced their sensations and thoughts in more varied combinations1 and have been prevented from forming many of these inseparable associations4 ,but this advantage has necessarily its limits4 ,the most practiced intellect is not exempt from the universal laws of our conceptive faculty4 ,if daily habit presents to any one for a long period two facts in combination1 and if he is not led during that period either by accident or by his voluntary mental operations to think of them apart1 he will probably in time become incapable of doing so even by the strongest effort2 and the supposition that the two facts can be separated in nature1 will at last present itself to his mind with all the characters of an inconceivable phenomenon47#gi7 ,there are remarkable instances of this in the history of science3 instances in which the most instructed men rejected as impossible1 because inconceivable1 things which their posterity1 by earlier practice and longer perseverance in the attempt1 found it quite easy to conceive1 and which every body now knows to be true4 ,there was a time when men of the most cultivated intellects1 and the most emancipated from the dominion of early prejudice1 could not credit the existence of antipodes2 were unable to conceive1 in opposition to old association1 the force of gravity acting upward instead of downward4 ,the ,cartesians long rejected the ,newtonian doctrine of the gravitation of all bodies toward one another1 on the faith of a general proposition1 the reverse of which seemed to them to be inconceivable--the proposition that a body can not act where it is not4 ,all the cumbrous machinery of imaginary vortices1 assumed without the smallest particle of evidence1 appeared to these philosophers a more rational mode of explaining the heavenly motions1 than one which involved what seemed to them so great an absurdity47#hj7 ,and they no doubt found it as impossible to conceive that a body should act upon the earth from the distance of the sun or moon1 as we find it to conceive an end to space or time1 or two straight lines inclosing a space4 ,newton himself had not been able to realize the conception1 or we should not have had his hypothesis of a subtle ether1 the occult cause of gravitation2 and his writings prove1 that though he deemed the particular nature of the intermediate agency a matter of conjecture1 the necessity of some such agency appeared to him indubitable4 ,if1 then1 it be so natural to the human mind1 even in a high state of culture1 to be incapable of conceiving1 and on that ground to believe impossible1 what is afterward not only found to be conceivable but proved to be true2 what wonder if in cases where the association is still older1 more confirmed1 and more familiar1 and in which nothing ever occurs to shake our conviction1 or even suggest to us any conception at variance with the association1 the acquired incapacity should continue1 and be mistaken for a natural incapacity8 ,it is true1 our experience of the varieties in nature enables us1 within certain limits1 to conceive other varieties analogous to them4 ,we can conceive the sun or moon falling2 for though we never saw them fall1 nor ever1 perhaps1 imagined them falling1 we have seen so many other things fall1 that we have innumerable familiar analogies to assist the conception2 which1 after all1 we should probably have some difficulty in framing1 were we not well accustomed to see the sun and moon move 7or appear to move71 so that we are only called upon to conceive a slight change in the direction of motion1 a circumstance familiar to our experience4 ,but when experience affords no model on which to shape the new conception1 how is it possible for us to form it8 ,how1 for example1 can we imagine an end to space or time8 ,we never saw any object without something beyond it1 nor experienced any feeling without something following it4 ,when1 therefore1 we attempt to conceive the last point of space1 we have the idea irresistibly raised of other points beyond it4 ,when we try to imagine the last instant of time1 we can not help conceiving another instant after it4 ,nor is there any necessity to assume1 as is done by a modern school of metaphysicians1 a peculiar fundamental law of the mind to account for the feeling of infinity inherent in our conceptions of space and time2 that apparent infinity is sufficiently accounted for by simpler and universally acknowledged laws4 ,now1 in the case of a geometrical axiom1 such1 for example1 as that two straight lines can not inclose a space--a truth which is testified to us by our very earliest impressions of the external world--how is it possible 7whether those external impressions be or be not the ground of our belief7 that the reverse of the proposition could be otherwise than inconceivable to us8 ,what analogy have we1 what similar order of facts in any other branch of our experience1 to facilitate to us the conception of two straight lines inclosing a space8 ,nor is even this all4 ,i have already called attention to the peculiar property of our impressions of form1 that the ideas or mental images exactly resemble their prototypes1 and adequately represent them for the purposes of scientific observation4 ,from this1 and from the intuitive character of the observation1 which in this case reduces itself to simple inspection1 we can not so much as call up in our imagination two straight lines1 in order to attempt to conceive them inclosing a space1 without by that very act repeating the scientific experiment which establishes the contrary4 ,will it really be contended that the inconceivableness of the thing1 in such circumstances1 proves any thing against the experimental origin of the conviction8 ,is it not clear that in whichever mode our belief in the proposition may have originated1 the impossibility of our conceiving the negative of it must1 on either hypothesis1 be the same8 ,as1 then1 ,dr4 ,whewell exhorts those who have any difficulty in recognizing the distinction held by him between necessary and contingent truths1 to study geometry--a condition which ,i can assure him ,i have conscientiously fulfilled--,i1 in return1 with equal confidence1 exhort those who agree with him1 to study the general laws of association2 being convinced that nothing more is requisite than a moderate familiarity with those laws1 to dispel the illusion which ascribes a peculiar necessity to our earliest inductions from experience1 and measures the possibility of things in themselves1 by the human capacity of conceiving them4 ,i hope to be pardoned for adding1 that ,dr4 ,whewell himself has both confirmed by his testimony the effect of habitual association in giving to an experimental truth the appearance of a necessary one1 and afforded a striking instance of that remarkable law in his own person4 ,in his ,philosophy of the ,inductive ,sciences he continually asserts1 that propositions which not only are not self-evident1 but which we know to have been discovered gradually1 and by great efforts of genius and patience1 have1 when once established1 appeared so self-evident that1 but for historical proof1 it would have been impossible to conceive that they had not been recognized from the first by all persons in a sound state of their faculties4 8,we now despise those who1 in the ,copernican controversy1 could not conceive the apparent motion of the sun on the heliocentric hypothesis2 or those who1 in opposition to ,galileo1 thought that a uniform force might be that which generated a velocity proportional to the space2 or those who held there was something absurd in ,newton's doctrine of the different refrangibility of differently colored rays2 or those who imagined that when elements combine1 their sensible qualities must be manifest in the compound2 or those who were reluctant to give up the distinction of vegetables into herbs1 shrubs1 and trees4 ,we can not help thinking that men must have been singularly dull of comprehension1 to find a difficulty in admitting what is to us so plain and simple4 ,we have a latent persuasion that we in their place should have been wiser and more clear-sighted2 that we should have taken the right side1 and given our assent at once to the truth4 ,yet in reality such a persuasion is a mere delusion4 ,the persons who1 in such instances as the above1 were on the losing side1 were very far1 in most cases1 from being persons more prejudiced1 or stupid1 or narrow-minded1 than the greater part of mankind now are2 and the cause for which they fought was far from being a manifestly bad one1 till it had been so decided by the result of the war4444 ,so complete has been the victory of truth in most of these instances1 that at present we can hardly imagine the struggle to have been necessary4 ,the very essence of these triumphs is1 that they lead us to regard the views we reject as not only false but inconceivable407#ha7 ,this last proposition is precisely what ,i contend for2 and ,i ask no more1 in order to overthrow the whole theory of its author on the nature of the evidence of axioms4 ,for what is that theory8 ,that the truth of axioms can not have been learned from experience1 because their falsity is inconceivable4 ,but ,dr4 ,whewell himself says1 that we are continually led1 by the natural progress of thought1 to regard as inconceivable what our forefathers not only conceived but believed1 nay even 7he might have added7 were unable to conceive the reverse of4 ,he can not intend to justify this mode of thought3 he can not mean to say1 that we can be right in regarding as inconceivable what others have conceived1 and as self-evident what to others did not appear evident at all4 ,after so complete an admission that inconceivableness is an accidental thing1 not inherent in the phenomenon itself1 but dependent on the mental history of the person who tries to conceive it1 how can he ever call upon us to reject a proposition as impossible on no other ground than its inconceivableness8 ,yet he not only does so1 but has unintentionally afforded some of the most remarkable examples which can be cited of the very illusion which he has himself so clearly pointed out4 ,i select as specimens1 his remarks on the evidence of the three laws of motion1 and of the atomic theory4 ,with respect to the laws of motion1 ,dr4 ,whewell says3 8,no one can doubt that1 in historical fact1 these laws were collected from experience4 ,that such is the case1 is no matter of conjecture4 ,we know the time1 the persons1 the circumstances1 belonging to each step of each discovery407#hb7 ,after this testimony1 to adduce evidence of the fact would be superfluous4 ,and not only were these laws by no means intuitively evident1 but some of them were originally paradoxes4 ,the first law was especially so4 ,that a body1 once in motion1 would continue forever to move in the same direction with undiminished velocity unless acted upon by some new force1 was a proposition which mankind found for a long time the greatest difficulty in crediting4 ,it stood opposed to apparent experience of the most familiar kind1 which taught that it was the nature of motion to abate gradually1 and at last terminate of itself4 ,yet when once the contrary doctrine was firmly established1 mathematicians1 as ,dr4 ,whewell observes1 speedily began to believe that laws1 thus contradictory to first appearances1 and which1 even after full proof had been obtained1 it had required generations to render familiar to the minds of the scientific world1 were under 8a demonstrable necessity1 compelling them to be such as they are and no other20 and he himself1 though not venturing 8absolutely to pronounce0 that all these laws 8can be rigorously traced to an absolute necessity in the nature of things107#hc7 does actually so think of the law just mentioned2 of which he says3 8,though the discovery of the first law of motion was made1 historically speaking1 by means of experiment1 we have now attained a point of view in which we see that it might have been certainly known to be true1 independently of experience407#hd7 ,can there be a more striking exemplification than is here afforded1 of the effect of association which we have described8 ,philosophers1 for generations1 have the most extraordinary difficulty in putting certain ideas together2 they at last succeed in doing so2 and after a sufficient repetition of the process1 they first fancy a natural bond between the ideas1 then experience a growing difficulty1 which at last1 by the continuation of the same progress1 becomes an impossibility1 of severing them from one another4 ,if such be the progress of an experimental conviction of which the date is of yesterday1 and which is in opposition to first appearances1 how must it fare with those which are conformable to appearances familiar from the first dawn of intelligence1 and of the conclusiveness of which1 from the earliest records of human thought1 no skeptic has suggested even a momentary doubt8 ,the other instance which ,i shall quote is a truly astonishing one1 and may be called the reductio ad absurdum of the theory of inconceivableness4 ,speaking of the laws of chemical composition1 ,dr4 ,whewell says37#he7 8,that they could never have been clearly understood1 and therefore never firmly established1 without laborious and exact experiments1 is certain2 but yet we may venture to say1 that being once known1 they possess an evidence beyond that of mere experiment4 ,for how in fact can we conceive combinations1 otherwise than as definite in kind and quality8 ,if we were to suppose each element ready to combine with any other indifferently1 and indifferently in any quantity1 we should have a world in which all would be confusion and indefiniteness4 ,there would be no fixed kinds of bodies4 ,salts1 and stones1 and ores1 would approach to and graduate into each other by insensible degrees4 ,instead of this1 we know that the world consists of bodies distinguishable from each other by definite differences1 capable of being classified and named1 and of having general propositions asserted concerning them4 ,and as we can not conceive a world in which this should not be the case1 it would appear that we can not conceive a state of things in which the laws of the combination of elements should not be of that definite and measured kind which we have above asserted40 ,that a philosopher of ,dr4 ,whewell's eminence should gravely assert that we can not conceive a world in which the simple elements should combine in other than definite proportions2 that by dint of meditating on a scientific truth1 the original discoverer of which was still living1 he should have rendered the association in his own mind between the idea of combination and that of constant proportions so familiar and intimate as to be unable to conceive the one fact without the other2 is so signal an instance of the mental law for which ,i am contending1 that one word more in illustration must be superfluous4 ,in the latest and most complete elaboration of his metaphysical system 7the ,philosophy of ,discovery71 as well as in the earlier discourse on the ,fundamental ,antithesis of ,philosophy1 reprinted as an appendix to that work1 ,dr4 ,whewell1 while very candidly admitting that his language was open to misconception1 disclaims having intended to say that mankind in general can now perceive the law of definite proportions in chemical combination to be a necessary truth4 ,all he meant was that philosophical chemists in a future generation may possibly see this4 8,some truths may be seen by intuition1 but yet the intuition of them may be a rare and a difficult attainment407#hf7 ,and he explains that the inconceivableness which1 according to his theory1 is the test of axioms1 8depends entirely upon the clearness of the ,ideas which the axioms involve4 ,so long as those ideas are vague and indistinct1 the contrary of an axiom may be assented to1 though it can not be distinctly conceived4 ,it may be assented to1 not because it is possible1 but because we do not see clearly what is possible4 ,to a person who is only beginning to think geometrically1 there may appear nothing absurd in the assertion that two straight lines may inclose a space4 ,and in the same manner1 to a person who is only beginning to think of mechanical truths1 it may not appear to be absurd1 that in mechanical processes1 ,reaction should be greater or less than ,action2 and so1 again1 to a person who has not thought steadily about ,substance1 it may not appear inconceivable1 that by chemical operations1 we should generate new matter1 or destroy matter which already exists407#hg7 ,necessary truths1 therefore1 are not those of which we can not conceive1 but 8those of which we can not distinctly conceive1 the contrary407#hh7 ,so long as our ideas are indistinct altogether1 we do not know what is or is not capable of being distinctly conceived2 but1 by the ever increasing distinctness with which scientific men apprehend the general conceptions of science1 they in time come to perceive that there are certain laws of nature1 which1 though historically and as a matter of fact they were learned from experience1 we can not1 now that we know them1 distinctly conceive to be other than they are4 ,the account which ,i should give of this progress of the scientific mind is somewhat different4 ,after a general law of nature has been ascertained1 men's minds do not at first acquire a complete facility of familiarly representing to themselves the phenomena of nature in the character which that law assigns to them4 ,the habit which constitutes the scientific cast of mind1 that of conceiving facts of all descriptions conformably to the laws which regulate them--phenomena of all descriptions according to the relations which have been ascertained really to exist between them2 this habit1 in the case of newly-discovered relations1 comes only by degrees4 ,so long as it is not thoroughly formed1 no necessary character is ascribed to the new truth4 ,but in time1 the philosopher attains a state of mind in which his mental picture of nature spontaneously represents to him all the phenomena with which the new theory is concerned1 in the exact light in which the theory regards them3 all images or conceptions derived from any other theory1 or from the confused view of the facts which is anterior to any theory1 having entirely disappeared from his mind4 ,the mode of representing facts which results from the theory1 has now become1 to his faculties1 the only natural mode of conceiving them4 ,it is a known truth1 that a prolonged habit of arranging phenomena in certain groups1 and explaining them by means of certain principles1 makes any other arrangement or explanation of these facts be felt as unnatural3 and it may at last become as difficult to him to represent the facts to himself in any other mode1 as it often was1 originally1 to represent them in that mode4 ,but1 further 7if the theory is true1 as we are supposing it to be71 any other mode in which he tries1 or in which he was formerly accustomed1 to represent the phenomena1 will be seen by him to be inconsistent with the facts that suggested the new theory--facts which now form a part of his mental picture of nature4 ,and since a contradiction is always inconceivable1 his imagination rejects these false theories1 and declares itself incapable of conceiving them4 ,their inconceivableness to him does not1 however1 result from any thing in the theories themselves1 intrinsically and a priori repugnant to the human faculties2 it results from the repugnance between them and a portion of the facts2 which facts as long as he did not know1 or did not distinctly realize in his mental representations1 the false theory did not appear other than conceivable2 it becomes inconceivable1 merely from the fact that contradictory elements can not be combined in the same conception4 ,although1 then1 his real reason for rejecting theories at variance with the true one1 is no other than that they clash with his experience1 he easily falls into the belief1 that he rejects them because they are inconceivable1 and that he adopts the true theory because it is self-evident1 and does not need the evidence of experience at all4 ,this ,i take to be the real and sufficient explanation of the paradoxical truth1 on which so much stress is laid by ,dr4 ,whewell1 that a scientifically cultivated mind is actually1 in virtue of that cultivation1 unable to conceive suppositions which a common man conceives without the smallest difficulty4 ,for there is nothing inconceivable in the suppositions themselves2 the impossibility is in combining them with facts inconsistent with them1 as part of the same mental picture2 an obstacle of course only felt by those who know the facts1 and are able to perceive the inconsistency4 ,as far as the suppositions themselves are concerned1 in the case of many of ,dr4 ,whewell's necessary truths the negative of the axiom is1 and probably will be as long as the human race lasts1 as easily conceivable as the affirmative4 ,there is no axiom 7for example7 to which ,dr4 ,whewell ascribes a more thorough character of necessity and self-evidence1 than that of the indestructibility of matter4 ,that this is a true law of nature ,i fully admit2 but ,i imagine there is no human being to whom the opposite supposition is inconceivable--who has any difficulty in imagining a portion of matter annihilated3 inasmuch as its apparent annihilation1 in no respect distinguishable from real by our unassisted senses1 takes place every time that water dries up1 or fuel is consumed4 ,again1 the law that bodies combine chemically in definite proportions is undeniably true2 but few besides ,dr4 ,whewell have reached the point which he seems personally to have arrived at 7though he only dares prophesy similar success to the multitude after the lapse of generations71 that of being unable to conceive a world in which the elements are ready to combine with one another 8indifferently in any quantity20 nor is it likely that we shall ever rise to this sublime height of inability1 so long as all the mechanical mixtures in our planet1 whether solid1 liquid1 or ariform1 exhibit to our daily observation the very phenomenon declared to be inconceivable4 ,according to ,dr4 ,whewell1 these and similar laws of nature can not be drawn from experience1 inasmuch as they are1 on the contrary1 assumed in the interpretation of experience4 ,our inability to 8add to or diminish the quantity of matter in the world10 is a truth which 8neither is nor can be derived from experience2 for the experiments which we make to verify it presuppose its truth4444 ,when men began to use the balance in chemical analysis1 they did not prove by trial1 but took for granted1 as self-evident1 that the weight of the whole must be found in the aggregate weight of the elements407#hi7 ,true1 it is assumed2 but1 ,i apprehend1 no otherwise than as all experimental inquiry assumes provisionally some theory or hypothesis1 which is to be finally held true or not1 according as the experiments decide4 ,the hypothesis chosen for this purpose will naturally be one which groups together some considerable number of facts already known4 ,the proposition that the material of the world1 as estimated by weight1 is neither increased nor diminished by any of the processes of nature or art1 had many appearances in its favor to begin with4 ,it expressed truly a great number of familiar facts4 ,there were other facts which it had the appearance of conflicting with1 and which made its truth1 as a universal law of nature1 at first doubtful4 ,because it was doubtful1 experiments were devised to verify it4 ,men assumed its truth hypothetically1 and proceeded to try whether1 on more careful examination1 the phenomena which apparently pointed to a different conclusion1 would not be found to be consistent with it4 ,this turned out to be the case2 and from that time the doctrine took its place as a universal truth1 but as one proved to be such by experience4 ,that the theory itself preceded the proof of its truth--that it had to be conceived before it could be proved1 and in order that it might be proved--does not imply that it was self-evident1 and did not need proof4 ,otherwise all the true theories in the sciences are necessary and self-evident2 for no one knows better than ,dr4 ,whewell that they all began by being assumed1 for the purpose of connecting them by deductions with those facts of experience on which1 as evidence1 they now confessedly rest47#ij7 ,chapter ,,vi4 ,the ,same ,subject ,continued4 #a4 ,in the examination which formed the subject of the last chapter1 into the nature of the evidence of those deductive sciences which are commonly represented to be systems of necessary truth1 we have been led to the following conclusions4 ,the results of those sciences are indeed necessary1 in the sense of necessarily following from certain first principles1 commonly called axioms and definitions2 that is1 of being certainly true if those axioms and definitions are so2 for the word necessity1 even in this acceptation of it1 means no more than certainty4 ,but their claim to the character of necessity in any sense beyond this1 as implying an evidence independent of and superior to observation and experience1 must depend on the previous establishment of such a claim in favor of the definitions and axioms themselves4 ,with regard to axioms1 we found that1 considered as experimental truths1 they rest on superabundant and obvious evidence4 ,we inquired1 whether1 since this is the case1 it be imperative to suppose any other evidence of those truths than experimental evidence1 any other origin for our belief of them than an experimental origin4 ,we decided1 that the burden of proof lies with those who maintain the affirmative1 and we examined1 at considerable length1 such arguments as they have produced4 ,the examination having led to the rejection of those arguments1 we have thought ourselves warranted in concluding that axioms are but a class1 the most universal class1 of inductions from experience2 the simplest and easiest cases of generalization from the facts furnished to us by our senses or by our internal consciousness4 ,while the axioms of demonstrative sciences thus appeared to be experimental truths1 the definitions1 as they are incorrectly called1 in those sciences1 were found by us to be generalizations from experience which are not even1 accurately speaking1 truths2 being propositions in which1 while we assert of some kind of object1 some property or properties which observation shows to belong to it1 we at the same time deny that it possesses any other properties1 though in truth other properties do in every individual instance accompany1 and in almost all instances modify1 the property thus exclusively predicated4 ,the denial1 therefore1 is a mere fiction1 or supposition1 made for the purpose of excluding the consideration of those modifying circumstances1 when their influence is of too trifling amount to be worth considering1 or adjourning it1 when important to a more convenient moment4 ,from these considerations it would appear that ,deductive or ,demonstrative ,sciences are all1 without exception1 ,inductive ,sciences2 that their evidence is that of experience2 but that they are also1 in virtue of the peculiar character of one indispensable portion of the general formul according to which their inductions are made1 ,hypothetical ,sciences4 ,their conclusions are only true on certain suppositions1 which are1 or ought to be1 approximations to the truth1 but are seldom1 if ever1 exactly true2 and to this hypothetical character is to be ascribed the peculiar certainty1 which is supposed to be inherent in demonstration4 ,what we have now asserted1 however1 cannot be received as universally true of ,deductive or ,demonstrative ,sciences1 until verified by being applied to the most remarkable of all those sciences1 that of ,numbers2 the theory of the ,calculus2 ,arithmetic and ,algebra4 ,it is harder to believe of the doctrines of this science than of any other1 either that they are not truths a priori1 but experimental truths1 or that their peculiar certainty is owing to their being not absolute but only conditional truths4 ,this1 therefore1 is a case which merits examination apart2 and the more so1 because on this subject we have a double set of doctrines to contend with2 that of the a priori philosophers on one side2 and on the other1 a theory the most opposite to theirs1 which was at one time very generally received1 and is still far from being altogether exploded1 among metaphysicians4 #b4 ,this theory attempts to solve the difficulty apparently inherent in the case1 by representing the propositions of the science of numbers as merely verbal1 and its processes as simple transformations of language1 substitutions of one expression for another4 ,the proposition1 ,two and one is equal to three1 according to these writers1 is not a truth1 is not the assertion of a really existing fact1 but a definition of the word three2 a statement that mankind have agreed to use the name three as a sign exactly equivalent to two and one2 to call by the former name whatever is called by the other more clumsy phrase4 ,according to this doctrine1 the longest process in algebra is but a succession of changes in terminology1 by which equivalent expressions are substituted one for another2 a series of translations of the same fact1 from one into another language2 though how1 after such a series of translations1 the fact itself comes out changed 7as when we demonstrate a new geometrical theorem by algebra71 they have not explained2 and it is a difficulty which is fatal to their theory4 ,it must be acknowledged that there are peculiarities in the processes of arithmetic and algebra which render the theory in question very plausible1 and have not unnaturally made those sciences the stronghold of ,nominalism4 ,the doctrine that we can discover facts1 detect the hidden processes of nature1 by an artful manipulation of language1 is so contrary to common sense1 that a person must have made some advances in philosophy to believe it3 men fly to so paradoxical a belief to avoid1 as they think1 some even greater difficulty1 which the vulgar do not see4 ,what has led many to believe that reasoning is a mere verbal process1 is1 that no other theory seemed reconcilable with the nature of the ,science of ,numbers4 ,for we do not carry any ideas along with us when we use the symbols of arithmetic or of algebra4 ,in a geometrical demonstration we have a mental diagram1 if not one on paper2 ,,ab1 ,,ac1 are present to our imagination as lines1 intersecting other lines1 forming an angle with one another1 and the like2 but not so a and b4 ,these may represent lines or any other magnitudes1 but those magnitudes are never thought of2 nothing is realized in our imagination but a and b4 ,the ideas which1 on the particular occasion1 they happen to represent1 are banished from the mind during every intermediate part of the process1 between the beginning1 when the premises are translated from things into signs1 and the end1 when the conclusion is translated back from signs into things4 ,nothing1 then1 being in the reasoner's mind but the symbols1 what can seem more inadmissible than to contend that the reasoning process has to do with any thing more8 ,we seem to have come to one of ,bacon's ,prerogative ,instances2 an experimentum crucis on the nature of reasoning itself4 ,nevertheless1 it will appear on consideration1 that this apparently so decisive instance is no instance at all2 that there is in every step of an arithmetical or algebraical calculation a real induction1 a real inference of facts from facts2 and that what disguises the induction is simply its comprehensive nature1 and the consequent extreme generality of the language4 ,all numbers must be numbers of something3 there are no such things as numbers in the abstract4 ,ten must mean ten bodies1 or ten sounds1 or ten beatings of the pulse4 ,but though numbers must be numbers of something1 they may be numbers of any thing4 ,propositions1 therefore1 concerning numbers1 have the remarkable peculiarity that they are propositions concerning all things whatever2 all objects1 all existences of every kind1 known to our experience4 ,all things possess quantity2 consist of parts which can be numbered2 and in that character possess all the properties which are called properties of numbers4 ,that half of four is two1 must be true whatever the word four represents1 whether four hours1 four miles1 or four pounds weight4 ,we need only conceive a thing divided into four equal parts 7and all things may be conceived as so divided71 to be able to predicate of it every property of the number four1 that is1 every arithmetical proposition in which the number four stands on one side of the equation4 ,algebra extends the generalization still farther3 every number represents that particular number of all things without distinction1 but every algebraical symbol does more1 it represents all numbers without distinction4 ,as soon as we conceive a thing divided into equal parts1 without knowing into what number of parts1 we may call it a or x1 and apply to it1 without danger of error1 every algebraical formula in the books4 ,the proposition1 #b 7a b7 #b a #b b1 is a truth co-extensive with all nature4 ,since then algebraical truths are true of all things whatever1 and not1 like those of geometry1 true of lines only or of angles only1 it is no wonder that the symbols should not excite in our minds ideas of any things in particular4 ,when we demonstrate the forty-seventh proposition of ,euclid1 it is not necessary that the words should raise in us an image of all right-angled triangles1 but only of some one right-angled triangle3 so in algebra we need not1 under the symbol a1 picture to ourselves all things whatever1 but only some one thing2 why not1 then1 the letter itself8 ,the mere written characters1 a1 b1 x1 y1 z1 serve as well for representatives of ,things in general1 as any more complex and apparently more concrete conception4 ,that we are conscious of them1 however1 in their character of things1 and not of mere signs1 is evident from the fact that our whole process of reasoning is carried on by predicating of them the properties of things4 ,in resolving an algebraic equation1 by what rules do we proceed8 ,by applying at each step to a1 b1 and x1 the proposition that equals added to equals make equals2 that equals taken from equals leave equals2 and other propositions founded on these two4 ,these are not properties of language1 or of signs as such1 but of magnitudes1 which is as much as to say1 of all things4 ,the inferences1 therefore1 which are successively drawn1 are inferences concerning things1 not symbols2 though as any ,things whatever will serve the turn1 there is no necessity for keeping the idea of the ,thing at all distinct1 and consequently the process of thought may1 in this case1 be allowed without danger to do what all processes of thought1 when they have been performed often1 will do if permitted1 namely1 to become entirely mechanical4 ,hence the general language of algebra comes to be used familiarly without exciting ideas1 as all other general language is prone to do from mere habit1 though in no other case than this can it be done with complete safety4 ,but when we look back to see from whence the probative force of the process is derived1 we find that at every single step1 unless we suppose ourselves to be thinking and talking of the things1 and not the mere symbols1 the evidence fails4 ,there is another circumstance1 which1 still more than that which we have now mentioned1 gives plausibility to the notion that the propositions of arithmetic and algebra are merely verbal4 ,that is1 that when considered as propositions respecting ,things1 they all have the appearance of being identical propositions4 ,the assertion1 ,two and one is equal to three1 considered as an assertion respecting objects1 as for instance1 8,two pebbles and one pebble are equal to three pebbles10 does not affirm equality between two collections of pebbles1 but absolute identity4 ,it affirms that if we put one pebble to two pebbles1 those very pebbles are three4 ,the objects1 therefore1 being the very same1 and the mere assertion that 8objects are themselves0 being insignificant1 it seems but natural to consider the proposition1 ,two and one is equal to three1 as asserting mere identity of signification between the two names4 ,this1 however1 though it looks so plausible1 will not bear examination4 ,the expression 8two pebbles and one pebble10 and the expression 8three pebbles10 stand indeed for the same aggregation of objects1 but they by no means stand for the same physical fact4 ,they are names of the same objects1 but of those objects in two different states3 though they denote the same things1 their connotation is different4 ,three pebbles in two separate parcels1 and three pebbles in one parcel1 do not make the same impression on our senses2 and the assertion that the very same pebbles may by an alteration of place and arrangement be made to produce either the one set of sensations or the other1 though a very familiar proposition1 is not an identical one4 ,it is a truth known to us by early and constant experience3 an inductive truth2 and such truths are the foundation of the science of ,number4 ,the fundamental truths of that science all rest on the evidence of sense2 they are proved by showing to our eyes and our fingers that any given number of objects--ten balls1 for example--may by separation and re-arrangement exhibit to our senses all the different sets of numbers the sums of which is equal to ten4 ,all the improved methods of teaching arithmetic to children proceed on a knowledge of this fact4 ,all who wish to carry the child's mind along with them in learning arithmetic2 all who wish to teach numbers1 and not mere ciphers--now teach it through the evidence of the senses1 in the manner we have described4 ,we may1 if we please1 call the proposition1 8,three is two and one10 a definition of the number three1 and assert that arithmetic1 as it has been asserted that geometry1 is a science founded on definitions4 ,but they are definitions in the geometrical sense1 not the logical2 asserting not the meaning of a term only1 but along with it an observed matter of fact4 ,the proposition1 8,a circle is a figure bounded by a line which has all its points equally distant from a point within it10 is called the definition of a circle2 but the proposition from which so many consequences follow1 and which is really a first principle in geometry1 is1 that figures answering to this description exist4 ,and thus we may call 8,three is two and one0 a definition of three2 but the calculations which depend on that proposition do not follow from the definition itself1 but from an arithmetical theorem presupposed in it1 namely1 that collections of objects exist1 which while they impress the senses thus1 ,symbol3 three circles1 two above one1 may be separated into two parts1 thus1 ,symbol3 two circles1 a space1 and a third circle4 ,this proposition being granted1 we term all such parcels ,threes1 after which the enunciation of the above-mentioned physical fact will serve also for a definition of the word ,three4 ,the ,science of ,number is thus no exception to the conclusion we previously arrived at1 that the processes even of deductive sciences are altogether inductive1 and that their first principles are generalizations from experience4 ,it remains to be examined whether this science resembles geometry in the further circumstance1 that some of its inductions are not exactly true2 and that the peculiar certainty ascribed to it1 on account of which its propositions are called ,necessary ,truths1 is fictitious and hypothetical1 being true in no other sense than that those propositions legitimately follow from the hypothesis of the truth of premises which are avowedly mere approximations to truth4 #c4 ,the inductions of arithmetic are of two sorts3 first1 those which we have just expounded1 such as ,one and one are two1 ,two and one are three1 etc41 which may be called the definitions of the various numbers1 in the improper or geometrical sense of the word ,definition2 and secondly1 the two following axioms3 ,the sums of equals are equal1 ,the differences of equals are equal4 ,these two are sufficient2 for the corresponding propositions respecting unequals may be proved from these by a reductio ad absurdum4 ,these axioms1 and likewise the so-called definitions1 are1 as has already been said1 results of induction2 true of all objects whatever1 and1 as it may seem1 exactly true1 without the hypothetical assumption of unqualified truth where an approximation to it is all that exists4 ,the conclusions1 therefore1 it will naturally be inferred1 are exactly true1 and the science of number is an exception to other demonstrative sciences in this1 that the categorical certainty which is predicable of its demonstrations is independent of all hypothesis4 ,on more accurate investigation1 however1 it will be found that1 even in this case1 there is one hypothetical element in the ratiocination4 ,in all propositions concerning numbers1 a condition is implied1 without which none of them would be true2 and that condition is an assumption which may be false4 ,the condition is1 that #aa2 that all the numbers are numbers of the same or of equal units4 ,let this be doubtful1 and not one of the propositions of arithmetic will hold true4 ,how can we know that one pound and one pound make two pounds1 if one of the pounds may be troy1 and the other avoirdupois8 ,they may not make two pounds of either1 or of any weight4 ,how can we know that a forty-horse power is always equal to itself1 unless we assume that all horses are of equal strength8 ,it is certain that #a is always equal in number to #a2 and where the mere number of objects1 or of the parts of an object1 without supposing them to be equivalent in any other respect1 is all that is material1 the conclusions of arithmetic1 so far as they go to that alone1 are true without mixture of hypothesis4 ,there are such cases in statistics2 as1 for instance1 an inquiry into the amount of the population of any country4 ,it is indifferent to that inquiry whether they are grown people or children1 strong or weak1 tall or short2 the only thing we want to ascertain is their number4 ,but whenever1 from equality or inequality of number1 equality or inequality in any other respect is to be inferred1 arithmetic carried into such inquiries becomes as hypothetical a science as geometry4 ,all units must be assumed to be equal in that other respect2 and this is never accurately true1 for one actual pound weight is not exactly equal to another1 nor one measured mile's length to another2 a nicer balance1 or more accurate measuring instruments1 would always detect some difference4 ,what is commonly called mathematical certainty1 therefore1 which comprises the twofold conception of unconditional truth and perfect accuracy1 is not an attribute of all mathematical truths1 but of those only which relate to pure ,number1 as distinguished from ,quantity in the more enlarged sense2 and only so long as we abstain from supposing that the numbers are a precise index to actual quantities4 ,the certainty usually ascribed to the conclusions of geometry1 and even to those of mechanics1 is nothing whatever but certainty of inference4 ,we can have full assurance of particular results under particular suppositions1 but we can not have the same assurance that these suppositions are accurately true1 nor that they include all the data which may exercise an influence over the result in any given instance4 #d4 ,it appears1 therefore1 that the method of all ,deductive ,sciences is hypothetical4 ,they proceed by tracing the consequences of certain assumptions2 leaving for separate consideration whether the assumptions are true or not1 and if not exactly true1 whether they are a sufficiently near approximation to the truth4 ,the reason is obvious4 ,since it is only in questions of pure number that the assumptions are exactly true1 and even there only so long as no conclusions except purely numerical ones are to be founded on them2 it must1 in all other cases of deductive investigation1 form a part of the inquiry1 to determine how much the assumptions want of being exactly true in the case in hand4 ,this is generally a matter of observation1 to be repeated in every fresh case2 or if it has to be settled by argument instead of observation1 may require in every different case different evidence1 and present every degree of difficulty1 from the lowest to the highest4 ,but the other part of the process--namely1 to determine what else may be concluded if we find1 and in proportion as we find1 the assumptions to be true--may be performed once for all1 and the results held ready to be employed as the occasions turn up for use4 ,we thus do all beforehand that can be so done1 and leave the least possible work to be performed when cases arise and press for a decision4 ,this inquiry into the inferences which can be drawn from assumptions1 is what properly constitutes ,demonstrative ,science4 ,it is of course quite as practicable to arrive at new conclusions from facts assumed1 as from facts observed2 from fictitious1 as from real1 inductions4 ,deduction1 as we have seen1 consists of a series of inferences in this form--a is a mark of b1 b of c1 c of d1 therefore a is a mark of d1 which last may be a truth inaccessible to direct observation4 ,in like manner it is allowable to say1 suppose that a were a mark of b1 b of c1 and c of d1 a would be a mark of d1 which last conclusion was not thought of by those who laid down the premises4 ,a system of propositions as complicated as geometry might be deduced from assumptions which are false2 as was done by ,ptolemy1 ,descartes1 and others1 in their attempts to explain synthetically the phenomena of the solar system on the supposition that the apparent motions of the heavenly bodies were the real motions1 or were produced in some way more or less different from the true one4 ,sometimes the same thing is knowingly done1 for the purpose of showing the falsity of the assumption2 which is called a reductio ad absurdum4 ,in such cases1 the reasoning is as follows3 a is a mark of b1 and b of c2 now if c were also a mark of d1 a would be a mark of d2 but d is known to be a mark of the absence of a2 consequently a would be a mark of its own absence1 which is a contradiction2 therefore c is not a mark of d4 #e4 ,it has even been held by some writers1 that all ratiocination rests in the last resort on a reductio ad absurdum2 since the way to enforce assent to it1 in case of obscurity1 would be to show that if the conclusion be denied we must deny some one at least of the premises1 which1 as they are all supposed true1 would be a contradiction4 ,and in accordance with this1 many have thought that the peculiar nature of the evidence of ratiocination consisted in the impossibility of admitting the premises and rejecting the conclusion without a contradiction in terms4 ,this theory1 however1 is inadmissible as an explanation of the grounds on which ratiocination itself rests4 ,if any one denies the conclusion notwithstanding his admission of the premises1 he is not involved in any direct and express contradiction until he is compelled to deny some premise2 and he can only be forced to do this by a reductio ad absurdum1 that is1 by another ratiocination3 now1 if he denies the validity of the reasoning process itself1 he can no more be forced to assent to the second syllogism than to the first4 ,in truth1 therefore1 no one is ever forced to a contradiction in terms3 he can only be forced to a contradiction 7or rather an infringement7 of the fundamental maxim of ratiocination1 namely1 that whatever has a mark1 has what it is a mark of2 or 7in the case of universal propositions71 that whatever is a mark of any thing1 is a mark of whatever else that thing is a mark of4 ,for in the case of every correct argument1 as soon as thrown into the syllogistic form1 it is evident without the aid of any other syllogism1 that he who1 admitting the premises1 fails to draw the conclusion1 does not conform to the above axiom4 ,we have now proceeded as far in the theory of ,deduction as we can advance in the present stage of our inquiry4 ,any further insight into the subject requires that the foundation shall have been laid of the philosophic theory of ,induction itself2 in which theory that of ,deduction1 as a mode of ,induction1 which we have now shown it to be1 will assume spontaneously the place which belongs to it1 and will receive its share of whatever light may be thrown upon the great intellectual operation of which it forms so important a part4 ,chapter ,,vii4 ,examination ,of ,some ,opinions ,opposed ,to ,the ,preceding ,doctrines4 #a4 ,polemical discussion is foreign to the plan of this work4 ,but an opinion which stands in need of much illustration1 can often receive it most effectually1 and least tediously1 in the form of a defense against objections4 ,and on subjects concerning which speculative minds are still divided1 a writer does but half his duty by stating his own doctrine1 if he does not also examine1 and to the best of his ability judge1 those of other thinkers4 ,in the dissertation which ,mr4 ,herbert ,spencer has prefixed to his1 in many respects1 highly philosophical treatise on the ,mind17#ia7 he criticises some of the doctrines of the two preceding chapters1 and propounds a theory of his own on the subject of first principles4 ,mr4 ,spencer agrees with me in considering axioms to be 8simply our earliest inductions from experience40 ,but he differs from me 8widely as to the worth of the test of inconceivableness40 ,he thinks that it is the ultimate test of all beliefs4 ,he arrives at this conclusion by two steps4 ,first1 we never can have any stronger ground for believing any thing1 than that the belief of it 8invariably exists40 ,whenever any fact or proposition is invariably believed2 that is1 if ,i understand ,mr4 ,spencer rightly1 believed by all persons1 and by one's self at all times2 it is entitled to be received as one of the primitive truths1 or original premises of our knowledge4 ,secondly1 the criterion by which we decide whether any thing is invariably believed to be true1 is our inability to conceive it as false4 8,the inconceivability of its negation is the test by which we ascertain whether a given belief invariably exists or not40 8,for our primary beliefs1 the fact of invariable existence1 tested by an abortive effort to cause their non-existence1 is the only reason assignable40 ,he thinks this the sole ground of our belief in our own sensations4 ,if ,i believe that ,i feel cold1 ,i only receive this as true because ,i can not conceive that ,i am not feeling cold4 8,while the proposition remains true1 the negation of it remains inconceivable40 ,there are numerous other beliefs which ,mr4 ,spencer considers to rest on the same basis2 being chiefly those1 or a part of those1 which the metaphysicians of the ,reid and ,stewart school consider as truths of immediate intuition4 ,that there exists a material world2 that this is the very world which we directly and immediately perceive1 and not merely the hidden cause of our perceptions2 that ,space1 ,time1 ,force1 ,extension1 ,figure1 are not modes of our consciousness1 but objective realities2 are regarded by ,mr4 ,spencer as truths known by the inconceivableness of their negatives4 ,we can not1 he says1 by any effort1 conceive these objects of thought as mere states of our mind2 as not having an existence external to us4 ,their real existence is1 therefore1 as certain as our sensations themselves4 ,the truths which are the subject of direct knowledge1 being1 according to this doctrine1 known to be truths only by the inconceivability of their negation2 and the truths which are not the object of direct knowledge1 being known as inferences from those which are2 and those inferences being believed to follow from the premises1 only because we can not conceive them not to follow2 inconceivability is thus the ultimate ground of all assured beliefs4 ,thus far1 there is no very wide difference between ,mr4 ,spencer's doctrine and the ordinary one of philosophers of the intuitive school1 from ,descartes to ,dr4 ,whewell2 but at this point ,mr4 ,spencer diverges from them4 ,for he does not1 like them1 set up the test of inconceivability as infallible4 ,on the contrary1 he holds that it may be fallacious1 not from any fault in the test itself1 but because 8men have mistaken for inconceivable things1 some things which were not inconceivable40 ,and he himself1 in this very book1 denies not a few propositions usually regarded as among the most marked examples of truths whose negations are inconceivable4 ,but occasional failure1 he says1 is incident to all tests4 ,if such failure vitiates 8the test of inconceivableness10 it 8must similarly vitiate all tests whatever4 ,we consider an inference logically drawn from established premises to be true4 ,yet in millions of cases men have been wrong in the inferences they have thought thus drawn4 ,do we therefore argue that it is absurd to consider an inference true on no other ground than that it is logically drawn from established premises8 ,no3 we say that though men may have taken for logical inferences1 inferences that were not logical1 there nevertheless are logical inferences1 and that we are justified in assuming the truth of what seem to us such1 until better instructed4 ,similarly1 though men may have thought some things inconceivable which were not so1 there may still be inconceivable things2 and the inability to conceive the negation of a thing1 may still be our best warrant for believing it4444 ,though occasionally it may prove an imperfect test1 yet1 as our most certain beliefs are capable of no better1 to doubt any one belief because we have no higher guarantee for it1 is really to doubt all beliefs40 ,mr4 ,spencer's doctrine1 therefore1 does not erect the curable1 but only the incurable limitations of the human conceptive faculty1 into laws of the outward universe4 #b4 ,the doctrine1 that 8a belief which is proved by the inconceivableness of its negation to invariably exist1 is true10 ,mr4 ,spencer enforces by two arguments1 one of which may be distinguished as positive1 and the other as negative4 ,the positive argument is1 that every such belief represents the aggregate of all past experience4 8,conceding the entire truth of0 the 8position1 that during any phase of human progress1 the ability or inability to form a specific conception wholly depends on the experiences men have had2 and that1 by a widening of their experiences1 they may1 by and by1 be enabled to conceive things before inconceivable to them1 it may still be argued that as1 at any time1 the best warrant men can have for a belief is the perfect agreement of all pre-existing experience in support of it1 it follows that1 at any time1 the inconceivableness of its negation is the deepest test any belief admits of4444 ,objective facts are ever impressing themselves upon us2 our experience is a register of these objective facts2 and the inconceivableness of a thing implies that it is wholly at variance with the register4 ,even were this all1 it is not clear how1 if every truth is primarily inductive1 any better test of truth could exist4 ,but it must be remembered that while many of these facts1 impressing themselves upon us1 are occasional2 while others again are very general2 some are universal and unchanging4 ,these universal and unchanging facts are1 by the hypothesis1 certain to establish beliefs of which the negations are inconceivable2 while the others are not certain to do this2 and if they do1 subsequent facts will reverse their action4 ,hence if1 after an immense accumulation of experiences1 there remain beliefs of which the negations are still inconceivable1 most1 if not all of them1 must correspond to universal objective facts4 ,if there be 444 certain absolute uniformities in nature2 if these uniformities produce1 as they must1 absolute uniformities in our experience2 and if 444 these absolute uniformities in our experience disable us from conceiving the negations of them2 then answering to each absolute uniformity in nature which we can cognize1 there must exist in us a belief of which the negation is inconceivable1 and which is absolutely true4 ,in this wide range of cases subjective inconceivableness must correspond to objective impossibility4 ,further experience will produce correspondence where it may not yet exist2 and we may expect the correspondence to become ultimately complete4 ,in nearly all cases this test of inconceivableness must be valid now0 7,i wish ,i could think we were so nearly arrived at omniscience72 8and where it is not1 it still expresses the net result of our experience up to the present time2 which is the most that any test can do40 ,to this ,i answer1 first1 that it is by no means true that the inconceivability1 by us1 of the negative of a proposition proves all1 or even any1 8pre-existing experience0 to be in favor of the affirmative4 ,there may have been no such pre-existing experiences1 but only a mistaken supposition of experience4 ,how did the inconceivability of antipodes prove that experience had given any testimony against their possibility8 ,how did the incapacity men felt of conceiving sunset otherwise than as a motion of the sun1 represent any 8net result0 of experience in support of its being the sun and not the earth that moves8 ,it is not experience that is represented1 it is only a superficial semblance of experience4 ,the only thing proved with regard to real experience1 is the negative fact1 that men have not had it of the kind which would have made the inconceivable proposition conceivable4 ,next3 ,even if it were true that inconceivableness represents the net result of all past experience1 why should we stop at the representative when we can get at the thing represented8 ,if our incapacity to conceive the negation of a given supposition is proof of its truth1 because proving that our experience has hitherto been uniform in its favor1 the real evidence for the supposition is not the inconceivableness1 but the uniformity of experience4 ,now this1 which is the substantial and only proof1 is directly accessible4 ,we are not obliged to presume it from an incidental consequence4 ,if all past experience is in favor of a belief1 let this be stated1 and the belief openly rested on that ground3 after which the question arises1 what that fact may be worth as evidence of its truth8 ,for uniformity of experience is evidence in very different degrees3 in some cases it is strong evidence1 in others weak1 in others it scarcely amounts to evidence at all4 ,that all metals sink in water1 was a uniform experience1 from the origin of the human race to the discovery of potassium in the present century by ,sir ,humphry ,davy4 ,that all swans are white1 was a uniform experience down to the discovery of ,australia4 ,in the few cases in which uniformity of experience does amount to the strongest possible proof1 as with such propositions as these1 ,two straight lines can not inclose a space1 ,every event has a cause1 it is not because their negations are inconceivable1 which is not always the fact2 but because the experience1 which has been thus uniform1 pervades all nature4 ,it will be shown in the following ,book that none of the conclusions either of induction or of deduction can be considered certain1 except as far as their truth is shown to be inseparably bound up with truths of this class4 ,i maintain then1 first1 that uniformity of past experience is very far from being universally a criterion of truth4 ,but secondly1 inconceivableness is still further from being a test even of that test4 ,uniformity of contrary experience is only one of many causes of inconceivability4 ,tradition handed down from a period of more limited knowledge1 is one of the commonest4 ,the mere familiarity of one mode of production of a phenomenon often suffices to make every other mode appear inconceivable4 ,whatever connects two ideas by a strong association may1 and continually does1 render their separation in thought impossible2 as ,mr4 ,spencer1 in other parts of his speculations1 frequently recognizes4 ,it was not for want of experience that the ,cartesians were unable to conceive that one body could produce motion in another without contact4 ,they had as much experience of other modes of producing motion as they had of that mode4 ,the planets had revolved1 and heavy bodies had fallen1 every hour of their lives4 ,but they fancied these phenomena to be produced by a hidden machinery which they did not see1 because without it they were unable to conceive what they did see4 ,the inconceivableness1 instead of representing their experience1 dominated and overrode their experience4 ,without dwelling further on what ,i have termed the positive argument of ,mr4 ,spencer in support of his criterion of truth1 ,i pass to his negative argument1 on which he lays more stress4 #c4 ,the negative argument is1 that1 whether inconceivability be good evidence or bad1 no stronger evidence is to be obtained4 ,that what is inconceivable can not be true1 is postulated in every act of thought4 ,it is the foundation of all our original premises4 ,still more it is assumed in all conclusions from those premises4 ,the invariability of belief1 tested by the inconceivableness of its negation1 8is our sole warrant for every demonstration4 ,logic is simply a systematization of the process by which we indirectly obtain this warrant for beliefs that do not directly possess it4 ,to gain the strongest conviction possible respecting any complex fact1 we either analytically descend from it by successive steps1 each of which we unconsciously test by the inconceivableness of its negation1 until we reach some axiom or truth which we have similarly tested2 or we synthetically ascend from such axiom or truth by such steps4 ,in either case we connect some isolated belief1 with a belief which invariably exists1 by a series of intermediate beliefs which invariably exist40 ,the following passage sums up the theory3 8,when we perceive that the negation of the belief is inconceivable1 we have all possible warrant for asserting the invariability of its existence3 and in asserting this1 we express alike our logical justification of it1 and the inexorable necessity we are under of holding it4444 ,we have seen that this is the assumption on which every conclusion whatever ultimately rests4 ,we have no other guarantee for the reality of consciousness1 of sensations1 of personal existence2 we have no other guarantee for any axiom2 we have no other guarantee for any step in a demonstration4 ,hence1 as being taken for granted in every act of the understanding1 it must be regarded as the ,universal ,postulate40 ,but as this postulate1 which we are under an 8inexorable necessity0 of holding true1 is sometimes false2 as 8beliefs that once were shown by the inconceivableness of their negations to invariably exist1 have since been found untrue10 and as 8beliefs that now possess this character may some day share the same fate20 the canon of belief laid down by ,mr4 ,spencer is1 that 8the most certain conclusion0 is that 8which involves the postulate the fewest times40 ,reasoning1 therefore1 never ought to prevail against one of the immediate beliefs 7the belief in ,matter1 in the outward reality of ,extension1 ,space1 and the like71 because each of these involves the postulate only once2 while an argument1 besides involving it in the premises1 involves it again in every step of the ratiocination1 no one of the successive acts of inference being recognized as valid except because we can not conceive the conclusion not to follow from the premises4 ,it will be convenient to take the last part of this argument first4 ,in every reasoning1 according to ,mr4 ,spencer1 the assumption of the postulate is renewed at every step4 ,at each inference we judge that the conclusion follows from the premises1 our sole warrant for that judgment being that we can not conceive it not to follow4 ,consequently if the postulate is fallible1 the conclusions of reasoning are more vitiated by that uncertainty than direct intuitions2 and the disproportion is greater1 the more numerous the steps of the argument4 ,to test this doctrine1 let us first suppose an argument consisting only of a single step1 which would be represented by one syllogism4 ,this argument does rest on an assumption1 and we have seen in the preceding chapters what the assumption is4 ,it is1 that whatever has a mark1 has what it is a mark of4 ,the evidence of this axiom ,i shall not consider at present27#ib7 let us suppose it 7with ,mr4 ,spencer7 to be the inconceivableness of its reverse4 ,let us now add a second step to the argument3 we require1 what8 ,another assumption8 ,no3 the same assumption a second time2 and so on to a third1 and a fourth4 ,i confess ,i do not see how1 on ,mr4 ,spencer's own principles1 the repetition of the assumption at all weakens the force of the argument4 ,if it were necessary the second time to assume some other axiom1 the argument would no doubt be weakened1 since it would be necessary to its validity that both axioms should be true1 and it might happen that one was true and not the other3 making two chances of error instead of one4 ,but since it is the same axiom1 if it is true once it is true every time2 and if the argument1 being of a hundred links1 assumed the axiom a hundred times1 these hundred assumptions would make but one chance of error among them all4 ,it is satisfactory that we are not obliged to suppose the deductions of pure mathematics to be among the most uncertain of argumentative processes1 which on ,mr4 ,spencer's theory they could hardly fail to be1 since they are the longest4 ,but the number of steps in an argument does not subtract from its reliableness1 if no new premises1 of an uncertain character1 are taken up by the way47#ic7 ,to speak next of the premises4 ,our assurance of their truth1 whether they be generalities or individual facts1 is grounded1 in ,mr4 ,spencer's opinion1 on the inconceivableness of their being false4 ,it is necessary to advert to a double meaning of the word inconceivable1 which ,mr4 ,spencer is aware of1 and would sincerely disclaim founding an argument upon1 but from which his case derives no little advantage notwithstanding4 ,by inconceivableness is sometimes meant1 inability to form or get rid of an idea2 sometimes1 inability to form or get rid of a belief4 ,the former meaning is the most conformable to the analogy of language2 for a conception always means an idea1 and never a belief4 ,the wrong meaning of 8inconceivable0 is1 however1 fully as frequent in philosophical discussion as the right meaning1 and the intuitive school of metaphysicians could not well do without either4 ,to illustrate the difference1 we will take two contrasted examples4 ,the early physical speculators considered antipodes incredible1 because inconceivable4 ,but antipodes were not inconceivable in the primitive sense of the word4 ,an idea of them could be formed without difficulty3 they could be completely pictured to the mental eye4 ,what was difficult1 and1 as it then seemed1 impossible1 was to apprehend them as believable4 ,the idea could be put together1 of men sticking on by their feet to the under side of the earth2 but the belief would follow1 that they must fall off4 ,antipodes were not unimaginable1 but they were unbelievable4 ,on the other hand1 when ,i endeavor to conceive an end to extension1 the two ideas refuse to come together4 ,when ,i attempt to form a conception of the last point of space1 ,i can not help figuring to myself a vast space beyond that last point4 ,the combination is1 under the conditions of our experience1 unimaginable4 ,this double meaning of inconceivable it is very important to bear in mind1 for the argument from inconceivableness almost always turns on the alternate substitution of each of those meanings for the other4 ,in which of these two senses does ,mr4 ,spencer employ the term1 when he makes it a test of the truth of a proposition that its negation is inconceivable8 ,until ,mr4 ,spencer expressly stated the contrary1 ,i inferred from the course of his argument1 that he meant unbelievable4 ,he has1 however1 in a paper published in the fifth number of the ,fortnightly ,review1 disclaimed this meaning1 and declared that by an inconceivable proposition he means1 now and always1 8one of which the terms can not1 by any effort1 be brought before consciousness in that relation which the proposition asserts between them--a proposition of which the subject and predicate offer an insurmountable resistance to union in thought40 ,we now1 therefore1 know positively that ,mr4 ,spencer always endeavors to use the word inconceivable in this1 its proper1 sense3 but it may yet be questioned whether his endeavor is always successful2 whether the other1 and popular use of the word1 does not sometimes creep in with its associations1 and prevent him from maintaining a clear separation between the two4 ,when1 for example1 he says1 that when ,i feel cold1 ,i can not conceive that ,i am not feeling cold1 this expression can not be translated into 8,i can not conceive myself not feeling cold10 for it is evident that ,i can3 the word conceive1 therefore1 is here used to express the recognition of a matter of fact--the perception of truth or falsehood2 which ,i apprehend to be exactly the meaning of an act of belief1 as distinguished from simple conception4 ,again1 ,mr4 ,spencer calls the attempt to conceive something which is inconceivable 8an abortive effort to cause the non-existence10 not of a conception or mental representation1 but of a belief4 ,there is need1 therefore1 to revise a considerable part of ,mr4 ,spencer's language1 if it is to be kept always consistent with his definition of inconceivability4 ,but in truth the point is of little importance2 since inconceivability1 in ,mr4 ,spencer's theory1 is only a test of truth1 inasmuch as it is a test of believability4 ,the inconceivableness of a supposition is the extreme case of its unbelievability4 ,this is the very foundation of ,mr4 ,spencer's doctrine4 ,the invariability of the belief is with him the real guarantee4 ,the attempt to conceive the negative is made in order to test the inevitableness of the belief4 ,it should be called1 an attempt to believe the negative4 ,when ,mr4 ,spencer says that while looking at the sun a man can not conceive that he is looking into darkness1 he should have said that a man can not believe that he is doing so4 ,for it is surely possible1 in broad daylight1 to imagine one's self looking into darkness47#id7 ,as ,mr4 ,spencer himself says1 speaking of the belief of our own existence1 8,that he might not exist1 he can conceive well enough2 but that he does not exist1 he finds it impossible to conceive10 i4e41 to believe4 ,so that the statement resolves itself into this3 ,that ,i exist1 and that ,i have sensations1 ,i believe1 because ,i can not believe otherwise4 ,and in this case every one will admit that the impossibility is real4 ,any one's present sensations1 or other states of subjective consciousness1 that one person inevitably believes4 ,they are facts known per se3 it is impossible to ascend beyond them4 ,their negative is really unbelievable1 and therefore there is never any question about believing it4 ,mr4 ,spencer's theory is not needed for these truths4 ,but according to ,mr4 ,spencer there are other beliefs1 relating to other things than our own subjective feelings1 for which we have the same guarantee--which are1 in a similar manner1 invariable and necessary4 ,with regard to these other beliefs1 they can not be necessary1 since they do not always exist4 ,there have been1 and are1 many persons who do not believe the reality of an external world1 still less the reality of extension and figure as the forms of that external world2 who do not believe that space and time have an existence independent of the mind--nor any other of ,mr4 ,spencer's objective intuitions4 ,the negations of these alleged invariable beliefs are not unbelievable1 for they are believed4 ,it may be maintained1 without obvious error1 that we can not imagine tangible objects as mere states of our own and other people's consciousness2 that the perception of them irresistibly suggests to us the idea of something external to ourselves3 and ,i am not in a condition to say that this is not the fact 7though ,i do not think any one is entitled to affirm it of any person besides himself74 ,but many thinkers have believed1 whether they could conceive it or not1 that what we represent to ourselves as material objects1 are mere modifications of consciousness2 complex feelings of touch and of muscular action4 ,mr4 ,spencer may think the inference correct from the unimaginable to the unbelievable1 because he holds that belief itself is but the persistence of an idea1 and that what we can succeed in imagining we can not at the moment help apprehending as believable4 ,but of what consequence is it what we apprehend at the moment1 if the moment is in contradiction to the permanent state of our mind8 ,a person who has been frightened when an infant by stories of ghosts1 though he disbelieves them in after years 7and perhaps never believed them71 may be unable all his life to be in a dark place1 in circumstances stimulating to the imagination1 without mental discomposure4 ,the idea of ghosts1 with all its attendant terrors1 is irresistibly called up in his mind by the outward circumstances4 ,mr4 ,spencer may say1 that while he is under the influence of this terror he does not disbelieve in ghosts1 but has a temporary and uncontrollable belief in them4 ,be it so2 but allowing it to be so1 which would it be truest to say of this man on the whole--that he believes in ghosts1 or that he does not believe in them8 ,assuredly that he does not believe in them4 ,the case is similar with those who disbelieve a material world4 ,though they can not get rid of the idea2 though while looking at a solid object they can not help having the conception1 and therefore1 according to ,mr4 ,spencer's metaphysics1 the momentary belief1 of its externality2 even at that moment they would sincerely deny holding that belief3 and it would be incorrect to call them other than disbelievers of the doctrine4 ,the belief therefore is not invariable2 and the test of inconceivableness fails in the only cases to which there could ever be any occasion to apply it4 ,that a thing may be perfectly believable1 and yet may not have become conceivable1 and that we may habitually believe one side of an alternative1 and conceive only in the other1 is familiarly exemplified in the state of mind of educated persons respecting sunrise and sunset4 ,all educated persons either know by investigation1 or believe on the authority of science1 that it is the earth and not the sun which moves3 but there are probably few who habitually conceive the phenomenon otherwise than as the ascent or descent of the sun4 ,assuredly no one can do so without a prolonged trial2 and it is probably not easier now than in the first generation after ,copernicus4 ,mr4 ,spencer does not say1 8,in looking at sunrise it is impossible not to conceive that it is the sun which moves1 therefore this is what every body believes1 and we have all the evidence for it that we can have for any truth40 ,yet this would be an exact parallel to his doctrine about the belief in matter4 ,the existence of matter1 and other ,noumena1 as distinguished from the phenomenal world1 remains a question of argument1 as it was before2 and the very general1 but neither necessary nor universal1 belief in them1 stands as a psychological phenomenon to be explained1 either on the hypothesis of its truth1 or on some other4 ,the belief is not a conclusive proof of its own truth1 unless there are no such things as idola tribs2 but being a fact1 it calls on antagonists to show1 from what except the real existence of the thing believed1 so general and apparently spontaneous a belief can have originated4 ,and its opponents have never hesitated to accept this challenge47#ie7 ,the amount of their success in meeting it will probably determine the ultimate verdict of philosophers on the question4 #d4 ,in the revision1 or rather reconstruction1 of his 8,principles of ,psychology10 as one of the stages or platforms in the imposing structure of his ,system of ,philosophy1 ,mr4 ,spencer has resumed what he justly terms7#if7 the 8amicable controversy that has been long pending between us20 expressing at the same time a regret1 which ,i cordially share1 that 8this lengthened exposition of a single point of difference1 unaccompanied by an exposition of the numerous points of concurrence1 unavoidably produces an appearance of dissent very far greater than that which exists40 ,i believe1 with ,mr4 ,spencer1 that the difference between us1 if measured by our conclusions1 is 8superficial rather than substantial20 and the value ,i attach to so great an amount of agreement1 in the field of analytic psychology1 with a thinker of his force and depth1 is such as ,i can hardly overstate4 ,but ,i also agree with him that the difference which exists in our premises is one of 8profound importance1 philosophically considered20 and not to be dismissed while any part of the case of either of us has not been fully examined and discussed4 ,in his present statement of the ,universal ,postulate1 ,mr4 ,spencer has exchanged his former expression1 8beliefs which invariably exist10 for the following3 8cognitions of which the predicates invariably exist along with their subjects40 ,and he says that 8an abortive effort to conceive the negation of a proposition1 shows that the cognition expressed is one of which the predicate invariably exists along with its subject2 and the discovery that the predicate invariably exists along with its subject1 is the discovery that this cognition is one we are compelled to accept40 ,both these premises of ,mr4 ,spencer's syllogism ,i am able to assent to1 but in different senses of the middle term4 ,if the invariable existence of the predicate along with its subject1 is to be understood in the most obvious meaning1 as an existence in actual ,nature1 or in other words1 in our objective1 or sensational1 experience1 ,i of course admit that this1 once ascertained1 compels us to accept the proposition3 but then ,i do not admit that the failure of an attempt to conceive the negative1 proves the predicate to be always co-existent with the subject in actual ,nature4 ,if1 on the other hand 7which ,i believe to be ,mr4 ,spencer's meaning7 the invariable existence of the predicate along with the subject is to be understood only of our conceptive faculty1 i4e41 that the one is inseparable from the other in our thoughts2 then1 indeed1 the inability to separate the two ideas proves their inseparable conjunction1 here and now1 in the mind which has failed in the attempt2 but this inseparability in thought does not prove a corresponding inseparability in fact2 nor even in the thoughts of other people1 or of the same person in a possible future4 8,that some propositions have been wrongly accepted as true1 because their negations were supposed inconceivable when they were not10 does not1 in ,mr4 ,spencer's opinion1 8disprove the validity of the test20 not only because any test whatever 8is liable to yield untrue results1 either from incapacity or from carelessness in those who use it10 but because the propositions in question 8were complex propositions1 not to be established by a test applicable to propositions no further decomposable40 8,a test legitimately applicable to a simple proposition1 the subject and predicate of which are in direct relation1 can not be legitimately applied to a complex proposition1 the subject and predicate of which are indirectly related through the many simple propositions implied40 8,that things which are equal to the same thing are equal to one another1 is a fact which can be known by direct comparison of actual or ideal relations4444 ,but that the square of the hypothenuse of a right-angled triangle equals the sum of the squares of the other two sides1 can not be known immediately by comparison of two states of consciousness3 here the truth can be reached only mediately1 through a series of simple judgments respecting the likenesses or unlikenesses of certain relations40 ,moreover1 even when the proposition admits of being tested by immediate consciousness1 people often neglect to do it4 ,a school-boy1 in adding up a column of figures1 will say 8#ce and #i are #df10 though this is contrary to the verdict which consciousness gives when #ce and #i are really called up before it2 but this is not done4 ,and not only school-boys1 but men and thinkers1 do not always 8distinctly translate into their equivalent states of consciousness the words they use40 ,it is but just to give ,mr4 ,spencer's doctrine the benefit of the limitation he claims--viz41 that it is only applicable to propositions which are assented to on simple inspection1 without any intervening media of proof4 ,but this limitation does not exclude some of the most marked instances of propositions now known to be false or groundless1 but whose negative was once found inconceivable3 such as1 that in sunrise and sunset it is the sun which moves2 that gravitation may exist without an intervening medium2 and even the case of antipodes4 ,the distinction drawn by ,mr4 ,spencer is real2 but1 in the case of the propositions classed by him as complex1 consciousness1 until the media of proof are supplied1 gives no verdict at all3 it neither declares the equality of the square of the hypothenuse with the sum of the squares of the sides to be inconceivable1 nor their inequality to be inconceivable4 ,but in all the three cases which ,i have just cited1 the inconceivability seems to be apprehended directly2 no train of argument was needed1 as in the case of the square of the hypothenuse1 to obtain the verdict of consciousness on the point4 ,neither is any of the three a case like that of the school-boy's mistake1 in which the mind was never really brought into contact with the proposition4 ,they are cases in which one of two opposite predicates1 mero adspectu1 seemed to be incompatible with the subject1 and the other1 therefore1 to be proved always to exist with it47#ig7 ,as now limited by ,mr4 ,spencer1 the ultimate cognitions fit to be submitted to his test are only those of so universal and elementary a character as to be represented in the earliest and most unvarying experience1 or apparent experience1 of all mankind4 ,in such cases the inconceivability of the negative1 if real1 is accounted for by the experience3 and why 7,i have asked7 should the truth be tested by the inconceivability1 when we can go further back for proof--namely1 to the experience itself8 ,to this ,mr4 ,spencer answers1 that the experiences can not be all recalled to mind1 and if recalled1 would be of unmanageable multitude4 ,to test a proposition by experience seems to him to mean that 8before accepting as certain the proposition that any rectilineal figure must have as many angles as it has sides10 ,i have 8to think of every triangle1 square1 pentagon1 hexagon1 etc41 which ,i have ever seen1 and to verify the asserted relation in each case40 ,i can only say1 with surprise1 that ,i do not understand this to be the meaning of an appeal to experience4 ,it is enough to know that one has been seeing the fact all one's life1 and has never remarked any instance to the contrary1 and that other people1 with every opportunity of observation1 unanimously declare the same thing4 ,it is true1 even this experience may be insufficient1 and so it might be even if ,i could recall to mind every instance of it2 but its insufficiency1 instead of being brought to light1 is disguised1 if instead of sifting the experience itself1 ,i appeal to a test which bears no relation to the sufficiency of the experience1 but1 at the most1 only to its familiarity4 ,these remarks do not lose their force even if we believe1 with ,mr4 ,spencer1 that mental tendencies originally derived from experience impress themselves permanently on the cerebral structure and are transmitted by inheritance1 so that modes of thinking which are acquired by the race become innate and a priori in the individual1 thus representing1 in ,mr4 ,spencer's opinion1 the experience of his progenitors1 in addition to his own4 ,all that would follow from this is1 that a conviction might be really innate1 i4e41 prior to individual experience1 and yet not be true1 since the inherited tendency to accept it may have been originally the result of other causes than its truth4 ,mr4 ,spencer would have a much stronger case1 if he could really show that the evidence of ,reasoning rests on the ,postulate1 or1 in other words1 that we believe that a conclusion follows from premises only because we can not conceive it not to follow4 ,but this statement seems to me to be of the same kind as one ,i have previously commented on1 viz41 that ,i believe ,i see light1 because ,i can not1 while the sensation remains1 conceive that ,i am looking into darkness4 ,both these statements seem to me incompatible with the meaning 7as very rightly limited by ,mr4 ,spencer7 of the verb to conceive4 ,to say that when ,i apprehend that ,a is ,b and that ,b is ,c1 ,i can not conceive that ,a is not ,c1 is to my mind merely to say that ,i am compelled to believe that ,a is ,c4 ,if to conceive be taken in its proper meaning1 viz41 to form a mental representation1 ,i may be able to conceive ,a as not being ,c4 ,after assenting1 with full understanding1 to the ,copernican proof that it is the earth and not the sun that moves1 ,i not only can conceive1 or represent to myself1 sunset as a motion of the sun1 but almost every one finds this conception of sunset easier to form1 than that which they nevertheless know to be the true one4 #e4 ,sir ,william ,hamilton holds as ,i do1 that inconceivability is no criterion of impossibility4 8,there is no ground for inferring a certain fact to be impossible1 merely from our inability to conceive its possibility40 8,things there are which may1 nay must1 be true1 of which the understanding is wholly unable to construe to itself the possibility407#ih7 ,sir ,william ,hamilton is1 however1 a firm believer in the a priori character of many axioms1 and of the sciences deduced from them2 and is so far from considering those axioms to rest on the evidence of experience1 that he declares certain of them to be true even of ,noumena--of the ,unconditioned--of which it is one of the principal aims of his philosophy to prove that the nature of our faculties debars us from having any knowledge4 ,the axioms to which he attributes this exceptional emancipation from the limits which confine all our other possibilities of knowledge2 the chinks through which1 as he represents1 one ray of light finds its way to us from behind the curtain which veils from us the mysterious world of ,things in themselves--are the two principles1 which he terms1 after the school-men1 the ,principle of ,contradiction1 and the ,principle of ,excluded ,middle3 the first1 that two contradictory propositions can not both be true2 the second1 that they can not both be false4 ,armed with these logical weapons1 we may boldly face ,things in themselves1 and tender to them the double alternative1 sure that they must absolutely elect one or the other side1 though we may be forever precluded from discovering which4 ,to take his favorite example1 we can not conceive the infinite divisibility of matter1 and we can not conceive a minimum1 or end to divisibility3 yet one or the other must be true4 ,as ,i have hitherto said nothing of the two axioms in question1 those of ,contradiction and of ,excluded ,middle1 it is not unseasonable to consider them here4 ,the former asserts that an affirmative proposition and the corresponding negative proposition can not both be true2 which has generally been held to be intuitively evident4 ,sir ,william ,hamilton and the ,germans consider it to be the statement in words of a form or law of our thinking faculty4 ,other philosophers1 not less deserving of consideration1 deem it to be an identical proposition2 an assertion involved in the meaning of terms2 a mode of defining ,negation1 and the word ,not4 ,i am able to go one step with these last4 ,an affirmative assertion and its negative are not two independent assertions1 connected with each other only as mutually incompatible4 ,that if the negative be true1 the affirmative must be false1 really is a mere identical proposition2 for the negative proposition asserts nothing but the falsity of the affirmative1 and has no other sense or meaning whatever4 ,the ,principium ,contradictionis should therefore put off the ambitious phraseology which gives it the air of a fundamental antithesis pervading nature1 and should be enunciated in the simpler form1 that the same proposition can not at the same time be false and true4 ,but ,i can go no further with the ,nominalists2 for ,i can not look upon this last as a merely verbal proposition4 ,i consider it to be1 like other axioms1 one of our first and most familiar generalizations from experience4 ,the original foundation of it ,i take to be1 that ,belief and ,disbelief are two different mental states1 excluding one another4 ,this we know by the simplest observation of our own minds4 ,and if we carry our observation outward1 we also find that light and darkness1 sound and silence1 motion and quiescence1 equality and inequality1 preceding and following1 succession and simultaneousness1 any positive phenomenon whatever and its negative1 are distinct phenomena1 pointedly contrasted1 and the one always absent where the other is present4 ,i consider the maxim in question to be a generalization from all these facts4 ,in like manner as the ,principle of ,contradiction 7that one of two contradictories must be false7 means that an assertion can not be both true and false1 so the ,principle of ,excluded ,middle1 or that one of two contradictories must be true1 means that an assertion must be either true or false3 either the affirmative is true1 or otherwise the negative is true1 which means that the affirmative is false4 ,i can not help thinking this principle a surprising specimen of a so-called necessity of ,thought1 since it is not even true1 unless with a large qualification4 ,a proposition must be either true or false1 provided that the predicate be one which can in any intelligible sense be attributed to the subject2 7and as this is always assumed to be the case in treatises on logic1 the axiom is always laid down there as of absolute truth74 8,abracadabra is a second intention0 is neither true nor false4 ,between the true and the false there is a third possibility1 the ,unmeaning3 and this alternative is fatal to ,sir ,william ,hamilton's extension of the maxim to ,noumena4 ,that ,matter must either have a minimum of divisibility or be infinitely divisible1 is more than we can ever know4 ,for in the first place1 ,matter1 in any other than the phenomenal sense of the term1 may not exist3 and it will scarcely be said that a nonentity must be either infinitely or finitely divisible4 ,in the second place1 though matter1 considered as the occult cause of our sensations1 do really exist1 yet what we call divisibility may be an attribute only of our sensations of sight and touch1 and not of their uncognizable cause4 ,divisibility may not be predicable at all1 in any intelligible sense1 of ,things in themselves1 nor therefore of ,matter in itself2 and the assumed necessity of being either infinitely or finitely divisible1 may be an inapplicable alternative4 ,on this question ,i am happy to have the full concurrence of ,mr4 ,herbert ,spencer1 from whose paper in the ,fortnightly ,review ,i extract the following passage4 ,the germ of an idea identical with that of ,mr4 ,spencer may be found in the present chapter1 on a preceding page2 but in ,mr4 ,spencer it is not an undeveloped thought1 but a philosophical theory4 8,when remembering a certain thing as in a certain place1 the place and the thing are mentally represented together2 while to think of the non-existence of the thing in that place implies a consciousness in which the place is represented1 but not the thing4 ,similarly1 if instead of thinking of an object as colorless1 we think of its having color1 the change consists in the addition to the concept of an element that was before absent from it--the object can not be thought of first as red and then as not red1 without one component of the thought being totally expelled from the mind by another4 ,the law of the ,excluded ,middle1 then1 is simply a generalization of the universal experience that some mental states are directly destructive of other states4 ,it formulates a certain absolutely constant law1 that the appearance of any positive mode of consciousness can not occur without excluding a correlative negative mode2 and that the negative mode can not occur without excluding the correlative positive mode3 the antithesis of positive and negative being1 indeed1 merely an expression of this experience4 ,hence it follows that if consciousness is not in one of the two modes it must be in the other407#ii7 ,i must here close this supplementary chapter1 and with it the ,second ,book4 ,the theory of ,induction1 in the most comprehensive sense of the term1 will form the subject of the ,third4 ,book ,,iii4 ,,of ,,induction4 8,according to the doctrine now stated1 the highest1 or rather the only proper object of physics1 is to ascertain those established conjunctions of successive events1 which constitute the order of the universe2 to record the phenomena which it exhibits to our observations1 or which it discloses to our experiments2 and to refer these phenomena to their general laws40--,d4 ,,stewart1 ,elements of the ,philosophy of the ,human ,mind1 vol4 ii41 chap4 iv41 sect4 #a4 8,in such cases the inductive and deductive methods of inquiry may be said to go hand in hand1 the one verifying the conclusions deduced by the other2 and the combination of experiment and theory1 which may thus be brought to bear in such cases1 forms an engine of discovery infinitely more powerful than either taken separately4 ,this state of any department of science is perhaps of all others the most interesting1 and that which promises the most to research40--,,sir ,j4 ,,herschel1 ,discourse on the ,study of ,natural ,philosophy4 ,chapter ,i4 ,preliminary ,observations ,on ,induction ,in ,general4 #a4 ,the portion of the present inquiry upon which we are now about to enter1 may be considered as the principal1 both from its surpassing in intricacy all the other branches1 and because it relates to a process which has been shown in the preceding ,book to be that in which the investigation of nature essentially consists4 ,we have found that all ,inference1 consequently all ,proof1 and all discovery of truths not self-evident1 consists of inductions1 and the interpretation of inductions3 that all our knowledge1 not intuitive1 comes to us exclusively from that source4 ,what ,induction is1 therefore1 and what conditions render it legitimate1 can not but be deemed the main question of the science of logic--the question which includes all others4 ,it is1 however1 one which professed writers on logic have almost entirely passed over4 ,the generalities of the subject have not been altogether neglected by metaphysicians2 but1 for want of sufficient acquaintance with the processes by which science has actually succeeded in establishing general truths1 their analysis of the inductive operation1 even when unexceptionable as to correctness1 has not been specific enough to be made the foundation of practical rules1 which might be for induction itself what the rules of the syllogism are for the interpretation of induction3 while those by whom physical science has been carried to its present state of improvement--and who1 to arrive at a complete theory of the process1 needed only to generalize1 and adapt to all varieties of problems1 the methods which they themselves employed in their habitual pursuits--never until very lately made any serious attempt to philosophize on the subject1 nor regarded the mode in which they arrived at their conclusions as deserving of study1 independently of the conclusions themselves4 #b4 ,for the purposes of the present inquiry1 ,induction may be defined1 the operation of discovering and proving general propositions4 ,it is true that 7as already shown7 the process of indirectly ascertaining individual facts1 is as truly inductive as that by which we establish general truths4 ,but it is not a different kind of induction2 it is a form of the very same process3 since1 on the one hand1 generals are but collections of particulars1 definite in kind but indefinite in number2 and on the other hand1 whenever the evidence which we derive from observation of known cases justifies us in drawing an inference respecting even one unknown case1 we should on the same evidence be justified in drawing a similar inference with respect to a whole class of cases4 ,the inference either does not hold at all1 or it holds in all cases of a certain description2 in all cases which1 in certain definable respects1 resemble those we have observed4 ,if these remarks are just2 if the principles and rules of inference are the same whether we infer general propositions or individual facts2 it follows that a complete logic of the sciences would be also a complete logic of practical business and common life4 ,since there is no case of legitimate inference from experience1 in which the conclusion may not legitimately be a general proposition2 an analysis of the process by which general truths are arrived at1 is virtually an analysis of all induction whatever4 ,whether we are inquiring into a scientific principle or into an individual fact1 and whether we proceed by experiment or by ratiocination1 every step in the train of inferences is essentially inductive1 and the legitimacy of the induction depends in both cases on the same conditions4 ,true it is that in the case of the practical inquirer1 who is endeavoring to ascertain facts not for the purposes of science but for those of business1 such1 for instance1 as the advocate or the judge1 the chief difficulty is one in which the principles of induction will afford him no assistance4 ,it lies not in making his inductions1 but in the selection of them2 in choosing from among all general propositions ascertained to be true1 those which furnish marks by which he may trace whether the given subject possesses or not the predicate in question4 ,in arguing a doubtful question of fact before a jury1 the general propositions or principles to which the advocate appeals are mostly1 in themselves1 sufficiently trite1 and assented to as soon as stated3 his skill lies in bringing his case under those propositions or principles2 in calling to mind such of the known or received maxims of probability as admit of application to the case in hand1 and selecting from among them those best adapted to his object4 ,success is here dependent on natural or acquired sagacity1 aided by knowledge of the particular subject1 and of subjects allied with it4 ,invention1 though it can be cultivated1 can not be reduced to rule2 there is no science which will enable a man to bethink himself of that which will suit his purpose4 ,but when he has thought of something1 science can tell him whether that which he has thought of will suit his purpose or not4 ,the inquirer or arguer must be guided by his own knowledge and sagacity in the choice of the inductions out of which he will construct his argument4 ,but the validity of the argument when constructed1 depends on principles1 and must be tried by tests which are the same for all descriptions of inquiries1 whether the result be to give ,a an estate1 or to enrich science with a new general truth4 ,in the one case and in the other1 the senses1 or testimony1 must decide on the individual facts2 the rules of the syllogism will determine whether1 those facts being supposed correct1 the case really falls within the formul of the different inductions under which it has been successively brought2 and finally1 the legitimacy of the inductions themselves must be decided by other rules1 and these it is now our purpose to investigate4 ,if this third part of the operation be1 in many of the questions of practical life1 not the most1 but the least arduous portion of it1 we have seen that this is also the case in some great departments of the field of science2 in all those which are principally deductive1 and most of all in mathematics2 where the inductions themselves are few in number1 and so obvious and elementary that they seem to stand in no need of the evidence of experience1 while to combine them so as to prove a given theorem or solve a problem1 may call for the utmost powers of invention and contrivance with which our species is gifted4 ,if the identity of the logical processes which prove particular facts and those which establish general scientific truths1 required any additional confirmation1 it would be sufficient to consider that in many branches of science1 single facts have to be proved1 as well as principles2 facts as completely individual as any that are debated in a court of justice2 but which are proved in the same manner as the other truths of the science1 and without disturbing in any degree the homogeneity of its method4 ,a remarkable example of this is afforded by astronomy4 ,the individual facts on which that science grounds its most important deductions1 such facts as the magnitudes of the bodies of the solar system1 their distances from one another1 the figure of the earth1 and its rotation1 are scarcely any of them accessible to our means of direct observation3 they are proved indirectly1 by the aid of inductions founded on other facts which we can more easily reach4 ,for example1 the distance of the moon from the earth was determined by a very circuitous process4 ,the share which direct observation had in the work consisted in ascertaining1 at one and the same instant1 the zenith distances of the moon1 as seen from two points very remote from one another on the earth's surface4 ,the ascertainment of these angular distances ascertained their supplements2 and since the angle at the earth's centre subtended by the distance between the two places of observation was deducible by spherical trigonometry from the latitude and longitude of those places1 the angle at the moon subtended by the same line became the fourth angle of a quadrilateral of which the other three angles were known4 ,the four angles being thus ascertained1 and two sides of the quadrilateral being radii of the earth2 the two remaining sides and the diagonal1 or1 in other words1 the moon's distance from the two places of observation and from the centre of the earth1 could be ascertained1 at least in terms of the earth's radius1 from elementary theorems of geometry4 ,at each step in this demonstration a new induction is taken in1 represented in the aggregate of its results by a general proposition4 ,not only is the process by which an individual astronomical fact was thus ascertained1 exactly similar to those by which the same science establishes its general truths1 but also 7as we have shown to be the case in all legitimate reasoning7 a general proposition might have been concluded instead of a single fact4 ,in strictness1 indeed1 the result of the reasoning is a general proposition2 a theorem respecting the distance1 not of the moon in particular1 but of any inaccessible object2 showing in what relation that distance stands to certain other quantities4 ,and although the moon is almost the only heavenly body the distance of which from the earth can really be thus ascertained1 this is merely owing to the accidental circumstances of the other heavenly bodies1 which render them incapable of affording such data as the application of the theorem requires2 for the theorem itself is as true of them as it is of the moon47#ajj7 ,we shall fall into no error1 then1 if in treating of ,induction1 we limit our attention to the establishment of general propositions4 ,the principles and rules of ,induction as directed to this end1 are the principles and rules of all ,induction2 and the logic of ,science is the universal ,logic1 applicable to all inquiries in which man can engage4 ,chapter ,,ii4 ,of ,inductions ,improperly ,so ,called4 #a4 ,induction1 then1 is that operation of the mind1 by which we infer that what we know to be true in a particular case or cases1 will be true in all cases which resemble the former in certain assignable respects4 ,in other words1 ,induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class1 or that what is true at certain times will be true in similar circumstances at all times4 ,this definition excludes from the meaning of the term ,induction1 various logical operations1 to which it is not unusual to apply that name4 ,induction1 as above defined1 is a process of inference2 it proceeds from the known to the unknown2 and any operation involving no inference1 any process in which what seems the conclusion is no wider than the premises from which it is drawn1 does not fall within the meaning of the term4 ,yet in the common books of ,logic we find this laid down as the most perfect1 indeed the only quite perfect1 form of induction4 ,in those books1 every process which sets out from a less general and terminates in a more general expression--which admits of being stated in the form1 8,this and that ,a are ,b1 therefore every ,a is ,b0--is called an induction1 whether any thing be really concluded or not3 and the induction is asserted not to be perfect1 unless every single individual of the class ,a is included in the antecedent1 or premise3 that is1 unless what we affirm of the class has already been ascertained to be true of every individual in it1 so that the nominal conclusion is not really a conclusion1 but a mere re-assertion of the premises4 ,if we were to say1 ,all the planets shine by the sun's light1 from observation of each separate planet1 or ,all the ,apostles were ,jews1 because this is true of ,peter1 ,paul1 ,john1 and every other apostle--these1 and such as these1 would1 in the phraseology in question1 be called perfect1 and the only perfect1 ,inductions4 ,this1 however1 is a totally different kind of induction from ours2 it is not an inference from facts known to facts unknown1 but a mere short-hand registration of facts known4 ,the two simulated arguments which we have quoted1 are not generalizations2 the propositions purporting to be conclusions from them1 are not really general propositions4 ,a general proposition is one in which the predicate is affirmed or denied of an unlimited number of individuals2 namely1 all1 whether few or many1 existing or capable of existing1 which possess the properties connoted by the subject of the proposition4 8,all men are mortal0 does not mean all now living1 but all men past1 present1 and to come4 ,when the signification of the term is limited so as to render it a name not for any and every individual falling under a certain general description1 but only for each of a number of individuals1 designated as such1 and as it were counted off individually1 the proposition1 though it may be general in its language1 is no general proposition1 but merely that number of singular propositions1 written in an abridged character4 ,the operation may be very useful1 as most forms of abridged notation are2 but it is no part of the investigation of truth1 though often bearing an important part in the preparation of the materials for that investigation4 ,as we may sum up a definite number of singular propositions in one proposition1 which will be apparently1 but not really1 general1 so we may sum up a definite number of general propositions in one proposition1 which will be apparently1 but not really1 more general4 ,if by a separate induction applied to every distinct species of animals1 it has been established that each possesses a nervous system1 and we affirm thereupon that all animals have a nervous system2 this looks like a generalization1 though as the conclusion merely affirms of all what has already been affirmed of each1 it seems to tell us nothing but what we knew before4 ,a distinction1 however1 must be made4 ,if in concluding that all animals have a nervous system1 we mean the same thing and no more as if we had said 8all known animals10 the proposition is not general1 and the process by which it is arrived at is not induction4 ,but if our meaning is that the observations made of the various species of animals have discovered to us a law of animal nature1 and that we are in a condition to say that a nervous system will be found even in animals yet undiscovered1 this indeed is an induction2 but in this case the general proposition contains more than the sum of the special propositions from which it is inferred4 ,the distinction is still more forcibly brought out when we consider1 that if this real generalization be legitimate at all1 its legitimacy probably does not require that we should have examined without exception every known species4 ,it is the number and nature of the instances1 and not their being the whole of those which happen to be known1 that makes them sufficient evidence to prove a general law3 while the more limited assertion1 which stops at all known animals1 can not be made unless we have rigorously verified it in every species4 ,in like manner 7to return to a former example7 we might have inferred1 not that all the planets1 but that all planets1 shine by reflected light3 the former is no induction2 the latter is an induction1 and a bad one1 being disproved by the case of double stars--self-luminous bodies which are properly planets1 since they revolve round a centre4 #b4 ,there are several processes used in mathematics which require to be distinguished from ,induction1 being not unfrequently called by that name1 and being so far similar to ,induction properly so called1 that the propositions they lead to are really general propositions4 ,for example1 when we have proved with respect to the circle1 that a straight line can not meet it in more than two points1 and when the same thing has been successively proved of the ellipse1 the parabola1 and the hyperbola1 it may be laid down as a universal property of the sections of the cone4 ,the distinction drawn in the two previous examples can have no place here1 there being no difference between all known sections of the cone and all sections1 since a cone demonstrably can not be intersected by a plane except in one of these four lines4 ,it would be difficult1 therefore1 to refuse to the proposition arrived at1 the name of a generalization1 since there is no room for any generalization beyond it4 ,but there is no induction1 because there is no inference3 the conclusion is a mere summing up of what was asserted in the various propositions from which it is drawn4 ,a case somewhat1 though not altogether1 similar1 is the proof of a geometrical theorem by means of a diagram4 ,whether the diagram be on paper or only in the imagination1 the demonstration 7as formerly observed7#aja77 does not prove directly the general theorem2 it proves only that the conclusion1 which the theorem asserts generally1 is true of the particular triangle or circle exhibited in the diagram2 but since we perceive that in the same way in which we have proved it of that circle1 it might also be proved of any other circle1 we gather up into one general expression all the singular propositions susceptible of being thus proved1 and embody them in a universal proposition4 ,having shown that the three angles of the triangle ,,abc are together equal to two right angles1 we conclude that this is true of every other triangle1 not because it is true of ,,abc1 but for the same reason which proved it to be true of ,,abc4 ,if this were to be called ,induction1 an appropriate name for it would be1 induction by parity of reasoning4 ,but the term can not properly belong to it2 the characteristic quality of ,induction is wanting1 since the truth obtained1 though really general1 is not believed on the evidence of particular instances4 ,we do not conclude that all triangles have the property because some triangles have1 but from the ulterior demonstrative evidence which was the ground of our conviction in the particular instances4 ,there are nevertheless1 in mathematics1 some examples of so-called ,induction1 in which the conclusion does bear the appearance of a generalization grounded on some of the particular cases included in it4 ,a mathematician1 when he has calculated a sufficient number of the terms of an algebraical or arithmetical series to have ascertained what is called the law of the series1 does not hesitate to fill up any number of the succeeding terms without repeating the calculations4 ,but ,i apprehend he only does so when it is apparent from a priori considerations 7which might be exhibited in the form of demonstration7 that the mode of formation of the subsequent terms1 each from that which preceded it1 must be similar to the formation of the terms which have been already calculated4 ,and when the attempt has been hazarded without the sanction of such general considerations1 there are instances on record in which it has led to false results4 ,it is said that ,newton discovered the binomial theorem by induction2 by raising a binomial successively to a certain number of powers1 and comparing those powers with one another until he detected the relation in which the algebraic formula of each power stands to the exponent of that power1 and to the two terms of the binomial4 ,the fact is not improbable3 but a mathematician like ,newton1 who seemed to arrive per saltum at principles and conclusions that ordinary mathematicians only reached by a succession of steps1 certainly could not have performed the comparison in question without being led by it to the a priori ground of the law2 since any one who understands sufficiently the nature of multiplication to venture upon multiplying several lines of symbols at one operation1 can not but perceive that in raising a binomial to a power1 the co-efficients must depend on the laws of permutation and combination3 and as soon as this is recognized1 the theorem is demonstrated4 ,indeed1 when once it was seen that the law prevailed in a few of the lower powers1 its identity with the law of permutation would at once suggest the considerations which prove it to obtain universally4 ,even1 therefore1 such cases as these1 are but examples of what ,i have called ,induction by parity of reasoning1 that is1 not really ,induction1 because not involving inference of a general proposition from particular instances4 #c4 ,there remains a third improper use of the term ,induction1 which it is of real importance to clear up1 because the theory of ,induction has been1 in no ordinary degree1 confused by it1 and because the confusion is exemplified in the most recent and elaborate treatise on the inductive philosophy which exists in our language4 ,the error in question is that of confounding a mere description1 by general terms1 of a set of observed phenomena1 with an induction from them4 ,suppose that a phenomenon consists of parts1 and that these parts are only capable of being observed separately1 and as it were piecemeal4 ,when the observations have been made1 there is a convenience 7amounting for many purposes to a necessity7 in obtaining a representation of the phenomenon as a whole1 by combining1 or as we may say1 piecing these detached fragments together4 ,a navigator sailing in the midst of the ocean discovers land3 he can not at first1 or by any one observation1 determine whether it is a continent or an island2 but he coasts along it1 and after a few days finds himself to have sailed completely round it3 he then pronounces it an island4 ,now there was no particular time or place of observation at which he could perceive that this land was entirely surrounded by water3 he ascertained the fact by a succession of partial observations1 and then selected a general expression which summed up in two or three words the whole of what he so observed4 ,but is there any thing of the nature of an induction in this process8 ,did he infer any thing that had not been observed1 from something else which had8 ,certainly not4 ,he had observed the whole of what the proposition asserts4 ,that the land in question is an island1 is not an inference from the partial facts which the navigator saw in the course of his circumnavigation2 it is the facts themselves2 it is a summary of those facts2 the description of a complex fact1 to which those simpler ones are as the parts of a whole4 ,now there is1 ,i conceive1 no difference in kind between this simple operation1 and that by which ,kepler ascertained the nature of the planetary orbits3 and ,kepler's operation1 all at least that was characteristic in it1 was not more an inductive act than that of our supposed navigator4 ,the object of ,kepler was to determine the real path described by each of the planets1 or let us say by the planet ,mars 7since it was of that body that he first established the two of his three laws which did not require a comparison of planets74 ,to do this there was no other mode than that of direct observation3 and all which observation could do was to ascertain a great number of the successive places of the planet2 or rather1 of its apparent places4 ,that the planet occupied successively all these positions1 or at all events1 positions which produced the same impressions on the eye1 and that it passed from one of these to another insensibly1 and without any apparent breach of continuity2 thus much the senses1 with the aid of the proper instruments1 could ascertain4 ,what ,kepler did more than this1 was to find what sort of a curve these different points would make1 supposing them to be all joined together4 ,he expressed the whole series of the observed places of ,mars by what ,dr4 ,whewell calls the general conception of an ellipse4 ,this operation was far from being as easy as that of the navigator who expressed the series of his observations on successive points of the coast by the general conception of an island4 ,but it is the very same sort of operation2 and if the one is not an induction but a description1 this must also be true of the other4 ,the only real induction concerned in the case1 consisted in inferring that because the observed places of ,mars were correctly represented by points in an imaginary ellipse1 therefore ,mars would continue to revolve in that same ellipse2 and in concluding 7before the gap had been filled up by further observations7 that the positions of the planet during the time which intervened between two observations1 must have coincided with the intermediate points of the curve4 ,for these were facts which had not been directly observed4 ,they were inferences from the observations2 facts inferred1 as distinguished from facts seen4 ,but these inferences were so far from being a part of ,kepler's philosophical operation1 that they had been drawn long before he was born4 ,astronomers had long known that the planets periodically returned to the same places4 ,when this had been ascertained1 there was no induction left for ,kepler to make1 nor did he make any further induction4 ,he merely applied his new conception to the facts inferred1 as he did to the facts observed4 ,knowing already that the planets continued to move in the same paths2 when he found that an ellipse correctly represented the past path1 he knew that it would represent the future path4 ,in finding a compendious expression for the one set of facts1 he found one for the other3 but he found the expression only1 not the inference2 nor did he 7which is the true test of a general truth7 add any thing to the power of prediction already possessed4 #d4 ,the descriptive operation which enables a number of details to be summed up in a single proposition1 ,dr4 ,whewell1 by an aptly chosen expression1 has termed the ,colligation of ,facts4 ,in most of his observations concerning that mental process ,i fully agree1 and would gladly transfer all that portion of his book into my own pages4 ,i only think him mistaken in setting up this kind of operation1 which according to the old and received meaning of the term1 is not induction at all1 as the type of induction generally2 and laying down1 throughout his work1 as principles of induction1 the principles of mere colligation4 ,dr4 ,whewell maintains that the general proposition which binds together the particular facts1 and makes them1 as it were1 one fact1 is not the mere sum of those facts1 but something more1 since there is introduced a conception of the mind1 which did not exist in the facts themselves4 8,the particular facts10 says he17#ajb7 8are not merely brought together1 but there is a new element added to the combination by the very act of thought by which they are combined4444 ,when the ,greeks1 after long observing the motions of the planets1 saw that these motions might be rightly considered as produced by the motion of one wheel revolving in the inside of another wheel1 these wheels were creations of their minds1 added to the facts which they perceived by sense4 ,and even if the wheels were no longer supposed to be material1 but were reduced to mere geometrical spheres or circles1 they were not the less products of the mind alone--something additional to the facts observed4 ,the same is the case in all other discoveries4 ,the facts are known1 but they are insulated and unconnected1 till the discoverer supplies from his own store a principle of connection4 ,the pearls are there1 but they will not hang together till some one provides the string40 ,let me first remark that ,dr4 ,whewell1 in this passage1 blends together1 indiscriminately1 examples of both the processes which ,i am endeavoring to distinguish from one another4 ,when the ,greeks abandoned the supposition that the planetary motions were produced by the revolution of material wheels1 and fell back upon the idea of 8mere geometrical spheres or circles10 there was more in this change of opinion than the mere substitution of an ideal curve for a physical one4 ,there was the abandonment of a theory1 and the replacement of it by a mere description4 ,no one would think of calling the doctrine of material wheels a mere description4 ,that doctrine was an attempt to point out the force by which the planets were acted upon1 and compelled to move in their orbits4 ,but when1 by a great step in philosophy1 the materiality of the wheels was discarded1 and the geometrical forms alone retained1 the attempt to account for the motions was given up1 and what was left of the theory was a mere description of the orbits4 ,the assertion that the planets were carried round by wheels revolving in the inside of other wheels1 gave place to the proposition1 that they moved in the same lines which would be traced by bodies so carried3 which was a mere mode of representing the sum of the observed facts2 as ,kepler's was another and a better mode of representing the same observations4 ,it is true that for these simply descriptive operations1 as well as for the erroneous inductive one1 a conception of the mind was required4 ,the conception of an ellipse must have presented itself to ,kepler's mind1 before he could identify the planetary orbits with it4 ,according to ,dr4 ,whewell1 the conception was something added to the facts4 ,he expresses himself as if ,kepler had put something into the facts by his mode of conceiving them4 ,but ,kepler did no such thing4 ,the ellipse was in the facts before ,kepler recognized it2 just as the island was an island before it had been sailed round4 ,kepler did not put what he had conceived into the facts1 but saw it in them4 ,a conception implies1 and corresponds to1 something conceived3 and though the conception itself is not in the facts1 but in our mind1 yet if it is to convey any knowledge relating to them1 it must be a conception of something which really is in the facts1 some property which they actually possess1 and which they would manifest to our senses1 if our senses were able to take cognizance of it4 ,if1 for instance1 the planet left behind it in space a visible track1 and if the observer were in a fixed position at such a distance from the plane of the orbit as would enable him to see the whole of it at once1 he would see it to be an ellipse2 and if gifted with appropriate instruments and powers of locomotion1 he could prove it to be such by measuring its different dimensions4 ,nay1 further3 if the track were visible1 and he were so placed that he could see all parts of it in succession1 but not all of them at once1 he might be able1 by piecing together his successive observations1 to discover both that it was an ellipse and that the planet moved in it4 ,the case would then exactly resemble that of the navigator who discovers the land to be an island by sailing round it4 ,if the path was visible1 no one ,i think would dispute that to identify it with an ellipse is to describe it3 and ,i can not see why any difference should be made by its not being directly an object of sense1 when every point in it is as exactly ascertained as if it were so4 ,subject to the indispensable condition which has just been stated1 ,i do not conceive that the part which conceptions have in the operation of studying facts1 has ever been overlooked or undervalued4 ,no one ever disputed that in order to reason about any thing we must have a conception of it2 or that when we include a multitude of things under a general expression1 there is implied in the expression a conception of something common to those things4 ,but it by no means follows that the conception is necessarily pre-existent1 or constructed by the mind out of its own materials4 ,if the facts are rightly classed under the conception1 it is because there is in the facts themselves something of which the conception is itself a copy2 and which if we can not directly perceive1 it is because of the limited power of our organs1 and not because the thing itself is not there4 ,the conception itself is often obtained by abstraction from the very facts which1 in ,dr4 ,whewell's language1 it is afterward called in to connect4 ,this he himself admits1 when he observes 7which he does on several occasions71 how great a service would be rendered to the science of physiology by the philosopher 8who should establish a precise1 tenable1 and consistent conception of life407#ajc7 ,such a conception can only be abstracted from the phenomena of life itself2 from the very facts which it is put in requisition to connect4 ,in other cases1 no doubt1 instead of collecting the conception from the very phenomena which we are attempting to colligate1 we select it from among those which have been previously collected by abstraction from other facts4 ,in the instance of ,kepler's laws1 the latter was the case4 ,the facts being out of the reach of being observed1 in any such manner as would have enabled the senses to identify directly the path of the planet1 the conception requisite for framing a general description of that path could not be collected by abstraction from the observations themselves2 the mind had to supply hypothetically1 from among the conceptions it had obtained from other portions of its experience1 some one which would correctly represent the series of the observed facts4 ,it had to frame a supposition respecting the general course of the phenomenon1 and ask itself1 ,if this be the general description1 what will the details be8 and then compare these with the details actually observed4 ,if they agreed1 the hypothesis would serve for a description of the phenomenon3 if not1 it was necessarily abandoned1 and another tried4 ,it is such a case as this which gives rise to the doctrine that the mind1 in framing the descriptions1 adds something of its own which it does not find in the facts4 ,yet it is a fact surely1 that the planet does describe an ellipse2 and a fact which we could see1 if we had adequate visual organs and a suitable position4 ,not having these advantages1 but possessing the conception of an ellipse1 or 7to express the meaning in less technical language7 knowing what an ellipse was1 ,kepler tried whether the observed places of the planet were consistent with such a path4 ,he found they were so2 and he1 consequently1 asserted as a fact that the planet moved in an ellipse4 ,but this fact1 which ,kepler did not add to1 but found in1 the motions of the planet1 namely1 that it occupied in succession the various points in the circumference of a given ellipse1 was the very fact1 the separate parts of which had been separately observed2 it was the sum of the different observations4 ,having stated this fundamental difference between my opinion and that of ,dr4 ,whewell1 ,i must add1 that his account of the manner in which a conception is selected1 suitable to express the facts1 appears to me perfectly just4 ,the experience of all thinkers will1 ,i believe1 testify that the process is tentative2 that it consists of a succession of guesses2 many being rejected1 until one at last occurs fit to be chosen4 ,we know from ,kepler himself that before hitting upon the 8conception0 of an ellipse1 he tried nineteen other imaginary paths1 which1 finding them inconsistent with the observations1 he was obliged to reject4 ,but as ,dr4 ,whewell truly says1 the successful hypothesis1 though a guess1 ought generally to be called1 not a lucky1 but a skillful guess4 ,the guesses which serve to give mental unity and wholeness to a chaos of scattered particulars1 are accidents which rarely occur to any minds but those abounding in knowledge and disciplined in intellectual combinations4 ,how far this tentative method1 so indispensable as a means to the colligation of facts for purposes of description1 admits of application to ,induction itself1 and what functions belong to it in that department1 will be considered in the chapter of the present ,book which relates to ,hypotheses4 ,on the present occasion we have chiefly to distinguish this process of ,colligation from ,induction properly so called2 and that the distinction may be made clearer1 it is well to advert to a curious and interesting remark1 which is as strikingly true of the former operation1 as it appears to me unequivocally false of the latter4 ,in different stages of the progress of knowledge1 philosophers have employed1 for the colligation of the same order of facts1 different conceptions4 ,the early rude observations of the heavenly bodies1 in which minute precision was neither attained nor sought1 presented nothing inconsistent with the representation of the path of a planet as an exact circle1 having the earth for its centre4 ,as observations increased in accuracy1 facts were disclosed which were not reconcilable with this simple supposition3 for the colligation of those additional facts1 the supposition was varied2 and varied again and again as facts became more numerous and precise4 ,the earth was removed from the centre to some other point within the circle2 the planet was supposed to revolve in a smaller circle called an epicycle1 round an imaginary point which revolved in a circle round the earth3 in proportion as observation elicited fresh facts contradictory to these representations1 other epicycles and other eccentrics were added1 producing additional complication2 until at last ,kepler swept all these circles away1 and substituted the conception of an exact ellipse4 ,even this is found not to represent with complete correctness the accurate observations of the present day1 which disclose many slight deviations from an orbit exactly elliptical4 ,now ,dr4 ,whewell has remarked that these successive general expressions1 though apparently so conflicting1 were all correct3 they all answered the purpose of colligation2 they all enabled the mind to represent to itself with facility1 and by a simultaneous glance1 the whole body of facts at the time ascertained3 each in its turn served as a correct description of the phenomena1 so far as the senses had up to that time taken cognizance of them4 ,if a necessity afterward arose for discarding one of these general descriptions of the planet's orbit1 and framing a different imaginary line1 by which to express the series of observed positions1 it was because a number of new facts had now been added1 which it was necessary to combine with the old facts into one general description4 ,but this did not affect the correctness of the former expression1 considered as a general statement of the only facts which it was intended to represent4 ,and so true is this1 that1 as is well remarked by ,m4 ,comte1 these ancient generalizations1 even the rudest and most imperfect of them1 that of uniform movement in a circle1 are so far from being entirely false1 that they are even now habitually employed by astronomers when only a rough approximation to correctness is required4 8,l'astronomie moderne1 en dtruisant sans retour les hypothses primitives1 envisages comme lois relles du monde1 a soigneusement maintenu leur valeur positive et permanente1 la proprit de reprsenter commodment les phnomnes quand il s'agit d'une premire bauche4 ,nos ressources cet gard sont mme bien plus tendues1 prcisment cause que nous ne nous faisons aucune illusion sur la ralit des hypothses2 ce qui nous permet d'employer sans scrupule1 en chaque cas1 celle que nous jugeons la plus avantageuse407#ajd7 ,dr4 ,whewell's remark1 therefore1 is philosophically correct4 ,successive expressions for the colligation of observed facts1 or1 in other words1 successive descriptions of a phenomenon as a whole1 which has been observed only in parts1 may1 though conflicting1 be all correct as far as they go4 ,but it would surely be absurd to assert this of conflicting inductions4 ,the scientific study of facts may be undertaken for three different purposes3 the simple description of the facts2 their explanation2 or their prediction3 meaning by prediction1 the determination of the conditions under which similar facts may be expected again to occur4 ,to the first of these three operations the name of ,induction does not properly belong3 to the other two it does4 ,now1 ,dr4 ,whewell's observation is true of the first alone4 ,considered as a mere description1 the circular theory of the heavenly motions represents perfectly well their general features3 and by adding epicycles without limit1 those motions1 even as now known to us1 might be expressed with any degree of accuracy that might be required4 ,the elliptical theory1 as a mere description1 would have a great advantage in point of simplicity1 and in the consequent facility of conceiving it and reasoning about it2 but it would not really be more true than the other4 ,different descriptions1 therefore1 may be all true3 but not1 surely1 different explanations4 ,the doctrine that the heavenly bodies moved by a virtue inherent in their celestial nature2 the doctrine that they were moved by impact 7which led to the hypothesis of vortices as the only impelling force capable of whirling bodies in circles71 and the ,newtonian doctrine1 that they are moved by the composition of a centripetal with an original projectile force2 all these are explanations1 collected by real induction from supposed parallel cases2 and they were all successively received by philosophers1 as scientific truths on the subject of the heavenly bodies4 ,can it be said of these1 as was said of the different descriptions1 that they are all true as far as they go8 ,is it not clear that only one can be true in any degree1 and the other two must be altogether false8 ,so much for explanations3 let us now compare different predictions3 the first1 that eclipses will occur when one planet or satellite is so situated as to cast its shadow upon another2 the second1 that they will occur when some great calamity is impending over mankind4 ,do these two doctrines only differ in the degree of their truth1 as expressing real facts with unequal degrees of accuracy8 ,assuredly the one is true1 and the other absolutely false47#aje7 ,in every way1 therefore1 it is evident that to explain induction as the colligation of facts by means of appropriate conceptions1 that is1 conceptions which will really express them1 is to confound mere description of the observed facts with inference from those facts1 and ascribe to the latter what is a characteristic property of the former4 ,there is1 however1 between ,colligation and ,induction1 a real correlation1 which it is important to conceive correctly4 ,colligation is not always induction2 but induction is always colligation4 ,the assertion that the planets move in ellipses1 was but a mode of representing observed facts2 it was but a colligation2 while the assertion that they are drawn1 or tend1 toward the sun1 was the statement of a new fact1 inferred by induction4 ,but the induction1 once made1 accomplishes the purposes of colligation likewise4 ,it brings the same facts1 which ,kepler had connected by his conception of an ellipse1 under the additional conception of bodies acted upon by a central force1 and serves1 therefore1 as a new bond of connection for those facts2 a new principle for their classification4 ,further1 the descriptions which are improperly confounded with induction1 are nevertheless a necessary preparation for induction2 no less necessary than correct observation of the facts themselves4 ,without the previous colligation of detached observations by means of one general conception1 we could never have obtained any basis for an induction1 except in the case of phenomena of very limited compass4 ,we should not be able to affirm any predicates at all1 of a subject incapable of being observed otherwise than piecemeal3 much less could we extend those predicates by induction to other similar subjects4 ,induction1 therefore1 always presupposes1 not only that the necessary observations are made with the necessary accuracy1 but also that the results of these observations are1 so far as practicable1 connected together by general descriptions1 enabling the mind to represent to itself as wholes whatever phenomena are capable of being so represented4 #e4 ,dr4 ,whewell has replied at some length to the preceding observations1 restating his opinions1 but without 7as far as ,i can perceive7 adding any thing material to his former arguments4 ,since1 however1 mine have not had the good fortune to make any impression upon him1 ,i will subjoin a few remarks1 tending to show more clearly in what our difference of opinion consists1 as well as1 in some measure1 to account for it4 ,nearly all the definitions of induction1 by writers of authority1 make it consist in drawing inferences from known cases to unknown2 affirming of a class1 a predicate which has been found true of some cases belonging to the class2 concluding because some things have a certain property1 that other things which resemble them have the same property--or because a thing has manifested a property at a certain time1 that it has and will have that property at other times4 ,it will scarcely be contended that ,kepler's operation was an ,induction in this sense of the term4 ,the statement1 that ,mars moves in an elliptical orbit1 was no generalization from individual cases to a class of cases4 ,neither was it an extension to all time1 of what had been found true at some particular time4 ,the whole amount of generalization which the case admitted of1 was already completed1 or might have been so4 ,long before the elliptic theory was thought of1 it had been ascertained that the planets returned periodically to the same apparent places2 the series of these places was1 or might have been1 completely determined1 and the apparent course of each planet marked out on the celestial globe in an uninterrupted line4 ,kepler did not extend an observed truth to other cases than those in which it had been observed3 he did not widen the subject of the proposition which expressed the observed facts4 ,the alteration he made was in the predicate4 ,instead of saying1 the successive places of ,mars are so and so1 he summed them up in the statement1 that the successive places of ,mars are points in an ellipse4 ,it is true1 this statement1 as ,dr4 ,whewell says1 was not the sum of the observations merely2 it was the sum of the observations seen under a new point of view47#ajf7 ,but it was not the sum of more than the observations1 as a real induction is4 ,it took in no cases but those which had been actually observed1 or which could have been inferred from the observations before the new point of view presented itself4 ,there was not that transition from known cases to unknown1 which constitutes ,induction in the original and acknowledged meaning of the term4 ,old definitions1 it is true1 can not prevail against new knowledge3 and if the ,keplerian operation1 as a logical process1 be really identical with what takes place in acknowledged induction1 the definition of induction ought to be so widened as to take it in2 since scientific language ought to adapt itself to the true relations which subsist between the things it is employed to designate4 ,here then it is that ,i am at issue with ,dr4 ,whewell4 ,he does think the operations identical4 ,he allows of no logical process in any case of induction1 other than what there was in ,kepler's case1 namely1 guessing until a guess is found which tallies with the facts2 and accordingly1 as we shall see hereafter1 he rejects all canons of induction1 because it is not by means of them that we guess4 ,dr4 ,whewell's theory of the logic of science would be very perfect if it did not pass over altogether the question of ,proof4 ,but in my apprehension there is such a thing as proof1 and inductions differ altogether from descriptions in their relation to that element4 ,induction is proof2 it is inferring something unobserved from something observed3 it requires1 therefore1 an appropriate test of proof2 and to provide that test1 is the special purpose of inductive logic4 ,when1 on the contrary1 we merely collate known observations1 and1 in ,dr4 ,whewell's phraseology1 connect them by means of a new conception2 if the conception does serve to connect the observations1 we have all we want4 ,as the proposition in which it is embodied pretends to no other truth than what it may share with many other modes of representing the same facts1 to be consistent with the facts is all it requires3 it neither needs nor admits of proof2 though it may serve to prove other things1 inasmuch as1 by placing the facts in mental connection with other facts1 not previously seen to resemble them1 it assimilates the case to another class of phenomena1 concerning which real ,inductions have already been made4 ,thus ,kepler's so-called law brought the orbit of ,mars into the class ellipse1 and by doing so1 proved all the properties of an ellipse to be true of the orbit3 but in this proof ,kepler's law supplied the minor premise1 and not 7as is the case with real ,inductions7 the major4 ,dr4 ,whewell calls nothing ,induction where there is not a new mental conception introduced1 and every thing induction where there is4 ,but this is to confound two very different things1 ,invention and ,proof4 ,the introduction of a new conception belongs to ,invention3 and invention may be required in any operation1 but is the essence of none4 ,a new conception may be introduced for descriptive purposes1 and so it may for inductive purposes4 ,but it is so far from constituting induction1 that induction does not necessarily stand in need of it4 ,most inductions require no conception but what was present in every one of the particular instances on which the induction is grounded4 ,that all men are mortal is surely an inductive conclusion2 yet no new conception is introduced by it4 ,whoever knows that any man has died1 has all the conceptions involved in the inductive generalization4 ,but ,dr4 ,whewell considers the process of invention which consists in framing a new conception consistent with the facts1 to be not merely a necessary part of all induction1 but the whole of it4 ,the mental operation which extracts from a number of detached observations certain general characters in which the observed phenomena resemble one another1 or resemble other known facts1 is what ,bacon1 ,locke1 and most subsequent metaphysicians1 have understood by the word ,abstraction4 ,a general expression obtained by abstraction1 connecting known facts by means of common characters1 but without concluding from them to unknown1 may1 ,i think1 with strict logical correctness1 be termed a ,description2 nor do ,i know in what other way things can ever be described4 ,my position1 however1 does not depend on the employment of that particular word2 ,i am quite content to use ,dr4 ,whewell's term ,colligation1 or the more general phrases1 8mode of representing1 or of expressing1 phenomena30 provided it be clearly seen that the process is not ,induction1 but something radically different4 ,what more may usefully be said on the subject of ,colligation1 or of the correlative expression invented by ,dr4 ,whewell1 the ,explication of ,conceptions1 and generally on the subject of ideas and mental representations as connected with the study of facts1 will find a more appropriate place in the ,fourth ,book1 on the ,operations ,subsidiary to ,induction3 to which ,i must refer the reader for the removal of any difficulty which the present discussion may have left4 ,chapter ,,iii4 ,of ,the ,ground ,of ,induction4 #a4 ,induction properly so called1 as distinguished from those mental operations1 sometimes1 though improperly1 designated by the name1 which ,i have attempted in the preceding chapter to characterize1 may1 then1 be summarily defined as ,generalization from ,experience4 ,it consists in inferring from some individual instances in which a phenomenon is observed to occur1 that it occurs in all instances of a certain class2 namely1 in all which resemble the former1 in what are regarded as the material circumstances4 ,in what way the material circumstances are to be distinguished from those which are immaterial1 or why some of the circumstances are material and others not so1 we are not yet ready to point out4 ,we must first observe1 that there is a principle implied in the very statement of what ,induction is2 an assumption with regard to the course of nature and the order of the universe2 namely1 that there are such things in nature as parallel cases2 that what happens once1 will1 under a sufficient degree of similarity of circumstances1 happen again1 and not only again1 but as often as the same circumstances recur4 ,this1 ,i say1 is an assumption1 involved in every case of induction4 ,and1 if we consult the actual course of nature1 we find that the assumption is warranted4 ,the universe1 so far as known to us1 is so constituted1 that whatever is true in any one case1 is true in all cases of a certain description2 the only difficulty is1 to find what description4 ,this universal fact1 which is our warrant for all inferences from experience1 has been described by different philosophers in different forms of language3 that the course of nature is uniform2 that the universe is governed by general laws2 and the like4 ,one of the most usual of these modes of expression1 but also one of the most inadequate1 is that which has been brought into familiar use by the metaphysicians of the school of ,reid and ,stewart4 ,the disposition of the human mind to generalize from experience--a propensity considered by these philosophers as an instinct of our nature--they usually describe under some such name as 8our intuitive conviction that the future will resemble the past40 ,now it has been well pointed out by ,mr4 ,bailey17#ajg7 that 7whether the tendency be or not an original and ultimate element of our nature71 ,time1 in its modifications of past1 present1 and future1 has no concern either with the belief itself1 or with the grounds of it4 ,we believe that fire will burn to-morrow1 because it burned to-day and yesterday2 but we believe1 on precisely the same grounds1 that it burned before we were born1 and that it burns this very day in ,cochin-,china4 ,it is not from the past to the future1 as past and future1 that we infer1 but from the known to the unknown2 from facts observed to facts unobserved2 from what we have perceived1 or been directly conscious of1 to what has not come within our experience4 ,in this last predicament is the whole region of the future2 but also the vastly greater portion of the present and of the past4 ,whatever be the most proper mode of expressing it1 the proposition that the course of nature is uniform1 is the fundamental principle1 or general axiom of ,induction4 ,it would yet be a great error to offer this large generalization as any explanation of the inductive process4 ,on the contrary1 ,i hold it to be itself an instance of induction1 and induction by no means of the most obvious kind4 ,far from being the first induction we make1 it is one of the last1 or at all events one of those which are latest in attaining strict philosophical accuracy4 ,as a general maxim1 indeed1 it has scarcely entered into the minds of any but philosophers2 nor even by them1 as we shall have many opportunities of remarking1 have its extent and limits been always very justly conceived4 ,the truth is1 that this great generalization is itself founded on prior generalizations4 ,the obscurer laws of nature were discovered by means of it1 but the more obvious ones must have been understood and assented to as general truths before it was ever heard of4 ,we should never have thought of affirming that all phenomena take place according to general laws1 if we had not first arrived1 in the case of a great multitude of phenomena1 at some knowledge of the laws themselves2 which could be done no otherwise than by induction4 ,in what sense1 then1 can a principle1 which is so far from being our earliest induction1 be regarded as our warrant for all the others8 ,in the only sense1 in which 7as we have already seen7 the general propositions which we place at the head of our reasonings when we throw them into syllogisms1 ever really contribute to their validity4 ,as ,archbishop ,whately remarks1 every induction is a syllogism with the major premise suppressed2 or 7as ,i prefer expressing it7 every induction may be thrown into the form of a syllogism1 by supplying a major premise4 ,if this be actually done1 the principle which we are now considering1 that of the uniformity of the course of nature1 will appear as the ultimate major premise of all inductions1 and will1 therefore1 stand to all inductions in the relation in which1 as has been shown at so much length1 the major proposition of a syllogism always stands to the conclusion2 not contributing at all to prove it1 but being a necessary condition of its being proved2 since no conclusion is proved1 for which there can not be found a true major premise47#ajh7 ,the statement1 that the uniformity of the course of nature is the ultimate major premise in all cases of induction1 may be thought to require some explanation4 ,the immediate major premise in every inductive argument1 it certainly is not4 ,of that1 ,archbishop ,whately's must be held to be the correct account4 ,the induction1 8,john1 ,peter1 etc41 are mortal1 therefore all mankind are mortal10 may1 as he justly says1 be thrown into a syllogism by prefixing as a major premise 7what is at any rate a necessary condition of the validity of the argument71 namely1 that what is true of ,john1 ,peter1 etc41 is true of all mankind4 ,but how came we by this major premise8 ,it is not self-evident2 nay1 in all cases of unwarranted generalization1 it is not true4 ,how1 then1 is it arrived at8 ,necessarily either by induction or ratiocination2 and if by induction1 the process1 like all other inductive arguments1 may be thrown into the form of a syllogism4 ,this previous syllogism it is1 therefore1 necessary to construct4 ,there is1 in the long run1 only one possible construction4 ,the real proof that what is true of ,john1 ,peter1 etc41 is true of all mankind1 can only be1 that a different supposition would be inconsistent with the uniformity which we know to exist in the course of nature4 ,whether there would be this inconsistency or not1 may be a matter of long and delicate inquiry2 but unless there would1 we have no sufficient ground for the major of the inductive syllogism4 ,it hence appears1 that if we throw the whole course of any inductive argument into a series of syllogisms1 we shall arrive by more or fewer steps at an ultimate syllogism1 which will have for its major premise the principle1 or axiom1 of the uniformity of the course of nature47#aji7 ,it was not to be expected that in the case of this axiom1 any more than of other axioms1 there should be unanimity among thinkers with respect to the grounds on which it is to be received as true4 ,i have already stated that ,i regard it as itself a generalization from experience4 ,others hold it to be a principle which1 antecedently to any verification by experience1 we are compelled by the constitution of our thinking faculty to assume as true4 ,having so recently1 and at so much length1 combated a similar doctrine as applied to the axioms of mathematics1 by arguments which are in a great measure applicable to the present case1 ,i shall defer the more particular discussion of this controverted point in regard to the fundamental axiom of induction1 until a more advanced period of our inquiry47#aaj7 ,at present it is of more importance to understand thoroughly the import of the axiom itself4 ,for the proposition1 that the course of nature is uniform1 possesses rather the brevity suitable to popular1 than the precision requisite in philosophical language3 its terms require to be explained1 and a stricter than their ordinary signification given to them1 before the truth of the assertion can be admitted4 #b4 ,every person's consciousness assures him that he does not always expect uniformity in the course of events2 he does not always believe that the unknown will be similar to the known1 that the future will resemble the past4 ,nobody believes that the succession of rain and fine weather will be the same in every future year as in the present4 ,nobody expects to have the same dreams repeated every night4 ,on the contrary1 every body mentions it as something extraordinary1 if the course of nature is constant1 and resembles itself1 in these particulars4 ,to look for constancy where constancy is not to be expected1 as for instance that a day which has once brought good fortune will always be a fortunate day1 is justly accounted superstition4 ,the course of nature1 in truth1 is not only uniform1 it is also infinitely various4 ,some phenomena are always seen to recur in the very same combinations in which we met with them at first2 others seem altogether capricious2 while some1 which we had been accustomed to regard as bound down exclusively to a particular set of combinations1 we unexpectedly find detached from some of the elements with which we had hitherto found them conjoined1 and united to others of quite a contrary description4 ,to an inhabitant of ,central ,africa1 fifty years ago1 no fact probably appeared to rest on more uniform experience than this1 that all human beings are black4 ,to ,europeans1 not many years ago1 the proposition1 ,all swans are white1 appeared an equally unequivocal instance of uniformity in the course of nature4 ,further experience has proved to both that they were mistaken2 but they had to wait fifty centuries for this experience4 ,during that long time1 mankind believed in a uniformity of the course of nature where no such uniformity really existed4 ,according to the notion which the ancients entertained of induction1 the foregoing were cases of as legitimate inference as any inductions whatever4 ,in these two instances1 in which1 the conclusion being false1 the ground of inference must have been insufficient1 there was1 nevertheless1 as much ground for it as this conception of induction admitted of4 ,the induction of the ancients has been well described by ,bacon1 under the name of 8,inductio per enumerationem simplicem1 ubi non reperitur instantia contradictoria40 ,it consists in ascribing the character of general truths to all propositions which are true in every instance that we happen to know of4 ,this is the kind of induction which is natural to the mind when unaccustomed to scientific methods4 ,the tendency1 which some call an instinct1 and which others account for by association1 to infer the future from the past1 the known from the unknown1 is simply a habit of expecting that what has been found true once or several times1 and never yet found false1 will be found true again4 ,whether the instances are few or many1 conclusive or inconclusive1 does not much affect the matter3 these are considerations which occur only on reflection2 the unprompted tendency of the mind is to generalize its experience1 provided this points all in one direction2 provided no other experience of a conflicting character comes unsought4 ,the notion of seeking it1 of experimenting for it1 of interrogating nature 7to use ,bacon's expression7 is of much later growth4 ,the observation of nature1 by uncultivated intellects1 is purely passive3 they accept the facts which present themselves1 without taking the trouble of searching for more3 it is a superior mind only which asks itself what facts are needed to enable it to come to a safe conclusion1 and then looks out for these4 ,but though we have always a propensity to generalize from unvarying experience1 we are not always warranted in doing so4 ,before we can be at liberty to conclude that something is universally true because we have never known an instance to the contrary1 we must have reason to believe that if there were in nature any instances to the contrary1 we should have known of them4 ,this assurance1 in the great majority of cases1 we can not have1 or can have only in a very moderate degree4 ,the possibility of having it1 is the foundation on which we shall see hereafter that induction by simple enumeration may in some remarkable cases amount practically to proof47#aaa7 ,no such assurance1 however1 can be had1 on any of the ordinary subjects of scientific inquiry4 ,popular notions are usually founded on induction by simple enumeration2 in science it carries us but a little way4 ,we are forced to begin with it2 we must often rely on it provisionally1 in the absence of means of more searching investigation4 ,but1 for the accurate study of nature1 we require a surer and a more potent instrument4 ,it was1 above all1 by pointing out the insufficiency of this rude and loose conception of ,induction1 that ,bacon merited the title so generally awarded to him1 of ,founder of the ,inductive ,philosophy4 ,the value of his own contributions to a more philosophical theory of the subject has certainly been exaggerated4 ,although 7along with some fundamental errors7 his writings contain1 more or less fully developed1 several of the most important principles of the ,inductive ,method1 physical investigation has now far outgrown the ,baconian conception of ,induction4 ,moral and political inquiry1 indeed1 are as yet far behind that conception4 ,the current and approved modes of reasoning on these subjects are still of the same vicious description against which ,bacon protested2 the method almost exclusively employed by those professing to treat such matters inductively1 is the very inductio per enumerationem simplicem which he condemns2 and the experience which we hear so confidently appealed to by all sects1 parties1 and interests1 is still1 in his own emphatic words1 mera palpatio4 #c4 ,in order to a better understanding of the problem which the logician must solve if he would establish a scientific theory of ,induction1 let us compare a few cases of incorrect inductions with others which are acknowledged to be legitimate4 ,some1 we know1 which were believed for centuries to be correct1 were nevertheless incorrect4 ,that all swans are white1 can not have been a good induction1 since the conclusion has turned out erroneous4 ,the experience1 however1 on which the conclusion rested1 was genuine4 ,from the earliest records1 the testimony of the inhabitants of the known world was unanimous on the point4 ,the uniform experience1 therefore1 of the inhabitants of the known world1 agreeing in a common result1 without one known instance of deviation from that result1 is not always sufficient to establish a general conclusion4 ,but let us now turn to an instance apparently not very dissimilar to this4 ,mankind were wrong1 it seems1 in concluding that all swans were white3 are we also wrong1 when we conclude that all men's heads grow above their shoulders1 and never below1 in spite of the conflicting testimony of the naturalist ,pliny8 ,as there were black swans1 though civilized people had existed for three thousand years on the earth without meeting with them1 may there not also be 8men whose heads do grow beneath their shoulders10 notwithstanding a rather less perfect unanimity of negative testimony from observers8 ,most persons would answer ,no2 it was more credible that a bird should vary in its color1 than that men should vary in the relative position of their principal organs4 ,and there is no doubt that in so saying they would be right3 but to say why they are right1 would be impossible1 without entering more deeply than is usually done1 into the true theory of ,induction4 ,again1 there are cases in which we reckon with the most unfailing confidence upon uniformity1 and other cases in which we do not count upon it at all4 ,in some we feel complete assurance that the future will resemble the past1 the unknown be precisely similar to the known4 ,in others1 however invariable may be the result obtained from the instances which have been observed1 we draw from them no more than a very feeble presumption that the like result will hold in all other cases4 ,that a straight line is the shortest distance between two points1 we do not doubt to be true even in the region of the fixed stars47#aab7 ,when a chemist announces the existence and properties of a newly-discovered substance1 if we confide in his accuracy1 we feel assured that the conclusions he has arrived at will hold universally1 though the induction be founded but on a single instance4 ,we do not withhold our assent1 waiting for a repetition of the experiment2 or if we do1 it is from a doubt whether the one experiment was properly made1 not whether if properly made it would be conclusive4 ,here1 then1 is a general law of nature1 inferred without hesitation from a single instance2 a universal proposition from a singular one4 ,now mark another case1 and contrast it with this4 ,not all the instances which have been observed since the beginning of the world1 in support of the general proposition that all crows are black1 would be deemed a sufficient presumption of the truth of the proposition1 to outweigh the testimony of one unexceptionable witness who should affirm that in some region of the earth not fully explored1 he had caught and examined a crow1 and had found it to be gray4 ,why is a single instance1 in some cases1 sufficient for a complete induction1 while in others1 myriads of concurring instances1 without a single exception known or presumed1 go such a very little way toward establishing a universal proposition8 ,whoever can answer this question knows more of the philosophy of logic than the wisest of the ancients1 and has solved the problem of induction4 ,chapter ,,iv4 ,of ,laws ,of ,nature4 #a4 ,in the contemplation of that uniformity in the course of nature1 which is assumed in every inference from experience1 one of the first observations that present themselves is1 that the uniformity in question is not properly uniformity1 but uniformities4 ,the general regularity results from the co-existence of partial regularities4 ,the course of nature in general is constant1 because the course of each of the various phenomena that compose it is so4 ,a certain fact invariably occurs whenever certain circumstances are present1 and does not occur when they are absent2 the like is true of another fact2 and so on4 ,from these separate threads of connection between parts of the great whole which we term nature1 a general tissue of connection unavoidably weaves itself1 by which the whole is held together4 ,if ,a is always accompanied by ,d1 ,b by ,e1 and ,c by ,f1 it follows that ,a ,b is accompanied by ,d ,e1 ,a ,c by ,d ,f1 ,b ,c by ,e ,f1 and finally ,a ,b ,c by ,d ,e ,f2 and thus the general character of regularity is produced1 which1 along with and in the midst of infinite diversity1 pervades all nature4 ,the first point1 therefore1 to be noted in regard to what is called the uniformity of the course of nature1 is1 that it is itself a complex fact1 compounded of all the separate uniformities which exist in respect to single phenomena4 ,these various uniformities1 when ascertained by what is regarded as a sufficient induction1 we call1 in common parlance1 ,laws of ,nature4 ,scientifically speaking1 that title is employed in a more restricted sense1 to designate the uniformities when reduced to their most simple expression4 ,thus in the illustration already employed1 there were seven uniformities2 all of which1 if considered sufficiently certain1 would1 in the more lax application of the term1 be called laws of nature4 ,but of the seven1 three alone are properly distinct and independent3 these being presupposed1 the others follow of course4 ,the first three1 therefore1 according to the stricter acceptation1 are called laws of nature2 the remainder not2 because they are in truth mere cases of the first three2 virtually included in them2 said1 therefore1 to result from them3 whoever affirms those three has already affirmed all the rest4 ,to substitute real examples for symbolical ones1 the following are three uniformities1 or call them laws of nature3 the law that air has weight1 the law that pressure on a fluid is propagated equally in all directions1 and the law that pressure in one direction1 not opposed by equal pressure in the contrary direction1 produces motion1 which does not cease until equilibrium is restored4 ,from these three uniformities we should be able to predict another uniformity1 namely1 the rise of the mercury in the ,torricellian tube4 ,this1 in the stricter use of the phrase1 is not a law of nature4 ,it is the result of laws of nature4 ,it is a case of each and every one of the three laws3 and is the only occurrence by which they could all be fulfilled4 ,if the mercury were not sustained in the barometer1 and sustained at such a height that the column of mercury were equal in weight to a column of the atmosphere of the same diameter2 here would be a case1 either of the air not pressing upon the surface of the mercury with the force which is called its weight1 or of the downward pressure on the mercury not being propagated equally in an upward direction1 or of a body pressed in one direction and not in the direction opposite1 either not moving in the direction in which it is pressed1 or stopping before it had attained equilibrium4 ,if we knew1 therefore1 the three simple laws1 but had never tried the ,torricellian experiment1 we might deduce its result from those laws4 ,the known weight of the air1 combined with the position of the apparatus1 would bring the mercury within the first of the three inductions2 the first induction would bring it within the second1 and the second within the third1 in the manner which we characterized in treating of ,ratiocination4 ,we should thus come to know the more complex uniformity1 independently of specific experience1 through our knowledge of the simpler ones from which it results2 though1 for reasons which will appear hereafter1 verification by specific experience would still be desirable1 and might possibly be indispensable4 ,complex uniformities which1 like this1 are mere cases of simpler ones1 and have1 therefore1 been virtually affirmed in affirming those1 may with propriety be called laws1 but can scarcely1 in the strictness of scientific speech1 be termed ,laws of ,nature4 ,it is the custom in science1 wherever regularity of any kind can be traced1 to call the general proposition which expresses the nature of that regularity1 a law2 as when1 in mathematics1 we speak of the law of decrease of the successive terms of a converging series4 ,but the expression law of nature has generally been employed with a sort of tacit reference to the original sense of the word law1 namely1 the expression of the will of a superior4 ,when1 therefore1 it appeared that any of the uniformities which were observed in nature1 would result spontaneously from certain other uniformities1 no separate act of creative will being supposed necessary for the production of the derivative uniformities1 these have not usually been spoken of as laws of nature4 ,according to one mode of expression1 the question1 ,what are the laws of nature8 may be stated thus3 ,what are the fewest and simplest assumptions1 which being granted1 the whole existing order of nature would result8 ,another mode of stating it would be thus3 ,what are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred8 ,every great advance which marks an epoch in the progress of science1 has consisted in a step made toward the solution of this problem4 ,even a simple colligation of inductions already made1 without any fresh extension of the inductive inference1 is already an advance in that direction4 ,when ,kepler expressed the regularity which exists in the observed motions of the heavenly bodies1 by the three general propositions called his laws1 he1 in so doing1 pointed out three simple suppositions which1 instead of a much greater number1 would suffice to construct the whole scheme of the heavenly motions1 so far as it was known up to that time4 ,a similar and still greater step was made when these laws1 which at first did not seem to be included in any more general truths1 were discovered to be cases of the three laws of motion1 as obtaining among bodies which mutually tend toward one another with a certain force1 and have had a certain instantaneous impulse originally impressed upon them4 ,after this great discovery1 ,kepler's three propositions1 though still called laws1 would hardly1 by any person accustomed to use language with precision1 be termed laws of nature3 that phrase would be reserved for the simpler and more general laws into which ,newton is said to have resolved them4 ,according to this language1 every well-grounded inductive generalization is either a law of nature1 or a result of laws of nature1 capable1 if those laws are known1 of being predicted from them4 ,and the problem of ,inductive ,logic may be summed up in two questions3 how to ascertain the laws of nature2 and how1 after having ascertained them1 to follow them into their results4 ,on the other hand1 we must not suffer ourselves to imagine that this mode of statement amounts to a real analysis1 or to any thing but a mere verbal transformation of the problem2 for the expression1 ,laws of ,nature1 means nothing but the uniformities which exist among natural phenomena 7or1 in other words1 the results of induction71 when reduced to their simplest expression4 ,it is1 however1 something to have advanced so far1 as to see that the study of nature is the study of laws1 not a law2 of uniformities1 in the plural number3 that the different natural phenomena have their separate rules or modes of taking place1 which1 though much intermixed and entangled with one another1 may1 to a certain extent1 be studied apart3 that 7to resume our former metaphor7 the regularity which exists in nature is a web composed of distinct threads1 and only to be understood by tracing each of the threads separately2 for which purpose it is often necessary to unravel some portion of the web1 and exhibit the fibres apart4 ,the rules of experimental inquiry are the contrivances for unraveling the web4 #b4 ,in thus attempting to ascertain the general order of nature by ascertaining the particular order of the occurrence of each one of the phenomena of nature1 the most scientific proceeding can be no more than an improved form of that which was primitively pursued by the human understanding1 while undirected by science4 ,when mankind first formed the idea of studying phenomena according to a stricter and surer method than that which they had in the first instance spontaneously adopted1 they did not1 conformably to the well-meant but impracticable precept of ,descartes1 set out from the supposition that nothing had been already ascertained4 ,many of the uniformities existing among phenomena are so constant1 and so open to observation1 as to force themselves upon involuntary recognition4 ,some facts are so perpetually and familiarly accompanied by certain others1 that mankind learned1 as children learn1 to expect the one where they found the other1 long before they knew how to put their expectation into words by asserting1 in a proposition1 the existence of a connection between those phenomena4 ,no science was needed to teach that food nourishes1 that water drowns1 or quenches thirst1 that the sun gives light and heat1 that bodies fall to the ground4 ,the first scientific inquirers assumed these and the like as known truths1 and set out from them to discover others which were unknown3 nor were they wrong in so doing1 subject1 however1 as they afterward began to see1 to an ulterior revision of these spontaneous generalizations themselves1 when the progress of knowledge pointed out limits to them1 or showed their truth to be contingent on some circumstance not originally attended to4 ,it will appear1 ,i think1 from the subsequent part of our inquiry1 that there is no logical fallacy in this mode of proceeding2 but we may see already that any other mode is rigorously impracticable3 since it is impossible to frame any scientific method of induction1 or test of the correctness of inductions1 unless on the hypothesis that some inductions deserving of reliance have been already made4 ,let us revert1 for instance1 to one of our former illustrations1 and consider why it is that1 with exactly the same amount of evidence1 both negative and positive1 we did not reject the assertion that there are black swans1 while we should refuse credence to any testimony which asserted that there were men wearing their heads underneath their shoulders4 ,the first assertion was more credible than the latter4 ,but why more credible8 ,so long as neither phenomenon had been actually witnessed1 what reason was there for finding the one harder to be believed than the other8 ,apparently because there is less constancy in the colors of animals1 than in the general structure of their anatomy4 ,but how do we know this8 ,doubtless1 from experience4 ,it appears1 then1 that we need experience to inform us1 in what degree1 and in what cases1 or sorts of cases1 experience is to be relied on4 ,experience must be consulted in order to learn from it under what circumstances arguments from it will be valid4 ,we have no ulterior test to which we subject experience in general2 but we make experience its own test4 ,experience testifies1 that among the uniformities which it exhibits or seems to exhibit1 some are more to be relied on than others2 and uniformity1 therefore1 may be presumed1 from any given number of instances1 with a greater degree of assurance1 in proportion as the case belongs to a class in which the uniformities have hitherto been found more uniform4 ,this mode of correcting one generalization by means of another1 a narrower generalization by a wider1 which common sense suggests and adopts in practice1 is the real type of scientific ,induction4 ,all that art can do is but to give accuracy and precision to this process1 and adapt it to all varieties of cases1 without any essential alteration in its principle4 ,there are of course no means of applying such a test as that above described1 unless we already possess a general knowledge of the prevalent character of the uniformities existing throughout nature4 ,the indispensable foundation1 therefore1 of a scientific formula of induction1 must be a survey of the inductions to which mankind have been conducted in unscientific practice2 with the special purpose of ascertaining what kinds of uniformities have been found perfectly invariable1 pervading all nature1 and what are those which have been found to vary with difference of time1 place1 or other changeable circumstances4 #c4 ,the necessity of such a survey is confirmed by the consideration1 that the stronger inductions are the touch-stone to which we always endeavor to bring the weaker4 ,if we find any means of deducing one of the less strong inductions from stronger ones1 it acquires1 at once1 all the strength of those from which it is deduced2 and even adds to that strength2 since the independent experience on which the weaker induction previously rested1 becomes additional evidence of the truth of the better established law in which it is now found to be included4 ,we may have inferred1 from historical evidence1 that the uncontrolled power of a monarch1 of an aristocracy1 or of the majority1 will often be abused3 but we are entitled to rely on this generalization with much greater assurance when it is shown to be a corollary from still better established facts2 the very low degree of elevation of character ever yet attained by the average of mankind1 and the little efficacy1 for the most part1 of the modes of education hitherto practiced1 in maintaining the predominance of reason and conscience over the selfish propensities4 ,it is at the same time obvious that even these more general facts derive an accession of evidence from the testimony which history bears to the effects of despotism4 ,the strong induction becomes still stronger when a weaker one has been bound up with it4 ,on the other hand1 if an induction conflicts with stronger inductions1 or with conclusions capable of being correctly deduced from them1 then1 unless on reconsideration it should appear that some of the stronger inductions have been expressed with greater universality than their evidence warrants1 the weaker one must give way4 ,the opinion so long prevalent that a comet1 or any other unusual appearance in the heavenly regions1 was the precursor of calamities to mankind1 or to those at least who witnessed it2 the belief in the veracity of the oracles of ,delphi or ,dodona2 the reliance on astrology1 or on the weather-prophecies in almanacs1 were doubtless inductions supposed to be grounded on experience37#aac7 and faith in such delusions seems quite capable of holding out against a great multitude of failures1 provided it be nourished by a reasonable number of casual coincidences between the prediction and the event4 ,what has really put an end to these insufficient inductions1 is their inconsistency with the stronger inductions subsequently obtained by scientific inquiry1 respecting the causes on which terrestrial events really depend2 and where those scientific truths have not yet penetrated1 the same or similar delusions still prevail4 ,it may be affirmed as a general principle1 that all inductions1 whether strong or weak1 which can be connected by ratiocination1 are confirmatory of one another2 while any which lead deductively to consequences that are incompatible1 become mutually each other's test1 showing that one or other must be given up1 or at least more guardedly expressed4 ,in the case of inductions which confirm each other1 the one which becomes a conclusion from ratiocination rises to at least the level of certainty of the weakest of those from which it is deduced2 while in general all are more or less increased in certainty4 ,thus the ,torricellian experiment1 though a mere case of three more general laws1 not only strengthened greatly the evidence on which those laws rested1 but converted one of them 7the weight of the atmosphere7 from a still doubtful generalization into a completely established doctrine4 ,if1 then1 a survey of the uniformities which have been ascertained to exist in nature1 should point out some which1 as far as any human purpose requires certainty1 may be considered quite certain and quite universal2 then by means of these uniformities we may be able to raise multitudes of other inductions to the same point in the scale4 ,for if we can show1 with respect to any inductive inference1 that either it must be true1 or one of these certain and universal inductions must admit of an exception2 the former generalization will attain the same certainty1 and indefeasibleness within the bounds assigned to it1 which are the attributes of the latter4 ,it will be proved to be a law2 and if not a result of other and simpler laws1 it will be a law of nature4 ,there are such certain and universal inductions2 and it is because there are such1 that a ,logic of ,induction is possible4 ,chapter ,v4 ,of ,the ,law ,of ,universal ,causation4 #a4 ,the phenomena of nature exist in two distinct relations to one another2 that of simultaneity1 and that of succession4 ,every phenomenon is related1 in a uniform manner1 to some phenomena that co-exist with it1 and to some that have preceded and will follow it4 ,of the uniformities which exist among synchronous phenomena1 the most important1 on every account1 are the laws of number2 and next to them those of space1 or1 in other words1 of extension and figure4 ,the laws of number are common to synchronous and successive phenomena4 ,that two and two make four1 is equally true whether the second two follow the first two or accompany them4 ,it is as true of days and years as of feet and inches4 ,the laws of extension and figure 7in other words1 the theorems of geometry1 from its lowest to its highest branches7 are1 on the contrary1 laws of simultaneous phenomena only4 ,the various parts of space1 and of the objects which are said to fill space1 co-exist2 and the unvarying laws which are the subject of the science of geometry1 are an expression of the mode of their co-existence4 ,this is a class of laws1 or in other words1 of uniformities1 for the comprehension and proof of which it is not necessary to suppose any lapse of time1 any variety of facts or events succeeding one another4 ,the propositions of geometry are independent of the succession of events4 ,all things which possess extension1 or1 in other words1 which fill space1 are subject to geometrical laws4 ,possessing extension1 they possess figure2 possessing figure1 they must possess some figure in particular1 and have all the properties which geometry assigns to that figure4 ,if one body be a sphere and another a cylinder1 of equal height and diameter1 the one will be exactly two-thirds of the other1 let the nature and quality of the material be what it will4 ,again1 each body1 and each point of a body1 must occupy some place or position among other bodies2 and the position of two bodies relatively to each other1 of whatever nature the bodies be1 may be unerringly inferred from the position of each of them relatively to any third body4 ,in the laws of number1 then1 and in those of space1 we recognize in the most unqualified manner1 the rigorous universality of which we are in quest4 ,those laws have been in all ages the type of certainty1 the standard of comparison for all inferior degrees of evidence4 ,their invariability is so perfect1 that it renders us unable even to conceive any exception to them2 and philosophers have been led1 though 7as ,i have endeavored to show7 erroneously1 to consider their evidence as lying not in experience1 but in the original constitution of the intellect4 ,if1 therefore1 from the laws of space and number1 we were able to deduce uniformities of any other description1 this would be conclusive evidence to us that those other uniformities possessed the same rigorous certainty4 ,but this we can not do4 ,from laws of space and number alone1 nothing can be deduced but laws of space and number4 ,of all truths relating to phenomena1 the most valuable to us are those which relate to the order of their succession4 ,on a knowledge of these is founded every reasonable anticipation of future facts1 and whatever power we possess of influencing those facts to our advantage4 ,even the laws of geometry are chiefly of practical importance to us as being a portion of the premises from which the order of the succession of phenomena may be inferred4 ,inasmuch as the motion of bodies1 the action of forces1 and the propagation of influences of all sorts1 take place in certain lines and over definite spaces1 the properties of those lines and spaces are an important part of the laws to which those phenomena are themselves subject4 ,again1 motions1 forces1 or other influences1 and times1 are numerable quantities2 and the properties of number are applicable to them as to all other things4 ,but though the laws of number and space are important elements in the ascertainment of uniformities of succession1 they can do nothing toward it when taken by themselves4 ,they can only be made instrumental to that purpose when we combine with them additional premises1 expressive of uniformities of succession already known4 ,by taking1 for instance1 as premises these propositions1 that bodies acted upon by an instantaneous force move with uniform velocity in straight lines2 that bodies acted upon by a continuous force move with accelerated velocity in straight lines2 and that bodies acted upon by two forces in different directions move in the diagonal of a parallelogram1 whose sides represent the direction and quantity of those forces2 we may by combining these truths with propositions relating to the properties of straight lines and of parallelograms 7as that a triangle is half a parallelogram of the same base and altitude71 deduce another important uniformity of succession1 viz41 that a body moving round a centre of force describes areas proportional to the times4 ,but unless there had been laws of succession in our premises1 there could have been no truths of succession in our conclusions4 ,a similar remark might be extended to every other class of phenomena really peculiar2 and1 had it been attended to1 would have prevented many chimerical attempts at demonstrations of the indemonstrable1 and explanations which do not explain4 ,it is not1 therefore1 enough for us that the laws of space1 which are only laws of simultaneous phenomenon1 and the laws of number1 which though true of successive phenomena do not relate to their succession1 possess the rigorous certainty and universality of which we are in search4 ,we must endeavor to find some law of succession which has those same attributes1 and is therefore fit to be made the foundation of processes for discovering1 and of a test for verifying1 all other uniformities of succession4 ,this fundamental law must resemble the truths of geometry in their most remarkable peculiarity1 that of never being1 in any instance whatever1 defeated or suspended by any change of circumstances4 ,now among all those uniformities in the succession of phenomena1 which common observation is sufficient to bring to light1 there are very few which have any1 even apparent1 pretension to this rigorous indefeasibility3 and of those few1 one only has been found capable of completely sustaining it4 ,in that one1 however1 we recognize a law which is universal also in another sense2 it is co-extensive with the entire field of successive phenomena1 all instances whatever of succession being examples of it4 ,this law is the ,law of ,causation4 ,the truth that every fact which has a beginning has a cause1 is co-extensive with human experience4 ,this generalization may appear to some minds not to amount to much1 since after all it asserts only this3 8it is a law1 that every event depends on some law30 8it is a law1 that there is a law for every thing40 ,we must not1 however1 conclude that the generality of the principle is merely verbal2 it will be found on inspection to be no vague or unmeaning assertion1 but a most important and really fundamental truth4 #b4 ,the notion of ,cause being the root of the whole theory of ,induction1 it is indispensable that this idea should1 at the very outset of our inquiry1 be1 with the utmost practicable degree of precision1 fixed and determined4 ,if1 indeed1 it were necessary for the purpose of inductive logic that the strife should be quelled1 which has so long raged among the different schools of metaphysicians1 respecting the origin and analysis of our idea of causation2 the promulgation1 or at least the general reception1 of a true theory of induction1 might be considered desperate for a long time to come4 ,but the science of the ,investigation of ,truth by means of ,evidence1 is happily independent of many of the controversies which perplex the science of the ultimate constitution of the human mind1 and is under no necessity of pushing the analysis of mental phenomenon to that extreme limit which alone ought to satisfy a metaphysician4 ,i premise1 then1 that when in the course of this inquiry ,i speak of the cause of any phenomenon1 ,i do not mean a cause which is not itself a phenomenon2 ,i make no research into the ultimate or ontological cause of any thing4 ,to adopt a distinction familiar in the writings of the ,scotch metaphysicians1 and especially of ,reid1 the causes with which ,i concern myself are not efficient1 but physical causes4 ,they are causes in that sense alone1 in which one physical fact is said to be the cause of another4 ,of the efficient causes of phenomena1 or whether any such causes exist at all1 ,i am not called upon to give an opinion4 ,the notion of causation is deemed1 by the schools of metaphysics most in vogue at the present moment1 to imply a mysterious and most powerful tie1 such as can not1 or at least does not1 exist between any physical fact and that other physical fact on which it is invariably consequent1 and which is popularly termed its cause3 and thence is deduced the supposed necessity of ascending higher1 into the essences and inherent constitution of things1 to find the true cause1 the cause which is not only followed by1 but actually produces1 the effect4 ,no such necessity exists for the purposes of the present inquiry1 nor will any such doctrine be found in the following pages4 ,the only notion of a cause1 which the theory of induction requires1 is such a notion as can be gained from experience4 ,the ,law of ,causation1 the recognition of which is the main pillar of inductive science1 is but the familiar truth1 that invariability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it2 independently of all considerations respecting the ultimate mode of production of phenomena1 and of every other question regarding the nature of 8,things in themselves40 ,between the phenomena1 then1 which exist at any instant1 and the phenomena which exist at the succeeding instant1 there is an invariable order of succession2 and1 as we said in speaking of the general uniformity of the course of nature1 this web is composed of separate fibres2 this collective order is made up of particular sequences1 obtaining invariably among the separate parts4 ,to certain facts1 certain facts always do1 and1 as we believe1 will continue to1 succeed4 ,the invariable antecedent is termed the cause2 the invariable consequent1 the effect4 ,and the universality of the law of causation consists in this1 that every consequent is connected in this manner with some particular antecedent1 or set of antecedents4 ,let the fact be what it may1 if it has begun to exist1 it was preceded by some fact or facts1 with which it is invariably connected4 ,for every event there exists some combination of objects or events1 some given concurrence of circumstances1 positive and negative1 the occurrence of which is always followed by that phenomenon4 ,we may not have found out what this concurrence of circumstances may be2 but we never doubt that there is such a one1 and that it never occurs without having the phenomenon in question as its effect or consequence4 ,on the universality of this truth depends the possibility of reducing the inductive process to rules4 ,the undoubted assurance we have that there is a law to be found if we only knew how to find it1 will be seen presently to be the source from which the canons of the ,inductive ,logic derive their validity4 #c4 ,it is seldom1 if ever1 between a consequent and a single antecedent1 that this invariable sequence subsists4 ,it is usually between a consequent and the sum of several antecedents2 the concurrence of all of them being requisite to produce1 that is1 to be certain of being followed by1 the consequent4 ,in such cases it is very common to single out one only of the antecedents under the denomination of ,cause1 calling the others merely ,conditions4 ,thus1 if a person eats of a particular dish1 and dies in consequence1 that is1 would not have died if he had not eaten of it1 people would be apt to say that eating of that dish was the cause of his death4 ,there needs not1 however1 be any invariable connection between eating of the dish and death2 but there certainly is1 among the circumstances which took place1 some combination or other on which death is invariably consequent3 as1 for instance1 the act of eating of the dish1 combined with a particular bodily constitution1 a particular state of present health1 and perhaps even a certain state of the atmosphere2 the whole of which circumstances perhaps constituted in this particular case the conditions of the phenomenon1 or1 in other words1 the set of antecedents which determined it1 and but for which it would not have happened4 ,the real ,cause1 is the whole of these antecedents2 and we have1 philosophically speaking1 no right to give the name of cause to one of them1 exclusively of the others4 ,what1 in the case we have supposed1 disguises the incorrectness of the expression1 is this3 that the various conditions1 except the single one of eating the food1 were not events 7that is1 instantaneous changes1 or successions of instantaneous changes7 but states1 possessing more or less of permanency2 and might therefore have preceded the effect by an indefinite length of duration1 for want of the event which was requisite to complete the required concurrence of conditions3 while as soon as that event1 eating the food1 occurs1 no other cause is waited for1 but the effect begins immediately to take place3 and hence the appearance is presented of a more immediate and close connection between the effect and that one antecedent1 than between the effect and the remaining conditions4 ,but though we may think proper to give the name of cause to that one condition1 the fulfillment of which completes the tale1 and brings about the effect without further delay2 this condition has really no closer relation to the effect than any of the other conditions has4 ,all the conditions were equally indispensable to the production of the consequent2 and the statement of the cause is incomplete1 unless in some shape or other we introduce them all4 ,a man takes mercury1 goes out-of-doors1 and catches cold4 ,we say1 perhaps1 that the cause of his taking cold was exposure to the air4 ,it is clear1 however1 that his having taken mercury may have been a necessary condition of his catching cold2 and though it might consist with usage to say that the cause of his attack was exposure to the air1 to be accurate we ought to say that the cause was exposure to the air while under the effect of mercury4 ,if we do not1 when aiming at accuracy1 enumerate all the conditions1 it is only because some of them will in most cases be understood without being expressed1 or because for the purpose in view they may without detriment be overlooked4 ,for example1 when we say1 the cause of a man's death was that his foot slipped in climbing a ladder1 we omit as a thing unnecessary to be stated the circumstance of his weight1 though quite as indispensable a condition of the effect which took place4 ,when we say that the assent of the crown to a bill makes it law1 we mean that the assent1 being never given until all the other conditions are fulfilled1 makes up the sum of the conditions1 though no one now regards it as the principal one4 ,when the decision of a legislative assembly has been determined by the casting vote of the chairman1 we sometimes say that this one person was the cause of all the effects which resulted from the enactment4 ,yet we do not really suppose that his single vote contributed more to the result than that of any other person who voted in the affirmative2 but1 for the purpose we have in view1 which is to insist on his individual responsibility1 the part which any other person had in the transaction is not material4 ,in all these instances the fact which was dignified with the name of cause1 was the one condition which came last into existence4 ,but it must not be supposed that in the employment of the term this or any other rule is always adhered to4 ,nothing can better show the absence of any scientific ground for the distinction between the cause of a phenomenon and its conditions1 than the capricious manner in which we select from among the conditions that which we choose to denominate the cause4 ,however numerous the conditions may be1 there is hardly any of them which may not1 according to the purpose of our immediate discourse1 obtain that nominal pre-eminence4 ,this will be seen by analyzing the conditions of some one familiar phenomenon4 ,for example1 a stone thrown into water falls to the bottom4 ,what are the conditions of this event8 ,in the first place there must be a stone1 and water1 and the stone must be thrown into the water2 but these suppositions forming part of the enunciation of the phenomenon itself1 to include them also among the conditions would be a vicious tautology2 and this class of conditions1 therefore1 have never received the name of cause from any but the ,aristotelians1 by whom they were called the material cause1 causa materialis4 ,the next condition is1 there must be an earth3 and accordingly it is often said1 that the fall of a stone is caused by the earth2 or by a power or property of the earth1 or a force exerted by the earth1 all of which are merely roundabout ways of saying that it is caused by the earth2 or1 lastly1 the earth's attraction2 which also is only a technical mode of saying that the earth causes the motion1 with the additional particularity that the motion is toward the earth1 which is not a character of the cause1 but of the effect4 ,let us now pass to another condition4 ,it is not enough that the earth should exist2 the body must be within that distance from it1 in which the earth's attraction preponderates over that of any other body4 ,accordingly we may say1 and the expression would be confessedly correct1 that the cause of the stone's falling is its being within the sphere of the earth's attraction4 ,we proceed to a further condition4 ,the stone is immersed in water3 it is therefore a condition of its reaching the ground1 that its specific gravity exceed that of the surrounding fluid1 or in other words that it surpass in weight an equal volume of water4 ,accordingly any one would be acknowledged to speak correctly who said1 that the cause of the stone's going to the bottom is its exceeding in specific gravity the fluid in which it is immersed4 ,thus we see that each and every condition of the phenomenon may be taken in its turn1 and1 with equal propriety in common parlance1 but with equal impropriety in scientific discourse1 may be spoken of as if it were the entire cause4 ,and in practice1 that particular condition is usually styled the cause1 whose share in the matter is superficially the most conspicuous1 or whose requisiteness to the production of the effect we happen to be insisting on at the moment4 ,so great is the force of this last consideration1 that it sometimes induces us to give the name of cause even to one of the negative conditions4 ,we say1 for example1 ,the army was surprised because the sentinel was off his post4 ,but since the sentinel's absence was not what created the enemy1 or put the soldiers asleep1 how did it cause them to be surprised8 ,all that is really meant is1 that the event would not have happened if he had been at his duty4 ,his being off his post was no producing cause1 but the mere absence of a preventing cause3 it was simply equivalent to his non-existence4 ,from nothing1 from a mere negation1 no consequences can proceed4 ,all effects are connected1 by the law of causation1 with some set of positive conditions2 negative ones1 it is true1 being almost always required in addition4 ,in other words1 every fact or phenomenon which has a beginning1 invariably arises when some certain combination of positive facts exists1 provided certain other positive facts do not exist4 ,there is1 no doubt1 a tendency 7which our first example1 that of death from taking a particular food1 sufficiently illustrates7 to associate the idea of causation with the proximate antecedent event1 rather than with any of the antecedent states1 or permanent facts1 which may happen also to be conditions of the phenomenon2 the reason being that the event not only exists1 but begins to exist immediately previous2 while the other conditions may have pre-existed for an indefinite time4 ,and this tendency shows itself very visibly in the different logical fictions which are resorted to1 even by men of science1 to avoid the necessity of giving the name of cause to any thing which had existed for an indeterminate length of time before the effect4 ,thus1 rather than say that the earth causes the fall of bodies1 they ascribe it to a force exerted by the earth1 or an attraction by the earth1 abstractions which they can represent to themselves as exhausted by each effort1 and therefore constituting at each successive instant a fresh fact1 simultaneous with1 or only immediately preceding1 the effect4 ,inasmuch as the coming of the circumstance which completes the assemblage of conditions1 is a change or event1 it thence happens that an event is always the antecedent in closest apparent proximity to the consequent3 and this may account for the illusion which disposes us to look upon the proximate event as standing more peculiarly in the position of a cause than any of the antecedent states4 ,but even this peculiarity1 of being in closer proximity to the effect than any other of its conditions1 is1 as we have already seen1 far from being necessary to the common notion of a cause2 with which notion1 on the contrary1 any one of the conditions1 either positive or negative1 is found1 on occasion1 completely to accord47#aad7 ,the cause1 then1 philosophically speaking1 is the sum total of the conditions1 positive and negative taken together2 the whole of the contingencies of every description1 which being realized1 the consequent invariably follows4 ,the negative conditions1 however1 of any phenomenon1 a special enumeration of which would generally be very prolix1 may be all summed up under one head1 namely1 the absence of preventing or counteracting causes4 ,the convenience of this mode of expression is mainly grounded on the fact1 that the effects of any cause in counteracting another cause may in most cases be1 with strict scientific exactness1 regarded as a mere extension of its own proper and separate effects4 ,if gravity retards the upward motion of a projectile1 and deflects it into a parabolic trajectory1 it produces1 in so doing1 the very same kind of effect1 and even 7as mathematicians know7 the same quantity of effect1 as it does in its ordinary operation of causing the fall of bodies when simply deprived of their support4 ,if an alkaline solution mixed with an acid destroys its sourness1 and prevents it from reddening vegetable blues1 it is because the specific effect of the alkali is to combine with the acid1 and form a compound with totally different qualities4 ,this property1 which causes of all descriptions possess1 of preventing the effects of other causes by virtue 7for the most part7 of the same laws according to which they produce their own17#aae7 enables us1 by establishing the general axiom that all causes are liable to be counteracted in their effects by one another1 to dispense with the consideration of negative conditions entirely1 and limit the notion of cause to the assemblage of the positive conditions of the phenomenon3 one negative condition invariably understood1 and the same in all instances 7namely1 the absence of counteracting causes7 being sufficient1 along with the sum of the positive conditions1 to make up the whole set of circumstances on which the phenomenon is dependent4 #d4 ,among the positive conditions1 as we have seen that there are some to which1 in common parlance1 the term cause is more readily and frequently awarded1 so there are others to which it is1 in ordinary circumstances1 refused4 ,in most cases of causation a distinction is commonly drawn between something which acts1 and some other thing which is acted upon2 between an agent and a patient4 ,both of these1 it would be universally allowed1 are conditions of the phenomenon2 but it would be thought absurd to call the latter the cause1 that title being reserved for the former4 ,the distinction1 however1 vanishes on examination1 or rather is found to be only verbal2 arising from an incident of mere expression1 namely1 that the object said to be acted upon1 and which is considered as the scene in which the effect takes place1 is commonly included in the phrase by which the effect is spoken of1 so that if it were also reckoned as part of the cause1 the seeming incongruity would arise of its being supposed to cause itself4 ,in the instance which we have already had1 of falling bodies1 the question was thus put3 ,what is the cause which makes a stone fall8 and if the answer had been 8the stone itself10 the expression would have been in apparent contradiction to the meaning of the word cause4 ,the stone1 therefore1 is conceived as the patient1 and the earth 7or1 according to the common and most unphilosophical practice1 an occult quality of the earth7 is represented as the agent or cause4 ,but that there is nothing fundamental in the distinction may be seen from this1 that it is quite possible to conceive the stone as causing its own fall1 provided the language employed be such as to save the mere verbal incongruity4 ,we might say that the stone moves toward the earth by the properties of the matter composing it2 and according to this mode of presenting the phenomenon1 the stone itself might without impropriety be called the agent2 though1 to save the established doctrine of the inactivity of matter1 men usually prefer here also to ascribe the effect to an occult quality1 and say that the cause is not the stone itself1 but the weight or gravitation of the stone4 ,those who have contended for a radical distinction between agent and patient1 have generally conceived the agent as that which causes some state of1 or some change in the state of1 another object which is called the patient4 ,but a little reflection will show that the license we assume of speaking of phenomena as states of the various objects which take part in them 7an artifice of which so much use has been made by some philosophers1 ,brown in particular1 for the apparent explanation of phenomena71 is simply a sort of logical fiction1 useful sometimes as one among several modes of expression1 but which should never be supposed to be the enunciation of a scientific truth4 ,even those attributes of an object which might seem with greatest propriety to be called states of the object itself1 its sensible qualities1 its color1 hardness1 shape1 and the like1 are in reality 7as no one has pointed out more clearly than ,brown himself7 phenomena of causation1 in which the substance is distinctly the agent1 or producing cause1 the patient being our own organs1 and those of other sentient beings4 ,what we call states of objects1 are always sequences into which the objects enter1 generally as antecedents or causes2 and things are never more active than in the production of those phenomena in which they are said to be acted upon4 ,thus1 in the example of a stone falling to the earth1 according to the theory of gravitation the stone is as much an agent as the earth1 which not only attracts1 but is itself attracted by1 the stone4 ,in the case of a sensation produced in our organs1 the laws of our organization1 and even those of our minds1 are as directly operative in determining the effect produced1 as the laws of the outward object4 ,though we call prussic acid the agent of a person's death1 the whole of the vital and organic properties of the patient are as actively instrumental as the poison1 in the chain of effects which so rapidly terminates his sentient existence4 ,in the process of education1 we may call the teacher the agent1 and the scholar only the material acted upon2 yet in truth all the facts which pre-existed in the scholar's mind exert either co-operating or counteracting agencies in relation to the teacher's efforts4 ,it is not light alone which is the agent in vision1 but light coupled with the active properties of the eye and brain1 and with those of the visible object4 ,the distinction between agent and patient is merely verbal3 patients are always agents2 in a great proportion1 indeed1 of all natural phenomena1 they are so to such a degree as to react forcibly on the causes which acted upon them3 and even when this is not the case1 they contribute1 in the same manner as any of the other conditions1 to the production of the effect of which they are vulgarly treated as the mere theatre4 ,all the positive conditions of a phenomenon are alike agents1 alike active2 and in any expression of the cause which professes to be complete1 none of them can with reason be excluded1 except such as have already been implied in the words used for describing the effect2 nor by including even these would there be incurred any but a merely verbal impropriety4 #e4 ,there is a case of causation which calls for separate notice1 as it possesses a peculiar feature1 and presents a greater degree of complexity than the common case4 ,it often happens that the effect1 or one of the effects1 of a cause1 is1 not to produce of itself a certain phenomenon1 but to fit something else for producing it4 ,in other words1 there is a case of causation in which the effect is to invest an object with a certain property4 ,when sulphur1 charcoal1 and nitre are put together in certain proportions and in a certain manner1 the effect is1 not an explosion1 but that the mixture acquires a property by which1 in given circumstances1 it will explode4 ,the various causes1 natural and artificial1 which educate the human body or the human mind1 have for their principal effect1 not to make the body or mind immediately do any thing1 but to endow it with certain properties--in other words1 to give assurance that in given circumstances certain results will take place in it1 or as consequences of it4 ,physiological agencies often have for the chief part of their operation to predispose the constitution to some mode of action4 ,to take a simpler instance than all these3 putting a coat of white paint upon a wall does not merely produce in those who see it done1 the sensation of white2 it confers on the wall the permanent property of giving that kind of sensation4 ,regarded in reference to the sensation1 the putting on of the paint is a condition of a condition2 it is a condition of the wall's causing that particular fact4 ,the wall may have been painted years ago1 but it has acquired a property which has lasted till now1 and will last longer2 the antecedent condition necessary to enable the wall to become in its turn a condition1 has been fulfilled once for all4 ,in a case like this1 where the immediate consequent in the sequence is a property produced in an object1 no one now supposes the property to be a substantive entity 8inherent0 in the object4 ,what has been produced is what1 in other language1 may be called a state of preparation in an object for producing an effect4 ,the ingredients of the gunpowder have been brought into a state of preparation for exploding as soon as the other conditions of an explosion shall have occurred4 ,in the case of the gunpowder1 this state of preparation consists in a certain collocation of its particles relatively to one another4 ,in the example of the wall1 it consists in a new collocation of two things relatively to each other--the wall and the paint4 ,in the example of the molding influences on the human mind1 its being a collocation at all is only conjectural2 for1 even on the materialistic hypothesis1 it would remain to be proved that the increased facility with which the brain sums up a column of figures when it has been long trained to calculation1 is the result of a permanent new arrangement of some of its material particles4 ,we must1 therefore1 content ourselves with what we know1 and must include among the effects of causes1 the capacities given to objects of being causes of other effects4 ,this capacity is not a real thing existing in the objects2 it is but a name for our conviction that they will act in a particular manner when certain new circumstances arise4 ,we may invest this assurance of future events with a fictitious objective existence1 by calling it a state of the object4 ,but unless the state consists1 as in the case of the gunpowder it does1 in a collocation of particles1 it expresses no present fact2 it is but the contingent future fact brought back under another name4 ,it may be thought that this form of causation requires us to admit an exception to the doctrine that the conditions of a phenomenon--the antecedents required for calling it into existence--must all be found among the facts immediately1 not remotely1 preceding its commencement4 ,but what we have arrived at is not a correction1 it is only an explanation1 of that doctrine4 ,in the enumeration of the conditions required for the occurrence of any phenomenon1 it always has to be included that objects must be present1 possessed of given properties4 ,it is a condition of the phenomenon explosion that an object should be present1 of one or other of certain kinds1 which for that reason are called explosive4 ,the presence of one of these objects is a condition immediately precedent to the explosion4 ,the condition which is not immediately precedent is the cause which produced1 not the explosion1 but the explosive property4 ,the conditions of the explosion itself were all present immediately before it took place1 and the general law1 therefore1 remains intact4 #f4 ,it now remains to advert to a distinction which is of first-rate importance both for clearing up the notion of cause1 and for obviating a very specious objection often made against the view which we have taken of the subject4 ,when we define the cause of any thing 7in the only sense in which the present inquiry has any concern with causes7 to be 8the antecedent which it invariably follows10 we do not use this phrase as exactly synonymous with 8the antecedent which it invariably has followed in our past experience40 ,such a mode of conceiving causation would be liable to the objection very plausibly urged by ,dr4 ,reid1 namely1 that according to this doctrine night must be the cause of day1 and day the cause of night2 since these phenomena have invariably succeeded one another from the beginning of the world4 ,but it is necessary to our using the word cause1 that we should believe not only that the antecedent always has been followed by the consequent1 but that1 as long as the present constitution of things7#aaf7 endures1 it always will be so4 ,and this would not be true of day and night4 ,we do not believe that night will be followed by day under all imaginable circumstances1 but only that it will be so provided the sun rises above the horizon4 ,if the sun ceased to rise1 which1 for aught we know1 may be perfectly compatible with the general laws of matter1 night would be1 or might be1 eternal4 ,on the other hand1 if the sun is above the horizon1 his light not extinct1 and no opaque body between us and him1 we believe firmly that unless a change takes place in the properties of matter1 this combination of antecedents will be followed by the consequent1 day2 that if the combination of antecedents could be indefinitely prolonged1 it would be always day2 and that if the same combination had always existed1 it would always have been day1 quite independently of night as a previous condition4 ,therefore is it that we do not call night the cause1 nor even a condition1 of day4 ,the existence of the sun 7or some such luminous body71 and there being no opaque medium in a straight line7#aag7 between that body and the part of the earth where we are situated1 are the sole conditions2 and the union of these1 without the addition of any superfluous circumstance1 constitutes the cause4 ,this is what writers mean when they say that the notion of cause involves the idea of necessity4 ,if there be any meaning which confessedly belongs to the term necessity1 it is unconditionalness4 ,that which is necessary1 that which must be1 means that which will be1 whatever supposition we may make in regard to all other things4 ,the succession of day and night evidently is not necessary in this sense4 ,it is conditional on the occurrence of other antecedents4 ,that which will be followed by a given consequent when1 and only when1 some third circumstance also exists1 is not the cause1 even though no case should ever have occurred in which the phenomenon took place without it4 ,invariable sequence1 therefore1 is not synonymous with causation1 unless the sequence1 besides being invariable1 is unconditional4 ,there are sequences1 as uniform in past experience as any others whatever1 which yet we do not regard as cases of causation1 but as conjunctions in some sort accidental4 ,such1 to an accurate thinker1 is that of day and night4 ,the one might have existed for any length of time1 and the other not have followed the sooner for its existence2 it follows only if certain other antecedents exist2 and where those antecedents existed1 it would follow in any case4 ,no one1 probably1 ever called night the cause of day2 mankind must so soon have arrived at the very obvious generalization1 that the state of general illumination which we call day would follow from the presence of a sufficiently luminous body1 whether darkness had preceded or not4 ,we may define1 therefore1 the cause of a phenomenon1 to be the antecedent1 or the concurrence of antecedents1 on which it is invariably and unconditionally consequent4 ,or if we adopt the convenient modification of the meaning of the word cause1 which confines it to the assemblage of positive conditions without the negative1 then instead of 8unconditionally10 we must say1 8subject to no other than negative conditions40 ,to some it may appear1 that the sequence between night and day being invariable in our experience1 we have as much ground in this case as experience can give in any case1 for recognizing the two phenomena as cause and effect2 and that to say that more is necessary--to require a belief that the succession is unconditional1 or1 in other words1 that it would be invariable under all changes of circumstances1 is to acknowledge in causation an element of belief not derived from experience4 ,the answer to this is1 that it is experience itself which teaches us that one uniformity of sequence is conditional and another unconditional4 ,when we judge that the succession of night and day is a derivative sequence1 depending on something else1 we proceed on grounds of experience4 ,it is the evidence of experience which convinces us that day could equally exist without being followed by night1 and that night could equally exist without being followed by day4 ,to say that these beliefs are 8not generated by our mere observation of sequence107#aah7 is to forget that twice in every twenty-four hours1 when the sky is clear1 we have an experimentum crucis that the cause of day is the sun4 ,we have an experimental knowledge of the sun which justifies us on experimental grounds in concluding1 that if the sun were always above the horizon there would be day1 though there had been no night1 and that if the sun were always below the horizon there would be night1 though there had been no day4 ,we thus know from experience that the succession of night and day is not unconditional4 ,let me add1 that the antecedent which is only conditionally invariable1 is not the invariable antecedent4 ,though a fact may1 in experience1 have always been followed by another fact1 yet if the remainder of our experience teaches us that it might not always be so followed1 or if the experience itself is such as leaves room for a possibility that the known cases may not correctly represent all possible cases1 the hitherto invariable antecedent is not accounted the cause2 but why8 ,because we are not sure that it is the invariable antecedent4 ,such cases of sequence as that of day and night not only do not contradict the doctrine which resolves causation into invariable sequence1 but are necessarily implied in that doctrine4 ,it is evident1 that from a limited number of unconditional sequences1 there will result a much greater number of conditional ones4 ,certain causes being given1 that is1 certain antecedents which are unconditionally followed by certain consequents2 the mere co-existence of these causes will give rise to an unlimited number of additional uniformities4 ,if two causes exist together1 the effects of both will exist together2 and if many causes co-exist1 these causes 7by what we shall term hereafter the intermixture of their laws7 will give rise to new effects1 accompanying or succeeding one another in some particular order1 which order will be invariable while the causes continue to co-exist1 but no longer4 ,the motion of the earth in a given orbit round the sun1 is a series of changes which follow one another as antecedents and consequents1 and will continue to do so while the sun's attraction1 and the force with which the earth tends to advance in a direct line through space1 continue to co-exist in the same quantities as at present4 ,but vary either of these causes1 and this particular succession of motions would cease to take place4 ,the series of the earth's motions1 therefore1 though a case of sequence invariable within the limits of human experience1 is not a case of causation4 ,it is not unconditional4 ,this distinction between the relations of succession which1 so far as we know1 are unconditional1 and those relations1 whether of succession or of co-existence1 which1 like the earth's motions1 or the succession of day and night1 depend on the existence or on the co-existence of other antecedent facts--corresponds to the great division which ,dr4 ,whewell and other writers have made of the field of science1 into the investigation of what they term the ,laws of ,phenomena1 and the investigation of causes2 a phraseology1 as ,i conceive1 not philosophically sustainable1 inasmuch as the ascertainment of causes1 such causes as the human faculties can ascertain1 namely1 causes which are themselves phenomena1 is1 therefore1 merely the ascertainment of other and more universal ,laws of ,phenomena4 ,and let me here observe1 that ,dr4 ,whewell1 and in some degree even ,sir ,john ,herschel1 seem to have misunderstood the meaning of those writers who1 like ,m4 ,comt1 limit the sphere of scientific investigation to ,laws of ,phenomena1 and speak of the inquiry into causes as vain and futile4 ,the causes which ,m4 ,comt designates as inaccessible1 are efficient causes4 ,the investigation of physical1 as opposed to efficient1 causes 7including the study of all the active forces in ,nature1 considered as facts of observation7 is as important a part of ,m4 ,comt's conception of science as of ,dr4 ,whewell's4 ,his objection to the word cause is a mere matter of nomenclature1 in which1 as a matter of nomenclature1 ,i consider him to be entirely wrong4 8,those10 it is justly remarked by ,mr4 ,bailey17#aai7 8who1 like ,m4 ,comt1 object to designate events as causes1 are objecting without any real ground to a mere but extremely convenient generalization1 to a very useful common name1 the employment of which involves1 or needs involve1 no particular theory40 ,to which it may be added1 that by rejecting this form of expression1 ,m4 ,comt leaves himself without any term for marking a distinction which1 however incorrectly expressed1 is not only real1 but is one of the fundamental distinctions in science2 indeed it is on this alone1 as we shall hereafter find1 that the possibility rests of framing a rigorous ,canon of ,induction4 ,and as things left without a name are apt to be forgotten1 a ,canon of that description is not one of the many benefits which the philosophy of ,induction has received from ,m4 ,comt's great powers4 #g4 ,does a cause always stand with its effect in the relation of antecedent and consequent8 ,do we not often say of two simultaneous facts that they are cause and effect--as when we say that fire is the cause of warmth1 the sun and moisture the cause of vegetation1 and the like8 ,since a cause does not necessarily perish because its effect has been produced1 the two things do very generally co-exist2 and there are some appearances1 and some common expressions1 seeming to imply not only that causes may1 but that they must1 be contemporaneous with their effects4 ,cessante caus cessat et effectus1 has been a dogma of the schools3 the necessity for the continued existence of the cause in order to the continuance of the effect1 seems to have been once a generally received doctrine4 ,kepler's numerous attempts to account for the motions of the heavenly bodies on mechanical principles1 were rendered abortive by his always supposing that the agency which set those bodies in motion must continue to operate in order to keep up the motion which it at first produced4 ,yet there were at all times many familiar instances of the continuance of effects1 long after their causes had ceased4 ,a coup de soleil gives a person brain-fever3 will the fever go off as soon as he is moved out of the sunshine8 ,a sword is run through his body3 must the sword remain in his body in order that he may continue dead8 ,a plowshare once made1 remains a plowshare1 without any continuance of heating and hammering1 and even after the man who heated and hammered it has been gathered to his fathers4 ,on the other hand1 the pressure which forces up the mercury in an exhausted tube must be continued in order to sustain it in the tube4 ,this 7it may be replied7 is because another force is acting without intermission1 the force of gravity1 which would restore it to its level1 unless counterpoised by a force equally constant4 ,but again3 a tight bandage causes pain1 which pain will sometimes go off as soon as the bandage is removed4 ,the illumination which the sun diffuses over the earth ceases when the sun goes down4 ,there is1 therefore1 a distinction to be drawn4 ,the conditions which are necessary for the first production of a phenomenon1 are occasionally also necessary for its continuance2 though more commonly its continuance requires no condition except negative ones4 ,most things1 once produced1 continue as they are1 until something changes or destroys them2 but some require the permanent presence of the agencies which produced them at first4 ,these may1 if we please1 be considered as instantaneous phenomena1 requiring to be renewed at each instant by the cause by which they were at first generated4 ,accordingly1 the illumination of any given point of space has always been looked upon as an instantaneous fact1 which perishes and is perpetually renewed as long as the necessary conditions subsist4 ,if we adopt this language we avoid the necessity of admitting that the continuance of the cause is ever required to maintain the effect4 ,we may say1 it is not required to maintain1 but to reproduce1 the effect1 or else to counteract some force tending to destroy it4 ,and this may be a convenient phraseology4 ,but it is only a phraseology4 ,the fact remains1 that in some cases 7though those are a minority7 the continuance of the conditions which produced an effect is necessary to the continuance of the effect4 ,as to the ulterior question1 whether it is strictly necessary that the cause1 or assemblage of conditions1 should precede1 by ever so short an instant1 the production of the effect 7a question raised and argued with much ingenuity by ,sir ,john ,herschel in an ,essay already quoted717#abj7 the inquiry is of no consequence for our present purpose4 ,there certainly are cases in which the effect follows without any interval perceptible by our faculties2 and when there is an interval1 we can not tell by how many intermediate links imperceptible to us that interval may really be filled up4 ,but even granting that an effect may commence simultaneously with its cause1 the view ,i have taken of causation is in no way practically affected4 ,whether the cause and its effect be necessarily successive or not1 the beginning of a phenomenon is what implies a cause1 and causation is the law of the succession of phenomena4 ,if these axioms be granted1 we can afford1 though ,i see no necessity for doing so1 to drop the words antecedent and consequent as applied to cause and effect4 ,i have no objection to define a cause1 the assemblage of phenomena1 which occurring1 some other phenomenon invariably commences1 or has its origin4 ,whether the effect coincides in point of time with1 or immediately follows1 the hindmost of its conditions1 is immaterial4 ,at all events1 it does not precede it2 and when we are in doubt1 between two co-existent phenomena1 which is cause and which effect1 we rightly deem the question solved if we can ascertain which of them preceded the other4 #h4 ,it continually happens that several different phenomena1 which are not in the slightest degree dependent or conditional on one another1 are found all to depend1 as the phrase is1 on one and the same agent2 in other words1 one and the same phenomenon is seen to be followed by several sorts of effects quite heterogeneous1 but which go on simultaneously one with another2 provided1 of course1 that all other conditions requisite for each of them also exist4 ,thus1 the sun produces the celestial motions2 it produces daylight1 and it produces heat4 ,the earth causes the fall of heavy bodies1 and it also1 in its capacity of a great magnet1 causes the phenomena of the magnetic needle4 ,a crystal of galena causes the sensations of hardness1 of weight1 of cubical form1 of gray color1 and many others between which we can trace no interdependence4 ,the purpose to which the phraseology of ,properties and ,powers is specially adapted1 is the expression of this sort of cases4 ,when the same phenomenon is followed 7either subject or not to the presence of other conditions7 by effects of different and dissimilar orders1 it is usual to say that each different sort of effect is produced by a different property of the cause4 ,thus we distinguish the attractive or gravitative property of the earth1 and its magnetic property3 the gravitative1 luminiferous1 and calorific properties of the sun3 the color1 shape1 weight1 and hardness of a crystal4 ,these are mere phrases1 which explain nothing1 and add nothing to our knowledge of the subject2 but1 considered as abstract names denoting the connection between the different effects produced and the object which produces them1 they are a very powerful instrument of abridgment1 and of that acceleration of the process of thought which abridgment accomplishes4 ,this class of considerations leads to a conception which we shall find to be of great importance1 that of a ,permanent ,cause1 or original natural agent4 ,there exist in nature a number of permanent causes1 which have subsisted ever since the human race has been in existence1 and for an indefinite and probably an enormous length of time previous4 ,the sun1 the earth1 and planets1 with their various constituents1 air1 water1 and other distinguishable substances1 whether simple or compound1 of which nature is made up1 are such ,permanent ,causes4 ,these have existed1 and the effects or consequences which they were fitted to produce have taken place 7as often as the other conditions of the production met71 from the very beginning of our experience4 ,but we can give no account of the origin of the ,permanent ,causes themselves4 ,why these particular natural agents existed originally and no others1 or why they are commingled in such and such proportions1 and distributed in such and such a manner throughout space1 is a question we can not answer4 ,more than this3 we can discover nothing regular in the distribution itself2 we can reduce it to no uniformity1 to no law4 ,there are no means by which1 from the distribution of these causes or agents in one part of space1 we could conjecture whether a similar distribution prevails in another4 ,the co-existence1 therefore1 of ,primeval ,causes ranks1 to us1 among merely casual concurrences3 and all those sequences or co-existences among the effects of several such causes1 which1 though invariable while those causes co-exist1 would1 if the co-existence terminated1 terminate along with it1 we do not class as cases of causation1 or laws of nature3 we can only calculate on finding these sequences or co-existences where we know by direct evidence1 that the natural agents on the properties of which they ultimately depend1 are distributed in the requisite manner4 ,these ,permanent ,causes are not always objects2 they are sometimes events1 that is to say1 periodical cycles of events1 that being the only mode in which events can possess the property of permanence4 ,not only1 for instance1 is the earth itself a permanent cause1 or primitive natural agent1 but the earth's rotation is so too3 it is a cause which has produced1 from the earliest period 7by the aid of other necessary conditions71 the succession of day and night1 the ebb and flow of the sea1 and many other effects1 while1 as we can assign no cause 7except conjecturally7 for the rotation itself1 it is entitled to be ranked as a primeval cause4 ,it is1 however1 only the origin of the rotation which is mysterious to us3 once begun1 its continuance is accounted for by the first law of motion 7that of the permanence of rectilinear motion once impressed7 combined with the gravitation of the parts of the earth toward one another4 ,all phenomena without exception which begin to exist1 that is1 all except the primeval causes1 are effects either immediate or remote of those primitive facts1 or of some combination of them4 ,there is no ,thing produced1 no event happening1 in the known universe1 which is not connected by a uniformity1 or invariable sequence1 with some one or more of the phenomena which preceded it2 insomuch that it will happen again as often as those phenomena occur again1 and as no other phenomenon having the character of a counteracting cause shall co-exist4 ,these antecedent phenomena1 again1 were connected in a similar manner with some that preceded them2 and so on1 until we reach1 as the ultimate step attainable by us1 either the properties of some one primeval cause1 or the conjunction of several4 ,the whole of the phenomena of nature were therefore the necessary1 or1 in other words1 the unconditional1 consequences of some former collocation of the ,permanent ,causes4 ,the state of the whole universe at any instant1 we believe to be the consequence of its state at the previous instant2 insomuch that one who knew all the agents which exist at the present moment1 their collocation in space1 and all their properties1 in other words1 the laws of their agency1 could predict the whole subsequent history of the universe1 at least unless some new volition of a power capable of controlling the universe should supervene47#aba7 ,and if any particular state of the entire universe could ever recur a second time1 all subsequent states would return too1 and history would1 like a circulating decimal of many figures1 periodically repeat itself3 ,jam redit et virgo1 redeunt ,saturnia regna4444 ,alter erit tum ,tiphys1 et altera qu vehat ,argo ,delectos heroas2 erunt quoque altera bella1 ,atque iterum ad ,trojam magnus mittetur ,achilles4 ,and though things do not really revolve in this eternal round1 the whole series of events in the history of the universe1 past and future1 is not the less capable1 in its own nature1 of being constructed a priori by any one whom we can suppose acquainted with the original distribution of all natural agents1 and with the whole of their properties1 that is1 the laws of succession existing between them and their effects3 saving the far more than human powers of combination and calculation which would be required1 even in one possessing the data1 for the actual performance of the task4 #i4 ,since every thing which occurs is determined by laws of causation and collocations of the original causes1 it follows that the co-existences which are observable among effects can not be themselves the subject of any similar set of laws1 distinct from laws of causation4 ,uniformities there are1 as well of co-existence as of succession1 among effects2 but these must in all cases be a mere result either of the identity or of the co-existence of their causes3 if the causes did not co-exist1 neither could the effects4 ,and these causes being also effects of prior causes1 and these of others1 until we reach the primeval causes1 it follows that 7except in the case of effects which can be traced immediately or remotely to one and the same cause7 the co-existences of phenomena can in no case be universal1 unless the co-existences of the primeval causes to which the effects are ultimately traceable can be reduced to a universal law3 but we have seen that they can not4 ,there are1 accordingly1 no original and independent1 in other words no unconditional1 uniformities of co-existence1 between effects of different causes2 if they co-exist1 it is only because the causes have casually co-existed4 ,the only independent and unconditional co-existences which are sufficiently invariable to have any claim to the character of laws1 are between different and mutually independent effects of the same cause2 in other words1 between different properties of the same natural agent4 ,this portion of the ,laws of ,nature will be treated of in the latter part of the present ,book1 under the name of the ,specific ,properties of ,kinds4 #aj4 ,since the first publication of the present treatise1 the sciences of physical nature have made a great advance in generalization1 through the doctrine known as the ,conservation or ,persistence of ,force4 ,this imposing edifice of theory1 the building and laying out of which has for some time been the principal occupation of the most systematic minds among physical inquirers1 consists of two stages3 one1 of ascertained fact1 the other containing a large element of hypothesis4 ,to begin with the first4 ,it is proved by numerous facts1 both natural and of artificial production1 that agencies which had been regarded as distinct and independent sources of force--heat1 electricity1 chemical action1 nervous and muscular action1 momentum of moving bodies--are interchangeable1 in definite and fixed quantities1 with one another4 ,it had long been known that these dissimilar phenomena had the power1 under certain conditions1 of producing one another3 what is new in the theory is a more accurate estimation of what this production consists in4 ,what happens is1 that the whole or part of the one kind of phenomena disappears1 and is replaced by phenomena of one of the other descriptions1 and that there is an equivalence in quantity between the phenomena that have disappeared and those which have been produced1 insomuch that if the process be reversed1 the very same quantity which had disappeared will re-appear1 without increase or diminution4 ,thus the amount of heat which will raise the temperature of a pound of water one degree of the thermometer1 will1 if expended1 say in the expansion of steam1 lift a weight of #ggb pounds one foot1 or a weight of one pound #ggb feet3 and the same exact quantity of heat can1 by certain means1 be recovered1 through the expenditure of exactly that amount of mechanical motion4 ,the establishment of this comprehensive law has led to a change in the language in which the scientific world had been accustomed to speak of what are called the ,forces of nature4 ,before this correlation between phenomena most unlike one another had been ascertained1 their unlikeness had caused them to be referred to so many distinct forces4 ,now that they are known to be convertible into one another without loss1 they are spoken of as all of them results of one and the same force1 manifesting itself in different modes4 ,this force 7it is said7 can only produce a limited and definite quantity of effect1 but always does produce that definite quantity2 and produces it1 according to circumstances1 in one or another of the forms1 or divides it among several1 but so as 7according to a scale of numerical equivalents established by experiment7 always to make up the same sum2 and no one of the manifestations can be produced1 save by the disappearance of the equivalent quantity of another1 which in its turn1 in appropriate circumstances1 will re-appear undiminished4 ,this mutual interchangeability of the forces of nature1 according to fixed numerical equivalents1 is the part of the new doctrine which rests on irrefragable fact4 ,to make the statement true1 however1 it is necessary to add1 that an indefinite and perhaps immense interval of time may elapse between the disappearance of the force in one form and its re-appearance in another4 ,a stone thrown up into the air with a given force1 and falling back immediately1 will1 by the time it reaches the earth1 recover the exact amount of mechanical momentum which was expended in throwing it up1 deduction being made of a small portion of motion which has been communicated to the air4 ,but if the stone has lodged on a height1 it may not fall back for years1 or perhaps ages1 and until it does1 the force expended in raising it is temporarily lost1 being represented only by what1 in the language of the new theory1 is called potential energy4 ,the coal imbedded in the earth is considered by the theory as a vast reservoir of force1 which has remained dormant for many geological periods1 and will so remain until1 by being burned1 it gives out the stored-up force in the form of heat4 ,yet it is not supposed that this force is a material thing which can be confined by bounds1 as used to be thought of latent heat when that important phenomenon was first discovered4 ,what is meant is that when the coal does at last1 by combustion1 generate a quantity of heat 7transformable like all other heat into mechanical momentum1 and the other forms of force71 this extrication of heat is the re-appearance of a force derived from the sun's rays1 expended myriads of ages ago in the vegetation of the organic substances which were the material of the coal4 ,let us now pass to the higher stage of the theory of ,conservation of ,force2 the part which is no longer a generalization of proved fact1 but a combination of fact and hypothesis4 ,stated in few words1 it is as follows3 ,that the ,conservation of ,force is really the ,conservation of ,motion2 that in the various interchanges between the forms of force1 it is always motion that is transformed into motion4 ,to establish this1 it is necessary to assume motions which are hypothetical4 ,the supposition is1 that there are motions which manifest themselves to our senses only as heat1 electricity1 etc41 being molecular motions2 oscillations1 invisible to us1 among the minute particles of bodies2 and that these molecular motions are transmutable into molar motions 7motions of masses71 and molar motions into molecular4 ,now there is a real basis of fact for this supposition3 we have positive evidence of the existence of molecular motion in these manifestations of force4 ,in the case of chemical action1 for instance1 the particles separate and form new combinations1 often with a great visible disturbance of the mass4 ,in the case of heat1 the evidence is equally conclusive1 since heat expands bodies 7that is1 causes their particles to move from one another72 and if of sufficient amount1 changes their mode of aggregation from solid to liquid1 or from liquid to gaseous4 ,again1 the mechanical actions which produce heat--friction1 and the collision of bodies--must from the nature of the case produce a shock1 that is1 an internal motion of particles1 which indeed1 we find1 is often so violent as to break them permanently asunder4 ,such facts are thought to warrant the inference1 that it is not1 as was supposed1 heat that causes the motion of particles1 but the motion of particles that causes heat2 the original cause of both being the previous motion 7whether molar or molecular--collision of bodies or combustion of fuel7 which formed the heating agency4 ,this inference already contains hypothesis2 but at least the supposed cause1 the intestine motion of molecules1 is a vera causa4 ,but in order to reduce the ,conservation of ,force to ,conservation of ,motion1 it was necessary to attribute to motion the heat propagated1 through apparently empty space1 from the sun4 ,this required the supposition 7already made for the explanation of the laws of light7 of a subtle ether pervading space1 which1 though impalpable to us1 must have the property which constitutes matter1 that of resistance1 since waves are propagated through it by an impulse from a given point4 ,the ether must be supposed 7a supposition not required by the theory of light7 to penetrate into the minute interstices of all bodies4 ,the vibratory motion supposed to be taking place in the heated mass of the sun1 is considered as imparted from that mass to the particles of the surrounding ether1 and through them to the particles of the same ether in the interstices of terrestrial bodies2 and this1 too1 with a sufficient mechanical force to throw the particles of those bodies into a state of similar vibration1 producing the expansion of their mass1 and the sensation of heat in sentient creatures4 ,all this is hypothesis1 though1 of its legitimacy as hypothesis1 ,i do not mean to express any doubt4 ,it would seem to follow as a consequence from this theory1 that ,force may and should be defined1 matter in motion4 ,this definition1 however1 will not stand1 for1 as has already been seen1 the matter needs not be in actual motion4 ,it is not necessary to suppose that the motion afterward manifested1 is actually taking place among the molecules of the coal during its sojourn in the earth27#abb7 certainly not in the stone which is at rest on the eminence to which it has been raised4 ,the true definition of ,force must be1 not motion1 but ,potentiality of ,motion2 and what the doctrine1 if established1 amounts to1 is1 not that there is at all times the same quantity of actual motion in the universe2 but that the possibilities of motion are limited to a definite quantity1 which can not be added to1 but which can not be exhausted2 and that all actual motion which takes place in ,nature is a draft upon this limited stock4 ,it needs not all of it have ever existed as actual motion4 ,there is a vast amount of potential motion in the universe in the form of gravitation1 which it would be a great abuse of hypothesis to suppose to have been stored up by the expenditure of an equal amount of actual motion in some former state of the universe4 ,nor does the motion produced by gravity take place1 so far as we know1 at the expense of any other motion1 either molar or molecular4 ,it is proper to consider whether the adoption of this theory as a scientific truth1 involving as it does a change in the conception hitherto entertained of the most general physical agencies1 requires any modification in the view ,i have taken of ,causation as a law of nature4 ,as it appears to me1 none whatever4 ,the manifestations which the theory regards as modes of motion1 are as much distinct and separate phenomena when referred to a single force1 as when attributed to several4 ,whether the phenomenon is called a transformation of force or the generation of one1 it has its own set or sets of antecedents1 with which it is connected by invariable and unconditional sequence2 and that set1 or those sets1 of antecedents are its cause4 ,the relation of the ,conservation theory to the principle of ,causation is discussed in much detail1 and very instructively1 by ,professor ,bain1 in the second volume of his ,logic4 ,the chief practical conclusion drawn by him1 bearing on ,causation1 is1 that we must distinguish in the assemblage of conditions which constitutes the ,cause of a phenomenon1 two elements3 one1 the presence of a force2 the other1 the collocation or position of objects which is required in order that the force may undergo the particular transmutation which constitutes the phenomenon4 ,now1 it might always have been said with acknowledged correctness1 that a force and a collocation were both of them necessary to produce any phenomenon4 ,the law of causation is1 that change can only be produced by change4 ,along with any number of stationary antecedents1 which are collocations1 there must be at least one changing antecedent1 which is a force4 ,to produce a bonfire1 there must not only be fuel1 and air1 and a spark1 which are collocations1 but chemical action between the air and the materials1 which is a force4 ,to grind corn1 there must be a certain collocation of the parts composing a mill1 relatively to one another and to the corn2 but there must also be the gravitation of water1 or the motion of wind1 to supply a force4 ,but as the force in these cases was regarded as a property of the objects in which it is embodied1 it seemed tautology to say that there must be the collocation and the force4 ,as the collocation must be a collocation of objects possessing the force-giving property1 the collocation1 so understood1 included the force4 ,how1 then1 shall we have to express these facts1 if the theory be finally substantiated that all ,force is reducible to a previous ,motion8 ,we shall have to say1 that one of the conditions of every phenomenon is an antecedent ,motion4 ,but it will have to be explained that this needs not be actual motion4 ,the coal which supplies the force exerted in combustion is not shown to have been exerting that force in the form of molecular motion in the pit2 it was not even exerting pressure4 ,the stone on the eminence is exerting a pressure1 but only equivalent to its weight1 not to the additional momentum it would acquire by falling4 ,the antecedent1 therefore1 is not a force in action2 and we can still only call it a property of the objects1 by which they would exert a force on the occurrence of a fresh collocation4 ,the collocation1 therefore1 still includes the force4 ,the force said to be stored up1 is simply a particular property which the object has acquired4 ,the cause we are in search of1 is a collocation of objects possessing that particular property4 ,when1 indeed1 we inquire further into the cause from which they derive that property1 the new conception introduced by the ,conservation theory comes in3 the property is itself an effect1 and its cause1 according to the theory1 is a former motion of exactly equivalent amount1 which has been impressed on the particles of the body1 perhaps at some very distant period4 ,but the case is simply one of those we have already considered1 in which the efficacy of a cause consists in its investing an object with a property4 ,the force said to be laid up1 and merely potential1 is no more a really existing thing than any other properties of objects are really existing things4 ,the expression is a mere artifice of language1 convenient for describing the phenomena3 it is unnecessary to suppose that any thing has been in continuous existence except an abstract potentiality4 ,a force suspended in its operation1 neither manifesting itself by motion nor by pressure1 is not an existing fact1 but a name for our conviction that in appropriate circumstances a fact would take place4 ,we know that a pound weight1 were it to fall from the earth into the sun1 would acquire in falling a momentum equal to millions of pounds2 but we do not credit the pound weight with more of actually existing force than is equal to the pressure it is now exerting on the earth1 and that is exactly a pound4 ,we might as well say that a force of millions of pounds exists in a pound1 as that the force which will manifest itself when the coal is burned is a real thing existing in the coal4 ,what is fixed in the coal is only a certain property3 it has become fit to be the antecedent of an effect called combustion1 which partly consists in giving out1 under certain conditions1 a given definite quantity of heat4 ,we thus see that no new general conception of ,causation is introduced by the ,conservation theory4 ,the indestructibility of ,force no more interferes with the theory of ,causation than the indestructibility of ,matter1 meaning by matter the element of resistance in the sensible world4 ,it only enables us to understand better than before the nature and laws of some of the sequences4 ,this better understanding1 however1 enables us1 with ,mr4 ,bain1 to admit1 as one of the tests for distinguishing causation from mere concomitance1 the expenditure or transfer of energy4 ,if the effect1 or any part of the effect1 to be accounted for1 consists in putting matter in motion1 then any of the objects present which has lost motion has contributed to the effect2 and this is the true meaning of the proposition that the cause is that one of the antecedents which exerts active force4 #aa4 ,it is proper in this place to advert to a rather ancient doctrine respecting causation1 which has been revived during the last few years in many quarters1 and at present gives more signs of life than any other theory of causation at variance with that set forth in the preceding pages4 ,according to the theory in question1 ,mind1 or to speak move precisely1 ,will1 is the only cause of phenomena4 ,the type of ,causation1 as well as the exclusive source from which we derive the idea1 is our own voluntary agency4 ,here1 and here only 7it is said71 we have direct evidence of causation4 ,we know that we can move our bodies4 ,respecting the phenomena of inanimate nature1 we have no other direct knowledge than that of antecedence and sequence4 ,but in the case of our voluntary actions1 it is affirmed that we are conscious of power before we have experience of results4 ,an act of volition1 whether followed by an effect or not1 is accompanied by a consciousness of effort1 8of force exerted1 of power in action1 which is necessarily causal1 or causative40 ,this feeling of energy or force1 inherent in an act of will1 is knowledge a priori2 assurance1 prior to experience1 that we have the power of causing effects4 ,volition1 therefore1 it is asserted1 is something more than an unconditional antecedent2 it is a cause1 in a different sense from that in which physical phenomena are said to cause one another3 it is an ,efficient ,cause4 ,from this the transition is easy to the further doctrine1 that ,volition is the sole ,efficient ,cause of all phenomena4 8,it is inconceivable that dead force could continue unsupported for a moment beyond its creation4 ,we can not even conceive of change or phenomena without the energy of a mind40 8,the word action0 itself1 says another writer of the same school1 8has no real significance except when applied to the doings of an intelligent agent4 ,let any one conceive1 if he can1 of any power1 energy1 or force inherent in a lump of matter40 ,phenomena may have the semblance of being produced by physical causes1 but they are in reality produced1 say these writers1 by the immediate agency of mind4 ,all things which do not proceed from a human 7or1 ,i suppose1 an animal7 will proceed1 they say1 directly from divine will4 ,the earth is not moved by the combination of a centripetal and a projectile force2 this is but a mode of speaking1 which serves to facilitate our conceptions4 ,it is moved by the direct volition of an omnipotent ,being1 in a path coinciding with that which we deduce from the hypothesis of these two forces4 ,as ,i have so often observed1 the general question of the existence of ,efficient ,causes does not fall within the limits of our subject2 but a theory which represents them as capable of being subjects of human knowledge1 and which passes off as efficient causes what are only physical or phenomenal causes1 belongs as much to ,logic as to metaphysics1 and is a fit subject for discussion here4 ,to my apprehension1 a volition is not an efficient1 but simply a physical cause4 ,our will causes our bodily actions in the same sense1 and in no other1 in which cold causes ice1 or a spark causes an explosion of gunpowder4 ,the volition1 a state of our mind1 is the antecedent2 the motion of our limbs in conformity to the volition1 is the consequent4 ,this sequence ,i conceive to be not a subject of direct consciousness1 in the sense intended by the theory4 ,the antecedent1 indeed1 and the consequent1 are subjects of consciousness4 ,but the connection between them is a subject of experience4 ,i can not admit that our consciousness of the volition contains in itself any a priori knowledge that the muscular motion will follow4 ,if our nerves of motion were paralyzed1 or our muscles stiff and inflexible1 and had been so all our lives1 ,i do not see the slightest ground for supposing that we should ever 7unless by information from other people7 have known any thing of volition as a physical power1 or been conscious of any tendency in feelings of our mind to produce motions of our body1 or of other bodies4 ,i will not undertake to say whether we should in that case have had the physical feeling which ,i suppose is meant when these writers speak of 8consciousness of effort30 ,i see no reason why we should not2 since that physical feeling is probably a state of nervous sensation beginning and ending in the brain1 without involving the motory apparatus3 but we certainly should not have designated it by any term equivalent to effort1 since effort implies consciously aiming at an end1 which we should not only in that case have had no reason to do1 but could not even have had the idea of doing4 ,if conscious at all of this peculiar sensation1 we should have been conscious of it1 ,i conceive1 only as a kind of uneasiness1 accompanying our feelings of desire4 ,it is well argued by ,sir ,william ,hamilton against the theory in question1 that it 8is refuted by the consideration that between the overt fact of corporeal movement of which we are cognizant1 and the internal act of mental determination of which we are also cognizant1 there intervenes a numerous series of intermediate agencies of which we have no knowledge2 and1 consequently1 that we can have no consciousness of any causal connection between the extreme links of this chain1 the volition to move and the limb moving1 as this hypothesis asserts4 ,no one is immediately conscious1 for example1 of moving his arm through his volition4 ,previously to this ultimate movement1 muscles1 nerves1 a multitude of solid and fluid parts1 must be set in motion by the will1 but of this motion we know1 from consciousness1 absolutely nothing4 ,a person struck with paralysis is conscious of no inability in his limb to fulfill the determinations of his will2 and it is only after having willed1 and finding that his limbs do not obey his volition1 that he learns by this experience1 that the external movement does not follow the internal act4 ,but as the paralytic learns after the volition that his limbs do not obey his mind2 so it is only after volition that the man in health learns1 that his limbs do obey the mandates of his will407#abc7 ,those against whom ,i am contending have never produced1 and do not pretend to produce1 any positive evidence7#abd7 that the power of our will to move our bodies would be known to us independently of experience4 ,what they have to say on the subject is1 that the production of physical events by a will seems to carry its own explanation with it1 while the action of matter upon matter seems to require something else to explain it2 and is even1 according to them1 8inconceivable0 on any other supposition than that some will intervenes between the apparent cause and its apparent effect4 ,they thus rest their case on an appeal to the inherent laws of our conceptive faculty2 mistaking1 as ,i apprehend1 for the laws of that faculty its acquired habits1 grounded on the spontaneous tendencies of its uncultured state4 ,the succession between the will to move a limb and the actual motion is one of the most direct and instantaneous of all sequences which come under our observation1 and is familiar to every moment's experience from our earliest infancy2 more familiar than any succession of events exterior to our bodies1 and especially more so than any other case of the apparent origination 7as distinguished from the mere communication7 of motion4 ,now1 it is the natural tendency of the mind to be always attempting to facilitate its conception of unfamiliar facts by assimilating them to others which are familiar4 ,accordingly1 our voluntary acts1 being the most familiar to us of all cases of causation1 are1 in the infancy and early youth of the human race1 spontaneously taken as the type of causation in general1 and all phenomena are supposed to be directly produced by the will of some sentient being4 ,this original ,fetichism ,i shall not characterize in the words of ,hume1 or of any follower of ,hume1 but in those of a religious metaphysician1 ,dr4 ,reid1 in order more effectually to show the unanimity which exists on the subject among all competent thinkers4 8,when we turn our attention to external objects1 and begin to exercise our rational faculties about them1 we find that there are some motions and changes in them which we have power to produce1 and that there are many which must have some other cause4 ,either the objects must have life and active power1 as we have1 or they must be moved or changed by something that has life and active power1 as external objects are moved by us4 8,our first thoughts seem to be1 that the objects in which we perceive such motion have understanding and active power as we have4 #8,savages1' says the ,abb ,raynal1 #8wherever they see motion which they can not account for1 there they suppose a soul4' ,all men may be considered as savages in this respect1 until they are capable of instruction1 and of using their faculties in a more perfect manner than savages do4 8,the ,abb ,raynal's observation is sufficiently confirmed1 both from fact1 and from the structure of all languages4 8,rude nations do really believe sun1 moon1 and stars1 earth1 sea1 and air1 fountains1 and lakes1 to have understanding and active power4 ,to pay homage to them1 and implore their favor1 is a kind of idolatry natural to savages4 8,all languages carry in their structure the marks of their being formed when this belief prevailed4 ,the distinction of verbs and participles into active and passive1 which is found in all languages1 must have been originally intended to distinguish what is really active from what is merely passive2 and in all languages1 we find active verbs applied to those objects1 in which1 according to the ,abb ,raynal's observation1 savages suppose a soul4 8,thus we say the sun rises and sets1 and comes to the meridian1 the moon changes1 the sea ebbs and flows1 the winds blow4 ,languages were formed by men who believed these objects to have life and active power in themselves4 ,it was therefore proper and natural to express their motions and changes by active verbs4 8,there is no surer way of tracing the sentiments of nations before they have records1 than by the structure of their language1 which1 notwithstanding the changes produced in it by time1 will always retain some signatures of the thoughts of those by whom it was invented4 ,when we find the same sentiments indicated in the structure of all languages1 those sentiments must have been common to the human species when languages were invented4 8,when a few1 of superior intellectual abilities1 find leisure for speculation1 they begin to philosophize1 and soon discover1 that many of those objects which at first they believed to be intelligent and active are really lifeless and passive4 ,this is a very important discovery4 ,it elevates the mind1 emancipates from many vulgar superstitions1 and invites to further discoveries of the same kind4 8,as philosophy advances1 life and activity in natural objects retires1 and leaves them dead and inactive4 ,instead of moving voluntarily1 we find them to be moved necessarily2 instead of acting1 we find them to be acted upon2 and ,nature appears as one great machine1 where one wheel is turned by another1 that by a third2 and how far this necessary succession may reach1 the philosopher does not know407#abe7 ,there is1 then1 a spontaneous tendency of the intellect to account to itself for all cases of causation by assimilating them to the intentional acts of voluntary agents like itself4 ,this is the instinctive philosophy of the human mind in its earliest stage1 before it has become familiar with any other invariable sequences than those between its own volitions or those of other human beings and their voluntary acts4 ,as the notion of fixed laws of succession among external phenomena gradually establishes itself1 the propensity to refer all phenomena to voluntary agency slowly gives way before it4 ,the suggestions1 however1 of daily life continuing to be more powerful than those of scientific thought1 the original instinctive philosophy maintains its ground in the mind1 underneath the growths obtained by cultivation1 and keeps up a constant resistance to their throwing their roots deep into the soil4 ,the theory against which ,i am contending derives its nourishment from that substratum4 ,its strength does not lie in argument1 but in its affinity to an obstinate tendency of the infancy of the human mind4 ,that this tendency1 however1 is not the result of an inherent mental law1 is proved by superabundant evidence4 ,the history of science1 from its earliest dawn1 shows that mankind have not been unanimous in thinking either that the action of matter upon matter was not conceivable1 or that the action of mind upon matter was4 ,to some thinkers1 and some schools of thinkers1 both in ancient and in modern times1 this last has appeared much more inconceivable than the former4 ,sequences entirely physical and material1 as soon as they had become sufficiently familiar to the human mind1 came to be thought perfectly natural1 and were regarded not only as needing no explanation themselves1 but as being capable of affording it to others1 and even of serving as the ultimate explanation of things in general4 ,one of the ablest recent supporters of the ,volitional theory has furnished an explanation1 at once historically true and philosophically acute1 of the failure of the ,greek philosophers in physical inquiry1 in which1 as ,i conceive1 he unconsciously depicts his own state of mind4 8,their stumbling-block was one as to the nature of the evidence they had to expect for their conviction4444 ,they had not seized the idea that they must not expect to understand the processes of outward causes1 but only their results2 and consequently1 the whole physical philosophy of the ,greeks was an attempt to identify mentally the effect with its cause1 to feel after some not only necessary but natural connection1 where they meant by natural that which would per se carry some presumption to their own mind4444 ,they wanted to see some reason why the physical antecedent should produce this particular consequent1 and their only attempts were in directions where they could find such reasons407#abf7 ,in other words1 they were not content merely to know that one phenomenon was always followed by another2 they thought that they had not attained the true aim of science1 unless they could perceive something in the nature of the one phenomenon from which it might have been known or presumed previous to trial that it would be followed by the other3 just what the writer1 who has so clearly pointed out their error1 thinks that he perceives in the nature of the phenomenon ,volition4 ,and to complete the statement of the case1 he should have added that these early speculators not only made this their aim1 but were quite satisfied with their success in it2 not only sought for causes which should carry in their mere statement evidence of their efficiency1 but fully believed that they had found such causes4 ,the reviewer can see plainly that this was an error1 because he does not believe that there exist any relations between material phenomena which can account for their producing one another2 but the very fact of the persistency of the ,greeks in this error1 shows that their minds were in a very different state3 they were able to derive from the assimilation of physical facts to other physical facts1 the kind of mental satisfaction which we connect with the word explanation1 and which the reviewer would have us think can only be found in referring phenomena to a will4 ,when ,thales and ,hippo held that moisture was the universal cause1 and external element1 of which all other things were but the infinitely various sensible manifestations2 when ,anaximenes predicated the same thing of air1 ,pythagoras of numbers1 and the like1 they all thought that they had found a real explanation2 and were content to rest in this explanation as ultimate4 ,the ordinary sequences of the external universe appeared to them1 no less than to their critic1 to be inconceivable without the supposition of some universal agency to connect the antecedents with the consequents2 but they did not think that ,volition1 exerted by minds1 was the only agency which fulfilled this requirement4 ,moisture1 or air1 or numbers1 carried to their minds a precisely similar impression of making intelligible what was otherwise inconceivable1 and gave the same full satisfaction to the demands of their conceptive faculty4 ,it was not the ,greeks alone1 who 8wanted to see some reason why the physical antecedent should produce this particular consequent10 some connection 8which would per se carry some presumption to their own mind40 ,among modern philosophers1 ,leibnitz laid it down as a self-evident principle that all physical causes without exception must contain in their own nature something which makes it intelligible that they should be able to produce the effects which they do produce4 ,far from admitting ,volition as the only kind of cause which carried internal evidence of its own power1 and as the real bond of connection between physical antecedents and their consequents1 he demanded some naturally and per se efficient physical antecedent as the bond of connection between ,volition itself and its effects4 ,he distinctly refused to admit the will of ,god as a sufficient explanation of any thing except miracles2 and insisted upon finding something that would account better for the phenomena of nature than a mere reference to divine volition47#abg7 ,again1 and conversely1 the action of mind upon matter 7which1 we are now told1 not only needs no explanation itself1 but is the explanation of all other effects71 has appeared to some thinkers to be itself the grand inconceivability4 ,it was to get over this very difficulty that the ,cartesians invented the system of ,occasional ,causes4 ,they could not conceive that thoughts in a mind could produce movements in a body1 or that bodily movements could produce thoughts4 ,they could see no necessary connection1 no relation a priori1 between a motion and a thought4 ,and as the ,cartesians1 more than any other school of philosophical speculation before or since1 made their own minds the measure of all things1 and refused1 on principle1 to believe that ,nature had done what they were unable to see any reason why she must do1 they affirmed it to be impossible that a material and a mental fact could be causes one of another4 ,they regarded them as mere ,occasions on which the real agent1 ,god1 thought fit to exert his power as a ,cause4 ,when a man wills to move his foot1 it is not his will that moves it1 but ,god 7they said7 moves it on the occasion of his will4 ,god1 according to this system1 is the only efficient cause1 not qu mind1 or qu endowed with volition1 but qu omnipotent4 ,this hypothesis was1 as ,i said1 originally suggested by the supposed inconceivability of any real mutual action between ,mind and ,matter2 but it was afterward extended to the action of ,matter upon ,matter1 for on a nicer examination they found this inconceivable too1 and therefore1 according to their logic1 impossible4 ,the deus ex machin was ultimately called in to produce a spark on the occasion of a flint and steel coming together1 or to break an egg on the occasion of its falling on the ground4 ,all this1 undoubtedly1 shows that it is the disposition of mankind in general1 not to be satisfied with knowing that one fact is invariably antecedent and another consequent1 but to look out for something which may seem to explain their being so4 ,but we also see that this demand may be completely satisfied by an agency purely physical1 provided it be much more familiar than that which it is invoked to explain4 ,to ,thales and ,anaximenes1 it appeared inconceivable that the antecedents which we see in nature should produce the consequents2 but perfectly natural that water1 or air1 should produce them4 ,the writers whom ,i oppose declare this inconceivable1 but can conceive that mind1 or volition1 is per se an efficient cause3 while the ,cartesians could not conceive even that1 but peremptorily declared that no mode of production of any fact whatever was conceivable1 except the direct agency of an omnipotent being2 thus giving additional proof of what finds new confirmation in every stage of the history of science3 that both what persons can1 and what they can not1 conceive1 is very much an affair of accident1 and depends altogether on their experience1 and their habits of thought2 that by cultivating the requisite associations of ideas1 people may make themselves unable to conceive any given thing2 and may make themselves able to conceive most things1 however inconceivable these may at first appear2 and the same facts in each person's mental history which determine what is or is not conceivable to him1 determine also which among the various sequences in nature will appear to him so natural and plausible1 as to need no other proof of their existence2 to be evident by their own light1 independent equally of experience and of explanation4 ,by what rule is any one to decide between one theory of this description and another8 ,the theorists do not direct us to any external evidence2 they appeal each to his own subjective feelings4 ,one says1 the succession ,c ,b appears to me more natural1 conceivable1 and credible per se1 than the succession ,a ,b2 you are therefore mistaken in thinking that ,b depends upon ,a2 ,i am certain1 though ,i can give no other evidence of it1 that ,c comes in between ,a and ,b1 and is the real and only cause of ,b4 ,the other answers1 the successions ,c ,b and ,a ,b appear to me equally natural and conceivable1 or the latter more so than the former3 ,a is quite capable of producing ,b without any other intervention4 ,a third agrees with the first in being unable to conceive that ,a can produce ,b1 but finds the sequence ,d ,b still more natural than ,c ,b1 or of nearer kin to the subject-matter1 and prefers his ,d theory to the ,c theory4 ,it is plain that there is no universal law operating here1 except the law that each person's conceptions are governed and limited by his individual experiences and habits of thought4 ,we are warranted in saying of all three1 what each of them already believes of the other two1 namely1 that they exalt into an original law of the human intellect and of outward nature one particular sequence of phenomena1 which appears to them more natural and more conceivable than other sequences1 only because it is more familiar4 ,and from this judgment ,i am unable to except the theory1 that ,volition is an ,efficient ,cause4 ,i am unwilling to leave the subject without adverting to the additional fallacy contained in the corollary from this theory2 in the inference that because ,volition is an efficient cause1 therefore it is the only cause1 and the direct agent in producing even what is apparently produced by something else4 ,volitions are not known to produce any thing directly except nervous action1 for the will influences even the muscles only through the nerves4 ,though it were granted1 then1 that every phenomenon has an efficient1 and not merely a phenomenal cause1 and that volition1 in the case of the peculiar phenomena which are known to be produced by it1 is that efficient cause2 are we therefore to say1 with these writers1 that since we know of no other efficient cause1 and ought not to assume one without evidence1 there is no other1 and volition is the direct cause of all phenomena8 ,a more outrageous stretch of inference could hardly be made4 ,because among the infinite variety of the phenomena of nature there is one1 namely1 a particular mode of action of certain nerves1 which has for its cause1 and as we are now supposing for its efficient cause1 a state of our mind2 and because this is the only efficient cause of which we are conscious1 being the only one of which in the nature of the case we can be conscious1 since it is the only one which exists within ourselves2 does this justify us in concluding that all other phenomena must have the same kind of efficient cause with that one eminently special1 narrow1 and peculiarly human or animal1 phenomenon8 ,the nearest parallel to this specimen of generalization is suggested by the recently revived controversy on the old subject of ,plurality of ,worlds1 in which the contending parties have been so conspicuously successful in overthrowing one another4 ,here also we have experience only of a single case1 that of the world in which we live1 but that this is inhabited we know absolutely1 and without possibility of doubt4 ,now if on this evidence any one were to infer that every heavenly body without exception1 sun1 planet1 satellite1 comet1 fixed star or nebula1 is inhabited1 and must be so from the inherent constitution of things1 his inference would exactly resemble that of the writers who conclude that because volition is the efficient cause of our own bodily motions1 it must be the efficient cause of every thing else in the universe4 ,it is true there are cases in which1 with acknowledged propriety1 we generalize from a single instance to a multitude of instances4 ,but they must be instances which resemble the one known instance1 and not such as have no circumstance in common with it except that of being instances4 ,i have1 for example1 no direct evidence that any creature is alive except myself1 yet ,i attribute1 with full assurance1 life and sensation to other human beings and animals4 ,but ,i do not conclude that all other things are alive merely because ,i am4 ,i ascribe to certain other creatures a life like my own1 because they manifest it by the same sort of indications by which mine is manifested4 ,i find that their phenomena and mine conform to the same laws1 and it is for this reason that ,i believe both to arise from a similar cause4 ,accordingly ,i do not extend the conclusion beyond the grounds for it4 ,earth1 fire1 mountains1 trees1 are remarkable agencies1 but their phenomena do not conform to the same laws as my actions do1 and ,i therefore do not believe earth or fire1 mountains or trees1 to possess animal life4 ,but the supporters of the ,volition ,theory ask us to infer that volition causes every thing1 for no reason except that it causes one particular thing2 although that one phenomenon1 far from being a type of all natural phenomena1 is eminently peculiar2 its laws bearing scarcely any resemblance to those of any other phenomenon1 whether of inorganic or of organic nature4 ,,note ,,supplementary ,,to ,,the ,,preceding ,,chapter4 ,the author of the ,second ,burnett ,prize ,essay 7,dr4 ,tulloch71 who has employed a considerable number of pages in controverting the doctrines of the preceding chapter1 has somewhat surprised me by denying a fact1 which ,i imagined too well known to require proof--that there have been philosophers who found in physical explanations of phenomena the same complete mental satisfaction which we are told is only given by volitional explanation1 and others who denied the ,volitional ,theory on the same ground of inconceivability on which it is defended4 ,the assertion of the ,essayist is countersigned still more positively by an able reviewer of the ,essay37#abh7 8,two illustrations10 says the reviewer1 8are advanced by ,mr4 ,mill3 the case of ,thales and ,anaximenes1 stated by him to have maintained1 the one ,moisture and the other ,air to be the origin of all things2 and that of ,descartes and ,leibnitz1 whom he asserts to have found the action of ,mind upon ,matter the grand inconceivability4 ,in counter-statement as to the first of these cases the author shows--what we believe now hardly admits of doubt--that the ,greek philosophers distinctly recognized as beyond and above their primal material source1 the 1 or ,divine ,intelligence1 as the efficient and originating ,source of all2 and as to the second1 by proof that it was the mode1 not the fact1 of that action on matter1 which was represented as inconceivable40 ,a greater quantity of historical error has seldom been comprised in a single sentence4 ,with regard to ,thales1 the assertion that he considered water as a mere material in the hands of rests on a passage of ,cicero de ,natur ,deorum2 and whoever will refer to any of the accurate historians of philosophy1 will find that they treat this as a mere fancy of ,cicero1 resting on no authority1 opposed to all the evidence2 and make surmises as to the manner in which ,cicero may have been led into the error4 7,see ,rutter1 vol4 i41 p4 #baa1 #b;d ed42 ,brandis1 vol4 i41 pp4 #aah-i1 #ast ed42 ,preller1 ,historia ,philosophi ,grco-,roman1 p4 #aj4 8,schiefe ,ansicht1 durchaus zu verwerfen20 8augenscheinlich folgernd statt zu berichten20 8quibus vera sententia ,thaletis plane detorquetur10 are the expressions of these writers47 ,as for ,anaximenes1 he even according to ,cicero1 maintained1 not that air was the material out of which ,god made the world1 but that the air was a god3 8,anaximenes ara deum statuit20 or1 according to ,st4 ,augustine1 that it was the material out of which the gods were made2 8non tamen ab ipsis ,diis arem factum1 sed ipsos ex are ortos credidit40 ,those who are not familiar with the metaphysical terminology of antiquity1 must not be misled by finding it stated that ,anaximenes attributed 7translated soul1 or life7 to his universal element1 the air4 ,the ,greek philosophers acknowledged several kinds of 1 the nutritive1 the sensitive1 and the intellective47#abi7 ,even the moderns1 with admitted correctness1 attribute life to plants4 ,as far as we can make out the meaning of ,anaximenes1 he made choice of ,air as the universal agent1 on the ground that it is perpetually in motion1 without any apparent cause external to itself3 so that he conceived it as exercising spontaneous force1 and as the principle of life and activity in all things1 men and gods inclusive4 ,if this be not representing it as the ,efficient ,cause the dispute altogether has no meaning4 ,if either ,anaximenes1 or ,thales1 or any of their contemporaries1 had held the doctrine that was the ,efficient ,cause1 that doctrine could not have been reputed1 as it was throughout antiquity1 to have originated with ,anaxagoras4 ,the testimony of ,aristotle1 in the first book of his ,metaphysics1 is perfectly decisive with respect to these early speculations4 ,after enumerating four kinds of causes1 or rather four different meanings of the word ,cause1 viz41 the ,essence of a thing1 the ,matter of it1 the ,origin of ,motion 7,efficient ,cause71 and the ,end or ,final ,cause1 he proceeds to say1 that most of the early philosophers recognized only the second kind of ,cause1 the ,matter of a thing1 4 ,as his first example he specifies ,thales1 whom he describes as taking the lead in this view of the subject1 1 and goes on to ,hippon1 ,anaximenes1 ,diogenes 7of ,apollonia71 ,hippasus of ,metapontum1 ,heraclitus1 and ,empedocles4 ,anaxagoras1 however 7he proceeds to say71 taught a different doctrine1 as we know1 and it is alleged that ,hermotimus of ,clazomen taught it before him4 ,anaxagoras represented1 that even if these various theories of the universal material were true1 there would be need of some other cause to account for the transformations of the materials1 since the material can not originate its own changes3 2 1 1 1 viz41 the other kind of cause1 --an ,efficient ,cause4 ,aristotle expresses great approbation of this doctrine 7which he says made its author appear the only sober man among persons raving1 72 but while describing the influence which it exercised over subsequent speculation1 he remarks that the philosophers against whom this1 as he thinks1 insuperable difficulty was urged1 had not felt it to be any difficulty3 4 ,it is surely unnecessary to say more in proof of the matter of fact which ,dr4 ,tulloch and his reviewer disbelieve4 ,having pointed out what he thinks the error of these early speculators in not recognizing the need of an efficient cause1 ,aristotle goes on to mention two other efficient causes to which they might have had recourse1 instead of intelligence3 1 chance1 and 1 spontaneity4 ,he indeed puts these aside as not sufficiently worthy causes for the order in the universe1 2 but he does not reject them as incapable of producing any effect1 but only as incapable of producing that effect4 ,he himself recognizes and as co-ordinate agents with ,mind in producing the phenomena of the universe2 the department allotted to them being composed of all the classes of phenomena which are not supposed to follow any uniform law4 ,by thus including ,chance among efficient causes1 ,aristotle fell into an error which philosophy has now outgrown1 but which is by no means so alien to the spirit even of modern speculation as it may at first sight appear4 ,up to quite a recent period philosophers went on ascribing1 and many of them have not yet ceased to ascribe1 a real existence to the results of abstraction4 ,chance could make out as good a title to that dignity as many other of the mind's abstract creations3 it had had a name given to it1 and why should it not be a reality8 ,as for 1 it is recognized even yet as one of the modes of origination of phenomena by all those thinkers who maintain what is called the ,freedom of the ,will4 ,the same self-determining power which that doctrine attributes to volitions1 was supposed by the ancients to be possessed also by some other natural phenomena3 a circumstance which throws considerable light on more than one of the supposed invincible necessities of belief4 ,i have introduced it here1 because this belief of ,aristotle1 or rather of the ,greek philosophers generally1 is as fatal as the doctrines of ,thales and the ,ionic school to the theory that the human mind is compelled by its constitution to conceive volition as the origin of all force1 and the efficient cause of all phenomena47#acj7 ,with regard to the modern philosophers 7,leibnitz and the ,cartesians7 whom ,i had cited as having maintained that the action of mind upon matter1 so far from being the only conceivable origin of material phenomena1 is itself inconceivable2 the attempt to rebut this argument by asserting that the mode1 not the fact1 of the action of mind on matter was represented as inconceivable1 is an abuse of the privilege of writing confidently about authors without reading them2 for any knowledge whatever of ,leibnitz would have taught those who thus speak of him1 that the inconceivability of the mode1 and the impossibility of the thing1 were in his mind convertible expressions4 ,what was his famous ,principle of the ,sufficient ,reason1 the very corner-stone of his ,philosophy1 from which the ,pre-established ,harmony1 the doctrine of ,monads1 and all the opinions most characteristic of ,leibnitz1 were corollaries8 ,it was1 that nothing exists1 the existence of which is not capable of being proved and explained a priori2 the proof and explanation in the case of contingent facts being derived from the nature of their causes2 which could not be the causes unless there was something in their nature showing them to be capable of producing those particular effects4 ,and this 8something0 which accounts for the production of physical effects1 he was able to find in many physical causes1 but could not find it in any finite minds1 which therefore he unhesitatingly asserted to be incapable of producing any physical effects whatever4 8,on ne saurait concevoir10 he says1 8une action rciproque de la matire et de l'intelligence l'une sur l'autre10 and there is therefore 7he contends7 no choice but between the ,occasional ,causes of the ,cartesians and his own ,pre-established ,harmony1 according to which there is no more connection between our volitions and our muscular actions than there is between two clocks which are wound up to strike at the same instant4 ,but he felt no similar difficulty as to physical causes2 and throughout his speculations1 as in the passage ,i have already cited respecting gravitation1 he distinctly refuses to consider as part of the order of nature any fact which is not explicable from the nature of its physical cause4 ,with regard to the ,cartesians 7not ,descartes2 ,i did not make that mistake1 though the reviewer of ,dr4 ,tulloch's ,essay attributes it to me7 ,i take a passage almost at random from ,malebranche1 who is the best known of the ,cartesians1 and1 though not the inventor of the system of ,occasional ,causes1 is its principal expositor4 ,in ,part ,,ii41 chap4 iii41 of his ,sixth ,book1 having first said that matter can not have the power of moving itself1 he proceeds to argue that neither can mind have the power of moving it4 8,quand on examine l'ide que l'on a de tous les esprits finis1 on ne voit point de liaison ncessaire entre leur volont et le mouvement de quelque corps que ce soit1 on voit au contraire qu'il n'y en a point1 et qu'il n'y en peut avoir0 7there is nothing in the idea of finite mind which can account for its causing the motion of a body72 8on doit aussi conclure1 si on vent raisonner selon ses lumires1 qu'il n'y a aucun esprit cr qui puisse remuer quelque corps que ce soit comme cause vritable on principale1 de mme que l'on a dit qu'aucun corps ne se pouvait remuer soi-mme30 thus the idea of ,mind is according to him as incompatible as the idea of ,matter with the exercise of active force4 ,but when1 he continues1 we consider not a created but a ,divine ,mind1 the case is altered2 for the idea of a ,divine ,mind includes omnipotence2 and the idea of omnipotence does contain the idea of being able to move bodies4 ,thus it is the nature of omnipotence which renders the motion of bodies even by the ,divine ,mind credible or conceivable1 while1 so far as depended on the mere nature of mind1 it would have been inconceivable and incredible4 ,if ,malebranche had not believed in an omnipotent ,being1 he would have held all action of mind on body to be a demonstrated impossibility47#aca7 ,a doctrine more precisely the reverse of the ,volitional theory of causation can not well be imagined4 ,the ,volitional theory is1 that we know by intuition or by direct experience the action of our own mental volitions on matter2 that we may hence infer all other action upon matter to be that of volition1 and might thus know1 without any other evidence1 that matter is under the government of a ,divine ,mind4 ,leibnitz and the ,cartesians1 on the contrary1 maintain that our volitions do not and can not act upon matter1 and that it is only the existence of an all-governing ,being1 and that ,being omnipotent1 which can account for the sequence between our volitions and our bodily actions4 ,when we consider that each of these two theories1 which1 as theories of causation1 stand at the opposite extremes of possible divergence from one another1 invokes not only as its evidence1 but as its sole evidence1 the absolute inconceivability of any theory but itself1 we are enabled to measure the worth of this kind of evidence3 and when we find the ,volitional theory entirely built upon the assertion that by our mental constitution we are compelled to recognize our volitions as efficient causes1 and then find other thinkers maintaining that we know that they are not and can not be such causes1 and can not conceive them to be so1 ,i think we have a right to say that this supposed law of our mental constitution does not exist4 ,dr4 ,tulloch 7pp4 #de-dg7 thinks it a sufficient answer to this1 that ,leibnitz and the ,cartesians were ,theists1 and believed the will of ,god to be an efficient cause4 ,doubtless they did1 and the ,cartesians even believed 7though ,leibnitz did not7 that it is the only such cause4 ,dr4 ,tulloch mistakes the nature of the question4 ,i was not writing on ,theism1 as ,dr4 ,tulloch is1 but against a particular theory of causation1 which1 if it be unfounded1 can give no effective support to ,theism or to any thing else4 ,i found it asserted that volition is the only efficient cause1 on the ground that no other efficient cause is conceivable4 ,to this assertion ,i oppose the instances of ,leibnitz and of the ,cartesians1 who affirmed with equal positiveness that volition as an efficient cause is itself not conceivable1 and that omnipotence1 which renders all things conceivable1 can alone take away the impossibility4 ,this ,i thought1 and think1 a conclusive answer to the argument on which this theory of causation avowedly depends4 ,but ,i certainly did not imagine that ,theism was bound up with that theory2 nor expected to be charged with denying ,leibnitz and the ,cartesians to be ,theists because ,i denied that they held the theory4 ,chapter ,,vi4 ,on ,the ,composition ,of ,causes4 #a4 ,to complete the general notion of causation on which the rules of experimental inquiry into the laws of nature must be founded1 one distinction still remains to be pointed out3 a distinction so radical1 and of so much importance1 as to require a chapter to itself4 ,the preceding discussions have rendered us familiar with the case in which several agents1 or causes1 concur as conditions to the production of an effect2 a case1 in truth1 almost universal1 there being very few effects to the production of which no more than one agent contributes4 ,suppose1 then1 that two different agents1 operating jointly1 are followed1 under a certain set of collateral conditions1 by a given effect4 ,if either of these agents1 instead of being joined with the other1 had operated alone1 under the same set of conditions in all other respects1 some effect would probably have followed1 which would have been different from the joint effect of the two1 and more or less dissimilar to it4 ,now1 if we happen to know what would be the effect of each cause when acting separately from the other1 we are often able to arrive deductively1 or a priori1 at a correct prediction of what will arise from their conjunct agency4 ,to render this possible1 it is only necessary that the same law which expresses the effect of each cause acting by itself1 shall also correctly express the part due to that cause of the effect which follows from the two together4 ,this condition is realized in the extensive and important class of phenomena commonly called mechanical1 namely the phenomena of the communication of motion 7or of pressure1 which is tendency to motion7 from one body to another4 ,in this important class of cases of causation1 one cause never1 properly speaking1 defeats or frustrates another2 both have their full effect4 ,if a body is propelled in two directions by two forces1 one tending to drive it to the north and the other to the east1 it is caused to move in a given time exactly as far in both directions as the two forces would separately have carried it2 and is left precisely where it would have arrived if it had been acted upon first by one of the two forces1 and afterward by the other4 ,this law of nature is called1 in dynamics1 the principle of the ,composition of ,forces2 and in imitation of that well-chosen expression1 ,i shall give the name of the ,composition of ,causes to the principle which is exemplified in all cases in which the joint effect of several causes is identical with the sum of their separate effects4 ,this principle1 however1 by no means prevails in all departments of the field of nature4 ,the chemical combination of two substances produces1 as is well known1 a third substance1 with properties different from those of either of the two substances separately1 or of both of them taken together4 ,not a trace of the properties of hydrogen or of oxygen is observable in those of their compound1 water4 ,the taste of sugar of lead is not the sum of the tastes of its component elements1 acetic acid and lead or its oxide2 nor is the color of blue vitriol a mixture of the colors of sulphuric acid and copper4 ,this explains why mechanics is a deductive or demonstrative science1 and chemistry not4 ,in the one1 we can compute the effects of combinations of causes1 whether real or hypothetical1 from the laws which we know to govern those causes when acting separately1 because they continue to observe the same laws when in combination which they observe when separate3 whatever would have happened in consequence of each cause taken by itself1 happens when they are together1 and we have only to cast up the results4 ,not so in the phenomena which are the peculiar subject of the science of chemistry4 ,there most of the uniformities to which the causes conform when separate1 cease altogether when they are conjoined2 and we are not1 at least in the present state of our knowledge1 able to foresee what result will follow from any new combination until we have tried the specific experiment4 ,if this be true of chemical combinations1 it is still more true of those far more complex combinations of elements which constitute organized bodies2 and in which those extraordinary new uniformities arise which are called the laws of life4 ,all organized bodies are composed of parts similar to those composing inorganic nature1 and which have even themselves existed in an inorganic state2 but the phenomena of life1 which result from the juxtaposition of those parts in a certain manner1 bear no analogy to any of the effects which would be produced by the action of the component substances considered as mere physical agents4 ,to whatever degree we might imagine our knowledge of the properties of the several ingredients of a living body to be extended and perfected1 it is certain that no mere summing up of the separate actions of those elements will ever amount to the action of the living body itself4 ,the tongue1 for instance1 is1 like all other parts of the animal frame1 composed of gelatine1 fibrine1 and other products of the chemistry of digestion2 but from no knowledge of the properties of those substances could we ever predict that it could taste1 unless gelatine or fibrine could themselves taste2 for no elementary fact can be in the conclusion which was not in the premises4 ,there are thus two different modes of the conjunct action of causes2 from which arise two modes of conflict1 or mutual interference1 between laws of nature4 ,suppose1 at a given point of time and space1 two or more causes1 which1 if they acted separately1 would produce effects contrary1 or at least conflicting with each other2 one of them tending to undo1 wholly or partially1 what the other tends to do4 ,thus the expansive force of the gases generated by the ignition of gunpowder tends to project a bullet toward the sky1 while its gravity tends to make it fall to the ground4 ,a stream running into a reservoir at one end tends to fill it higher and higher1 while a drain at the other extremity tends to empty it4 ,now1 in such cases as these1 even if the two causes which are in joint action exactly annul one another1 still the laws of both are fulfilled2 the effect is the same as if the drain had been open for half an hour first17#acb7 and the stream had flowed in for as long afterward4 ,each agent produces the same amount of effect as if it had acted separately1 though the contrary effect which was taking place during the same time obliterated it as fast as it was produced4 ,here1 then1 are two causes1 producing by their joint operations an effect which at first seems quite dissimilar to those which they produce separately1 but which on examination proves to be really the sum of those separate effects4 ,it will be noticed that we here enlarge the idea of the sum of two effects1 so as to include what is commonly called their difference1 but which is in reality the result of the addition of opposites2 a conception to which mankind are indebted for that admirable extension of the algebraical calculus1 which has so vastly increased its powers as an instrument of discovery1 by introducing into its reasonings 7with the sign of subtraction prefixed1 and under the name of ,negative ,quantities7 every description whatever of positive phenomena1 provided they are of such a quality in reference to those previously introduced1 that to add the one is equivalent to subtracting an equal quantity of the other4 ,there is1 then1 one mode of the mutual interference of laws of nature1 in which1 even when the concurrent causes annihilate each other's effects1 each exerts its full efficacy according to its own law--its law as a separate agent4 ,but in the other description of cases1 the agencies which are brought together cease entirely1 and a totally different set of phenomena arise3 as in the experiment of two liquids which1 when mixed in certain proportions1 instantly become1 not a larger amount of liquid1 but a solid mass4 #b4 ,this difference between the case in which the joint effect of causes is the sum of their separate effects1 and the case in which it is heterogeneous to them--between laws which work together without alteration1 and laws which1 when called upon to work together1 cease and give place to others--is one of the fundamental distinctions in nature4 ,the former case1 that of the ,composition of ,causes1 is the general one2 the other is always special and exceptional4 ,there are no objects which do not1 as to some of their phenomena1 obey the principle of the ,composition of ,causes2 none that have not some laws which are rigidly fulfilled in every combination into which the objects enter4 ,the weight of a body1 for instance1 is a property which it retains in all the combinations in which it is placed4 ,the weight of a chemical compound1 or of an organized body1 is equal to the sum of the weights of the elements which compose it4 ,the weight either of the elements or of the compound will vary1 if they be carried farther from their centre of attraction1 or brought nearer to it2 but whatever effects the one effects the other4 ,they always remain precisely equal4 ,so1 again1 the component parts of a vegetable or animal substance do not lose their mechanical and chemical properties as separate agents1 when1 by a peculiar mode of juxtaposition1 they1 as an aggregate whole1 acquire physiological or vital properties in addition4 ,those bodies continue1 as before1 to obey mechanical and chemical laws1 in so far as the operation of those laws is not counteracted by the new laws which govern them as organized beings2 when1 in short1 a concurrence of causes takes place which calls into action new laws bearing no analogy to any that we can trace in the separate operation of the causes1 the new laws1 while they supersede one portion of the previous laws1 may co-exist with another portion1 and may even compound the effect of those previous laws with their own4 ,again1 laws which were themselves generated in the second mode1 may generate others in the first4 ,though there are laws which1 like those of chemistry and physiology1 owe their existence to a breach of the principle of ,composition of ,causes1 it does not follow that these peculiar1 or1 as they might be termed1 heteropathic laws1 are not capable of composition with one another4 ,the causes which by one combination have had their laws altered1 may carry their new laws with them unaltered into their ulterior combinations4 ,and hence there is no reason to despair of ultimately raising chemistry and physiology to the condition of deductive sciences2 for though it is impossible to deduce all chemical and physiological truths from the laws or properties of simple substances or elementary agents1 they may possibly be deducible from laws which commence when these elementary agents are brought together into some moderate number of not very complex combinations4 ,the ,laws of ,life will never be deducible from the mere laws of the ingredients1 but the prodigiously complex ,facts of ,life may all be deducible from comparatively simple laws of life2 which laws 7depending indeed on combinations1 but on comparatively simple combinations1 of antecedents7 may1 in more complex circumstances1 be strictly compounded with one another1 and with the physical and chemical laws of the ingredients4 ,the details of the vital phenomena1 even now1 afford innumerable exemplifications of the ,composition of ,causes2 and in proportion as these phenomena are more accurately studied1 there appears more reason to believe that the same laws which operate in the simpler combinations of circumstances do1 in fact1 continue to be observed in the more complex4 ,this will be found equally true in the phenomena of mind2 and even in social and political phenomena1 the results of the laws of mind4 ,it is in the case of chemical phenomena that the least progress has yet been made in bringing the special laws under general ones from which they may be deduced2 but there are even in chemistry many circumstances to encourage the hope that such general laws will hereafter be discovered4 ,the different actions of a chemical compound will never1 undoubtedly1 be found to be the sums of the actions of its separate elements2 but there may exist1 between the properties of the compound and those of its elements1 some constant relation1 which1 if discoverable by a sufficient induction1 would enable us to foresee the sort of compound which will result from a new combination before we have actually tried it1 and to judge of what sort of elements some new substance is compounded before we have analyzed it4 ,the law of definite proportions1 first discovered in its full generality by ,dalton1 is a complete solution of this problem in one1 though but a secondary aspect1 that of quantity2 and in respect to quality1 we have already some partial generalizations1 sufficient to indicate the possibility of ultimately proceeding farther4 ,we can predicate some common properties of the kind of compounds which result from the combination1 in each of the small number of possible proportions1 of any acid whatever with any base4 ,we have also the curious law1 discovered by ,berthollet1 that two soluble salts mutually decompose one another whenever the new combinations which result produce an insoluble compound1 or one less soluble than the two former4 ,another uniformity is that called the law of isomorphism2 the identity of the crystalline forms of substances which possess in common certain peculiarities of chemical composition47#acc7 ,thus it appears that even heteropathic laws1 such laws of combined agency as are not compounded of the laws of the separate agencies1 are yet1 at least in some cases1 derived from them according to a fixed principle4 ,there may1 therefore1 be laws of the generation of laws from others dissimilar to them2 and in chemistry1 these undiscovered laws of the dependence of the properties of the compound on the properties of its elements1 may1 together with the laws of the elements themselves1 furnish the premises by which the science is perhaps destined one day to be rendered deductive4 ,it would seem1 therefore1 that there is no class of phenomena in which the ,composition of ,causes does not obtain3 that as a general rule1 causes in combination produce exactly the same effects as when acting singly3 but that this rule1 though general1 is not universal3 that in some instances1 at some particular points in the transition from separate to united action1 the laws change1 and an entirely new set of effects are either added to1 or take the place of1 those which arise from the separate agency of the same causes3 the laws of these new effects being again susceptible of composition1 to an indefinite extent1 like the laws which they superseded4 #c4 ,that effects are proportional to their causes is laid down by some writers as an axiom in the theory of causation2 and great use is sometimes made of this principle in reasonings respecting the laws of nature1 though it is encumbered with many difficulties and apparent exceptions1 which much ingenuity has been expended in showing not to be real ones4 ,this proposition1 in so far as it is true1 enters as a particular case into the general principle of the ,composition of ,causes2 the causes compounded being1 in this instance1 homogeneous2 in which case1 if in any1 their joint effect might be expected to be identical with the sum of their separate effects4 ,if a force equal to one hundred weight will raise a certain body along an inclined plane1 a force equal to two hundred weight will raise two bodies exactly similar1 and thus the effect is proportional to the cause4 ,but does not a force equal to two hundred weight actually contain in itself two forces each equal to one hundred weight1 which1 if employed apart1 would separately raise the two bodies in question8 ,the fact1 therefore1 that when exerted jointly they raise both bodies at once1 results from the ,composition of ,causes1 and is a mere instance of the general fact that mechanical forces are subject to the law of ,composition4 ,and so in every other case which can be supposed4 ,for the doctrine of the proportionality of effects to their causes can not of course be applicable to cases in which the augmentation of the cause alters the kind of effect2 that is1 in which the surplus quantity superadded to the cause does not become compounded with it1 but the two together generate an altogether new phenomenon4 ,suppose that the application of a certain quantity of heat to a body merely increases its bulk1 that a double quantity melts it1 and a triple quantity decomposes it3 these three effects being heterogeneous1 no ratio1 whether corresponding or not to that of the quantities of heat applied1 can be established between them4 ,thus the supposed axiom of the proportionality of effects to their causes fails at the precise point where the principle of the ,composition of ,causes also fails2 viz41 where the concurrence of causes is such as to determine a change in the properties of the body generally1 and render it subject to new laws1 more or less dissimilar to those to which it conformed in its previous state4 ,the recognition1 therefore1 of any such law of proportionality is superseded by the more comprehensive principle1 in which as much of it as is true is implicitly asserted47#acd7 ,the general remarks on causation1 which seemed necessary as an introduction to the theory of the inductive process1 may here terminate4 ,that process is essentially an inquiry into cases of causation4 ,all the uniformities which exist in the succession of phenomena1 and most of the uniformities in their co-existence1 are either1 as we have seen1 themselves laws of causation1 or consequences resulting from1 and corollaries capable of being deduced from1 such laws4 ,if we could determine what causes are correctly assigned to what effects1 and what effects to what causes1 we should be virtually acquainted with the whole course of nature4 ,all those uniformities which are mere results of causation might then be explained and accounted for2 and every individual fact or event might be predicted1 provided we had the requisite data1 that is1 the requisite knowledge of the circumstances which1 in the particular instance1 preceded it4 ,to ascertain1 therefore1 what are the laws of causation which exist in nature2 to determine the effect of every cause1 and the causes of all effects1 is the main business of ,induction2 and to point out how this is done is the chief object of ,inductive ,logic4 ,chapter ,,vii4 ,on ,observation ,and ,experiment4 #a4 ,it results from the preceding exposition1 that the process of ascertaining what consequents1 in nature1 are invariably connected with what antecedents1 or in other words what phenomena are related to each other as causes and effects1 is in some sort a process of analysis4 ,that every fact which begins to exist has a cause1 and that this cause must be found in some fact or concourse of facts which immediately preceded the occurrence1 may be taken for certain4 ,the whole of the present facts are the infallible result of all past facts1 and more immediately of all the facts which existed at the moment previous4 ,here1 then1 is a great sequence1 which we know to be uniform4 ,if the whole prior state of the entire universe could again recur1 it would again be followed by the present state4 ,the question is1 how to resolve this complex uniformity into the simpler uniformities which compose it1 and assign to each portion of the vast antecedent the portion of the consequent which is attendant on it4 ,this operation1 which we have called analytical1 inasmuch as it is the resolution of a complex whole into the component elements1 is more than a merely mental analysis4 ,no mere contemplation of the phenomena1 and partition of them by the intellect alone1 will of itself accomplish the end we have now in view4 ,nevertheless1 such a mental partition is an indispensable first step4 ,the order of nature1 as perceived at a first glance1 presents at every instant a chaos followed by another chaos4 ,we must decompose each chaos into single facts4 ,we must learn to see in the chaotic antecedent a multitude of distinct antecedents1 in the chaotic consequent a multitude of distinct consequents4 ,this1 supposing it done1 will not of itself tell us on which of the antecedents each consequent is invariably attendant4 ,to determine that point1 we must endeavor to effect a separation of the facts from one another1 not in our minds only1 but in nature4 ,the mental analysis1 however1 must take place first4 ,and every one knows that in the mode of performing it1 one intellect differs immensely from another4 ,it is the essence of the act of observing2 for the observer is not he who merely sees the thing which is before his eyes1 but he who sees what parts that thing is composed of4 ,to do this well is a rare talent4 ,one person1 from inattention1 or attending only in the wrong place1 overlooks half of what he sees2 another sets down much more than he sees1 confounding it with what he imagines1 or with what he infers2 another takes note of the kind of all the circumstances1 but being inexpert in estimating their degree1 leaves the quantity of each vague and uncertain2 another sees indeed the whole1 but makes such an awkward division of it into parts1 throwing things into one mass which require to be separated1 and separating others which might more conveniently be considered as one1 that the result is much the same1 sometimes even worse1 than if no analysis had been attempted at all4 ,it would be possible to point out what qualities of mind1 and modes of mental culture1 fit a person for being a good observer3 that1 however1 is a question not of ,logic1 but of the ,theory of ,education1 in the most enlarged sense of the term4 ,there is not properly an ,art of ,observing4 ,there may be rules for observing4 ,but these1 like rules for inventing1 are properly instructions for the preparation of one's own mind2 for putting it into the state in which it will be most fitted to observe1 or most likely to invent4 ,they are1 therefore1 essentially rules of self-education1 which is a different thing from ,logic4 ,they do not teach how to do the thing1 but how to make ourselves capable of doing it4 ,they are an art of strengthening the limbs1 not an art of using them4 ,the extent and minuteness of observation which may be requisite1 and the degree of decomposition to which it may be necessary to carry the mental analysis1 depend on the particular purpose in view4 ,to ascertain the state of the whole universe at any particular moment is impossible1 but would also be useless4 ,in making chemical experiments1 we do not think it necessary to note the position of the planets2 because experience has shown1 as a very superficial experience is sufficient to show1 that in such cases that circumstance is not material to the result3 and accordingly1 in the ages when men believed in the occult influences of the heavenly bodies1 it might have been unphilosophical to omit ascertaining the precise condition of those bodies at the moment of the experiment4 ,as to the degree of minuteness of the mental subdivision1 if we were obliged to break down what we observe into its very simplest elements1 that is1 literally into single facts1 it would be difficult to say where we should find them2 we can hardly ever affirm that our divisions of any kind have reached the ultimate unit4 ,but this1 too1 is fortunately unnecessary4 ,the only object of the mental separation is to suggest the requisite physical separation1 so that we may either accomplish it ourselves1 or seek for it in nature2 and we have done enough when we have carried the subdivision as far as the point at which we are able to see what observations or experiments we require4 ,it is only essential1 at whatever point our mental decomposition of facts may for the present have stopped1 that we should hold ourselves ready and able to carry it further as occasion requires1 and should not allow the freedom of our discriminating faculty to be imprisoned by the swathes and bands of ordinary classification2 as was the case with all early speculative inquirers1 not excepting the ,greeks1 to whom it seldom occurred that what was called by one abstract name might1 in reality1 be several phenomena1 or that there was a possibility of decomposing the facts of the universe into any elements but those which ordinary language already recognized4 #b4 ,the different antecedents and consequents being1 then1 supposed to be1 so far as the case requires1 ascertained and discriminated from one another1 we are to inquire which is connected with which4 ,in every instance which comes under our observation1 there are many antecedents and many consequents4 ,if those antecedents could not be severed from one another except in thought1 or if those consequents never were found apart1 it would be impossible for us to distinguish 7a posteriori at least7 the real laws1 or to assign to any cause its effect1 or to any effect its cause4 ,to do so1 we must be able to meet with some of the antecedents apart from the rest1 and observe what follows from them2 or some of the consequents1 and observe by what they are preceded4 ,we must1 in short1 follow the ,baconian rule of varying the circumstances4 ,this is1 indeed1 only the first rule of physical inquiry1 and not1 as some have thought1 the sole rule2 but it is the foundation of all the rest4 ,for the purpose of varying the circumstances1 we may have recourse 7according to a distinction commonly made7 either to observation or to experiment2 we may either find an instance in nature suited to our purposes1 or1 by an artificial arrangement of circumstances1 make one4 ,the value of the instance depends on what it is in itself1 not on the mode in which it is obtained3 its employment for the purposes of induction depends on the same principles in the one case and in the other2 as the uses of money are the same whether it is inherited or acquired4 ,there is1 in short1 no difference in kind1 no real logical distinction1 between the two processes of investigation4 ,there are1 however1 practical distinctions to which it is of considerable importance to advert4 #c4 ,the first and most obvious distinction between ,observation and ,experiment is1 that the latter is an immense extension of the former4 ,it not only enables us to produce a much greater number of variations in the circumstances than nature spontaneously offers1 but also1 in thousands of cases1 to produce the precise sort of variation which we are in want of for discovering the law of the phenomenon2 a service which nature1 being constructed on a quite different scheme from that of facilitating our studies1 is seldom so friendly as to bestow upon us4 ,for example1 in order to ascertain what principle in the atmosphere enables it to sustain life1 the variation we require is that a living animal should be immersed in each component element of the atmosphere separately4 ,but nature does not supply either oxygen or azote in a separate state4 ,we are indebted to artificial experiment for our knowledge that it is the former1 and not the latter1 which supports respiration2 and for our knowledge of the very existence of the two ingredients4 ,thus far the advantage of experimentation over simple observation is universally recognized3 all are aware that it enables us to obtain innumerable combinations of circumstances which are not to be found in nature1 and so add to nature's experiments a multitude of experiments of our own4 ,but there is another superiority 7or1 as ,bacon would have expressed it1 another prerogative7 of instances artificially obtained over spontaneous instances--of our own experiments over even the same experiments when made by nature--which is not of less importance1 and which is far from being felt and acknowledged in the same degree4 ,when we can produce a phenomenon artificially1 we can take it1 as it were1 home with us1 and observe it in the midst of circumstances with which in all other respects we are accurately acquainted4 ,if we desire to know what are the effects of the cause ,a1 and are able to produce ,a by means at our disposal1 we can generally determine at our own discretion1 so far as is compatible with the nature of the phenomenon ,a1 the whole of the circumstances which shall be present along with it3 and thus1 knowing exactly the simultaneous state of every thing else which is within the reach of ,a's influence1 we have only to observe what alteration is made in that state by the presence of ,a4 ,for example1 by the electric machine we can produce1 in the midst of known circumstances1 the phenomena which nature exhibits on a grander scale in the form of lightning and thunder4 ,now let any one consider what amount of knowledge of the effects and laws of electric agency mankind could have obtained from the mere observation of thunder-storms1 and compare it with that which they have gained1 and may expect to gain1 from electrical and galvanic experiments4 ,this example is the more striking1 now that we have reason to believe that electric action is of all natural phenomena 7except heat7 the most pervading and universal1 which1 therefore1 it might antecedently have been supposed could stand least in need of artificial means of production to enable it to be studied2 while the fact is so much the contrary1 that without the electric machine1 the ,leyden jar1 and the voltaic battery1 we probably should never have suspected the existence of electricity as one of the great agents in nature2 the few electric phenomena we should have known of would have continued to be regarded either as supernatural1 or as a sort of anomalies and eccentricities in the order of the universe4 ,when we have succeeded in insulating the phenomenon which is the subject of inquiry1 by placing it among known circumstances1 we may produce further variations of circumstances to any extent1 and of such kinds as we think best calculated to bring the laws of the phenomenon into a clear light4 ,by introducing one well-defined circumstance after another into the experiment1 we obtain assurance of the manner in which the phenomenon behaves under an indefinite variety of possible circumstances4 ,thus1 chemists1 after having obtained some newly-discovered substance in a pure state 7that is1 having made sure that there is nothing present which can interfere with and modify its agency71 introduce various other substances1 one by one1 to ascertain whether it will combine with them1 or decompose them1 and with what result2 and also apply heat1 or electricity1 or pressure1 to discover what will happen to the substance under each of these circumstances4 ,but if1 on the other hand1 it is out of our power to produce the phenomenon1 and we have to seek for instances in which nature produces it1 the task before us is very different4 ,instead of being able to choose what the concomitant circumstances shall be1 we now have to discover what they are2 which1 when we go beyond the simplest and most accessible cases1 it is next to impossible to do with any precision and completeness4 ,let us take1 as an exemplification of a phenomenon which we have no means of fabricating artificially1 a human mind4 ,nature produces many2 but the consequence of our not being able to produce them by art is1 that in every instance in which we see a human mind developing itself1 or acting upon other things1 we see it surrounded and obscured by an indefinite multitude of unascertainable circumstances1 rendering the use of the common experimental methods almost delusive4 ,we may conceive to what extent this is true1 if we consider1 among other things1 that whenever ,nature produces a human mind1 she produces1 in close connection with it1 a body2 that is1 a vast complication of physical facts1 in no two cases perhaps exactly similar1 and most of which 7except the mere structure1 which we can examine in a sort of coarse way after it has ceased to act71 are radically out of the reach of our means of exploration4 ,if1 instead of a human mind1 we suppose the subject of investigation to be a human society or ,state1 all the same difficulties recur in a greatly augmented degree4 ,we have thus already come within sight of a conclusion1 which the progress of the inquiry will1 ,i think1 bring before us with the clearest evidence3 namely1 that in the sciences which deal with phenomena in which artificial experiments are impossible 7as in the case of astronomy71 or in which they have a very limited range 7as in mental philosophy1 social science1 and even physiology71 induction from direct experience is practiced at a disadvantage in most cases equivalent to impracticability2 from which it follows that the methods of those sciences1 in order to accomplish any thing worthy of attainment1 must be to a great extent1 if not principally1 deductive4 ,this is already known to be the case with the first of the sciences we have mentioned1 astronomy2 that it is not generally recognized as true of the others1 is probably one of the reasons why they are not in a more advanced state4 #d4 ,if what is called pure observation is at so great a disadvantage1 compared with artificial experimentation1 in one department of the direct exploration of phenomena1 there is another branch in which the advantage is all on the side of the former4 ,inductive inquiry having for its object to ascertain what causes are connected with what effects1 we may begin this search at either end of the road which leads from the one point to the other3 we may either inquire into the effects of a given cause or into the causes of a given effect4 ,the fact that light blackens chloride of silver might have been discovered either by experiments on light1 trying what effect it would produce on various substances1 or by observing that portions of the chloride had repeatedly become black1 and inquiring into the circumstances4 ,the effect of the urali poison might have become known either by administering it to animals1 or by examining how it happened that the wounds which the ,indians of ,guiana inflict with their arrows prove so uniformly mortal4 ,now it is manifest from the mere statement of the examples1 without any theoretical discussion1 that artificial experimentation is applicable only to the former of these modes of investigation4 ,we can take a cause1 and try what it will produce2 but we can not take an effect1 and try what it will be produced by4 ,we can only watch till we see it produced1 or are enabled to produce it by accident4 ,this would be of little importance1 if it always depended on our choice from which of the two ends of the sequence we would undertake our inquiries4 ,but we have seldom any option4 ,as we can only travel from the known to the unknown1 we are obliged to commence at whichever end we are best acquainted with4 ,if the agent is more familiar to us than its effects1 we watch for1 or contrive1 instances of the agent1 under such varieties of circumstances as are open to us1 and observe the result4 ,if1 on the contrary1 the conditions on which a phenomenon depends are obscure1 but the phenomenon itself familiar1 we must commence our inquiry from the effect4 ,if we are struck with the fact that chloride of silver has been blackened1 and have no suspicion of the cause1 we have no resource but to compare instances in which the fact has chanced to occur1 until by that comparison we discover that in all those instances the substances had been exposed to light4 ,if we knew nothing of the ,indian arrows but their fatal effect1 accident alone could turn our attention to experiments on the urali2 in the regular course of investigation1 we could only inquire1 or try to observe1 what had been done to the arrows in particular instances4 ,wherever1 having nothing to guide us to the cause1 we are obliged to set out from the effect1 and to apply the rule of varying the circumstances to the consequents1 not the antecedents1 we are necessarily destitute of the resource of artificial experimentation4 ,we can not1 at our choice1 obtain consequents1 as we can antecedents1 under any set of circumstances compatible with their nature4 ,there are no means of producing effects but through their causes1 and by the supposition the causes of the effect in question are not known to us4 ,we have1 therefore1 no expedient but to study it where it offers itself spontaneously4 ,if nature happens to present us with instances sufficiently varied in their circumstances1 and if we are able to discover1 either among the proximate antecedents or among some other order of antecedents1 something which is always found when the effect is found1 however various the circumstances1 and never found when it is not1 we may discover1 by mere observation without experiment1 a real uniformity in nature4 ,but though this is certainly the most favorable case for sciences of pure observation1 as contrasted with those in which artificial experiments are possible1 there is in reality no case which more strikingly illustrates the inherent imperfection of direct induction when not founded on experimentation4 ,suppose that1 by a comparison of cases of the effect1 we have found an antecedent which appears to be1 and perhaps is1 invariably connected with it3 we have not yet proved that antecedent to be the cause until we have reversed the process1 and produced the effect by means of that antecedent4 ,if we can produce the antecedent artificially1 and if1 when we do so1 the effect follows1 the induction is complete2 that antecedent is the cause of that consequent47#ace7 ,but we have then added the evidence of experiment to that of simple observation4 ,until we had done so1 we had only proved invariable antecedence within the limits of experience1 but not unconditional antecedence1 or causation4 ,until it had been shown by the actual production of the antecedent under known circumstances1 and the occurrence thereupon of the consequent1 that the antecedent was really the condition on which it depended2 the uniformity of succession which was proved to exist between them might1 for aught we knew1 be 7like the succession of day and night7 not a case of causation at all2 both antecedent and consequent might be successive stages of the effect of an ulterior cause4 ,observation1 in short1 without experiment 7supposing no aid from deduction7 can ascertain sequences and co-existences1 but can not prove causation4 ,in order to see these remarks verified by the actual state of the sciences1 we have only to think of the condition of natural history4 ,in zoology1 for example1 there is an immense number of uniformities ascertained1 some of co-existence1 others of succession1 to many of which1 notwithstanding considerable variations of the attendant circumstances1 we know not any exception3 but the antecedents1 for the most part1 are such as we can not artificially produce2 or if we can1 it is only by setting in motion the exact process by which nature produces them2 and this being to us a mysterious process1 of which the main circumstances are not only unknown but unobservable1 we do not succeed in obtaining the antecedents under known circumstances4 ,what is the result8 ,that on this vast subject1 which affords so much and such varied scope for observation1 we have made most scanty progress in ascertaining any laws of causation4 ,we know not with certainty1 in the case of most of the phenomena that we find conjoined1 which is the condition of the other2 which is cause1 and which effect1 or whether either of them is so1 or they are not rather conjunct effects of causes yet to be discovered1 complex results of laws hitherto unknown4 ,although some of the foregoing observations may be1 in technical strictness of arrangement1 premature in this place1 it seemed that a few general remarks on the difference between sciences of mere observation and sciences of experimentation1 and the extreme disadvantage under which directly inductive inquiry is necessarily carried on in the former1 were the best preparation for discussing the methods of direct induction2 a preparation rendering superfluous much that must otherwise have been introduced1 with some inconvenience1 into the heart of that discussion4 ,to the consideration of these methods we now proceed4 ,chapter ,,viii4 ,of ,the ,four ,methods ,of ,experimental ,inquiry4 #a4 ,the simplest and most obvious modes of singling out from among the circumstances which precede or follow a phenomenon1 those with which it is really connected by an invariable law1 are two in number4 ,one is1 by comparing together different instances in which the phenomenon occurs4 ,the other is1 by comparing instances in which the phenomenon does occur1 with instances in other respects similar in which it does not4 ,these two methods may be respectively denominated1 the ,method of ,agreement1 and the ,method of ,difference4 ,in illustrating these methods1 it will be necessary to bear in mind the twofold character of inquiries into the laws of phenomena2 which may be either inquiries into the cause of a given effect1 or into the effects or properties of a given cause4 ,we shall consider the methods in their application to either order of investigation1 and shall draw our examples equally from both4 ,we shall denote antecedents by the large letters of the alphabet1 and the consequents corresponding to them by the small4 ,let ,a1 then1 be an agent or cause1 and let the object of our inquiry be to ascertain what are the effects of this cause4 ,if we can either find1 or produce1 the agent ,a in such varieties of circumstances that the different cases have no circumstance in common except ,a2 then whatever effect we find to be produced in all our trials1 is indicated as the effect of ,a4 ,suppose1 for example1 that ,a is tried along with ,b and ,c1 and that the effect is a b c2 and suppose that ,a is next tried with ,d and ,e1 but without ,b and ,c1 and that the effect is a d e4 ,then we may reason thus3 b and c are not effects of ,a1 for they were not produced by it in the second experiment2 nor are d and e1 for they were not produced in the first4 ,whatever is really the effect of ,a must have been produced in both instances2 now this condition is fulfilled by no circumstance except a4 ,the phenomenon a can not have been the effect of ,b or ,c1 since it was produced where they were not2 nor of ,d or ,e1 since it was produced where they were not4 ,therefore it is the effect of ,a4 ,for example1 let the antecedent ,a be the contact of an alkaline substance and an oil4 ,this combination being tried under several varieties of circumstances1 resembling each other in nothing else1 the results agree in the production of a greasy and detersive or saponaceous substance3 it is therefore concluded that the combination of an oil and an alkali causes the production of a soap4 ,it is thus we inquire1 by the ,method of ,agreement1 into the effect of a given cause4 ,in a similar manner we may inquire into the cause of a given effect4 ,let a be the effect4 ,here1 as shown in the last chapter1 we have only the resource of observation without experiment3 we can not take a phenomenon of which we know not the origin1 and try to find its mode of production by producing it3 if we succeeded in such a random trial it could only be by accident4 ,but if we can observe a in two different combinations1 a b c and a d e2 and if we know1 or can discover1 that the antecedent circumstances in these cases respectively were ,a ,b ,c and ,a ,d ,e1 we may conclude by a reasoning similar to that in the preceding example1 that ,a is the antecedent connected with the consequent a by a law of causation4 ,b and ,c1 we may say1 can not be causes of a1 since on its second occurrence they were not present2 nor are ,d and ,e1 for they were not present on its first occurrence4 ,a1 alone of the five circumstances1 was found among the antecedents of a in both instances4 ,for example1 let the effect a be crystallization4 ,we compare instances in which bodies are known to assume crystalline structure1 but which have no other point of agreement2 and we find them to have one1 and as far as we can observe1 only one1 antecedent in common3 the deposition of a solid matter from a liquid state1 either a state of fusion or of solution4 ,we conclude1 therefore1 that the solidification of a substance from a liquid state is an invariable antecedent of its crystallization4 ,in this example we may go further1 and say1 it is not only the invariable antecedent but the cause2 or at least the proximate event which completes the cause4 ,for in this case we are able1 after detecting the antecedent ,a1 to produce it artificially1 and by finding that a follows it1 verify the result of our induction4 ,the importance of thus reversing the proof was strikingly manifested when1 by keeping a phial of water charged with siliceous particles undisturbed for years1 a chemist 7,i believe ,dr4 ,wollaston7 succeeded in obtaining crystals of quartz2 and in the equally interesting experiment in which ,sir ,james ,hall produced artificial marble by the cooling of its materials from fusion under immense pressure3 two admirable examples of the light which may be thrown upon the most secret processes of ,nature by well-contrived interrogation of her4 ,but if we can not artificially produce the phenomenon ,a1 the conclusion that it is the cause of a remains subject to very considerable doubt4 ,though an invariable1 it may not be the unconditional antecedent of a1 but may precede it as day precedes night or night day4 ,this uncertainty arises from the impossibility of assuring ourselves that ,a is the only immediate antecedent common to both the instances4 ,if we could be certain of having ascertained all the invariable antecedents1 we might be sure that the unconditional invariable antecedent1 or cause1 must be found somewhere among them4 ,unfortunately it is hardly ever possible to ascertain all the antecedents1 unless the phenomenon is one which we can produce artificially4 ,even then1 the difficulty is merely lightened1 not removed3 men knew how to raise water in pumps long before they adverted to what was really the operating circumstance in the means they employed1 namely1 the pressure of the atmosphere on the open surface of the water4 ,it is1 however1 much easier to analyze completely a set of arrangements made by ourselves1 than the whole complex mass of the agencies which nature happens to be exerting at the moment of the production of a given phenomenon4 ,we may overlook some of the material circumstances in an experiment with an electrical machine2 but we shall1 at the worst1 be better acquainted with them than with those of a thunder-storm4 ,the mode of discovering and proving laws of nature1 which we have now examined1 proceeds on the following axiom3 ,whatever circumstances can be excluded1 without prejudice to the phenomenon1 or can be absent notwithstanding its presence1 is not connected with it in the way of causation4 ,the casual circumstances being thus eliminated1 if only one remains1 that one is the cause which we are in search of3 if more than one1 they either are1 or contain among them1 the cause2 and so1 mutatis mutandis1 of the effect4 ,as this method proceeds by comparing different instances to ascertain in what they agree1 ,i have termed it the ,method of ,agreement2 and we may adopt as its regulating principal the following canon3 ,,first ,,canon4 ,if two or more instances of the phenomenon under investigation have only one circumstance in common1 the circumstance in which alone all the instances agree1 is the cause 7or effect7 of the given phenomenon4 ,quitting for the present the ,method of ,agreement1 to which we shall almost immediately return1 we proceed to a still more potent instrument of the investigation of nature1 the ,method of ,difference4 #b4 ,in the ,method of ,agreement1 we endeavored to obtain instances which agreed in the given circumstance but differed in every other3 in the present method we require1 on the contrary1 two instances resembling one another in every other respect1 but differing in the presence or absence of the phenomenon we wish to study4 ,if our object be to discover the effects of an agent ,a1 we must procure ,a in some set of ascertained circumstances1 as ,a ,b ,c1 and having noted the effects produced1 compare them with the effect of the remaining circumstances ,b ,c1 when ,a is absent4 ,if the effect of ,a ,b ,c is a b c1 and the effect of ,b ,c b c1 it is evident that the effect of ,a is a4 ,so again1 if we begin at the other end1 and desire to investigate the cause of an effect a1 we must select an instance1 as a b c1 in which the effect occurs1 and in which the antecedents were ,a ,b ,c1 and we must look out for another instance in which the remaining circumstances1 b c1 occur without a4 ,if the antecedents1 in that instance1 are ,b ,c1 we know that the cause of a must be ,a3 either ,a alone1 or ,a in conjunction with some of the other circumstances present4 ,it is scarcely necessary to give examples of a logical process to which we owe almost all the inductive conclusions we draw in daily life4 ,when a man is shot through the heart1 it is by this method we know that it was the gunshot which killed him3 for he was in the fullness of life immediately before1 all circumstances being the same1 except the wound4 ,the axioms implied in this method are evidently the following4 ,whatever antecedent can not be excluded without preventing the phenomenon1 is the cause1 or a condition1 of that phenomenon3 whatever consequent can be excluded1 with no other difference in the antecedents than the absence of a particular one1 is the effect of that one4 ,instead of comparing different instances of a phenomenon1 to discover in what they agree1 this method compares an instance of its occurrence with an instance of its non-occurrence1 to discover in what they differ4 ,the canon which is the regulating principle of the ,method of ,difference may be expressed as follows3 ,,second ,,canon4 ,if an instance in which the phenomenon under investigation occurs1 and an instance in which it does not occur1 have every circumstance in common save one1 that one occurring only in the former2 the circumstance in which alone the two instances differ1 is the effect1 or the cause1 or an indispensable part of the cause1 of the phenomenon4 #c4 ,the two methods which we have now stated have many features of resemblance1 but there are also many distinctions between them4 ,both are methods of elimination4 ,this term 7employed in the theory of equations to denote the process by which one after another of the elements of a question is excluded1 and the solution made to depend on the relation between the remaining elements only7 is well suited to express the operation1 analogous to this1 which has been understood since the time of ,bacon to be the foundation of experimental inquiry3 namely1 the successive exclusion of the various circumstances which are found to accompany a phenomenon in a given instance1 in order to ascertain what are those among them which can be absent consistently with the existence of the phenomenon4 ,the ,method of ,agreement stands on the ground that whatever can be eliminated1 is not connected with the phenomenon by any law4 ,the ,method of ,difference has for its foundation1 that whatever can not be eliminated1 is connected with the phenomenon by a law4 ,of these methods1 that of ,difference is more particularly a method of artificial experiment2 while that of ,agreement is more especially the resource employed where experimentation is impossible4 ,a few reflections will prove the fact1 and point out the reason of it4 ,it is inherent in the peculiar character of the ,method of ,difference1 that the nature of the combinations which it requires is much more strictly defined than in the ,method of ,agreement4 ,the two instances which are to be compared with one another must be exactly similar1 in all circumstances except the one which we are attempting to investigate3 they must be in the relation of ,a ,b ,c and ,b ,c1 or of a b c and b c4 ,it is true that this similarity of circumstances needs not extend to such as are already known to be immaterial to the result4 ,and in the case of most phenomena we learn at once1 from the commonest experience1 that most of the co-existent phenomena of the universe may be either present or absent without affecting the given phenomenon2 or1 if present1 are present indifferently when the phenomenon does not happen and when it does4 ,still1 even limiting the identity which is required between the two instances1 ,a ,b ,c and ,b ,c1 to such circumstances as are not already known to be indifferent1 it is very seldom that nature affords two instances1 of which we can be assured that they stand in this precise relation to one another4 ,in the spontaneous operations of nature there is generally such complication and such obscurity1 they are mostly either on so overwhelmingly large or on so inaccessibly minute a scale1 we are so ignorant of a great part of the facts which really take place1 and even those of which we are not ignorant are so multitudinous1 and therefore so seldom exactly alike in any two cases1 that a spontaneous experiment1 of the kind required by the ,method of ,difference1 is commonly not to be found4 ,when1 on the contrary1 we obtain a phenomenon by an artificial experiment1 a pair of instances such as the method requires is obtained almost as a matter of course1 provided the process does not last a long time4 ,a certain state of surrounding circumstances existed before we commenced the experiment2 this is ,b ,c4 ,we then introduce ,a2 say1 for instance1 by merely bringing an object from another part of the room1 before there has been time for any change in the other elements4 ,it is1 in short 7as ,m4 ,comt observes71 the very nature of an experiment1 to introduce into the pre-existing state of circumstances a change perfectly definite4 ,we choose a previous state of things with which we are well acquainted1 so that no unforeseen alteration in that state is likely to pass unobserved2 and into this we introduce1 as rapidly as possible1 the phenomenon which we wish to study2 so that in general we are entitled to feel complete assurance that the pre-existing state1 and the state which we have produced1 differ in nothing except the presence or absence of that phenomenon4 ,if a bird is taken from a cage1 and instantly plunged into carbonic acid gas1 the experimentalist may be fully assured 7at all events after one or two repetitions7 that no circumstance capable of causing suffocation had supervened in the interim1 except the change from immersion in the atmosphere to immersion in carbonic acid gas4 ,there is one doubt1 indeed1 which may remain in some cases of this description2 the effect may have been produced not by the change1 but by the means employed to produce the change4 ,the possibility1 however1 of this last supposition generally admits of being conclusively tested by other experiments4 ,it thus appears that in the study of the various kinds of phenomena which we can1 by our voluntary agency1 modify or control1 we can in general satisfy the requisitions of the ,method of ,difference2 but that by the spontaneous operations of nature those requisitions are seldom fulfilled4 ,the reverse of this is the case with the ,method of ,agreement4 ,we do not here require instances of so special and determinate a kind4 ,any instances whatever1 in which nature presents us with a phenomenon1 may be examined for the purposes of this method2 and if all such instances agree in any thing1 a conclusion of considerable value is already attained4 ,we can seldom1 indeed1 be sure that the one point of agreement is the only one2 but this ignorance does not1 as in the ,method of ,difference1 vitiate the conclusion2 the certainty of the result1 as far as it goes1 is not affected4 ,we have ascertained one invariable antecedent or consequent1 however many other invariable antecedents or consequents may still remain unascertained4 ,if ,a ,b ,c1 ,a ,d ,e1 ,a ,f ,g1 are all equally followed by a1 then a is an invariable consequent of ,a4 ,if a b c1 a d e1 a f g1 all number ,a among their antecedents1 then ,a is connected as an antecedent1 by some invariable law1 with a4 ,but to determine whether this invariable antecedent is a cause1 or this invariable consequent an effect1 we must be able1 in addition1 to produce the one by means of the other2 or1 at least1 to obtain that which alone constitutes our assurance of having produced any thing1 namely1 an instance in which the effect1 a1 has come into existence1 with no other change in the pre-existing circumstances than the addition of ,a4 ,and this1 if we can do it1 is an application of the ,method of ,difference1 not of the ,method of ,agreement4 ,it thus appears to be by the ,method of ,difference alone that we can ever1 in the way of direct experience1 arrive with certainty at causes4 ,the ,method of ,agreement leads only to laws of phenomena 7as some writers call them1 but improperly1 since laws of causation are also laws of phenomena73 that is1 to uniformities1 which either are not laws of causation1 or in which the question of causation must for the present remain undecided4 ,the ,method of ,agreement is chiefly to be resorted to1 as a means of suggesting applications of the ,method of ,difference 7as in the last example the comparison of ,a ,b ,c1 ,a ,d ,e1 ,a ,f ,g1 suggested that ,a was the antecedent on which to try the experiment whether it could produce a72 or as an inferior resource1 in case the ,method of ,difference is impracticable2 which1 as we before showed1 generally arises from the impossibility of artificially producing the phenomena4 ,and hence it is that the ,method of ,agreement1 though applicable in principle to either case1 is more emphatically the method of investigation on those subjects where artificial experimentation is impossible2 because on those it is1 generally1 our only resource of a directly inductive nature2 while1 in the phenomena which we can produce at pleasure1 the ,method of ,difference generally affords a more efficacious process1 which will ascertain causes as well as mere laws4 #d4 ,there are1 however1 many cases in which1 though our power of producing the phenomenon is complete1 the ,method of ,difference either can not be made available at all1 or not without a previous employment of the ,method of ,agreement4 ,this occurs when the agency by which we can produce the phenomenon is not that of one single antecedent1 but a combination of antecedents1 which we have no power of separating from each other1 and exhibiting apart4 ,for instance1 suppose the subject of inquiry to be the cause of the double refraction of light4 ,we can produce this phenomenon at pleasure1 by employing any one of the many substances which are known to refract light in that peculiar manner4 ,but if1 taking one of those substances1 as ,iceland spar1 for example1 we wish to determine on which of the properties of ,iceland spar this remarkable phenomenon depends1 we can make no use1 for that purpose1 of the ,method of ,difference2 for we can not find another substance precisely resembling ,iceland spar except in some one property4 ,the only mode1 therefore1 of prosecuting this inquiry is that afforded by the ,method of ,agreement2 by which1 in fact1 through a comparison of all the known substances which have the property of doubly refracting light1 it was ascertained that they agree in the circumstance of being crystalline substances2 and though the converse does not hold1 though all crystalline substances have not the property of double refraction1 it was concluded1 with reason1 that there is a real connection between these two properties2 that either crystalline structure1 or the cause which gives rise to that structure1 is one of the conditions of double refraction4 ,out of this employment of the ,method of ,agreement arises a peculiar modification of that method1 which is sometimes of great avail in the investigation of nature4 ,in cases similar to the above1 in which it is not possible to obtain the precise pair of instances which our second canon requires--instances agreeing in every antecedent except ,a1 or in every consequent except a1 we may yet be able1 by a double employment of the ,method of ,agreement1 to discover in what the instances which contain ,a or a differ from those which do not4 ,if we compare various instances in which a occurs1 and find that they all have in common the circumstance ,a1 and 7as far as can be observed7 no other circumstance1 the ,method of ,agreement1 so far1 bears testimony to a connection between ,a and a4 ,in order to convert this evidence of connection into proof of causation by the direct ,method of ,difference1 we ought to be able1 in some one of these instances1 as for example1 ,a ,b ,c1 to leave out ,a1 and observe whether by doing so1 a is prevented4 ,now supposing 7what is often the case7 that we are not able to try this decisive experiment2 yet1 provided we can by any means discover what would be its result if we could try it1 the advantage will be the same4 ,suppose1 then1 that as we previously examined a variety of instances in which a occurred1 and found them to agree in containing ,a1 so we now observe a variety of instances in which a does not occur1 and find them agree in not containing ,a2 which establishes1 by the ,method of ,agreement1 the same connection between the absence of ,a and the absence of a1 which was before established between their presence4 ,as1 then1 it had been shown that whenever ,a is present a is present1 so1 it being now shown that when ,a is taken away a is removed along with it1 we have by the one proposition ,a ,b ,c1 a b c1 by the other ,b ,c1 b c1 the positive and negative instances which the ,method of ,difference requires4 ,this method may be called the ,indirect ,method of ,difference1 or the ,joint ,method of ,agreement and ,difference2 and consists in a double employment of the ,method of ,agreement1 each proof being independent of the other1 and corroborating it4 ,but it is not equivalent to a proof by the direct ,method of ,difference4 ,for the requisitions of the ,method of ,difference are not satisfied1 unless we can be quite sure either that the instances affirmative of a agree in no antecedent whatever but ,a1 or that the instances negative of a agree in nothing but the negation of ,a4 ,now1 if it were possible1 which it never is1 to have this assurance1 we should not need the joint method2 for either of the two sets of instances separately would then be sufficient to prove causation4 ,this indirect method1 therefore1 can only be regarded as a great extension and improvement of the ,method of ,agreement1 but not as participating in the more cogent nature of the ,method of ,difference4 ,the following may be stated as its canon3 ,,third ,,canon4 ,if two or more instances in which the phenomenon occurs have only one circumstance in common1 while two or more instances in which it does not occur have nothing in common save the absence of that circumstance1 the circumstance in which alone the two sets of instances differ1 is the effect1 or the cause1 or an indispensable part of the cause1 of the phenomenon4 ,we shall presently see that the ,joint ,method of ,agreement and ,difference constitutes1 in another respect not yet adverted to1 an improvement upon the common ,method of ,agreement1 namely1 in being unaffected by a characteristic imperfection of that method1 the nature of which still remains to be pointed out4 ,but as we can not enter into this exposition without introducing a new element of complexity into this long and intricate discussion1 ,i shall postpone it to a subsequent chapter1 and shall at once proceed to a statement of two other methods1 which will complete the enumeration of the means which mankind possess for exploring the laws of nature by specific observation and experience4 #e4 ,the first of these has been aptly denominated the ,method of ,residues4 ,its principle is very simple4 ,subducting from any given phenomenon all the portions which1 by virtue of preceding inductions1 can be assigned to known causes1 the remainder will be the effect of the antecedents which had been overlooked1 or of which the effect was as yet an unknown quantity4 ,suppose1 as before1 that we have the antecedents ,a ,b ,c1 followed by the consequents a b c1 and that by previous inductions 7founded1 we will suppose1 on the ,method of ,difference7 we have ascertained the causes of some of these effects1 or the effects of some of these causes2 and are thence apprised that the effect of ,a is a1 and that the effect of ,b is b4 ,subtracting the sum of these effects from the total phenomenon1 there remains c1 which now1 without any fresh experiments1 we may know to be the effect of ,c4 ,this ,method of ,residues is in truth a peculiar modification of the ,method of ,difference4 ,if the instance ,a ,b ,c1 a b c1 could have been compared with a single instance ,a ,b1 a b1 we should have proved ,c to be the cause of c1 by the common process of the ,method of ,difference4 ,in the present case1 however1 instead of a single instance ,a ,b1 we have had to study separately the causes ,a and ,b1 and to infer from the effects which they produce separately what effect they must produce in the case ,a ,b ,c1 where they act together4 ,of the two instances1 therefore1 which the ,method of ,difference requires--the one positive1 the other negative--the negative one1 or that in which the given phenomenon is absent1 is not the direct result of observation and experiment1 but has been arrived at by deduction4 ,as one of the forms of the ,method of ,difference1 the ,method of ,residues partakes of its rigorous certainty1 provided the previous inductions1 those which gave the effects of ,a and ,b1 were obtained by the same infallible method1 and provided we are certain that ,c is the only antecedent to which the residual phenomenon c can be referred2 the only agent of which we had not already calculated and subducted the effect4 ,but as we can never be quite certain of this1 the evidence derived from the ,method of ,residues is not complete unless we can obtain ,c artificially1 and try it separately1 or unless its agency1 when once suggested1 can be accounted for1 and proved deductively from known laws4 ,even with these reservations1 the ,method of ,residues is one of the most important among our instruments of discovery4 ,of all the methods of investigating laws of nature1 this is the most fertile in unexpected results3 often informing us of sequences in which neither the cause nor the effect were sufficiently conspicuous to attract of themselves the attention of observers4 ,the agent ,c may be an obscure circumstance1 not likely to have been perceived unless sought for1 nor likely to have been sought for until attention had been awakened by the insufficiency of the obvious causes to account for the whole of the effect4 ,and c may be so disguised by its intermixture with a and b1 that it would scarcely have presented itself spontaneously as a subject of separate study4 ,of these uses of the method1 we shall presently cite some remarkable examples4 ,the canon of the ,method of ,residues is as follows3 ,,fourth ,,canon4 ,subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents1 and the residue of the phenomenon is the effect of the remaining antecedents4 #f4 ,there remains a class of laws which it is impracticable to ascertain by any of the three methods which ,i have attempted to characterize3 namely1 the laws of those ,permanent ,causes1 or indestructible natural agents1 which it is impossible either to exclude or to isolate2 which we can neither hinder from being present1 nor contrive that they shall be present alone4 ,it would appear at first sight that we could by no means separate the effects of these agents from the effects of those other phenomena with which they can not be prevented from co-existing4 ,in respect1 indeed1 to most of the permanent causes1 no such difficulty exists2 since1 though we can not eliminate them as co-existing facts1 we can eliminate them as influencing agents1 by simply trying our experiment in a local situation beyond the limits of their influence4 ,the pendulum1 for example1 has its oscillations disturbed by the vicinity of a mountain3 we remove the pendulum to a sufficient distance from the mountain1 and the disturbance ceases3 from these data we can determine by the ,method of ,difference1 the amount of effect due to the mountain2 and beyond a certain distance every thing goes on precisely as it would do if the mountain exercised no influence whatever1 which1 accordingly1 we1 with sufficient reason1 conclude to be the fact4 ,the difficulty1 therefore1 in applying the methods already treated of to determine the effects of ,permanent ,causes1 is confined to the cases in which it is impossible for us to get out of the local limits of their influence4 ,the pendulum can be removed from the influence of the mountain1 but it can not be removed from the influence of the earth3 we can not take away the earth from the pendulum1 nor the pendulum from the earth1 to ascertain whether it would continue to vibrate if the action which the earth exerts upon it were withdrawn4 ,on what evidence1 then1 do we ascribe its vibrations to the earth's influence8 ,not on any sanctioned by the ,method of ,difference2 for one of the two instances1 the negative instance1 is wanting4 ,nor by the ,method of ,agreement2 for though all pendulums agree in this1 that during their oscillations the earth is always present1 why may we not as well ascribe the phenomenon to the sun1 which is equally a co-existent fact in all the experiments8 ,it is evident that to establish even so simple a fact of causation as this1 there was required some method over and above those which we have yet examined4 ,as another example1 let us take the phenomenon ,heat4 ,independently of all hypothesis as to the real nature of the agency so called1 this fact is certain1 that we are unable to exhaust any body of the whole of its heat4 ,it is equally certain that no one ever perceived heat not emanating from a body4 ,being unable1 then1 to separate ,body and ,heat1 we can not effect such a variation of circumstances as the foregoing three methods require2 we can not ascertain1 by those methods1 what portion of the phenomena exhibited by any body is due to the heat contained in it4 ,if we could observe a body with its heat1 and the same body entirely divested of heat1 the ,method of ,difference would show the effect due to the heat1 apart from that due to the body4 ,if we could observe heat under circumstances agreeing in nothing but heat1 and therefore not characterized also by the presence of a body1 we could ascertain the effects of heat1 from an instance of heat with a body and an instance of heat without a body1 by the ,method of ,agreement2 or we could determine by the ,method of ,difference what effect was due to the body1 when the remainder which was due to the heat would be given by the ,method of ,residues4 ,but we can do none of these things2 and without them the application of any of the three methods to the solution of this problem would be illusory4 ,it would be idle1 for instance1 to attempt to ascertain the effect of heat by subtracting from the phenomena exhibited by a body all that is due to its other properties2 for as we have never been able to observe any bodies without a portion of heat in them1 effects due to that heat might form a part of the very results which we were affecting to subtract1 in order that the effect of heat might be shown by the residue4 ,if1 therefore1 there were no other methods of experimental investigation than these three1 we should be unable to determine the effects due to heat as a cause4 ,but we have still a resource4 ,though we can not exclude an antecedent altogether1 we may be able to produce1 or nature may produce for us some modification in it4 ,by a modification is here meant1 a change in it not amounting to its total removal4 ,if some modification in the antecedent ,a is always followed by a change in the consequent a1 the other consequents b and c remaining the same2 or vic versa1 if every change in a is found to have been preceded by some modification in ,a1 none being observable in any of the other antecedents1 we may safely conclude that a is1 wholly or in part1 an effect traceable to ,a1 or at least in some way connected with it through causation4 ,for example1 in the case of heat1 though we can not expel it altogether from any body1 we can modify it in quantity1 we can increase or diminish it2 and doing so1 we find by the various methods of experimentation or observation already treated of1 that such increase or diminution of heat is followed by expansion or contraction of the body4 ,in this manner we arrive at the conclusion1 otherwise unattainable by us1 that one of the effects of heat is to enlarge the dimensions of bodies2 or1 what is the same thing in other words1 to widen the distances between their particles4 ,a change in a thing1 not amounting to its total removal1 that is1 a change which leaves it still the same thing it was1 must be a change either in its quantity1 or in some of its variable relations to other things1 of which variable relations the principal is its position in space4 ,in the previous example1 the modification which was produced in the antecedent was an alteration in its quantity4 ,let us now suppose the question to be1 what influence the moon exerts on the surface of the earth4 ,we can not try an experiment in the absence of the moon1 so as to observe what terrestrial phenomena her annihilation would put an end to2 but when we find that all the variations in the position of the moon are followed by corresponding variations in the time and place of high water1 the place being always either the part of the earth which is nearest to1 or that which is most remote from1 the moon1 we have ample evidence that the moon is1 wholly or partially1 the cause which determines the tides4 ,it very commonly happens1 as it does in this instance1 that the variations of an effect are correspondent1 or analogous1 to those of its cause2 as the moon moves farther toward the east1 the high-water point does the same3 but this is not an indispensable condition1 as may be seen in the same example1 for along with that high-water point there is at the same instant another high-water point diametrically opposite to it1 and which1 therefore1 of necessity1 moves toward the west1 as the moon1 followed by the nearer of the tide waves1 advances toward the east3 and yet both these motions are equally effects of the moon's motion4 ,that the oscillations of the pendulum are caused by the earth1 is proved by similar evidence4 ,those oscillations take place between equidistant points on the two sides of a line1 which1 being perpendicular to the earth1 varies with every variation in the earth's position1 either in space or relatively to the object4 ,speaking accurately1 we only know by the method now characterized1 that all terrestrial bodies tend to the earth1 and not to some unknown fixed point lying in the same direction4 ,in every twenty-four hours1 by the earth's rotation1 the line drawn from the body at right angles to the earth coincides successively with all the radii of a circle1 and in the course of six months the place of that circle varies by nearly two hundred millions of miles2 yet in all these changes of the earth's position1 the line in which bodies tend to fall continues to be directed toward it3 which proves that terrestrial gravity is directed to the earth1 and not1 as was once fancied by some1 to a fixed point of space4 ,the method by which these results were obtained may be termed the ,method of ,concomitant ,variations2 it is regulated by the following canon3 ,,fifth ,,canon4 ,whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner1 is either a cause or an effect of that phenomenon1 or is connected with it through some fact of causation4 ,the last clause is subjoined1 because it by no means follows when two phenomena accompany each other in their variations1 that the one is cause and the other effect4 ,the same thing may1 and indeed must happen1 supposing them to be two different effects of a common cause3 and by this method alone it would never be possible to ascertain which of the suppositions is the true one4 ,the only way to solve the doubt would be that which we have so often adverted to1 viz41 by endeavoring to ascertain whether we can produce the one set of variations by means of the other4 ,in the case of heat1 for example1 by increasing the temperature of a body we increase its bulk1 but by increasing its bulk we do not increase its temperature2 on the contrary 7as in the rarefaction of air under the receiver of an air-pump71 we generally diminish it3 therefore heat is not an effect1 but a cause1 of increase of bulk4 ,if we can not ourselves produce the variations1 we must endeavor1 though it is an attempt which is seldom successful1 to find them produced by nature in some case in which the preexisting circumstances are perfectly known to us4 ,it is scarcely necessary to say1 that in order to ascertain the uniform concomitance of variations in the effect with variations in the cause1 the same precautions must be used as in any other case of the determination of an invariable sequence4 ,we must endeavor to retain all the other antecedents unchanged1 while that particular one is subjected to the requisite series of variations2 or1 in other words1 that we may be warranted in inferring causation from concomitance of variations1 the concomitance itself must be proved by the ,method of ,difference4 ,it might at first appear that the ,method of ,concomitant ,variations assumes a new axiom1 or law of causation in general1 namely1 that every modification of the cause is followed by a change in the effect4 ,and it does usually happen that when a phenomenon ,a causes a phenomenon a1 any variation in the quantity or in the various relations of ,a1 is uniformly followed by a variation in the quantity or relations of a4 ,to take a familiar instance1 that of gravitation4 ,the sun causes a certain tendency to motion in the earth2 here we have cause and effect2 but that tendency is toward the sun1 and therefore varies in direction as the sun varies in the relation of position2 and1 moreover1 the tendency varies in intensity1 in a certain numerical correspondence to the sun's distance from the earth1 that is1 according to another relation of the sun4 ,thus we see that there is not only an invariable connection between the sun and the earth's gravitation1 but that two of the relations of the sun1 its position with respect to the earth and its distance from the earth1 are invariably connected as antecedents with the quantity and direction of the earth's gravitation4 ,the cause of the earth's gravitating at all1 is simply the sun2 but the cause of its gravitating with a given intensity and in a given direction1 is the existence of the sun in a given direction and at a given distance4 ,it is not strange that a modified cause1 which is in truth a different cause1 should produce a different effect4 ,although it is for the most part true that a modification of the cause is followed by a modification of the effect1 the ,method of ,concomitant ,variations does not1 however1 presuppose this as an axiom4 ,it only requires the converse proposition3 that any thing on whose modifications1 modifications of an effect are invariably consequent1 must be the cause 7or connected with the cause7 of that effect2 a proposition1 the truth of which is evident2 for if the thing itself had no influence on the effect1 neither could the modifications of the thing have any influence4 ,if the stars have no power over the fortunes of mankind1 it is implied in the very terms that the conjunctions or oppositions of different stars can have no such power4 ,although the most striking applications of the ,method of ,concomitant ,variations take place in the cases in which the ,method of ,difference1 strictly so called1 is impossible1 its use is not confined to those cases2 it may often usefully follow after the ,method of ,difference1 to give additional precision to a solution which that has found4 ,when by the ,method of ,difference it has first been ascertained that a certain object produces a certain effect1 the ,method of ,concomitant ,variations may be usefully called in1 to determine according to what law the quantity or the different relations of the effect follow those of the cause4 #g4 ,the case in which this method admits of the most extensive employment1 is that in which the variations of the cause are variations of quantity4 ,of such variations we may in general affirm with safety1 that they will be attended not only with variations1 but with similar variations1 of the effect3 the proposition that more of the cause is followed by more of the effect1 being a corollary from the principle of the ,composition of ,causes1 which1 as we have seen1 is the general rule of causation2 cases of the opposite description1 in which causes change their properties on being conjoined with one another1 being1 on the contrary1 special and exceptional4 ,suppose1 then1 that when ,a changes in quantity1 a also changes in quantity1 and in such a manner that we can trace the numerical relation which the changes of the one bear to such changes of the other as take place within our limits of observation4 ,we may then1 with certain precautions1 safely conclude that the same numerical relation will hold beyond those limits4 ,if1 for instance1 we find that when ,a is double1 a is double2 that when ,a is treble or quadruple1 a is treble or quadruple2 we may conclude that if ,a were a half or a third1 a would be a half or a third1 and finally1 that if ,a were annihilated1 a would be annihilated2 and that a is wholly the effect of ,a1 or wholly the effect of the same cause with ,a4 ,and so with any other numerical relation according to which ,a and a would vanish simultaneously2 as1 for instance1 if a were proportional to the square of ,a4 ,if1 on the other hand1 a is not wholly the effect of ,a1 but yet varies when ,a varies1 it is probably a mathematical function not of ,a alone1 but of ,a and something else3 its changes1 for example1 may be such as would occur if part of it remained constant1 or varied on some other principle1 and the remainder varied in some numerical relations to the variations of ,a4 ,in that case1 when ,a diminishes1 a will be seen to approach not toward zero1 but toward some other limit2 and when the series of variations is such as to indicate what that limit is1 if constant1 or the law of its variation1 if variable1 the limit will exactly measure how much of a is the effect of some other and independent cause1 and the remainder will be the effect of ,a 7or of the cause of ,a74 ,these conclusions1 however1 must not be drawn without certain precautions4 ,in the first place1 the possibility of drawing them at all1 manifestly supposes that we are acquainted not only with the variations1 but with the absolute quantities both of ,a and a4 ,if we do not know the total quantities1 we can not1 of course1 determine the real numerical relation according to which those quantities vary4 ,it is1 therefore1 an error to conclude1 as some have concluded1 that because increase of heat expands bodies1 that is1 increases the distance between their particles1 therefore the distance is wholly the effect of heat1 and that if we could entirely exhaust the body of its heat1 the particles would be in complete contact4 ,this is no more than a guess1 and of the most hazardous sort1 not a legitimate induction3 for since we neither know how much heat there is in any body1 nor what is the real distance between any two of its particles1 we can not judge whether the contraction of the distance does or does not follow the diminution of the quantity of heat according to such a numerical relation that the two quantities would vanish simultaneously4 ,in contrast with this1 let us consider a case in which the absolute quantities are known2 the case contemplated in the first law of motion3 viz41 that all bodies in motion continue to move in a straight line with uniform velocity until acted upon by some new force4 ,this assertion is in open opposition to first appearances2 all terrestrial objects1 when in motion1 gradually abate their velocity1 and at last stop2 which accordingly the ancients1 with their inductio per enumerationem simplicem1 imagined to be the law4 ,every moving body1 however1 encounters various obstacles1 as friction1 the resistance of the atmosphere1 etc41 which we know by daily experience to be causes capable of destroying motion4 ,it was suggested that the whole of the retardation might be owing to these causes4 ,how was this inquired into8 ,if the obstacles could have been entirely removed1 the case would have been amenable to the ,method of ,difference4 ,they could not be removed1 they could only be diminished1 and the case1 therefore1 admitted only of the ,method of ,concomitant ,variations4 ,this accordingly being employed1 it was found that every diminution of the obstacles diminished the retardation of the motion3 and inasmuch as in this case 7unlike the case of heat7 the total quantities both of the antecedent and of the consequent were known1 it was practicable to estimate1 with an approach to accuracy1 both the amount of the retardation and the amount of the retarding causes1 or resistances1 and to judge how near they both were to being exhausted2 and it appeared that the effect dwindled as rapidly1 and at each step was as far on the road toward annihilation1 as the cause was4 ,the simple oscillation of a weight suspended from a fixed point1 and moved a little out of the perpendicular1 which in ordinary circumstances lasts but a few minutes1 was prolonged in ,borda's experiments to more than thirty hours1 by diminishing as much as possible the friction at the point of suspension1 and by making the body oscillate in a space exhausted as nearly as possible of its air4 ,there could therefore be no hesitation in assigning the whole of the retardation of motion to the influence of the obstacles2 and since1 after subducting this retardation from the total phenomenon1 the remainder was a uniform velocity1 the result was the proposition known as the first law of motion4 ,there is also another characteristic uncertainty affecting the inference that the law of variation which the quantities observe within our limits of observation1 will hold beyond those limits4 ,there is1 of course1 in the first instance1 the possibility that beyond the limits1 and in circumstances therefore of which we have no direct experience1 some counteracting cause might develop itself2 either a new agent or a new property of the agents concerned1 which lies dormant in the circumstances we are able to observe4 ,this is an element of uncertainty which enters largely into all our predictions of effects2 but it is not peculiarly applicable to the ,method of ,concomitant ,variations4 ,the uncertainty1 however1 of which ,i am about to speak1 is characteristic of that method2 especially in the cases in which the extreme limits of our observation are very narrow1 in comparison with the possible variations in the quantities of the phenomena4 ,any one who has the slightest acquaintance with mathematics1 is aware that very different laws of variation may produce numerical results which differ but slightly from one another within narrow limits2 and it is often only when the absolute amounts of variation are considerable1 that the difference between the results given by one law and by another becomes appreciable4 ,when1 therefore1 such variations in the quantity of the antecedents as we have the means of observing are small in comparison with the total quantities1 there is much danger lest we should mistake the numerical law1 and be led to miscalculate the variations which would take place beyond the limits2 a miscalculation which would vitiate any conclusion respecting the dependence of the effect upon the cause1 that could be founded on those variations4 ,examples are not wanting of such mistakes4 8,the formul10 says ,sir ,john ,herschel17#acf7 8which have been empirically deduced for the elasticity of steam 7till very recently71 and those for the resistance of fluids1 and other similar subjects10 when relied on beyond the limits of the observations from which they were deduced1 8have almost invariably failed to support the theoretical structures which have been erected on them40 ,in this uncertainty1 the conclusion we may draw from the concomitant variations of a and ,a1 to the existence of an invariable and exclusive connection between them1 or to the permanency of the same numerical relation between their variations when the quantities are much greater or smaller than those which we have had the means of observing1 can not be considered to rest on a complete induction4 ,all that in such a case can be regarded as proved on the subject of causation is1 that there is some connection between the two phenomena2 that ,a1 or something which can influence ,a1 must be one of the causes which collectively determine a4 ,we may1 however1 feel assured that the relation which we have observed to exist between the variations of ,a and a1 will hold true in all cases which fall between the same extreme limits2 that is1 wherever the utmost increase or diminution in which the result has been found by observation to coincide with the law1 is not exceeded4 ,the four methods which it has now been attempted to describe1 are the only possible modes of experimental inquiry--of direct induction a posteriori1 as distinguished from deduction3 at least1 ,i know not1 nor am able to imagine any others4 ,and even of these1 the ,method of ,residues1 as we have seen1 is not independent of deduction2 though1 as it also requires specific experience1 it may1 without impropriety1 be included among methods of direct observation and experiment4 ,these1 then1 with such assistance as can be obtained from ,deduction1 compose the available resources of the human mind for ascertaining the laws of the succession of phenomena4 ,before proceeding to point out certain circumstances by which the employment of these methods is subjected to an immense increase of complication and of difficulty1 it is expedient to illustrate the use of the methods1 by suitable examples drawn from actual physical investigations4 ,these1 accordingly1 will form the subject of the succeeding chapter4 ,chapter ,,ix4 ,miscellaneous ,examples ,of ,the ,four ,methods4 #a4 ,i shall select1 as a first example1 an interesting speculation of one of the most eminent of theoretical chemists1 ,baron ,liebig4 ,the object in view is to ascertain the immediate cause of the death produced by metallic poisons4 ,arsenious acid1 and the salts of lead1 bismuth1 copper1 and mercury1 if introduced into the animal organism1 except in the smallest doses1 destroy life4 ,these facts have long been known1 as insulated truths of the lowest order of generalization2 but it was reserved for ,liebig1 by an apt employment of the first two of our methods of experimental inquiry1 to connect these truths together by a higher induction1 pointing out what property1 common to all these deleterious substances1 is the really operating cause of their fatal effect4 ,when solutions of these substances are placed in sufficiently close contact with many animal products1 albumen1 milk1 muscular fibre1 and animal membranes1 the acid or salt leaves the water in which it was dissolved1 and enters into combination with the animal substance1 which substance1 after being thus acted upon1 is found to have lost its tendency to spontaneous decomposition1 or putrefaction4 ,observation also shows1 in cases where death has been produced by these poisons1 that the parts of the body with which the poisonous substances have been brought into contact1 do not afterward putrefy4 ,and1 finally1 when the poison has been supplied in too small a quantity to destroy life1 eschars are produced1 that is1 certain superficial portions of the tissues are destroyed1 which are afterward thrown off by the reparative process taking place in the healthy parts4 ,these three sets of instances admit of being treated according to the ,method of ,agreement4 ,in all of them the metallic compounds are brought into contact with the substances which compose the human or animal body2 and the instances do not seem to agree in any other circumstance4 ,the remaining antecedents are as different1 and even opposite1 as they could possibly be made2 for in some the animal substances exposed to the action of the poisons are in a state of life1 in others only in a state of organization1 in others not even in that4 ,and what is the result which follows in all the cases8 ,the conversion of the animal substance 7by combination with the poison7 into a chemical compound1 held together by so powerful a force as to resist the subsequent action of the ordinary causes of decomposition4 ,now1 organic life 7the necessary condition of sensitive life7 consisting in a continual state of decomposition and recomposition of the different organs and tissues1 whatever incapacitates them for this decomposition destroys life4 ,and thus the proximate cause of the death produced by this description of poisons is ascertained1 as far as the ,method of ,agreement can ascertain it4 ,let us now bring our conclusion to the test of the ,method of ,difference4 ,setting out from the cases already mentioned1 in which the antecedent is the presence of substances forming with the tissues a compound incapable of putrefaction1 7and a fortiori incapable of the chemical actions which constitute life71 and the consequent is death1 either of the whole organism1 or of some portion of it2 let us compare with these cases other cases1 as much resembling them as possible1 but in which that effect is not produced4 ,and1 first1 8many insoluble basic salts of arsenious acid are known not to be poisonous4 ,the substance called alkargen1 discovered by ,bunsen1 which contains a very large quantity of arsenic1 and approaches very closely in composition to the organic arsenious compounds found in the body1 has not the slightest injurious action upon the organism40 ,now when these substances are brought into contact with the tissues in any way1 they do not combine with them2 they do not arrest their progress to decomposition4 ,as far1 therefore1 as these instances go1 it appears that when the effect is absent1 it is by reason of the absence of that antecedent which we had already good ground for considering as the proximate cause4 ,but the rigorous conditions of the ,method of ,difference are not yet satisfied2 for we can not be sure that these unpoisonous bodies agree with the poisonous substances in every property1 except the particular one of entering into a difficultly decomposable compound with the animal tissues4 ,to render the method strictly applicable1 we need an instance1 not of a different substance1 but of one of the very same substances1 in circumstances which would prevent it from forming1 with the tissues1 the sort of compound in question2 and then1 if death does not follow1 our case is made out4 ,now such instances are afforded by the antidotes to these poisons4 ,for example1 in case of poisoning by arsenious acid1 if hydrated peroxide of iron is administered1 the destructive agency is instantly checked4 ,now this peroxide is known to combine with the acid1 and form a compound1 which1 being insoluble1 can not act at all on animal tissues4 ,so1 again1 sugar is a well-known antidote to poisoning by salts of copper2 and sugar reduces those salts either into metallic copper1 or into the red sub-oxide1 neither of which enters into combination with animal matter4 ,the disease called painter's colic1 so common in manufactories of white-lead1 is unknown where the workmen are accustomed to take1 as a preservative1 sulphuric acid lemonade 7a solution of sugar rendered acid by sulphuric acid74 ,now diluted sulphuric acid has the property of decomposing all compounds of lead with organic matter1 or of preventing them from being formed4 ,there is another class of instances1 of the nature required by the ,method of ,difference1 which seem at first sight to conflict with the theory4 ,soluble salts of silver1 such for instance as the nitrate1 have the same stiffening antiseptic effect on decomposing animal substances as corrosive sublimate and the most deadly metallic poisons2 and when applied to the external parts of the body1 the nitrate is a powerful caustic1 depriving those parts of all active vitality1 and causing them to be thrown off by the neighboring living structures1 in the form of an eschar4 ,the nitrate and the other salts of silver ought1 then1 it would seem1 if the theory be correct1 to be poisonous2 yet they may be administered internally with perfect impunity4 ,from this apparent exception arises the strongest confirmation which the theory has yet received4 ,nitrate of silver1 in spite of its chemical properties1 does not poison when introduced into the stomach2 but in the stomach1 as in all animal liquids1 there is common salt2 and in the stomach there is also free muriatic acid4 ,these substances operate as natural antidotes1 combining with the nitrate1 and if its quantity is not too great1 immediately converting it into chloride of silver1 a substance very slightly soluble1 and therefore incapable of combining with the tissues1 although to the extent of its solubility it has a medicinal influence1 though an entirely different class of organic actions4 ,the preceding instances have afforded an induction of a high order of conclusiveness1 illustrative of the two simplest of our four methods2 though not rising to the maximum of certainty which the ,method of ,difference1 in its most perfect exemplification1 is capable of affording4 ,for 7let us not forget7 the positive instance and the negative one which the rigor of that method requires1 ought to differ only in the presence or absence of one single circumstance4 ,now1 in the preceding argument1 they differ in the presence or absence not of a single circumstance1 but of a single substance3 and as every substance has innumerable properties1 there is no knowing what number of real differences are involved in what is nominally and apparently only one difference4 ,it is conceivable that the antidote1 the peroxide of iron for example1 may counteract the poison through some other of its properties than that of forming an insoluble compound with it2 and if so1 the theory would fall to the ground1 so far as it is supported by that instance4 ,this source of uncertainty1 which is a serious hinderance to all extensive generalizations in chemistry1 is1 however1 reduced in the present case to almost the lowest degree possible1 when we find that not only one substance1 but many substances1 possess the capacity of acting as antidotes to metallic poisons1 and that all these agree in the property of forming insoluble compounds with the poisons1 while they can not be ascertained to agree in any other property whatsoever4 ,we have thus1 in favor of the theory1 all the evidence which can be obtained by what we termed the ,indirect ,method of ,difference1 or the ,joint ,method of ,agreement and ,difference2 the evidence of which1 though it never can amount to that of the ,method of ,difference properly so called1 may approach indefinitely near to it4 #b4 ,let the object be7#acg7 to ascertain the law of what is termed induced electricity2 to find under what conditions any electrified body1 whether positively or negatively electrified1 gives rise to a contrary electric state in some other body adjacent to it4 ,the most familiar exemplification of the phenomenon to be investigated is the following4 ,around the prime conductors of an electrical machine the atmosphere to some distance1 or any conducting surface suspended in that atmosphere1 is found to be in an electric condition opposite to that of the prime conductor itself4 ,near and around the positive prime conductor there is negative electricity1 and near and around the negative prime conductor there is positive electricity4 ,when pith balls are brought near to either of the conductors1 they become electrified with the opposite electricity to it2 either receiving a share from the already electrified atmosphere by conduction1 or acted upon by the direct inductive influence of the conductor itself3 they are then attracted by the conductor to which they are in opposition2 or1 if withdrawn in their electrified state1 they will be attracted by any other oppositely charged body4 ,in like manner the hand1 if brought near enough to the conductor1 receives or gives an electric discharge2 now we have no evidence that a charged conductor can be suddenly discharged unless by the approach of a body oppositely electrified4 ,in the case1 therefore1 of the electric machine1 it appears that the accumulation of electricity in an insulated conductor is always accompanied by the excitement of the contrary electricity in the surrounding atmosphere1 and in every conductor placed near the former conductor4 ,it does not seem possible1 in this case1 to produce one electricity by itself4 ,let us now examine all the other instances which we can obtain1 resembling this instance in the given consequent1 namely1 the evolution of an opposite electricity in the neighborhood of an electrified body4 ,as one remarkable instance we have the ,leyden jar2 and after the splendid experiments of ,faraday in complete and final establishment of the substantial identity of magnetism and electricity1 we may cite the magnet1 both the natural and the electro-magnet1 in neither of which it is possible to produce one kind of electricity by itself1 or to charge one pole without charging an opposite pole with the contrary electricity at the same time4 ,we can not have a magnet with one pole3 if we break a natural loadstone into a thousand pieces1 each piece will have its two oppositely electrified poles complete within itself4 ,in the voltaic circuit1 again1 we can not have one current without its opposite4 ,in the ordinary electric machine1 the glass cylinder or plate1 and the rubber1 acquire opposite electricities4 ,from all these instances1 treated by the ,method of ,agreement1 a general law appears to result4 ,the instances embrace all the known modes in which a body can become charged with electricity2 and in all of them there is found1 as a concomitant or consequent1 the excitement of the opposite electric state in some other body or bodies4 ,it seems to follow that the two facts are invariably connected1 and that the excitement of electricity in any body has for one of its necessary conditions the possibility of a simultaneous excitement of the opposite electricity in some neighboring body4 ,as the two contrary electricities can only be produced together1 so they can only cease together4 ,this may be shown by an application of the ,method of ,difference to the example of the ,leyden jar4 ,it needs scarcely be here remarked that in the ,leyden jar1 electricity can be accumulated and retained in considerable quantity1 by the contrivance of having two conducting surfaces of equal extent1 and parallel to each other through the whole of that extent1 with a non-conducting substance such as glass between them4 ,when one side of the jar is charged positively1 the other is charged negatively1 and it was by virtue of this fact that the ,leyden jar served just now as an instance in our employment of the ,method of ,agreement4 ,now it is impossible to discharge one of the coatings unless the other can be discharged at the same time4 ,a conductor held to the positive side can not convey away any electricity unless an equal quantity be allowed to pass from the negative side3 if one coating be perfectly insulated1 the charge is safe4 ,the dissipation of one must proceed pari passu with that of the other4 ,the law thus strongly indicated admits of corroboration by the ,method of ,concomitant ,variations4 ,the ,leyden jar is capable of receiving a much higher charge than can ordinarily be given to the conductor of an electrical machine4 ,now in the case of the ,leyden jar1 the metallic surface which receives the induced electricity is a conductor exactly similar to that which receives the primary charge1 and is therefore as susceptible of receiving and retaining the one electricity1 as the opposite surface of receiving and retaining the other2 but in the machine1 the neighboring body which is to be oppositely electrified is the surrounding atmosphere1 or any body casually brought near to the conductor2 and as these are generally much inferior in their capacity of becoming electrified1 to the conductor itself1 their limited power imposes a corresponding limit to the capacity of the conductor for being charged4 ,as the capacity of the neighboring body for supporting the opposition increases1 a higher charge becomes possible3 and to this appears to be owing the great superiority of the ,leyden jar4 ,a further and most decisive confirmation by the ,method of ,difference1 is to be found in one of ,faraday's experiments in the course of his researches on the subject of ,induced ,electricity4 ,since common or machine electricity1 and voltaic electricity1 may be considered for the present purpose to be identical1 ,faraday wished to know whether1 as the prime conductor develops opposite electricity upon a conductor in its vicinity1 so a voltaic current running along a wire would induce an opposite current upon another wire laid parallel to it at a short distance4 ,now this case is similar to the cases previously examined1 in every circumstance except the one to which we have ascribed the effect4 ,we found in the former instances that whenever electricity of one kind was excited in one body1 electricity of the opposite kind must be excited in a neighboring body4 ,but in ,faraday's experiment this indispensable opposition exists within the wire itself4 ,from the nature of a voltaic charge1 the two opposite currents necessary to the existence of each other are both accommodated in one wire2 and there is no need of another wire placed beside it to contain one of them1 in the same way as the ,leyden jar must have a positive and a negative surface4 ,the exciting cause can and does produce all the effect which its laws require1 independently of any electric excitement of a neighboring body4 ,now the result of the experiment with the second wire was1 that no opposite current was produced4 ,there was an instantaneous effect at the closing and breaking of the voltaic circuit2 electric inductions appeared when the two wires were moved to and from one another2 but these are phenomena of a different class4 ,there was no induced electricity in the sense in which this is predicated of the ,leyden jar2 there was no sustained current running up the one wire while an opposite current ran down the neighboring wire2 and this alone would have been a true parallel case to the other4 ,it thus appears by the combined evidence of the ,method of ,agreement1 the ,method of ,concomitant ,variations1 and the most rigorous form of the ,method of ,difference1 that neither of the two kinds of electricity can be excited without an equal excitement of the other and opposite kind3 that both are effects of the same cause2 that the possibility of the one is a condition of the possibility of the other1 and the quantity of the one an impassable limit to the quantity of the other4 ,a scientific result of considerable interest in itself1 and illustrating those three methods in a manner both characteristic and easily intelligible47#ach7 #c4 ,our third example shall be extracted from ,sir ,john ,herschel's ,discourse course on the ,study of ,natural ,philosophy1 a work replete with happily-selected exemplifications of inductive processes from almost every department of physical science1 and in which alone1 of all books which ,i have met with1 the four methods of induction are distinctly recognized1 though not so clearly characterized and defined1 nor their correlation so fully shown1 as has appeared to me desirable4 ,the present example is described by ,sir ,john ,herschel as 8one of the most beautiful specimens0 which can be cited 8of inductive experimental inquiry lying within a moderate compass20 the theory of dew1 first promulgated by the late ,dr4 ,wells1 and now universally adopted by scientific authorities4 ,the passages in inverted commas are extracted verbatim from the ,discourse47#aci7 8,suppose dew were the phenomenon proposed1 whose cause we would know4 ,in the first place0 we must determine precisely what we mean by dew3 what the fact really is whose cause we desire to investigate4 8,we must separate dew from rain1 and the moisture of fogs1 and limit the application of the term to what is really meant1 which is the spontaneous appearance of moisture on substances exposed in the open air when no rain or visible wet is falling40 ,this answers to a preliminary operation which will be characterized in the ensuing book1 treating of operations subsidiary to induction47#adj7 8,now1 here we have analogous phenomena in the moisture which bedews a cold metal or stone when we breathe upon it2 that which appears on a glass of water fresh from the well in hot weather2 that which appears on the inside of windows when sudden rain or hail chills the external air2 that which runs down our walls when1 after a long frost1 a warm1 moist thaw comes on40 ,comparing these cases1 we find that they all contain the phenomenon which was proposed as the subject of investigation4 ,now 8all these instances agree in one point1 the coldness of the object dewed1 in comparison with the air in contact with it40 ,but there still remains the most important case of all1 that of nocturnal dew3 does the same circumstance exist in this case8 8,is it a fact that the object dewed is colder than the air8 ,certainly not1 one would at first be inclined to say2 for what is to make it so8 ,but 444 the experiment is easy3 we have only to lay a thermometer in contact with the dewed substance1 and hang one at a little distance above it1 out of reach of its influence4 ,the experiment has been therefore made1 the question has been asked1 and the answer has been invariably in the affirmative4 ,whenever an object contracts dew1 it is colder than the air40 ,here1 then1 is a complete application of the ,method of ,agreement1 establishing the fact of an invariable connection between the deposition of dew on a surface1 and the coldness of that surface compared with the external air4 ,but which of these is cause1 and which effect8 or are they both effects of something else8 ,on this subject the ,method of ,agreement can afford us no light3 we must call in a more potent method4 8,we must collect more facts1 or1 which comes to the same thing1 vary the circumstances2 since every instance in which the circumstances differ is a fresh fact3 and especially1 we must note the contrary or negative cases1 i4e41 where no dew is produced30 a comparison between instances of dew and instances of no dew1 being the condition necessary to bring the ,method of ,difference into play4 8,now1 first1 no dew is produced on the surface of polished metals1 but it is very copiously on glass1 both exposed with their faces upward1 and in some cases the under side of a horizontal plate of glass is also dewed40 ,here is an instance in which the effect is produced1 and another instance in which it is not produced2 but we can not yet pronounce1 as the canon of the ,method of ,difference requires1 that the latter instance agrees with the former in all its circumstances except one2 for the differences between glass and polished metals are manifold1 and the only thing we can as yet be sure of is1 that the cause of dew will be found among the circumstances by which the former substance is distinguished from the latter4 ,but if we could be sure that glass1 and the various other substances on which dew is deposited1 have only one quality in common1 and that polished metals and the other substances on which dew is not deposited1 have also nothing in common but the one circumstance of not having the one quality which the others have2 the requisitions of the ,method of ,difference would be completely satisfied1 and we should recognize1 in that quality of the substances1 the cause of dew4 ,this1 accordingly1 is the path of inquiry which is next to be pursued4 8,in the cases of polished metal and polished glass1 the contrast shows evidently that the substance has much to do with the phenomenon2 therefore let the substance alone be diversified as much as possible1 by exposing polished surfaces of various kinds4 ,this done1 a scale of intensity becomes obvious4 ,those polished substances are found to be most strongly dewed which conduct heat worst2 while those which conduct heat well1 resist dew most effectually40 ,the complication increases2 here is the ,method of ,concomitant ,variations called to our assistance2 and no other method was practicable on this occasion2 for the quality of conducting heat could not be excluded1 since all substances conduct heat in some degree4 ,the conclusion obtained is1 that cteris paribus the deposition of dew is in some proportion to the power which the body possesses of resisting the passage of heat2 and that this1 therefore 7or something connected with this71 must be at least one of the causes which assist in producing the deposition of dew on the surface4 8,but if we expose rough surfaces instead of polished1 we sometimes find this law interfered with4 ,thus1 roughened iron1 especially if painted over or blackened1 becomes dewed sooner than varnished paper2 the kind of surface1 therefore1 has a great influence4 ,expose1 then1 the same material in very diversified states1 as to surface0 7that is1 employ the ,method of ,difference to ascertain concomitance of variations71 8and another scale of intensity becomes at once apparent2 those surfaces which part with their heat most readily by radiation are found to contract dew most copiously40 ,here1 therefore1 are the requisites for a second employment of the ,method of ,concomitant ,variations2 which in this case also is the only method available1 since all substances radiate heat in some degree or other4 ,the conclusion obtained by this new application of the method is1 that cteris paribus the deposition of dew is also in some proportion to the power of radiating heat2 and that the quality of doing this abundantly 7or some cause on which that quality depends7 is another of the causes which promote the deposition of dew on the substance4 8,again1 the influence ascertained to exist of substance and surface leads us to consider that of texture3 and here1 again1 we are presented on trial with remarkable differences1 and with a third scale of intensity1 pointing out substances of a close1 firm texture1 such as stones1 metals1 etc41 as unfavorable1 but those of a loose one1 as cloth1 velvet1 wool1 eider-down1 cotton1 etc41 as eminently favorable to the contraction of dew40 ,the ,method of ,concomitant ,variations is here1 for the third time1 had recourse to2 and1 as before1 from necessity1 since the texture of no substance is absolutely firm or absolutely loose4 ,looseness of texture1 therefore1 or something which is the cause of that quality1 is another circumstance which promotes the deposition of dew2 but this third course resolves itself into the first1 viz41 the quality of resisting the passage of heat3 for substances of loose texture 8are precisely those which are best adapted for clothing1 or for impeding the free passage of heat from the skin into the air1 so as to allow their outer surfaces to be very cold1 while they remain warm within20 and this last is1 therefore1 an induction 7from fresh instances7 simply corroborative of a former induction4 ,it thus appears that the instances in which much dew is deposited1 which are very various1 agree in this1 and1 so far as we are able to observe1 in this only1 that they either radiate heat rapidly or conduct it slowly3 qualities between which there is no other circumstance of agreement than that by virtue of either1 the body tends to lose heat from the surface more rapidly than it can be restored from within4 ,the instances1 on the contrary1 in which no dew1 or but a small quantity of it1 is formed1 and which are also extremely various1 agree 7as far as we can observe7 in nothing except in not having this same property4 ,we seem1 therefore1 to have detected the characteristic difference between the substances on which dew is produced and those on which it is not produced4 ,and thus have been realized the requisitions of what we have termed the ,indirect ,method of ,difference1 or the ,joint ,method of ,agreement and ,difference4 ,the example afforded of this indirect method1 and of the manner in which the data are prepared for it by the ,methods of ,agreement and of ,concomitant ,variations1 is the most important of all the illustrations of induction afforded by this interesting speculation4 ,we might now consider the question1 on what the deposition of dew depends1 to be completely solved1 if we could be quite sure that the substances on which dew is produced differ from those on which it is not1 in nothing but in the property of losing heat from the surface faster than the loss can be repaired from within4 ,and though we never can have that complete certainty1 this is not of so much importance as might at first be supposed2 for we have1 at all events1 ascertained that even if there be any other quality hitherto unobserved which is present in all the substances which contract dew1 and absent in those which do not1 this other property must be one which1 in all that great number of substances1 is present or absent exactly where the property of being a better radiator than conductor is present or absent2 an extent of coincidence which affords a strong presumption of a community of cause1 and a consequent invariable co-existence between the two properties2 so that the property of being a better radiator than conductor1 if not itself the cause1 almost certainly always accompanies the cause1 and for purposes of prediction1 no error is likely to be committed by treating it as if it were really such4 ,reverting now to an earlier stage of the inquiry1 let us remember that we had ascertained that1 in every instance where dew is formed1 there is actual coldness of the surface below the temperature of the surrounding air2 but we were not sure whether this coldness was the cause of dew1 or its effect4 ,this doubt we are now able to resolve4 ,we have found that1 in every such instance1 the substance is one which1 by its own properties or laws1 would1 if exposed in the night1 become colder than the surrounding air4 ,the coldness1 therefore1 being accounted for independently of the dew1 while it is proved that there is a connection between the two1 it must be the dew which depends on the coldness2 or1 in other words1 the coldness is the cause of the dew4 ,this law of causation1 already so amply established1 admits1 however1 of efficient additional corroboration in no less than three ways4 ,first1 by deduction from the known laws of aqueous vapor when diffused through air or any other gas2 and though we have not yet come to the ,deductive ,method1 we will not omit what is necessary to render this speculation complete4 ,it is known by direct experiment that only a limited quantity of water can remain suspended in the state of vapor at each degree of temperature1 and that this maximum grows less and less as the temperature diminishes4 ,from this it follows1 deductively1 that if there is already as much vapor suspended as the air will contain at its existing temperature1 any lowering of that temperature will cause a portion of the vapor to be condensed1 and become water4 ,but again1 we know deductively1 from the laws of heat1 that the contact of the air with a body colder than itself will necessarily lower the temperature of the stratum of air immediately applied to its surface2 and will1 therefore1 cause it to part with a portion of its water1 which accordingly will1 by the ordinary laws of gravitation or cohesion1 attach itself to the surface of the body1 thereby constituting dew4 ,this deductive proof1 it will have been seen1 has the advantage of at once proving causation as well as co-existence2 and it has the additional advantage that it also accounts for the exceptions to the occurrence of the phenomenon1 the cases in which1 although the body is colder than the air1 yet no dew is deposited2 by showing that this will necessarily be the case when the air is so under-supplied with aqueous vapor1 comparatively to its temperature1 that even when somewhat cooled by the contact of the colder body it can still continue to hold in suspension all the vapor which was previously suspended in it3 thus in a very dry summer there are no dews1 in a very dry winter no hoar-frost4 ,here1 therefore1 is an additional condition of the production of dew1 which the methods we previously made use of failed to detect1 and which might have remained still undetected1 if recourse had not been had to the plan of deducing the effect from the ascertained properties of the agents known to be present4 ,the second corroboration of the theory is by direct experiment1 according to the canon of the ,method of ,difference4 ,we can1 by cooling the surface of any body1 find in all cases some temperature 7more or less inferior to that of the surrounding air1 according to its hygrometric condition7 at which dew will begin to be deposited4 ,here1 too1 therefore1 the causation is directly proved4 ,we can1 it is true1 accomplish this only on a small scale1 but we have ample reason to conclude that the same operation1 if conducted in nature's great laboratory1 would equally produce the effect4 ,and1 finally1 even on that great scale we are able to verify the result4 ,the case is one of those rare cases1 as we have shown them to be1 in which nature works the experiment for us in the same manner in which we ourselves perform it2 introducing into the previous state of things a single and perfectly definite new circumstance1 and manifesting the effect so rapidly that there is not time for any other material change in the pre-existing circumstances4 8,it is observed that dew is never copiously deposited in situations much screened from the open sky1 and not at all in a cloudy night2 but if the clouds withdraw even for a few minutes1 and leave a clear opening1 a deposition of dew presently begins1 and goes on increasing444 ,dew formed in clear intervals will often even evaporate again when the sky becomes thickly overcast40 ,the proof1 therefore1 is complete1 that the presence or absence of an uninterrupted communication with the sky causes the deposition or non-deposition of dew4 ,now1 since a clear sky is nothing but the absence of clouds1 and it is a known property of clouds1 as of all other bodies between which and any given object nothing intervenes but an elastic fluid1 that they tend to raise or keep up the superficial temperature of the object by radiating heat to it1 we see at once that the disappearance of clouds will cause the surface to cool2 so that nature1 in this case1 produces a change in the antecedent by definite and known means1 and the consequent follows accordingly3 a natural experiment which satisfies the requisitions of the ,method of ,difference47#ada7 ,the accumulated proof of which the ,theory of ,dew has been found susceptible1 is a striking instance of the fullness of assurance which the inductive evidence of laws of causation may attain1 in cases in which the invariable sequence is by no means obvious to a superficial view4 #d4 ,the admirable physiological investigations of ,dr4 ,brown-,squard afford brilliant examples of the application of the ,inductive ,methods to a class of inquiries in which1 for reasons which will presently be given1 direct induction takes place under peculiar difficulties and disadvantages4 ,as one of the most apt instances1 ,i select his speculation 7in the proceedings of the ,royal ,society for ,may #af1 #ahfa7 on the relations between muscular irritability1 cadaveric rigidity1 and putrefaction4 ,the law which ,dr4 ,brown-,squard's investigation tends to establish1 is the following3 8,the greater the degree of muscular irritability at the time of death1 the later the cadaveric rigidity sets in1 and the longer it lasts1 and the later also putrefaction appears1 and the slower it progresses40 ,one would say at first sight that the method here required must be that of ,concomitant ,variations4 ,but this is a delusive appearance1 arising from the circumstance that the conclusion to be tested is itself a fact of concomitant variations4 ,for the establishment of that fact any of the ,methods may be put in requisition1 and it will be found that the fourth ,method1 though really employed1 has only a subordinate place in this particular investigation4 ,the evidences by which ,dr4 ,brown-,squard establishes the law may be enumerated as follows3 #ast4 ,paralyzed muscles have greater irritability than healthy muscles4 ,now1 paralyzed muscles are later in assuming the cadaveric rigidity than healthy muscles1 the rigidity lasts longer1 and putrefaction sets in later1 and proceeds more slowly4 ,both these propositions had to be proved by experiment2 and for the experiments which prove them1 science is also indebted to ,dr4 ,brown-,squard4 ,the former of the two--that paralyzed muscles have greater irritability than healthy muscles--he ascertained in various ways1 but most decisively by 8comparing the duration of irritability in a paralyzed muscle and in the corresponding healthy one of the opposite side1 while they are both submitted to the same excitation40 ,he 8often found1 in experimenting in that way1 that the paralyzed muscle remained irritable twice1 three times1 or even four times as long as the healthy one40 ,this is a case of induction by the ,method of ,difference4 ,the two limbs1 being those of the same animal1 were presumed to differ in no circumstance material to the case except the paralysis1 to the presence and absence of which1 therefore1 the difference in the muscular irritability was to be attributed4 ,this assumption of complete resemblance in all material circumstances save one1 evidently could not be safely made in any one pair of experiments1 because the two legs of any given animal might be accidentally in very different pathological conditions2 but if1 besides taking pains to avoid any such difference1 the experiment was repeated sufficiently often in different animals to exclude the supposition that any abnormal circumstance could be present in them all1 the conditions of the ,method of ,difference were adequately secured4 ,in the same manner in which ,dr4 ,brown-,squard proved that paralyzed muscles have greater irritability1 he also proved the correlative proposition respecting cadaveric rigidity and putrefaction4 ,having1 by section of the roots of the sciatic nerve1 and again of a lateral half of the spinal cord1 produced paralysis in one hind leg of an animal while the other remained healthy1 he found that not only did muscular irritability last much longer in the paralyzed limb1 but rigidity set in later and ended later1 and putrefaction began later and was less rapid than on the healthy side4 ,this is a common case of the ,method of ,difference1 requiring no comment4 ,a further and very important corroboration was obtained by the same method4 ,when the animal was killed1 not shortly after the section of the nerve1 but a month later1 the effect was reversed2 rigidity set in sooner1 and lasted a shorter time1 than in the healthy muscles4 ,but after this lapse of time1 the paralyzed muscles1 having been kept by the paralysis in a state of rest1 had lost a great part of their irritability1 and instead of more1 had become less irritable than those on the healthy side4 ,this gives the ,a ,b ,c1 a b c1 and ,b ,c1 b c1 of the ,method of ,difference4 ,one antecedent1 increased irritability1 being changed1 and the other circumstances being the same1 the consequence did not follow2 and1 moreover1 when a new antecedent1 contrary to the first1 was supplied1 it was followed by a contrary consequent4 ,this instance is attended with the special advantage of proving that the retardation and prolongation of the rigidity do not depend directly on the paralysis1 since that was the same in both the instances2 but specifically on one effect of the paralysis1 namely1 the increased irritability2 since they ceased when it ceased1 and were reversed when it was reversed4 #b;d4 ,diminution of the temperature of muscles before death increases their irritability4 ,but diminution of their temperature also retards cadaveric rigidity and putrefaction4 ,both these truths were first made known by ,dr4 ,brown-,squard himself1 through experiments which conclude according to the ,method of ,difference4 ,there is nothing in the nature of the process requiring specific analysis4 #c;d4 ,muscular exercise1 prolonged to exhaustion1 diminishes the muscular irritability4 ,this is a well-known truth1 dependent on the most general laws of muscular action1 and proved by experiments under the ,method of ,difference1 constantly repeated4 ,now1 it has been shown by observation that overdriven cattle1 if killed before recovery from their fatigue1 become rigid and putrefy in a surprisingly short time4 ,a similar fact has been observed in the case of animals hunted to death2 cocks killed during or shortly after a fight2 and soldiers slain in the field of battle4 ,these various cases agree in no circumstance1 directly connected with the muscles1 except that these have just been subjected to exhausting exercise4 ,under the canon1 therefore1 of the ,method of ,agreement1 it may be inferred that there is a connection between the two facts4 ,the ,method of ,agreement1 indeed1 as has been shown1 is not competent to prove causation4 ,the present case1 however1 is already known to be a case of causation1 it being certain that the state of the body after death must somehow depend upon its state at the time of death4 ,we are1 therefore1 warranted in concluding that the single circumstance in which all the instances agree1 is the part of the antecedent which is the cause of that particular consequent4 #dth4 ,in proportion as the nutrition of muscles is in a good state1 their irritability is high4 ,this fact also rests on the general evidence of the laws of physiology1 grounded on many familiar applications of the ,method of ,difference4 ,now1 in the case of those who die from accident or violence1 with their muscles in a good state of nutrition1 the muscular irritability continues long after death1 rigidity sets in late1 and persists long without the putrefactive change4 ,on the contrary1 in cases of disease in which nutrition has been diminished for a long time before death1 all these effects are reversed4 ,these are the conditions of the ,joint ,method of ,agreement and ,difference4 ,the cases of retarded and long continued rigidity here in question agree only in being preceded by a high state of nutrition of the muscles2 the cases of rapid and brief rigidity agree only in being preceded by a low state of muscular nutrition2 a connection is1 therefore1 inductively proved between the degree of the nutrition1 and the slowness and prolongation of the rigidity4 #eth4 ,convulsions1 like exhausting exercise1 but in a still greater degree1 diminish the muscular irritability4 ,now1 when death follows violent and prolonged convulsions1 as in tetanus1 hydrophobia1 some cases of cholera1 and certain poisons1 rigidity sets in very rapidly1 and after a very brief duration1 gives place to putrefaction4 ,this is another example of the ,method of ,agreement1 of the same character with ,no4 #c4 #fth4 ,the series of instances which we shall take last1 is of a more complex character1 and requires a more minute analysis4 ,it has long been observed that in some cases of death by lightning1 cadaveric rigidity either does not take place at all1 or is of such extremely brief duration as to escape notice1 and that in these cases putrefaction is very rapid4 ,in other cases1 however1 the usual cadaveric rigidity appears4 ,there must be some difference in the cause1 to account for this difference in the effect4 ,now1 8death by lightning may be the result of1 #ast1 a syncope by fright1 or in consequence of a direct or reflex influence of lightning on the par vagum2 #b;d1 hemorrhage in or around the brain1 or in the lungs1 the pericardium1 etc42 #c;d1 concussion1 or some other alteration in the brain20 none of which phenomena have any known property capable of accounting for the suppression1 or almost suppression1 of the cadaveric rigidity4 ,but the cause of death may also be that the lightning produces 8a violent convulsion of every muscle in the body10 of which1 if of sufficient intensity1 the known effect would be that 8muscular irritability ceases almost at once40 ,if ,dr4 ,brown-,squard's generalization is a true law1 these will be the very cases in which rigidity is so much abridged as to escape notice2 and the cases in which1 on the contrary1 rigidity takes place as usual1 will be those in which the stroke of lightning operates in some of the other modes which have been enumerated4 ,how1 then1 is this brought to the test8 ,by experiments1 not on lightning1 which can not be commanded at pleasure1 but on the same natural agency in a manageable form1 that of artificial galvanism4 ,dr4 ,brown-,squard galvanized the entire bodies of animals immediately after death4 ,galvanism can not operate in any of the modes in which the stroke of lightning may have operated1 except the single one of producing muscular convulsions4 ,if1 therefore1 after the bodies have been galvanized1 the duration of rigidity is much shortened and putrefaction much accelerated1 it is reasonable to ascribe the same effects when produced by lightning to the property which galvanism shares with lightning1 and not to those which it does not4 ,now this ,dr4 ,brown-,squard found to be the fact4 ,the galvanic experiment was tried with charges of very various degrees of strength2 and the more powerful the charge1 the shorter was found to be the duration of rigidity1 and the more speedy and rapid the putrefaction4 ,in the experiment in which the charge was strongest1 and the muscular irritability most promptly destroyed1 the rigidity only lasted fifteen minutes4 ,on the principle1 therefore1 of the ,method of ,concomitant ,variations1 it may be inferred that the duration of the rigidity depends on the degree of the irritability2 and that if the charge had been as much stronger than ,dr4 ,brown-,squard's strongest1 as a stroke of lightning must be stronger than any electric shock which we can produce artificially1 the rigidity would have been shortened in a corresponding ratio1 and might have disappeared altogether4 ,this conclusion having been arrived at1 the case of an electric shock1 whether natural or artificial1 becomes an instance1 in addition to all those already ascertained1 of correspondence between the irritability of the muscle and the duration of rigidity4 ,all these instances are summed up in the following statement3 8,that when the degree of muscular irritability at the time of death is considerable1 either in consequence of a good state of nutrition1 as in persons who die in full health from an accidental cause1 or in consequence of rest1 as in cases of paralysis1 or on account of the influence of cold1 cadaveric rigidity in all these cases sets in late and lasts long1 and putrefaction appears late1 and progresses slowly20 but 8that when the degree of muscular irritability at the time of death is slight1 either in consequence of a bad state of nutrition1 or of exhaustion from overexertion1 or from convulsions caused by disease or poison1 cadaveric rigidity sets in and ceases soon1 and putrefaction appears and progresses quickly40 ,these facts present1 in all their completeness1 the conditions of the ,joint ,method of ,agreement and ,difference4 ,early and brief rigidity takes place in cases which agree only in the circumstance of a low state of muscular irritability4 ,rigidity begins late and lasts long in cases which agree only in the contrary circumstance1 of a muscular irritability high and unusually prolonged4 ,it follows that there is a connection through causation between the degree of muscular irritability after death1 and the tardiness and prolongation of the cadaveric rigidity4 ,this investigation places in a strong light the value and efficacy of the ,joint ,method4 ,for1 as we have already seen1 the defect of that ,method is1 that like the ,method of ,agreement1 of which it is only an improved form1 it can not prove causation4 ,but in the present case 7as in one of the steps in the argument which led up to it7 causation is already proved2 since there could never be any doubt that the rigidity altogether1 and the putrefaction which follows it1 are caused by the fact of death3 the observations and experiments on which this rests are too familiar to need analysis1 and fall under the ,method of ,difference4 ,it being1 therefore1 beyond doubt that the aggregate antecedent1 the death1 is the actual cause of the whole train of consequents1 whatever of the circumstances attending the death can be shown to be followed in all its variations by variations in the effect under investigation1 must be the particular feature of the fact of death on which that effect depends4 ,the degree of muscular irritability at the time of death fulfills this condition4 ,the only point that could be brought into question1 would be whether the effect depended on the irritability itself1 or on something which always accompanied the irritability3 and this doubt is set at rest by establishing1 as the instances do1 that by whatever cause the high or low irritability is produced1 the effect equally follows2 and can not1 therefore1 depend upon the causes of irritability1 nor upon the other effects of those causes1 which are as various as the causes themselves1 but upon the irritability1 solely4 #e4 ,the last two examples will have conveyed to any one by whom they have been duly followed1 so clear a conception of the use and practical management of three of the four methods of experimental inquiry1 as to supersede the necessity of any further exemplification of them4 ,the remaining method1 that of ,residues1 not having found a place in any of the preceding investigations1 ,i shall quote from ,sir ,john ,herschel some examples of that method1 with the remarks by which they are introduced4 8,it is by this process1 in fact1 that science1 in its present advanced state1 is chiefly promoted4 ,most of the phenomena which ,nature presents are very complicated2 and when the effects of all known causes are estimated with exactness1 and subducted1 the residual facts are constantly appearing in the form of phenomena altogether new1 and leading to the most important conclusions4 8,for example3 the return of the comet predicted by ,professor ,eucke a great many times in succession1 and the general good agreement of its calculated with its observed place during any one of its periods of visibility1 would lead us to say that its gravitation toward the sun and planets is the sole and sufficient cause of all the phenomena of its orbitual motion2 but when the effect of this cause is strictly calculated and subducted from the observed motion1 there is found to remain behind a residual phenomenon1 which would never have been otherwise ascertained to exist1 which is a small anticipation of the time of its re-appearance1 or a diminution of its periodic time1 which can not be accounted for by gravity1 and whose cause is therefore to be inquired into4 ,such an anticipation would be caused by the resistance of a medium disseminated through the celestial regions2 and as there are other good reasons for believing this to be a vera causa0 7an actually existing antecedent71 8it has therefore been ascribed to such a resistance47#adb7 8,m4 ,arago1 having suspended a magnetic needle by a silk thread1 and set it in vibration1 observed1 that it came much sooner to a state of rest when suspended over a plate of copper1 than when no such plate was beneath it4 ,now1 in both cases there were two ver caus0 7antecedents known to exist7 8why it should come at length to rest1 viz41 the resistance of the air1 which opposes1 and at length destroys1 all motions performed in it2 and the want of perfect mobility in the silk thread4 ,but the effect of these causes being exactly known by the observation made in the absence of the copper1 and being thus allowed for and subducted1 a residual phenomenon appeared1 in the fact that a retarding influence was exerted by the copper itself2 and this fact1 once ascertained1 speedily led to the knowledge of an entirely new and unexpected class of relations40 ,this example belongs1 however1 not to the ,method of ,residues but to the ,method of ,difference1 the law being ascertained by a direct comparison of the results of two experiments1 which differed in nothing but the presence or absence of the plate of copper4 ,to have made it exemplify the ,method of ,residues1 the effect of the resistance of the air and that of the rigidity of the silk should have been calculated a priori1 from the laws obtained by separate and foregone experiments4 8,unexpected and peculiarly striking confirmations of inductive laws frequently occur in the form of residual phenomena1 in the course of investigations of a widely different nature from those which gave rise to the inductions themselves4 ,a very elegant example may be cited in the unexpected confirmation of the law of the development of heat in elastic fluids by compression1 which is afforded by the phenomena of sound4 ,the inquiry into the cause of sound had led to conclusions respecting its mode of propagation1 from which its velocity in the air could be precisely calculated4 ,the calculations were performed2 but1 when compared with fact1 though the agreement was quite sufficient to show the general correctness of the cause and mode of propagation assigned1 yet the whole velocity could not be shown to arise from this theory4 ,there was still a residual velocity to be accounted for1 which placed dynamical philosophers for a long time in great dilemma4 ,at length ,laplace struck on the happy idea1 that this might arise from the heat developed in the act of that condensation which necessarily takes place at every vibration by which sound is conveyed4 ,the matter was subjected to exact calculation1 and the result was at once the complete explanation of the residual phenomenon1 and a striking confirmation of the general law of the development of heat by compression1 under circumstances beyond artificial imitation40 8,many of the new elements of chemistry have been detected in the investigation of residual phenomena4 ,thus ,arfwedson discovered lithia by perceiving an excess of weight in the sulphate produced from a small portion of what he considered as magnesia present in a mineral he had analyzed4 ,it is on this principle1 too1 that the small concentrated residues of great operations in the arts are almost sure to be the lurking-places of new chemical ingredients3 witness iodine1 brome1 selenium1 and the new metals accompanying platina in the experiments of ,wollaston and ,tennant4 ,it was a happy thought of ,glauber to examine what every body else threw away407#adc7 8,almost all the greatest discoveries in ,astronomy10 says the same author17#add7 8have resulted from the consideration of residual phenomena of a quantitative or numerical kind4444 ,it was thus that the grand discovery of the precession of the equinoxes resulted as a residual phenomenon1 from the imperfect explanation of the return of the seasons by the return of the sun to the same apparent place among the fixed stars4 ,thus1 also1 aberration and nutation resulted as residual phenomena from that portion of the changes of the apparent places of the fixed stars which was left unaccounted for by precession4 ,and thus again the apparent proper motions of the stars are the observed residues of their apparent movements outstanding and unaccounted for by strict calculation of the effects of precession1 nutation1 and aberration4 ,the nearest approach which human theories can make to perfection is to diminish this residue1 this caput mortuum of observation1 as it may be considered1 as much as practicable1 and1 if possible1 to reduce it to nothing1 either by showing that something has been neglected in our estimation of known causes1 or by reasoning upon it as a new fact1 and on the principle of the inductive philosophy ascending from the effect to its cause or causes40 ,the disturbing effects mutually produced by the earth and planets upon each other's motions were first brought to light as residual phenomena1 by the difference which appeared between the observed places of those bodies1 and the places calculated on a consideration solely of their gravitation toward the sun4 ,it was this which determined astronomers to consider the law of gravitation as obtaining between all bodies whatever1 and therefore between all particles of matter2 their first tendency having been to regard it as a force acting only between each planet or satellite and the central body to whose system it belonged4 ,again1 the catastrophists1 in geology1 be their opinion right or wrong1 support it on the plea1 that after the effect of all causes now in operation has been allowed for1 there remains in the existing constitution of the earth a large residue of facts1 proving the existence at former periods either of other forces1 or of the same forces in a much greater degree of intensity4 ,to add one more example3 those who assert1 what no one has shown any real ground for believing1 that there is in one human individual1 one sex1 or one race of mankind over another1 an inherent and inexplicable superiority in mental faculties1 could only substantiate their proposition by subtracting from the differences of intellect which we in fact see1 all that can be traced by known laws either to the ascertained differences of physical organization1 or to the differences which have existed in the outward circumstances in which the subjects of the comparison have hitherto been placed4 ,what these causes might fail to account for would constitute a residual phenomenon1 which and which alone would be evidence of an ulterior original distinction1 and the measure of its amount4 ,but the asserters of such supposed differences have not provided themselves with these necessary logical conditions of the establishment of their doctrine4 ,the spirit of the ,method of ,residues being1 it is hoped1 sufficiently intelligible from these examples1 and the other three methods having already been so fully exemplified1 we may here close our exposition of the four methods1 considered as employed in the investigation of the simpler and more elementary order of the combinations of phenomena4 #f4 ,dr4 ,whewell has expressed a very unfavorable opinion of the utility of the ,four ,methods1 as well as of the aptness of the examples by which ,i have attempted to illustrate them4 ,his words are these37#ade7 8,upon these methods1 the obvious thing to remark is1 that they take for granted the very thing which is most difficult to discover1 the reduction of the phenomena to formul such as are here presented to us4 ,when we have any set of complex facts offered to us2 for instance1 those which were offered in the cases of discovery which ,i have mentioned--the facts of the planetary paths1 of falling bodies1 of refracted rays1 of cosmical motions1 of chemical analysis2 and when1 in any of these cases1 we would discover the law of nature which governs them1 or1 if any one chooses so to term it1 the feature in which all the cases agree1 where are we to look for our ,a1 ,b1 ,c1 and a1 b1 c8 ,nature does not present to us the cases in this form2 and how are we to reduce them to this form8 ,you say when we find the combination of ,a ,b ,c with a b c and ,a ,b ,d with a b d1 then we may draw our inference4 ,granted2 but when and where are we to find such combinations8 ,even now that the discoveries are made1 who will point out to us what are the ,a1 ,b1 ,c1 and a1 b1 c1 elements of the cases which have just been enumerated8 ,who will tell us which of the methods of inquiry those historically real and successful inquiries exemplify8 ,who will carry these formul through the history of the sciences1 as they have really grown up1 and show us that these four methods have been operative in their formation2 or that any light is thrown upon the steps of their progress by reference to these formul80 ,he adds that1 in this work1 the methods have not been applied 8to a large body of conspicuous and undoubted examples of discovery1 extending along the whole history of science20 which ought to have been done in order that the methods might be shown to possess the 8advantage0 7which he claims as belonging to his own7 of being those 8by which all great discoveries in science have really been made40--7,p4 #bgg47 ,there is a striking similarity between the objections here made against ,canons of ,induction1 and what was alleged1 in the last century1 by as able men as ,dr4 ,whewell1 against the acknowledged ,canon of ,ratiocination4 ,those who protested against the ,aristotelian ,logic said of the ,syllogism1 what ,dr4 ,whewell says of the ,inductive ,methods1 that it 8takes for granted the very thing which is most difficult to discover1 the reduction of the argument to formul such as are here presented to us40 ,the grand difficulty1 they said1 is to obtain your syllogism1 not to judge of its correctness when obtained4 ,on the matter of fact1 both they and ,dr4 ,whewell are right4 ,the greatest difficulty in both cases is1 first1 that of obtaining the evidence1 and next1 of reducing it to the form which tests its conclusiveness4 ,but if we try to reduce it without knowing what it is to be reduced to1 we are not likely to make much progress4 ,it is a more difficult thing to solve a geometrical problem1 than to judge whether a proposed solution is correct3 but if people were not able to judge of the solution when found1 they would have little chance of finding it4 ,and it can not be pretended that to judge of an induction when found is perfectly easy1 is a thing for which aids and instruments are superfluous2 for erroneous inductions1 false inferences from experience1 are quite as common1 on some subjects much commoner than true ones4 ,the business of ,inductive ,logic is to provide rules and models 7such as the ,syllogism and its rules are for ratiocination7 to which if inductive arguments conform1 those arguments are conclusive1 and not otherwise4 ,this is what the ,four ,methods profess to be1 and what ,i believe they are universally considered to be by experimental philosophers1 who had practiced all of them long before any one sought to reduce the practice to theory4 ,the assailants of the ,syllogism had also anticipated ,dr4 ,whewell in the other branch of his argument4 ,they said that no discoveries were ever made by syllogism2 and ,dr4 ,whewell says1 or seems to say1 that none were ever made by the ,four ,methods of ,induction4 ,to the former objectors1 ,archbishop ,whately very pertinently answered1 that their argument1 if good at all1 was good against the reasoning process altogether2 for whatever can not be reduced to syllogism1 is not reasoning4 ,and ,dr4 ,whewell's argument1 if good at all1 is good against all inferences from experience4 ,in saying that no discoveries were ever made by the ,four ,methods1 he affirms that none were ever made by observation and experiment2 for assuredly if any were1 it was by processes reducible to one or other of those methods4 ,this difference between us accounts for the dissatisfaction which my examples give him2 for ,i did not select them with a view to satisfy any one who required to be convinced that observation and experiment are modes of acquiring knowledge3 ,i confess that in the choice of them ,i thought only of illustration1 and of facilitating the conception of the ,methods by concrete instances4 ,if it had been my object to justify the processes themselves as means of investigation1 there would have been no need to look far off1 or make use of recondite or complicated instances4 ,as a specimen of a truth ascertained by the ,method of ,agreement1 ,i might have chosen the proposition1 8,dogs bark40 ,this dog1 and that dog1 and the other dog1 answer to ,a ,b ,c1 ,a ,d ,e1 ,a ,f ,g4 ,the circumstance of being a dog answers to ,a4 ,barking answers to a4 ,as a truth made known by the ,method of ,difference1 8,fire burns0 might have sufficed4 ,before ,i touch the fire ,i am not burned2 this is ,b ,c3 ,i touch it1 and am burned2 this is ,a ,b ,c1 a ,b ,c4 ,such familiar experimental processes are not regarded as inductions by ,dr4 ,whewell2 but they are perfectly homogeneous with those by which1 even on his own showing1 the pyramid of science is supplied with its base4 ,in vain he attempts to escape from this conclusion by laying the most arbitrary restrictions on the choice of examples admissible as instances of ,induction3 they must neither be such as are still matter of discussion 7p4 #bfe71 nor must any of them be drawn from mental and social subjects 7p4 #bfi71 nor from ordinary observation and practical life 7pp4 #bda-bdg74 ,they must be taken exclusively from the generalizations by which scientific thinkers have ascended to great and comprehensive laws of natural phenomena4 ,now it is seldom possible1 in these complicated inquiries1 to go much beyond the initial steps1 without calling in the instrument of ,deduction1 and the temporary aid of hypothesis2 as ,i myself1 in common with ,dr4 ,whewell1 have maintained against the purely empirical school4 ,since1 therefore1 such cases could not conveniently be selected to illustrate the principles of mere observation and experiment1 ,dr4 ,whewell is misled by their absence into representing the ,experimental ,methods as serving no purpose in scientific investigation2 forgetting that if those methods had not supplied the first generalizations1 there would have been no materials for his own conception of ,induction to work upon4 ,his challenge1 however1 to point out which of the four methods are exemplified in certain important cases of scientific inquiry1 is easily answered4 8,the planetary paths10 as far as they are a case of induction at all17#adf7 fall under the ,method of ,agreement4 ,the law of 8falling bodies10 namely1 that they describe spaces proportional to the squares of the times1 was historically a deduction from the first law of motion2 but the experiments by which it was verified1 and by which it might have been discovered1 were examples of the ,method of ,agreement2 and the apparent variation from the true law1 caused by the resistance of the air1 was cleared up by experiments in vacuo1 constituting an application of the ,method of ,difference4 ,the law of 8refracted rays0 7the constancy of the ratio between the sines of incidence and of refraction for each refracting substance7 was ascertained by direct measurement1 and therefore by the ,method of ,agreement4 ,the 8cosmical motions0 were determined by highly complex processes of thought1 in which ,deduction was predominant1 but the ,methods of ,agreement and of ,concomitant ,variations had a large part in establishing the empirical laws4 ,every case without exception of 8chemical analysis0 constitutes a well-marked example of the ,method of ,difference4 ,to any one acquainted with the subjects--to ,dr4 ,whewell himself1 there would not be the smallest difficulty in setting out 8the ,a ,b ,c and a b c elements0 of these cases4 ,if discoveries are ever made by observation and experiment without ,deduction1 the four methods are methods of discovery3 but even if they were not methods of discovery1 it would not be the less true that they are the sole methods of ,proof2 and in that character1 even the results of deduction are amenable to them4 ,the great generalizations which begin as ,hypotheses1 must end by being proved1 and are in reality 7as will be shown hereafter7 proved1 by the ,four ,methods4 ,now it is with ,proof1 as such1 that ,logic is principally concerned4 ,this distinction has indeed no chance of finding favor with ,dr4 ,whewell2 for it is the peculiarity of his system1 not to recognize1 in cases of ,induction1 any necessity for proof4 ,if1 after assuming an hypothesis and carefully collating it with facts1 nothing is brought to light inconsistent with it1 that is1 if experience does not disprove it1 he is content3 at least until a simpler hypothesis1 equally consistent with experience1 presents itself4 ,if this be ,induction1 doubtless there is no necessity for the four methods4 ,but to suppose that it is so1 appears to me a radical misconception of the nature of the evidence of physical truths4 ,so real and practical is the need of a test for induction1 similar to the syllogistic test of ratiocination1 that inferences which bid defiance to the most elementary notions of inductive logic are put forth without misgiving by persons eminent in physical science1 as soon as they are off the ground on which they are conversant with the facts1 and not reduced to judge only by the arguments2 and as for educated persons in general1 it may be doubted if they are better judges of a good or a bad induction than they were before ,bacon wrote4 ,the improvement in the results of thinking has seldom extended to the processes2 or has reached1 if any process1 that of investigation only1 not that of proof4 ,a knowledge of many laws of nature has doubtless been arrived at1 by framing hypotheses and finding that the facts corresponded to them2 and many errors have been got rid of by coming to a knowledge of facts which were inconsistent with them1 but not by discovering that the mode of thought which led to the errors was itself faulty1 and might have been known to be such independently of the facts which disproved the specific conclusion4 ,hence it is1 that while the thoughts of mankind have on many subjects worked themselves practically right1 the thinking power remains as weak as ever3 and on all subjects on which the facts which would check the result are not accessible1 as in what relates to the invisible world1 and even1 as has been seen lately1 to the visible world of the planetary regions1 men of the greatest scientific acquirements argue as pitiably as the merest ignoramus4 ,for though they have made many sound inductions1 they have not learned from them 7and ,dr4 ,whewell thinks there is no necessity that they should learn7 the principles of inductive evidence4 ,chapter ,x4 ,of ,plurality ,of ,causes1 ,and ,of ,the ,intermixture ,of ,effects4 #a4 ,in the preceding exposition of the four methods of observation and experiment1 by which we contrive to distinguish among a mass of co-existent phenomena the particular effect due to a given cause1 or the particular cause which gave birth to a given effect1 it has been necessary to suppose1 in the first instance1 for the sake of simplification1 that this analytical operation is encumbered by no other difficulties than what are essentially inherent in its nature2 and to represent to ourselves1 therefore1 every effect1 on the one hand as connected exclusively with a single cause1 and on the other hand as incapable of being mixed and confounded with any other co-existent effect4 ,we have regarded a b c d e1 the aggregate of the phenomena existing at any moment1 as consisting of dissimilar facts1 a1 b1 c1 d1 and e1 for each of which one1 and only one1 cause needs be sought2 the difficulty being only that of singling out this one cause from the multitude of antecedent circumstances1 ,a1 ,b1 ,c1 ,d1 and ,e4 ,the cause indeed may not be simple2 it may consist of an assemblage of conditions2 but we have supposed that there was only one possible assemblage of conditions from which the given effect could result4 ,if such were the fact1 it would be comparatively an easy task to investigate the laws of nature4 ,but the supposition does not hold in either of its parts4 ,in the first place1 it is not true that the same phenomenon is always produced by the same cause3 the effect a may sometimes arise from ,a1 sometimes from ,b4 ,and1 secondly1 the effects of different causes are often not dissimilar1 but homogeneous1 and marked out by no assignable boundaries from one another3 ,a and ,b may produce not a and b1 but different portions of an effect a4 ,the obscurity and difficulty of the investigation of the laws of phenomena is singularly increased by the necessity of adverting to these two circumstances3 ,intermixture of ,effects1 and ,plurality of ,causes4 ,to the latter1 being the simpler of the two considerations1 we shall first direct our attention4 ,it is not true1 then1 that one effect must be connected with only one cause1 or assemblage of conditions2 that each phenomenon can be produced only in one way4 ,there are often several independent modes in which the same phenomenon could have originated4 ,one fact may be the consequent in several invariable sequences2 it may follow1 with equal uniformity1 any one of several antecedents1 or collections of antecedents4 ,many causes may produce mechanical motion2 many causes may produce some kinds of sensation2 many causes may produce death4 ,a given effect may really be produced by a certain cause1 and yet be perfectly capable of being produced without it4 #b4 ,one of the principal consequences of this fact of ,plurality of ,causes is1 to render the first of the inductive methods1 that of ,agreement1 uncertain4 ,to illustrate that method1 we supposed two instances1 ,a ,b ,c followed by a b c1 and ,a ,d ,e followed by a d e4 ,from these instances it might apparently be concluded that ,a is an invariable antecedent of a1 and even that it is the unconditional invariable antecedent1 or cause1 if we could be sure that there is no other antecedent common to the two cases4 ,that this difficulty may not stand in the way1 let us suppose the two cases positively ascertained to have no antecedent in common except ,a4 ,the moment1 however1 that we let in the possibility of a plurality of causes1 the conclusion fails4 ,for it involves a tacit supposition1 that a must have been produced in both instances by the same cause4 ,if there can possibly have been two causes1 those two may1 for example1 be ,c and ,e3 the one may have been the cause of a in the former of the instances1 the other in the latter1 ,a having no influence in either case4 ,suppose1 for example1 that two great artists or great philosophers1 that two extremely selfish or extremely generous characters1 were compared together as to the circumstances of their education and history1 and the two cases were found to agree only in one circumstance3 would it follow that this one circumstance was the cause of the quality which characterized both those individuals8 ,not at all2 for the causes which may produce any type of character are very numerous2 and the two persons might equally have agreed in their character1 though there had been no manner of resemblance in their previous history4 ,this1 therefore1 is a characteristic imperfection of the ,method of ,agreement1 from which imperfection the ,method of ,difference is free4 ,for if we have two instances1 ,a ,b ,c and ,b ,c1 of which ,b ,c gives b c1 and ,a being added converts it into a b c1 it is certain that in this instance at least1 ,a was either the cause of a1 or an indispensable portion of its cause1 even though the cause which produces it in other instances may be altogether different4 ,plurality of ,causes1 therefore1 not only does not diminish the reliance due to the ,method of ,difference1 but does not even render a greater number of observations or experiments necessary3 two instances1 the one positive and the other negative1 are still sufficient for the most complete and rigorous induction4 ,not so1 however1 with the ,method of ,agreement4 ,the conclusions which that yields1 when the number of instances compared is small1 are of no real value1 except as1 in the character of suggestions1 they may lead either to experiments bringing them to the test of the ,method of ,difference1 or to reasonings which may explain and verify them deductively4 ,it is only when the instances1 being indefinitely multiplied and varied1 continue to suggest the same result1 that this result acquires any high degree of independent value4 ,if there are but two instances1 ,a ,b ,c and ,a ,d ,e1 though these instances have no antecedent in common except ,a1 yet as the effect may possibly have been produced in the two cases by different causes1 the result is at most only a slight probability in favor of ,a2 there may be causation1 but it is almost equally probable that there was only a coincidence4 ,but the oftener we repeat the observation1 varying the circumstances1 the more we advance toward a solution of this doubt4 ,for if we try ,a ,f ,g1 ,a ,h ,k1 etc41 all unlike one another except in containing the circumstance ,a1 and if we find the effect a entering into the result in all these cases1 we must suppose one of two things1 either that it is caused by ,a1 or that it has as many different causes as there are instances4 ,with each addition1 therefore1 to the number of instances1 the presumption is strengthened in favor of ,a4 ,the inquirer1 of course1 will not neglect1 if an opportunity present itself1 to exclude ,a from some one of these combinations1 from ,a ,h ,k for instance1 and by trying ,h ,k separately1 appeal to the ,method of ,difference in aid of the ,method of ,agreement4 ,by the ,method of ,difference alone can it be ascertained that ,a is the cause of a2 but that it is either the cause1 or another effect of the same cause1 may be placed beyond any reasonable doubt by the ,method of ,agreement1 provided the instances are very numerous as well as sufficiently various4 ,after how great a multiplication1 then1 of varied instances1 all agreeing in no other antecedent except ,a1 is the supposition of a plurality of causes sufficiently rebutted1 and the conclusion that a is connected with ,a divested of the characteristic imperfection1 and reduced to a virtual certainty8 ,this is a question which we can not be exempted from answering3 but the consideration of it belongs to what is called the ,theory of ,probability1 which will form the subject of a chapter hereafter4 ,it is seen1 however1 at once1 that the conclusion does amount to a practical certainty after a sufficient number of instances1 and that the method1 therefore1 is not radically vitiated by the characteristic imperfection4 ,the result of these considerations is only1 in the first place1 to point out a new source of inferiority in the ,method of ,agreement as compared with other modes of investigation1 and new reasons for never resting contented with the results obtained by it1 without attempting to confirm them either by the ,method of ,difference1 or by connecting them deductively with some law or laws already ascertained by that superior method4 ,and1 in the second place1 we learn from this the true theory of the value of mere number of instances in inductive inquiry4 ,the ,plurality of ,causes is the only reason why mere number is of any importance4 ,the tendency of unscientific inquirers is to rely too much on number1 without analyzing the instances2 without looking closely enough into their nature to ascertain what circumstances are or are not eliminated by means of them4 ,most people hold their conclusions with a degree of assurance proportioned to the mere mass of the experience on which they appear to rest2 not considering that by the addition of instances to instances1 all of the same kind1 that is1 differing from one another only in points already recognized as immaterial1 nothing whatever is added to the evidence of the conclusion4 ,a single instance eliminating some antecedent which existed in all the other cases1 is of more value than the greatest multitude of instances which are reckoned by their number alone4 ,it is necessary1 no doubt1 to assure ourselves1 by repetition of the observation or experiment1 that no error has been committed concerning the individual facts observed2 and until we have assured ourselves of this1 instead of varying the circumstances1 we can not too scrupulously repeat the same experiment or observation without any change4 ,but when once this assurance has been obtained1 the multiplication of instances which do not exclude any more circumstances is entirely useless1 provided there have been already enough to exclude the supposition of ,plurality of ,causes4 ,it is of importance to remark1 that the peculiar modification of the ,method of ,agreement1 which1 as partaking in some degree of the nature of the ,method of ,difference1 ,i have called the ,joint ,method of ,agreement and ,difference1 is not affected by the characteristic imperfection now pointed out4 ,for1 in the joint method1 it is supposed not only that the instances in which a is1 agree only in containing ,a1 but also that the instances in which a is not1 agree only in not containing ,a4 ,now1 if this be so1 ,a must be not only the cause of a1 but the only possible cause3 for if there were another1 as for example ,b1 then in the instances in which a is not1 ,b must have been absent as well as ,a1 and it would not be true that these instances agree only in not containing ,a4 ,this1 therefore1 constitutes an immense advantage of the joint method over the simple ,method of ,agreement4 ,it may seem1 indeed1 that the advantage does not belong so much to the joint method1 as to one of its two premises 7if they may be so called71 the negative premise4 ,the ,method of ,agreement1 when applied to negative instances1 or those in which a phenomenon does not take place1 is certainly free from the characteristic imperfection which affects it in the affirmative case4 ,the negative premise1 it might therefore be supposed1 could be worked as a simple case of the ,method of ,agreement1 without requiring an affirmative premise to be joined with it4 ,but though this is true in principle1 it is generally altogether impossible to work the ,method of ,agreement by negative instances without positive ones2 it is so much more difficult to exhaust the field of negation than that of affirmation4 ,for instance1 let the question be what is the cause of the transparency of bodies2 with what prospect of success could we set ourselves to inquire directly in what the multifarious substances which are not transparent agree8 ,but we might hope much sooner to seize some point of resemblance among the comparatively few and definite species of objects which are transparent2 and this being attained1 we should quite naturally be put upon examining whether the absence of this one circumstance be not precisely the point in which all opaque substances will be found to resemble4 ,the ,joint ,method of ,agreement and ,difference1 therefore1 or as ,i have otherwise called it1 the ,indirect ,method of ,difference 7because1 like the ,method of ,difference properly so-called1 it proceeds by ascertaining how and in what the cases where the phenomenon is present differ from those in which it is absent7 is1 after the ,direct ,method of ,difference1 the most powerful of the remaining instruments of inductive investigation2 and in the sciences which depend on pure observation1 with little or no aid from experiment1 this method1 so well exemplified in the speculation on the cause of dew1 is the primary resource1 so far as direct appeals to experience are concerned4 #c4 ,we have thus far treated ,plurality of ,causes only as a possible supposition1 which1 until removed1 renders our inductions uncertain2 and have only considered by what means1 where the plurality does not really exist1 we may be enabled to disprove it4 ,but we must also consider it as a case actually occurring in nature1 and which1 as often as it does occur1 our methods of induction ought to be capable of ascertaining and establishing4 ,for this1 however1 there is required no peculiar method4 ,when an effect is really producible by two or more causes1 the process for detecting them is in no way different from that by which we discover single causes4 ,they may 7first7 be discovered as separate sequences1 by separate sets of instances4 ,one set of observations or experiments shows that the sun is a cause of heat1 another that friction is a source of it1 another that percussion1 another that electricity1 another that chemical action is such a source4 ,or 7secondly7 the plurality may come to light in the course of collating a number of instances1 when we attempt to find some circumstance in which they all agree1 and fail in doing so4 ,we find it impossible to trace1 in all the cases in which the effect is met with1 any common circumstance4 ,we find that we can eliminate all the antecedents2 that no one of them is present in all the instances1 no one of them indispensable to the effect4 ,on closer scrutiny1 however1 it appears that though no one is always present1 one or other of several always is4 ,if1 on further analysis1 we can detect in these any common element1 we may be able to ascend from them to some one cause which is the really operative circumstance in them all4 ,thus it is now thought that in the production of heat by friction1 percussion1 chemical action1 etc41 the ultimate source is one and the same4 ,but if 7as continually happens7 we can not take this ulterior step1 the different antecedents must be set down provisionally as distinct causes1 each sufficient of itself to produce the effect4 ,we here close our remarks on the ,plurality of ,causes1 and proceed to the still more peculiar and more complex case of the ,intermixture of ,effects1 and the interference of causes with one another3 a case constituting the principal part of the complication and difficulty of the study of nature2 and with which the four only possible methods of directly inductive investigation by observation and experiment1 are1 for the most part1 as will appear presently1 quite unequal to cope4 ,the instrument of ,deduction alone is adequate to unravel the complexities proceeding from this source2 and the four methods have little more in their power than to supply premises for1 and a verification of1 our deductions4 #d4 ,a concurrence of two or more causes1 not separately producing each its own effect1 but interfering with or modifying the effects of one another1 takes place1 as has already been explained in two different ways4 ,in the one1 which is exemplified by the joint operation of different forces in mechanics1 the separate effects of all the causes continue to be produced1 but are compounded with one another1 and disappear in one total4 ,in the other1 illustrated by the case of chemical action1 the separate effects cease entirely1 and are succeeded by phenomena altogether different1 and governed by different laws4 ,of these cases the former is by far the more frequent1 and this case it is which1 for the most part1 eludes the grasp of our experimental methods4 ,the other and exceptional case is essentially amenable to them4 ,when the laws of the original agents cease entirely1 and a phenomenon makes its appearance1 which1 with reference to those laws1 is quite heterogeneous2 when1 for example1 two gaseous substances1 hydrogen and oxygen1 on being brought together1 throw off their peculiar properties1 and produce the substance called water2 in such cases the new fact may be subjected to experimental inquiry1 like any other phenomenon2 and the elements which are said to compose it may be considered as the mere agents of its production--the conditions on which it depends1 the facts which make up its cause4 ,the effects of the new phenomenon1 the properties of water1 for instance1 are as easily found by experiment as the effects of any other cause4 ,but to discover the cause of it1 that is1 the particular conjunction of agents from which it results1 is often difficult enough4 ,in the first place1 the origin and actual production of the phenomenon are most frequently inaccessible to our observation4 ,if we could not have learned the composition of water until we found instances in which it was actually produced from oxygen and hydrogen1 we should have been forced to wait until the casual thought struck some one of passing an electric spark through a mixture of the two gases1 or inserting a lighted taper into it1 merely to try what would happen4 ,besides1 many substances1 though they can be analyzed1 can not by any known artificial means be recompounded4 ,further1 even if we could have ascertained1 by the ,method of ,agreement1 that oxygen and hydrogen were both present when water is produced1 no experimentation on oxygen and hydrogen separately1 no knowledge of their laws1 could have enabled us deductively to infer that they would produce water4 ,we require a specific experiment on the two combined4 ,under these difficulties1 we should generally have been indebted for our knowledge of the causes of this class of effects1 not to any inquiry directed specifically toward that end1 but either to accident1 or to the gradual progress of experimentation on the different combinations of which the producing agents are susceptible2 if it were not for a peculiarity belonging to effects of this description1 that they often1 under some particular combination of circumstances1 reproduce their causes4 ,if water results from the juxtaposition of hydrogen and oxygen whenever this can be made sufficiently close and intimate1 so1 on the other hand1 if water itself be placed in certain situations1 hydrogen and oxygen are reproduced from it3 an abrupt termination is put to the new laws1 and the agents re-appear separately with their own properties as at first4 ,what is called chemical analysis is the process of searching for the causes of a phenomenon among its effects1 or rather among the effects produced by the action of some other causes upon it4 ,lavoisier1 by heating mercury to a high temperature in a close vessel containing air1 found that the mercury increased in weight1 and became what was then called red precipitate1 while the air1 on being examined after the experiment1 proved to have lost weight1 and to have become incapable of supporting life or combustion4 ,when red precipitate was exposed to a still greater heat1 it became mercury again1 and gave off a gas which did support life and flame4 ,thus the agents which by their combination produced red precipitate1 namely1 the mercury and the gas1 reappear as effects resulting from that precipitate when acted upon by heat4 ,so1 if we decompose water by means of iron filings1 we produce two effects1 rust and hydrogen4 ,now rust is already known1 by experiments upon the component substances1 to be an effect of the union of iron and oxygen3 the iron we ourselves supplied1 but the oxygen must have been produced from the water4 ,the result1 therefore1 is that water has disappeared1 and hydrogen and oxygen have appeared in its stead2 or1 in other words1 the original laws of these gaseous agents1 which had been suspended by the superinduction of the new laws called the properties of water1 have again started into existence1 and the causes of water are found among its effects4 ,where two phenomena1 between the laws or properties of which1 considered in themselves1 no connection can be traced1 are thus reciprocally cause and effect1 each capable in its turn of being produced from the other1 and each1 when it produces the other1 ceasing itself to exist 7as water is produced from oxygen and hydrogen1 and oxygen and hydrogen are reproduced from water72 this causation of the two phenomena by one another1 each being generated by the other's destruction1 is properly transformation4 ,the idea of chemical composition is an idea of transformation1 but of a transformation which is incomplete2 since we consider the oxygen and hydrogen to be present in the water as oxygen and hydrogen1 and capable of being discovered in it if our senses were sufficiently keen3 a supposition 7for it is no more7 grounded solely on the fact that the weight of the water is the sum of the separate weights of the two ingredients4 ,if there had not been this exception to the entire disappearance1 in the compound1 of the laws of the separate ingredients2 if the combined agents had not1 in this one particular of weight1 preserved their own laws1 and produced a joint result equal to the sum of their separate results2 we should never1 probably1 have had the notion now implied by the words chemical composition2 and1 in the facts of water produced from hydrogen and oxygen1 and hydrogen and oxygen produced from water1 as the transformation would have been complete1 we should have seen only a transformation4 ,in these cases1 where the heteropathic effect 7as we called it in a former chapter77#adg7 is but a transformation of its cause1 or in other words1 where the effect and its cause are reciprocally such1 and mutually convertible into each other2 the problem of finding the cause resolves itself into the far easier one of finding an effect1 which is the kind of inquiry that admits of being prosecuted by direct experiment4 ,but there are other cases of heteropathic effects to which this mode of investigation is not applicable4 ,take1 for instance1 the heteropathic laws of mind2 that portion of the phenomena of our mental nature which are analogous to chemical rather than to dynamical phenomena2 as when a complex passion is formed by the coalition of several elementary impulses1 or a complex emotion by several simple pleasures or pains1 of which it is the result without being the aggregate1 or in any respect homogeneous with them4 ,the product1 in these cases1 is generated by its various factors2 but the factors can not be reproduced from the product2 just as a youth can grow into an old man1 but an old man can not grow into a youth4 ,we can not ascertain from what simple feelings any of our complex states of mind are generated1 as we ascertain the ingredients of a chemical compound1 by making it1 in its turn1 generate them4 ,we can only1 therefore1 discover these laws by the slow process of studying the simple feelings themselves1 and ascertaining synthetically1 by experimenting on the various combinations of which they are susceptible1 what they1 by their mutual action upon one another1 are capable of generating4 #e4 ,it might have been supposed that the other1 and apparently simpler variety of the mutual interference of causes1 where each cause continues to produce its own proper effect according to the same laws to which it conforms in its separate state1 would have presented fewer difficulties to the inductive inquirer than that of which we have just finished the consideration4 ,it presents1 however1 so far as direct induction apart from deduction is concerned1 infinitely greater difficulties4 ,when a concurrence of causes gives rise to a new effect1 bearing no relation to the separate effects of those causes1 the resulting phenomenon stands forth undisguised1 inviting attention to its peculiarity1 and presenting no obstacle to our recognizing its presence or absence among any number of surrounding phenomena4 ,it admits1 therefore1 of being easily brought under the canons of ,induction1 provided instances can be obtained such as those canons require2 and the non-occurrence of such instances1 or the want of means to produce them artificially1 is the real and only difficulty in such investigations2 a difficulty not logical but in some sort physical4 ,it is otherwise with cases of what1 in a preceding chapter1 has been denominated the ,composition of ,causes4 ,there1 the effects of the separate causes do not terminate and give place to others1 thereby ceasing to form any part of the phenomenon to be investigated2 on the contrary1 they still take place1 but are intermingled with1 and disguised by1 the homogeneous and closely allied effects of other causes4 ,they are no longer a1 b1 c1 d1 e1 existing side by side1 and continuing to be separately discernible2 they are a1 -a1 b1 -b1 #b;b1 etc42 some of which cancel one another1 while many others do not appear distinguishably1 but merge in one sum2 forming altogether a result1 between which and the causes whereby it was produced there is often an insurmountable difficulty in tracing by observation any fixed relation whatever4 ,the general idea of the ,composition of ,causes has been seen to be1 that though two or more laws interfere with one another1 and apparently frustrate or modify one another's operation1 yet in reality all are fulfilled1 the collective effect being the exact sum of the effects of the causes taken separately4 ,a familiar instance is that of a body kept in equilibrium by two equal and contrary forces4 ,one of the forces if acting alone would carry the body in a given time a certain distance to the west1 the other if acting alone would carry it exactly as far toward the east2 and the result is the same as if it had been first carried to the west as far as the one force would carry it1 and then back toward the east as far as the other would carry it--that is1 precisely the same distance2 being ultimately left where it was found at first4 ,all laws of causation are liable to be in this manner counteracted1 and seemingly frustrated1 by coming into conflict with other laws1 the separate result of which is opposite to theirs1 or more or less inconsistent with it4 ,and hence1 with almost every law1 many instances in which it really is entirely fulfilled1 do not1 at first sight1 appear to be cases of its operation at all4 ,it is so in the example just adduced3 a force in mechanics means neither more nor less than a cause of motion1 yet the sum of the effects of two causes of motion may be rest4 ,again1 a body solicited by two forces in directions making an angle with one another1 moves in the diagonal2 and it seems a paradox to say that motion in the diagonal is the sum of two motions in two other lines4 ,motion1 however1 is but change of place1 and at every instant the body is in the exact place it would have been in if the forces had acted during alternate instants instead of acting in the same instant 7saving that if we suppose two forces to act successively which are in truth simultaneous we must of course allow them double the time74 ,it is evident1 therefore1 that each force has had1 during each instant1 all the effect which belonged to it2 and that the modifying influence which one of two concurrent causes is said to exercise with respect to the other may be considered as exerted not over the action of the cause itself1 but over the effect after it is completed4 ,for all purposes of predicting1 calculating1 or explaining their joint result1 causes which compound their effects may be treated as if they produced simultaneously each of them its own effect1 and all these effects co-existed visibly4 ,since the laws of causes are as really fulfilled when the causes are said to be counteracted by opposing causes1 as when they are left to their own undisturbed action1 we must be cautious not to express the laws in such terms as would render the assertion of their being fulfilled in those cases a contradiction4 ,if1 for instance1 it were stated as a law of nature that a body to which a force is applied moves in the direction of the force1 with a velocity proportioned to the force directly1 and to its own mass inversely2 when in point of fact some bodies to which a force is applied do not move at all1 and those which do move 7at least in the region of our earth7 are1 from the very first1 retarded by the action of gravity and other resisting forces1 and at last stopped altogether2 it is clear that the general proposition1 though it would be true under a certain hypothesis1 would not express the facts as they actually occur4 ,to accommodate the expression of the law to the real phenomena1 we must say1 not that the object moves1 but that it tends to move1 in the direction and with the velocity specified4 ,we might1 indeed1 guard our expression in a different mode1 by saying that the body moves in that manner unless prevented1 or except in so far as prevented1 by some counteracting cause4 ,but the body does not only move in that manner unless counteracted2 it tends to move in that manner even when counteracted2 it still exerts1 in the original direction1 the same energy of movement as if its first impulse had been undisturbed1 and produces1 by that energy1 an exactly equivalent quantity of effect4 ,this is true even when the force leaves the body as it found it1 in a state of absolute rest2 as when we attempt to raise a body of three tons' weight with a force equal to one ton4 ,for if1 while we are applying this force1 wind or water or any other agent supplies an additional force just exceeding two tons1 the body will be raised2 thus proving that the force we applied exerted its full effect1 by neutralizing an equivalent portion of the weight which it was insufficient altogether to overcome4 ,and if1 while we are exerting this force of one ton upon the object in a direction contrary to that of gravity1 it be put into a scale and weighed1 it will be found to have lost a ton of its weight1 or1 in other words1 to press downward with a force only equal to the difference of the two forces4 ,these facts are correctly indicated by the expression tendency4 ,all laws of causation1 in consequence of their liability to be counteracted1 require to be stated in words affirmative of tendencies only1 and not of actual results4 ,in those sciences of causation which have an accurate nomenclature1 there are special words which signify a tendency to the particular effect with which the science is conversant2 thus pressure1 in mechanics1 is synonymous with tendency to motion1 and forces are not reasoned on as causing actual motion1 but as exerting pressure4 ,a similar improvement in terminology would be very salutary in many other branches of science4 ,the habit of neglecting this necessary element in the precise expression of the laws of nature1 has given birth to the popular prejudice that all general truths have exceptions2 and much unmerited distrust has thence accrued to the conclusions of science1 when they have been submitted to the judgment of minds insufficiently disciplined and cultivated4 ,the rough generalizations suggested by common observation usually have exceptions2 but principles of science1 or1 in other words1 laws of causation1 have not4 8,what is thought to be an exception to a principle0 7to quote words used on a different occasion71 8is always some other and distinct principle cutting into the former2 some other force which impinges7#adh7 against the first force1 and deflects it from its direction4 ,there are not a law and an exception to that law1 the law acting in ninety-nine cases1 and the exception in one4 ,there are two laws1 each possibly acting in the whole hundred cases1 and bringing about a common effect by their conjunct operation4 ,if the force which1 being the less conspicuous of the two1 is called the disturbing force1 prevails sufficiently over the other force in some one case1 to constitute that case what is commonly called an exception1 the same disturbing force probably acts as a modifying cause in many other cases which no one will call exceptions4 8,thus if it were stated to be a law of nature that all heavy bodies fall to the ground1 it would probably be said that the resistance of the atmosphere1 which prevents a balloon from falling1 constitutes the balloon an exception to that pretended law of nature4 ,but the real law is1 that all heavy bodies tend to fall2 and to this there is no exception1 not even the sun and moon2 for even they1 as every astronomer knows1 tend toward the earth1 with a force exactly equal to that with which the earth tends toward them4 ,the resistance of the atmosphere might1 in the particular case of the balloon1 from a misapprehension of what the law of gravitation is1 be said to prevail over the law2 but its disturbing effect is quite as real in every other case1 since though it does not prevent1 it retards the fall of all bodies whatever4 ,the rule1 and the so-called exception1 do not divide the cases between them2 each of them is a comprehensive rule extending to all cases4 ,to call one of these concurrent principles an exception to the other1 is superficial1 and contrary to the correct principles of nomenclature and arrangement4 ,an effect of precisely the same kind1 and arising from the same cause1 ought not to be placed in two different categories1 merely as there does or does not exist another cause preponderating over it407#adi7 #f4 ,we have now to consider according to what method these complex effects1 compounded of the effects of many causes1 are to be studied2 how we are enabled to trace each effect to the concurrence of causes in which it originated1 and ascertain the conditions of its recurrence--the circumstances in which it may be expected again to occur4 ,the conditions of a phenomenon which arises from a composition of causes1 may be investigated either deductively or experimentally4 ,the case1 it is evident1 is naturally susceptible of the deductive mode of investigation4 ,the law of an effect of this description is a result of the laws of the separate causes on the combination of which it depends1 and is1 therefore1 in itself capable of being deduced from these laws4 ,this is called the method a priori4 ,the other1 or a posteriori method1 professes to proceed according to the canons of experimental inquiry4 ,considering the whole assemblage of concurrent causes which produced the phenomenon1 as one single cause1 it attempts to ascertain the cause in the ordinary manner1 by a comparison of instances4 ,this second method subdivides itself into two different varieties4 ,if it merely collates instances of the effect1 it is a method of pure observation4 ,if it operates upon the causes1 and tries different combinations of them1 in hopes of ultimately hitting the precise combination which will produce the given total effect1 it is a method of experiment4 ,in order more completely to clear up the nature of each of these three methods1 and determine which of them deserves the preference1 it will be expedient 7conformably to a favorite maxim of ,lord ,chancellor ,eldon1 to which1 though it has often incurred philosophical ridicule1 a deeper philosophy will not refuse its sanction7 to 8clothe them in circumstances40 ,we shall select for this purpose a case which as yet furnishes no very brilliant example of the success of any of the three methods1 but which is all the more suited to illustrate the difficulties inherent in them4 ,let the subject of inquiry be1 the conditions of health and disease in the human body2 or 7for greater simplicity7 the conditions of recovery from a given disease2 and in order to narrow the question still more1 let it be limited1 in the first instance1 to this one inquiry3 ,is1 or is not1 some particular medicament 7mercury1 for instance7 a remedy for the given disease4 ,now1 the deductive method would set out from known properties of mercury1 and known laws of the human body1 and by reasoning from these1 would attempt to discover whether mercury will act upon the body when in the morbid condition supposed1 in such a manner as would tend to restore health4 ,the experimental method would simply administer mercury in as many cases as possible1 noting the age1 sex1 temperament1 and other peculiarities of bodily constitution1 the particular form or variety of the disease1 the particular stage of its progress1 etc41 remarking in which of these cases it was attended with a salutary effect1 and with what circumstances it was on those occasions combined4 ,the method of simple observation would compare instances of recovery1 to find whether they agreed in having been preceded by the administration of mercury2 or would compare instances of recovery with instances of failure1 to find cases which1 agreeing in all other respects1 differed only in the fact that mercury had been administered1 or that it had not4 #g4 ,that the last of these three modes of investigation is applicable to the case1 no one has ever seriously contended4 ,no conclusions of value on a subject of such intricacy ever were obtained in that way4 ,the utmost that could result would be a vague general impression for or against the efficacy of mercury1 of no avail for guidance unless confirmed by one of the other two methods4 ,not that the results1 which this method strives to obtain1 would not be of the utmost possible value if they could be obtained4 ,if all the cases of recovery which presented themselves1 in an examination extending to a great number of instances1 were cases in which mercury had been administered1 we might generalize with confidence from this experience1 and should have obtained a conclusion of real value4 ,but no such basis for generalization can we1 in a case of this description1 hope to obtain4 ,the reason is that which we have spoken of as constituting the characteristic imperfection of the ,method of ,agreement1 ,plurality of ,causes4 ,supposing even that mercury does tend to cure the disease1 so many other causes1 both natural and artificial1 also tend to cure it1 that there are sure to be abundant instances of recovery in which mercury has not been administered1 unless1 indeed1 the practice be to administer it in all cases2 on which supposition it will equally be found in the cases of failure4 ,when an effect results from the union of many causes1 the share which each has in the determination of the effect can not in general be great1 and the effect is not likely1 even in its presence or absence1 still less in its variations1 to follow1 even approximately1 any one of the causes4 ,recovery from a disease is an event to which1 in every case1 many influences must concur4 ,mercury may be one such influence2 but from the very fact that there are many other such1 it will necessarily happen that although mercury is administered1 the patient1 for want of other concurring influences1 will often not recover1 and that he often will recover when it is not administered1 the other favorable influences being sufficiently powerful without it4 ,neither1 therefore1 will the instances of recovery agree in the administration of mercury1 nor will the instances of failure agree in its non-administration4 ,it is much if1 by multiplied and accurate returns from hospitals and the like1 we can collect that there are rather more recoveries and rather fewer failures when mercury is administered than when it is not2 a result of very secondary value even as a guide to practice1 and almost worthless as a contribution to the theory of the subject47#aej7 #h4 ,the inapplicability of the method of simple observation to ascertain the conditions of effects dependent on many concurring causes1 being thus recognized1 we shall next inquire whether any greater benefit can be expected from the other branch of the a posteriori method1 that which proceeds by directly trying different combinations of causes1 either artificially produced or found in nature1 and taking notice what is their effect2 as1 for example1 by actually trying the effect of mercury in as many different circumstances as possible4 ,this method differs from the one which we have just examined in turning our attention directly to the causes or agents1 instead of turning it to the effect1 recovery from the disease4 ,and since1 as a general rule1 the effects of causes are far more accessible to our study than the causes of effects1 it is natural to think that this method has a much better chance of proving successful than the former4 ,the method now under consideration is called the ,empirical ,method2 and in order to estimate it fairly1 we must suppose it to be completely1 not incompletely1 empirical4 ,we must exclude from it every thing which partakes of the nature not of an experimental but of a deductive operation4 ,if1 for instance1 we try experiments with mercury upon a person in health1 in order to ascertain the general laws of its action upon the human body1 and then reason from these laws to determine how it will act upon persons affected with a particular disease1 this may be a really effectual method2 but this is deduction4 ,the experimental method does not derive the law of a complex case from the simpler laws which conspire to produce it1 but makes its experiments directly upon the complex case4 ,we must make entire abstraction of all knowledge of the simpler tendencies1 the modi operandi of mercury in detail4 ,our experimentation must aim at obtaining a direct answer to the specific question1 ,does or does not mercury tend to cure the particular disease8 ,let us see1 therefore1 how far the case admits of the observance of those rules of experimentation which it is found necessary to observe in other cases4 ,when we devise an experiment to ascertain the effect of a given agent1 there are certain precautions which we never1 if we can help it1 omit4 ,in the first place1 we introduce the agent into the midst of a set of circumstances which we have exactly ascertained4 ,it needs hardly be remarked how far this condition is from being realized in any case connected with the phenomena of life2 how far we are from knowing what are all the circumstances which pre-exist in any instance in which mercury is administered to a living being4 ,this difficulty1 however1 though insuperable in most cases1 may not be so in all2 there are sometimes concurrences of many causes1 in which we yet know accurately what the causes are4 ,moreover1 the difficulty may be attenuated by sufficient multiplication of experiments1 in circumstances rendering it improbable that any of the unknown causes should exist in them all4 ,but when we have got clear of this obstacle1 we encounter another still more serious4 ,in other cases1 when we intend to try an experiment1 we do not reckon it enough that there be no circumstance in the case the presence of which is unknown to us4 ,we require1 also1 that none of the circumstances which we do know shall have effects susceptible of being confounded with those of the agents whose properties we wish to study4 ,we take the utmost pains to exclude all causes capable of composition with the given cause2 or1 if forced to let in any such causes1 we take care to make them such that we can compute and allow for their influence1 so that the effect of the given cause may1 after the subduction of those other effects1 be apparent as a residual phenomenon4 ,these precautions are inapplicable to such cases as we are now considering4 ,the mercury of our experiment being tried with an unknown multitude 7or even let it be a known multitude7 of other influencing circumstances1 the mere fact of their being influencing circumstances implies that they disguise the effect of the mercury1 and preclude us from knowing whether it has any effect or not4 ,unless we already knew what and how much is owing to every other circumstance 7that is1 unless we suppose the very problem solved which we are considering the means of solving71 we can not tell that those other circumstances may not have produced the whole of the effect1 independently or even in spite of the mercury4 ,the ,method of ,difference1 in the ordinary mode of its use1 namely1 by comparing the state of things following the experiment with the state which preceded it1 is thus1 in the case of intermixture of effects1 entirely unavailing2 because other causes than that whose effect we are seeking to determine have been operating during the transition4 ,as for the other mode of employing the ,method of ,difference1 namely1 by comparing1 not the same case at two different periods1 but different cases1 this in the present instance is quite chimerical4 ,in phenomena so complicated it is questionable if two cases1 similar in all respects but one1 ever occurred2 and were they to occur1 we could not possibly know that they were so exactly similar4 ,any thing like a scientific use of the method of experiment1 in these complicated cases1 is therefore out of the question4 ,we can generally1 even in the most favorable cases1 only discover by a succession of trials1 that a certain cause is very often followed by a certain effect4 ,for1 in one of these conjunct effects1 the portion which is determined by any one of the influencing agents1 is usually1 as we before remarked1 but small2 and it must be a more potent cause than most1 if even the tendency which it really exerts is not thwarted by other tendencies in nearly as many cases as it is fulfilled4 ,some causes indeed there are which are more potent than any counteracting causes to which they are commonly exposed2 and accordingly there are some truths in medicine which are sufficiently proved by direct experiment4 ,of these the most familiar are those that relate to the efficacy of the substances known as ,specifics for particular diseases1 8quinine1 colchicum1 lime-juice1 cod-liver oil107#aea7 and a few others4 ,even these are not invariably followed by success2 but they succeed in so large a proportion of cases1 and against such powerful obstacles1 that their tendency to restore health in the disorders for which they are prescribed may be regarded as an experimental truth47#aeb7 ,if so little can be done by the experimental method to determine the conditions of an effect of many combined causes1 in the case of medical science2 still less is this method applicable to a class of phenomena more complicated than even those of physiology1 the phenomena of politics and history4 ,there1 ,plurality of ,causes exists in almost boundless excess1 and effects are1 for the most part1 inextricably interwoven with one another4 ,to add to the embarrassment1 most of the inquiries in political science relate to the production of effects of a most comprehensive description1 such as the public wealth1 public security1 public morality1 and the like3 results liable to be affected directly or indirectly either in plus or in minus by nearly every fact which exists1 or event which occurs1 in human society4 ,the vulgar notion1 that the safe methods on political subjects are those of ,baconian induction--that the true guide is not general reasoning1 but specific experience--will one day be quoted as among the most unequivocal marks of a low state of the speculative faculties in any age in which it is accredited4 ,nothing can be more ludicrous than the sort of parodies on experimental reasoning which one is accustomed to meet with1 not in popular discussion only1 but in grave treatises1 when the affairs of nations are the theme4 8,how10 it is asked1 8can an institution be bad1 when the country has prospered under it80 8,how can such or such causes have contributed to the prosperity of one country1 when another has prospered without them80 ,whoever makes use of an argument of this kind1 not intending to deceive1 should be sent back to learn the elements of some one of the more easy physical sciences4 ,such reasoners ignore the fact of ,plurality of ,causes in the very case which affords the most signal example of it4 ,so little could be concluded1 in such a case1 from any possible collation of individual instances1 that even the impossibility1 in social phenomena1 of making artificial experiments1 a circumstance otherwise so prejudicial to directly inductive inquiry1 hardly affords1 in this case1 additional reason of regret4 ,for even if we could try experiments upon a nation or upon the human race1 with as little scruple as ,m4 ,magendie tried them on dogs and rabbits1 we should never succeed in making two instances identical in every respect except the presence or absence of some one definite circumstance4 ,the nearest approach to an experiment in the philosophical sense1 which takes place in politics1 is the introduction of a new operative element into national affairs by some special and assignable measure of government1 such as the enactment or repeal of a particular law4 ,but where there are so many influences at work1 it requires some time for the influence of any new cause upon national phenomena to become apparent2 and as the causes operating in so extensive a sphere are not only infinitely numerous1 but in a state of perpetual alteration1 it is always certain that before the effect of the new cause becomes conspicuous enough to be a subject of induction1 so many of the other influencing circumstances will have changed as to vitiate the experiment47#aec7 ,two1 therefore1 of the three possible methods for the study of phenomena resulting from the composition of many causes1 being1 from the very nature of the case1 inefficient and illusory1 there remains only the third--that which considers the causes separately1 and infers the effect from the balance of the different tendencies which produce it3 in short1 the deductive1 or a priori method4 ,the more particular consideration of this intellectual process requires a chapter to itself4 ,chapter ,,xi4 ,of ,the ,deductive ,method4 #a4 ,the mode of investigation which1 from the proved inapplicability of direct methods of observation and experiment1 remains to us as the main source of the knowledge we possess or can acquire respecting the conditions and laws of recurrence1 of the more complex phenomena1 is called1 in its most general expression1 the ,deductive ,method2 and consists of three operations3 the first1 one of direct induction2 the second1 of ratiocination2 the third1 of verification4 ,i call the first step in the process an inductive operation1 because there must be a direct induction as the basis of the whole2 though in many particular investigations the place of the induction may be supplied by a prior deduction2 but the premises of this prior deduction must have been derived from induction4 ,the problem of the ,deductive ,method is1 to find the law of an effect1 from the laws of the different tendencies of which it is the joint result4 ,the first requisite1 therefore1 is to know the laws of those tendencies2 the law of each of the concurrent causes3 and this supposes a previous process of observation or experiment upon each cause separately2 or else a previous deduction1 which also must depend for its ultimate premises on observation or experiment4 ,thus1 if the subject be social or historical phenomena1 the premises of the ,deductive ,method must be the laws of the causes which determine that class of phenomena2 and those causes are human actions1 together with the general outward circumstances under the influence of which mankind are placed1 and which constitute man's position on the earth4 ,the ,deductive ,method1 applied to social phenomena1 must begin1 therefore1 by investigating1 or must suppose to have been already investigated1 the laws of human action1 and those properties of outward things by which the actions of human beings in society are determined4 ,some of these general truths will naturally be obtained by observation and experiment1 others by deduction3 the more complex laws of human action1 for example1 may be deduced from the simpler ones2 but the simple or elementary laws will always1 and necessarily1 have been obtained by a directly inductive process4 ,to ascertain1 then1 the laws of each separate cause which takes a share in producing the effect1 is the first desideratum of the ,deductive ,method4 ,to know what the causes are which must be subjected to this process of study1 may or may not be difficult4 ,in the case last mentioned1 this first condition is of easy fulfillment4 ,that social phenomena depend on the acts and mental impressions of human beings1 never could have been a matter of any doubt1 however imperfectly it may have been known either by what laws those impressions and actions are governed1 or to what social consequences their laws naturally lead4 ,neither1 again1 after physical science had attained a certain development1 could there be any real doubt where to look for the laws on which the phenomena of life depend1 since they must be the mechanical and chemical laws of the solid and fluid substances composing the organized body and the medium in which it subsists1 together with the peculiar vital laws of the different tissues constituting the organic structure4 ,in other cases1 really far more simple than these1 it was much less obvious in what quarter the causes were to be looked for3 as in the case of the celestial phenomena4 ,until1 by combining the laws of certain causes1 it was found that those laws explained all the facts which experience had proved concerning the heavenly motions1 and led to predictions which it always verified1 mankind never knew that those were the causes4 ,but whether we are able to put the question before1 or not until after1 we have become capable of answering it1 in either case it must be answered2 the laws of the different causes must be ascertained1 before we can proceed to deduce from them the conditions of the effect4 ,the mode of ascertaining those laws neither is1 nor can be any other than the fourfold method of experimental inquiry1 already discussed4 ,a few remarks on the application of that method to cases of the ,composition of ,causes are all that is requisite4 ,it is obvious that we can not expect to find the law of a tendency by an induction from cases in which the tendency is counteracted4 ,the laws of motion could never have been brought to light from the observation of bodies kept at rest by the equilibrium of opposing forces4 ,even where the tendency is not1 in the ordinary sense of the word1 counteracted1 but only modified1 by having its effects compounded with the effects arising from some other tendency or tendencies1 we are still in an unfavorable position for tracing1 by means of such cases1 the law of the tendency itself4 ,it would have been scarcely possible to discover the law that every body in motion tends to continue moving in a straight line1 by an induction from instances in which the motion is deflected into a curve1 by being compounded with the effect of an accelerating force4 ,notwithstanding the resources afforded in this description of cases by the ,method of ,concomitant ,variations1 the principles of a judicious experimentation prescribe that the law of each of the tendencies should be studied1 if possible1 in cases in which that tendency operates alone1 or in combination with no agencies but those of which the effect can1 from previous knowledge1 be calculated and allowed for4 ,accordingly1 in the cases1 unfortunately very numerous and important1 in which the causes do not suffer themselves to be separated and observed apart1 there is much difficulty in laying down with due certainty the inductive foundation necessary to support the deductive method4 ,this difficulty is most of all conspicuous in the case of physiological phenomena2 it being seldom possible to separate the different agencies which collectively compose an organized body1 without destroying the very phenomena which it is our object to investigate3 ----following life1 in creatures we dissect1 ,we lose it1 in the moment we detect4 ,and for this reason ,i am inclined to the opinion that physiology 7greatly and rapidly progressive as it now is7 is embarrassed by greater natural difficulties1 and is probably susceptible of a less degree of ultimate perfection1 than even the social science2 inasmuch as it is possible to study the laws and operations of one human mind apart from other minds1 much less imperfectly than we can study the laws of one organ or tissue of the human body apart from the other organs or tissues4 ,it has been judiciously remarked that pathological facts1 or1 to speak in common language1 diseases in their different forms and degrees afford in the case of physiological investigation the most valuable equivalent to experimentation properly so called2 inasmuch as they often exhibit to us a definite disturbance in some one organ or organic function1 the remaining organs and functions being1 in the first instance at least1 unaffected4 ,it is true that from the perpetual actions and reactions which are going on among all parts of the organic economy1 there can be no prolonged disturbance in any one function without ultimately involving many of the others2 and when once it has done so1 the experiment for the most part loses its scientific value4 ,all depends on observing the early stages of the derangement2 which1 unfortunately1 are of necessity the least marked4 ,if1 however1 the organs and functions not disturbed in the first instance become affected in a fixed order of succession1 some light is thereby thrown upon the action which one organ exercises over another3 and we occasionally obtain a series of effects which we can refer with some confidence to the original local derangement2 but for this it is necessary that we should know that the original derangement was local4 ,if it was what is termed constitutional2 that is1 if we do not know in what part of the animal economy it took its rise1 or the precise nature of the disturbance which took place in that part1 we are unable to determine which of the various derangements was cause and which effect2 which of them were produced by one another1 and which by the direct1 though perhaps tardy1 action of the original cause4 ,besides natural pathological facts1 we can produce pathological facts artificially3 we can try experiments1 even in the popular sense of the term1 by subjecting the living being to some external agent1 such as the mercury of our former example1 or the section of a nerve to ascertain the functions of different parts of the nervous system4 ,as this experimentation is not intended to obtain a direct solution of any practical question1 but to discover general laws1 from which afterward the conditions of any particular effect may be obtained by deduction1 the best cases to select are those of which the circumstances can be best ascertained3 and such are generally not those in which there is any practical object in view4 ,the experiments are best tried1 not in a state of disease1 which is essentially a changeable state1 but in the condition of health1 comparatively a fixed state4 ,in the one1 unusual agencies are at work1 the results of which we have no means of predicting3 in the other1 the course of the accustomed physiological phenomena would1 it may generally be presumed1 remain undisturbed1 were it not for the disturbing cause which we introduce4 ,such1 with the occasional aid of the ,method of ,concomitant ,variations 7the latter not less encumbered than the more elementary methods by the peculiar difficulties of the subject71 are our inductive resources for ascertaining the laws of the causes considered separately1 when we have it not in our power to make trial of them in a state of actual separation4 ,the insufficiency of these resources is so glaring1 that no one can be surprised at the backward state of the science of physiology2 in which indeed our knowledge of causes is so imperfect1 that we can neither explain1 nor could without specific experience have predicted1 many of the facts which are certified to us by the most ordinary observation4 ,fortunately1 we are much better informed as to the empirical laws of the phenomena1 that is1 the uniformities respecting which we can not yet decide whether they are cases of causation1 or mere results of it4 ,not only has the order in which the facts of organization and life successively manifest themselves1 from the first germ of existence to death1 been found to be uniform1 and very accurately ascertainable2 but1 by a great application of the ,method of ,concomitant ,variations to the entire facts of comparative anatomy and physiology1 the characteristic organic structure corresponding to each class of functions has been determined with considerable precision4 ,whether these organic conditions are the whole of the conditions1 and in many cases whether they are conditions at all1 or mere collateral effects of some common cause1 we are quite ignorant2 nor are we ever likely to know1 unless we could construct an organized body and try whether it would live4 ,under such disadvantages do we1 in cases of this description1 attempt the initial1 or inductive step1 in the application of the ,deductive ,method to complex phenomena4 ,but such1 fortunately1 is not the common case4 ,in general1 the laws of the causes on which the effect depends may be obtained by an induction from comparatively simple instances1 or1 at the worst1 by deduction from the laws of simpler causes1 so obtained4 ,by simple instances are meant1 of course1 those in which the action of each cause was not intermixed or interfered with1 or not to any great extent1 by other causes whose laws were unknown4 ,and only when the induction which furnished the premises to the ,deductive method rested on such instances has the application of such a method to the ascertainment of the laws of a complex effect1 been attended with brilliant results4 #b4 ,when the laws of the causes have been ascertained1 and the first stage of the great logical operation now under discussion satisfactorily accomplished1 the second part follows2 that of determining from the laws of the causes what effect any given combination of those causes will produce4 ,this is a process of calculation1 in the wider sense of the term2 and very often involves processes of calculation in the narrowest sense4 ,it is a ratiocination2 and when our knowledge of the causes is so perfect as to extend to the exact numerical laws which they observe in producing their effects1 the ratiocination may reckon among its premises the theorems of the science of number1 in the whole immense extent of that science4 ,not only are the most advanced truths of mathematics often required to enable us to compute an effect1 the numerical law of which we already know2 but1 even by the aid of those most advanced truths1 we can go but a little way4 ,in so simple a case as the common problem of three bodies gravitating toward one another1 with a force directly as their mass and inversely as the square of the distance1 all the resources of the calculus have not hitherto sufficed to obtain any general solution1 but an approximate one4 ,in a case a little more complex1 but still one of the simplest which arise in practice1 that of the motion of a projectile1 the causes which affect the velocity and range 7for example7 of a cannon-ball may be all known and estimated3 the force of the gunpowder1 the angle of elevation1 the density of the air1 the strength and direction of the wind2 but it is one of the most difficult of mathematical problems to combine all these1 so as to determine the effect resulting from their collective action4 ,besides the theorems of number1 those of geometry also come in as premises1 where the effects take place in space1 and involve motion and extension1 as in mechanics1 optics1 acoustics1 astronomy4 ,but when the complication increases1 and the effects are under the influence of so many and such shifting causes as to give no room either for fixed numbers1 or for straight lines and regular curves 7as in the case of physiological1 to say nothing of mental and social phenomena71 the laws of number and extension are applicable1 if at all1 only on that large scale on which precision of details becomes unimportant4 ,although these laws play a conspicuous part in the most striking examples of the investigation of nature by the ,deductive ,method1 as for example in the ,newtonian theory of the celestial motions1 they are by no means an indispensable part of every such process4 ,all that is essential in it is reasoning from a general law to a particular case1 that is1 determining by means of the particular circumstances of that case1 what result is required in that instance to fulfill the law4 ,thus in the ,torricellian experiment1 if the fact that air has weight had been previously known1 it would have been easy1 without any numerical data1 to deduce from the general law of equilibrium1 that the mercury would stand in the tube at such a height that the column of mercury would exactly balance a column of the atmosphere of equal diameter2 because1 otherwise1 equilibrium would not exist4 ,by such ratiocinations from the separate laws of the causes1 we may1 to a certain extent1 succeed in answering either of the following questions3 ,given a certain combination of causes1 what effect will follow8 and1 ,what combination of causes1 if it existed1 would produce a given effect8 ,in the one case1 we determine the effect to be expected in any complex circumstances of which the different elements are known3 in the other case we learn1 according to what law--under what antecedent conditions--a given complex effect will occur4 #c4 ,but 7it may here be asked7 are not the same arguments by which the methods of direct observation and experiment were set aside as illusory when applied to the laws of complex phenomena1 applicable with equal force against the ,method of ,deduction8 ,when in every single instance a multitude1 often an unknown multitude1 of agencies1 are clashing and combining1 what security have we that in our computation a priori we have taken all these into our reckoning8 ,how many must we not generally be ignorant of8 ,among those which we know1 how probable that some have been overlooked2 and1 even were all included1 how vain the pretense of summing up the effects of many causes1 unless we know accurately the numerical law of each--a condition in most cases not to be fulfilled2 and even when it is fulfilled1 to make the calculation transcends1 in any but very simple cases1 the utmost power of mathematical science with all its most modern improvements4 ,these objections have real weight1 and would be altogether unanswerable1 if there were no test by which1 when we employ the ,deductive ,method1 we might judge whether an error of any of the above descriptions had been committed or not4 ,such a test1 however1 there is3 and its application forms1 under the name of ,verification1 the third essential component part of the ,deductive ,method2 without which all the results it can give have little other value than that of conjecture4 ,to warrant reliance on the general conclusions arrived at by deduction1 these conclusions must be found1 on careful comparison1 to accord with the results of direct observation wherever it can be had4 ,if1 when we have experience to compare with them1 this experience confirms them1 we may safely trust to them in other cases of which our specific experience is yet to come4 ,but if our deductions have led to the conclusion that from a particular combination of causes a given effect would result1 then in all known cases where that combination can be shown to have existed1 and where the effect has not followed1 we must be able to show 7or at least to make a probable surmise7 what frustrated it3 if we can not1 the theory is imperfect1 and not yet to be relied upon4 ,nor is the verification complete1 unless some of the cases in which the theory is borne out by the observed result are of at least equal complexity with any other cases in which its application could be called for4 ,if direct observation and collation of instances have furnished us with any empirical laws of the effect 7whether true in all observed cases1 or only true for the most part71 the most effectual verification of which the theory could be susceptible1 would be1 that it led deductively to those empirical laws2 that the uniformities1 whether complete or incomplete1 which were observed to exist among the phenomena1 were accounted for by the laws of the causes--were such as could not but exist if those be really the causes by which the phenomena are produced4 ,thus it was very reasonably deemed an essential requisite of any true theory of the causes of the celestial motions1 that it should lead by deduction to ,kepler's laws2 which1 accordingly1 the ,newtonian theory did4 ,in order1 therefore1 to facilitate the verification of theories obtained by deduction1 it is important that as many as possible of the empirical laws of the phenomena should be ascertained1 by a comparison of instances1 conformably to the ,method of ,agreement3 as well as 7it must be added7 that the phenomena themselves should be described1 in the most comprehensive as well as accurate manner possible2 by collecting from the observation of parts1 the simplest possible correct expressions for the corresponding wholes3 as when the series of the observed places of a planet was first expressed by a circle1 then by a system of epicycles1 and subsequently by an ellipse4 ,it is worth remarking1 that complex instances which would have been of no use for the discovery of the simple laws into which we ultimately analyze their phenomena1 nevertheless1 when they have served to verify the analysis1 become additional evidence of the laws themselves4 ,although we could not have got at the law from complex cases1 still when the law1 got at otherwise1 is found to be in accordance with the result of a complex case1 that case becomes a new experiment on the law1 and helps to confirm what it did not assist to discover4 ,it is a new trial of the principle in a different set of circumstances2 and occasionally serves to eliminate some circumstance not previously excluded1 and the exclusion of which might require an experiment impossible to be executed4 ,this was strikingly conspicuous in the example formerly quoted1 in which the difference between the observed and the calculated velocity of sound was ascertained to result from the heat extricated by the condensation which takes place in each sonorous vibration4 ,this was a trial1 in new circumstances1 of the law of the development of heat by compression2 and it added materially to the proof of the universality of that law4 ,accordingly1 any law of nature is deemed to have gained in point of certainty1 by being found to explain some complex case which had not previously been thought of in connection with it2 and this indeed is a consideration to which it is the habit of scientific inquirers to attach rather too much value than too little4 ,to the ,deductive ,method1 thus characterized in its three constituent parts1 ,induction1 ,ratiocination1 and ,verification1 the human mind is indebted for its most conspicuous triumphs in the investigation of nature4 ,to it we owe all the theories by which vast and complicated phenomena are embraced under a few simple laws1 which1 considered as the laws of those great phenomena1 could never have been detected by their direct study4 ,we may form some conception of what the method has done for us from the case of the celestial motions3 one of the simplest among the greater instances of the ,composition of ,causes1 since 7except in a few cases not of primary importance7 each of the heavenly bodies may be considered1 without material inaccuracy1 to be never at one time influenced by the attraction of more than two bodies1 the sun and one other planet or satellite2 making1 with the reaction of the body itself1 and the force generated by the body's own motion and acting in the direction of the tangent1 only four different agents on the concurrence of which the motions of that body depend2 a much smaller number1 no doubt1 than that by which any other of the great phenomena of nature is determined or modified4 ,yet how could we ever have ascertained the combination of forces on which the motions of the earth and planets are dependent1 by merely comparing the orbits or velocities of different planets1 or the different velocities or positions of the same planet8 ,notwithstanding the regularity which manifests itself in those motions1 in a degree so rare among the effects of concurrence of causes2 and although the periodical recurrence of exactly the same effect1 affords positive proof that all the combinations of causes which occur at all1 recur periodically2 we should not have known what the causes were1 if the existence of agencies precisely similar on our own earth had not1 fortunately1 brought the causes themselves within the reach of experimentation under simple circumstances4 ,as we shall have occasion to analyze1 further on1 this great example of the ,method of ,deduction1 we shall not occupy any time with it here1 but shall proceed to that secondary application of the ,deductive ,method1 the result of which is not to prove laws of phenomena1 but to explain them4 ,chapter ,,xii4 ,of ,the ,explanation ,of ,laws ,of ,nature4 #a4 ,the deductive operation by which we derive the law of an effect from the laws of the causes1 the concurrence of which gives rise to it1 may be undertaken either for the purpose of discovering the law1 or of explaining a law already discovered4 ,the word explanation occurs so continually1 and holds so important a place in philosophy1 that a little time spent in fixing the meaning of it will be profitably employed4 ,an individual fact is said to be explained1 by pointing out its cause1 that is1 by stating the law or laws of causation1 of which its production is an instance4 ,thus1 a conflagration is explained1 when it is proved to have arisen from a spark falling into the midst of a heap of combustibles4 ,and in a similar manner1 a law or uniformity in nature is said to be explained1 when another law or laws are pointed out1 of which that law itself is but a case1 and from which it could be deduced4 #b4 ,there are three distinguishable sets of circumstances in which a law of causation may be explained from1 or1 as it also is often expressed1 resolved into1 other laws4 ,the first is the case already so fully considered2 an intermixture of laws1 producing a joint effect equal to the sum of the effects of the causes taken separately4 ,the law of the complex effect is explained1 by being resolved into the separate laws of the causes which contribute to it4 ,thus1 the law of the motion of a planet is resolved into the law of the acquired force1 which tends to produce a uniform motion in the tangent1 and the law of the centripetal force1 which tends to produce an accelerating motion toward the sun2 the real motion being a compound of the two4 ,it is necessary here to remark1 that in this resolution of the law of a complex effect1 the laws of which it is compounded are not the only elements4 ,it is resolved into the laws of the separate causes1 together with the fact of their co-existence4 ,the one is as essential an ingredient as the other2 whether the object be to discover the law of the effect1 or only to explain it4 ,to deduce the laws of the heavenly motions1 we require not only to know the law of a rectilineal and that of a gravitative force1 but the existence of both these forces in the celestial regions1 and even their relative amount4 ,the complex laws of causation are thus resolved into two distinct kinds of elements3 the one1 simpler laws of causation1 the other 7in the aptly selected expression of ,dr4 ,chalmers7 collocations2 the collocations consisting in the existence of certain agents or powers1 in certain circumstances of place and time4 ,we shall hereafter have occasion to return to this distinction1 and to dwell on it at such length as dispenses with the necessity of further insisting on it here4 ,the first mode1 then1 of the explanation of ,laws of ,causation1 is when the law of an effect is resolved into the various tendencies of which it is the result1 together with the laws of those tendencies4 #c4 ,a second case is when1 between what seemed the cause and what was supposed to be its effect1 further observation detects an intermediate link2 a fact caused by the antecedent1 and in its turn causing the consequent2 so that the cause at first assigned is but the remote cause1 operating through the intermediate phenomenon4 ,a seemed the cause of ,c1 but it subsequently appeared that ,a was only the cause of ,b1 and that it is ,b which was the cause of ,c4 ,for example3 mankind were aware that the act of touching an outward object caused a sensation4 ,it was subsequently discovered that after we have touched the object1 and before we experience the sensation1 some change takes place in a kind of thread called a nerve1 which extends from our outward organs to the brain4 ,touching the object1 therefore1 is only the remote cause of our sensation2 that is1 not the cause1 properly speaking1 but the cause of the cause2 the real cause of the sensation is the change in the state of the nerve4 ,future experience may not only give us more knowledge than we now have of the particular nature of this change1 but may also interpolate another link3 between the contact 7for example7 of the object with our outward organs1 and the production of the change of state in the nerve1 there may take place some electric phenomenon1 or some phenomenon of a nature not resembling the effects of any known agency4 ,hitherto1 however1 no such intermediate link has been discovered2 and the touch of the object must be considered1 provisionally1 as the proximate cause of the affection of the nerve4 ,the sequence1 therefore1 of a sensation of touch on contact with an object is ascertained not to be an ultimate law2 it is resolved1 as the phrase is1 into two other laws--the law that contact with an object produces an affection of the nerve1 and the law that an affection of the nerve produces sensation4 ,to take another example3 the more powerful acids corrode or blacken organic compounds4 ,this is a case of causation1 but of remote causation2 and is said to be explained when it is shown that there is an intermediate link1 namely1 the separation of some of the chemical elements of the organic structure from the rest1 and their entering into combination with the acid4 ,the acid causes this separation of the elements1 and the separation of the elements causes the disorganization1 and often the charring of the structure4 ,so1 again1 chlorine extracts coloring matters 7whence its efficacy in bleaching7 and purifies the air from infection4 ,this law is resolved into the two following laws3 ,chlorine has a powerful affinity for bases of all kinds1 particularly metallic bases and hydrogen3 such bases are essential elements of coloring matters and contagious compounds1 which substances1 therefore1 are decomposed and destroyed by chlorine4 #d4 ,it is of importance to remark1 that when a sequence of phenomena is thus resolved into other laws1 they are always laws more general than itself4 ,the law that ,a is followed by ,c1 is less general than either of the laws which connect ,b with ,c and ,a with ,b4 ,this will appear from very simple considerations4 ,all laws of causation are liable to be counteracted or frustrated1 by the non-fulfillment of some negative condition2 the tendency1 therefore1 of ,b to produce ,c may be defeated4 ,now the law that ,a produces ,b1 is equally fulfilled whether ,b is followed by ,c or not2 but the law that ,a produces ,c by means of ,b1 is of course only fulfilled when ,b is really followed by ,c1 and is1 therefore1 less general than the law that ,a produces ,b4 ,it is also less general than the law that ,b produces ,c4 ,for ,b may have other causes besides ,a2 and as ,a produces ,c only by means of ,b1 while ,b produces ,c1 whether it has itself been produced by ,a or by any thing else1 the second law embraces a greater number of instances1 covers as it were a greater space of ground1 than the first4 ,thus1 in our former example1 the law that the contact of an object causes a change in the state of the nerve1 is more general than the law that contact with an object causes sensation1 since1 for aught we know1 the change in the nerve may equally take place when1 from a counteracting cause1 as1 for instance1 strong mental excitement1 the sensation does not follow2 as in a battle1 where wounds are sometimes received without any consciousness of receiving them4 ,and again1 the law that change in the state of a nerve produces sensation1 is more general than the law that contact with an object produces sensation2 since the sensation equally follows the change in the nerve when not produced by contact with an object1 but by some other cause2 as in the well-known case1 when a person who has lost a limb feels the same sensation which he has been accustomed to call a pain in the limb4 ,not only are the laws of more immediate sequence into which the law of a remote sequence is resolved1 laws of greater generality than that law is1 but 7as a consequence of1 or rather as implied in1 their greater generality7 they are more to be relied on2 there are fewer chances of their being ultimately found not to be universally true4 ,from the moment when the sequence of ,a and ,c is shown not to be immediate1 but to depend on an intervening phenomenon1 then1 however constant and invariable the sequence of ,a and ,c has hitherto been found1 possibilities arise of its failure1 exceeding those which can effect either of the more immediate sequences1 ,a1 ,b1 and ,b1 ,c4 ,the tendency of ,a to produce ,c may be defeated by whatever is capable of defeating either the tendency of ,a to produce ,b1 or the tendency of ,b to produce ,c2 it is1 therefore1 twice as liable to failure as either of those more elementary tendencies2 and the generalization that ,a is always followed by ,c1 is twice as likely to be found erroneous4 ,and so of the converse generalization1 that ,c is always preceded and caused by ,a2 which will be erroneous not only if there should happen to be a second immediate mode of production of ,c itself1 but moreover if there be a second mode of production of ,b1 the immediate antecedent of ,c in the sequence4 ,the resolution of the one generalization into the other two1 not only shows that there are possible limitations of the former1 from which its two elements are exempt1 but shows also where these are to be looked for4 ,as soon as we know that ,b intervenes between ,a and ,c1 we also know that if there be cases in which the sequence of ,a and ,c does not hold1 these are most likely to be found by studying the effects or the conditions of the phenomenon ,b4 ,it appears1 then1 that in the second of the three modes in which a law may be resolved into other laws1 the latter are more general1 that is1 extend to more cases1 and are also less likely to require limitation from subsequent experience1 than the law which they serve to explain4 ,they are more nearly unconditional2 they are defeated by fewer contingencies2 they are a nearer approach to the universal truth of nature4 ,the same observations are still more evidently true with regard to the first of the three modes of resolution4 ,when the law of an effect of combined forces is resolved into the separate laws of the causes1 the nature of the case implies that the law of the effect is less general than the law of any of the causes1 since it only holds when they are combined2 while the law of any one of the causes holds good both then1 and also when that cause acts apart from the rest4 ,it is also manifest that the complex law is liable to be oftener unfulfilled than any one of the simpler laws of which it is the result1 since every contingency which defeats any of the laws prevents so much of the effect as depends on it1 and thereby defeats the complex law4 ,the mere rusting1 for example1 of some small part of a great machine1 often suffices entirely to prevent the effect which ought to result from the joint action of all the parts4 ,the law of the effect of a combination of causes is always subject to the whole of the negative conditions which attach to the action of all the causes severally4 ,there is another and an equally strong reason why the law of a complex effect must be less general than the laws of the causes which conspire to produce it4 ,the same causes1 acting according to the same laws1 and differing only in the proportions in which they are combined1 often produce effects which differ not merely in quantity1 but in kind4 ,the combination of a centripetal with a projectile force1 in the proportions which obtain in all the planets and satellites of our solar system1 gives rise to an elliptical motion2 but if the ratio of the two forces to each other were slightly altered1 it is demonstrated that the motion produced would be in a circle1 or a parabola1 or an hyperbola2 and it is thought that in the case of some comets one of these is probably the fact4 ,yet the law of the parabolic motion would be resolvable into the very same simple laws into which that of the elliptical motion is resolved1 namely1 the law of the permanence of rectilineal motion1 and the law of gravitation4 ,if1 therefore1 in the course of ages1 some circumstance were to manifest itself which1 without defeating the law of either of those forces1 should merely alter their proportion to one another 7such as the shock of some solid body1 or even the accumulating effect of the resistance of the medium in which astronomers have been led to surmise that the motions of the heavenly bodies take place71 the elliptical motion might be changed into a motion in some other conic section2 and the complex law1 that the planetary motions take place in ellipses1 would be deprived of its universality1 though the discovery would not at all detract from the universality of the simpler laws into which that complex law is resolved4 ,the law1 in short1 of each of the concurrent causes remains the same1 however their collocations may vary2 but the law of their joint effect varies with every difference in the collocations4 ,there needs no more to show how much more general the elementary laws must be than any of the complex laws which are derived from them4 #e4 ,besides the two modes which have been treated of1 there is a third mode in which laws are resolved into one another2 and in this it is self-evident that they are resolved into laws more general than themselves4 ,this third mode is the subsumption 7as it has been called7 of one law under another2 or 7what comes to the same thing7 the gathering up of several laws into one more general law which includes them all4 ,the most splendid example of this operation was when terrestrial gravity and the central force of the solar system were brought together under the general law of gravitation4 ,it had been proved antecedently that the earth and the other planets tend to the sun2 and it had been known from the earliest times that terrestrial bodies tend toward the earth4 ,these were similar phenomena2 and to enable them both to be subsumed under one law1 it was only necessary to prove that1 as the effects were similar in quality so also they1 as to quantity1 conform to the same rules4 ,this was first shown to be true of the moon1 which agreed with terrestrial objects not only in tending to a centre1 but in the fact that this centre was the earth4 ,the tendency of the moon toward the earth being ascertained to vary as the inverse square of the distance1 it was deduced from this1 by direct calculation1 that if the moon were as near to the earth as terrestrial objects are1 and the acquired force in the direction of the tangent were suspended1 the moon would fall toward the earth through exactly as many feet in a second as those objects do by virtue of their weight4 ,hence the inference was irresistible1 that the moon also tends to the earth by virtue of its weight3 and that the two phenomena1 the tendency of the moon to the earth and the tendency of terrestrial objects to the earth1 being not only similar in quality1 but1 when in the same circumstances1 identical in quantity1 are cases of one and the same law of causation4 ,but the tendency of the moon to the earth1 and the tendency of the earth and planets to the sun1 were already known to be cases of the same law of causation2 and thus the law of all these tendencies1 and the law of terrestrial gravity1 were recognized as identical1 and were subsumed under one general law1 that of gravitation4 ,in a similar manner1 the laws of magnetic phenomena have more recently been subsumed under known laws of electricity4 ,it is thus that the most general laws of nature are usually arrived at3 we mount to them by successive steps4 ,for1 to arrive by correct induction at laws which hold under such an immense variety of circumstances1 laws so general as to be independent of any varieties of space or time which we are able to observe1 requires for the most part many distinct sets of experiments or observations1 conducted at different times and by different people4 ,one part of the law is first ascertained1 afterward another part3 one set of observations teaches us that the law holds good under some conditions1 another that it holds good under other conditions1 by combining which observations we find that it holds good under conditions much more general1 or even universally4 ,the general law1 in this case1 is literally the sum of all the partial ones2 it is a recognition of the same sequence in different sets of instances2 and may1 in fact1 be regarded as merely one step in the process of elimination4 ,the tendency of bodies toward one another1 which we now call gravity1 had at first been observed only on the earth's surface1 where it manifested itself only as a tendency of all bodies toward the earth1 and might1 therefore1 be ascribed to a peculiar property of the earth itself3 one of the circumstances1 namely1 the proximity of the earth1 had not been eliminated4 ,to eliminate this circumstance required a fresh set of instances in other parts of the universe3 these we could not ourselves create2 and though nature had created them for us1 we were placed in very unfavorable circumstances for observing them4 ,to make these observations1 fell naturally to the lot of a different set of persons from those who studied terrestrial phenomena2 and had1 indeed1 been a matter of great interest at a time when the idea of explaining celestial facts by terrestrial laws was looked upon as the confounding of an indefeasible distinction4 ,when1 however1 the celestial motions were accurately ascertained1 and the deductive processes performed1 from which it appeared that their laws and those of terrestrial gravity corresponded1 those celestial observations became a set of instances which exactly eliminated the circumstance of proximity to the earth2 and proved that in the original case1 that of terrestrial objects1 it was not the earth1 as such1 that caused the motion or the pressure1 but the circumstance common to that case with the celestial instances1 namely1 the presence of some great body within certain limits of distance4 #f4 ,there are1 then1 three modes of explaining laws of causation1 or1 which is the same thing1 resolving them into other laws4 ,first1 when the law of an effect of combined causes is resolved into the separate laws of the causes1 together with the fact of their combination4 ,secondly1 when the law which connects any two links1 not proximate1 in a chain of causation1 is resolved into the laws which connect each with the intermediate links4 ,both of these are cases of resolving one law into two or more2 in the third1 two or more are resolved into one3 when1 after the law has been shown to hold good in several different classes of cases1 we decide that what is true in each of these classes of cases1 is true under some more general supposition1 consisting of what all those classes of cases have in common4 ,we may here remark that this last operation involves none of the uncertainties attendant on induction by the ,method of ,agreement1 since we need not suppose the result to be extended by way of inference to any new class of cases different from those by the comparison of which it was engendered4 ,in all these three processes1 laws are1 as we have seen1 resolved into laws more general than themselves2 laws extending to all the cases which the former extended to1 and others besides4 ,in the first two modes they are also resolved into laws more certain1 in other words1 more universally true than themselves2 they are1 in fact1 proved not to be themselves laws of nature1 the character of which is to be universally true1 but results of laws of nature1 which may be only true conditionally1 and for the most part4 ,no difference of this sort exists in the third case2 since here the partial laws are1 in fact1 the very same law as the general one1 and any exception to them would be an exception to it too4 ,by all the three processes1 the range of deductive science is extended2 since the laws1 thus resolved1 may be thenceforth deduced demonstratively from the laws into which they are resolved4 ,as already remarked1 the same deductive process which proves a law or fact of causation if unknown1 serves to explain it when known4 ,the word explanation is here used in its philosophical sense4 ,what is called explaining one law of nature by another1 is but substituting one mystery for another2 and does nothing to render the general course of nature other than mysterious3 we can no more assign a why for the more extensive laws than for the partial ones4 ,the explanation may substitute a mystery which has become familiar1 and has grown to seem not mysterious1 for one which is still strange4 ,and this is the meaning of explanation1 in common parlance4 ,but the process with which we are here concerned often does the very contrary3 it resolves a phenomenon with which we are familiar into one of which we previously knew little or nothing2 as when the common fact of the fall of heavy bodies was resolved into the tendency of all particles of matter toward one another4 ,it must be kept constantly in view1 therefore1 that in science1 those who speak of explaining any phenomenon mean 7or should mean7 pointing out not some more familiar1 but merely some more general1 phenomenon1 of which it is a partial exemplification2 or some laws of causation which produce it by their joint or successive action1 and from which1 therefore1 its conditions may be determined deductively4 ,every such operation brings us a step nearer toward answering the question which was stated in a previous chapter as comprehending the whole problem of the investigation of nature1 viz43 what are the fewest assumptions1 which being granted1 the order of nature as it exists would be the result8 ,what are the fewest1 general propositions from which all the uniformities existing in nature could be deduced8 ,the laws1 thus explained or resolved1 are sometimes said to be accounted for2 but the expression is incorrect1 if taken to mean any thing more than what has been already stated4 ,in minds not habituated to accurate thinking1 there is often a confused notion that the general laws are the causes of the partial ones2 that the law of general gravitation1 for example1 causes the phenomenon of the fall of bodies to the earth4 ,but to assert this would be a misuse of the word cause3 terrestrial gravity is not an effect of general gravitation1 but a case of it2 that is1 one kind of the particular instances in which that general law obtains4 ,to account for a law of nature means1 and can mean1 nothing more than to assign other laws more general1 together with collocations1 which laws and collocations being supposed1 the partial law follows without any additional supposition4 ,chapter ,,xiii4 ,miscellaneous ,examples ,of ,the ,explanation ,of ,laws ,of ,nature4 #a4 ,the most striking example which the history of science presents1 of the explanation of laws of causation and other uniformities of sequence among special phenomena1 by resolving them into laws of greater simplicity and generality1 is the great ,newtonian generalization2 respecting which typical instance1 so much having already been said1 it is sufficient to call attention to the great number and variety of the special observed uniformities1 which are in this case accounted for1 either as particular cases1 or as consequences1 of one very simple law of universal nature4 ,the simple fact of a tendency of every particle of matter toward every other particle1 varying inversely as the square of the distance1 explains the fall of bodies to the earth1 the revolutions of the planets and satellites1 the motions 7so far as known7 of comets1 and all the various regularities which have been observed in these special phenomena2 such as the elliptical orbits1 and the variations from exact ellipses2 the relation between the solar distances of the planets and the duration of their revolutions2 the precession of the equinoxes2 the tides1 and a vast number of minor astronomical truths4 ,mention has also been made in the preceding chapter of the explanation of the phenomena of magnetism from laws of electricity2 the special laws of magnetic agency having been affiliated by deduction to observed laws of electric action1 in which they have ever since been considered to be included as special cases4 ,an example not so complete in itself1 but even more fertile in consequences1 having been the starting-point of the really scientific study of physiology1 is the affiliation1 commenced by ,bichat1 and carried on by subsequent biologists1 of the properties of the bodily organs1 to the elementary properties of the tissues into which they are anatomically decomposed4 ,another striking instance is afforded by ,dalton's generalization1 commonly known as the atomic theory4 ,it had been known from the very commencement of accurate chemical observation1 that any two bodies combine chemically with one another in only a certain number of proportions2 but those proportions were in each case expressed by a percentage--so many parts 7by weight7 of each ingredient1 in #ajj of the compound 7say #ce and a fraction of one element1 #fd and a fraction of the other72 in which mode of statement no relation was perceived between the proportion in which a given element combines with one substance1 and that in which it combines with others4 ,the great step made by ,dalton consisted in perceiving that a unit of weight might be established for each substance1 such that by supposing the substance to enter into all its combinations in the ratio either of that unit1 or of some low multiple of that unit1 all the different proportions1 previously expressed by percentages1 were found to result4 ,thus #a being assumed as the unit of hydrogen1 if #h were then taken as that of oxygen1 the combination of one unit of hydrogen with one unit of oxygen would produce the exact proportion of weight between the two substances which is known to exist in water2 the combination of one unit of hydrogen with two units of oxygen would produce the proportion which exists in the other compound of the same two elements1 called peroxide of hydrogen2 and the combinations of hydrogen and of oxygen with all other substances1 would correspond with the supposition that those elements enter into combination by single units1 or twos1 or threes1 of the numbers assigned to them1 #a and #h1 and the other substances by ones or twos or threes of other determinate numbers proper to each4 ,the result is that a table of the equivalent numbers1 or1 as they are called1 atomic weights1 of all the elementary substances1 comprises in itself1 and scientifically explains1 all the proportions in which any substance1 elementary or compound1 is found capable of entering into chemical combination with any other substance whatever4 #b4 ,some interesting cases of the explanation of old uniformities by newly ascertained laws are afforded by the researches of ,professor ,graham4 ,that eminent chemist was the first who drew attention to the distinction which may be made of all substances into two classes1 termed by him crystalloids and colloids2 or rather1 of all states of matter into the crystalloid and the colloidal states1 for many substances are capable of existing in either4 ,when in the colloidal state1 their sensible properties are very different from those of the same substance when crystallized1 or when in a state easily susceptible of crystallization4 ,colloid substances pass with extreme difficulty and slowness into the crystalline state1 and are extremely inert in all the ordinary chemical relations4 ,substances in the colloid state are almost always1 when combined with water1 more or less viscous or gelatinous4 ,the most prominent examples of the state are certain animal and vegetable substances1 particularly gelatine1 albumen1 starch1 the gums1 caramel1 tannin1 and some others4 ,among substances not of organic origin1 the most notable instances are hydrated silicic acid1 and hydrated alumina1 with other metallic peroxides of the aluminous class4 ,now it is found1 that while colloidal substances are easily penetrated by water1 and by the solutions of crystalloid substances1 they are very little penetrable by one another3 which enabled ,professor ,graham to introduce a highly effective process 7termed dialysis7 for separating the crystalloid substances contained in any liquid mixture1 by passing them through a thin septum of colloidal matter1 which does not suffer any thing colloidal to pass1 or suffers it only in very minute quantity4 ,this property of colloids enabled ,mr4 ,graham to account for a number of special results of observation1 not previously explained4 ,for instance1 8while soluble crystalloids are always highly sapid1 soluble colloids are singularly insipid10 as might be expected2 for1 as the sentient extremities of the nerves of the palate 8are probably protected by a colloidal membrane10 impermeable to other colloids1 a colloid1 when tasted1 probably never reaches those nerves4 ,again1 8it has been observed that vegetable gum is not digested in the stomach2 the coats of that organ dialyse the soluble food1 absorbing crystalloids1 and rejecting all colloids40 ,one of the mysterious processes accompanying digestion1 the secretion of free muriatic acid by the coats of the stomach1 obtains a probable hypothetical explanation through the same law4 ,finally1 much light is thrown upon the observed phenomena of osmose 7the passage of fluids outward and inward through animal membranes7 by the fact that the membranes are colloidal4 ,in consequence1 the water and saline solutions contained in the animal body pass easily and rapidly through the membranes1 while the substances directly applicable to nutrition1 which are mostly colloidal1 are detained by them47#aed7 ,the property which salt possesses of preserving animal substances from putrefaction is resolved by ,liebig into two more general laws1 the strong attraction of salt for water1 and the necessity of the presence of water as a condition of putrefaction4 ,the intermediate phenomenon which is interpolated between the remote cause and the effect1 can here be not merely inferred but seen2 for it is a familiar fact1 that flesh upon which salt has been thrown is speedily found swimming in brine4 ,the second of the two factors 7as they may be termed7 into which the preceding law has been resolved1 the necessity of water to putrefaction1 itself affords an additional example of the ,resolution of ,laws4 ,the law itself is proved by the ,method of ,difference1 since flesh completely dried and kept in a dry atmosphere does not putrefy2 as we see in the case of dried provisions and human bodies in very dry climates4 ,a deductive explanation of this same law results from ,liebig's speculations4 ,the putrefaction of animal and other azotized bodies is a chemical process1 by which they are gradually dissipated in a gaseous form1 chiefly in that of carbonic acid and ammonia2 now to convert the carbon of the animal substance into carbonic acid requires oxygen1 and to convert the azote into ammonia requires hydrogen1 which are the elements of water4 ,the extreme rapidity of the putrefaction of azotized substances1 compared with the gradual decay of non-azotized bodies 7such as wood and the like7 by the action of oxygen alone1 he explains from the general law that substances are much more easily decomposed by the action of two different affinities upon two of their elements than by the action of only one4 #c4 ,among the many important properties of the nervous system which have either been first discovered or strikingly illustrated by ,dr4 ,brown-,squard1 ,i select the reflex influence of the nervous system on nutrition and secretion4 ,by reflex nervous action is meant1 action which one part of the nervous system exerts over another part1 without any intermediate action on the brain1 and consequently without consciousness2 or which1 if it does pass through the brain1 at least produces its effects independently of the will4 ,there are many experiments which prove that irritation of a nerve in one part of the body may in this manner excite powerful action in another part2 for example1 food injected into the stomach through a divided sophagus1 nevertheless produces secretion of saliva2 warm water injected into the bowels1 and various other irritations of the lower intestines1 have been found to excite secretion of the gastric juice1 and so forth4 ,the reality of the power being thus proved1 its agency explains a great variety of apparently anomalous phenomena2 of which ,i select the following from ,dr4 ,brown-,squard's ,lectures on the ,nervous ,system3 ,the production of tears by irritation of the eye1 or of the mucous membrane of the nose2 ,the secretions of the eye and nose increased by exposure of other parts of the body to cold2 ,inflammation of the eye1 especially when of traumatic origin1 very frequently excites a similar affection in the other eye1 which may be cured by section of the intervening nerve2 ,loss of sight sometimes produced by neuralgia1 and has been known to be at once cured by the extirpation 7for instance7 of a carious tooth2 ,even cataract has been produced in a healthy eye by cataract in the other eye1 or by neuralgia1 or by a wound of the frontal nerve2 ,the well-known phenomenon of a sudden stoppage of the heart's action1 and consequent death1 produced by irritation of some of the nervous extremities2 e4g41 by drinking very cold water1 or by a blow on the abdomen1 or other sudden excitation of the abdominal sympathetic nerve1 though this nerve may be irritated to any extent without stopping the heart's action1 if a section be made of the communicating nerves2 ,the extraordinary effects produced on the internal organs by an extensive burn on the surface of the body1 consisting in violent inflammation of the tissues of the abdomen1 chest1 or head1 which1 when death ensues from this kind of injury1 is one of the most frequent causes of it2 ,paralysis and ansthesia of one part of the body from neuralgia in another part2 and muscular atrophy from neuralgia1 even when there is no paralysis2 ,tetanus produced by the lesion of a nerve4 ,dr4 ,brown-,squard thinks it highly probable that hydrophobia is a phenomenon of a similar nature2 ,morbid changes in the nutrition of the brain and spinal cord1 manifesting themselves by epilepsy1 chorea1 hysteria1 and other diseases1 occasioned by lesion of some of the nervous extremities in remote places1 as by worms1 calculi1 tumors1 carious bones1 and in some cases even by very slight irritations of the skin4 #d4 ,from the foregoing and similar instances1 we may see the importance1 when a law of nature previously unknown has been brought to light1 or when new light has been thrown upon a known law by experiment1 of examining all cases which present the conditions necessary for bringing that law into action2 a process fertile in demonstrations of special laws previously unsuspected1 and explanations of others already empirically known4 ,for instance1 ,faraday discovered by experiment1 that voltaic electricity could be evolved from a natural magnet1 provided a conducting body were set in motion at right angles to the direction of the magnet2 and this he found to hold not only of small magnets1 but of that great magnet1 the earth4 ,the law being thus established experimentally1 that electricity is evolved1 by a magnet1 and a conductor moving at right angles to the direction of its poles1 we may now look out for fresh instances in which these conditions meet4 ,wherever a conductor moves or revolves at right angles to the direction of the earth's magnetic poles1 there we may expect an evolution of electricity4 ,in the northern regions1 where the polar direction is nearly perpendicular to the horizon1 all horizontal motions of conductors will produce electricity2 horizontal wheels1 for example1 made of metal2 likewise all running streams will evolve a current of electricity1 which will circulate round them2 and the air thus charged with electricity may be one of the causes of the ,aurora ,borealis4 ,in the equatorial regions1 on the contrary1 upright wheels placed parallel to the equator will originate a voltaic circuit1 and water-falls will naturally become electric4 ,for a second example1 it has been proved1 chiefly by the researches of ,professor ,graham1 that gases have a strong tendency to permeate animal membranes1 and diffuse themselves through the spaces which such membranes inclose1 notwithstanding the presence of other gases in those spaces4 ,proceeding from this general law1 and reviewing a variety of cases in which gases lie contiguous to membranes1 we are enabled to demonstrate or to explain the following more special laws3 #ast4 ,the human or animal body1 when surrounded with any gas not already contained within the body1 absorbs it rapidly2 such1 for instance1 as the gases of putrefying matters3 which helps to explain malaria4 #b;d4 ,the carbonic acid gas of effervescing drinks1 evolved in the stomach1 permeates its membranes1 and rapidly spreads through the system4 #c;d4 ,alcohol taken into the stomach passes into vapor1 and spreads through the system with great rapidity 7which1 combined with the high combustibility of alcohol1 or in other words its ready combination with oxygen1 may perhaps help to explain the bodily warmth immediately consequent on drinking spirituous liquors74 #dth4 ,in any state of the body in which peculiar gases are formed within it1 these will rapidly exhale through all parts of the body2 and hence the rapidity with which1 in certain states of disease1 the surrounding atmosphere becomes tainted4 #eth4 ,the putrefaction of the interior parts of a carcass will proceed as rapidly as that of the exterior1 from the ready passage outward of the gaseous products4 #fth4 ,the exchange of oxygen and carbonic acid in the lungs is not prevented1 but rather promoted1 by the intervention of the membrane of the lungs and the coats of the blood-vessels between the blood and the air4 ,it is necessary1 however1 that there should be a substance in the blood with which the oxygen of the air may immediately combine2 otherwise1 instead of passing into the blood1 it would permeate the whole organism3 and it is necessary that the carbonic acid1 as it is formed in the capillaries1 should also find a substance in the blood with which it can combine2 otherwise it would leave the body at all points1 instead of being discharged through the lungs4 #e4 ,the following is a deduction which confirms1 by explaining1 the empirical generalization1 that soda powders weaken the human system4 ,these powders1 consisting of a mixture of tartaric acid with bicarbonate of soda1 from which the carbonic acid is set free1 must pass into the stomach as tartrate of soda4 ,now1 neutral tartrates1 citrates1 and acetates of the alkalis are found1 in their passage through the system1 to be changed into carbonates2 and to convert a tartrate into a carbonate requires an additional quantity of oxygen1 the abstraction of which must lessen the oxygen destined for assimilation with the blood1 on the quantity of which the vigorous action of the human system partly depends4 ,the instances of new theories agreeing with and explaining old empiricisms1 are innumerable4 ,all the just remarks made by experienced persons on human character and conduct1 are so many special laws1 which the general laws of the human mind explain and resolve4 ,the empirical generalizations on which the operations of the arts have usually been founded1 are continually justified and confirmed on the one hand1 or corrected and improved on the other1 by the discovery of the simpler scientific laws on which the efficacy of those operations depends4 ,the effects of the rotation of crops1 of the various manures1 and other processes of improved agriculture1 have been for the first time resolved in our own day into known laws of chemical and organic action1 by ,davy1 ,liebig1 and others4 ,the processes of the medical art are even now mostly empirical3 their efficacy is concluded1 in each instance1 from a special and most precarious experimental generalization3 but as science advances in discovering the simple laws of chemistry and physiology1 progress is made in ascertaining the intermediate links in the series of phenomena1 and the more general laws on which they depend2 and thus1 while the old processes are either exploded1 or their efficacy1 in so far as real1 explained1 better processes1 founded on the knowledge of proximate causes1 are continually suggested and brought into use47#aee7 ,many even of the truths of geometry were generalizations from experience before they were deduced from first principles4 ,the quadrature of the cycloid is said to have been first effected by measurement1 or rather by weighing a cycloidal card1 and comparing its weight with that of a piece of similar card of known dimensions4 #f4 ,to the foregoing examples from physical science1 let us add another from mental4 ,the following is one of the simple laws of mind3 ,ideas of a pleasurable or painful character form associations more easily and strongly than other ideas1 that is1 they become associated after fewer repetitions1 and the association is more durable4 ,this is an experimental law1 grounded on the ,method of ,difference4 ,by deduction from this law1 many of the more special laws which experience shows to exist among particular mental phenomena may be demonstrated and explained3 the ease and rapidity1 for instance1 with which thoughts connected with our passions or our more cherished interests are excited1 and the firm hold which the facts relating to them have on our memory2 the vivid recollection we retain of minute circumstances which accompanied any object or event that deeply interested us1 and of the times and places in which we have been very happy or very miserable2 the horror with which we view the accidental instrument of any occurrence which shocked us1 or the locality where it took place and the pleasure we derive from any memorial of past enjoyment2 all these effects being proportional to the sensibility of the individual mind1 and to the consequent intensity of the pain or pleasure from which the association originated4 ,it has been suggested by the able writer of a biographical sketch of ,dr4 ,priestley in a monthly periodical17#aef7 that the same elementary law of our mental constitution1 suitably followed out1 would explain a variety of mental phenomena previously inexplicable1 and in particular some of the fundamental diversities of human character and genius4 ,associations being of two sorts1 either between synchronous1 or between successive impressions2 and the influence of the law which renders associations stronger in proportion to the pleasurable or painful character of the impressions1 being felt with peculiar force in the synchronous class of associations2 it is remarked by the writer referred to1 that in minds of strong organic sensibility synchronous associations will be likely to predominate1 producing a tendency to conceive things in pictures and in the concrete1 richly clothed in attributes and circumstances1 a mental habit which is commonly called ,imagination1 and is one of the peculiarities of the painter and the poet2 while persons of more moderate susceptibility to pleasure and pain will have a tendency to associate facts chiefly in the order of their succession1 and such persons1 if they possess mental superiority1 will addict themselves to history or science rather than to creative art4 ,this interesting speculation the author of the present work has endeavored1 on another occasion1 to pursue further1 and to examine how far it will avail toward explaining the peculiarities of the poetical temperament47#aeg7 ,it is at least an example which may serve1 instead of many others1 to show the extensive scope which exists for deductive investigation in the important and hitherto so imperfect ,science of ,mind4 #g4 ,the copiousness with which the discovery and explanation of special laws of phenomena by deduction from simpler and more general ones has here been exemplified1 was prompted by a desire to characterize clearly1 and place in its due position of importance1 the ,deductive ,method2 which1 in the present state of knowledge1 is destined henceforth irrevocably to predominate in the course of scientific investigation4 ,a revolution is peaceably and progressively effecting itself in philosophy1 the reverse of that to which ,bacon has attached his name4 ,that great man changed the method of the sciences from deductive to experimental1 and it is now rapidly reverting from experimental to deductive4 ,but the deductions which ,bacon abolished were from premises hastily snatched up1 or arbitrarily assumed4 ,the principles were neither established by legitimate canons of experimental inquiry1 nor the results tested by that indispensable element of a rational ,deductive ,method1 verification by specific experience4 ,between the primitive method of ,deduction and that which ,i have attempted to characterize1 there is all the difference which exists between the ,aristotelian physics and the ,newtonian theory of the heavens4 ,it would1 however1 be a mistake to expect that those great generalizations1 from which the subordinate truths of the more backward sciences will probably at some future period be deduced by reasoning 7as the truths of astronomy are deduced from the generalities of the ,newtonian theory71 will be found in all1 or even in most cases1 among truths now known and admitted4 ,we may rest assured1 that many of the most general laws of nature are as yet entirely unthought of2 and that many others1 destined hereafter to assume the same character1 are known1 if at all1 only as laws or properties of some limited class of phenomena2 just as electricity1 now recognized as one of the most universal of natural agencies1 was once known only as a curious property which certain substances acquired by friction1 of first attracting and then repelling light bodies4 ,if the theories of heat1 cohesion1 crystallization1 and chemical action are destined1 as there can be little doubt that they are1 to become deductive1 the truths which will then be regarded as the principia of those sciences would probably1 if now announced1 appear quite as novel7#aeh7 as the law of gravitation appeared to the contemporaries of ,newton2 possibly even more so1 since ,newton's law1 after all1 was but an extension of the law of weight--that is1 of a generalization familiar from of old1 and which already comprehended a not inconsiderable body of natural phenomena4 ,the general laws of a similarly commanding character1 which we still look forward to the discovery of1 may not always find so much of their foundations already laid4 ,these general truths will doubtless make their first appearance in the character of hypotheses2 not proved1 nor even admitting of proof1 in the first instance1 but assumed as premises for the purpose of deducing from them the known laws of concrete phenomena4 ,but this1 though their initial1 can not be their final state4 ,to entitle an hypothesis to be received as one of the truths of nature1 and not as a mere technical help to the human faculties1 it must be capable of being tested by the canons of legitimate induction1 and must actually have been submitted to that test4 ,when this shall have been done1 and done successfully1 premises will have been obtained from which all the other propositions of the science will thenceforth be presented as conclusions1 and the science will1 by means of a new and unexpected ,induction1 be rendered ,deductive4 ,chapter ,,xiv4 ,of ,the ,limits ,to ,the ,explanation ,of ,laws ,of ,nature2 ,and ,of ,hypotheses4 #a4 ,the preceding considerations have led us to recognize a distinction between two kinds of laws1 or observed uniformities in nature3 ultimate laws1 and what may be termed derivative laws4 ,derivative laws are such as are deducible from1 and may1 in any of the modes which we have pointed out1 be resolved into1 other and more general ones4 ,ultimate laws are those which can not4 ,we are not sure that any of the uniformities with which we are yet acquainted are ultimate laws2 but we know that there must be ultimate laws2 and that every resolution of a derivative law into more general laws brings us nearer to them4 ,since we are continually discovering that uniformities1 not previously known to be other than ultimate1 are derivative1 and resolvable into more general laws2 since 7in other words7 we are continually discovering the explanation of some sequence which was previously known only as a fact2 it becomes an interesting question whether there are any necessary limits to this philosophical operation1 or whether it may proceed until all the uniform sequences in nature are resolved into some one universal law4 ,for this seems1 at first sight1 to be the ultimatum toward which the progress of induction by the ,deductive ,method1 resting on a basis of observation and experiment1 is tending4 ,projects of this kind were universal in the infancy of philosophy2 any speculations which held out a less brilliant prospect being in these early times deemed not worth pursuing4 ,and the idea receives so much apparent countenance from the nature of the most remarkable achievements of modern science1 that speculators are even now frequently appearing1 who profess either to have solved the problem1 or to suggest modes in which it may one day be solved4 ,even where pretensions of this magnitude are not made1 the character of the solutions which are given or sought of particular classes of phenomena1 often involves such conceptions of what constitutes explanation1 as would render the notion of explaining all phenomena whatever by means of some one cause or law1 perfectly admissible4 #b4 ,it is1 therefore1 useful to remark that the ultimate ,laws of ,nature can not possibly be less numerous than the distinguishable sensations or other feelings of our nature2 those1 ,i mean1 which are distinguishable from one another in quality1 and not merely in quantity or degree4 ,for example3 since there is a phenomenon sui generis1 called color1 which our consciousness testifies to be not a particular degree of some other phenomenon1 as heat or odor or motion1 but intrinsically unlike all others1 it follows that there are ultimate laws of color2 that though the facts of color may admit of explanation1 they never can be explained from laws of heat or odor alone1 or of motion alone1 but that1 however far the explanation may be carried1 there will always remain in it a law of color4 ,i do not mean that it might not possibly be shown that some other phenomenon1 some chemical or mechanical action1 for example1 invariably precedes1 and is the cause of1 every phenomenon of color4 ,but though this1 if proved1 would be an important extension of our knowledge of nature1 it would not explain how or why a motion1 or a chemical action1 can produce a sensation of color2 and1 however diligent might be our scrutiny of the phenomena1 whatever number of hidden links we might detect in the chain of causation terminating in the color1 the last link would still be a law of color1 not a law of motion1 nor of any other phenomenon whatever4 ,nor does this observation apply only to color1 as compared with any other of the great classes of sensations2 it applies to every particular color1 as compared with others4 ,white color can in no manner be explained exclusively by the laws of the production of red color4 ,in any attempt to explain it1 we can not but introduce1 as one element of the explanation1 the proposition that some antecedent or other produces the sensation of white4 ,the ideal limit1 therefore1 of the explanation of natural phenomena 7toward which as toward other ideal limits we are constantly tending1 without the prospect of ever completely attaining it7 would be to show that each distinguishable variety of our sensations1 or other states of consciousness1 has only one sort of cause2 that1 for example1 whenever we perceive a white color1 there is some one condition or set of conditions which is always present1 and the presence of which always produces in us that sensation4 ,as long as there are several known modes of production of a phenomenon 7several different substances1 for instance1 which have the property of whiteness1 and between which we can not trace any other resemblance7 so long it is not impossible that one of these modes of production may be resolved into another1 or that all of them may be resolved into some more general mode of production not hitherto recognized4 ,but when the modes of production are reduced to one1 we can not1 in point of simplification1 go any further4 ,this one may not1 after all1 be the ultimate mode2 there may be other links to be discovered between the supposed cause and the effect2 but we can only further resolve the known law1 by introducing some other law hitherto unknown1 which will not diminish the number of ultimate laws4 ,in what cases1 accordingly1 has science been most successful in explaining phenomena1 by resolving their complex laws into laws of greater simplicity and generality8 ,hitherto chiefly in cases of the propagation of various phenomena through space2 and1 first and principally1 the most extensive and important of all facts of that description1 mechanical motion4 ,now this is exactly what might be expected from the principles here laid down4 ,not only is motion one of the most universal of all phenomena1 it is also 7as might be expected from that circumstance7 one of those which1 apparently at least1 are produced in the greatest number of ways2 but the phenomenon itself is always1 to our sensations1 the same in every respect but degree4 ,differences of duration or of velocity1 are evidently differences in degree only2 and differences of direction in space1 which alone has any semblance of being a distinction in kind1 entirely disappear 7so far as our sensations are concerned7 by a change in our own position2 indeed1 the very same motion appears to us1 according to our position1 to take place in every variety of direction1 and motions in every different direction to take place in the same4 ,and again1 motion in a straight line and in a curve are no otherwise distinct than that the one is motion continuing in the same direction1 the other is motion which at each instant changes its direction4 ,there is1 therefore1 according to the principles ,i have stated1 no absurdity in supposing that all motion may be produced in one and the same way1 by the same kind of cause4 ,accordingly1 the greatest achievements in physical science have consisted in resolving one observed law of the production of motion into the laws of other known modes of production1 or the laws of several such modes into one more general mode2 as when the fall of bodies to the earth1 and the motions of the planets1 were brought under the one law of the mutual attraction of all particles of matter2 when the motions said to be produced by magnetism were shown to be produced by electricity2 when the motions of fluids in a lateral direction1 or even contrary to the direction of gravity1 were shown to be produced by gravity2 and the like4 ,there is an abundance of distinct causes of motion still unresolved into one another3 gravitation1 heat1 electricity1 chemical action1 nervous action1 and so forth2 but whether the efforts of the present generation of savants to resolve all these different modes of production into one are ultimately successful or not1 the attempt so to resolve them is perfectly legitimate4 ,for1 though these various causes produce1 in other respects1 sensations intrinsically different1 and are not1 therefore1 capable of being resolved into one another1 yet1 in so far as they all produce motion1 it is quite possible that the immediate antecedent of the motion may in all these different cases be the same2 nor is it impossible that these various agencies themselves may1 as the new doctrines assert1 all of them have for their own immediate antecedent modes of molecular motion4 ,we need not extend our illustration to other cases1 as1 for instance1 to the propagation of light1 sound1 heat1 electricity1 etc41 through space1 or any of the other phenomena which have been found susceptible of explanation by the resolution of their observed laws into more general laws4 ,enough has been said to display the difference between the kind of explanation and resolution of laws which is chimerical1 and that of which the accomplishment is the great aim of science2 and to show into what sort of elements the resolution must be effected1 if at all47#aei7 #c4 ,as1 however1 there is scarcely any one of the principles of a true method of philosophizing which does not require to be guarded against errors on both sides1 ,i must enter a caveat against another misapprehension1 of a kind directly contrary to the preceding4 ,m4 ,comte1 among other occasions on which he has condemned1 with some asperity1 any attempt to explain phenomena which are 8evidently primordial0 7meaning1 apparently1 no more than that every peculiar phenomenon must have at least one peculiar and therefore inexplicable law71 has spoken of the attempt to furnish any explanation of the color belonging to each substance1 8la couleur lmentaire propre chaque substance10 as essentially illusory4 8,no one10 says he1 8in our time attempts to explain the particular specific gravity of each substance or of each structure4 ,why should it be otherwise as to the specific color1 the notion of which is undoubtedly no less primordial807#afj7 ,now although1 as he elsewhere observes1 a color must always remain a different thing from a weight or a sound1 varieties of color might nevertheless follow1 or correspond to1 given varieties of weight1 or sound1 or some other phenomenon as different as these are from color itself4 ,it is one question what a thing is1 and another what it depends on2 and though to ascertain the conditions of an elementary phenomenon is not to obtain any new insight into the nature of the phenomenon itself1 that is no reason against attempting to discover the conditions4 ,the interdict against endeavoring to reduce distinctions of color to any common principle1 would have held equally good against a like attempt on the subject of distinctions of sound2 which nevertheless have been found to be immediately preceded and caused by distinguishable varieties in the vibrations of elastic bodies2 though a sound1 no doubt1 is quite as different as a color is from any motion of particles1 vibratory or otherwise4 ,we might add1 that1 in the case of colors1 there are strong positive indications that they are not ultimate properties of the different kinds of substances1 but depend on conditions capable of being superinduced upon all substances2 since there is no substance which can not1 according to the kind of light thrown upon it1 be made to assume almost any color2 and since almost every change in the mode of aggregation of the particles of the same substance is attended with alterations in its color1 and in its optical properties generally4 ,the really weak point in the attempts which have been made to account for colors by the vibrations of a fluid1 is not that the attempt itself is unphilosophical1 but that the existence of the fluid1 and the fact of its vibratory motion1 are not proved1 but are assumed1 on no other ground than the facility they are supposed to afford of explaining the phenomena4 ,and this consideration leads to the important question of the proper use of scientific hypotheses1 the connection of which with the subject of the explanation of the phenomena of nature1 and of the necessary limits to that explanation1 need not be pointed out4 #d4 ,an hypothesis is any supposition which we make 7either without actual evidence1 or on evidence avowedly insufficient7 in order to endeavor to deduce from it conclusions in accordance with facts which are known to be real2 under the idea that if the conclusions to which the hypothesis leads are known truths1 the hypothesis itself either must be1 or at least is likely to be1 true4 ,if the hypothesis relates to the cause or mode of production of a phenomenon1 it will serve1 if admitted1 to explain such facts as are found capable of being deduced from it4 ,and this explanation is the purpose of many1 if not most hypotheses4 ,since explaining1 in the scientific sense1 means resolving a uniformity which is not a law of causation1 into the laws of causation from which it results1 or a complex law of causation into simpler and more general ones from which it is capable of being deductively inferred1 if there do not exist any known laws which fulfill this requirement1 we may feign or imagine some which would fulfill it2 and this is making an hypothesis4 ,an hypothesis being a mere supposition1 there are no other limits to hypotheses than those of the human imagination2 we may1 if we please1 imagine1 by way of accounting for an effect1 some cause of a kind utterly unknown1 and acting according to a law altogether fictitious4 ,but as hypotheses of this sort would not have any of the plausibility belonging to those which ally themselves by analogy with known laws of nature1 and besides would not supply the want which arbitrary hypotheses are generally invented to satisfy1 by enabling the imagination to represent to itself an obscure phenomenon in a familiar light1 there is probably no hypothesis in the history of science in which both the agent itself and the law of its operation were fictitious4 ,either the phenomenon assigned as the cause is real1 but the law according to which it acts merely supposed2 or the cause is fictitious1 but is supposed to produce its effects according to laws similar to those of some known class of phenomena4 ,an instance of the first kind is afforded by the different suppositions made respecting the law of the planetary central force1 anterior to the discovery of the true law1 that the force varies as the inverse square of the distance2 which also suggested itself to ,newton1 in the first instance1 as an hypothesis1 and was verified by proving that it led deductively to ,kepler's laws4 ,hypotheses of the second kind are such as the vortices of ,descartes1 which were fictitious1 but were supposed to obey the known laws of rotatory motion2 or the two rival hypotheses respecting the nature of light1 the one ascribing the phenomena to a fluid emitted from all luminous bodies1 the other 7now generally received7 attributing them to vibratory motions among the particles of an ether pervading all space4 ,of the existence of either fluid there is no evidence1 save the explanation they are calculated to afford of some of the phenomena2 but they are supposed to produce their effects according to known laws3 the ordinary laws of continued locomotion in the one case1 and in the other those of the propagation of undulatory movements among the particles of an elastic fluid4 ,according to the foregoing remarks1 hypotheses are invented to enable the ,deductive ,method to be earlier applied to phenomena4 ,but7#afa7 in order to discover the cause of any phenomenon by the ,deductive ,method1 the process must consist of three parts3 induction1 ratiocination1 and verification4 ,induction 7the place of which1 however1 may be supplied by a prior deduction71 to ascertain the laws of the causes2 ratiocination1 to compute from those laws how the causes will operate in the particular combination known to exist in the case in hand2 verification1 by comparing this calculated effect with the actual phenomenon4 ,no one of these three parts of the process can be dispensed with4 ,in the deduction which proves the identity of gravity with the central force of the solar system1 all the three are found4 ,first1 it is proved from the moon's motions1 that the earth attracts her with a force varying as the inverse square of the distance4 ,this 7though partly dependent on prior deductions7 corresponds to the first1 or purely inductive1 step3 the ascertainment of the law of the cause4 ,secondly1 from this law1 and from the knowledge previously obtained of the moon's mean distance from the earth1 and of the actual amount of her deflection from the tangent1 it is ascertained with what rapidity the earth's attraction would cause the moon to fall1 if she were no further off1 and no more acted upon by extraneous forces1 than terrestrial bodies are3 that is the second step1 the ratiocination4 ,finally1 this calculated velocity being compared with the observed velocity with which all heavy bodies fall1 by mere gravity1 toward the surface of the earth 7sixteen feet in the first second1 forty-eight in the second1 and so forth1 in the ratio of the odd numbers1 #a1 #c1 #e1 etc471 the two quantities are found to agree4 ,the order in which the steps are here presented was not that of their discovery2 but it is their correct logical order1 as portions of the proof that the same attraction of the earth which causes the moon's motion causes also the fall of heavy bodies to the earth3 a proof which is thus complete in all its parts4 ,now1 the ,hypothetical ,method suppresses the first of the three steps1 the induction to ascertain the law2 and contents itself with the other two operations1 ratiocination and verification2 the law which is reasoned from being assumed instead of proved4 ,this process may evidently be legitimate on one supposition1 namely1 if the nature of the case be such that the final step1 the verification1 shall amount to1 and fulfill the conditions of1 a complete induction4 ,we want to be assured that the law we have hypothetically assumed is a true one2 and its leading deductively to true results will afford this assurance1 provided the case be such that a false law can not lead to a true result2 provided no law1 except the very one which we have assumed1 can lead deductively to the same conclusions which that leads to4 ,and this proviso is often realized4 ,for example1 in the very complete specimen of deduction which we just cited1 the original major premise of the ratiocination1 the law of the attractive force1 was ascertained in this mode2 by this legitimate employment of the ,hypothetical ,method4 ,newton began by an assumption that the force which at each instant deflects a planet from its rectilineal course1 and makes it describe a curve round the sun1 is a force tending directly toward the sun4 ,he then proved that if this be so1 the planet will describe1 as we know by ,kepler's first law that it does describe1 equal areas in equal times2 and1 lastly1 he proved that if the force acted in any other direction whatever1 the planet would not describe equal areas in equal times4 ,it being thus shown that no other hypothesis would accord with the facts1 the assumption was proved2 the hypothesis became an inductive truth4 ,not only did ,newton ascertain by this hypothetical process the direction of the deflecting force2 he proceeded in exactly the same manner to ascertain the law of variation of the quantity of that force4 ,he assumed that the force varied inversely as the square of the distance2 showed that from this assumption the remaining two of ,kepler's laws might be deduced2 and1 finally1 that any other law of variation would give results inconsistent with those laws1 and inconsistent1 therefore1 with the real motions of the planets1 of which ,kepler's laws were known to be a correct expression4 ,i have said that in this case the verification fulfills the conditions of an induction2 but an induction of what sort8 ,on examination we find that it conforms to the canon of the ,method of ,difference4 ,it affords the two instances1 ,a ,b ,c1 a b c1 and ,b ,c1 b c4 ,a represents central force2 ,a ,b ,c1 the planets plus a central force2 ,b ,c1 the planets apart from a central force4 ,the planets with a central force give a1 areas proportional to the times2 the planets without a central force give b c 7a set of motions7 without a1 or with something else instead of a4 ,this is the ,method of ,difference in all its strictness4 ,it is true1 the two instances which the method requires are obtained in this case1 not by experiment1 but by a prior deduction4 ,but that is of no consequence4 ,it is immaterial what is the nature of the evidence from which we derive the assurance that ,a ,b ,c will produce a b c1 and ,b ,c only b c2 it is enough that we have that assurance4 ,in the present case1 a process of reasoning furnished ,newton with the very instances which1 if the nature of the case had admitted of it1 he would have sought by experiment4 ,it is thus perfectly possible1 and indeed is a very common occurrence1 that what was an hypothesis at the beginning of the inquiry becomes a proved law of nature before its close4 ,but in order that this should happen1 we must be able1 either by deduction or experiment1 to obtain both the instances which the ,method of ,difference requires4 ,that we are able from the hypothesis to deduce the known facts1 gives only the affirmative instance1 ,a ,b ,c1 a b c4 ,it is equally necessary that we should be able to obtain1 as ,newton did1 the negative instance ,b ,c1 b c2 by showing that no antecedent1 except the one assumed in the hypothesis1 would in conjunction with ,b ,c produce a4 ,now it appears to me that this assurance can not be obtained1 when the cause assumed in the hypothesis is an unknown cause imagined solely to account for a4 ,when we are only seeking to determine the precise law of a cause already ascertained1 or to distinguish the particular agent which is in fact the cause1 among several agents of the same kind1 one or other of which it is already known to be1 we may then obtain the negative instance4 ,an inquiry which of the bodies of the solar system causes by its attraction some particular irregularity in the orbit or periodic time of some satellite or comet1 would be a case of the second description4 ,newton's was a case of the first4 ,if it had not been previously known that the planets were hindered from moving in straight lines by some force tending toward the interior of their orbit1 though the exact direction was doubtful2 or if it had not been known that the force increased in some proportion or other as the distance diminished1 and diminished as it increased1 ,newton's argument would not have proved his conclusion4 ,these facts1 however1 being already certain1 the range of admissible suppositions was limited to the various possible directions of a line1 and the various possible numerical relations between the variations of the distance1 and the variations of the attractive force4 ,now among these it was easily shown that different suppositions could not lead to identical consequences4 ,accordingly1 ,newton could not have performed his second great scientific operation3 that of identifying terrestrial gravity with the central force of the solar system by the same hypothetical method4 ,when the law of the moon's attraction had been proved from the data of the moon itself1 then1 on finding the same law to accord with the phenomena of terrestrial gravity1 he was warranted in adopting it as the law of those phenomena likewise2 but it would not have been allowable for him1 without any lunar data1 to assume that the moon was attracted toward the earth with a force as the inverse square of the distance1 merely because that ratio would enable him to account for terrestrial gravity2 for it would have been impossible for him to prove that the observed law of the fall of heavy bodies to the earth could not result from any force1 save one extending to the moon1 and proportional to the inverse square4 ,it appears1 then1 to be a condition of the most genuinely scientific hypothesis1 that it be not destined always to remain an hypothesis1 but be of such a nature as to be either proved or disproved by comparison with observed facts4 ,this condition is fulfilled when the effect is already known to depend on the very cause supposed1 and the hypothesis relates only to the precise mode of dependence2 the law of the variation of the effect according to the variations in the quantity or in the relations of the cause4 ,with these may be classed the hypotheses which do not make any supposition with regard to causation1 but only with regard to the law of correspondence between facts which accompany each other in their variations1 though there may be no relation of cause and effect between them4 ,such were the different false hypotheses which ,kepler made respecting the law of the refraction of light4 ,it was known that the direction of the line of refraction varied with every variation in the direction of the line of incidence1 but it was not known how2 that is1 what changes of the one corresponded to the different changes of the other4 ,in this case any law different from the true one must have led to false results4 ,and1 lastly1 we must add to these all hypothetical modes of merely representing or describing phenomena2 such as the hypothesis of the ancient astronomers that the heavenly bodies moved in circles2 the various hypotheses of eccentrics1 deferents1 and epicycles1 which were added to that original hypothesis2 the nineteen false hypotheses which ,kepler made and abandoned respecting the form of the planetary orbits2 and even the doctrine in which he finally rested1 that those orbits are ellipses1 which was but an hypothesis like the rest until verified by facts4 ,in all these cases1 verification is proof2 if the supposition accords with the phenomena there needs no other evidence of it4 ,but in order that this may be the case1 ,i conceive it to be necessary1 when the hypothesis relates to causation1 that the supposed cause should not only be a real phenomenon1 something actually existing in nature1 but should be already known to exercise1 or at least to be capable of exercising1 an influence of some sort over the effect4 ,in any other case1 it is no sufficient evidence of the truth of the hypothesis that we are able to deduce the real phenomena from it4 ,is it1 then1 never allowable1 in a scientific hypothesis1 to assume a cause1 but only to ascribe an assumed law to a known cause8 ,i do not assert this4 ,i only say1 that in the latter case alone can the hypothesis be received as true merely because it explains the phenomena4 ,in the former case it may be very useful by suggesting a line of investigation which may possibly terminate in obtaining real proof4 ,but for this purpose1 as is justly remarked by ,m4 ,comte1 it is indispensable that the cause suggested by the hypothesis should be in its own nature susceptible of being proved by other evidence4 ,this seems to be the philosophical import of ,newton's maxim1 7so often cited with approbation by subsequent writers71 that the cause assigned for any phenomenon must not only be such as if admitted would explain the phenomenon1 but must also be a vera causa4 ,what he meant by a vera causa ,newton did not indeed very explicitly define2 and ,dr4 ,whewell1 who dissents from the propriety of any such restriction upon the latitude of framing hypotheses1 has had little difficulty in showing7#afb7 that his conception of it was neither precise nor consistent with itself2 accordingly his optical theory was a signal instance of the violation of his own rule4 ,it is certainly not necessary that the cause assigned should be a cause already known2 otherwise we should sacrifice our best opportunities of becoming acquainted with new causes4 ,but what is true in the maxim is1 that the cause1 though not known previously1 should be capable of being known thereafter2 that its existence should be capable of being detected1 and its connection with the effect ascribed to it should be susceptible of being proved1 by independent evidence4 ,the hypothesis1 by suggesting observations and experiments1 puts us on the road to that independent evidence1 if it be really attainable2 and till it be attained1 the hypothesis ought only to count for a more or less plausible conjecture4 #e4 ,this function1 however1 of hypotheses1 is one which must be reckoned absolutely indispensable in science4 ,when ,newton said1 8,hypotheses non fingo10 he did not mean that he deprived himself of the facilities of investigation afforded by assuming in the first instance what he hoped ultimately to be able to prove4 ,without such assumptions1 science could never have attained its present state2 they are necessary steps in the progress to something more certain2 and nearly every thing which is now theory was once hypothesis4 ,even in purely experimental science1 some inducement is necessary for trying one experiment rather than another2 and though it is abstractedly possible that all the experiments which have been tried1 might have been produced by the mere desire to ascertain what would happen in certain circumstances1 without any previous conjecture as to the result2 yet1 in point of fact1 those unobvious1 delicate1 and often cumbrous and tedious processes of experiment1 which have thrown most light upon the general constitution of nature1 would hardly ever have been undertaken by the persons or at the time they were1 unless it had seemed to depend on them whether some general doctrine or theory which had been suggested1 but not yet proved1 should be admitted or not4 ,if this be true even of merely experimental inquiry1 the conversion of experimental into deductive truths could still less have been effected without large temporary assistance from hypotheses4 ,the process of tracing regularity in any complicated1 and at first sight confused1 set of appearances1 is necessarily tentative2 we begin by making any supposition1 even a false one1 to see what consequences will follow from it2 and by observing how these differ from the real phenomena1 we learn what corrections to make in our assumption4 ,the simplest supposition which accords with the more obvious facts is the best to begin with2 because its consequences are the most easily traced4 ,this rude hypothesis is then rudely corrected1 and the operation repeated2 and the comparison of the consequences deducible from the corrected hypothesis1 with the observed facts1 suggests still further correction1 until the deductive results are at last made to tally with the phenomena4 8,some fact is as yet little understood1 or some law is unknown2 we frame on the subject an hypothesis as accordant as possible with the whole of the data already possessed2 and the science1 being thus enabled to move forward freely1 always ends by leading to new consequences capable of observation1 which either confirm or refute1 unequivocally1 the first supposition40 ,neither induction nor deduction would enable us to understand even the simplest phenomena1 8if we did not often commence by anticipating on the results2 by making a provisional supposition1 at first essentially conjectural1 as to some of the very notions which constitute the final object of the inquiry407#afc7 ,let any one watch the manner in which he himself unravels a complicated mass of evidence2 let him observe how1 for instance1 he elicits the true history of any occurrence from the involved statements of one or of many witnesses2 he will find that he does not take all the items of evidence into his mind at once1 and attempt to weave them together2 he extemporizes1 from a few of the particulars1 a first rude theory of the mode in which the facts took place1 and then looks at the other statements one by one1 to try whether they can be reconciled with that provisional theory1 or what alterations or additions it requires to make it square with them4 ,in this way1 which has been justly compared to the ,methods of ,approximation of mathematicians1 we arrive1 by means of hypotheses1 at conclusions not hypothetical47#afd7 #f4 ,it is perfectly consistent with the spirit of the method1 to assume in this provisional manner not only an hypothesis respecting the law of what we already know to be the cause1 but an hypothesis respecting the cause itself4 ,it is allowable1 useful1 and often even necessary1 to begin by asking ourselves what cause may have produced the effect1 in order that we may know in what direction to look out for evidence to determine whether it actually did4 ,the vortices of ,descartes would have been a perfectly legitimate hypothesis1 if it had been possible1 by any mode of exploration which we could entertain the hope of ever possessing1 to bring the reality of the vortices1 as a fact in nature1 conclusively to the test of observation4 ,the vice of the hypothesis was that it could not lead to any course of investigation capable of converting it from an hypothesis into a proved fact4 ,it might chance to be disproved1 either by some want of correspondence with the phenomena it purported to explain1 or 7as actually happened7 by some extraneous fact4 8,the free passage of comets through the spaces in which these vortices should have been1 convinced men that these vortices did not exist407#afe7 ,but the hypothesis would have been false1 though no such direct evidence of its falsity had been procurable4 ,direct evidence of its truth there could not be4 ,the prevailing hypothesis of a luminiferous ether1 in other respects not without analogy to that of ,descartes1 is not in its own nature entirely cut off from the possibility of direct evidence in its favor4 ,it is well known that the difference between the calculated and the observed times of the periodical return of ,encke's comet1 has led to a conjecture that a medium capable of opposing resistance to motion is diffused through space4 ,if this surmise should be confirmed1 in the course of ages1 by the gradual accumulation of a similar variance in the case of the other bodies of the solar system1 the luminiferous ether would have made a considerable advance toward the character of a vera causa1 since the existence would have been ascertained of a great cosmical agent1 possessing some of the attributes which the hypothesis assumes2 though there would still remain many difficulties1 and the identification of the ether with the resisting medium would even1 ,i imagine1 give rise to new ones4 ,at present1 however1 this supposition can not be looked upon as more than a conjecture2 the existence of the ether still rests on the possibility of deducing from its assumed laws a considerable number of actual phenomena2 and this evidence ,i can not regard as conclusive1 because we can not have1 in the case of such an hypothesis1 the assurance that if the hypothesis be false it must lead to results at variance with the true facts4 ,accordingly1 most thinkers of any degree of sobriety allow that an hypothesis of this kind is not to be received as probably true because it accounts for all the known phenomena2 since this is a condition sometimes fulfilled tolerably well by two conflicting hypotheses2 while there are probably many others which are equally possible1 but which1 for want of any thing analogous in our experience1 our minds are unfitted to conceive4 ,but it seems to be thought that an hypothesis of the sort in question is entitled to a more favorable reception1 if1 besides accounting for all the facts previously known1 it has led to the anticipation and prediction of others which experience afterward verified2 as the undulatory theory of light led to the prediction1 subsequently realized by experiment1 that two luminous rays might meet each other in such a manner as to produce darkness4 ,such predictions and their fulfillment are1 indeed1 well calculated to impress the uninformed1 whose faith in science rests solely on similar coincidences between its prophecies and what comes to pass4 ,but it is strange that any considerable stress should be laid upon such a coincidence by persons of scientific attainments4 ,if the laws of the propagation of light accord with those of the vibrations of an elastic fluid in as many respects as is necessary to make the hypothesis afford a correct expression of all or most of the phenomena known at the time1 it is nothing strange that they should accord with each other in one respect more4 ,though twenty such coincidences should occur1 they would not prove the reality of the undulatory ether2 it would not follow that the phenomena of light were results of the laws of elastic fluids1 but at most that they are governed by laws partially identical with these2 which1 we may observe1 is already certain1 from the fact that the hypothesis in question could be for a moment tenable47#aff7 ,cases may be cited1 even in our imperfect acquaintance with nature1 where agencies that we have good reason to consider as radically distinct produce their effects1 or some of their effects1 according to laws which are identical4 ,the law1 for example1 of the inverse square of the distance1 is the measure of the intensity not only of gravitation1 but 7it is believed7 of illumination1 and of heat diffused from a centre4 ,yet no one looks upon this identity as proving similarity in the mechanism by which the three kinds of phenomena are produced4 ,according to ,dr4 ,whewell1 the coincidence of results predicted from an hypothesis with facts afterward observed1 amounts to a conclusive proof of the truth of the theory4 8,if ,i copy a long series of letters1 of which the last half-dozen are concealed1 and if ,i guess these aright1 as is found to be the case when they are afterward uncovered1 this must be because ,i have made out the import of the inscription4 ,to say that because ,i have copied all that ,i could see1 it is nothing strange that ,i should guess those which ,i can not see1 would be absurd1 without supposing such a ground for guessing407#afg7 ,if any one1 from examining the greater part of a long inscription1 can interpret the characters so that the inscription gives a rational meaning in a known language1 there is a strong presumption that his interpretation is correct2 but ,i do not think the presumption much increased by his being able to guess the few remaining letters without seeing them2 for we should naturally expect 7when the nature of the case excludes chance7 that even an erroneous interpretation which accorded with all the visible parts of the inscription would accord also with the small remainder2 as would be the case1 for example1 if the inscription had been designedly so contrived as to admit of a double sense4 ,i assume that the uncovered characters afford an amount of coincidence too great to be merely casual2 otherwise the illustration is not a fair one4 ,no one supposes the agreement of the phenomena of light with the theory of undulations to be merely fortuitous4 ,it must arise from the actual identity of some of the laws of undulations with some of those of light2 and if there be that identity1 it is reasonable to suppose that its consequences would not end with the phenomena which first suggested the identification1 nor be even confined to such phenomena as were known at the time4 ,but it does not follow1 because some of the laws agree with those of undulations1 that there are any actual undulations2 no more than it followed because some 7though not so many7 of the same laws agreed with those of the projection of particles1 that there was actual emission of particles4 ,even the undulatory hypothesis does not account for all the phenomena of light4 ,the natural colors of objects1 the compound nature of the solar ray1 the absorption of light1 and its chemical and vital action1 the hypothesis leaves as mysterious as it found them2 and some of these facts are1 at least apparently1 more reconcilable with the emission theory than with that of ,young and ,fresnel4 ,who knows but that some third hypothesis1 including all these phenomena1 may in time leave the undulatory theory as far behind as that has left the theory of ,newton and his successors8 ,to the statement1 that the condition of accounting for all the known phenomena is often fulfilled equally well by two conflicting hypotheses1 ,dr4 ,whewell makes answer that he knows 8of no such case in the history of science1 where the phenomena are at all numerous and complicated407#afh7 ,such an affirmation1 by a writer of ,dr4 ,whewell's minute acquaintance with the history of science1 would carry great authority1 if he had not1 a few pages before1 taken pains to refute it17#afi7 by maintaining that even the exploded scientific hypotheses might always1 or almost always1 have been so modified as to make them correct representations of the phenomena4 ,the hypothesis of vortices1 he tells us1 was1 by successive modifications1 brought to coincide in its results with the ,newtonian theory and with the facts4 ,the vortices did not1 indeed1 explain all the phenomena which the ,newtonian theory was ultimately found to account for1 such as the precession of the equinoxes2 but this phenomenon was not1 at the time1 in the contemplation of either party1 as one of the facts to be accounted for4 ,all the facts which they did contemplate1 we may believe on ,dr4 ,whewell's authority to have accorded as accurately with the ,cartesian hypothesis1 in its finally improved state1 as with ,newton's4 ,but it is not1 ,i conceive1 a valid reason for accepting any given hypothesis1 that we are unable to imagine any other which will account for the facts4 ,there is no necessity for supposing that the true explanation must be one which1 with only our present experience1 we could imagine4 ,among the natural agents with which we are acquainted1 the vibrations of an elastic fluid may be the only one whose laws bear a close resemblance to those of light2 but we can not tell that there does not exist an unknown cause1 other than an elastic ether diffused through space1 yet producing effects identical in some respects with those which would result from the undulations of such an ether4 ,to assume that no such cause can exist1 appears to me an extreme case of assumption without evidence4 ,and at the risk of being charged with want of modesty1 ,i can not help expressing astonishment that a philosopher of ,dr4 ,whewell's abilities and attainments should have written an elaborate treatise on the philosophy of induction1 in which he recognizes absolutely no mode of induction except that of trying hypothesis after hypothesis until one is found which fits the phenomena2 which one1 when found1 is to be assumed as true1 with no other reservation than that if1 on re-examination1 it should appear to assume more than is needful for explaining the phenomena1 the superfluous part of the assumption should be cut off4 ,and this without the slightest distinction between the cases in which it may be known beforehand that two different hypotheses can not lead to the same result1 and those in which1 for aught we can ever know1 the range of suppositions1 all equally consistent with the phenomena1 may be infinite47#agj7 ,nevertheless1 ,i do not agree with ,m4 ,comte in condemning those who employ themselves in working out into detail the application of these hypotheses to the explanation of ascertained facts1 provided they bear in mind that the utmost they can prove is1 not that the hypothesis is1 but that it may be true4 ,the ether hypothesis has a very strong claim to be so followed out1 a claim greatly strengthened since it has been shown to afford a mechanism which would explain the mode of production1 not of light only1 but also of heat4 ,indeed1 the speculation has a smaller element of hypothesis in its application to heat1 than in the case for which it was originally framed4 ,we have proof by our senses of the existence of molecular movement among the particles of all heated bodies2 while we have no similar experience in the case of light4 ,when1 therefore1 heat is communicated from the sun to the earth across apparently empty space1 the chain of causation has molecular motion both at the beginning and end4 ,the hypothesis only makes the motion continuous by extending it to the middle4 ,now1 motion in a body is known to be capable of being imparted to another body contiguous to it2 and the intervention of a hypothetical elastic fluid occupying the space between the sun and the earth1 supplies the contiguity which is the only condition wanting1 and which can be supplied by no supposition but that of an intervening medium4 ,the supposition1 notwithstanding1 is at best a probable conjecture1 not a proved truth4 ,for there is no proof that contiguity is absolutely required for the communication of motion from one body to another4 ,contiguity does not always exist1 to our senses at least1 in the cases in which motion produces motion4 ,the forces which go under the name of attraction1 especially the greatest of all1 gravitation1 are examples of motion producing motion without apparent contiguity4 ,when a planet moves1 its distant satellites accompany its motion4 ,the sun carries the whole solar system along with it in the progress which it is ascertained to be executing through space4 ,and even if we were to accept as conclusive the geometrical reasonings 7strikingly similar to those by which the ,cartesians defended their vortices7 by which it has been attempted to show that the motions of the ether may account for gravitation itself1 even then it would only have been proved that the supposed mode of production may be1 but not that no other mode can be1 the true one4 #g4 ,it is necessary1 before quitting the subject of hypotheses1 to guard against the appearance of reflecting upon the scientific value of several branches of physical inquiry1 which1 though only in their infancy1 ,i hold to be strictly inductive4 ,there is a great difference between inventing agencies to account for classes of phenomena1 and endeavoring1 in conformity with known laws1 to conjecture what former collocations of known agents may have given birth to individual facts still in existence4 ,the latter is the legitimate operation of inferring from an observed effect the existence1 in time past1 of a cause similar to that by which we know it to be produced in all cases in which we have actual experience of its origin4 ,this1 for example1 is the scope of the inquiries of geology2 and they are no more illogical or visionary than judicial inquiries1 which also aim at discovering a past event by inference from those of its effects which still subsist4 ,as we can ascertain whether a man was murdered or died a natural death1 from the indications exhibited by the corpse1 the presence or absence of signs of struggling on the ground or on the adjacent objects1 the marks of blood1 the footsteps of the supposed murderers1 and so on1 proceeding throughout on uniformities ascertained by a perfect induction without any mixture of hypothesis2 so if we find1 on and beneath the surface of our planet1 masses exactly similar to deposits from water1 or to results of the cooling of matter melted by fire1 we may justly conclude that such has been their origin2 and if the effects1 though similar in kind1 are on a far larger scale than any which are now produced1 we may rationally1 and without hypothesis1 conclude either that the causes existed formerly with greater intensity1 or that they have operated during an enormous length of time4 ,further than this no geologist of authority has1 since the rise of the present enlightened school of geological speculation1 attempted to go4 ,in many geological inquiries it doubtless happens that though the laws to which the phenomena are ascribed are known laws1 and the agents known agents1 those agents are not known to have been present in the particular case4 ,in the speculation respecting the igneous origin of trap or granite1 the fact does not admit of direct proof that those substances have been actually subjected to intense heat4 ,but the same thing might be said of all judicial inquiries which proceed on circumstantial evidence4 ,we can conclude that a man was murdered1 though it is not proved by the testimony of eye-witnesses that some person who had the intention of murdering him was present on the spot4 ,it is enough for most purposes1 if no other known cause could have generated the effects shown to have been produced4 ------------------------------------ ,the celebrated speculation of ,laplace concerning the origin of the earth and planets1 participates essentially in the inductive character of modern geological theory4 ,the speculation is1 that the atmosphere of the sun originally extended to the present limits of the solar system2 from which1 by the process of cooling1 it has contracted to its present dimensions2 and since1 by the general principles of mechanics the rotation of the sun and of its accompanying atmosphere must increase in rapidity as its volume diminishes1 the increased centrifugal force generated by the more rapid rotation1 overbalancing the action of gravitation1 has caused the sun to abandon successive rings of vaporous matter1 which are supposed to have condensed by cooling1 and to have become the planets4 ,there is in this theory no unknown substance introduced on supposition1 nor any unknown property or law ascribed to a known substance4 ,the known laws of matter authorize us to suppose that a body which is constantly giving out so large an amount of heat as the sun is1 must be progressively cooling1 and that1 by the process of cooling it must contract2 if1 therefore1 we endeavor1 from the present state of that luminary1 to infer its state in a time long past1 we must necessarily suppose that its atmosphere extended much farther than at present1 and we are entitled to suppose that it extended as far as we can trace effects such as it might naturally leave behind it on retiring2 and such the planets are4 ,these suppositions being made1 it follows from known laws that successive zones of the solar atmosphere might be abandoned2 that these would continue to revolve round the sun with the same velocity as when they formed part of its substance2 and that they would cool down1 long before the sun itself1 to any given temperature1 and consequently to that at which the greater part of the vaporous matter of which they consisted would become liquid or solid4 ,the known law of gravitation would then cause them to agglomerate in masses1 which would assume the shape our planets actually exhibit2 would acquire1 each about its own axis1 a rotatory movement2 and would in that state revolve1 as the planets actually do1 about the sun1 in the same direction with the sun's rotation1 but with less velocity1 because in the same periodic time which the sun's rotation occupied when his atmosphere extended to that point4 ,there is thus1 in ,laplace's theory1 nothing1 strictly speaking1 hypothetical2 it is an example of legitimate reasoning from a present effect to a possible past cause1 according to the known laws of that cause4 ,the theory1 therefore1 is1 as ,i have said1 of a similar character to the theories of geologists2 but considerably inferior to them in point of evidence4 ,even if it were proved 7which it is not7 that the conditions necessary for determining the breaking off of successive rings would certainly occur1 there would still be a much greater chance of error in assuming that the existing laws of nature are the same which existed at the origin of the solar system1 than in merely presuming 7with geologists7 that those laws have lasted through a few revolutions and transformations of a single one among the bodies of which that system is composed4 ,chapter ,,xv4 ,of ,progressive ,effects2 ,and ,of ,the ,continued ,action ,of ,causes4 #a4 ,in the last four chapters we have traced the general outlines of the theory of the generation of derivative laws from ultimate ones4 ,in the present chapter our attention will be directed to a particular case of the derivation of laws from other laws1 but a case so general1 and so important as not only to repay1 but to require1 a separate examination4 ,this is the case of a complex phenomenon resulting from one simple law1 by the continual addition of an effect to itself4 ,there are some phenomena1 some bodily sensations1 for example1 which are essentially instantaneous1 and whose existence can only be prolonged by the prolongation of the existence of the cause by which they are produced4 ,but most phenomena are in their own nature permanent2 having begun to exist1 they would exist forever unless some cause intervened having a tendency to alter or destroy them4 ,such1 for example1 are all the facts of phenomena which we call bodies4 ,water1 once produced1 will not of itself relapse into a state of hydrogen and oxygen2 such a change requires some agent having the power of decomposing the compound4 ,such1 again1 are the positions in space and the movements of bodies4 ,no object at rest alters its position without the intervention of some conditions extraneous to itself2 and when once in motion1 no object returns to a state of rest1 or alters either its direction or its velocity1 unless some new external conditions are superinduced4 ,it1 therefore1 perpetually happens that a temporary cause gives rise to a permanent effect4 ,the contact of iron with moist air for a few hours1 produces a rust which may endure for centuries2 or a projectile force which launches a cannon-ball into space1 produces a motion which would continue forever unless some other force counteracted it4 ,between the two examples which we have here given1 there is a difference worth pointing out4 ,in the former 7in which the phenomenon produced is a substance1 and not a motion of a substance71 since the rust remains forever and unaltered unless some new cause supervenes1 we may speak of the contact of air a hundred years ago as even the proximate cause of the rust which has existed from that time until now4 ,but when the effect is motion1 which is itself a change1 we must use a different language4 ,the permanency of the effect is now only the permanency of a series of changes4 ,the second foot1 or inch1 or mile of motion is not the mere prolonged duration of the first foot1 or inch1 or mile1 but another fact which succeeds1 and which may in some respects be very unlike the former1 since it carries the body through a different region of space4 ,now1 the original projectile force which set the body moving is the remote cause of all its motion1 however long continued1 but the proximate cause of no motion except that which took place at the first instant4 ,the motion at any subsequent instant is proximately caused by the motion which took place at the instant preceding4 ,it is on that1 and not on the original moving cause1 that the motion at any given moment depends4 ,for1 suppose that the body passes through some resisting medium1 which partially counteracts the effect of the original impulse1 and retards the motion2 this counteraction 7it need scarcely here be repeated7 is as strict an example of obedience to the law of the impulse1 as if the body had gone on moving with its original velocity2 but the motion which results is different1 being now a compound of the effects of two causes acting in contrary directions1 instead of the single effect of one cause4 ,now1 what cause does the body obey in its subsequent motion8 ,the original cause of motion1 or the actual motion at the preceding instant8 ,the latter2 for when the object issues from the resisting medium1 it continues moving1 not with its original1 but with its retarded velocity4 ,the motion having once been diminished1 all that which follows is diminished4 ,the effect changes1 because the cause which it really obeys1 the proximate cause1 the real cause in fact1 has changed4 ,this principle is recognized by mathematicians when they enumerate among the causes by which the motion of a body is at any instant determined the force generated by the previous motion2 an expression which would be absurd if taken to imply that this 8force0 was an intermediate link between the cause and the effect1 but which really means only the previous motion itself1 considered as a cause of further motion4 ,we must1 therefore1 if we would speak with perfect precision1 consider each link in the succession of motions as the effect of the link preceding it4 ,but if1 for the convenience of discourse1 we speak of the whole series as one effect1 it must be as an effect produced by the original impelling force2 a permanent effect produced by an instantaneous cause1 and possessing the property of self-perpetuation4 ,let us now suppose that the original agent or cause1 instead of being instantaneous1 is permanent4 ,whatever effect has been produced up to a given time1 would 7unless prevented by the intervention of some new cause7 subsist permanently1 even if the cause were to perish4 ,since1 however1 the cause does not perish1 but continues to exist and to operate1 it must go on producing more and more of the effect2 and instead of a uniform effect1 we have a progressive series of effects1 arising from the accumulated influence of a permanent cause4 ,thus1 the contact of iron with the atmosphere causes a portion of it to rust2 and if the cause ceased1 the effect already produced would be permanent1 but no further effect would be added4 ,if1 however1 the cause1 namely1 exposure to moist air1 continues1 more and more of the iron becomes rusted1 until all which is exposed is converted into a red powder1 when one of the conditions of the production of rust1 namely1 the presence of unoxidized iron1 has ceased1 and the effect can not any longer be produced4 ,again1 the earth causes bodies to fall toward it2 that is1 the existence of the earth at a given instant causes an unsupported body to move toward it at the succeeding instant2 and if the earth were annihilated1 as much of the effect as is already produced would continue2 the object would go on moving in the same direction1 with its acquired velocity1 until intercepted by some body or deflected by some other force4 ,the earth1 however1 not being annihilated1 goes on producing in the second instant an effect similar and of equal amount with the first1 which two effects being added together1 there results an accelerated velocity2 and this operation being repeated at each successive instant1 the mere permanence of the cause1 though without increase1 gives rise to a constant progressive increase of the effect1 so long as all the conditions1 negative and positive1 of the production of that effect continue to be realized4 ,it is obvious that this state of things is merely a case of the ,composition of ,causes4 ,a cause which continues in action must on a strict analysis be considered as a number of causes exactly similar1 successively introduced1 and producing by their combination the sum of the effects which they would severally produce if they acted singly4 ,the progressive rusting of the iron is in strictness the sum of the effects of many particles of air acting in succession upon corresponding particles of iron4 ,the continued action of the earth upon a falling body is equivalent to a series of forces1 applied in successive instants1 each tending to produce a certain constant quantity of motion2 and the motion at each instant is the sum of the effects of the new force applied at the preceding instant1 and the motion already acquired4 ,in each instant a fresh effect1 of which gravity is the proximate cause1 is added to the effect of which it was the remote cause2 or 7to express the same thing in another manner71 the effect produced by the earth's influence at the instant last elapsed is added to the sum of the effects of which the remote causes were the influences exerted by the earth at all the previous instants since the motion began4 ,the case1 therefore1 comes under the principle of a concurrence of causes producing an effect equal to the sum of their separate effects4 ,but as the causes come into play not all at once1 but successively1 and as the effect at each instant is the sum of the effects of those causes only which have come into action up to that instant1 the result assumes the form of an ascending series2 a succession of sums1 each greater than that which preceded it2 and we have thus a progressive effect from the continued action of a cause4 ,since the continuance of the cause influences the effect only by adding to its quantity1 and since the addition takes place according to a fixed law 7equal quantities in equal times71 the result is capable of being computed on mathematical principles4 ,in fact1 this case1 being that of infinitesimal increments1 is precisely the case which the differential calculus was invented to meet4 ,the questions1 what effect will result from the continual addition of a given cause to itself1 and what amount of the cause1 being continually added to itself1 will produce a given amount of the effect1 are evidently mathematical questions1 and to be treated1 therefore1 deductively4 ,if1 as we have seen1 cases of the ,composition of ,causes are seldom adapted for any other than deductive investigation1 this is especially true in the case now examined1 the continual composition of a cause with its own previous effects2 since such a case is peculiarly amenable to the deductive method1 while the undistinguishable manner in which the effects are blended with one another and with the causes1 must make the treatment of such an instance experimentally still more chimerical than in any other case4 #b4 ,we shall next advert to a rather more intricate operation of the same principle1 namely1 when the cause does not merely continue in action1 but undergoes1 during the same time1 a progressive change in those of its circumstances which contribute to determine the effect4 ,in this case1 as in the former1 the total effect goes on accumulating by the continual addition of a fresh effect to that already produced1 but it is no longer by the addition of equal quantities in equal times2 the quantities added are unequal1 and even the quality may now be different4 ,if the change in the state of the permanent cause be progressive1 the effect will go through a double series of changes1 arising partly from the accumulated action of the cause1 and partly from the changes in its action4 ,the effect is still a progressive effect1 produced1 however1 not by the mere continuance of a cause1 but by its continuance and its progressiveness combined4 ,a familiar example is afforded by the increase of the temperature as summer advances1 that is1 as the sun draws nearer to a vertical position1 and remains a greater number of hours above the horizon4 ,this instance exemplifies in a very interesting manner the twofold operation on the effect1 arising from the continuance of the cause1 and from its progressive change4 ,when once the sun has come near enough to the zenith1 and remains above the horizon long enough1 to give more warmth during one diurnal rotation than the counteracting cause1 the earth's radiation1 can carry off1 the mere continuance of the cause would progressively increase the effect1 even if the sun came no nearer and the days grew no longer2 but in addition to this1 a change takes place in the accidents of the cause 7its series of diurnal positions71 tending to increase the quantity of the effect4 ,when the summer solstice has passed1 the progressive change in the cause begins to take place the reverse way1 but1 for some time1 the accumulating effect of the mere continuance of the cause exceeds the effect of the changes in it1 and the temperature continues to increase4 ,again1 the motion of a planet is a progressive effect1 produced by causes at once permanent and progressive4 ,the orbit of a planet is determined 7omitting perturbations7 by two causes3 first1 the action of the central body1 a permanent cause1 which alternately increases and diminishes as the planet draws nearer to or goes farther from its perihelion1 and which acts at every point in a different direction2 and1 secondly1 the tendency of the planet to continue moving in the direction and with the velocity which it has already acquired4 ,this force also grows greater as the planet draws nearer to its perihelion1 because as it does so its velocity increases1 and less1 as it recedes from its perihelion2 and this force as well as the other acts at each point in a different direction1 because at every point the action of the central force1 by deflecting the planet from its previous direction1 alters the line in which it tends to continue moving4 ,the motion at each instant is determined by the amount and direction of the motion1 and the amount and direction of the sun's action1 at the previous instant2 and if we speak of the entire revolution of the planet as one phenomenon 7which1 as it is periodical and similar to itself1 we often find it convenient to do71 that phenomenon is the progressive effect of two permanent and progressive causes1 the central force and the acquired motion4 ,those causes happening to be progressive in the particular way which is called periodical1 the effect necessarily is so too2 because the quantities to be added together returning in a regular order1 the same sums must also regularly return4 ,this example is worthy of consideration also in another respect4 ,though the causes themselves are permanent1 and independent of all conditions known to us1 the changes which take place in the quantities and relations of the causes are actually caused by the periodical changes in the effects4 ,the causes1 as they exist at any moment1 having produced a certain motion1 that motion1 becoming itself a cause1 reacts upon the causes1 and produces a change in them4 ,by altering the distance and direction of the central body relatively to the planet1 and the direction and quantity of the force in the direction of the tangent1 it alters the elements which determine the motion at the next succeeding instant4 ,this change renders the next motion somewhat different2 and this difference1 by a fresh reaction upon the causes1 renders the next motion again different1 and so on4 ,the original state of the causes might have been such that this series of actions modified by reactions would not have been periodical4 ,the sun's action1 and the original impelling force1 might have been in such a ratio to one another1 that the reaction of the effect would have been such as to alter the causes more and more1 without ever bringing them back to what they were at any former time4 ,the planet would then have moved in a parabola1 or an hyperbola1 curves not returning into themselves4 ,the quantities of the two forces were1 however1 originally such1 that the successive reactions of the effect bring back the causes1 after a certain time1 to what they were before2 and from that time all the variations continued to recur again and again in the same periodical order1 and must so continue while the causes subsist and are not counteracted4 #c4 ,in all cases of progressive effects1 whether arising from the accumulation of unchanging or of changing elements1 there is a uniformity of succession not merely between the cause and the effect1 but between the first stages of the effect and its subsequent stages4 ,that a body in vacuo falls sixteen feet in the first second1 forty-eight in the second1 and so on in the ratio of the odd numbers1 is as much a uniform sequence as that when the supports are removed the body falls4 ,the sequence of spring and summer is as regular and invariable as that of the approach of the sun and spring2 but we do not consider spring to be the cause of summer2 it is evident that both are successive effects of the heat received from the sun1 and that1 considered merely in itself1 spring might continue forever without having the slightest tendency to produce summer4 ,as we have so often remarked1 not the conditional1 but the unconditional invariable antecedent is termed the cause4 ,that which would not be followed by the effect unless something else had preceded1 and which if that something else had preceded1 would not have been required1 is not the cause1 however invaluable the sequence may in fact be4 ,it is in this way that most of those uniformities of succession are generated1 which are not cases of causation4 ,when a phenomenon goes on increasing1 or periodically increases and diminishes1 or goes through any continued and unceasing process of variation reducible to a uniform rule or law of succession1 we do not on this account presume that any two successive terms of the series are cause and effect4 ,we presume the contrary2 we expect to find that the whole series originates either from the continued action of fixed causes or from causes which go through a corresponding process of continuous change4 ,a tree grows from half an inch high to a hundred feet2 and some trees will generally grow to that height unless prevented by some counteracting cause4 ,but we do not call the seedling the cause of the full-grown tree2 the invariable antecedent it certainly is1 and we know very imperfectly on what other antecedents the sequence is contingent1 but we are convinced that it is contingent on something2 because the homogeneousness of the antecedent with the consequent1 the close resemblance of the seedling to the tree in all respects except magnitude1 and the graduality of the growth1 so exactly resembling the progressively accumulating effect produced by the long action of some one cause1 leave no possibility of doubting that the seedling and the tree are two terms in a series of that description1 the first term of which is yet to seek4 ,the conclusion is further confirmed by this1 that we are able to prove by strict induction the dependence of the growth of the tree1 and even of the continuance of its existence1 upon the continued repetition of certain processes of nutrition1 the rise of the sap1 the absorptions and exhalations by the leaves1 etc42 and the same experiments would probably prove to us that the growth of the tree is the accumulated sum of the effects of these continued processes1 were we not1 for want of sufficiently microscopic eyes1 unable to observe correctly and in detail what those effects are4 ,this supposition by no means requires that the effect should not1 during its progress1 undergo many modifications besides those of quantity1 or that it should not sometimes appear to undergo a very marked change of character4 ,this may be either because the unknown cause consists of several component elements or agents1 whose effects1 accumulating according to different laws1 are compounded in different proportions at different periods in the existence of the organized being2 or because1 at certain points in its progress1 fresh causes or agencies come in1 or are evolved1 which intermix their laws with those of the prime agent4 ,chapter ,,xvi4 ,of ,empirical ,laws4 #a4 ,scientific inquirers give the name of ,empirical ,laws to those uniformities which observation or experiment has shown to exist1 but on which they hesitate to rely in cases varying much from those which have been actually observed1 for want of seeing any reason why such a law should exist4 ,it is implied1 therefore1 in the notion of an empirical law1 that it is not an ultimate law2 that if true at all1 its truth is capable of being1 and requires to be1 accounted for4 ,it is a derivative law1 the derivation of which is not yet known4 ,to state the explanation1 the why1 of the empirical law1 would be to state the laws from which it is derived--the ultimate causes on which it is contingent4 ,and if we knew these1 we should also know what are its limits2 under what conditions it would cease to be fulfilled4 ,the periodical return of eclipses1 as originally ascertained by the persevering observation of the early ,eastern astronomers1 was an empirical law1 until the general laws of the celestial motions had accounted for it4 ,the following are empirical laws still waiting to be resolved into the simpler laws from which they are derived3 the local laws of the flux and reflux of the tides in different places2 the succession of certain kinds of weather to certain appearances of sky2 the apparent exceptions to the almost universal truth that bodies expand by increase of temperature2 the law that breeds1 both animal and vegetable1 are improved by crossing2 that gases have a strong tendency to permeate animal membranes2 that substances containing a very high proportion of nitrogen 7such as hydrocyanic acid and morphia7 are powerful poisons2 that when different metals are fused together the alloy is harder than the various elements2 that the number of atoms of acid required to neutralize one atom of any base is equal to the number of atoms of oxygen in the base2 that the solubility of substances in one another depends17#aga7 at least in some degree1 on the similarity of their elements4 ,an empirical law1 then1 is an observed uniformity1 presumed to be resolvable into simpler laws1 but not yet resolved into them4 ,the ascertainment of the empirical laws of phenomena often precedes by a long interval the explanation of those laws by the ,deductive ,method2 and the verification of a deduction usually consists in the comparison of its results with empirical laws previously ascertained4 #b4 ,from a limited number of ultimate laws of causation1 there are necessarily generated a vast number of derivative uniformities1 both of succession and co-existence4 ,some are laws of succession or of co-existence between different effects of the same cause2 of these we had examples in the last chapter4 ,some are laws of succession between effects and their remote causes1 resolvable into the laws which connect each with the intermediate link4 ,thirdly1 when causes act together and compound their effects1 the laws of those causes generate the fundamental law of the effect1 namely1 that it depends on the co-existence of those causes4 ,and1 finally1 the order of succession or of co-existence which obtains among effects necessarily depends on their causes4 ,if they are effects of the same cause1 it depends on the laws of that cause2 if on different causes1 it depends on the laws of those causes severally1 and on the circumstances which determine their co-existence4 ,if we inquire further when and how the causes will co-exist1 that1 again1 depends on their causes2 and we may thus trace back the phenomena higher and higher1 until the different series of effects meet in a point1 and the whole is shown to have depended ultimately on some common cause2 or until1 instead of converging to one point1 they terminate in different points1 and the order of the effects is proved to have arisen from the collocation of some of the primeval causes1 or natural agents4 ,for example1 the order of succession and of co-existence among the heavenly motions1 which is expressed by ,kepler's laws1 is derived from the co-existence of two primeval causes1 the sun1 and the original impulse or projectile force belonging to each planet47#agb7 ,kepler's laws are resolved into the laws of these causes and the fact of their co-existence4 ,derivative laws1 therefore1 do not depend solely on the ultimate laws into which they are resolvable2 they mostly depend on those ultimate laws1 and an ultimate fact2 namely1 the mode of co-existence of some of the component elements of the universe4 ,the ultimate laws of causation might be the same as at present1 and yet the derivative laws completely different1 if the causes co-existed in different proportions1 or with any difference in those of their relations by which the effects are influenced4 ,if1 for example1 the sun's attraction1 and the original projectile force1 had existed in some other ratio to one another than they did 7and we know of no reason why this should not have been the case71 the derivative laws of the heavenly motions might have been quite different from what they are4 ,the proportions which exist happen to be such as to produce regular elliptical motions2 any other proportions would have produced different ellipses1 or circular1 or parabolic1 or hyperbolic motions1 but still regular ones2 because the effects of each of the agents accumulate according to a uniform law2 and two regular series of quantities1 when their corresponding terms are added1 must produce a regular series of some sort1 whatever the quantities themselves are4 #c4 ,now this last-mentioned element in the resolution of a derivative law1 the element which is not a law of causation1 but a collocation of causes1 can not itself be reduced to any law4 ,there is1 as formerly remarked17#agc7 no uniformity1 no norma1 principle1 or rule1 perceivable in the distribution of the primeval natural agents through the universe4 ,the different substances composing the earth1 the powers that pervade the universe1 stand in no constant relation to one another4 ,one substance is more abundant than others1 one power acts through a larger extent of space than others1 without any pervading analogy that we can discover4 ,we not only do not know of any reason why the sun's attraction and the force in the direction of the tangent co-exist in the exact proportion they do1 but we can trace no coincidence between it and the proportions in which any other elementary powers in the universe are intermingled4 ,the utmost disorder is apparent in the combination of the causes1 which is consistent with the most regular order in their effects2 for when each agent carries on its own operations according to a uniform law1 even the most capricious combination of agencies will generate a regularity of some sort2 as we see in the kaleidoscope1 where any casual arrangement of colored bits of glass produces by the laws of reflection a beautiful regularity in the effect4 #d4 ,in the above considerations lies the justification of the limited degree of reliance which scientific inquirers are accustomed to place in empirical laws4 ,a derivative law which results wholly from the operation of some one cause1 will be as universally true as the laws of the cause itself2 that is1 it will always be true except where some one of those effects of the cause1 on which the derivative law depends1 is defeated by a counteracting cause4 ,but when the derivative law results not from different effects of one cause1 but from effects of several causes1 we can not be certain that it will be true under any variation in the mode of co-existence of those causes1 or of the primitive natural agents on which the causes ultimately depend4 ,the proposition that coal-beds rest on certain descriptions of strata exclusively1 though true on the earth1 so far as our observation has reached1 can not be extended to the moon or the other planets1 supposing coal to exist there2 because we can not be assured that the original constitution of any other planet was such as to produce the different depositions in the same order as in our globe4 ,the derivative law in this case depends not solely on laws1 but on a collocation2 and collocations can not be reduced to any law4 ,now it is the very nature of a derivative law which has not yet been resolved into its elements1 in other words1 an empirical law1 that we do not know whether it results from the different effects of one cause1 or from effects of different causes4 ,we can not tell whether it depends wholly on laws1 or partly on laws and partly on a collocation4 ,if it depends on a collocation1 it will be true in all the cases in which that particular collocation exists4 ,but1 since we are entirely ignorant1 in case of its depending on a collocation1 what the collocation is1 we are not safe in extending the law beyond the limits of time and place in which we have actual experience of its truth4 ,since within those limits the law has always been found true1 we have evidence that the collocations1 whatever they are1 on which it depends1 do really exist within those limits4 ,but1 knowing of no rule or principle to which the collocations themselves conform1 we can not conclude that because a collocation is proved to exist within certain limits of place or time1 it will exist beyond those limits4 ,empirical laws1 therefore1 can only be received as true within the limits of time and place in which they have been found true by observation2 and not merely the limits of time and place1 but of time1 place1 and circumstance2 for1 since it is the very meaning of an empirical law that we do not know the ultimate laws of causation on which it is dependent1 we can not foresee1 without actual trial1 in what manner or to what extent the introduction of any new circumstance may affect it4 #e4 ,but how are we to know that a uniformity ascertained by experience is only an empirical law8 ,since1 by the supposition1 we have not been able to resolve it into any other laws1 how do we know that it is not an ultimate law of causation8 ,i answer that no generalization amounts to more than an empirical law when the only proof on which it rests is that of the ,method of ,agreement4 ,for it has been seen that by that method alone we never can arrive at causes4 ,the utmost that the ,method of ,agreement can do is1 to ascertain the whole of the circumstances common to all cases in which a phenomenon is produced2 and this aggregate includes not only the cause of the phenomenon1 but all phenomena with which it is connected by any derivative uniformity1 whether as being collateral effects of the same cause1 or effects of any other cause which1 in all the instances we have been able to observe1 co-existed with it4 ,the method affords no means of determining which of these uniformities are laws of causation1 and which are merely derivative laws1 resulting from those laws of causation and from the collocation of the causes4 ,none of them1 therefore1 can be received in any other character than that of derivative laws1 the derivation of which has not been traced2 in other words1 empirical laws3 in which light all results obtained by the ,method of ,agreement 7and therefore almost all truths obtained by simple observation without experiment7 must be considered1 until either confirmed by the ,method of ,difference1 or explained deductively2 in other words1 accounted for a priori4 ,these empirical laws may be of greater or less authority1 according as there is reason to presume that they are resolvable into laws only1 or into laws and collocations together4 ,the sequences which we observe in the production and subsequent life of an animal or a vegetable1 resting on the ,method of ,agreement only1 are mere empirical laws2 but though the antecedents in those sequences may not be the causes of the consequents1 both the one and the other are doubtless1 in the main1 successive stages of a progressive effect originating in a common cause1 and therefore independent of collocations4 ,the uniformities1 on the other hand1 in the order of superposition of strata on the earth1 are empirical laws of a much weaker kind1 since they not only are not laws of causation1 but there is no reason to believe that they depend on any common cause2 all appearances are in favor of their depending on the particular collocation of natural agents which at some time or other existed on our globe1 and from which no inference can be drawn as to the collocation which exists or has existed in any other portion of the universe4 #f4 ,our definition of an empirical law1 including not only those uniformities which are not known to be laws of causation1 but also those which are1 provided there be reason to presume that they are not ultimate laws2 this is the proper place to consider by what signs we may judge that even if an observed uniformity be a law of causation1 it is not an ultimate1 but a derivative law4 ,the first sign is1 if between the antecedent a and the consequent b there be evidence of some intermediate link2 some phenomenon of which we can surmise the existence1 though from the imperfection of our senses or of our instruments we are unable to ascertain its precise nature and laws4 ,if there be such a phenomenon 7which may be denoted by the letter x71 it follows that even if a be the cause of b1 it is but the remote cause1 and that the law1 a causes b1 is resolvable into at least two laws1 a causes x1 and x causes b4 ,this is a very frequent case1 since the operations of nature mostly take place on so minute a scale1 that many of the successive steps are either imperceptible1 or very indistinctly perceived4 ,take1 for example1 the laws of the chemical composition of substances2 as that hydrogen and oxygen being combined1 water is produced4 ,all we see of the process is1 that the two gases being mixed in certain proportions1 and heat or electricity being applied1 an explosion takes place1 the gases disappear1 and water remains4 ,there is no doubt about the law1 or about its being a law of causation4 ,but between the antecedent 7the gases in a state of mechanical mixture1 heated or electrified71 and the consequent 7the production of water71 there must be an intermediate process which we do not see4 ,for if we take any portion whatever of the water1 and subject it to analysis1 we find that it always contains hydrogen and oxygen2 nay1 the very same proportions of them1 namely1 two-thirds1 in volume1 of hydrogen1 and one-third oxygen4 ,this is true of a single drop2 it is true of the minutest portion which our instruments are capable of appreciating4 ,since1 then1 the smallest perceptible portion of the water contains both those substances1 portions of hydrogen and oxygen smaller than the smallest perceptible must have come together in every such minute portion of space2 must have come closer together than when the gases were in a state of mechanical mixture1 since 7to mention no other reasons7 the water occupies far less space than the gases4 ,now1 as we can not see this contact or close approach of the minute particles1 we can not observe with what circumstances it is attended1 or according to what laws it produces its effects4 ,the production of water1 that is1 of the sensible phenomena which characterize the compound1 may be a very remote effect of those laws4 ,there may be innumerable intervening links2 and we are sure that there must be some4 ,having full proof that corpuscular action of some kind takes place previous to any of the great transformations in the sensible properties of substances1 we can have no doubt that the laws of chemical action1 as at present known1 are not ultimate1 but derivative laws2 however ignorant we may be1 and even though we should forever remain ignorant1 of the nature of the laws of corpuscular action from which they are derived4 ,in like manner1 all the processes of vegetative life1 whether in the vegetable properly so called or in the animal body1 are corpuscular processes4 ,nutrition is the addition of particles to one another1 sometimes merely replacing other particles separated and excreted1 sometimes occasioning an increase of bulk or weight so gradual that only after a long continuance does it become perceptible4 ,various organs1 by means of peculiar vessels1 secrete from the blood fluids1 the component particles of which must have been in the blood1 but which differ from it most widely both in mechanical properties and in chemical composition4 ,here1 then1 are abundance of unknown links to be filled up2 and there can be no doubt that the laws of the phenomena of vegetative or organic life are derivative laws1 dependent on properties of the corpuscles1 and of those elementary tissues which are comparatively simple combinations of corpuscles4 ,the first sign1 then1 from which a law of causation1 though hitherto unresolved1 may be inferred to be a derivative law1 is any indication of the existence of an intermediate link or links between the antecedent and the consequent4 ,the second is1 when the antecedent is an extremely complex phenomenon1 and its effects1 therefore1 probably in part at least1 compounded of the effects of its different elements2 since we know that the case in which the effect of the whole is not made up of the effects of its parts is exceptional1 the ,composition of ,causes being by far the more ordinary case4 ,we will illustrate this by two examples1 in one of which the antecedent is the sum of many homogeneous1 in the other of heterogeneous1 parts4 ,the weight of a body is made up of the weights of its minute particles2 a truth which astronomers express in its most general terms when they say that bodies1 at equal distances1 gravitate to one another in proportion to their quantity of matter4 ,all true propositions1 therefore1 which can be made concerning gravity1 are derivative laws2 the ultimate law into which they are all resolvable being1 that every particle of matter attracts every other4 ,as our second example1 we may take any of the sequences observed in meteorology2 for instance1 a diminution of the pressure of the atmosphere 7indicated by a fall of the barometer7 is followed by rain4 ,the antecedent is here a complex phenomenon1 made up of heterogeneous elements2 the column of the atmosphere over any particular place consisting of two parts1 a column of air1 and a column of aqueous vapor mixed with it2 and the change in the two together manifested by a fall of the barometer1 and followed by rain1 must be either a change in one of these1 or in the other1 or in both4 ,we might1 then1 even in the absence of any other evidence1 form a reasonable presumption1 from the invariable presence of both these elements in the antecedent1 that the sequence is probably not an ultimate law1 but a result of the laws of the two different agents2 a presumption only to be destroyed when we had made ourselves so well acquainted with the laws of both1 as to be able to affirm that those laws could not by themselves produce the observed result4 ,there are but few known cases of succession from very complex antecedents which have not either been actually accounted for from simpler laws1 or inferred with great probability 7from the ascertained existence of intermediate links of causation not yet understood7 to be capable of being so accounted for4 ,it is1 therefore1 highly probable that all sequences from complex antecedents are thus resolvable1 and that ultimate laws are in all cases comparatively simple4 ,if there were not the other reasons already mentioned for believing that the laws of organized nature are resolvable into simpler laws1 it would be almost a sufficient reason that the antecedents in most of the sequences are so very complex4 #g4 ,in the preceding discussion we have recognized two kinds of empirical laws3 those known to be laws of causation1 but presumed to be resolvable into simpler laws2 and those not known to be laws of causation at all4 ,both these kinds of laws agree in the demand which they make for being explained by deduction1 and agree in being the appropriate means of verifying such deduction1 since they represent the experience with which the result of the deduction must be compared4 ,they agree1 further1 in this1 that until explained1 and connected with the ultimate laws from which they result1 they have not attained the highest degree of certainty of which laws are susceptible4 ,it has been shown on a former occasion that laws of causation which are derivative1 and compounded of simpler laws1 are not only1 as the nature of the case implies1 less general1 but even less certain1 than the simpler laws from which they result2 not in the same degree to be relied on as universally true4 ,the inferiority of evidence1 however1 which attaches to this class of laws1 is trifling1 compared with that which is inherent in uniformities not known to be laws of causation at all4 ,so long as these are unresolved1 we can not tell on how many collocations1 as well as laws1 their truth may be dependent2 we can never1 therefore1 extend them with any confidence to cases in which we have not assured ourselves1 by trial1 that the necessary collocation of causes1 whatever it may be1 exists4 ,it is to this class of laws alone that the property1 which philosophers usually consider as characteristic of empirical laws1 belongs in all its strictness--the property of being unfit to be relied on beyond the limits of time1 place1 and circumstance in which the observations have been made4 ,these are empirical laws in a more emphatic sense2 and when ,i employ that term 7except where the context manifestly indicates the reverse7 ,i shall generally mean to designate those uniformities only1 whether of succession or of co-existence1 which are not known to be laws of causation4 ,chapter ,,xvii4 ,of ,chance ,and ,its ,elimination4 #a4 ,considering1 then1 as empirical laws only those observed uniformities respecting which the question whether they are laws of causation must remain undecided until they can be explained deductively1 or until some means are found of applying the ,method of ,difference to the case1 it has been shown in the preceding chapter that until a uniformity can1 in one or the other of these modes1 be taken out of the class of empirical laws1 and brought either into that of laws of causation or of the demonstrated results of laws of causation1 it can not with any assurance be pronounced true beyond the local and other limits within which it has been found so by actual observation4 ,it remains to consider how we are to assure ourselves of its truth even within those limits2 after what quantity of experience a generalization which rests solely on the ,method of ,agreement can be considered sufficiently established1 even as an empirical law4 ,in a former chapter1 when treating of the ,methods of ,direct ,induction1 we expressly reserved this question17#agd7 and the time is now come for endeavoring to solve it4 ,we found that the ,method of ,agreement has the defect of not proving causation1 and can1 therefore1 only be employed for the ascertainment of empirical laws4 ,but we also found that besides this deficiency1 it labors under a characteristic imperfection1 tending to render uncertain even such conclusions as it is in itself adapted to prove4 ,this imperfection arises from ,plurality of ,causes4 ,although two or more cases in which the phenomenon a has been met with may have no common antecedent except ,a1 this does not prove that there is any connection between a and ,a1 since a may have many causes1 and may have been produced1 in these different instances1 not by any thing which the instances had in common1 but by some of those elements in them which were different4 ,we nevertheless observed1 that in proportion to the multiplication of instances pointing to ,a as the antecedent1 the characteristic uncertainty of the method diminishes1 and the existence of a law of connection between ,a and a more nearly approaches to certainty4 ,it is now to be determined after what amount of experience this certainty may be deemed to be practically attained1 and the connection between ,a and a may be received as an empirical law4 ,this question may be otherwise stated in more familiar terms3 ,after how many and what sort of instances may it be concluded that an observed coincidence between two phenomena is not the effect of chance8 ,it is of the utmost importance for understanding the logic of induction1 that we should form a distinct conception of what is meant by chance1 and how the phenomena which common language ascribes to that abstraction are really produced4 #b4 ,chance is usually spoken of in direct antithesis to law2 whatever1 it is supposed1 can not be ascribed to any law is attributed to chance4 ,it is1 however1 certain that whatever happens is the result of some law2 is an effect of causes1 and could have been predicted from a knowledge of the existence of those causes1 and from their laws4 ,if ,i turn up a particular card1 that is a consequence of its place in the pack4 ,its place in the pack was a consequence of the manner in which the cards were shuffled1 or of the order in which they were played in the last game2 which1 again1 were effects of prior causes4 ,at every stage1 if we had possessed an accurate knowledge of the causes in existence1 it would have been abstractedly possible to foretell the effect4 ,an event occurring by chance may be better described as a coincidence from which we have no ground to infer a uniformity--the occurrence of a phenomenon in certain circumstances1 without our having reason on that account to infer that it will happen again in those circumstances4 ,this1 however1 when looked closely into1 implies that the enumeration of the circumstances is not complete4 ,whatever the fact be1 since it has occurred once1 we may be sure that if all the same circumstances were repeated it would occur again2 and not only if all1 but there is some particular portion of those circumstances on which the phenomenon is invariably consequent4 ,with most of them1 however1 it is not connected in any permanent manner2 its conjunction with those is said to be the effect of chance1 to be merely casual4 ,facts casually conjoined are separately the effects of causes1 and therefore of laws2 but of different causes1 and causes not connected by any law4 ,it is incorrect1 then1 to say that any phenomenon is produced by chance2 but we may say that two or more phenomena are conjoined by chance1 that they co-exist or succeed one another only by chance2 meaning that they are in no way related through causation2 that they are neither cause and effect1 nor effects of the same cause1 nor effects of causes between which there subsists any law of co-existence1 nor even effects of the same collocation of primeval causes4 ,if the same casual coincidence never occurred a second time1 we should have an easy test for distinguishing such from the coincidences which are the results of a law4 ,as long as the phenomena had been found together only once1 so long1 unless we knew some more general laws from which the coincidence might have resulted1 we could not distinguish it from a casual one2 but if it occurred twice1 we should know that the phenomena so conjoined must be in some way connected through their causes4 ,there is1 however1 no such test4 ,a coincidence may occur again and again1 and yet be only casual4 ,nay1 it would be inconsistent with what we know of the order of nature to doubt that every casual coincidence will sooner or later be repeated1 as long as the phenomena between which it occurred do not cease to exist1 or to be reproduced4 ,the recurrence1 therefore1 of the same coincidence more than once1 or even its frequent recurrence1 does not prove that it is an instance of any law2 does not prove that it is not casual1 or1 in common language1 the effect of chance4 ,and yet1 when a coincidence can not be deduced from known laws1 nor proved by experiment to be itself a case of causation1 the frequency of its occurrence is the only evidence from which we can infer that it is the result of a law4 ,not1 however1 its absolute frequency4 ,the question is not whether the coincidence occurs often or seldom1 in the ordinary sense of those terms2 but whether it occurs more often than chance will account for2 more often than might rationally be expected if the coincidence were casual4 ,we have to decide1 therefore1 what degree of frequency in a coincidence chance will account for2 and to this there can be no general answer4 ,we can only state the principle by which the answer must be determined2 the answer itself will be different in every different case4 ,suppose that one of the phenomena1 ,a1 exists always1 and the other phenomenon1 ,b1 only occasionally2 it follows that every instance of ,b will be an instance of its coincidence with ,a1 and yet the coincidence will be merely casual1 not the result of any connection between them4 ,the fixed stars have been constantly in existence since the beginning of human experience1 and all phenomena that have come under human observation have1 in every single instance1 co-existed with them2 yet this coincidence1 though equally invariable with that which exists between any of those phenomena and its own cause1 does not prove that the stars are its cause1 nor that they are in anywise connected with it4 ,as strong a case of coincidence1 therefore1 as can possibly exist1 and a much stronger one in point of mere frequency than most of those which prove laws1 does not here prove a law2 why8 because1 since the stars exist always1 they must co-exist with every other phenomenon1 whether connected with them by causation or not4 ,the uniformity1 great though it be1 is no greater than would occur on the supposition that no such connection exists4 ,on the other hand1 suppose that we were inquiring whether there be any connection between rain and any particular wind4 ,rain1 we know1 occasionally occurs with every wind2 therefore1 the connection1 if it exists1 can not be an actual law2 but still rain may be connected with some particular wind through causation2 that is1 though they can not be always effects of the same cause 7for if so they would regularly co-exist71 there may be some causes common to the two1 so that in so far as either is produced by those common causes1 they will1 from the laws of the causes1 be found to co-exist4 ,how1 then1 shall we ascertain this8 ,the obvious answer is1 by observing whether rain occurs with one wind more frequently than with any other4 ,that1 however1 is not enough2 for perhaps that one wind blows more frequently than any other2 so that its blowing more frequently in rainy weather is no more than would happen1 although it had no connection with the causes of rain1 provided it were not connected with causes adverse to rain4 ,in ,england1 westerly winds blow during about twice as great a portion of the year as easterly4 ,if1 therefore1 it rains only twice as often with a westerly as with an easterly wind1 we have no reason to infer that any law of nature is concerned in the coincidence4 ,if it rains more than twice as often1 we may be sure that some law is concerned2 either there is some cause in nature which1 in this climate1 tends to produce both rain and a westerly wind1 or a westerly wind has itself some tendency to produce rain4 ,but if it rains less than twice as often1 we may draw a directly opposite inference3 the one1 instead of being a cause1 or connected with causes of the other1 must be connected with causes adverse to it1 or with the absence of some cause which produces it2 and though it may still rain much oftener with a westerly wind than with an easterly1 so far would this be from proving any connection between the phenomena1 that the connection proved would be between rain and an easterly wind1 to which1 in mere frequency of coincidence1 it is less allied4 ,here1 then1 are two examples3 in one1 the greatest possible frequency of coincidence1 with no instance whatever to the contrary1 does not prove that there is any law2 in the other1 a much less frequency of coincidence1 even when non-coincidence is still more frequent1 does prove that there is a law4 ,in both cases the principle is the same4 ,in both we consider the positive frequency of the phenomena themselves1 and how great frequency of coincidence that must of itself bring about1 without supposing any connection between them1 provided there be no repugnance2 provided neither be connected with any cause tending to frustrate the other4 ,if we find a greater frequency of coincidence than this1 we conclude that there is some connection2 if a less frequency1 that there is some repugnance4 ,in the former case1 we conclude that one of the phenomena can under some circumstances cause the other1 or that there exists something capable of causing them both2 in the latter1 that one of them1 or some cause which produces one of them1 is capable of counteracting the production of the other4 ,we have thus to deduct from the observed frequency of coincidence as much as may be the effect of chance1 that is1 of the mere frequency of the phenomena themselves2 and if any thing remains1 what does remain is the residual fact which proves the existence of a law4 ,the frequency of the phenomena can only be ascertained within definite limits of space and time2 depending as it does on the quantity and distribution of the primeval natural agents1 of which we can know nothing beyond the boundaries of human observation1 since no law1 no regularity1 can be traced in it1 enabling us to infer the unknown from the known4 ,but for the present purpose this is no disadvantage1 the question being confined within the same limits as the data4 ,the coincidences occurred in certain places and times1 and within those we can estimate the frequency with which such coincidences would be produced by chance4 ,if1 then1 we find from observation that ,a exists in one case out of every two1 and ,b in one case out of every three2 then1 if there be neither connection nor repugnance between them1 or between any of their causes1 the instances in which ,a and ,b will both exist1 that is to say will co-exist1 will be one case in every six4 ,for ,a exists in three cases out of six2 and ,b1 existing in one case out of every three without regard to the presence or absence of ,a1 will exist in one case out of those three4 ,there will therefore be1 of the whole number of cases1 two in which ,a exists without ,b2 one case of ,b without ,a2 two in which neither ,b nor ,a exists1 and one case out of six in which they both exist4 ,if1 then1 in point of fact1 they are found to co-exist oftener than in one case out of six2 and1 consequently1 ,a does not exist without ,b so often as twice in three times1 nor ,b without ,a so often as once in every twice1 there is some cause in existence which tends to produce a conjunction between ,a and ,b4 ,generalizing the result1 we may say that if ,a occurs in a larger proportion of the cases where ,b is than of the cases where ,b is not1 then will ,b also occur in a larger proportion of the cases where ,a is than of the cases where ,a is not2 and there is some connection1 through causation1 between ,a and ,b4 ,if we could ascend to the causes of the two phenomena1 we should find1 at some stage1 either proximate or remote1 some cause or causes common to both2 and if we could ascertain what these are1 we could frame a generalization which would be true without restriction of place or time2 but until we can do so1 the fact of a connection between the two phenomena remains an empirical law4 #c4 ,having considered in what manner it may be determined whether any given conjunction of phenomena is casual1 or the result of some law1 to complete the theory of chance it is necessary that we should now consider those effects which are partly the result of chance and partly of law1 or1 in other words1 in which the effects of casual conjunctions of causes are habitually blended in one result with the effects of a constant cause4 ,this is a case of ,composition of ,causes2 and the peculiarity of it is1 that instead of two or more causes intermixing their effects in a regular manner with those of one another1 we have now one constant cause1 producing an effect which is successively modified by a series of variable causes4 ,thus1 as summer advances1 the approach of the sun to a vertical position tends to produce a constant increase of temperature2 but with this effect of a constant cause1 there are blended the effects of many variable causes1 winds1 clouds1 evaporation1 electric agencies and the like1 so that the temperature of any given day depends in part on these fleeting causes1 and only in part on the constant cause4 ,if the effect of the constant cause is always accompanied and disguised by effects of variable causes1 it is impossible to ascertain the law of the constant cause in the ordinary manner by separating it from all other causes and observing it apart4 ,hence arises the necessity of an additional rule of experimental inquiry4 ,when the action of a cause ,a is liable to be interfered with1 not steadily by the same cause or causes1 but by different causes at different times1 and when these are so frequent1 or so indeterminate1 that we can not possibly exclude all of them from any experiment1 though we may vary them2 our resource is1 to endeavor to ascertain what is the effect of all the variable causes taken together4 ,in order to do this1 we make as many trials as possible1 preserving ,a invariable4 ,the results of these different trials will naturally be different1 since the indeterminate modifying causes are different in each2 if1 then1 we do not find these results to be progressive1 but1 on the contrary1 to oscillate about a certain point1 one experiment giving a result a little greater1 another a little less1 one a result tending a little more in one direction1 another a little more in the contrary direction2 while the average or middle point does not vary1 but different sets of experiments 7taken in as great a variety of circumstances as possible7 yield the same mean1 provided only they be sufficiently numerous2 then that mean1 or average result1 is the part1 in each experiment1 which is due to the cause ,a1 and is the effect which would have been obtained if ,a could have acted alone2 the variable remainder is the effect of chance1 that is1 of causes the co-existence of which with the cause ,a was merely casual4 ,the test of the sufficiency of the induction in this case is1 when any increase of the number of trials from which the average is struck does not materially alter the average4 ,this kind of elimination1 in which we do not eliminate any one assignable cause1 but the multitude of floating unassignable ones1 may be termed the ,elimination of ,chance4 ,we afford an example of it when we repeat an experiment1 in order1 by taking the mean of different results1 to get rid of the effects of the unavoidable errors of each individual experiment4 ,when there is no permanent cause1 such as would produce a tendency to error peculiarly in one direction1 we are warranted by experience in assuming that the errors on one side will1 in a certain number of experiments1 about balance the errors on the contrary side4 ,we therefore repeat the experiment1 until any change which is produced in the average of the whole by further repetition1 falls within limits of error consistent with the degree of accuracy required by the purpose we have in view47#age7 #d4 ,in the supposition hitherto made1 the effect of the constant cause ,a has been assumed to form so great and conspicuous a part of the general result1 that its existence never could be a matter of uncertainty1 and the object of the eliminating process was only to ascertain how much is attributable to that cause2 what is its exact law4 ,cases1 however1 occur in which the effect of a constant cause is so small1 compared with that of some of the changeable causes with which it is liable to be casually conjoined1 that of itself it escapes notice1 and the very existence of any effect arising from a constant cause is first learned by the process which in general serves only for ascertaining the quantity of that effect4 ,this case of induction may be characterized as follows3 ,a given effect is known to be chiefly1 and not known not to be wholly1 determined by changeable causes4 ,if it be wholly so produced1 then if the aggregate be taken of a sufficient number of instances1 the effects of these different causes will cancel one another4 ,if1 therefore1 we do not find this to be the case1 but1 on the contrary1 after such a number of trials has been made that no further increase alters the average result1 we find that average to be1 not zero1 but some other quantity1 about which1 though small in comparison with the total effect1 the effect nevertheless oscillates1 and which is the middle point in its oscillation2 we may conclude this to be the effect of some constant cause2 which cause1 by some of the methods already treated of1 we may hope to detect4 ,this may be called the discovery of a residual phenomenon by eliminating the effects of chance4 ,it is in this manner1 for example1 that loaded dice may be discovered4 ,of course no dice are so clumsily loaded that they must always throw certain numbers2 otherwise the fraud would be instantly detected4 ,the loading1 a constant cause1 mingles with the changeable causes which determine what cast will be thrown in each individual instance4 ,if the dice were not loaded1 and the throw were left to depend entirely on the changeable causes1 these in a sufficient number of instances would balance one another1 and there would be no preponderant number of throws of any one kind4 ,if1 therefore1 after such a number of trials that no further increase of their number has any material effect upon the average1 we find a preponderance in favor of a particular throw2 we may conclude with assurance that there is some constant cause acting in favor of that throw1 or1 in other words1 that the dice are not fair2 and the exact amount of the unfairness4 ,in a similar manner1 what is called the diurnal variation of the barometer1 which is very small compared with the variations arising from the irregular changes in the state of the atmosphere1 was discovered by comparing the average height of the barometer at different hours of the day4 ,when this comparison was made1 it was found that there was a small difference1 which on the average was constant1 however the absolute quantities might vary1 and which difference1 therefore1 must be the effect of a constant cause4 ,this cause was afterward ascertained1 deductively1 to be the rarefaction of the air1 occasioned by the increase of temperature as the day advances4 #e4 ,after these general remarks on the nature of chance1 we are prepared to consider in what manner assurance may be obtained that a conjunction between two phenomena1 which has been observed a certain number of times1 is not casual1 but a result of causation1 and to be received1 therefore1 as one of the uniformities of nature1 though 7until accounted for a priori7 only as an empirical law4 ,we will suppose the strongest case1 namely1 that the phenomenon ,b has never been observed except in conjunction with ,a4 ,even then1 the probability that they are connected is not measured by the total number of instances in which they have been found together1 but by the excess of that number above the number due to the absolutely frequency of ,a4 ,if1 for example1 ,a exists always1 and therefore co-exists with every thing1 no number of instances of its co-existence with ,b would prove a connection2 as in our example of the fixed stars4 ,if ,a be a fact of such common occurrence that it may be presumed to be present in half of all the cases that occur1 and therefore in half the cases in which ,b occurs1 it is only the proportional excess above half that is to be reckoned as evidence toward proving a connection between ,a and ,b4 ,in addition to the question1 ,what is the number of coincidences which1 on an average of a great multitude of trials1 may be expected to arise from chance alone8 there is also another question1 namely1 ,of what extent of deviation from that average is the occurrence credible1 from chance alone1 in some number of instances smaller than that required for striking a fair average8 ,it is not only to be considered what is the general result of the chances in the long run1 but also what are the extreme limits of variation from the general result1 which may occasionally be expected as the result of some smaller number of instances4 ,the consideration of the latter question1 and any consideration of the former beyond that already given to it1 belong to what mathematicians term the doctrine of chances1 or1 in a phrase of greater pretension1 the ,theory of ,probabilities4 ,chapter ,,xviii4 ,of ,the ,calculation ,of ,chances4 #a4 8,probability10 says ,laplace17#agf7 8has reference partly to our ignorance1 partly to our knowledge4 ,we know that among three or more events1 one1 and only one1 must happen2 but there is nothing leading us to believe that any one of them will happen rather than the others4 ,in this state of indecision1 it is impossible for us to pronounce with certainty on their occurrence4 ,it is1 however1 probable that any one of these events1 selected at pleasure1 will not take place2 because we perceive several cases1 all equally possible1 which exclude its occurrence1 and only one which favors it4 8,the theory of chances consists in reducing all events of the same kind to a certain number of cases equally possible1 that is1 such that we are equally undecided as to their existence2 and in determining the number of these cases which are favorable to the event of which the probability is sought4 ,the ratio of that number to the number of all the possible cases is the measure of the probability2 which is thus a fraction1 having for its numerator the number of cases favorable to the event1 and for its denominator the number of all the cases which are possible40 ,to a calculation of chances1 then1 according to ,laplace1 two things are necessary2 we must know that of several events some one will certainly happen1 and no more than one2 and we must not know1 nor have any reason to expect1 that it will be one of these events rather than another4 ,it has been contended that these are not the only requisites1 and that ,laplace has overlooked1 in the general theoretical statement1 a necessary part of the foundation of the doctrine of chances4 ,to be able 7it has been said7 to pronounce two events equally probable1 it is not enough that we should know that one or the other must happen1 and should have no grounds for conjecturing which4 ,experience must have shown that the two events are of equally frequent occurrence4 ,why1 in tossing up a half-penny1 do we reckon it equally probable that we shall throw cross or pile8 ,because we know that in any great number of throws1 cross and pile are thrown about equally often2 and that the more throws we make1 the more nearly the equality is perfect4 ,we may know this if we please by actual experiment1 or by the daily experience which life affords of events of the same general character1 or1 deductively1 from the effect of mechanical laws on a symmetrical body acted upon by forces varying indefinitely in quantity and direction4 ,we may know it1 in short1 either by specific experience1 or on the evidence of our general knowledge of nature4 ,but1 in one way or the other1 we must know it1 to justify us in calling the two events equally probable2 and if we knew it not1 we should proceed as much at hap-hazard in staking equal sums on the result1 as in laying odds4 ,this view of the subject was taken in the first edition of the present work2 but ,i have since become convinced that the theory of chances1 as conceived by ,laplace and by mathematicians generally1 has not the fundamental fallacy which ,i had ascribed to it4 ,we must remember that the probability of an event is not a quality of the event itself1 but a mere name for the degree of ground which we1 or some one else1 have for expecting it4 ,the probability of an event to one person is a different thing from the probability of the same event to another1 or to the same person after he has acquired additional evidence4 ,the probability to me1 that an individual of whom ,i know nothing but his name will die within the year1 is totally altered by my being told the next minute that he is in the last stage of a consumption4 ,yet this makes no difference in the event itself1 nor in any of the causes on which it depends4 ,every event is in itself certain1 not probable2 if we knew all1 we should either know positively that it will happen1 or positively that it will not4 ,but its probability to us means the degree of expectation of its occurrence1 which we are warranted in entertaining by our present evidence4 ,bearing this in mind1 ,i think it must be admitted1 that even when we have no knowledge whatever to guide our expectations1 except the knowledge that what happens must be some one of a certain number of possibilities1 we may still reasonably judge1 that one supposition is more probable to us than another supposition2 and if we have any interest at stake1 we shall best provide for it by acting conformably to that judgment4 #b4 ,suppose that we are required to take a ball from a box1 of which we only know that it contains balls both black and white1 and none of any other color4 ,we know that the ball we select will be either a black or a white ball2 but we have no ground for expecting black rather than white1 or white rather than black4 ,in that case1 if we are obliged to make a choice1 and to stake something on one or the other supposition1 it will1 as a question of prudence1 be perfectly indifferent which2 and we shall act precisely as we should have acted if we had known beforehand that the box contained an equal number of black and white balls4 ,but though our conduct would be the same1 it would not be founded on any surmise that the balls were in fact thus equally divided2 for we might1 on the contrary1 know by authentic information that the box contained ninety-nine balls of one color1 and only one of the other2 still1 if we are not told which color has only one1 and which has ninety-nine1 the drawing of a white and of a black ball will be equally probable to us4 ,we shall have no reason for staking any thing on the one event rather than on the other2 the option between the two will be a matter of indifference2 in other words1 it will be an even chance4 ,but let it now be supposed that instead of two there are three colors--white1 black1 and red2 and that we are entirely ignorant of the proportion in which they are mingled4 ,we should then have no reason for expecting one more than another1 and if obliged to bet1 should venture our stake on red1 white1 or black with equal indifference4 ,but should we be indifferent whether we betted for or against some one color1 as1 for instance1 white8 ,surely not4 ,from the very fact that black and red are each of them separately equally probable to us with white1 the two together must be twice as probable4 ,we should in this case expect not white rather than white1 and so much rather that we would lay two to one upon it4 ,it is true1 there might1 for aught we knew1 be more white balls than black and red together2 and if so1 our bet would1 if we knew more1 be seen to be a disadvantageous one4 ,but so also1 for aught we knew1 might there be more red balls than black and white1 or more black balls than white and red1 and in such case the effect of additional knowledge would be to prove to us that our bet was more advantageous than we had supposed it to be4 ,there is in the existing state of our knowledge a rational probability of two to one against white2 a probability fit to be made a basis of conduct4 ,no reasonable person would lay an even wager in favor of white against black and red2 though against black alone or red alone he might do so without imprudence4 ,the common theory1 therefore1 of the calculation of chances1 appears to be tenable4 ,even when we know nothing except the number of the possible and mutually excluding contingencies1 and are entirely ignorant of their comparative frequency1 we may have grounds1 and grounds numerically appreciable1 for acting on one supposition rather than on another2 and this is the meaning of ,probability4 #c4 ,the principle1 however1 on which the reasoning proceeds1 is sufficiently evident4 ,it is the obvious one that when the cases which exist are shared among several kinds1 it is impossible that each of those kinds should be a majority of the whole3 on the contrary1 there must be a majority against each kind1 except one at most2 and if any kind has more than its share in proportion to the total number1 the others collectively must have less4 ,granting this axiom1 and assuming that we have no ground for selecting any one kind as more likely than the rest to surpass the average proportion1 it follows that we can not rationally presume this of any1 which we should do if we were to bet in favor of it1 receiving less odds than in the ratio of the number of the other kinds4 ,even1 therefore1 in this extreme case of the calculation of probabilities1 which does not rest on special experience at all1 the logical ground of the process is our knowledge--such knowledge as we then have--of the laws governing the frequency of occurrence of the different cases2 but in this case the knowledge is limited to that which1 being universal and axiomatic1 does not require reference to specific experience1 or to any considerations arising out of the special nature of the problem under discussion4 ,except1 however1 in such cases as games of chance1 where the very purpose in view requires ignorance instead of knowledge1 ,i can conceive no case in which we ought to be satisfied with such an estimate of chances as this--an estimate founded on the absolute minimum of knowledge respecting the subject4 ,it is plain that1 in the case of the colored balls1 a very slight ground of surmise that the white balls were really more numerous than either of the other colors1 would suffice to vitiate the whole of the calculations made in our previous state of indifference4 ,it would place us in that position of more advanced knowledge1 in which the probabilities1 to us1 would be different from what they were before2 and in estimating these new probabilities we should have to proceed on a totally different set of data1 furnished no longer by mere counting of possible suppositions1 but by specific knowledge of facts4 ,such data it should always be our endeavor to obtain2 and in all inquiries1 unless on subjects equally beyond the range of our means of knowledge and our practical uses1 they may be obtained1 if not good1 at least better than none at all47#agg7 ,it is obvious1 too1 that even when the probabilities are derived from observation and experiment1 a very slight improvement in the data1 by better observations1 or by taking into fuller consideration the special circumstances of the case1 is of more use than the most elaborate application of the calculus to probabilities founded on the data in their previous state of inferiority4 ,the neglect of this obvious reflection has given rise to misapplications of the calculus of probabilities which have made it the real opprobrium of mathematics4 ,it is sufficient to refer to the applications made of it to the credibility of witnesses1 and to the correctness of the verdicts of juries4 ,in regard to the first1 common sense would dictate that it is impossible to strike a general average of the veracity and other qualifications for true testimony of mankind1 or of any class of them2 and even if it were possible1 the employment of it for such a purpose implies a misapprehension of the use of averages1 which serve1 indeed1 to protect those whose interest is at stake1 against mistaking the general result of large masses of instances1 but are of extremely small value as grounds of expectation in any one individual instance1 unless the case be one of those in which the great majority of individual instances do not differ much from the average4 ,in the case of a witness1 persons of common sense would draw their conclusions from the degree of consistency of his statements1 his conduct under cross-examination1 and the relation of the case itself to his interests1 his partialities1 and his mental capacity1 instead of applying so rude a standard 7even if it were capable of being verified7 as the ratio between the number of true and the number of erroneous statements which he may be supposed to make in the course of his life4 ,again1 on the subject of juries or other tribunals1 some mathematicians have set out from the proposition that the judgment of any one judge or juryman is1 at least in some small degree1 more likely to be right than wrong1 and have concluded that the chance of a number of persons concurring in a wrong verdict is diminished the more the number is increased2 so that if the judges are only made sufficiently numerous1 the correctness of the judgment may be reduced almost to certainty4 ,i say nothing of the disregard shown to the effect produced on the moral position of the judges by multiplying their numbers1 the virtual destruction of their individual responsibility1 and weakening of the application of their minds to the subject4 ,i remark only the fallacy of reasoning from a wide average to cases necessarily differing greatly from any average4 ,it may be true that1 taking all causes one with another1 the opinion of any one of the judges would be oftener right than wrong2 but the argument forgets that in all but the more simple cases1 in all cases in which it is really of much consequence what the tribunal is1 the proposition might probably be reversed2 besides which1 the cause of error1 whether arising from the intricacy of the case or from some common prejudice or mental infirmity1 if it acted upon one judge1 would be extremely likely to affect all the others in the same manner1 or at least a majority1 and thus render a wrong instead of a right decision more probable the more the number was increased4 ,these are but samples of the errors frequently committed by men who1 having made themselves familiar with the difficult formul which algebra affords for the estimation of chances under suppositions of a complex character1 like better to employ those formul in computing what are the probabilities to a person half informed about a case than to look out for means of being better informed4 ,before applying the doctrine of chances to any scientific purpose1 the foundation must be laid for an evaluation of the chances1 by possessing ourselves of the utmost attainable amount of positive knowledge4 ,the knowledge required is that of the comparative frequency with which the different events in fact occur4 ,for the purposes1 therefore1 of the present work1 it is allowable to suppose that conclusions respecting the probability of a fact of a particular kind rest on our knowledge of the proportion between the cases in which facts of that kind occur1 and those in which they do not occur2 this knowledge being either derived from specific experiment1 or deduced from our knowledge of the causes in operation which tend to produce1 compared with those which tend to prevent1 the fact in question4 ,such calculation of chances is grounded on an induction2 and to render the calculation legitimate1 the induction must be a valid one4 ,it is not less an induction1 though it does not prove that the event occurs in all cases of a given description1 but only that out of a given number of such cases it occurs in about so many4 ,the fraction which mathematicians use to designate the probability of an event is the ratio of these two numbers2 the ascertained proportion between the number of cases in which the event occurs and the sum of all the cases1 those in which it occurs and in which it does not occur1 taken together4 ,in playing at cross and pile1 the description of cases concerned are throws1 and the probability of cross is one-half1 because if we throw often enough cross is thrown about once in every two throws4 ,in the cast of a die1 the probability of ace is one-sixth2 not simply because there are six possible throws1 of which ace is one1 and because we do not know any reason why one should turn up rather than another--though ,i have admitted the validity of this ground in default of a better--but because we do actually know1 either by reasoning or by experience1 that in a hundred or a million of throws ace is thrown in about one-sixth of that number1 or once in six times4 #d4 ,i say1 8either by reasoning or by experience10 meaning specific experience4 ,but in estimating probabilities1 it is not a matter of indifference from which of these two sources we derive our assurance4 ,the probability of events1 as calculated from their mere frequency in past experience1 affords a less secure basis for practical guidance than their probability as deduced from an equally accurate knowledge of the frequency of occurrence of their causes4 ,the generalization that an event occurs in ten out of every hundred cases of a given description1 is as real an induction as if the generalization were that it occurs in all cases4 ,but when we arrive at the conclusion by merely counting instances in actual experience1 and comparing the number of cases in which ,a has been present with the number in which it has been absent1 the evidence is only that of the ,method of ,agreement1 and the conclusion amounts only to an empirical law4 ,we can make a step beyond this when we can ascend to the causes on which the occurrence of ,a or its non-occurrence will depend1 and form an estimate of the comparative frequency of the causes favorable and of those unfavorable to the occurrence4 ,these are data of a higher order1 by which the empirical law derived from a mere numerical comparison of affirmative and negative instances will be either corrected or confirmed1 and in either case we shall obtain a more correct measure of probability than is given by that numerical comparison4 ,it has been well remarked that in the kind of examples by which the doctrine of chances is usually illustrated1 that of balls in a box1 the estimate of probabilities is supported by reasons of causation1 stronger than specific experience4 8,what is the reason that in a box where there are nine black balls and one white1 we expect to draw a black ball nine times as much 7in other words1 nine times as often1 frequency being the gauge of intensity in expectation7 as a white8 ,obviously because the local conditions are nine times as favorable2 because the hand may alight in nine places and get a black ball1 while it can only alight in one place and find a white ball2 just for the same reason that we do not expect to succeed in finding a friend in a crowd1 the conditions in order that we and he should come together being many and difficult4 ,this of course would not hold to the same extent were the white balls of smaller size than the black1 neither would the probability remain the same2 the larger ball would be much more likely to meet the hand407#agh7 ,it is1 in fact1 evident that when once causation is admitted as a universal law1 our expectation of events can only be rationally grounded on that law4 ,to a person who recognizes that every event depends on causes1 a thing's having happened once is a reason for expecting it to happen again1 only because proving that there exists1 or is liable to exist1 a cause adequate to produce it47#agi7 ,the frequency of the particular event1 apart from all surmise respecting its cause1 can give rise to no other induction than that per enumerationem simplicem2 and the precarious inferences derived from this are superseded1 and disappear from the field as soon as the principle of causation makes its appearance there4 ,notwithstanding1 however1 the abstract superiority of an estimate of probability grounded on causes1 it is a fact that in almost all cases in which chances admit of estimation sufficiently precise to render their numerical appreciation of any practical value1 the numerical data are not drawn from knowledge of the causes1 but from experience of the events themselves4 ,the probabilities of life at different ages or in different climates2 the probabilities of recovery from a particular disease2 the chances of the birth of male or female offspring2 the chances of the destruction of houses or other property by fire2 the chances of the loss of a ship in a particular voyage1 are deduced from bills of mortality1 returns from hospitals1 registers of births1 of shipwrecks1 etc41 that is1 from the observed frequency not of the causes1 but of the effects4 ,the reason is1 that in all these classes of facts the causes are either not amenable to direct observation at all1 or not with the requisite precision1 and we have no means of judging of their frequency except from the empirical law afforded by the frequency of the effects4 ,the inference does not the less depend on causation alone4 ,we reason from an effect to a similar effect by passing through the cause4 ,if the actuary of an insurance office infers from his tables that among a hundred persons now living of a particular age1 five on the average will attain the age of seventy1 his inference is legitimate1 not for the simple reason that this is the proportion who have lived till seventy in times past1 but because the fact of their having so lived shows that this is the proportion existing1 at that place and time1 between the causes which prolong life to the age of seventy and those tending to bring it to an earlier close47#ahj7 #e4 ,from the preceding principles it is easy to deduce the demonstration of that theorem of the doctrine of probabilities which is the foundation of its application to inquiries for ascertaining the occurrence of a given event1 or the reality of an individual fact4 ,the signs or evidences by which a fact is usually proved are some of its consequences2 and the inquiry hinges upon determining what cause is most likely to have produced a given effect4 ,the theorem applicable to such investigations is the ,sixth ,principle in ,laplace's 8,essai ,philosophique sur les ,probabilits10 which is described by him as the 8fundamental principle of that branch of the ,analysis of ,chances which consists in ascending from events to their causes407#aha7 ,given an effect to be accounted for1 and there being several causes which might have produced it1 but of the presence of which in the particular case nothing is known2 the probability that the effect was produced by any one of these causes is as the antecedent probability of the cause1 multiplied by the probability that the cause1 if it existed1 would have produced the given effect4 ,let ,m be the effect1 and ,a1 ,b1 two causes1 by either of which it might have been produced4 ,to find the probability that it was produced by the one and not by the other1 ascertain which of the two is most likely to have existed1 and which of them1 if it did exist1 was most likely to produce the effect ,m3 the probability sought is a compound of these two probabilities4 ,,case ,i4 ,let the causes be both alike in the second respect3 either ,a or ,b1 when it exists1 being supposed equally likely 7or equally certain7 to produce ,m2 but let ,a be in itself twice as likely as ,b to exist1 that is1 twice as frequent a phenomenon4 ,then it is twice as likely to have existed in this case1 and to have been the cause which produced ,m4 ,for1 since ,a exists in nature twice as often as ,b1 in any #cjj cases in which one or other existed1 ,a has existed #bjj times and ,b #ajj4 ,but either ,a or ,b must have existed wherever ,m is produced2 therefore1 in #cjj times that ,m is produced1 ,a was the producing cause #bjj times1 ,b only #ajj1 that is1 in the ratio of #b to #a4 ,thus1 then1 if the causes are alike in their capacity of producing the effect1 the probability as to which actually produced it is in the ratio of their antecedent probabilities4 ,,case ,,ii4 ,reversing the last hypothesis1 let us suppose that the causes are equally frequent1 equally likely to have existed1 but not equally likely1 if they did exist1 to produce ,m2 that in three times in which ,a occurs1 it produces that effect twice1 while ,b1 in three times1 produces it only once4 ,since the two causes are equally frequent in their occurrence2 in every six times that either one or the other exists1 ,a exists three times and ,b three times4 ,a1 of its three times1 produces ,m in two2 ,b1 of its three times1 produces ,m in one4 ,thus1 in the whole six times1 ,m is only produced thrice2 but of that thrice it is produced twice by ,a1 once only by ,b4 ,consequently1 when the antecedent probabilities of the causes are equal1 the chances that the effect was produced by them are in the ratio of the probabilities that if they did exist they would produce the effect4 ,,case ,,iii4 ,the third case1 that in which the causes are unlike in both respects1 is solved by what has preceded4 ,for1 when a quantity depends on two other quantities1 in such a manner that while either of them remains constant it is proportional to the other1 it must necessarily be proportional to the product of the two quantities1 the product being the only function of the two which obeys that law of variation4 ,therefore1 the probability that ,m was produced by either cause1 is as the antecedent probability of the cause1 multiplied by the probability that if it existed it would produce ,m4 ,which was to be demonstrated4 ,or we may prove the third case as we proved the first and second4 ,let ,a be twice as frequent as ,b1 and let them also be unequally likely1 when they exist1 to produce ,m2 let ,a produce it twice in four times1 ,b thrice in four times4 ,the antecedent probability of ,a is to that of ,b as #b to #a2 the probabilities of their producing ,m are as #b to #c2 the product of these ratios is the ratio of #d to #c2 and this will be the ratio of the probabilities that ,a or ,b was the producing cause in the given instance4 ,for1 since ,a is twice as frequent as ,b1 out of twelve cases in which one or other exists1 ,a exists in #h and ,b in #d4 ,but of its eight cases1 ,a1 by the supposition1 produces ,m in only #d1 while ,b of its four cases produces ,m in #c4 ,m1 therefore1 is only produced at all in seven of the twelve cases2 but in four of these it is produced by ,a1 in three by ,b2 hence the probabilities of its being produced by ,a and by ,b are as #d to #c1 and are expressed by the fractions and 4 ,which was to be demonstrated4 #f4 ,it remains to examine the bearing of the doctrine of chances on the peculiar problem which occupied us in the preceding chapter1 namely1 how to distinguish coincidences which are casual from those which are the result of law2 from those in which the facts which accompany or follow one another are somehow connected through causation4 ,the doctrine of chances affords means by which1 if we knew the average number of coincidences to be looked for between two phenomena connected only casually1 we could determine how often any given deviation from that average will occur by chance4 ,if the probability of any casual coincidence1 considered in itself1 be #a_/m1 the probability that the same coincidence will be repeated n times in succession is #a_/mn4 ,for example1 in one throw of a die the probability of ace being 2 the probability of throwing ace twice in succession will be #a divided by the square of #f1 or 4 ,for ace is thrown at the first throw once in six1 or six in thirty-six times1 and of those six1 the die being cast again1 ace will be thrown but once2 being altogether once in thirty-six times4 ,the chance of the same cast three times successively is1 by a similar reasoning1 or 2 that is1 the event will happen1 on a large average1 only once in two hundred and sixteen throws4 ,we have thus a rule by which to estimate the probability that any given series of coincidences arises from chance1 provided we can measure correctly the probability of a single coincidence4 ,if we can obtain an equally precise expression for the probability that the same series of coincidences arises from causation1 we should only have to compare the numbers4 ,this1 however1 can rarely be done4 ,let us see what degree of approximation can practically be made to the necessary precision4 ,the question falls within ,laplace's sixth principle1 just demonstrated4 ,the given fact1 that is to say1 the series of coincidences1 may have originated either in a casual conjunction of causes or in a law of nature4 ,the probabilities1 therefore1 that the fact originated in these two modes1 are as their antecedent probabilities1 multiplied by the probabilities that if they existed they would produce the effect4 ,but the particular combination of chances1 if it occurred1 or the law of nature if real1 would certainly produce the series of coincidences4 ,the probabilities1 therefore1 that the coincidences are produced by the two causes in question are as the antecedent probabilities of the causes4 ,one of these1 the antecedent probability of the combination of mere chances which would produce the given result1 is an appreciable quantity4 ,the antecedent probability of the other supposition may be susceptible of a more or less exact estimation1 according to the nature of the case4 ,in some cases1 the coincidence1 supposing it to be the result of causation at all1 must be the result of a known cause2 as the succession of aces1 if not accidental1 must arise from the loading of the die4 ,in such cases we may be able to form a conjecture as to the antecedent probability of such a circumstance from the characters of the parties concerned1 or other such evidence2 but it would be impossible to estimate that probability with any thing like numerical precision4 ,the counter-probability1 however1 that of the accidental origin of the coincidence1 dwindling so rapidly as it does at each new trial1 the stage is soon reached at which the chance of unfairness in the die1 however small in itself1 must be greater than that of a casual coincidence2 and on this ground1 a practical decision can generally be come to without much hesitation1 if there be the power of repeating the experiment4 ,when1 however1 the coincidence is one which can not be accounted for by any known cause1 and the connection between the two phenomena1 if produced by causation1 must be the result of some law of nature hitherto unknown2 which is the case we had in view in the last chapter2 then1 though the probability of a casual coincidence may be capable of appreciation1 that of the counter-supposition1 the existence of an undiscovered law of nature1 is clearly unsusceptible of even an approximate valuation4 ,in order to have the data which such a case would require1 it would be necessary to know what proportion of all the individual sequences or co-existences occurring in nature are the result of law1 and what proportion are mere casual coincidences4 ,it being evident that we can not form any plausible conjecture as to this proportion1 much less appreciate it numerically1 we can not attempt any precise estimation of the comparative probabilities4 ,but of this we are sure1 that the detection of an unknown law of nature--of some previously unrecognized constancy of conjunction among phenomena--is no uncommon event4 ,if1 therefore1 the number of instances in which a coincidence is observed1 over and above that which would arise on the average from the mere concurrence of chances1 be such that so great an amount of coincidences from accident alone would be an extremely uncommon event2 we have reason to conclude that the coincidence is the effect of causation1 and may be received 7subject to correction from further experience7 as an empirical law4 ,further than this1 in point of precision1 we can not go2 nor1 in most cases1 is greater precision required1 for the solution of any practical doubt47#ahb7 ,chapter ,,xix4 ,of ,the ,extension ,of ,derivative ,laws ,to ,adjacent ,cases4 #a4 ,we have had frequent occasion to notice the inferior generality of derivative laws1 compared with the ultimate laws from which they are derived4 ,this inferiority1 which affects not only the extent of the propositions themselves1 but their degree of certainty within that extent1 is most conspicuous in the uniformities of co-existence and sequence obtaining between effects which depend ultimately on different primeval causes4 ,such uniformities will only obtain where there exists the same collocation of those primeval causes4 ,if the collocation varies1 though the laws themselves remain the same1 a totally different set of derivative uniformities may1 and generally will1 be the result4 ,even where the derivative uniformity is between different effects of the same cause1 it will by no means obtain as universally as the law of the cause itself4 ,if a and b accompany or succeed one another as effects of the cause ,a1 it by no means follows that ,a is the only cause which can produce them1 or that if there be another cause1 as ,b1 capable of producing a1 it must produce b likewise4 ,the conjunction1 therefore1 of a and b perhaps does not hold universally1 but only in the instances in which a arises from ,a4 ,when it is produced by a cause other than ,a1 a and b may be dissevered4 ,day 7for example7 is always in our experience followed by night2 but day is not the cause of night2 both are successive effects of a common cause1 the periodical passage of the spectator into and out of the earth's shadow1 consequent on the earth's rotation1 and on the illuminating property of the sun4 ,if1 therefore1 day is ever produced by a different cause or set of causes from this1 day will not1 or at least may not1 be followed by night4 ,on the sun's own surface1 for instance1 this may be the case4 ,finally1 even when the derivative uniformity is itself a law of causation 7resulting from the combination of several causes71 it is not altogether independent of collocations4 ,if a cause supervenes1 capable of wholly or partially counteracting the effect of any one of the conjoined causes1 the effect will no longer conform to the derivative law4 ,while1 therefore1 each ultimate law is only liable to frustration from one set of counteracting causes1 the derivative law is liable to it from several4 ,now1 the possibility of the occurrence of counteracting causes which do not arise from any of the conditions involved in the law itself depends on the original collocations4 ,it is true that1 as we formerly remarked1 laws of causation1 whether ultimate or derivative1 are1 in most cases1 fulfilled even when counteracted2 the cause produces its effect1 though that effect is destroyed by something else4 ,that the effect may be frustrated1 is1 therefore1 no objection to the universality of laws of causation4 ,but it is fatal to the universality of the sequences or co-existences of effects1 which compose the greater part of the derivative laws flowing from laws of causation4 ,when1 from the law of a certain combination of causes1 there results a certain order in the effects2 as from the combination of a single sun with the rotation of an opaque body round its axis1 there results1 on the whole surface of that opaque body1 an alternation of day and night2 then1 if we suppose one of the combined causes counteracted1 the rotation stopped1 the sun extinguished1 or a second sun superadded1 the truth of that particular law of causation is in no way affected2 it is still true that one sun shining on an opaque revolving body will alternately produce day and night2 but since the sun no longer does shine on such a body1 the derivative uniformity1 the succession of day and night on the given planet1 is no longer true4 ,those derivative uniformities1 therefore1 which are not laws of causation1 are 7except in the rare case of their depending on one cause alone1 not on a combination of causes7 always more or less contingent on collocations2 and are hence subject to the characteristic infirmity of empirical laws--that of being admissible only where the collocations are known by experience to be such as are requisite for the truth of the law2 that is1 only within the conditions of time and place confirmed by actual observation4 #b4 ,this principle1 when stated in general terms1 seems clear and indisputable2 yet many of the ordinary judgments of mankind1 the propriety of which is not questioned1 have at least the semblance of being inconsistent with it4 ,on what grounds1 it may be asked1 do we expect that the sun will rise to-morrow8 ,to-morrow is beyond the limits of time comprehended in our observations4 ,they have extended over some thousands of years past1 but they do not include the future4 ,yet we infer with confidence that the sun will rise to-morrow2 and nobody doubts that we are entitled to do so4 ,let us consider what is the warrant for this confidence4 ,in the example in question1 we know the causes on which the derivative uniformity depends4 ,they are3 the sun giving out light1 the earth in a state of rotation and intercepting light4 ,the induction which shows these to be the real causes1 and not merely prior effects of a common cause1 being complete1 the only circumstances which could defeat the derivative law are such as would destroy or counteract one or other of the combined causes4 ,while the causes exist and are not counteracted1 the effect will continue4 ,if they exist and are not counteracted to-morrow1 the sun will rise to-morrow4 ,since the causes1 namely1 the sun and the earth1 the one in the state of giving out light1 the other in a state of rotation1 will exist until something destroys them1 all depends on the probabilities of their destruction1 or of their counteraction4 ,we know by observation 7omitting the inferential proofs of an existence for thousands of ages anterior7 that these phenomena have continued for 7say7 five thousand years4 ,within that time there has existed no cause sufficient to diminish them appreciably1 nor which has counteracted their effect in any appreciable degree4 ,the chance1 therefore1 that the sun may not rise to-morrow amounts to the chance that some cause1 which has not manifested itself in the smallest degree during five thousand years1 will exist to-morrow in such intensity as to destroy the sun or the earth1 the sun's light or the earth's rotation1 or to produce an immense disturbance in the effect resulting from those causes4 ,now1 if such a cause will exist to-morrow1 or at any future time1 some cause1 proximate or remote1 of that cause must exist now1 and must have existed during the whole of the five thousand years4 ,if1 therefore1 the sun do not rise to-morrow1 it will be because some cause has existed1 the effects of which1 though during five thousand years they have not amounted to a perceptible quantity1 will in one day become overwhelming4 ,since this cause has not been recognized during such an interval of time by observers stationed on our earth1 it must1 if it be a single agent1 be either one whose effects develop themselves gradually and very slowly1 or one which existed in regions beyond our observation1 and is now on the point of arriving in our part of the universe4 ,now all causes which we have experience of act according to laws incompatible with the supposition that their effects1 after accumulating so slowly as to be imperceptible for five thousand years1 should start into immensity in a single day4 ,no mathematical law of proportion between an effect and the quantity or relations of its cause could produce such contradictory results4 ,the sudden development of an effect of which there was no previous trace always arises from the coming together of several distinct causes1 not previously conjoined2 but if such sudden conjunction is destined to take place1 the causes1 or their causes1 must have existed during the entire five thousand years2 and their not having once come together during that period shows how rare that particular combination is4 ,we have1 therefore1 the warrant of a rigid induction for considering it probable1 in a degree undistinguishable from certainty1 that the known conditions requisite for the sun's rising will exist to-morrow4 #c4 ,but this extension of derivative laws1 not causative1 beyond the limits of observation can only be to adjacent cases4 ,if1 instead of to-morrow1 we had said this day twenty thousand years1 the inductions would have been any thing but conclusive4 ,that a cause which1 in opposition to very powerful causes1 produced no perceptible effect during five thousand years1 should produce a very considerable one by the end of twenty thousand1 has nothing in it which is not in conformity with our experience of causes4 ,we know many agents1 the effect of which in a short period does not amount to a perceptible quantity1 but by accumulating for a much longer period becomes considerable4 ,besides1 looking at the immense multitude of the heavenly bodies1 their vast distances1 and the rapidity of the motion of such of them as are known to move1 it is a supposition not at all contradictory to experience that some body may be in motion toward us1 or we toward it1 within the limits of whose influence we have not come during five thousand years1 but which in twenty thousand more may be producing effects upon us of the most extraordinary kind4 ,or the fact which is capable of preventing sunrise may be1 not the cumulative effect of one cause1 but some new combination of causes2 and the chances favorable to that combination1 though they have not produced it once in five thousand years1 may produce it once in twenty thousand4 ,so that the inductions which authorize us to expect future events1 grow weaker and weaker the further we look into the future1 and at length become inappreciable4 ,we have considered the probabilities of the sun's rising to-morrow1 as derived from the real laws2 that is1 from the laws of the causes on which that uniformity is dependent4 ,let us now consider how the matter would have stood if the uniformity had been known only as an empirical law2 if we had not been aware that the sun's light and the earth's rotation 7or the sun's motion7 were the causes on which the periodical occurrence of daylight depends4 ,we could have extended this empirical law to cases adjacent in time1 though not to so great a distance of time as we can now4 ,having evidence that the effects had remained unaltered and been punctually conjoined for five thousand years1 we could infer that the unknown causes on which the conjunction is dependent had existed undiminished and uncounteracted during the same period4 ,the same conclusions1 therefore1 would follow as in the preceding case1 except that we should only know that during five thousand years nothing had occurred to defeat perceptibly this particular effect2 while1 when we know the causes1 we have the additional assurance that during that interval no such change has been noticeable in the causes themselves as by any degree of multiplication or length of continuance could defeat the effect4 ,to this must be added1 that when we know the causes1 we may be able to judge whether there exists any known cause capable of counteracting them1 while as long as they are unknown1 we can not be sure but that if we did know them1 we could predict their destruction from causes actually in existence4 ,a bed-ridden savage1 who had never seen the cataract of ,niagara1 but who lived within hearing of it1 might imagine that the sound he heard would endure forever2 but if he knew it to be the effect of a rush of waters over a barrier of rock which is progressively wearing away1 he would know that within a number of ages which may be calculated it will be heard no more4 ,in proportion1 therefore1 to our ignorance of the causes on which the empirical law depends1 we can be less assured that it will continue to hold good2 and the further we look into futurity1 the less improbable is it that some one of the causes1 whose co-existence gives rise to the derivative uniformity1 may be destroyed or counteracted4 ,with every prolongation of time the chances multiply of such an event2 that is to say1 its non-occurrence hitherto becomes a less guarantee of its not occurring within the given time4 ,if1 then1 it is only to cases which in point of time are adjacent 7or nearly adjacent7 to those which we have actually observed1 that any derivative law1 not of causation1 can be extended with an assurance equivalent to certainty1 much more is this true of a merely empirical law4 ,happily1 for the purposes of life it is to such cases alone that we can almost ever have occasion to extend them4 ,in respect of place1 it might seem that a merely empirical law could not be extended even to adjacent cases2 that we could have no assurance of its being true in any place where it has not been specially observed4 ,the past duration of a cause is a guarantee for its future existence1 unless something occurs to destroy it2 but the existence of a cause in one or any number of places is no guarantee for its existence in any other place1 since there is no uniformity in the collocations of primeval causes4 ,when1 therefore1 an empirical law is extended beyond the local limits within which it has been found true by observation1 the cases to which it is thus extended must be such as are presumably within the influence of the same individual agents4 ,if we discover a new planet within the known bounds of the solar system 7or even beyond those bounds1 but indicating its connection with the system by revolving round the sun71 we may conclude1 with great probability1 that it revolves on its axis4 ,for all the known planets do so2 and this uniformity points to some common cause1 antecedent to the first records of astronomical observation2 and though the nature of this cause can only be matter of conjecture1 yet if it be1 as is not unlikely1 and as ,laplace's theory supposes1 not merely the same kind of cause1 but the same individual cause 7such as an impulse given to all the bodies at once71 that cause1 acting at the extreme points of the space occupied by the sun and planets1 is likely1 unless defeated by some counteracting cause1 to have acted at every intermediate point1 and probably somewhat beyond2 and therefore acted1 in all probability1 upon the supposed newly-discovered planet4 ,when1 therefore1 effects which are always found conjoined can be traced with any probability to an identical 7and not merely a similar7 origin1 we may with the same probability extend the empirical law of their conjunction to all places within the extreme local boundaries within which the fact has been observed1 subject to the possibility of counteracting causes in some portion of the field4 ,still more confidently may we do so when the law is not merely empirical2 when the phenomena which we find conjoined are effects of ascertained causes1 from the laws of which the conjunction of their effects is deducible4 ,in that case1 we may both extend the derivative uniformity over a larger space1 and with less abatement for the chance of counteracting causes4 ,the first1 because instead of the local boundaries of our observation of the fact itself1 we may include the extreme boundaries of the ascertained influence of its causes4 ,thus the succession of day and night1 we know1 holds true of all the bodies of the solar system except the sun itself2 but we know this only because we are acquainted with the causes4 ,if we were not1 we could not extend the proposition beyond the orbits of the earth and moon1 at both extremities of which we have the evidence of observation for its truth4 ,with respect to the probability of counteracting causes1 it has been seen that this calls for a greater abatement of confidence1 in proportion to our ignorance of the causes on which the phenomena depend4 ,on both accounts1 therefore1 a derivative law which we know how to resolve1 is susceptible of a greater extension to cases adjacent in place1 than a merely empirical law4 ,chapter ,,xx4 ,of ,analogy4 #a4 ,the word ,analogy1 as the name of a mode of reasoning1 is generally taken for some kind of argument supposed to be of an inductive nature1 but not amounting to a complete induction4 ,there is no word1 however1 which is used more loosely1 or in a greater variety of senses1 than ,analogy4 ,it sometimes stands for arguments which may be examples of the most rigorous induction4 ,archbishop ,whately1 for instance1 following ,ferguson and other writers1 defines ,analogy conformably to its primitive acceptation1 that which was given to it by mathematicians3 ,resemblance of ,relations4 ,in this sense1 when a country which has sent out colonies is termed the mother country1 the expression is analogical1 signifying that the colonies of a country stand in the same relation to her in which children stand to their parents4 ,and if any inference be drawn from this resemblance of relations1 as1 for instance1 that obedience or affection is due from colonies to the mother country1 this is called reasoning by analogy4 ,or1 if it be argued that a nation is most beneficially governed by an assembly elected by the people1 from the admitted fact that other associations for a common purpose1 such as joint-stock companies1 are best managed by a committee chosen by the parties interested2 this1 too1 is an argument from analogy in the preceding sense1 because its foundation is1 not that a nation is like a joint-stock company1 or ,parliament like a board of directors1 but that ,parliament stands in the same relation to the nation in which a board of directors stands to a joint-stock company4 ,now1 in an argument of this nature1 there is no inherent inferiority of conclusiveness4 ,like other arguments from resemblance1 it may amount to nothing1 or it may be a perfect and conclusive induction4 ,the circumstance in which the two cases resemble1 may be capable of being shown to be the material circumstance2 to be that on which all the consequences1 necessary to be taken into account in the particular discussion1 depend4 ,in the example last given1 the resemblance is one of relation2 the fundamentum relationis being the management1 by a few persons1 of affairs in which a much greater number are interested along with them4 ,now1 some may contend that this circumstance which is common to the two cases1 and the various consequences which follow from it1 have the chief share in determining all the effects which make up what we term good or bad administration4 ,if they can establish this1 their argument has the force of a rigorous induction2 if they can not1 they are said to have failed in proving the analogy between the two cases2 a mode of speech which implies that when the analogy can be proved1 the argument founded on it can not be resisted4 #b4 ,it is on the whole more usual1 however1 to extend the name of analogical evidence to arguments from any sort of resemblance1 provided they do not amount to a complete induction2 without peculiarly distinguishing resemblance of relations4 ,analogical reasoning1 in this sense1 may be reduced to the following formula3 ,two things resemble each other in one or more respects2 a certain proposition is true of the one2 therefore it is true of the other4 ,but we have nothing here by which to discriminate analogy from induction1 since this type will serve for all reasoning from experience4 ,in the strictest induction1 equally with the faintest analogy1 we conclude because ,a resembles ,b in one or more properties1 that it does so in a certain other property4 ,the difference is1 that in the case of a complete induction it has been previously shown1 by due comparison of instances1 that there is an invariable conjunction between the former property or properties and the latter property2 but in what is called analogical reasoning1 no such conjunction has been made out4 ,there have been no opportunities of putting in practice the ,method of ,difference1 or even the ,method of ,agreement2 but we conclude 7and that is all which the argument of analogy amounts to7 that a fact m1 known to be true of ,a1 is more likely to be true of ,b if ,b agrees with ,a in some of its properties 7even though no connection is known to exist between m and those properties71 than if no resemblance at all could be traced between ,b and any other thing known to possess the attribute m4 ,to this argument it is of course requisite that the properties common to ,a with ,b shall be merely not known to be connected with m2 they must not be properties known to be unconnected with it4 ,if1 either by processes of elimination1 or by deduction from previous knowledge of the laws of the properties in question1 it can be concluded that they have nothing to do with m1 the argument of analogy is put out of court4 ,the supposition must be that m is an effect really dependent on some property of ,a1 but we know not on which4 ,we can not point out any of the properties of ,a1 which is the cause of m1 or united with it by any law4 ,after rejecting all which we know to have nothing to do with it1 there remain several between which we are unable to decide2 of which remaining properties1 ,b possesses one or more4 ,this1 accordingly1 we consider as affording grounds1 of more or less strength1 for concluding by analogy that ,b possesses the attribute m4 ,there can be no doubt that every such resemblance which can be pointed out between ,b and ,a1 affords some degree of probability1 beyond what would otherwise exist1 in favor of the conclusion drawn from it4 ,if ,b resembled ,a in all its ultimate properties1 its possessing the attribute m would be a certainty1 not a probability2 and every resemblance which can be shown to exist between them1 places it by so much the nearer to that point4 ,if the resemblance be in an ultimate property1 there will be resemblance in all the derivative properties dependent on that ultimate property1 and of these m may be one4 ,if the resemblance be in a derivative property1 there is reason to expect resemblance in the ultimate property on which it depends1 and in the other derivative properties dependent on the same ultimate property4 ,every resemblance which can be shown to exist1 affords ground for expecting an indefinite number of other resemblances2 the particular resemblance sought will1 therefore1 be oftener found among things thus known to resemble1 than among things between which we know of no resemblance4 ,for example1 ,i might infer that there are probably inhabitants in the moon1 because there are inhabitants on the earth1 in the sea1 and in the air3 and this is the evidence of analogy4 ,the circumstance of having inhabitants is here assumed not to be an ultimate property1 but 7as is reasonable to suppose7 a consequence of other properties2 and depending1 therefore1 in the case of the earth1 on some of its properties as a portion of the universe1 but on which of those properties we know not4 ,now the moon resembles the earth in being a solid1 opaque1 nearly spherical substance1 appearing to contain1 or to have contained1 active volcanoes2 receiving heat and light from the sun1 in about the same quantity as our earth2 revolving on its axis2 composed of materials which gravitate1 and obeying all the various laws resulting from that property4 ,and ,i think no one will deny that if this were all that was known of the moon1 the existence of inhabitants in that luminary would derive from these various resemblances to the earth1 a greater degree of probability than it would otherwise have2 though the amount of the augmentation it would be useless to attempt to estimate4 ,if1 however1 every resemblance proved between ,b and ,a1 in any point not known to be immaterial with respect to m1 forms some additional reason for presuming that ,b has the attribute m2 it is clear1 contra1 that every dissimilarity which can be proved between them furnishes a counter-probability of the same nature on the other side4 ,it is not1 indeed1 unusual that different ultimate properties should1 in some particular instances1 produce the same derivative property2 but on the whole it is certain that things which differ in their ultimate properties1 will differ at least as much in the aggregate of their derivative properties1 and that the differences which are unknown will1 on the average of cases1 bear some proportion to those which are known4 ,there will1 therefore1 be a competition between the known points of agreement and the known points of difference in ,a and ,b2 and according as the one or the other may be deemed to preponderate1 the probability derived from analogy will be for or against ,b's having the property m4 ,the moon1 for instance1 agrees with the earth in the circumstances already mentioned2 but differs in being smaller1 in having its surface more unequal1 and apparently volcanic throughout1 in having1 at least on the side next the earth1 no atmosphere sufficient to refract light1 no clouds1 and 7it is therefore concluded7 no water4 ,these differences1 considered merely as such1 might perhaps balance the resemblances1 so that analogy would afford no presumption either way4 ,but considering that some of the circumstances which are wanting on the moon are among those which1 on the earth1 are found to be indispensable conditions of animal life1 we may conclude that if that phenomenon does exist in the moon 7or at all events on the nearer side71 it must be as an effect of causes totally different from those on which it depends here2 as a consequence1 therefore1 of the moon's differences from the earth1 not of the points of agreement4 ,viewed in this light1 all the resemblances which exist become presumptions against1 not in favor of1 the moon's being inhabited4 ,since life can not exist there in the manner in which it exists here1 the greater the resemblance of the lunar world to the terrestrial in other respects1 the less reason we have to believe that it can contain life4 ,there are1 however1 other bodies in our system1 between which and the earth there is a much closer resemblance2 which possess an atmosphere1 clouds1 consequently water 7or some fluid analogous to it71 and even give strong indications of snow in their polar regions2 while the cold1 or heat1 though differing greatly on the average from ours1 is1 in some parts at least of those planets1 possibly not more extreme than in some regions of our own which are habitable4 ,to balance these agreements1 the ascertained differences are chiefly in the average light and heat1 velocity of rotation1 density of material1 intensity of gravity1 and similar circumstances of a secondary kind4 ,with regard to these planets1 therefore1 the argument of analogy gives a decided preponderance in favor of their resembling the earth in any of its derivative properties1 such as that of having inhabitants2 though when we consider how immeasurably multitudinous are those of their properties which we are entirely ignorant of1 compared with the few which we know1 we can attach but trifling weight to any considerations of resemblance in which the known elements bear so inconsiderable a proportion to the unknown4 ,besides the competition between analogy and diversity1 there may be a competition of conflicting analogies4 ,the new case may be similar in some of its circumstances to cases in which the fact m exists1 but in others to cases in which it is known not to exist4 ,amber has some properties in common with vegetable1 others with mineral products4 ,a painting of unknown origin may resemble1 in certain of its characters1 known works of a particular master1 but in others it may as strikingly resemble those of some other painter4 ,a vase may bear some analogy to works of ,grecian1 and some to those of ,etruscan1 or ,egyptian art4 ,we are of course supposing that it does not possess any quality which has been ascertained1 by a sufficient induction1 to be a conclusive mark either of the one or of the other4 #c4 ,since the value of an analogical argument inferring one resemblance from other resemblances without any antecedent evidence of a connection between them1 depends on the extent of ascertained resemblance1 compared first with the amount of ascertained difference1 and next with the extent of the unexplored region of unascertained properties2 it follows that where the resemblance is very great1 the ascertained difference very small1 and our knowledge of the subject-matter tolerably extensive1 the argument from analogy may approach in strength very near to a valid induction4 ,if1 after much observation of ,b1 we find that it agrees with ,a in nine out of ten of its known properties1 we may conclude with a probability of nine to one1 that it will possess any given derivative property of ,a4 ,if we discover1 for example1 an unknown animal or plant1 resembling closely some known one in the greater number of the properties we observe in it1 but differing in some few1 we may reasonably expect to find in the unobserved remainder of its properties1 a general agreement with those of the former2 but also a difference corresponding proportionately to the amount of observed diversity4 ,it thus appears that the conclusions derived from analogy are only of any considerable value1 when the case to which we reason is an adjacent case2 adjacent1 not as before1 in place or time1 but in circumstances4 ,in the case of effects of which the causes are imperfectly or not at all known1 when consequently the observed order of their occurrence amounts only to an empirical law1 it often happens that the conditions which have co-existed whenever the effect was observed1 have been very numerous4 ,now if a new case presents itself1 in which all these conditions do not exist1 but the far greater part of them do1 some one or a few only being wanting1 the inference that the effect will occur1 notwithstanding this deficiency of complete resemblance to the cases in which it has been observed1 may1 though of the nature of analogy1 possess a high degree of probability4 ,it is hardly necessary to add that1 however considerable this probability may be1 no competent inquirer into nature will rest satisfied with it when a complete induction is attainable2 but will consider the analogy as a mere guide-post1 pointing out the direction in which more rigorous investigations should be prosecuted4 ,it is in this last respect that considerations of analogy have the highest scientific value4 ,the cases in which analogical evidence affords in itself any very high degree of probability1 are1 as we have observed1 only those in which the resemblance is very close and extensive2 but there is no analogy1 however faint1 which may not be of the utmost value in suggesting experiments or observations that may lead to more positive conclusions4 ,when the agents and their effects are out of the reach of further observation and experiment1 as in the speculations already alluded to respecting the moon and planets1 such slight probabilities are no more than an interesting theme for the pleasant exercise of imagination2 but any suspicion1 however slight1 that sets an ingenious person at work to contrive an experiment1 or affords a reason for trying one experiment rather than another1 may be of the greatest benefit to science4 ,on this ground1 though ,i can not accept as positive truths any of those scientific hypotheses which are unsusceptible of being ultimately brought to the test of actual induction1 such1 for instance1 as the two theories of light1 the emission theory of the last century1 and the undulatory theory which predominates in the present1 ,i am yet unable to agree with those who consider such hypotheses to be worthy of entire disregard4 ,as is well said by ,hartley 7and concurred in by a thinker in general so diametrically opposed to ,hartley's opinions as ,dugald ,stewart71 8any hypothesis which has so much plausibility as to explain a considerable number of facts1 helps us to digest these facts in proper order1 to bring new ones to light1 and make experimenta crucis for the sake of future inquirers407#ahc7 ,if an hypothesis both explains known facts1 and has led to the prediction of others previously unknown1 and since verified by experience1 the laws of the phenomenon which is the subject of inquiry must bear at least a great similarity to those of the class of phenomena to which the hypothesis assimilates it2 and since the analogy which extends so far may probably extend further1 nothing is more likely to suggest experiments tending to throw light upon the real properties of the phenomenon1 than the following out such an hypothesis4 ,but to this end it is by no means necessary that the hypothesis be mistaken for a scientific truth4 ,on the contrary1 that illusion is in this respect1 as in every other1 an impediment to the progress of real knowledge1 by leading inquirers to restrict themselves arbitrarily to the particular hypothesis which is most accredited at the time1 instead of looking out for every class of phenomena between the laws of which and those of the given phenomenon any analogy exists1 and trying all such experiments as may tend to the discovery of ulterior analogies pointing in the same direction4 ,chapter ,,xxi4 ,of ,the ,evidence ,of ,the ,law ,of ,universal ,causation4 #a4 ,we have now completed our review of the logical processes by which the laws1 or uniformities1 of the sequence of phenomena1 and those uniformities in their co-existence which depend on the laws of their sequence1 are ascertained or tested4 ,as we recognized in the commencement1 and have been enabled to see more clearly in the progress of the investigation1 the basis of all these logical operations is the law of causation4 ,the validity of all the ,inductive ,methods depends on the assumption that every event1 or the beginning of every phenomenon1 must have some cause2 some antecedent1 on the existence of which it is invariably and unconditionally consequent4 ,in the ,method of ,agreement this is obvious2 that method avowedly proceeding on the supposition that we have found the true cause as soon as we have negatived every other4 ,the assertion is equally true of the ,method of ,difference4 ,that method authorizes us to infer a general law from two instances2 one1 in which ,a exists together with a multitude of other circumstances1 and ,b follows2 another1 in which1 ,a being removed1 and all other circumstances remaining the same1 ,b is prevented4 ,what1 however1 does this prove8 ,it proves that ,b1 in the particular instance1 can not have had any other cause than ,a2 but to conclude from this that ,a was the cause1 or that ,a will on other occasions be followed by ,b1 is only allowable on the assumption that ,b must have some cause2 that among its antecedents in any single instance in which it occurs1 there must be one which has the capacity of producing it at other times4 ,this being admitted1 it is seen that in the case in question that antecedent can be no other than ,a2 but that if it be no other than ,a it must be ,a1 is not proved1 by these instances at least1 but taken for granted4 ,there is no need to spend time in proving that the same thing is true of the other ,inductive ,methods4 ,the universality of the law of causation is assumed in them all4 ,but is this assumption warranted8 ,doubtless 7it may be said7 most phenomena are connected as effects with some antecedent or cause1 that is1 are never produced unless some assignable fact has preceded them2 but the very circumstance that complicated processes of induction are sometimes necessary1 shows that cases exist in which this regular order of succession is not apparent to our unaided apprehension4 ,if1 then1 the processes which bring these cases within the same category with the rest1 require that we should assume the universality of the very law which they do not at first sight appear to exemplify1 is not this a petitio principii8 ,can we prove a proposition1 by an argument which takes it for granted8 ,and if not so proved1 on what evidence does it rest8 ,for this difficulty1 which ,i have purposely stated in the strongest terms it will admit of1 the school of metaphysicians who have long predominated in this country find a ready salvo4 ,they affirm1 that the universality of causation is a truth which we can not help believing2 that the belief in it is an instinct1 one of the laws of our believing faculty4 ,as the proof of this1 they say1 and they have nothing else to say1 that every body does believe it2 and they number it among the propositions1 rather numerous in their catalogue1 which may be logically argued against1 and perhaps can not be logically proved1 but which are of higher authority than logic1 and so essentially inherent in the human mind1 that even he who denies them in speculation1 shows by his habitual practice that his arguments make no impression upon himself4 ,into the merits of this question1 considered as one of psychology1 it would be foreign to my purpose to enter here2 but ,i must protest against adducing1 as evidence of the truth of a fact in external nature1 the disposition1 however strong or however general1 of the human mind to believe it4 ,belief is not proof1 and does not dispense with the necessity of proof4 ,i am aware1 that to ask for evidence of a proposition which we are supposed to believe instinctively1 is to expose one's self to the charge of rejecting the authority of the human faculties2 which of course no one can consistently do1 since the human faculties are all which any one has to judge by2 and inasmuch as the meaning of the word evidence is supposed to be1 something which when laid before the mind1 induces it to believe2 to demand evidence when the belief is insured by the mind's own laws1 is supposed to be appealing to the intellect against the intellect4 ,but this1 ,i apprehend1 is a misunderstanding of the nature of evidence4 ,by evidence is not meant any thing and every thing which produces belief4 ,there are many things which generate belief besides evidence4 ,a mere strong association of ideas often causes a belief so intense as to be unshakable by experience or argument4 ,evidence is not that which the mind does or must yield to1 but that which it ought to yield to1 namely1 that1 by yielding to which its belief is kept conformable to fact4 ,there is no appeal from the human faculties generally1 but there is an appeal from one human faculty to another2 from the judging faculty1 to those which take cognizance of fact1 the faculties of sense and consciousness4 ,the legitimacy of this appeal is admitted whenever it is allowed that our judgments ought to be conformable to fact4 ,to say that belief suffices for its own justification is making opinion the test of opinion2 it is denying the existence of any outward standard1 the conformity of an opinion to which constitutes its truth4 ,we call one mode of forming opinions right and another wrong1 because the one does1 and the other does not1 tend to make the opinion agree with the fact--to make people believe what really is1 and expect what really will be4 ,now a mere disposition to believe1 even if supposed instinctive1 is no guarantee for the truth of the thing believed4 ,if1 indeed1 the belief ever amounted to an irresistible necessity1 there would then be no use in appealing from it1 because there would be no possibility of altering it4 ,but even then the truth of the belief would not follow2 it would only follow that mankind were under a permanent necessity of believing what might possibly not be true2 in other words1 that a case might occur in which our senses or consciousness1 if they could be appealed to1 might testify one thing1 and our reason believe another4 ,but in fact there is no such permanent necessity4 ,there is no proposition of which it can be asserted that every human mind must eternally and irrevocably believe it4 ,many of the propositions of which this is most confidently stated1 great numbers of human beings have disbelieved4 ,the things which it has been supposed that nobody could possibly help believing1 are innumerable2 but no two generations would make out the same catalogue of them4 ,one age or nation believes implicitly what to another seems incredible and inconceivable2 one individual has not a vestige of a belief which another deems to be absolutely inherent in humanity4 ,there is not one of these supposed instinctive beliefs which is really inevitable4 ,it is in the power of every one to cultivate habits of thought which make him independent of them4 ,the habit of philosophical analysis 7of which it is the surest effect to enable the mind to command1 instead of being commanded by1 the laws of the merely passive part of its own nature71 by showing to us that things are not necessarily connected in fact because their ideas are connected in our minds1 is able to loosen innumerable associations which reign despotically over the undisciplined or early-prejudiced mind4 ,and this habit is not without power even over those associations which the school of which ,i have been speaking regard as connate and instinctive4 ,i am convinced that any one accustomed to abstraction and analysis1 who will fairly exert his faculties for the purpose1 will1 when his imagination has once learned to entertain the notion1 find no difficulty in conceiving that in some one1 for instance1 of the many firmaments into which sidereal astronomy now divides the universe1 events may succeed one another at random1 without any fixed law2 nor can any thing in our experience1 or in our mental nature1 constitute a sufficient1 or indeed any1 reason for believing that this is nowhere the case4 ,were we to suppose 7what it is perfectly possible to imagine7 that the present order of the universe were brought to an end1 and that a chaos succeeded in which there was no fixed succession of events1 and the past gave no assurance of the future2 if a human being were miraculously kept alive to witness this change1 he surely would soon cease to believe in any uniformity1 the uniformity itself no longer existing4 ,if this be admitted1 the belief in uniformity either is not an instinct1 or it is an instinct conquerable1 like all other instincts1 by acquired knowledge4 ,but there is no need to speculate on what might be1 when we have positive and certain knowledge of what has been4 ,it is not true1 as a matter of fact1 that mankind have always believed that all the successions of events were uniform and according to fixed laws4 ,the ,greek philosophers1 not even excepting ,aristotle1 recognized ,chance and ,spontaneity 7 and 7 as among the agents in nature2 in other words1 they believed that to that extent there was no guarantee that the past had been similar to itself1 or that the future would resemble the past4 ,even now a full half of the philosophical world1 including the very same metaphysicians who contend most for the instinctive character of the belief in uniformity1 consider one important class of phenomena1 volitions1 to be an exception to the uniformity1 and not governed by a fixed law47#ahd7 #b4 ,as was observed in a former place17#ahe7 the belief we entertain in the universality1 throughout nature1 of the law of cause and effect1 is itself an instance of induction2 and by no means one of the earliest which any of us1 or which mankind in general1 can have made4 ,we arrive at this universal law1 by generalization from many laws of inferior generality4 ,we should never have had the notion of causation 7in the philosophical meaning of the term7 as a condition of all phenomena1 unless many cases of causation1 or in other words1 many partial uniformities of sequence1 had previously become familiar4 ,the more obvious of the particular uniformities suggest1 and give evidence of1 the general uniformity1 and the general uniformity1 once established1 enables us to prove the remainder of the particular uniformities of which it is made up4 ,as1 however1 all rigorous processes of induction presuppose the general uniformity1 our knowledge of the particular uniformities from which it was first inferred was not1 of course1 derived from rigorous induction1 but from the loose and uncertain mode of induction per enumerationem simplicem2 and the law of universal causation1 being collected from results so obtained1 can not itself rest on any better foundation4 ,it would seem1 therefore1 that induction per enumerationem simplicem not only is not necessarily an illicit logical process1 but is in reality the only kind of induction possible2 since the more elaborate process depends for its validity on a law1 itself obtained in that inartificial mode4 ,is there not then an inconsistency in contrasting the looseness of one method with the rigidity of another1 when that other is indebted to the looser method for its own foundation8 ,the inconsistency1 however1 is only apparent4 ,assuredly1 if induction by simple enumeration were an invalid process1 no process grounded on it could be valid2 just as no reliance could be placed on telescopes1 if we could not trust our eyes4 ,but though a valid process1 it is a fallible one1 and fallible in very different degrees3 if1 therefore1 we can substitute for the more fallible forms of the process1 an operation grounded on the same process in a less fallible form1 we shall have effected a very material improvement4 ,and this is what scientific induction does4 ,a mode of concluding from experience must be pronounced untrustworthy when subsequent experience refuses to confirm it4 ,according to this criterion1 induction by simple enumeration--in other words1 generalization of an observed fact from the mere absence of any known instance to the contrary--affords in general a precarious and unsafe ground of assurance2 for such generalizations are incessantly discovered1 on further experience1 to be false4 ,still1 however1 it affords some assurance1 sufficient1 in many cases1 for the ordinary guidance of conduct4 ,it would be absurd to say1 that the generalizations arrived at by mankind in the outset of their experience1 such as these--food nourishes1 fire burns1 water drowns--were unworthy of reliance47#ahf7 ,there is a scale of trustworthiness in the results of the original unscientific induction2 and on this diversity 7as observed in the fourth chapter of the present book7 depend the rules for the improvement of the process4 ,the improvement consists in correcting one of these inartificial generalizations by means of another4 ,as has been already pointed out1 this is all that art can do4 ,to test a generalization1 by showing that it either follows from1 or conflicts with1 some stronger induction1 some generalization resting on a broader foundation of experience1 is the beginning and end of the logic of induction4 #c4 ,now the precariousness of the method of simple enumeration is in an inverse ratio to the largeness of the generalization4 ,the process is delusive and insufficient1 exactly in proportion as the subject-matter of the observation is special and limited in extent4 ,as the sphere widens1 this unscientific method becomes less and less liable to mislead2 and the most universal class of truths1 the law of causation1 for instance1 and the principles of number and of geometry1 are duly and satisfactorily proved by that method alone1 nor are they susceptible of any other proof4 ,with respect to the whole class of generalizations of which we have recently treated1 the uniformities which depend on causation1 the truth of the remark just made follows by obvious inference from the principles laid down in the preceding chapters4 ,when a fact has been observed a certain number of times to be true1 and is not in any instance known to be false1 if we at once affirm that fact as a universal truth or law of nature1 without either testing it by any of the four methods of induction1 or deducing it from other known laws1 we shall in general err grossly2 but we are perfectly justified in affirming it as an empirical law1 true within certain limits of time1 place1 and circumstance1 provided the number of coincidences be greater than can with any probability be ascribed to chance4 ,the reason for not extending it beyond those limits is1 that the fact of its holding true within them may be a consequence of collocations1 which can not be concluded to exist in one place because they exist in another2 or may be dependent on the accidental absence of counteracting agencies1 which any variation of time1 or the smallest change of circumstances1 may possibly bring into play4 ,if we suppose1 then1 the subject-matter of any generalization to be so widely diffused that there is no time1 no place1 and no combination of circumstances1 but must afford an example either of its truth or of its falsity1 and if it be never found otherwise than true1 its truth can not be contingent on any collocations1 unless such as exist at all times and places2 nor can it be frustrated by any counteracting agencies1 unless by such as never actually occur4 ,it is1 therefore1 an empirical law co-extensive with all human experience2 at which point the distinction between empirical laws and laws of nature vanishes1 and the proposition takes its place among the most firmly established as well as largest truths accessible to science4 ,now1 the most extensive in its subject-matter of all generalizations which experience warrants1 respecting the sequences and co-existences of phenomena1 is the law of causation4 ,it stands at the head of all observed uniformities1 in point of universality1 and therefore 7if the preceding observations are correct7 in point of certainty4 ,and if we consider1 not what mankind would have been justified in believing in the infancy of their knowledge1 but what may rationally be believed in its present more advanced state1 we shall find ourselves warranted in considering this fundamental law1 though itself obtained by induction from particular laws of causation1 as not less certain1 but on the contrary1 more so1 than any of those from which it was drawn4 ,it adds to them as much proof as it receives from them4 ,for there is probably no one even of the best established laws of causation which is not sometimes counteracted1 and to which1 therefore1 apparent exceptions do not present themselves1 which would have necessarily and justly shaken the confidence of mankind in the universality of those laws1 if inductive processes founded on the universal law had not enabled us to refer those exceptions to the agency of counteracting causes1 and thereby reconcile them with the law with which they apparently conflict4 ,errors1 moreover1 may have slipped into the statement of any one of the special laws1 through inattention to some material circumstance3 and instead of the true proposition1 another may have been enunciated1 false as a universal law1 though leading1 in all cases hitherto observed1 to the same result4 ,to the law of causation1 on the contrary1 we not only do not know of any exception1 but the exceptions which limit or apparently invalidate the special laws1 are so far from contradicting the universal one1 that they confirm it2 since in all cases which are sufficiently open to our observation1 we are able to trace the difference of result1 either to the absence of a cause which had been present in ordinary cases1 or to the presence of one which had been absent4 ,the law of cause and effect1 being thus certain1 is capable of imparting its certainty to all other inductive propositions which can be deduced from it2 and the narrower inductions may be regarded as receiving their ultimate sanction from that law1 since there is no one of them which is not rendered more certain than it was before1 when we are able to connect it with that larger induction1 and to show that it can not be denied1 consistently with the law that every thing which begins to exist has a cause4 ,and hence we are justified in the seeming inconsistency1 of holding induction by simple enumeration to be good for proving this general truth1 the foundation of scientific induction1 and yet refusing to rely on it for any of the narrower inductions4 ,i fully admit that if the law of causation were unknown1 generalization in the more obvious cases of uniformity in phenomena would nevertheless be possible1 and though in all cases more or less precarious1 and in some extremely so1 would suffice to constitute a certain measure of probability2 but what the amount of this probability might be1 we are dispensed from estimating1 since it never could amount to the degree of assurance which the proposition acquires1 when1 by the application to it of the ,four ,methods1 the supposition of its falsity is shown to be inconsistent with the ,law of ,causation4 ,we are therefore logically entitled1 and1 by the necessities of scientific induction1 required1 to disregard the probabilities derived from the early rude method of generalizing1 and to consider no minor generalization as proved except so far as the law of causation confirms it1 nor probable except so far as it may reasonably be expected to be so confirmed4 #d4 ,the assertion1 that our inductive processes assume the law of causation1 while the law of causation is itself a case of induction1 is a paradox1 only on the old theory of reasoning1 which supposes the universal truth1 or major premise1 in a ratiocination1 to be the real proof of the particular truths which are ostensibly inferred from it4 ,according to the doctrine maintained in the present treatise17#ahg7 the major premise is not the proof of the conclusion1 but is itself proved1 along with the conclusion from the same evidence4 8,all men are mortal0 is not the proof that ,lord ,palmerston is mortal2 but our past experience of mortality authorizes us to infer both the general truth and the particular fact1 and the one with exactly the same degree of assurance as the other4 ,the mortality of ,lord ,palmerston is not an inference from the mortality of all men1 but from the experience which proves the mortality of all men2 and is a correct inference from experience1 if that general truth is so too4 ,this relation between our general beliefs and their particular applications holds equally true in the more comprehensive case which we are now discussing4 ,any new fact of causation inferred by induction1 is rightly inferred1 if no other objection can be made to the inference than can be made to the general truth that every event has a cause4 ,the utmost certainty which can be given to a conclusion arrived at in the way of inference1 stops at this point4 ,when we have ascertained that the particular conclusion must stand or fall with the general uniformity of the laws of nature--that it is liable to no doubt except the doubt whether every event has a cause--we have done all that can be done for it4 ,the strongest assurance we can obtain of any theory respecting the cause of a given phenomenon1 is that the phenomenon has either that cause or none4 ,the latter supposition might have been an admissible one in a very early period of our study of nature4 ,but we have been able to perceive that in the stage which mankind have now reached1 the generalization which gives the ,law of ,universal ,causation has grown into a stronger and better induction1 one deserving of greater reliance1 than any of the subordinate generalizations4 ,we may even1 ,i think1 go a step further than this1 and regard the certainty of that great induction as not merely comparative1 but1 for all practical purposes1 complete4 ,the considerations1 which1 as ,i apprehend1 give1 at the present day1 to the proof of the law of uniformity of succession as true of all phenomena without exception1 this character of completeness and conclusiveness1 are the following3 ,first1 that we now know it directly to be true of far the greatest number of phenomena2 that there are none of which we know it not to be true1 the utmost that can be said being1 that of some we can not positively from direct evidence affirm its truth2 while phenomenon after phenomenon1 as they become better known to us1 are constantly passing from the latter class into the former2 and in all cases in which that transition has not yet taken place1 the absence of direct proof is accounted for by the rarity or the obscurity of the phenomena1 our deficient means of observing them1 or the logical difficulties arising from the complication of the circumstances in which they occur2 insomuch that1 notwithstanding as rigid a dependence on given conditions as exists in the case of any other phenomenon1 it was not likely that we should be better acquainted with those conditions than we are4 ,besides this first class of considerations1 there is a second1 which still further corroborates the conclusion4 ,although there are phenomena the production and changes of which elude all our attempts to reduce them universally to any ascertained law2 yet in every such case1 the phenomenon1 or the objects concerned in it1 are found in some instances to obey the known laws of nature4 ,the wind1 for example1 is the type of uncertainty and caprice1 yet we find it in some cases obeying with as much constancy as any phenomenon in nature the law of the tendency of fluids to distribute themselves so as to equalize the pressure on every side of each of their particles2 as in the case of the trade-winds and the monsoons4 ,lightning might once have been supposed to obey no laws2 but since it has been ascertained to be identical with electricity1 we know that the very same phenomenon in some of its manifestations is implicitly obedient to the action of fixed causes4 ,i do not believe that there is now one object or event in all our experience of nature1 within the bounds of the solar system at least1 which has not either been ascertained by direct observation to follow laws of its own1 or been proved to be closely similar to objects and events which1 in more familiar manifestations1 or on a more limited scale1 follow strict laws2 our inability to trace the same laws on a larger scale and in the more recondite instances1 being accounted for by the number and complication of the modifying causes1 or by their inaccessibility to observation4 ,the progress of experience1 therefore1 has dissipated the doubt which must have rested on the universality of the law of causation while there were phenomena which seemed to be sui generis1 not subject to the same laws with any other class of phenomena1 and not as yet ascertained to have peculiar laws of their own4 ,this great generalization1 however1 might reasonably have been1 as it in fact was1 acted on as a probability of the highest order1 before there were sufficient grounds for receiving it as a certainty4 ,in matters of evidence1 as in all other human things1 we neither require1 nor can attain1 the absolute4 ,we must hold even our strongest convictions with an opening left in our minds for the reception of facts which contradict them2 and only when we have taken this precaution1 have we earned the right to act upon our convictions with complete confidence when no such contradiction appears4 ,whatever has been found true in innumerable instances1 and never found to be false after due examination in any1 we are safe in acting on as universal provisionally1 until an undoubted exception appears2 provided the nature of the case be such that a real exception could scarcely have escaped notice4 ,when every phenomenon that we ever knew sufficiently well to be able to answer the question1 had a cause on which it was invariably consequent1 it was more rational to suppose that our inability to assign the causes of other phenomena arose from our ignorance1 than that there were phenomena which were uncaused1 and which happened to be exactly those which we had hitherto had no sufficient opportunity of studying4 ,it must1 at the same time1 be remarked1 that the reasons for this reliance do not hold in circumstances unknown to us1 and beyond the possible range of our experience4 ,in distant parts of the stellar regions1 where the phenomena may be entirely unlike those with which we are acquainted1 it would be folly to affirm confidently that this general law prevails1 any more than those special ones which we have found to hold universally on our own planet4 ,the uniformity in the succession of events1 otherwise called the law of causation1 must be received not as a law of the universe1 but of that portion of it only which is within the range of our means of sure observation1 with a reasonable degree of extension to adjacent cases4 ,to extend it further is to make a supposition without evidence1 and to which1 in the absence of any ground from experience for estimating its degree of probability1 it would be idle to attempt to assign any47#ahh7 ,chapter ,,xxii4 ,of ,uniformities ,of ,co-,existence ,not ,dependent ,on ,causation4 #a4 ,the order of the occurrence of phenomena in time1 is either successive or simultaneous2 the uniformities1 therefore1 which obtain in their occurrence1 are either uniformities of succession or of co-existence4 ,uniformities of succession are all comprehended under the law of causation and its consequences4 ,every phenomenon has a cause1 which it invariably follows2 and from this are derived other invariable sequences among the successive stages of the same effect1 as well as between the effects resulting from causes which invariably succeed one another4 ,in the same manner with these derivative uniformities of succession1 a great variety of uniformities of co-existence also take their rise4 ,co-ordinate effects of the same cause naturally co-exist with one another4 ,high water at any point on the earth's surface1 and high water at the point diametrically opposite to it1 are effects uniformly simultaneous1 resulting from the direction in which the combined attractions of the sun and moon act upon the waters of the ocean4 ,an eclipse of the sun to us1 and an eclipse of the earth to a spectator situated in the moon1 are in like manner phenomena invariably co-existent2 and their co-existence can equally be deduced from the laws of their production4 ,it is an obvious question1 therefore1 whether all the uniformities of co-existence among phenomena may not be accounted for in this manner4 ,and it can not be doubted that between phenomena which are themselves effects1 the co-existences must necessarily depend on the causes of those phenomena4 ,if they are effects immediately or remotely of the same cause1 they can not co-exist except by virtue of some laws or properties of that cause2 if they are effects of different causes1 they can not co-exist unless it be because their causes co-exist2 and the uniformity of co-existence1 if such there be1 between the effects1 proves that those particular causes1 within the limits of our observation1 have uniformly been co-existent4 #b4 ,but these same considerations compel us to recognize that there must be one class of co-existences which can not depend on causation3 the co-existences between the ultimate properties of things--those properties which are the causes of all phenomena1 but are not themselves caused by any phenomenon1 and a cause for which could only be sought by ascending to the origin of all things4 ,yet among these ultimate properties there are not only co-existences1 but uniformities of co-existence4 ,general propositions may be1 and are1 formed1 which assert that whenever certain properties are found1 certain others are found along with them4 ,we perceive an object2 say1 for instance1 water4 ,we recognize it to be water1 of course by certain of its properties4 ,having recognized it1 we are able to affirm of it innumerable other properties2 which we could not do unless it were a general truth1 a law or uniformity in nature1 that the set of properties by which we identify the substance as water always have those other properties conjoined with them4 ,in a former place7#ahi7 it has been explained1 in some detail1 what is meant by the ,kinds of objects2 those classes which differ from one another not by a limited and definite1 but by an indefinite and unknown1 number of distinctions4 ,to this we have now to add1 that every proposition by which any thing is asserted of a ,kind1 affirms a uniformity of co-existence4 ,since we know nothing of ,kinds but their properties1 the ,kind1 to us1 is the set of properties by which it is identified1 and which must of course be sufficient to distinguish it from every other kind47#aij7 ,in affirming any thing1 therefore1 of a ,kind1 we are affirming something to be uniformly co-existent with the properties by which the kind is recognized2 and that is the sole meaning of the assertion4 ,among the uniformities of co-existence which exist in nature1 may hence be numbered all the properties of ,kinds4 ,the whole of these1 however1 are not independent of causation1 but only a portion of them4 ,some are ultimate properties1 others derivative3 of some1 no cause can be assigned1 but others are manifestly dependent on causes4 ,thus1 pure oxygen gas is a ,kind1 and one of its most unequivocal properties is its gaseous form2 this property1 however1 has for its cause the presence of a certain quantity of latent heat2 and if that heat could be taken away 7as has been done from so many gases in ,faraday's experiments71 the gaseous form would doubtless disappear1 together with numerous other properties which depend on1 or are caused by1 that property4 ,in regard to all substances which are chemical compounds1 and which therefore may be regarded as products of the juxtaposition of substances different in ,kind from themselves1 there is considerable reason to presume that the specific properties of the compound are consequent1 as effects1 on some of the properties of the elements1 though little progress has yet been made in tracing any invariable relation between the latter and the former4 ,still more strongly will a similar presumption exist1 when the object itself1 as in the case of organized beings1 is no primeval agent1 but an effect1 which depends on a cause or causes for its very existence4 ,the ,kinds1 therefore1 which are called in chemistry simple substances1 or elementary natural agents1 are the only ones1 any of whose properties can with certainty be considered ultimate2 and of these the ultimate properties are probably much more numerous than we at present recognize1 since every successful instance of the resolution of the properties of their compounds into simpler laws1 generally leads to the recognition of properties in the elements distinct from any previously known4 ,the resolution of the laws of the heavenly motions established the previously unknown ultimate property of a mutual attraction between all bodies2 the resolution1 so far as it has yet proceeded1 of the laws of crystallization1 of chemical composition1 electricity1 magnetism1 etc41 points to various polarities1 ultimately inherent in the particles of which bodies are composed2 the comparative atomic weights of different kinds of bodies were ascertained by resolving into more general laws the uniformities observed in the proportions in which substances combine with one another1 and so forth4 ,thus1 although every resolution of a complex uniformity into simpler and more elementary laws has an apparent tendency to diminish the number of the ultimate properties1 and really does remove many properties from the list2 yet 7since the result of this simplifying process is to trace up an ever greater variety of different effects to the same agents7 the further we advance in this direction1 the greater number of distinct properties we are forced to recognize in one and the same object2 the co-existences of which properties must accordingly be ranked among the ultimate generalities of nature4 #c4 ,there are1 therefore1 only two kinds of propositions which assert uniformity of co-existence between properties4 ,either the properties depend on causes or they do not4 ,if they do1 the proposition which affirms them to be co-existent is a derivative law of co-existence between effects1 and1 until resolved into the laws of causation on which it depends1 is an empirical law1 and to be tried by the principles of induction to which such laws are amenable4 ,if1 on the other hand1 the properties do not depend on causes1 but are ultimate properties1 then1 if it be true that they invariably co-exist1 they must all be ultimate properties of one and the same ,kind2 and it is of these only that the co-existences can be classed as a peculiar sort of laws of nature4 ,when we affirm that all crows are black1 or that all negroes have woolly hair1 we assert a uniformity of co-existence4 ,we assert that the property of blackness or of having woolly hair invariably co-exists with the properties which1 in common language1 or in the scientific classification that we adopt1 are taken to constitute the class crow1 or the class negro4 ,now1 supposing blackness to be an ultimate property of black objects1 or woolly hair an ultimate property of the animals which possess it2 supposing that these properties are not results of causation1 are not connected with antecedent phenomena by any law2 then if all crows are black1 and all negroes have woolly hair1 these must be ultimate properties of the kind crow1 or negro1 or of some kind which includes them4 ,if1 on the contrary1 blackness or woolly hair be an effect depending on causes1 these general propositions are manifestly empirical laws2 and all that has already been said respecting that class of generalizations may be applied without modification to these4 ,now1 we have seen that in the case of all compounds--of all things1 in short1 except the elementary substances and primary powers of nature--the presumption is1 that the properties do really depend upon causes2 and it is impossible in any case whatever to be certain that they do not4 ,we therefore should not be safe in claiming for any generalization respecting the co-existence of properties1 a degree of certainty to which1 if the properties should happen to be the result of causes1 it would have no claim4 ,a generalization respecting co-existence1 or1 in other words1 respecting the properties of kinds1 may be an ultimate truth1 but it may also be merely a derivative one2 and since1 if so1 it is one of those derivative laws which are neither laws of causation nor have been resolved into the laws of causation on which they depend1 it can possess no higher degree of evidence than belongs to an empirical law4 #d4 ,this conclusion will be confirmed by the consideration of one great deficiency1 which precludes the application to the ultimate uniformities of co-existence1 of a system of rigorous scientific induction1 such as the uniformities in the succession of phenomena have been found to admit of4 ,the basis of such a system is wanting2 there is no general axiom standing in the same relation to the uniformities of co-existence as the law of causation does to those of succession4 ,the ,methods of ,induction applicable to the ascertainment of causes and effects are grounded on the principle that every thing which has a beginning must have some cause or other2 that among the circumstances which actually existed at the time of its commencement1 there is certainly some one combination1 on which the effect in question is unconditionally consequent1 and on the repetition of which it would certainly again recur4 ,but in an inquiry whether some kind 7as crow7 universally possesses a certain property 7as blackness71 there is no room for any assumption analogous to this4 ,we have no previous certainty that the property must have something which constantly co-exists with it2 must have an invariable co-existent1 in the same manner as an event must have an invariable antecedent4 ,when we feel pain1 we must be in some circumstances under which1 if exactly repeated1 we should always feel pain4 ,but when we are conscious of blackness1 it does not follow that there is something else present of which blackness is a constant accompaniment4 ,there is1 therefore1 no room for elimination2 no method of ,agreement or ,difference1 or of ,concomitant ,variations 7which is but a modification either of the ,method of ,agreement or of the ,method of ,difference74 ,we can not conclude that the blackness we see in crows must be an invariable property of crows merely because there is nothing else present of which it can be an invariable property4 ,we therefore inquire into the truth of a proposition like 8,all crows are black10 under the same disadvantage as if1 in our inquiries into causation1 we were compelled to let in1 as one of the possibilities1 that the effect may in that particular instance have arisen without any cause at all4 ,to overlook this grand distinction was1 as it seems to me1 the capital error in ,bacon's view of inductive philosophy4 ,the principle of elimination1 that great logical instrument which he had the immense merit of first bringing into general use1 he deemed applicable in the same sense1 and in as unqualified a manner1 to the investigation of the co-existences1 as to that of the successions of phenomena4 ,he seems to have thought that as every event has a cause1 or invariable antecedent1 so every property of an object has an invariable co-existent1 which he called its form2 and the examples he chiefly selected for the application and illustration of his method1 were inquiries into such forms2 attempts to determine in what else all those objects resembled1 which agreed in some one general property1 as hardness or softness1 dryness or moistness1 heat or coldness4 ,such inquiries could lead to no result4 ,the objects seldom have any such circumstances in common4 ,they usually agree in the one point inquired into1 and in nothing else4 ,a great proportion of the properties which1 so far as we can conjecture1 are the likeliest to be really ultimate1 would seem to be inherently properties of many different kinds of things not allied in any other respect4 ,and as for the properties which1 being effects of causes1 we are able to give some account of1 they have generally nothing to do with the ultimate resemblances or diversities in the objects themselves1 but depend on some outward circumstances1 under the influence of which any objects whatever are capable of manifesting those properties2 as is emphatically the case with those favorite subjects of ,bacon's scientific inquiries1 hotness and coldness1 as well as with hardness and softness1 solidity and fluidity1 and many other conspicuous qualities4 ,in the absence1 then1 of any universal law of co-existence similar to the universal law of causation which regulates sequence1 we are thrown back upon the unscientific induction of the ancients1 per enumerationem simplicem1 ubi non reperitur instantia contradictoria4 ,the reason we have for believing that all crows are black1 is simply that we have seen and heard of many black crows1 and never one of any other color4 ,it remains to be considered how far this evidence can reach1 and how we are to measure its strength in any given case4 #e4 ,it sometimes happens that a mere change in the mode of verbally enunciating a question1 though nothing is really added to the meaning expressed1 is of itself a considerable step toward its solution4 ,this1 ,i think1 happens in the present instance4 ,the degree of certainty of any generalization which rests on no other evidence than the agreement1 so far as it goes1 of all past observation1 is but another phrase for the degree of improbability that an exception1 if any existed1 could have hitherto remained unobserved4 ,the reason for believing that all crows are black1 is measured by the improbability that crows of any other color should have existed to the present time without our being aware of it4 ,let us state the question in this last mode1 and consider what is implied in the supposition that there may be crows which are not black1 and under what conditions we can be justified in regarding this as incredible4 ,if there really exist crows which are not black1 one of two things must be the fact4 ,either the circumstance of blackness1 in all crows hitherto observed1 must be1 as it were1 an accident1 not connected with any distinction of ,kind2 or if it be a property of ,kind1 the crows which are not black must be a new ,kind1 a ,kind hitherto overlooked1 though coming under the same general description by which crows have hitherto been characterized4 ,the first supposition would be proved true if we were to discover casually a white crow among black ones1 or if it were found that black crows sometimes turn white4 ,the second would be shown to be the fact if in ,australia or ,central ,africa a species or a race of white or gray crows were found to exist4 #f4 ,the former of these suppositions necessarily implies that the color is an effect of causation4 ,if blackness1 in the crows in which it has been observed1 be not a property of ,kind1 but can be present or absent without any difference generally in the properties of the object1 then it is not an ultimate fact in the individuals themselves1 but is certainly dependent on a cause4 ,there are1 no doubt1 many properties which vary from individual to individual of the same ,kind1 even the same infima species1 or lowest ,kind4 ,some flowers may be either white or red1 without differing in any other respect4 ,but these properties are not ultimate2 they depend on causes4 ,so far as the properties of a thing belong to its own nature1 and do not arise from some cause extrinsic to it1 they are always the same in the same ,kind4 ,take1 for instance1 all simple substances and elementary powers2 the only things of which we are certain that some at least of their properties are really ultimate4 ,color is generally esteemed the most variable of all properties3 yet we do not find that sulphur is sometimes yellow and sometimes white1 or that it varies in color at all1 except so far as color is the effect of some extrinsic cause1 as of the sort of light thrown upon it1 the mechanical arrangement of the particles 7as after fusion71 etc4 ,we do not find that iron is sometimes fluid and sometimes solid at the same temperature2 gold sometimes malleable and sometimes brittle2 that hydrogen will sometimes combine with oxygen and sometimes not2 or the like4 ,if from simple substances we pass to any of their definite compounds1 as water1 lime1 or sulphuric acid1 there is the same constancy in their properties4 ,when properties vary from individual to individual1 it is either in the case of miscellaneous aggregations1 such as atmospheric air or rock1 composed of heterogeneous substances1 and not constituting or belonging to any real ,kind17#aia7 or it is in the case of organic beings4 ,in them1 indeed1 there is variability in a high degree4 ,animals of the same species and race1 human beings of the same age1 sex1 and country1 will be most different1 for example1 in face and figure4 ,but organized beings 7from the extreme complication of the laws by which they are regulated7 being more eminently modifiable1 that is1 liable to be influenced by a greater number and variety of causes1 than any other phenomena whatever2 having also themselves had a beginning1 and therefore a cause2 there is reason to believe that none of their properties are ultimate1 but all of them derivative1 and produced by causation4 ,and the presumption is confirmed1 by the fact that the properties which vary from one individual to another1 also generally vary more or less at different times in the same individual2 which variation1 like any other event1 supposes a cause1 and implies1 consequently1 that the properties are not independent of causation4 ,if1 therefore1 blackness be merely accidental in crows1 and capable of varying while the ,kind remains the same1 its presence or absence is doubtless no ultimate fact1 but the effect of some unknown cause3 and in that case the universality of the experience that all crows are black is sufficient proof of a common cause1 and establishes the generalization as an empirical law4 ,since there are innumerable instances in the affirmative1 and hitherto none at all in the negative1 the causes on which the property depends must exist everywhere in the limits of the observations which have been made2 and the proposition may be received as universal within those limits1 and with the allowable degree of extension to adjacent cases4 #g4 ,if1 in the second place1 the property1 in the instances in which it has been observed1 is not an effect of causation1 it is a property of ,kind2 and in that case the generalization can only be set aside by the discovery of a new ,kind of crow4 ,that1 however1 a peculiar ,kind not hitherto discovered should exist in nature1 is a supposition so often realized that it can not be considered at all improbable4 ,we have nothing to authorize us in attempting to limit the ,kinds of things which exist in nature4 ,the only unlikelihood would be that a new ,kind should be discovered in localities which there was previously reason to believe had been thoroughly explored2 and even this improbability depends on the degree of conspicuousness of the difference between the newly-discovered ,kind and all others1 since new kinds of minerals1 plants1 and even animals1 previously overlooked or confounded with known species1 are still continually detected in the most frequented situations4 ,on this second ground1 therefore1 as well as on the first1 the observed uniformity of co-existence can only hold good as an empirical law1 within the limits not only of actual observation1 but of an observation as accurate as the nature of the case required4 ,and hence it is that 7as remarked in an early chapter of the present book7 we so often give up generalizations of this class at the first summons4 ,if any credible witness stated that he had seen a white crow1 under circumstances which made it not incredible that it should have escaped notice previously1 we should give full credence to the statement4 ,it appears1 then1 that the uniformities which obtain in the co-existence of phenomena--those which we have reason to consider as ultimate1 no less than those which arise from the laws of causes yet undetected--are entitled to reception only as empirical laws2 are not to be presumed true except within the limits of time1 place1 and circumstance1 in which the observations were made1 or except in cases strictly adjacent4 #h4 ,we have seen in the last chapter that there is a point of generality at which empirical laws become as certain as laws of nature1 or1 rather1 at which there is no longer any distinction between empirical laws and laws of nature4 ,as empirical laws approach this point1 in other words1 as they rise in their degree of generality1 they become more certain2 their universality may be more strongly relied on4 ,for1 in the first place1 if they are results of causation 7which1 even in the class of uniformities treated of in the present chapter1 we never can be certain that they are not7 the more general they are1 the greater is proved to be the space over which the necessary collocations prevail1 and within which no causes exist capable of counteracting the unknown causes on which the empirical law depends4 ,to say that any thing is an invariable property of some very limited class of objects1 is to say that it invariably accompanies some very numerous and complex group of distinguishing properties2 which1 if causation be at all concerned in the matter1 argues a combination of many causes1 and therefore a great liability to counteraction2 while the comparatively narrow range of the observations renders it impossible to predict to what extent unknown counteracting causes may be distributed throughout nature4 ,but when a generalization has been found to hold good of a very large proportion of all things whatever1 it is already proved that nearly all the causes which exist in nature have no power over it2 that very few changes in the combination of causes can affect it2 since the greater number of possible combinations must have already existed in some one or other of the instances in which it has been found true4 ,if1 therefore1 any empirical law is a result of causation1 the more general it is1 the more it may be depended on4 ,and even if it be no result of causation1 but an ultimate co-existence1 the more general it is1 the greater amount of experience it is derived from1 and the greater therefore is the probability that if exceptions had existed1 some would already have presented themselves4 ,for these reasons1 it requires much more evidence to establish an exception to one of the more general empirical laws than to the more special ones4 ,we should not have any difficulty in believing that there might be a new ,kind of crow2 or a new kind of bird resembling a crow in the properties hitherto considered distinctive of that ,kind4 ,but it would require stronger proof to convince us of the existence of a ,kind of crow having properties at variance with any generally recognized universal property of birds2 and a still higher degree if the properties conflict with any recognized universal property of animals4 ,and this is conformable to the mode of judgment recommended by the common sense and general practice of mankind1 who are more incredulous as to any novelties in nature1 according to the degree of generality of the experience which these novelties seem to contradict4 #i4 ,it is conceivable that the alleged properties might conflict with some recognized universal property of all matter4 ,in that case their improbability would be at the highest1 but would not even then amount to incredibility4 ,there are only two known properties common to all matter2 in other words1 there is but one known uniformity of co-existence of properties co-extensive with all physical nature1 namely1 that whatever opposes resistance to movement gravitates1 or1 as ,professor ,bain expresses it1 ,inertia and ,gravity are co-existent through all matter1 and proportionate in their amount4 ,these properties1 as he truly says1 are not mutually implicated2 from neither of them could we1 on grounds of causation1 presume the other4 ,but1 for this very reason1 we are never certain that a ,kind may not be discovered possessing one of the properties without the other4 ,the hypothetical ether1 if it exists1 may be such a ,kind4 ,our senses can not recognize in it either resistance or gravity2 but if the reality of a resisting medium should eventually be proved 7by alteration1 for example1 in the times of revolution of periodic comets1 combined with the evidences afforded by the phenomena of light and heat71 it would be rash to conclude from this alone1 without other proofs1 that it must gravitate4 ,for even the greater generalizations1 which embrace comprehensive ,kinds containing under them a great number and variety of infim species1 are only empirical laws1 resting on induction by simple enumeration merely1 and not on any process of elimination--a process wholly inapplicable to this sort of case4 ,such generalizations1 therefore1 ought to be grounded on an examination of all the infim species comprehended in them1 and not of a portion only4 ,we can not conclude 7where causation is not concerned71 because a proposition is true of a number of things resembling one another only in being animals1 that it is therefore true of all animals4 ,if1 indeed1 any thing be true of species which differ more from one another than either differs from a third1 especially if that third species occupies in most of its known properties a position between the two former1 there is some probability that the same thing will also be true of that intermediate species2 for it is often1 though by no means universally1 found1 that there is a sort of parallelism in the properties of different ,kinds1 and that their degree of unlikeness in one respect bears some proportion to their unlikeness in others4 ,we see this parallelism in the properties of the different metals2 in those of sulphur1 phosphorus1 and carbon2 of chlorine1 iodine1 and bromine2 in the natural orders of plants and animals1 etc4 ,but there are innumerable anomalies and exceptions to this sort of conformity2 if indeed the conformity itself be any thing but an anomaly and an exception in nature4 ,universal propositions1 therefore1 respecting the properties of superior ,kinds1 unless grounded on proved or presumed connection by causation1 ought not to be hazarded except after separately examining every known sub-kind included in the larger ,kind4 ,and even then such generalizations must be held in readiness to be given up on the occurrence of some new anomaly1 which1 when the uniformity is not derived from causation1 can never1 even in the case of the most general of these empirical laws1 be considered very improbable4 ,thus1 all the universal propositions which it has been attempted to lay down respecting simple substances1 or concerning any of the classes which have been formed among simple substances 7and the attempt has been often made71 have1 with the progress of experience1 either faded into inanity1 or been proved to be erroneous2 and each ,kind of simple substance remains1 with its own collection of properties apart from the rest1 saving a certain parallelism with a few other ,kinds1 the most similar to itself4 ,in organized beings1 indeed1 there are abundance of propositions ascertained to be universally true of superior genera1 to many of which the discovery hereafter of any exceptions must be regarded as extremely improbable4 ,but these1 as already observed1 are1 we have every reason to believe1 properties dependent on causation47#aib7 ,uniformities of co-existence1 then1 not only when they are consequences of laws of succession1 but also when they are ultimate truths1 must be ranked1 for the purpose of logic1 among empirical laws2 and are amenable in every respect to the same rules with those unresolved uniformities which are known to be dependent on causation47#aic7 ,chapter ,,xxiii4 ,of ,approximate ,generalizations1 ,and ,probable ,evidence4 #a4 ,in our inquiries into the nature of the inductive process1 we must not confine our notice to such generalizations from experience as profess to be universally true4 ,there is a class of inductive truths avowedly not universal2 in which it is not pretended that the predicate is always true of the subject2 but the value of which1 as generalizations1 is nevertheless extremely great4 ,an important portion of the field of inductive knowledge does not consist of universal truths1 but of approximations to such truths2 and when a conclusion is said to rest on probable evidence1 the premises it is drawn from are usually generalizations of this sort4 ,as every certain inference respecting a particular case implies that there is ground for a general proposition of the form1 every ,a is ,b2 so does every probable inference suppose that there is ground for a proposition of the form1 ,most ,a are ,b2 and the degree of probability of the inference in an average case will depend on the proportion between the number of instances existing in nature which accord with the generalization1 and the number of those which conflict with it4 #b4 ,propositions in the form1 ,most ,a are ,b1 are of a very different degree of importance in science1 and in the practice of life4 ,to the scientific inquirer they are valuable chiefly as materials for1 and steps toward universal truths4 ,the discovery of these is the proper end of science2 its work is not done if it stops at the proposition that a majority of ,a are ,b1 without circumscribing that majority by some common character1 fitted to distinguish them from the minority4 ,independently of the inferior precision of such imperfect generalizations1 and the inferior assurance with which they can be applied to individual cases1 it is plain that1 compared with exact generalizations1 they are almost useless as means of discovering ulterior truths by way of deduction4 ,we may1 it is true1 by combining the proposition ,most ,a are ,b1 with a universal proposition1 ,every ,b is ,c1 arrive at the conclusion that ,most ,a are ,c4 ,but when a second proposition of the approximate kind is introduced--or even when there is but one1 if that one be the major premise--nothing can1 in general1 be positively concluded4 ,when the major is ,most ,b are ,d1 then1 even if the minor be ,every ,a is ,b1 we can not infer that most ,a are ,d1 or with any certainty that even some ,a are ,d4 ,though the majority of the class ,b have the attribute signified by ,d1 the whole of the sub-class ,a may belong to the minority47#aid7 ,though so little use can be made1 in science1 of approximate generalizations1 except as a stage on the road to something better1 for practical guidance they are often all we have to rely on4 ,even when science has really determined the universal laws of any phenomenon1 not only are those laws generally too much encumbered with conditions to be adapted for everyday use1 but the cases which present themselves in life are too complicated1 and our decisions require to be taken too rapidly1 to admit of waiting till the existence of a phenomenon can be proved by what have been scientifically ascertained to be universal marks of it4 ,to be indecisive and reluctant to act1 because we have not evidence of a perfectly conclusive character to act on1 is a defect sometimes incident to scientific minds1 but which1 wherever it exists1 renders them unfit for practical emergencies4 ,if we would succeed in action1 we must judge by indications which1 though they do not generally mislead us1 sometimes do1 and must make up1 as far as possible1 for the incomplete conclusiveness of any one indication1 by obtaining others to corroborate it4 ,the principles of induction applicable to approximate generalization are therefore a not less important subject of inquiry than the rules for the investigation of universal truths2 and might reasonably be expected to detain us almost as long1 were it not that these principles are mere corollaries from those which have been already treated of4 #c4 ,there are two sorts of cases in which we are forced to guide ourselves by generalizations of the imperfect form1 ,most ,a are ,b4 ,the first is1 when we have no others2 when we have not been able to carry our investigation of the laws of the phenomena any further2 as in the following propositions--,most dark-eyed persons have dark hair2 ,most springs contain mineral substances2 ,most stratified formations contain fossils4 ,the importance of this class of generalizations is not very great2 for1 though it frequently happens that we see no reason why that which is true of most individuals of a class is not true of the remainder1 nor are able to bring the former under any general description which can distinguish them from the latter1 yet if we are willing to be satisfied with propositions of a less degree of generality1 and to break down the class ,a into sub-classes1 we may generally obtain a collection of propositions exactly true4 ,we do not know why most wood is lighter than water1 nor can we point out any general property which discriminates wood that is lighter than water from that which is heavier4 ,but we know exactly what species are the one and what the other4 ,and if we meet with a specimen not conformable to any known species 7the only case in which our previous knowledge affords no other guidance than the approximate generalization71 we can generally make a specific experiment1 which is a surer resource4 ,it often happens1 however1 that the proposition1 ,most ,a are ,b1 is not the ultimatum of our scientific attainments1 though the knowledge we possess beyond it can not conveniently be brought to bear upon the particular instance4 ,we may know well enough what circumstances distinguish the portion of ,a which has the attribute ,b from the portion which has it not1 but may have no means1 or may not have time1 to examine whether those characteristic circumstances exist or not in the individual case4 ,this is the situation we are generally in when the inquiry is of the kind called moral1 that is1 of the kind which has in view to predict human actions4 ,to enable us to affirm any thing universally concerning the actions of classes of human beings1 the classification must be grounded on the circumstances of their mental culture and habits1 which in an individual case are seldom exactly known2 and classes grounded on these distinctions would never precisely accord with those into which mankind are divided for social purposes4 ,all propositions which can be framed respecting the actions of human beings as ordinarily classified1 or as classified according to any kind of outward indications1 are merely approximate4 ,we can only say1 ,most persons of a particular age1 profession1 country1 or rank in society1 have such and such qualities2 or1 ,most persons1 when placed in certain circumstances1 act in such and such a way4 ,not that we do not often know well enough on what causes the qualities depend1 or what sort of persons they are who act in that particular way2 but we have seldom the means of knowing whether any individual person has been under the influence of those causes1 or is a person of that particular sort4 ,we could replace the approximate generalizations by propositions universally true2 but these would hardly ever be capable of being applied to practice4 ,we should be sure of our majors1 but we should not be able to get minors to fit2 we are forced1 therefore1 to draw our conclusions from coarser and more fallible indications4 #d4 ,proceeding now to consider what is to be regarded as sufficient evidence of an approximate generalization1 we can have no difficulty in at once recognizing that1 when admissible at all1 it is admissible only as an empirical law4 ,propositions of the form1 ,every ,a is ,b1 are not necessarily laws of causation1 or ultimate uniformities of co-existence2 propositions like ,most ,a are ,b1 can not be so4 ,propositions hitherto found true in every observed instance may yet be no necessary consequence of laws of causation1 or of ultimate uniformities1 and unless they are so1 may1 for aught we know1 be false beyond the limits of actual observation2 still more evidently must this be the case with propositions which are only true in a mere majority of the observed instances4 ,there is some difference1 however1 in the degree of certainty of the proposition1 ,most ,a are ,b1 according as that approximate generalization composes the whole of our knowledge of the subject1 or not4 ,suppose1 first1 that the former is the case4 ,we know only that most ,a are ,b1 not why they are so1 nor in what respect those which are differ from those which are not4 ,how1 then1 did we learn that most ,a are ,b8 ,precisely in the manner in which we should have learned1 had such happened to be the fact that all ,a are ,b4 ,we collected a number of instances sufficient to eliminate chance1 and1 having done so1 compared the number of instances in the affirmative with the number in the negative4 ,the result1 like other unresolved derivative laws1 can be relied on solely within the limits not only of place and time1 but also of circumstance1 under which its truth has been actually observed2 for1 as we are supposed to be ignorant of the causes which make the proposition true1 we can not tell in what manner any new circumstance might perhaps affect it4 ,the proposition1 ,most judges are inaccessible to bribes1 would probably be found true of ,englishmen1 ,frenchmen1 ,germans1 ,north ,americans1 and so forth2 but if on this evidence alone we extended the assertion to ,orientals1 we should step beyond the limits1 not only of place but of circumstance1 within which the fact had been observed1 and should let in possibilities of the absence of the determining causes1 or the presence of counteracting ones1 which might be fatal to the approximate generalization4 ,in the case where the approximate proposition is not the ultimatum of our scientific knowledge1 but only the most available form of it for practical guidance2 where we know1 not only that most ,a have the attribute ,b1 but also the causes of ,b1 or some properties by which the portion of ,a which has that attribute is distinguished from the portion which has it not1 we are rather more favorably situated than in the preceding case4 ,for we have now a double mode of ascertaining whether it be true that most ,a are ,b2 the direct mode1 as before1 and an indirect one1 that of examining whether the proposition admits of being deduced from the known cause1 or from any known criterion1 of ,b4 ,let the question1 for example1 be whether most ,scotchmen can read8 ,we may not have observed1 or received the testimony of others respecting1 a sufficient number and variety of ,scotchmen to ascertain this fact2 but when we consider that the cause of being able to read is the having been taught it1 another mode of determining the question presents itself1 namely1 by inquiring whether most ,scotchmen have been sent to schools where reading is effectually taught4 ,of these two modes1 sometimes one and sometimes the other is the more available4 ,in some cases1 the frequency of the effect is the more accessible to that extensive and varied observation which is indispensable to the establishment of an empirical law2 at other times1 the frequency of the causes1 or of some collateral indications4 ,it commonly happens that neither is susceptible of so satisfactory an induction as could be desired1 and that the grounds on which the conclusion is received are compounded of both4 ,thus a person may believe that most ,scotchmen can read1 because1 so far as his information extends1 most ,scotchmen have been sent to school1 and most ,scotch schools teach reading effectually2 and also because most of the ,scotchmen whom he has known or heard of could read2 though neither of these two sets of observations may by itself fulfill the necessary conditions of extent and variety4 ,although the approximate generalization may in most cases be indispensable for our guidance1 even when we know the cause1 or some certain mark1 of the attribute predicated1 it needs hardly be observed that we may always replace the uncertain indication by a certain one1 in any case in which we can actually recognize the existence of the cause or mark4 ,for example1 an assertion is made by a witness1 and the question is whether to believe it4 ,if we do not look to any of the individual circumstances of the case1 we have nothing to direct us but the approximate generalization1 that truth is more common than falsehood1 or1 in other words1 that most persons1 on most occasions1 speak truth4 ,but if we consider in what circumstances the cases where truth is spoken differ from those in which it is not1 we find1 for instance1 the following3 the witness's being an honest person or not2 his being an accurate observer or not2 his having an interest to serve in the matter or not4 ,now1 not only may we be able to obtain other approximate generalizations respecting the degree of frequency of these various possibilities1 but we may know which of them is positively realized in the individual case4 ,that the witness has or has not an interest to serve1 we perhaps know directly2 and the other two points indirectly1 by means of marks2 as1 for example1 from his conduct on some former occasion2 or from his reputation1 which1 though a very uncertain mark1 affords an approximate generalization 7as1 for instance1 ,most persons who are believed to be honest by those with whom they have had frequent dealings1 are really so71 which approaches nearer to a universal truth than the approximate general proposition with which we set out1 viz41 ,most persons on most occasions speak truth4 ,as it seems unnecessary to dwell further on the question of the evidence of approximate generalizations1 we shall proceed to a not less important topic1 that of the cautions to be observed in arguing from these incompletely universal propositions to particular cases4 #e4 ,so far as regards the direct application of an approximate generalization to an individual instance1 this question presents no difficulty4 ,if the proposition1 ,most ,a are ,b1 has been established1 by a sufficient induction1 as an empirical law1 we may conclude that any particular ,a is ,b with a probability proportioned to the preponderance of the number of affirmative instances over the number of exceptions4 ,if it has been found practicable to attain numerical precision in the data1 a corresponding degree of precision may be given to the evaluation of the chances of error in the conclusion4 ,if it can be established as an empirical law that nine out of every ten ,a are ,b1 there will be one chance in ten of error in assuming that any ,a1 not individually known to us1 is a ,b3 but this of course holds only within the limits of time1 place1 and circumstance1 embraced in the observations1 and therefore can not be counted on for any sub-class or variety of ,a 7or for ,a in any set of external circumstances7 which were not included in the average4 ,it must be added1 that we can guide ourselves by the proposition1 ,nine out of every ten ,a are ,b1 only in cases of which we know nothing except that they fall within the class ,a4 ,for if we know1 of any particular instances i1 not only that it falls under ,a1 but to what species or variety of ,a it belongs1 we shall generally err in applying to i the average struck for the whole genus1 from which the average corresponding to that species alone would1 in all probability1 materially differ4 ,and so if i1 instead of being a particular sort of instance1 is an instance known to be under the influence of a particular set of circumstances1 the presumption drawn from the numerical proportions in the whole genus would probably1 in such a case1 only mislead4 ,a general average should only be applied to cases which are neither known1 nor can be presumed1 to be other than average cases4 ,such averages1 therefore1 are commonly of little use for the practical guidance of any affairs but those which concern large numbers4 ,tables of the chances of life are useful to insurance offices1 but they go a very little way toward informing any one of the chances of his own life1 or any other life in which he is interested1 since almost every life is either better or worse than the average4 ,such averages can only be considered as supplying the first term in a series of approximations2 the subsequent terms proceeding on an appreciation of the circumstances belonging to the particular case4 #f4 ,from the application of a single approximate generalization to individual cases1 we proceed to the application of two or more of them together to the same case4 ,when a judgment applied to an individual instance is grounded on two approximate generalizations taken in conjunction1 the propositions may cooperate toward the result in two different ways4 ,in the one1 each proposition is separately applicable to the case in hand1 and our object in combining them is to give to the conclusion in that particular case the double probability arising from the two propositions separately4 ,this may be called joining two probabilities by way of ,addition2 and the result is a probability greater than either4 ,the other mode is1 when only one of the propositions is directly applicable to the case1 the second being only applicable to it by virtue of the application of the first4 ,this is joining two probabilities by way of ,ratiocination or ,deduction2 the result of which is a less probability than either4 ,the type of the first argument is1 ,most ,a are ,b2 most ,c are ,b2 this thing is both an ,a and a ,c2 therefore it is probably a ,b4 ,the type of the second is1 ,most ,a are ,b2 most ,c are ,a2 this is a ,c2 therefore it is probably an ,a1 therefore it is probably a ,b4 ,the first is exemplified when we prove a fact by the testimony of two unconnected witnesses2 the second1 when we adduce only the testimony of one witness that he has heard the thing asserted by another4 ,or again1 in the first mode it may be argued that the accused committed the crime1 because he concealed himself1 and because his clothes were stained with blood2 in the second1 that he committed it because he washed or destroyed his clothes1 which is supposed to render it probable that they were stained with blood4 ,instead of only two links1 as in these instances1 we may suppose chains of any length4 ,a chain of the former kind was termed by ,bentham7#aie7 a self-corroborative chain of evidence2 the second1 a self-infirmative chain4 ,when approximate generalizations are joined by way of addition1 we may deduce from the theory of probabilities laid down in a former chapter1 in what manner each of them adds to the probability of a conclusion which has the warrant of them all4 ,if1 on an average1 two of every three ,as are ,bs1 and three of every four ,cs are ,bs1 the probability that something which is both an ,a and a ,c is a ,b1 will be more than two in three1 or than three in four4 ,of every twelve things which are ,as1 all except four are ,bs by the supposition2 and if the whole twelve1 and consequently those four1 have the characters of ,c likewise1 three of these will be ,bs on that ground4 ,therefore1 out of twelve which are both ,as and ,cs1 eleven are ,bs4 ,to state the argument in another way2 a thing which is both an ,a and a ,c1 but which is not a ,b1 is found in only one of three sections of the class ,a1 and in only one of four sections of the class ,c2 but this fourth of ,c being spread over the whole of ,a indiscriminately1 only one-third part of it 7or one-twelfth of the whole number7 belongs to the third section of ,a2 therefore a thing which is not a ,b occurs only once1 among twelve things which are both ,as and ,cs4 ,the argument would1 in the language of the doctrine of chances1 be thus expressed3 the chance that an ,a is not a ,b is 1 the chance that a ,c is not a ,b is 2 hence if the thing be both an ,a and a ,c1 the chance is of 47#aif7 ,in this computation it is of course supposed that the probabilities arising from ,a and ,c are independent of each other4 ,there must not be any such connection between ,a and ,c1 that when a thing belongs to the one class it will therefore belong to the other1 or even have a greater chance of doing so4 ,otherwise the not-,bs which are ,cs may be1 most or even all of them1 identical with the not-,bs which are ,as2 in which last case the probability arising from ,a and ,c together will be no greater than that arising from ,a alone4 ,when approximate generalizations are joined together in the other mode1 that of deduction1 the degree of probability of the inference1 instead of increasing1 diminishes at each step4 ,from two such premises as ,most ,a are ,b1 ,most ,b are ,c1 we can not with certainty conclude that even a single ,a is ,c2 for the whole of the portion of ,a which in any way falls under ,b1 may perhaps be comprised in the exceptional part of it4 ,still1 the two propositions in question afford an appreciable probability that any given ,a is ,c1 provided the average on which the second proposition is grounded was taken fairly with reference to the first2 provided the proposition1 ,most ,b are ,c1 was arrived at in a manner leaving no suspicion that the probability arising from it is otherwise than fairly distributed over the section of ,b which belongs to ,a4 ,for though the instances which are ,a may be all in the minority1 they may1 also1 be all in the majority2 and the one possibility is to be set against the other4 ,on the whole1 the probability arising from the two propositions taken together1 will be correctly measured by the probability arising from the one1 abated in the ratio of that arising from the other4 ,if nine out of ten ,swedes have light hair1 and eight out of nine inhabitants of ,stockholm are ,swedes1 the probability arising from these two propositions1 that any given inhabitant of ,stockholm is light-haired1 will amount to eight in ten2 though it is rigorously possible that the whole ,swedish population of ,stockholm might belong to that tenth section of the people of ,sweden who are an exception to the rest4 ,if the premises are known to be true not of a bare majority1 but of nearly the whole1 of their respective subjects1 we may go on joining one such proposition to another for several steps1 before we reach a conclusion not presumably true even of a majority4 ,the error of the conclusion will amount to the aggregate of the errors of all the premises4 ,let the proposition1 most ,a are ,b1 be true of nine in ten2 ,most ,b are ,c1 of eight in nine2 then not only will one ,a in ten not be ,c1 because not ,b1 but even of the nine-tenths which are ,b1 only eight-ninths will be ,c2 that is1 the cases of ,a which are ,c will be only of 1 or four-fifths4 ,let us now add ,most ,c are ,d1 and suppose this to be true of seven cases out of eight2 the proportion of ,a which is ,d will be only of of 1 or 4 ,thus the probability progressively dwindles4 ,the experience1 however1 on which our approximate generalizations are grounded1 has so rarely been subjected to1 or admits of1 accurate numerical estimation1 that we can not in general apply any measurement to the diminution of probability which takes place at each illation2 but must be content with remembering that it does diminish at every step1 and that unless the premises approach very nearly indeed to being universally true1 the conclusion after a very few steps is worth nothing4 ,a hearsay of a hearsay1 or an argument from presumptive evidence depending not on immediate marks but on marks of marks1 is worthless at a very few removes from the first stage4 #g4 ,there are1 however1 two cases in which reasonings depending on approximate generalizations may be carried to any length we please with as much assurance1 and are as strictly scientific1 as if they were composed of universal laws of nature4 ,but these cases are exceptions of the sort which are currently said to prove the rule4 ,the approximate generalizations are as suitable1 in the cases in question1 for purposes of ratiocination1 as if they were complete generalizations1 because they are capable of being transformed into complete generalizations exactly equivalent4 ,first3 ,if the approximate generalization is of the class in which our reason for stopping at the approximation is not the impossibility1 but only the inconvenience1 of going further2 if we are cognizant of the character which distinguishes the cases that accord with the generalization from those which are exceptions to it2 we may then substitute for the approximate proposition1 a universal proposition with a proviso4 ,the proposition1 ,most persons who have uncontrolled power employ it ill1 is a generalization of this class1 and may be transformed into the following3 ,all persons who have uncontrolled power employ it ill1 provided they are not persons of unusual strength of judgment and rectitude of purpose4 ,the proposition1 carrying the hypothesis or proviso with it1 may then be dealt with no longer as an approximate1 but as a universal proposition2 and to whatever number of steps the reasoning may reach1 the hypothesis1 being carried forward to the conclusion1 will exactly indicate how far that conclusion is from being applicable universally4 ,if in the course of the argument other approximate generalizations are introduced1 each of them being in like manner expressed as a universal proposition with a condition annexed1 the sum of all the conditions will appear at the end as the sum of all the errors which affect the conclusion4 ,thus1 to the proposition last cited1 let us add the following3 ,all absolute monarchs have uncontrolled power1 unless their position is such that they need the active support of their subjects 7as was the case with ,queen ,elizabeth1 ,frederick of ,prussia1 and others74 ,combining these two propositions1 we can deduce from them a universal conclusion1 which will be subject to both the hypotheses in the premises2 ,all absolute monarchs employ their power ill1 unless their position makes them need the active support of their subjects1 or unless they are persons of unusual strength of judgment and rectitude of purpose4 ,it is of no consequence how rapidly the errors in our premises accumulate1 if we are able in this manner to record each error1 and keep an account of the aggregate as it swells up4 ,secondly3 there is a case in which approximate propositions1 even without our taking note of the conditions under which they are not true of individual cases1 are yet1 for the purposes of science1 universal ones2 namely1 in the inquiries which relate to the properties not of individuals1 but of multitudes4 ,the principal of these is the science of politics1 or of human society4 ,this science is principally concerned with the actions not of solitary individuals1 but of masses2 with the fortunes not of single persons1 but of communities4 ,for the statesman1 therefore1 it is generally enough to know that most persons act or are acted upon in a particular way2 since his speculations and his practical arrangements refer almost exclusively to cases in which the whole community1 or some large portion of it1 is acted upon at once1 and in which1 therefore1 what is done or felt by most persons determines the result produced by or upon the body at large4 ,he can get on well enough with approximate generalizations on human nature1 since what is true approximately of all individuals is true absolutely of all masses4 ,and even when the operations of individual men have a part to play in his deductions1 as when he is reasoning of kings1 or other single rulers1 still1 as he is providing for indefinite duration1 involving an indefinite succession of such individuals1 he must in general both reason and act as if what is true of most persons were true of all4 ,the two kinds of considerations above adduced are a sufficient refutation of the popular error1 that speculations on society and government1 as resting on merely probable evidence1 must be inferior in certainty and scientific accuracy to the conclusions of what are called the exact sciences1 and less to be relied on in practice4 ,there are reasons enough why the moral sciences must remain inferior to at least the more perfect of the physical2 why the laws of their more complicated phenomena can not be so completely deciphered1 nor the phenomena predicted with the same degree of assurance4 ,but though we can not attain to so many truths1 there is no reason that those we can attain should deserve less reliance1 or have less of a scientific character4 ,of this topic1 however1 ,i shall treat more systematically in the concluding ,book1 to which place any further consideration of it must be deferred4 ,chapter ,,xxiv4 ,of ,the ,remaining ,laws ,of ,nature4 #a4 ,in the ,first ,book we found that all the assertions which can be conveyed by language1 express some one or more of five different things3 ,existence2 ,order in ,place2 ,order in ,time2 ,causation2 and ,resemblance47#aig7 ,of these1 ,causation1 in our view of the subject1 not being fundamentally different from ,order in ,time1 the five species of possible assertions are reduced to four4 ,the propositions which affirm ,order in ,time in either of its two modes1 ,co-existence and ,succession1 have formed1 thus far1 the subject of the present ,book4 ,and we have now concluded the exposition1 so far as it falls within the limits assigned to this work1 of the nature of the evidence on which these propositions rest1 and the processes of investigation by which they are ascertained and proved4 ,there remain three classes of facts3 ,existence1 ,order in ,place1 and ,resemblance2 in regard to which the same questions are now to be resolved4 ,regarding the first of these1 very little needs be said4 ,existence in general1 is a subject not for our science1 but for metaphysics4 ,to determine what things can be recognized as really existing1 independently of our own sensible or other impressions1 and in what meaning the term is1 in that case1 predicated of them1 belongs to the consideration of 8,things in themselves10 from which1 throughout this work1 we have as much as possible kept aloof4 ,existence1 so far as ,logic is concerned about it1 has reference only to phenomena2 to actual1 or possible1 states of external or internal consciousness1 in ourselves or others4 ,feelings of sensitive beings1 or possibilities of having such feelings1 are the only things the existence of which can be a subject of logical induction1 because the only things of which the existence in individual cases can be a subject of experience4 ,it is true that a thing is said by us to exist1 even when it is absent1 and therefore is not and can not be perceived4 ,but even then1 its existence is to us only another word for our conviction that we should perceive it on a certain supposition2 namely1 if we were in the needful circumstances of time and place1 and endowed with the needful perfection of organs4 ,my belief that the ,emperor of ,china exists1 is simply my belief that if ,i were transported to the imperial palace or some other locality in ,pekin1 ,i should see him4 ,my belief that ,julius ,csar existed1 is my belief that ,i should have seen him if ,i had been present in the field of ,pharsalia1 or in the senate-house at ,rome4 ,when ,i believe that stars exist beyond the utmost range of my vision1 though assisted by the most powerful telescopes yet invented1 my belief1 philosophically expressed1 is1 that with still better telescopes1 if such existed1 ,i could see them1 or that they may be perceived by beings less remote from them in space1 or whose capacities of perception are superior to mine4 ,the existence1 therefore1 of a phenomenon1 is but another word for its being perceived1 or for the inferred possibility of perceiving it4 ,when the phenomenon is within the range of present observation1 by present observation we assure ourselves of its existence2 when it is beyond that range1 and is therefore said to be absent1 we infer its existence from marks or evidences4 ,but what can these evidences be8 ,other phenomena2 ascertained by induction to be connected with the given phenomenon1 either in the way of succession or of co-existence4 ,the simple existence1 therefore1 of an individual phenomenon1 when not directly perceived1 is inferred from some inductive law of succession or co-existence2 and is consequently not amenable to any peculiar inductive principles4 ,we prove the existence of a thing1 by proving that it is connected by succession or co-existence with some known thing4 ,with respect to general propositions of this class1 that is1 which affirm the bare fact of existence1 they have a peculiarity which renders the logical treatment of them a very easy matter2 they are generalizations which are sufficiently proved by a single instance4 ,that ghosts1 or unicorns1 or sea-serpents exist1 would be fully established if it could be ascertained positively that such things had been even once seen4 ,whatever has once happened1 is capable of happening again2 the only question relates to the conditions under which it happens4 ,so far1 therefore1 as relates to simple existence1 the ,inductive ,logic has no knots to untie4 ,and we may proceed to the remaining two of the great classes into which facts have been divided2 ,resemblance1 and ,order in ,place4 #b4 ,resemblance and its opposite1 except in the case in which they assume the names of ,equality and ,inequality1 are seldom regarded as subjects of science2 they are supposed to be perceived by simple apprehension2 by merely applying our senses or directing our attention to the two objects at once1 or in immediate succession4 ,and this simultaneous1 or virtually simultaneous1 application of our faculties to the two things which are to be compared1 does necessarily constitute the ultimate appeal1 wherever such application is practicable4 ,but1 in most cases1 it is not practicable3 the objects can not be brought so close together that the feeling of their resemblance 7at least a complete feeling of it7 directly arises in the mind4 ,we can only compare each of them with some third object1 capable of being transported from one to the other4 ,and besides1 even when the objects can be brought into immediate juxtaposition1 their resemblance or difference is but imperfectly known to us1 unless we have compared them minutely1 part by part4 ,until this has been done1 things in reality very dissimilar often appear undistinguishably alike4 ,two lines of very unequal length will appear about equal when lying in different directions2 but place them parallel with their farther extremities even1 and if we look at the nearer extremities1 their inequality becomes a matter of direct perception4 ,to ascertain whether1 and in what1 two phenomena resemble or differ1 is not always1 therefore1 so easy a thing as it might at first appear4 ,when the two can not be brought into juxtaposition1 or not so that the observer is able to compare their several parts in detail1 he must employ the indirect means of reasoning and general propositions4 ,when we can not bring two straight lines together1 to determine whether they are equal1 we do it by the physical aid of a foot-rule applied first to one and then to the other1 and the logical aid of the general proposition or formula1 8,things which are equal to the same thing are equal to one another40 ,the comparison of two things through the intervention of a third thing1 when their direct comparison is impossible1 is the appropriate scientific process for ascertaining resemblances and dissimilarities1 and is the sum total of what ,logic has to teach on the subject4 ,an undue extension of this remark induced ,locke to consider reasoning itself as nothing but the comparison of two ideas through the medium of a third1 and knowledge as the perception of the agreement or disagreement of two ideas2 doctrines which the ,condillac school blindly adopted1 without the qualifications and distinctions with which they were studiously guarded by their illustrious author4 ,where1 indeed1 the agreement or disagreement 7otherwise called resemblance or dissimilarity7 of any two things is the very matter to be determined1 as is the case particularly in the sciences of quantity and extension2 there1 the process by which a solution1 if not attainable by direct perception1 must be indirectly sought1 consists in comparing these two things through the medium of a third4 ,but this is far from being true of all inquiries4 ,the knowledge that bodies fall to the ground is not a perception of agreement or disagreement1 but of a series of physical occurrences1 a succession of sensations4 ,locke's definitions of knowledge and of reasoning required to be limited to our knowledge of1 and reasoning about1 resemblances4 ,nor1 even when thus restricted1 are the propositions strictly correct2 since the comparison is not made1 as he represents1 between the ideas of the two phenomena1 but between the phenomena themselves4 ,this mistake has been pointed out in an earlier part of our inquiry17#aih7 and we traced it to an imperfect conception of what takes place in mathematics1 where very often the comparison is really made between the ideas1 without any appeal to the outward senses2 only1 however1 because in mathematics a comparison of the ideas is strictly equivalent to a comparison of the phenomena themselves4 ,where1 as in the case of numbers1 lines1 and figures1 our idea of an object is a complete picture of the object1 so far as respects the matter in hand2 we can1 of course1 learn from the picture1 whatever could be learned from the object itself by mere contemplation of it as it exists at the particular instant when the picture is taken4 ,no mere contemplation of gunpowder would ever teach us that a spark would make it explode1 nor1 consequently1 would the contemplation of the idea of gunpowder do so2 but the mere contemplation of a straight line shows that it can not inclose a space2 accordingly the contemplation of the idea of it will show the same4 ,what takes place in mathematics is thus no argument that the comparison is between the ideas only4 ,it is always1 either indirectly or directly1 a comparison of the phenomena4 ,in cases in which we can not bring the phenomena to the test of direct inspection at all1 or not in a manner sufficiently precise1 but must judge of their resemblance by inference from other resemblances or dissimilarities more accessible to observation1 we of course require1 as in all cases of ratiocination1 generalizations or formul applicable to the subject4 ,we must reason from laws of nature2 from the uniformities which are observable in the fact of likeness or unlikeness4 #c4 ,of these laws or uniformities1 the most comprehensive are those supplied by mathematics2 the axioms relating to equality1 inequality1 and proportionality1 and the various theorems thereon founded4 ,and these are the only ,laws of ,resemblance which require to be1 or which can be1 treated apart4 ,it is true there are innumerable other theorems which affirm resemblances among phenomena2 as that the angle of the reflection of light is equal to its angle of incidence 7equality being merely exact resemblance in magnitude74 ,again1 that the heavenly bodies describe equal areas in equal times2 and that their periods of revolution are proportional 7another species of resemblance7 to the sesquiplicate powers of their distances from the centre of force4 ,these and similar propositions affirm resemblances1 of the same nature with those asserted in the theorems of mathematics2 but the distinction is1 that the propositions of mathematics are true of all phenomena whatever1 or at least without distinction of origin2 while the truths in question are affirmed only of special phenomena1 which originate in a certain way2 and the equalities1 proportionalities1 or other resemblances1 which exist between such phenomena1 must necessarily be either derived from1 or identical with1 the law of their origin--the law of causation on which they depend4 ,the equality of the areas described in equal times by the planets1 is derived from the laws of the causes2 and1 until its derivation was shown1 it was an empirical law4 ,the equality of the angles of reflection and incidence is identical with the law of the cause2 for the cause is the incidence of a ray of light upon a reflecting surface1 and the equality in question is the very law according to which that cause produces its effects4 ,this class1 therefore1 of the uniformities of resemblance between phenomena1 are inseparable1 in fact and in thought1 from the laws of the production of those phenomena2 and the principles of induction applicable to them are no other than those of which we have treated in the preceding chapters of this ,book4 ,it is otherwise with the truths of mathematics4 ,the laws of equality and inequality between spaces1 or between numbers1 have no connection with laws of causation4 ,that the angle of reflection is equal to the angle of incidence1 is a statement of the mode of action of a particular cause2 but that when two straight lines intersect each other the opposite angles are equal1 is true of all such lines and angles1 by whatever cause produced4 ,that the squares of the periodic times of the planets are proportional to the cubes of their distances from the sun1 is a uniformity derived from the laws of the causes 7or forces7 which produce the planetary motions2 but that the square of any number is four times the square of half the number1 is true independently of any cause4 ,the only laws of resemblance1 therefore1 which we are called upon to consider independently of causation1 belong to the province of mathematics4 #d4 ,the same thing is evident with respect to the only one remaining of our five categories1 ,order in ,place4 ,the order in place1 of the effects of a cause1 is 7like every thing else belonging to the effects7 a consequence of the laws of that cause4 ,the order in place1 or1 as we have termed it1 the collocation1 of the primeval causes1 is 7as well as their resemblance7 in each instance an ultimate fact1 in which no laws or uniformities are traceable4 ,the only remaining general propositions respecting order in place1 and the only ones which have nothing to do with causation1 are some of the truths of geometry2 laws through which we are able1 from the order in place of certain points1 lines1 or spaces1 to infer the order in place of others which are connected with the former in some known mode2 quite independently of the particular nature of those points1 lines1 or spaces1 in any other respect than position or magnitude1 as well as independently of the physical cause from which in any particular case they happen to derive their origin4 ,it thus appears that mathematics is the only department of science into the methods of which it still remains to inquire4 ,and there is the less necessity that this inquiry should occupy us long1 as we have already1 in the ,second ,book1 made considerable progress in it4 ,we there remarked1 that the directly inductive truths of mathematics are few in number2 consisting of the axioms1 together with certain propositions concerning existence1 tacitly involved in most of the so-called definitions4 ,and we gave what appeared conclusive reasons for affirming that these original premises1 from which the remaining truths of the science are deduced1 are1 notwithstanding all appearances to the contrary1 results of observation and experience2 founded1 in short1 on the evidence of the senses4 ,that things equal to the same thing are equal to one another1 and that two straight lines which have once intersected one another continue to diverge1 are inductive truths2 resting1 indeed1 like the law of universal causation1 only on induction per enumerationem simplicem2 on the fact that they have been perpetually perceived to be true1 and never once found to be false4 ,but1 as we have seen in a recent chapter that this evidence1 in the case of a law so completely universal as the law of causation1 amounts to the fullest proof1 so is this even more evidently true of the general propositions to which we are now adverting2 because1 as a perception of their truth in any individual case whatever1 requires only the simple act of looking at the objects in a proper position1 there never could have been in their case 7what1 for a long period1 there were in the case of the law of causation7 instances which were apparently1 though not really1 exceptions to them4 ,their infallible truth was recognized from the very dawn of speculation2 and as their extreme familiarity made it impossible for the mind to conceive the objects under any other law1 they were1 and still are1 generally considered as truths recognized by their own evidence1 or by instinct4 #e4 ,there is something which seems to require explanation1 in the fact that the immense multitude of truths 7a multitude still as far from being exhausted as ever7 comprised in the mathematical sciences1 can be elicited from so small a number of elementary laws4 ,one sees not1 at first1 how it is that there can be room for such an infinite variety of true propositions1 on subjects apparently so limited4 ,to begin with the science of number4 ,the elementary or ultimate truths of this science are the common axioms concerning equality1 namely1 8,things which are equal to the same thing are equal to one another10 and 8,equals added to equals make equal sums0 7no other axioms are required717#aii7 together with the definitions of the various numbers4 ,like other so-called definitions1 these are composed of two things1 the explanation of a name1 and the assertion of a fact2 of which the latter alone can form a first principle or premise of a science4 ,the fact asserted in the definition of a number is a physical fact4 ,each of the numbers two1 three1 four1 etc41 denotes physical phenomena1 and connotes a physical property of those phenomena4 ,two1 for instance1 denotes all pairs of things1 and twelve all dozens of things1 connoting what makes them pairs1 or dozens2 and that which makes them so is something physical2 since it can not be denied that two apples are physically distinguishable from three apples1 two horses from one horse1 and so forth2 that they are a different visible and tangible phenomenon4 ,i am not undertaking to say what the difference is2 it is enough that there is a difference of which the senses can take cognizance4 ,and although a hundred and two horses are not so easily distinguished from a hundred and three1 as two horses are from three--though in most positions the senses do not perceive any difference--yet they may be so placed that a difference will be perceptible1 or else we should never have distinguished them1 and given them different names4 ,weight is confessedly a physical property of things2 yet small differences between great weights are as imperceptible to the senses in most situations1 as small differences between great numbers2 and are only put in evidence by placing the two objects in a peculiar position--namely1 in the opposite scales of a delicate balance4 ,what1 then1 is that which is connoted by a name of number8 ,of course1 some property belonging to the agglomeration of things which we call by the name2 and that property is1 the characteristic manner in which the agglomeration is made up of1 and may be separated into1 parts4 ,i will endeavor to make this more intelligible by a few explanations4 ,when we call a collection of objects two1 three1 or four1 they are not two1 three1 or four in the abstract2 they are two1 three1 or four things of some particular kind2 pebbles1 horses1 inches1 pounds' weight4 ,what the name of number connotes is1 the manner in which single objects of the given kind must be put together1 in order to produce that particular aggregate4 ,if the aggregate be of pebbles1 and we call it two1 the name implies that1 to compose the aggregate1 one pebble must be joined to one pebble4 ,if we call it three1 one and one and one pebble must be brought together to produce it1 or else one pebble must be joined to an aggregate of the kind called two1 already existing4 ,the aggregate which we call four1 has a still greater number of characteristic modes of formation4 ,one and one and one and one pebble may be brought together2 or two aggregates of the kind called two may be united2 or one pebble may be added to an aggregate of the kind called three4 ,every succeeding number in the ascending series1 may be formed by the junction of smaller numbers in a progressively greater variety of ways4 ,even limiting the parts to two1 the number may be formed1 and consequently may be divided1 in as many different ways as there are numbers smaller than itself2 and1 if we admit of threes1 fours1 etc41 in a still greater variety4 ,other modes of arriving at the same aggregate present themselves1 not by the union of smaller1 but by the dismemberment of larger aggregates4 ,thus1 three pebbles may be formed by taking away one pebble from an aggregate of four2 two pebbles1 by an equal division of a similar aggregate2 and so on4 ,every arithmetical proposition2 every statement of the result of an arithmetical operation2 is a statement of one of the modes of formation of a given number4 ,it affirms that a certain aggregate might have been formed by putting together certain other aggregates1 or by withdrawing certain portions of some aggregate2 and that1 by consequence1 we might reproduce those aggregates from it1 by reversing the process4 ,thus1 when we say that the cube of #ab is #agbh1 what we affirm is this3 that if1 having a sufficient number of pebbles or of any other objects1 we put them together into the particular sort of parcels or aggregates called twelves2 and put together these twelves again into similar collections2 and1 finally1 make up twelve of these largest parcels2 the aggregate thus formed will be such a one as we call #agbh2 namely1 that which 7to take the most familiar of its modes of formation7 may be made by joining the parcel called a thousand pebbles1 the parcel called seven hundred pebbles1 the parcel called twenty pebbles1 and the parcel called eight pebbles4 ,the converse proposition that the cube root of #agbh is #ab1 asserts that this large aggregate may again be decomposed into the twelve twelves of twelves of pebbles which it consists of4 ,the modes of formation of any number are innumerable2 but when we know one mode of formation of each1 all the rest may be determined deductively4 ,if we know that a is formed from b and c1 b from a and e1 c from d and f1 and so forth1 until we have included all the numbers of any scale we choose to select 7taking care that for each number the mode of formation be really a distinct one1 not bringing us round again to the former numbers1 but introducing a new number71 we have a set of propositions from which we may reason to all the other modes of formation of those numbers from one another4 ,having established a chain of inductive truths connecting together all the numbers of the scale1 we can ascertain the formation of any one of those numbers from any other by merely traveling from one to the other along the chain4 ,suppose that we know only the following modes of formation3 #fdb1 #dg-c1 #geb1 #ei-d4 ,we could determine how #f may be formed from #i4 ,for #fdbg-cbeb-cbi-db-cb4 ,it may therefore be formed by taking away #d and #c1 and adding #b and #b4 ,if we know besides that #bbd1 we obtain #f from #i in a simpler mode1 by merely taking away #c4 ,it is sufficient1 therefore1 to select one of the various modes of formation of each number1 as a means of ascertaining all the rest4 ,and since things which are uniform1 and therefore simple1 are most easily received and retained by the understanding1 there is an obvious advantage in selecting a mode of formation which shall be alike for all2 in fixing the connotation of names of number on one uniform principle4 ,the mode in which our existing numerical nomenclature is contrived possesses this advantage1 with the additional one1 that it happily conveys to the mind two of the modes of formation of every number4 ,each number is considered as formed by the addition of a unit to the number next below it in magnitude1 and this mode of formation is conveyed by the place which it occupies in the series4 ,and each is also considered as formed by the addition of a number of units less than ten1 and a number of aggregates each equal to one of the successive powers of ten2 and this mode of its formation is expressed by its spoken name1 and by its numerical character4 ,what renders arithmetic the type of a deductive science1 is the fortunate applicability to it of a law so comprehensive as 8,the sums of equals are equals30 or 7to express the same principle in less familiar but more characteristic language71 ,whatever is made up of parts1 is made up of the parts of those parts4 ,this truth1 obvious to the senses in all cases which can be fairly referred to their decision1 and so general as to be co-extensive with nature itself1 being true of all sorts of phenomena 7for all admit of being numbered71 must be considered an inductive truth1 or law of nature1 of the highest order4 ,and every arithmetical operation is an application of this law1 or of other laws capable of being deduced from it4 ,this is our warrant for all calculations4 ,we believe that five and two are equal to seven1 on the evidence of this inductive law1 combined with the definitions of those numbers4 ,we arrive at that conclusion 7as all know who remember how they first learned it7 by adding a single unit at a time3 #e #af1 therefore #eaafag2 and again #baa1 therefore #ebeaag4 #f4 ,innumerable as are the true propositions which can be formed concerning particular numbers1 no adequate conception could be gained1 from these alone1 of the extent of the truths composing the science of number4 ,such propositions as we have spoken of are the least general of all numerical truths4 ,it is true that even these are co-extensive with all nature2 the properties of the number four are true of all objects that are divisible into four equal parts1 and all objects are either actually or ideally so divisible4 ,but the propositions which compose the science of algebra are true1 not of a particular number1 but of all numbers2 not of all things under the condition of being divided in a particular way1 but of all things under the condition of being divided in any way--of being designated by a number at all4 ,since it is impossible for different numbers to have any of their modes of formation completely in common1 it is a kind of paradox to say1 that all propositions which can be made concerning numbers relate to their modes of formation from other numbers1 and yet that there are propositions which are true of all numbers4 ,but this very paradox leads to the real principle of generalization concerning the properties of numbers4 ,two different numbers can not be formed in the same manner from the same numbers2 but they may be formed in the same manner from different numbers2 as nine is formed from three by multiplying it into itself1 and sixteen is formed from four by the same process4 ,thus there arises a classification of modes of formation1 or in the language commonly used by mathematicians1 a classification of ,functions4 ,any number1 considered as formed from any other number1 is called a function of it2 and there are as many kinds of functions as there are modes of formation4 ,the simple functions are by no means numerous1 most functions being formed by the combination of several of the operations which form simple functions1 or by successive repetitions of some one of those operations4 ,the simple functions of any number x are all reducible to the following forms3 xa1 x-a1 ax1 x_/a1 log4 x 7to the base a71 and the same expressions varied by putting x for a and a for x1 wherever that substitution would alter the value3 to which1 perhaps1 ought to be added sin x1 and arc 7sinx74 ,all other functions of x are formed by putting some one or more of the simple functions in the place of x or a1 and subjecting them to the same elementary operations4 ,in order to carry on general reasonings on the subject of ,functions1 we require a nomenclature enabling us to express any two numbers by names which1 without specifying what particular numbers they are1 shall show what function each is of the other2 or1 in other words1 shall put in evidence their mode of formation from one another4 ,the system of general language called algebraical notation does this4 ,the expressions a and a#bc;a denote1 the one any number1 the other the number formed from it in a particular manner4 ,the expressions a1 b1 n1 and 7ab7n1 denote any three numbers1 and a fourth which is formed from them in a certain mode4 ,the following may be stated as the general problem of the algebraical calculus3 ,f being a certain function of a given number1 to find what function ,f will be of any function of that number4 ,for example1 a binomial a b is a function of its two parts a and b1 and the parts are1 in their turn1 functions of a b3 now 7a b7n is a certain function of the binomial2 what function will this be of a and b1 the two parts8 ,the answer to this question is the binomial theorem4 ,the formula 7a b7n an n_/#a an-#a b n4n-#a_/a4b an-#b b#b1 etc41 shows in what manner the number which is formed by multiplying a b into itself n times1 might be formed without that process1 directly from a1 b1 and n4 ,and of this nature are all the theorems of the science of number4 ,they assert the identity of the result of different modes of formation4 ,they affirm that some mode of formation from x1 and some mode of formation from a certain function of x1 produce the same number4 ,such1 as above described1 is the aim and end of the calculus4 ,as for its processes1 every one knows that they are simply deductive4 ,in demonstrating an algebraical theorem1 or in resolving an equation1 we travel from the datum to the qusitum by pure ratiocination2 in which the only premises introduced1 besides the original hypotheses1 are the fundamental axioms already mentioned--that things equal to the same thing are equal to one another1 and that the sums of equal things are equal4 ,at each step in the demonstration or in the calculation1 we apply one or other of these truths1 or truths deducible from them1 as1 that the differences1 products1 etc41 of equal numbers are equal4 ,it would be inconsistent with the scale of this work1 and not necessary to its design1 to carry the analysis of the truths and processes of algebra any further2 which is also the less needful1 as the task has been1 to a very great extent1 performed by other writers4 ,peacock's ,algebra1 and ,dr4 ,whewell's ,doctrine of ,limits1 are full of instruction on the subject4 ,the profound treatises of a truly philosophical mathematician1 ,professor ,de ,morgan1 should be studied by every one who desires to comprehend the evidence of mathematical truths1 and the meaning of the obscurer processes of the calculus1 and the speculations of ,m4 ,comte1 in his ,cours de ,philosophie ,positive1 on the philosophy of the higher branches of mathematics1 are among the many valuable gifts for which philosophy is indebted to that eminent thinker4 #g4 ,if the extreme generality1 and remoteness not so much from sense as from the visual and tactual imagination1 of the laws of number1 renders it a somewhat difficult effort of abstraction to conceive those laws as being in reality physical truths obtained by observation2 the same difficulty does not exist with regard to the laws of extension4 ,the facts of which those laws are expressions1 are of a kind peculiarly accessible to the senses1 and suggesting eminently distinct images to the fancy4 ,that geometry is a strictly physical science would doubtless have been recognized in all ages1 had it not been for the illusions produced by two circumstances4 ,one of these is the characteristic property1 already noticed1 of the facts of geometry1 that they may be collected from our ideas or mental pictures of objects as effectually as from the objects themselves4 ,the other is1 the demonstrative character of geometrical truths2 which was at one time supposed to constitute a radical distinction between them and physical truths2 the latter1 as resting on merely probable evidence1 being deemed essentially uncertain and unprecise4 ,the advance of knowledge has1 however1 made it manifest that physical science1 in its better understood branches1 is quite as demonstrative as geometry4 ,the task of deducing its details from a few comparatively simple principles is found to be any thing but the impossibility it was once supposed to be2 and the notion of the superior certainty of geometry is an illusion1 arising from the ancient prejudice which1 in that science1 mistakes the ideal data from which we reason1 for a peculiar class of realities1 while the corresponding ideal data of any deductive physical science are recognized as what they really are1 hypotheses4 ,every theorem in geometry is a law of external nature1 and might have been ascertained by generalizing from observation and experiment1 which in this case resolve themselves into comparison and measurement4 ,but it was found practicable1 and1 being practicable1 was desirable1 to deduce these truths by ratiocination from a small number of general laws of nature1 the certainty and universality of which are obvious to the most careless observer1 and which compose the first principles and ultimate premises of the science4 ,among these general laws must be included the same two which we have noticed as ultimate principles of the ,science of ,number also1 and which are applicable to every description of quantity2 viz41 ,the sums of equals are equal1 and ,things which are equal to the same thing are equal to one another2 the latter of which may be expressed in a manner more suggestive of the inexhaustible multitude of its consequences1 by the following terms3 ,whatever is equal to any one of a number of equal magnitudes1 is equal to any other of them4 ,to these two must be added1 in geometry1 a third law of equality1 namely1 that lines1 surfaces1 or solid spaces1 which can be so applied to one another as to coincide1 are equal4 ,some writers have asserted that this law of nature is a mere verbal definition2 that the expression 8equal magnitudes0 means nothing but magnitudes which can be so applied to one another as to coincide4 ,but in this opinion ,i can not agree4 ,the equality of two geometrical magnitudes can not differ fundamentally in its nature from the equality of two weights1 two degrees of heat1 or two portions of duration1 to none of which would this definition of equality be suitable4 ,none of these things can be so applied to one another as to coincide1 yet we perfectly understand what we mean when we call them equal4 ,things are equal in magnitude1 as things are equal in weight1 when they are felt to be exactly similar in respect of the attribute in which we compare them3 and the application of the objects to each other in the one case1 like the balancing them with a pair of scales in the other1 is but a mode of bringing them into a position in which our senses can recognize deficiencies of exact resemblance that would otherwise escape our notice4 ,along with these three general principles or axioms1 the remainder of the premises of geometry consists of the so-called definitions3 that is to say1 propositions asserting the real existence of the various objects therein designated1 together with some one property of each4 ,in some cases more than one property is commonly assumed1 but in no case is more than one necessary4 ,it is assumed that there are such things in nature as straight lines1 and that any two of them setting out from the same point1 diverge more and more without limit4 ,this assumption 7which includes and goes beyond ,euclid's axiom that two straight lines can not inclose a space7 is as indispensable in geometry1 and as evident1 resting on as simple1 familiar1 and universal observation1 as any of the other axioms4 ,it is also assumed that straight lines diverge from one another in different degrees2 in other words1 that there are such things as angles1 and that they are capable of being equal or unequal4 ,it is assumed that there is such a thing as a circle1 and that all its radii are equal2 such things as ellipses1 and that the sums of the focal distances are equal for every point in an ellipse2 such things as parallel lines1 and that those lines are everywhere equally distant47#bjj7 #h4 ,it is a matter of more than curiosity to consider1 to what peculiarity of the physical truths which are the subject of geometry1 it is owing that they can all be deduced from so small a number of original premises2 why it is that we can set out from only one characteristic property of each kind of phenomenon1 and with that and two or three general truths relating to equality1 can travel from mark to mark until we obtain a vast body of derivative truths1 to all appearance extremely unlike those elementary ones4 ,the explanation of this remarkable fact seems to lie in the following circumstances4 ,in the first place1 all questions of position and figure may be resolved into questions of magnitude4 ,the position and figure of any object are determined by determining the position of a sufficient number of points in it2 and the position of any point may be determined by the magnitude of three rectangular co-ordinates1 that is1 of the perpendiculars drawn from the point to three planes at right angles to one another1 arbitrarily selected4 ,by this transformation of all questions of quality into questions only of quantity1 geometry is reduced to the single problem of the measurement of magnitudes1 that is1 the ascertainment of the equalities which exist between them4 ,now when we consider that by one of the general axioms1 any equality1 when ascertained1 is proof of as many other equalities as there are other things equal to either of the two equals2 and that by another of those axioms1 any ascertained equality is proof of the equality of as many pairs of magnitudes as can be formed by the numerous operations which resolve themselves into the addition of the equals to themselves or to other equals2 we cease to wonder that in proportion as a science is conversant about equality1 it should afford a more copious supply of marks of marks2 and that the sciences of number and extension1 which are conversant with little else than equality1 should be the most deductive of all the sciences4 ,there are also two or three of the principal laws of space or extension which are unusually fitted for rendering one position or magnitude a mark of another1 and thereby contributing to render the science largely deductive4 ,first1 the magnitudes of inclosed spaces1 whether superficial or solid1 are completely determined by the magnitudes of the lines and angles which bound them4 ,secondly1 the length of any line1 whether straight or curve1 is measured 7certain other things being given7 by the angle which it subtends1 and vic versa4 ,lastly1 the angle which any two straight lines make with each other at an inaccessible point1 is measured by the angles they severally make with any third line we choose to select4 ,by means of these general laws1 the measurement of all lines1 angles1 and spaces whatsoever might be accomplished by measuring a single straight line and a sufficient number of angles2 which is the plan actually pursued in the trigonometrical survey of a country2 and fortunate it is that this is practicable1 the exact measurement of long straight lines being always difficult1 and often impossible1 but that of angles very easy4 ,three such generalizations as the foregoing afford such facilities for the indirect measurement of magnitudes 7by supplying us with known lines or angles which are marks of the magnitude of unknown ones1 and thereby of the spaces which they inclose71 that it is easily intelligible how from a few data we can go on to ascertain the magnitude of an indefinite multitude of lines1 angles1 and spaces1 which we could not easily1 or could not at all1 measure by any more direct process4 #i4 ,such are the remarks which it seems necessary to make in this place1 respecting the laws of nature which are the peculiar subject of the sciences of number and extension4 ,the immense part which those laws take in giving a deductive character to the other departments of physical science1 is well known2 and is not surprising1 when we consider that all causes operate according to mathematical laws4 ,the effect is always dependent on1 or is a function of1 the quantity of the agent2 and generally of its position also4 ,we can not1 therefore1 reason respecting causation1 without introducing considerations of quantity and extension at every step2 and if the nature of the phenomena admits of our obtaining numerical data of sufficient accuracy1 the laws of quantity become the grand instrument for calculating forward to an effect1 or backward to a cause4 ,that in all other sciences1 as well as in geometry1 questions of quality are scarcely ever independent of questions of quantity1 may be seen from the most familiar phenomena4 ,even when several colors are mixed on a painter's palette1 the comparative quantity of each entirely determines the color of the mixture4 ,with this mere suggestion of the general causes which render mathematical principles and processes so predominant in those deductive sciences which afford precise numerical data1 ,i must1 on the present occasion1 content myself2 referring the reader who desires a more thorough acquaintance with the subject1 to the first two volumes of ,m4 ,comte's systematic work4 ,in the same work1 and more particularly in the third volume1 are also fully discussed the limits of the applicability of mathematical principles to the improvement of other sciences4 ,such principles are manifestly inapplicable1 where the causes on which any class of phenomena depend are so imperfectly accessible to our observation1 that we can not ascertain1 by a proper induction1 their numerical laws2 or where the causes are so numerous1 and intermixed in so complex a manner with one another1 that even supposing their laws known1 the computation of the aggregate effect transcends the powers of the calculus as it is1 or is likely to be2 or1 lastly1 where the causes themselves are in a state of perpetual fluctuation2 as in physiology1 and still more1 if possible1 in the social science4 ,the mathematical solutions of physical questions become progressively more difficult and imperfect1 in proportion as the questions divest themselves of their abstract and hypothetical character1 and approach nearer to the degree of complication actually existing in nature2 insomuch that beyond the limits of astronomical phenomena1 and of those most nearly analogous to them1 mathematical accuracy is generally obtained 8at the expense of the reality of the inquiry30 while even in astronomical questions1 8notwithstanding the admirable simplicity of their mathematical elements1 our feeble intelligence becomes incapable of following out effectually the logical combinations of the laws on which the phenomena are dependent1 as soon as we attempt to take into simultaneous consideration more than two or three essential influences407#bja7 ,of this1 the problem of the ,three ,bodies has already been cited1 more than once1 as a remarkable instance2 the complete solution of so comparatively simple a question having vainly tried the skill of the most profound mathematicians4 ,we may conceive1 then1 how chimerical would be the hope that mathematical principles could be advantageously applied to phenomena dependent on the mutual action of the innumerable minute particles of bodies1 as those of chemistry1 and still more1 of physiology2 and for similar reasons those principles remain inapplicable to the still more complex inquiries1 the subjects of which are phenomena of society and government4 ,the value of mathematical instruction as a preparation for those more difficult investigations1 consists in the applicability not of its doctrines1 but of its method4 ,mathematics will ever remain the most perfect type of the ,deductive ,method in general2 and the applications of mathematics to the deductive branches of physics1 furnish the only school in which philosophers can effectually learn the most difficult and important portion of their art1 the employment of the laws of simpler phenomena for explaining and predicting those of the more complex4 ,these grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education1 and regarding 7according to the dictum which an old but unauthentic tradition ascribes to ,plato7 one who is 1 as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy4 ,chapter ,,xxv4 ,of ,the ,grounds ,of ,disbelief4 #a4 ,the method of arriving at general truths1 or general propositions fit to be believed1 and the nature of the evidence on which they are grounded1 have been discussed1 as far as space and the writer's faculties permitted1 in the twenty-four preceding chapters4 ,but the result of the examination of evidence is not always belief1 nor even suspension of judgment2 it is sometimes disbelief4 ,the philosophy1 therefore1 of induction and experimental inquiry is incomplete1 unless the grounds not only of belief1 but of disbelief1 are treated of2 and to this topic we shall devote one1 and the final1 chapter4 ,by disbelief is not here to be understood the mere absence of belief4 ,the ground for abstaining from belief is simply the absence or insufficiency of proof2 and in considering what is sufficient evidence to support any given conclusion1 we have already1 by implication1 considered what evidence is not sufficient for the same purpose4 ,by disbelief is here meant1 not the state of mind in which we form no opinion concerning a subject1 but that in which we are fully persuaded that some opinion is not true2 insomuch that if evidence1 even of great apparent strength 7whether grounded on the testimony of others or on our own supposed perceptions71 were produced in favor of the opinion1 we should believe that the witnesses spoke falsely1 or that they1 or we ourselves if we were the direct percipients1 were mistaken4 ,that there are such cases1 no one is likely to dispute4 ,assertions for which there is abundant positive evidence are often disbelieved1 on account of what is called their improbability1 or impossibility4 ,and the question for consideration is what1 in the present case1 these words mean1 and how far and in what circumstances the properties which they express are sufficient grounds for disbelief4 #b4 ,it is to be remarked1 in the first place1 that the positive evidence produced in support of an assertion which is nevertheless rejected on the score of impossibility or improbability1 is never such as amounts to full proof4 ,it is always grounded on some approximate generalization4 ,the fact may have been asserted by a hundred witnesses2 but there are many exceptions to the universality of the generalization that what a hundred witnesses affirm is true4 ,we may seem to ourselves to have actually seen the fact2 but that we really see what we think we see1 is by no means a universal truth2 our organs may have been in a morbid state2 or we may have inferred something1 and imagined that we perceived it4 ,the evidence1 then1 in the affirmative being never more than an approximate generalization1 all will depend on what the evidence in the negative is4 ,if that also rests on an approximate generalization1 it is a case for comparison of probabilities4 ,if the approximate generalizations leading to the affirmative are1 when added together1 less strong1 or1 in other words1 farther from being universal1 than the approximate generalizations which support the negative side of the question1 the proposition is said to be improbable1 and is to be disbelieved provisionally4 ,if1 however1 an alleged fact be in contradiction1 not to any number of approximate generalizations1 but to a completed generalization grounded on a rigorous induction1 it is said to be impossible1 and is to be disbelieved totally4 ,this last principle1 simple and evident as it appears1 is the doctrine which1 on the occasion of an attempt to apply it to the question of the credibility of miracles1 excited so violent a controversy4 ,hume's celebrated doctrine1 that nothing is credible which is contradictory to experience1 or at variance with laws of nature1 is merely this very plain and harmless proposition1 that whatever is contradictory to a complete induction is incredible4 ,that such a maxim as this should either be accounted a dangerous heresy1 or mistaken for a great and recondite truth1 speaks ill for the state of philosophical speculation on such subjects4 ,but does not 7it may be asked7 the very statement of the proposition imply a contradiction8 ,an alleged fact1 according to this theory1 is not to be believed if it contradict a complete induction4 ,but it is essential to the completeness of an induction that it shall not contradict any known fact4 ,is it not1 then1 a petitio principii to say1 that the fact ought to be disbelieved because the induction opposed to it is complete8 ,how can we have a right to declare the induction complete1 while facts1 supported by credible evidence1 present themselves in opposition to it8 ,i answer1 we have that right whenever the scientific canons of induction give it to us2 that is1 whenever the induction can be complete4 ,we have it1 for example1 in a case of causation in which there has been an experimentum crucis4 ,if an antecedent ,a1 superadded to a set of antecedents in all other respects unaltered1 is followed by an effect ,b which did not exist before1 ,a is1 in that instance at least1 the cause of ,b1 or an indispensable part of its cause2 and if ,a be tried again with many totally different sets of antecedents and ,b still follows1 then it is the whole cause4 ,if these observations or experiments have been repeated so often1 and by so many persons1 as to exclude all supposition of error in the observer1 a law of nature is established2 and so long as this law is received as such1 the assertion that on any particular occasion ,a took place1 and yet ,b did not follow1 without any counteracting cause1 must be disbelieved4 ,such an assertion is not to be credited on any less evidence than what would suffice to overturn the law4 ,the general truths1 that whatever has a beginning has a cause1 and that when none but the same causes exist1 the same effects follow1 rest on the strongest inductive evidence possible2 the proposition that things affirmed by even a crowd of respectable witnesses are true1 is but an approximate generalization2 and--even if we fancy we actually saw or felt the fact which is in contradiction to the law--what a human being can see is no more than a set of appearances2 from which the real nature of the phenomenon is merely an inference1 and in this inference approximate generalizations usually have a large share4 ,if1 therefore1 we make our election to hold by the law1 no quantity of evidence whatever ought to persuade us that there has occurred any thing in contradiction to it4 ,if1 indeed1 the evidence produced is such that it is more likely that the set of observations and experiments on which the law rests should have been inaccurately performed or incorrectly interpreted1 than that the evidence in question should be false1 we may believe the evidence2 but then we must abandon the law4 ,and since the law was received on what seemed a complete induction1 it can only be rejected on evidence equivalent2 namely1 as being inconsistent not with any number of approximate generalizations1 but with some other and better established law of nature4 ,this extreme case1 of a conflict between two supposed laws of nature1 has probably never actually occurred where1 in the process of investigating both the laws1 the true canons of scientific induction had been kept in view2 but if it did occur1 it must terminate in the total rejection of one of the supposed laws4 ,it would prove that there must be a flaw in the logical process by which either one or the other was established2 and if there be so1 that supposed general truth is no truth at all4 ,we can not admit a proposition as a law of nature1 and yet believe a fact in real contradiction to it4 ,we must disbelieve the alleged fact1 or believe that we were mistaken in admitting the supposed law4 ,but in order that any alleged fact should be contradictory to a law of causation1 the allegation must be1 not simply that the cause existed without being followed by the effect1 for that would be no uncommon occurrence2 but that this happened in the absence of any adequate counteracting cause4 ,now in the case of an alleged miracle1 the assertion is the exact opposite of this4 ,it is1 that the effect was defeated1 not in the absence1 but in consequence of a counteracting cause1 namely1 a direct interposition of an act of the will of some being who has power over nature2 and in particular of a ,being1 whose will being assumed to have endowed all the causes with the powers by which they produce their effects1 may well be supposed able to counteract them4 ,a miracle 7as was justly remarked by ,brown77#bjb7 is no contradiction to the law of cause and effect2 it is a new effect1 supposed to be produced by the introduction of a new cause4 ,of the adequacy of that cause1 if present1 there can be no doubt2 and the only antecedent improbability which can be ascribed to the miracle1 is the improbability that any such cause existed4 ,all1 therefore1 which ,hume has made out1 and this he must be considered to have made out1 is1 that 7at least in the imperfect state of our knowledge of natural agencies1 which leaves it always possible that some of the physical antecedents may have been hidden from us7 no evidence can prove a miracle to any one who did not previously believe the existence of a being or beings with supernatural power2 or who believes himself to have full proof that the character of the ,being whom he recognizes is inconsistent with his having seen fit to interfere on the occasion in question4 ,if we do not already believe in supernatural agencies1 no miracle can prove to us their existence4 ,the miracle itself1 considered merely as an extraordinary fact1 may be satisfactorily certified by our senses or by testimony2 but nothing can ever prove that it is a miracle2 there is still another possible hypothesis1 that of its being the result of some unknown natural cause2 and this possibility can not be so completely shut out1 as to leave no alternative but that of admitting the existence and intervention of a being superior to nature4 ,those1 however1 who already believe in such a being have two hypotheses to choose from1 a supernatural and an unknown natural agency2 and they have to judge which of the two is the most probable in the particular case4 ,in forming this judgment1 an important element of the question will be the conformity of the result to the laws of the supposed agent1 that is1 to the character of the ,deity as they conceive it4 ,but with the knowledge which we now possess of the general uniformity of the course of nature1 religion1 following in the wake of science1 has been compelled to acknowledge the government of the universe as being on the whole carried on by general laws1 and not by special interpositions4 ,to whoever holds this belief1 there is a general presumption against any supposition of divine agency not operating through general laws1 or1 in other words1 there is an antecedent improbability in every miracle1 which1 in order to outweigh it1 requires an extraordinary strength of antecedent probability derived from the special circumstances of the case4 #c4 ,it appears from what has been said1 that the assertion that a cause has been defeated of an effect which is connected with it by a completely ascertained law of causation1 is to be disbelieved or not1 according to the probability or improbability that there existed in the particular instance an adequate counteracting cause4 ,to form an estimate of this1 is not more difficult than of other probabilities4 ,with regard to all known causes capable of counteracting the given causes1 we have generally some previous knowledge of the frequency or rarity of their occurrence1 from which we may draw an inference as to the antecedent improbability of their having been present in any particular case4 ,and neither in respect to known nor unknown causes are we required to pronounce on the probability of their existing in nature1 but only of their having existed at the time and place at which the transaction is alleged to have happened4 ,we are seldom1 therefore1 without the means 7when the circumstances of the case are at all known to us7 of judging how far it is likely that such a cause should have existed at that time and place without manifesting its presence by some other marks1 and 7in the case of an unknown cause7 without having hitherto manifested its existence in any other instance4 ,according as this circumstance1 or the falsity of the testimony1 appears more improbable--that is1 conflicts with an approximate generalization of a higher order--we believe the testimony1 or disbelieve it2 with a stronger or a weaker degree of conviction1 according to the preponderance2 at least until we have sifted the matter further4 ,so much1 then1 for the case in which the alleged fact conflicts1 or appears to conflict1 with a real law of causation4 ,but a more common case1 perhaps1 is that of its conflicting with uniformities of mere co-existence1 not proved to be dependent on causation2 in other words1 with the properties of ,kinds4 ,it is with these uniformities principally that the marvelous stories related by travelers are apt to be at variance2 as of men with tails1 or with wings1 and 7until confirmed by experience7 of flying fish2 or of ice1 in the celebrated anecdote of the ,dutch travelers and the ,king of ,siam4 ,facts of this description1 facts previously unheard of1 but which could not from any known law of causation be pronounced impossible1 are what ,hume characterizes as not contrary to experience1 but merely unconformable to it2 and ,bentham1 in his treatise on ,evidence1 denominates them facts disconformable in specie1 as distinguished from such as are disconformable in toto or in degree ,in a case of this description1 the fact asserted is the existence of a new ,kind2 which in itself is not in the slightest degree incredible1 and only to be rejected if the improbability that any variety of object existing at the particular place and time should not have been discovered sooner1 be greater than that of error or mendacity in the witnesses4 ,accordingly1 such assertions1 when made by credible persons1 and of unexplored places1 are not disbelieved1 but at most regarded as requiring confirmation from subsequent observers2 unless the alleged properties of the supposed new ,kind are at variance with known properties of some larger kind which includes it2 or1 in other words1 unless1 in the new ,kind which is asserted to exist1 some properties are said to have been found disjoined from others which have always been known to accompany them2 as in the case of ,pliny's men1 or any other kind of animal of a structure different from that which has always been found to co-exist with animal life4 ,on the mode of dealing with any such case1 little needs be added to what has been said on the same topic in the twenty-second chapter47#bjc7 ,when the uniformities of co-existence which the alleged fact would violate1 are such as to raise a strong presumption of their being the result of causation1 the fact which conflicts with them is to be disbelieved2 at least provisionally1 and subject to further investigation4 ,when the presumption amounts to a virtual certainty1 as in the case of the general structure of organized beings1 the only question requiring consideration is whether1 in phenomena so little understood1 there may not be liabilities to counteraction from causes hitherto unknown2 or whether the phenomena may not be capable of originating in some other way1 which would produce a different set of derivative uniformities4 ,where 7as in the case of the flying fish1 or the ornithorhynchus7 the generalization to which the alleged fact would be an exception is very special and of limited range1 neither of the above suppositions can be deemed very improbable2 and it is generally1 in the case of such alleged anomalies1 wise to suspend our judgment1 pending the subsequent inquiries which will not fail to confirm the assertion if it be true4 ,but when the generalization is very comprehensive1 embracing a vast number and variety of observations1 and covering a considerable province of the domain of nature2 then1 for reasons which have been fully explained1 such an empirical law comes near to the certainty of an ascertained law of causation2 and any alleged exception to it can not be admitted1 unless on the evidence of some law of causation proved by a still more complete induction4 ,such uniformities in the course of nature as do not bear marks of being the results of causation are1 as we have already seen1 admissible as universal truths with a degree of credence proportioned to their generality4 ,those which are true of all things whatever1 or at least which are totally independent of the varieties of ,kinds1 namely1 the laws of number and extension1 to which we may add the law of causation itself1 are probably the only ones1 an exception to which is absolutely and permanently incredible4 ,accordingly1 it is to assertions supposed to be contradictory to these laws1 or to some others coming near to them in generality1 that the word impossibility 7at least total impossibility7 seems to be generally confined4 ,violations of other laws1 of special laws of causation1 for instance1 are said1 by persons studious of accuracy in expression1 to be impossible in the circumstances of the case2 or impossible unless some cause had existed which did not exist in the particular case47#bjd7 ,of no assertion1 not in contradiction to some of these very general laws1 will more than improbability be asserted by any cautious person2 and improbability not of the highest degree1 unless the time and place in which the fact is said to have occurred1 render it almost certain that the anomaly1 if real1 could not have been overlooked by other observers4 ,suspension of judgment is in all other cases the resource of the judicious inquirer2 provided the testimony in favor of the anomaly presents1 when well sifted1 no suspicious circumstances4 ,but the testimony is scarcely ever found to stand that test1 in cases in which the anomaly is not real4 ,in the instances on record in which a great number of witnesses1 of good reputation and scientific acquirements1 have testified to the truth of something which has turned out untrue1 there have almost always been circumstances which1 to a keen observer who had taken due pains to sift the matter1 would have rendered the testimony untrustworthy4 ,there have generally been means of accounting for the impression on the senses or minds of the alleged percipients1 by fallacious appearances2 or some epidemic delusion1 propagated by the contagious influence of popular feeling1 has been concerned in the case2 or some strong interest has been implicated--religious zeal1 party feeling1 vanity1 or at least the passion for the marvelous1 in persons strongly susceptible of it4 ,when none of these or similar circumstances exist to account for the apparent strength of the testimony2 and where the assertion is not in contradiction either to those universal laws which know no counteraction or anomaly1 or to the generalizations next in comprehensiveness to them1 but would only amount1 if admitted1 to the existence of an unknown cause or an anomalous ,kind1 in circumstances not so thoroughly explored but that it is credible that things hitherto unknown may still come to light2 a cautious person will neither admit nor reject the testimony1 but will wait for confirmation at other times and from other unconnected sources4 ,such ought to have been the conduct of the ,king of ,siam when the ,dutch travelers affirmed to him the existence of ice4 ,but an ignorant person is as obstinate in his contemptuous incredulity as he is unreasonably credulous4 ,any thing unlike his own narrow experience he disbelieves1 if it flatters no propensity2 any nursery tale is swallowed implicitly by him if it does4 #d4 ,i shall now advert to a very serious misapprehension of the principles of the subject1 which has been committed by some of the writers against ,hume's ,essay on ,miracles1 and by ,bishop ,butler before them1 in their anxiety to destroy what appeared to them a formidable weapon of assault against the ,christian religion2 and the effect of which is entirely to confound the doctrine of the ,grounds of ,disbelief4 ,the mistake consists in overlooking the distinction between 7what may be called7 improbability before the fact and improbability after it2 or 7since1 as ,mr4 ,venn remarks1 the distinction of past and future is not the material circumstance7 between the improbability of a mere guess being right1 and the improbability of an alleged fact being true4 ,many events are altogether improbable to us1 before they have happened1 or before we are informed of their happening1 which are not in the least incredible when we are informed of them1 because not contrary to any1 even approximate1 induction4 ,in the cast of a perfectly fair die1 the chances are five to one against throwing ace1 that is1 ace will be thrown on an average only once in six throws4 ,but this is no reason against believing that ace was thrown on a given occasion1 if any credible witness asserts it2 since though ace is only thrown once in six times1 some number which is only thrown once in six times must have been thrown if the die was thrown at all4 ,the improbability1 then1 or1 in other words1 the unusualness1 of any fact1 is no reason for disbelieving it1 if the nature of the case renders it certain that either that or something equally improbable1 that is1 equally unusual1 did happen4 ,nor is this all2 for even if the other five sides of the die were all twos1 or all threes1 yet as ace would still1 on the average1 come up once in every six throws1 its coming up in a given throw would be not in any way contradictory to experience4 ,if we disbelieved all facts which had the chances against them beforehand1 we should believe hardly any thing4 ,we are told that ,a4 ,b4 died yesterday2 the moment before we were so told1 the chances against his having died on that day may have been ten thousand to one2 but since he was certain to die at some time or other1 and when he died must necessarily die on some particular day1 while the preponderance of chances is very great against every day in particular1 experience affords no ground for discrediting any testimony which may be produced to the event's having taken place on a given day4 ,yet it has been considered by ,dr4 ,campbell and others1 as a complete answer to ,hume's doctrine 7that things are incredible which are contrary to the uniform course of experience71 that we do not disbelieve1 merely because the chances were against them1 things in strict conformity to the uniform course of experience2 that we do not disbelieve an alleged fact merely because the combination of causes on which it depends occurs only once in a certain number of times4 ,it is evident that whatever is shown by observation1 or can be proved from laws of nature1 to occur in a certain proportion 7however small7 of the whole number of possible cases1 is not contrary to experience2 though we are right in disbelieving it1 if some other supposition respecting the matter in question involves1 on the whole1 a less departure from the ordinary course of events4 ,yet on such grounds as this have able writers been led to the extraordinary conclusion1 that nothing supported by credible testimony ought ever to be disbelieved4 #e4 ,we have considered two species of events1 commonly said to be improbable2 one kind which are in no way extraordinary1 but which1 having an immense preponderance of chances against them1 are improbable until they are affirmed1 but no longer2 another kind which1 being contrary to some recognized law of nature1 are incredible on any amount of testimony except such as would be sufficient to shake our belief in the law itself4 ,but between these two classes of events1 there is an intermediate class1 consisting of what are commonly termed ,coincidences3 in other words1 those combinations of chances which present some peculiar and unexpected regularity1 assimilating them1 in so far1 to the results of law4 ,as if1 for example1 in a lottery of a thousand tickets1 the numbers should be drawn in the exact order of what are called the natural numbers1 #a1 #b1 #c1 etc4 ,we have still to consider the principles of evidence applicable to this case3 whether there is any difference between coincidences and ordinary events1 in the amount of testimony or other evidence necessary to render them credible4 ,it is certain that on every rational principle of expectation1 a combination of this peculiar sort may be expected quite as often as any other given series of a thousand numbers2 that with perfectly fair dice1 sixes will be thrown twice1 thrice1 or any number of times in succession1 quite as often in a thousand or a million throws1 as any other succession of numbers fixed upon beforehand2 and that no judicious player would give greater odds against the one series than against the other4 ,notwithstanding this1 there is a general disposition to regard the one as much more improbable than the other1 and as requiring much stronger evidence to make it credible4 ,such is the force of this impression1 that it has led some thinkers to the conclusion1 that nature has greater difficulty in producing regular combinations than irregular ones2 or in other words1 that there is some general tendency of things1 some law1 which prevents regular combinations from occurring1 or at least from occurring so often as others4 ,among these thinkers may be numbered ,d',alembert2 who1 in an ,essay on ,probabilities to be found in the fifth volume of his ,mlanges1 contends that regular combinations1 though equally probable according to the mathematical theory with any others1 are physically less probable4 ,he appeals to common sense1 or1 in other words1 to common impressions2 saying1 if dice thrown repeatedly in our presence gave sixes every time1 should we not1 before the number of throws had reached ten 7not to speak of thousands of millions71 be ready to affirm1 with the most positive conviction1 that the dice were false8 ,the common and natural impression is in favor of ,d',alembert3 the regular series would be thought much more unlikely than an irregular4 ,but this common impression is1 ,i apprehend1 merely grounded on the fact1 that scarcely any body remembers to have ever seen one of these peculiar coincidences3 the reason of which is simply that no one's experience extends to any thing like the number of trials1 within which that or any other given combination of events can be expected to happen4 ,the chance of sixes on a single throw of two dice being 1 the chance of sixes ten times in succession is #a divided by the tenth power of #cf2 in other words1 such a concurrence is only likely to happen once in #c1fef1aeh1ddj1jfb1igf trials1 a number which no dice-player's experience comes up to a millionth part of4 ,but if1 instead of sixes ten times1 any other given succession of ten throws had been fixed upon1 it would have been exactly as unlikely that in any individual's experience that particular succession had ever occurred2 although this does not seem equally improbable1 because no one would be likely to have remembered whether it had occurred or not1 and because the comparison is tacitly made1 not between sixes ten times and any one particular series of throws1 but between all regular and all irregular successions taken together4 ,that 7as ,d',alembert says7 if the succession of sixes was actually thrown before our eyes1 we should ascribe it not to chance1 but to unfairness in the dice1 is unquestionably true4 ,but this arises from a totally different principle4 ,we should then be considering1 not the probability of the fact in itself1 but the comparative probability with which1 when it is known to have happened1 it may be referred to one or to another cause4 ,the regular series is not at all less likely than the irregular one to be brought about by chance1 but it is much more likely than the irregular one to be produced by design2 or by some general cause operating through the structure of the dice4 ,it is the nature of casual combinations to produce a repetition of the same event1 as often and no oftener than any other series of events4 ,but it is the nature of general causes to reproduce1 in the same circumstances1 always the same event4 ,common sense and science alike dictate that1 all other things being the same1 we should rather attribute the effect to a cause which if real would be very likely to produce it1 than to a cause which would be very unlikely to produce it4 ,according to ,laplace's sixth theorem1 which we demonstrated in a former chapter1 the difference of probability arising from the superior efficacy of the constant cause1 unfairness in the dice1 would after a very few throws far outweigh any antecedent probability which there could be against its existence4 ,d',alembert should have put the question in another manner4 ,he should have supposed that we had ourselves previously tried the dice1 and knew by ample experience that they were fair4 ,another person then tries them in our absence1 and assures us that he threw sixes ten times in succession4 ,is the assertion credible or not8 ,here the effect to be accounted for is not the occurrence itself1 but the fact of the witness's asserting it4 ,this may arise either from its having really happened1 or from some other cause4 ,what we have to estimate is the comparative probability of these two suppositions4 ,if the witness affirmed that he had thrown any other series of numbers1 supposing him to be a person of veracity1 and tolerable accuracy1 and to profess that he took particular notice1 we should believe him4 ,but the ten sixes are exactly as likely to have been really thrown as the other series4 ,if1 therefore1 this assertion is less credible than the other1 the reason must be1 not that it is less likely than the other to be made truly1 but that it is more likely than the other to be made falsely4 ,one reason obviously presents itself why what is called a coincidence1 should be oftener asserted falsely than an ordinary combination4 ,it excites wonder4 ,it gratifies the love of the marvelous4 ,the motives1 therefore1 to falsehood1 one of the most frequent of which is the desire to astonish1 operate more strongly in favor of this kind of assertion than of the other kind4 ,thus far there is evidently more reason for discrediting an alleged coincidence1 than a statement in itself not more probable1 but which if made would not be thought remarkable4 ,there are cases1 however1 in which the presumption on this ground would be the other way4 ,there are some witnesses who1 the more extraordinary an occurrence might appear1 would be the more anxious to verify it by the utmost carefulness of observation before they would venture to believe it1 and still more before they would assert it to others4 #f4 ,independently1 however1 of any peculiar chances of mendacity arising from the nature of the assertion1 ,laplace contends1 that merely on the general ground of the fallibility of testimony1 a coincidence is not credible on the same amount of testimony on which we should be warranted in believing an ordinary combination of events4 ,in order to do justice to his argument1 it is necessary to illustrate it by the example chosen by himself4 ,if1 says ,laplace1 there were one thousand tickets in a box1 and one only has been drawn out1 then if an eye-witness affirms that the number drawn was #gi1 this1 though the chances were #iii in #ajjj against it1 is not on that account the less credible2 its credibility is equal to the antecedent probability of the witness's veracity4 ,but if there were in the box #iii black balls and only one white1 and the witness affirms that the white ball was drawn1 the case according to ,laplace is very different3 the credibility of his assertion is but a small fraction of what it was in the former case2 the reason of the difference being as follows3 ,the witnesses of whom we are speaking must1 from the nature of the case1 be of a kind whose credibility falls materially short of certainty2 let us suppose1 then1 the credibility of the witness in the case in question to be 2 that is1 let us suppose that in every ten statements which the witness makes1 nine on an average are correct1 and one incorrect4 ,let us now suppose that there have taken place a sufficient number of drawings to exhaust all the possible combinations1 the witness deposing in every one4 ,in one case out of every ten in all these drawings he will actually have made a false announcement4 ,but in the case of the thousand tickets these false announcements will have been distributed impartially over all the numbers1 and of the #iii cases in which ,no4 #gi was not drawn1 there will have been only one case in which it was announced4 ,on the contrary1 in the case of the thousand balls 7the announcement being always either 8black0 or 8white071 if white was not drawn1 and there was a false announcement1 that false announcement must have been white2 and since by the supposition there was a false announcement once in every ten times1 white will have been announced falsely in one-tenth part of all the cases in which it was not drawn1 that is1 in one-tenth part of #iii cases out of every thousand4 ,white1 then1 is drawn1 on an average1 exactly as often as ,no4 #gi1 but it is announced1 without having been really drawn1 #iii times as often as ,no4 #gi2 the announcement1 therefore1 requires a much greater amount of testimony to render it credible47#bje7 ,to make this argument valid it must of course be supposed1 that the announcements made by the witness are average specimens of his general veracity and accuracy2 or1 at least1 that they are neither more nor less so in the case of the black and white balls1 than in the case of the thousand tickets4 ,this assumption1 however1 is not warranted4 ,a person is far less likely to mistake1 who has only one form of error to guard against1 than if he had #iii different errors to avoid4 ,for instance1 in the example chosen1 a messenger who might make a mistake once in ten times in reporting the number drawn in a lottery1 might not err once in a thousand times if sent simply to observe whether a ball was black or white4 ,laplace's argument1 therefore1 is faulty even as applied to his own case4 ,still less can that case be received as completely representing all cases of coincidence4 ,laplace has so contrived his example1 that though black answers to #iii distinct possibilities1 and white only to one1 the witness has nevertheless no bias which can make him prefer black to white4 ,the witness did not know that there were #iii black balls in the box and only one white2 or if he did1 ,laplace has taken care to make all the #iii cases so undistinguishably alike1 that there is hardly a possibility of any cause of falsehood or error operating in favor of any of them1 which would not operate in the same manner if there were only one4 ,alter this supposition1 and the whole argument falls to the ground4 ,let the balls1 for instance1 be numbered1 and let the white ball be ,no4 #gi4 ,considered in respect of their color1 there are but two things which the witness can be interested in asserting1 or can have dreamed or hallucinated1 or has to choose from if he answers at random1 viz41 black and white2 but considered in respect of the numbers attached to them1 there are a thousand2 and if his interest or error happens to be connected with the numbers1 though the only assertion he makes is about the color1 the case becomes precisely assimilated to that of the thousand tickets4 ,or instead of the balls suppose a lottery1 with #ajjj tickets and but one prize1 and that ,i hold ,no4 #gi1 and being interested only in that1 ask the witness not what was the number drawn1 but whether it was #gi or some other4 ,there are now only two cases1 as in ,laplace's example2 yet he surely would not say that if the witness answered #gi1 the assertion would be in an enormous proportion less credible1 than if he made the same answer to the same question asked in the other way4 ,if1 for instance 7to put a case supposed by ,laplace himself71 he has staked a large sum on one of the chances1 and thinks that by announcing its occurrence he shall increase his credit2 he is equally likely to have betted on any one of the #iii numbers which are attached to black balls1 and so far as the chances of mendacity from this cause are concerned1 there will be #iii times as many chances of his announcing black falsely as white4 ,or suppose a regiment of #ajjj men1 #iii ,englishmen and one ,frenchman1 and that of these one man has been killed1 and it is not known which4 ,i ask the question1 and the witness answers1 the ,frenchman4 ,this was not only as improbable a priori1 but is in itself as singular a circumstance1 as remarkable a coincidence1 as the drawing of the white ball2 yet we should believe the statement as readily1 as if the answer had been ,john ,thompson4 ,because1 though the #iii ,englishmen were all alike in the point in which they differed from the ,frenchman1 they were not1 like the #iii black balls1 undistinguishable in every other respect2 but being all different1 they admitted as many chances of interest or error1 as if each man had been of a different nation2 and if a lie was told or a mistake made1 the misstatement was as likely to fall on any ,jones or ,thompson of the set1 as on the ,frenchman4 ,the example of a coincidence selected by ,d',alembert1 that of sixes thrown on a pair of dice ten times in succession1 belongs to this sort of cases rather than to such as ,laplace's4 ,the coincidence is here far more remarkable1 because of far rarer occurrence1 than the drawing of the white ball4 ,but though the improbability of its really occurring is greater1 the superior probability of its being announced falsely can not be established with the same evidence4 ,the announcement 8black0 represented #iii cases1 but the witness may not have known this1 and if he did1 the #iii cases are so exactly alike1 that there is really only one set of possible causes of mendacity corresponding to the whole4 ,the announcement 8sixes not drawn ten times10 represents1 and is known by the witness to represent1 a great multitude of contingencies1 every one of which being unlike every other1 there may be a different and a fresh set of causes of mendacity corresponding to each4 ,it appears to me1 therefore1 that ,laplace's doctrine is not strictly true of any coincidences1 and is wholly inapplicable to most2 and that to know whether a coincidence does or does not require more evidence to render it credible than an ordinary event1 we must refer1 in every instance1 to first principles1 and estimate afresh what is the probability that the given testimony would have been delivered in that instance1 supposing the fact which it asserts not to be true4 ,with these remarks we close the discussion of the ,grounds of ,disbelief2 and along with it1 such exposition as space admits1 and as the writer has it in his power to furnish1 of the ,logic of ,induction4 ,book ,,iv4 ,,of ,,operations ,,subsidiary ,,to ,,induction4 8,clear and distinct ideas are terms which1 though familiar and frequent in men's mouths1 ,i have reason to think every one who uses does not perfectly understand4 ,and possibly it is but here and there one who gives himself the trouble to consider them so far as to know what he himself or others precisely mean by them2 ,i have1 therefore1 in most places1 chose to put determinate or determined1 instead of clear and distinct1 as more likely to direct men's thoughts to my meaning in this matter40--,,locke',s ,essay on the ,human ,understanding2 ,epistle to the ,reader4 8,il ne peut y avoir qu'une mthode parfaite1 qui est la mthode naturelle2 on nomme ainsi un arrangement dans lequel les tres du mme genre seraient plus voisins entre eux que ceux de tous les autres genres2 les genres du mme ordre1 plus que ceux de tous les autres ordres2 et ainsi de suite4 ,cette mthode est l'idal auquel l'histoire naturelle doit tendre2 car il est vident que si l'on y parvenait1 l'on aurait l'expression exacte et complte de la nature entire40--,,cuvier1 ,rgne ,animal1 ,introduction4 8,deux grandes notions philosophiques dominent la thorie fondamentale de la mthode naturelle proprement dite1 savoir la formation des groupes naturels1 et ensuite leur succession hirarchique40--,,comte1 ,cours de ,philosophie ,positive1 #dbme leon4 ,chapter ,i4 ,of ,observation ,and ,description4 #a4 ,the inquiry which occupied us in the two preceding ,books1 has conducted us to what appears a satisfactory solution of the principal problem of ,logic1 according to the conception ,i have formed of the science4 ,we have found1 that the mental process with which ,logic is conversant1 the operation of ascertaining truths by means of evidence1 is always1 even when appearances point to a different theory of it1 a process of induction4 ,and we have particularized the various modes of induction1 and obtained a clear view of the principles to which it must conform1 in order to lead to results which can be relied on4 ,the consideration of ,induction1 however1 does not end with the direct rules for its performance4 ,something must be said of those other operations of the mind1 which are either necessarily presupposed in all induction1 or are instrumental to the more difficult and complicated inductive processes4 ,the present ,book will be devoted to the consideration of these subsidiary operations2 among which our attention must first be given to those1 which are indispensable preliminaries to all induction whatsoever4 ,induction being merely the extension to a class of cases1 of something which has been observed to be true in certain individual instances of the class2 the first place among the operations subsidiary to induction1 is claimed by ,observation4 ,this is not1 however1 the place to lay down rules for making good observers2 nor is it within the competence of ,logic to do so1 but of the art of intellectual ,education4 ,our business with observation is only in its connection with the appropriate problem of logic1 the estimation of evidence4 ,we have to consider1 not how or what to observe1 but under what conditions observation is to be relied on2 what is needful1 in order that the fact1 supposed to be observed1 may safely be received as true4 #b4 ,the answer to this question is very simple1 at least in its first aspect4 ,the sole condition is1 that what is supposed to have been observed shall really have been observed2 that it be an observation1 not an inference4 ,for in almost every act of our perceiving faculties1 observation and inference are intimately blended4 ,what we are said to observe is usually a compound result1 of which one-tenth may be observation1 and the remaining nine-tenths inference4 ,i affirm1 for example1 that ,i hear a man's voice4 ,this would pass1 in common language1 for a direct perception4 ,all1 however1 which is really perception1 is that ,i hear a sound4 ,that the sound is a voice1 and that voice the voice of a man1 are not perceptions but inferences4 ,i affirm1 again1 that ,i saw my brother at a certain hour this morning4 ,if any proposition concerning a matter of fact would commonly be said to be known by the direct testimony of the senses1 this surely would be so4 ,the truth1 however1 is far otherwise4 ,i only saw a certain colored surface2 or rather ,i had the kind of visual sensations which are usually produced by a colored surface2 and from these as marks1 known to be such by previous experience1 ,i concluded that ,i saw my brother4 ,i might have had sensations precisely similar1 when my brother was not there4 ,i might have seen some other person so nearly resembling him in appearance1 as1 at the distance1 and1 with the degree of attention which ,i bestowed1 to be mistaken for him4 ,i might have been asleep1 and have dreamed that ,i saw him2 or in a state of nervous disorder1 which brought his image before me in a waking hallucination4 ,in all these modes1 many have been led to believe that they saw persons well known to them1 who were dead or far distant4 ,if any of these suppositions had been true1 the affirmation that ,i saw my brother would have been erroneous2 but whatever was matter of direct perception1 namely the visual sensations1 would have been real4 ,the inference only would have been ill grounded2 ,i should have ascribed those sensations to a wrong cause4 ,innumerable instances might be given1 and analyzed in the same manner1 of what are vulgarly called errors of sense4 ,there are none of them properly errors of sense2 they are erroneous inferences from sense4 ,when ,i look at a candle through a multiplying glass1 ,i see what seems a dozen candles instead of one2 and if the real circumstances of the case were skillfully disguised1 ,i might suppose that there were really that number2 there would be what is called an optical deception4 ,in the kaleidoscope there really is that deception2 when ,i look through the instrument1 instead of what is actually there1 namely a casual arrangement of colored fragments1 the appearance presented is that of the same combination several times repeated in symmetrical arrangement round a point4 ,the delusion is of course effected by giving me the same sensations which ,i should have had if such a symmetrical combination had really been presented to me4 ,if ,i cross two of my fingers1 and bring any small object1 a marble for instance1 into contact with both1 at points not usually touched simultaneously by one object1 ,i can hardly1 if my eyes are shut1 help believing that there are two marbles instead of one4 ,but it is not my touch in this case1 nor my sight in the other1 which is deceived2 the deception1 whether durable or only momentary1 is in my judgment4 ,from my senses ,i have only the sensations1 and those are genuine4 ,being accustomed to have those or similar sensations when1 and only when1 a certain arrangement of outward objects is present to my organs1 ,i have the habit of instantly1 when ,i experience the sensations1 inferring the existence of that state of outward things4 ,this habit has become so powerful1 that the inference1 performed with the speed and certainty of an instinct1 is confounded with intuitive perceptions4 ,when it is correct1 ,i am unconscious that it ever needed proof2 even when ,i know it to be incorrect1 ,i can not without considerable effort abstain from making it4 ,in order to be aware that it is not made by instinct but by an acquired habit1 ,i am obliged to reflect on the slow process through which ,i learned to judge by the eye of many things which ,i now appear to perceive directly by sight2 and on the reverse operation performed by persons learning to draw1 who with difficulty and labor divest themselves of their acquired perceptions1 and learn afresh to see things as they appear to the eye4 ,it would be easy to prolong these illustrations1 were there any need to expatiate on a topic so copiously exemplified in various popular works4 ,from the examples already given1 it is seen sufficiently1 that the individual facts from which we collect our inductive generalizations are scarcely ever obtained by observation alone4 ,observation extends only to the sensations by which we recognize objects2 but the propositions which we make use of1 either in science or in common life1 relate mostly to the objects themselves4 ,in every act of what is called observation1 there is at least one inference--from the sensations to the presence of the object2 from the marks or diagnostics1 to the entire phenomenon4 ,and hence1 among other consequences1 follows the seeming paradox1 that a general proposition collected from particulars is often more certainly true than any one of the particular propositions from which1 by an act of induction1 it was inferred4 ,for1 each of those particular 7or rather singular7 propositions involved an inference1 from the impression on the senses to the fact which caused that impression2 and this inference may have been erroneous in any one of the instances1 but can not well have been erroneous in all of them1 provided their number was sufficient to eliminate chance4 ,the conclusion1 therefore1 that is1 the general proposition1 may deserve more complete reliance than it would be safe to repose in any one of the inductive premises4 ,the logic of observation1 then1 consists solely in a correct discrimination between that1 in a result of observation1 which has really been perceived1 and that which is an inference from the perception4 ,whatever portion is inference1 is amenable to the rules of induction already treated of1 and requires no further notice here2 the question for us in this place is1 when all which is inference is taken away what remains8 ,there remains1 in the first place1 the mind's own feelings or states of consciousness1 namely1 its outward feelings or sensations1 and its inward feelings--its thoughts1 emotions1 and volitions4 ,whether any thing else remains1 or all else is inference from this2 whether the mind is capable of directly perceiving or apprehending any thing except states of its own consciousness--is a problem of metaphysics not to be discussed in this place4 ,but after excluding all questions on which metaphysicians differ1 it remains true1 that for most purposes the discrimination we are called upon practically to exercise is that between sensations or other feelings1 of our own or of other people1 and inferences drawn from them4 ,and on the theory of ,observation this is all which seems necessary to be said for the purposes of the present work4 #c4 ,if1 in the simplest observation1 or in what passes for such1 there is a large part which is not observation but something else2 so in the simplest description of an observation1 there is1 and must always be1 much more asserted than is contained in the perception itself4 ,we can not describe a fact1 without implying more than the fact4 ,the perception is only of one individual thing2 but to describe it is to affirm a connection between it and every other thing which is either denoted or connoted by any of the terms used4 ,to begin with an example1 than which none can be conceived more elementary3 ,i have a sensation of sight1 and ,i endeavor to describe it by saying that ,i see something white4 ,in saying this1 ,i do not solely affirm my sensation2 ,i also class it4 ,i assert a resemblance between the thing ,i see1 and all things which ,i and others are accustomed to call white4 ,i assert that it resembles them in the circumstance in which they all resemble one another1 in that which is the ground of their being called by the name4 ,this is not merely one way of describing an observation1 but the only way4 ,if ,i would either register my observation for my own future use1 or make it known for the benefit of others1 ,i must assert a resemblance between the fact which ,i have observed and something else4 ,it is inherent in a description1 to be the statement of a resemblance1 or resemblances4 ,we thus see that it is impossible to express in words any result of observation1 without performing an act possessing what ,dr4 ,whewell considers to be characteristic of ,induction4 ,there is always something introduced which was not included in the observation itself2 some conception common to the phenomenon with other phenomena to which it is compared4 ,an observation can not be spoken of in language at all without declaring more than that one observation2 without assimilating it to other phenomena already observed and classified4 ,but this identification of an object--this recognition of it as possessing certain known characteristics--has never been confounded with ,induction4 ,it is an operation which precedes all induction1 and supplies it with its materials4 ,it is a perception of resemblances1 obtained by comparison4 ,these resemblances are not always apprehended directly1 by merely comparing the object observed with some other present object1 or with our recollection of an object which is absent4 ,they are often ascertained through intermediate marks1 that is1 deductively4 ,in describing some new kind of animal1 suppose me to say that it measures ten feet in length1 from the forehead to the extremity of the tail4 ,i did not ascertain this by the unassisted eye4 ,i had a two-foot rule which ,i applied to the object1 and1 as we commonly say1 measured it2 an operation which was not wholly manual1 but partly also mathematical1 involving the two propositions1 ,five times two is ten1 and ,things which are equal to the same thing are equal to one another4 ,hence1 the fact that the animal is ten feet long is not an immediate perception1 but a conclusion from reasoning2 the minor premises alone being furnished by observation of the object4 ,nevertheless1 this is called an observation1 or a description of the animal1 not an induction respecting it4 ,to pass at once from a very simple to a very complex example3 ,i affirm that the earth is globular4 ,the assertion is not grounded on direct perception2 for the figure of the earth can not1 by us1 be directly perceived1 though the assertion would not be true unless circumstances could be supposed under which its truth could be so perceived4 ,that the form of the earth is globular is inferred from certain marks1 as for instance from this1 that its shadow thrown upon the moon is circular2 or this1 that on the sea1 or any extensive plain1 our horizon is always a circle2 either of which marks is incompatible with any other than a globular form4 ,i assert further1 that the earth is that particular kind of a globe which is termed an oblate spheroid2 because it is found by measurement in the direction of the meridian1 that the length on the surface of the earth which subtends a given angle at its centre1 diminishes as we recede from the equator and approach the poles4 ,but these propositions1 that the earth is globular1 and that it is an oblate spheroid1 assert1 each of them1 an individual fact2 in its own nature capable of being perceived by the senses when the requisite organs and the necessary position are supposed1 and only not actually perceived because those organs and that position are wanting4 ,this identification of the earth1 first as a globe1 and next as an oblate spheroid1 which1 if the fact could have been seen1 would have been called a description of the figure of the earth1 may without impropriety be so called when1 instead of being seen1 it is inferred4 ,but we could not without impropriety call either of these assertions an induction from facts respecting the earth4 ,they are not general propositions collected from particular facts1 but particular facts deduced from general propositions4 ,they are conclusions obtained deductively1 from premises originating in induction3 but of these premises some were not obtained by observation of the earth1 nor had any peculiar reference to it4 ,if1 then1 the truth respecting the figure of the earth is not an induction1 why should the truth respecting the figure of the earth's orbit be so8 ,the two cases only differ in this1 that the form of the orbit was not1 like the form of the earth itself1 deduced by ratiocination from facts which were marks of ellipticity1 but was got at by boldly guessing that the path was an ellipse1 and finding afterward1 on examination1 that the observations were in harmony with the hypothesis4 ,according to ,dr4 ,whewell1 however1 this process of guessing and verifying our guesses is not only induction1 but the whole of induction3 no other exposition can be given of that logical operation4 ,that he is wrong in the latter assertion1 the whole of the preceding book has1 ,i hope1 sufficiently proved2 and that the process by which the ellipticity of the planetary orbits was ascertained1 is not induction at all1 was attempted to be shown in the second chapter of the same ,book47#bjf7 ,we are now1 however1 prepared to go more into the heart of the matter than at that earlier period of our inquiry1 and to show1 not merely what the operation in question is not1 but what it is4 #d4 ,we observed1 in the second chapter1 that the proposition 8the earth moves in an ellipse10 so far as it only serves for the colligation or connecting together of actual observations 7that is1 as it only affirms that the observed positions of the earth may be correctly represented by as many points in the circumference of an imaginary ellipse71 is not an induction1 but a description3 it is an induction1 only when it affirms that the intermediate positions1 of which there has been no direct observation1 would be found to correspond to the remaining points of the same elliptic circumference4 ,now1 though this real induction is one thing1 and the description another1 we are in a very different condition for making the induction before we have obtained the description1 and after it4 ,for inasmuch as the description1 like all other descriptions1 contains the assertion of a resemblance between the phenomenon described and something else2 in pointing out something which the series of observed places of a planet resembles1 it points out something in which the several places themselves agree4 ,if the series of places correspond to as many points of an ellipse1 the places themselves agree in being situated in that ellipse4 ,we have1 therefore1 by the same process which gave us the description1 obtained the requisites for an induction by the ,method of ,agreement4 ,the successive observed places of the earth being considered as effects1 and its motion as the cause which produces them1 we find that those effects1 that is1 those places1 agree in the circumstance of being in an ellipse4 ,we conclude that the remaining effects1 the places which have not been observed1 agree in the same circumstance1 and that the law of the motion of the earth is motion in an ellipse4 ,the ,colligation of ,facts1 therefore1 by means of hypotheses1 or1 as ,dr4 ,whewell prefers to say1 by means of ,conceptions1 instead of being1 as he supposes1 ,induction itself1 takes its proper place among operations subsidiary to ,induction4 ,all ,induction supposes that we have previously compared the requisite number of individual instances1 and ascertained in what circumstances they agree4 ,the ,colligation of ,facts is no other than this preliminary operation4 ,when ,kepler1 after vainly endeavoring to connect the observed places of a planet by various hypotheses of circular motion1 at last tried the hypotheses of an ellipse and found it answer to the phenomena2 what he really attempted1 first unsuccessfully and at last successfully1 was to discover the circumstance in which all the observed positions of the planet agreed4 ,and when he in like manner connected another set of observed facts1 the periodic times of the different planets1 by the proposition that the squares of the times are proportional to the cubes of the distances1 what he did was simply to ascertain the property in which the periodic times of all the different planets agreed4 ,since1 therefore1 all that is true and to the purpose in ,dr4 ,whewell's doctrine of ,conceptions might be fully expressed by the more familiar term ,hypothesis2 and since his ,colligation of ,facts by means of appropriate ,conceptions1 is but the ordinary process of finding by a comparison of phenomena1 in what consists their agreement or resemblance2 ,i would willingly have confined myself to those better understood expressions1 and persevered to the end in the same abstinence which ,i have hitherto observed from ideological discussions2 considering the mechanism of our thoughts to be a topic distinct from and irrelevant to the principles and rules by which the trustworthiness of the results of thinking is to be estimated4 ,since1 however1 a work of such high pretensions1 and1 it must also be said1 of so much real merit1 has rested the whole theory of ,induction upon such ideological considerations1 it seems necessary for others who follow to claim for themselves and their doctrines whatever position may properly belong to them on the same metaphysical ground4 ,and this is the object of the succeeding chapter4 ,chapter ,,ii4 ,of ,abstraction1 ,or ,the ,formation ,of ,conceptions4 #a4 ,the metaphysical inquiry into the nature and composition of what have been called ,abstract ,ideas1 or1 in other words1 of the notions which answer in the mind to classes and to general names1 belongs not to ,logic1 but to a different science1 and our purpose does not require that we should enter upon it here4 ,we are only concerned with the universally acknowledged fact1 that such notions or conceptions do exist4 ,the mind can conceive a multitude of individual things as one assemblage or class2 and general names do really suggest to us certain ideas or mental representations1 otherwise we could not use the names with consciousness of a meaning4 ,whether the idea called up by a general name is composed of the various circumstances in which all the individuals denoted by the name agree1 and of no others 7which is the doctrine of ,locke1 ,brown1 and the ,conceptualists72 or whether it be the idea of some one of those individuals1 clothed in its individualizing peculiarities1 but with the accompanying knowledge that those peculiarities are not properties of the class 7which is the doctrine of ,berkeley1 ,mr4 ,bailey17#bjg7 and the modern ,nominalists72 or whether 7as held by ,mr4 ,james ,mill7 the idea of the class is that of a miscellaneous assemblage of individuals belonging to the class2 or whether1 finally1 it be any one or any other of all these1 according to the accidental circumstances of the case2 certain it is1 that some idea or mental conception is suggested by a general name1 whenever we either hear it or employ it with consciousness of a meaning4 ,and this1 which we may call1 if we please1 a general idea1 represents in our minds the whole class of things to which the name is applied4 ,whenever we think or reason concerning the class1 we do so by means of this idea4 ,and the voluntary power which the mind has1 of attending to one part of what is present to it at any moment1 and neglecting another part1 enables us to keep our reasonings and conclusions respecting the class unaffected by any thing in the idea or mental image which is not really1 or at least which we do not really believe to be common1 to the whole class47#bjh7 ,there are1 then1 such things as general conceptions1 or conceptions by means of which we can think generally2 and when we form a set of phenomena into a class1 that is1 when we compare them with one another to ascertain in what they agree1 some general conception is implied in this mental operation4 ,and inasmuch as such a comparison is a necessary preliminary to ,induction1 it is most true that ,induction could not go on without general conceptions4 #b4 ,but it does not therefore follow that these general conceptions must have existed in the mind previously to the comparison4 ,it is not a law of our intellect1 that in comparing things with each other and taking note of their agreement we merely recognize as realized in the outward world something that we already had in our minds4 ,the conception originally found its way to us as the result of such a comparison4 ,it was obtained 7in metaphysical phrase7 by abstraction from individual things4 ,these things may be things which we perceived or thought of on former occasions1 but they may also be the things which we are perceiving or thinking of on the very occasion4 ,when ,kepler compared the observed places of the planet ,mars1 and found that they agreed in being points of an elliptic circumference1 he applied a general conception which was already in his mind1 having been derived from his former experience4 ,but this is by no means universally the case4 ,when we compare several objects and find them to agree in being white1 or when we compare the various species of ruminating animals and find them to agree in being cloven-footed1 we have just as much a general conception in our minds as ,kepler had in his3 we have the conception of 8a white thing10 or the conception of 8a cloven-footed animal40 ,but no one supposes that we necessarily bring these conceptions with us1 and superinduce them 7to adopt ,dr4 ,whewell's expression7 upon the facts3 because in these simple cases every body sees that the very act of comparison which ends in our connecting the facts by means of the conception1 may be the source from which we derive the conception itself4 ,if we had never seen any white object or had never seen any cloven-footed animal before1 we should at the same time and by the same mental act acquire the idea1 and employ it for the colligation of the observed phenomena4 ,kepler1 on the contrary1 really had to bring the idea with him1 and superinduce it upon the facts2 he could not evolve it out of them3 if he had not already had the idea1 he would not have been able to acquire it by a comparison of the planet's positions4 ,but this inability was a mere accident2 the idea of an ellipse could have been acquired from the paths of the planets as effectually as from any thing else1 if the paths had not happened to be invisible4 ,if the planet had left a visible track1 and we had been so placed that we could see it at the proper angle1 we might have abstracted our original idea of an ellipse from the planetary orbit4 ,indeed1 every conception which can be made the instrument for connecting a set of facts1 might have been originally evolved from those very facts4 ,the conception is a conception of something2 and that which it is a conception of1 is really in the facts1 and might1 under some supposable circumstances1 or by some supposable extension of the faculties which we actually possess1 have been detected in them4 ,and not only is this always in itself possible1 but it actually happens in almost all cases in which the obtaining of the right conception is a matter of any considerable difficulty4 ,for if there be no new conception required2 if one of those already familiar to mankind will serve the purpose1 the accident of being the first to whom the right one occurs1 may happen to almost any body2 at least in the case of a set of phenomena which the whole scientific world are engaged in attempting to connect4 ,the honor1 in ,kepler's case1 was that of the accurate1 patient1 and toilsome calculations by which he compared the results that followed from his different guesses1 with the observations of ,tycho ,brahe2 but the merit was very small of guessing an ellipse2 the only wonder is that men had not guessed it before1 nor could they have failed to do so if there had not existed an obstinate a priori prejudice that the heavenly bodies must move1 if not in a circle1 in some combination of circles4 ,the really difficult cases are those in which the conception destined to create light and order out of darkness and confusion has to be sought for among the very phenomena which it afterward serves to arrange4 ,why1 according to ,dr4 ,whewell himself1 did the ancients fail in discovering the laws of mechanics1 that is1 of equilibrium and of the communication of motion8 ,because they had not1 or at least had not clearly1 the ideas or conceptions of pressure and resistance1 momentum1 and uniform and accelerating force4 ,and whence could they have obtained these ideas except from the very facts of equilibrium and motion8 ,the tardy development of several of the physical sciences1 for example1 of optics1 electricity1 magnetism1 and the higher generalizations of chemistry1 he ascribes to the fact that mankind had not yet possessed themselves of the ,idea of ,polarity1 that is1 the idea of opposite properties in opposite directions4 ,but what was there to suggest such an idea1 until1 by a separate examination of several of these different branches of knowledge1 it was shown that the facts of each of them did present1 in some instances at least1 the curious phenomenon of opposite properties in opposite directions8 ,the thing was superficially manifest only in two cases1 those of the magnet and of electrified bodies2 and there the conception was encumbered with the circumstance of material poles1 or fixed points in the body itself1 in which points this opposition of properties seemed to be inherent4 ,the first comparison and abstraction had led only to this conception of poles2 and if any thing corresponding to that conception had existed in the phenomena of chemistry or optics1 the difficulty now justly considered so great1 would have been extremely small4 ,the obscurity arose from the fact1 that the polarities in chemistry and optics were distinct species1 though of the same genus1 with the polarities in electricity and magnetism2 and that in order to assimilate the phenomena to one another1 it was necessary to compare a polarity without poles1 such for instance as is exemplified in the polarization of light1 and the polarity with 7apparent7 poles1 which we see in the magnet2 and to recognize that these polarities1 while different in many other respects1 agree in the one character which is expressed by the phrase1 opposite properties in opposite directions4 ,from the result of such a comparison it was that the minds of scientific men formed this new general conception2 between which1 and the first confused feeling of an analogy between some of the phenomena of light and those of electricity and magnetism1 there is a long interval1 filled up by the labors and more or less sagacious suggestions of many superior minds4 ,the conceptions1 then1 which we employ for the colligation and methodization of facts1 do not develop themselves from within1 but are impressed upon the mind from without2 they are never obtained otherwise than by way of comparison and abstraction1 and1 in the most important and the most numerous cases1 are evolved by abstraction from the very phenomena which it is their office to colligate4 ,i am far1 however1 from wishing to imply that it is not often a very difficult thing to perform this process of abstraction well1 or that the success of an inductive operation does not1 in many cases1 principally depend on the skill with which we perform it4 ,bacon was quite justified in designating as one of the principal obstacles to good induction1 general conceptions wrongly formed1 8notiones temer rebus abstract20 to which ,dr4 ,whewell adds1 that not only does bad abstraction make bad induction1 but that1 in order to perform induction well1 we must have abstracted well2 our general conceptions must be 8clear0 and 8appropriate0 to the matter in hand4 #c4 ,in attempting to show what the difficulty in this matter really is1 and how it is surmounted1 ,i must beg the reader1 once for all1 to bear this in mind2 that although1 in discussing the opinions of a different school of philosophy1 ,i am willing to adopt their language1 and to speak1 therefore1 of connecting facts through the instrumentality of a conception1 this technical phraseology means neither more nor less than what is commonly called comparing the facts with one another and determining in what they agree4 ,nor has the technical expression even the advantage of being metaphysically correct4 ,the facts are not connected1 except in a merely metaphorical acceptation of the term4 ,the ideas of the facts may become connected1 that is1 we may be led to think of them together2 but this consequence is no more than what may be produced by any casual association4 ,what really takes place1 is1 ,i conceive1 more philosophically expressed by the common word ,comparison1 than by the phrases 8to connect0 or 8to superinduce40 ,for1 as the general conception is itself obtained by a comparison of particular phenomena1 so1 when obtained1 the mode in which we apply it to other phenomena is again by comparison4 ,we compare phenomena with each other to get the conception1 and we then compare those and other phenomena with the conception4 ,we get the conception of an animal 7for instance7 by comparing different animals1 and when we afterward see a creature resembling an animal1 we compare it with our general conception of an animal2 and if it agrees with that general conception1 we include it in the class4 ,the conception becomes the type of comparison4 ,and we need only consider what comparison is1 to see that where the objects are more than two1 and still more when they are an indefinite number1 a type of some sort is an indispensable condition of the comparison4 ,when we have to arrange and classify a great number of objects according to their agreements and differences1 we do not make a confused attempt to compare all with all4 ,we know that two things are as much as the mind can easily attend to at a time1 and we therefore fix upon one of the objects1 either at hazard or because it offers in a peculiarly striking manner some important character1 and1 taking this as our standard1 compare it with one object after another4 ,if we find a second object which presents a remarkable agreement with the first1 inducing us to class them together1 the question instantly arises1 in what particular circumstances do they agree8 and to take notice of these circumstances is already a first stage of abstraction1 giving rise to a general conception4 ,having advanced thus far1 when we now take in hand a third object we naturally ask ourselves the question1 not merely whether this third object agrees with the first1 but whether it agrees with it in the same circumstances in which the second did8 in other words1 whether it agrees with the general conception which has been obtained by abstraction from the first and second8 ,thus we see the tendency of general conceptions1 as soon as formed1 to substitute themselves as types1 for whatever individual objects previously answered that purpose in our comparisons4 ,we may1 perhaps1 find that no considerable number of other objects agree with this first general conception2 and that we must drop the conception1 and beginning again with a different individual case1 proceed by fresh comparisons to a different general conception4 ,sometimes1 again1 we find that the same conception will serve1 by merely leaving out some of its circumstances2 and by this higher effort of abstraction1 we obtain a still more general conception2 as in the case formerly referred to1 the scientific world rose from the conception of poles to the general conception of opposite properties in opposite directions2 or as those ,south-,sea islanders1 whose conception of a quadruped had been abstracted from hogs 7the only animals of that description which they had seen71 when they afterward compared that conception with other quadrupeds1 dropped some of the circumstances1 and arrived at the more general conception which ,europeans associate with the term4 ,these brief remarks contain1 ,i believe1 all that is well grounded in the doctrine1 that the conception by which the mind arranges and gives unity to phenomena must be furnished by the mind itself1 and that we find the right conception by a tentative process1 trying first one and then another until we hit the mark4 ,the conception is not furnished by the mind until it has been furnished to the mind2 and the facts which supply it are sometimes extraneous facts1 but more often the very facts which we are attempting to arrange by it4 ,it is quite true1 however1 that in endeavoring to arrange the facts1 at whatever point we begin1 we never advance three steps without forming a general conception1 more or less distinct and precise2 and that this general conception becomes the clue which we instantly endeavor to trace through the rest of the facts1 or rather1 becomes the standard with which we thenceforth compare them4 ,if we are not satisfied with the agreements which we discover among the phenomena by comparing them with this type1 or with some still more general conception which by an additional stage of abstraction we can form from the type2 we change our path1 and look out for other agreements2 we recommence the comparison from a different starting-point1 and so generate a different set of general conceptions4 ,this is the tentative process which ,dr4 ,whewell speaks of2 and which has not unnaturally suggested the theory1 that the conception is supplied by the mind itself2 since the different conceptions which the mind successively tries1 it either already possessed from its previous experience1 or they were supplied to it in the first stage of the corresponding act of comparison2 so that1 in the subsequent part of the process1 the conception manifested itself as something compared with the phenomena1 not evolved from them4 #d4 ,if this be a correct account of the instrumentality of general conceptions in the comparison which necessarily precedes ,induction1 we are now able to translate into our own language what ,dr4 ,whewell means by saying that conceptions1 to be subservient to ,induction1 must be 8clear0 and 8appropriate40 ,if the conception corresponds to a real agreement among the phenomena2 if the comparison which we have made of a set of objects has led us to class them according to real resemblances and differences2 the conception which does this can not fail to be appropriate1 for some purpose or other4 ,the question of appropriateness is relative to the particular object we have in view4 ,as soon as1 by our comparison1 we have ascertained some agreement1 something which can be predicated in common of a number of objects2 we have obtained a basis on which an inductive process is capable of being founded4 ,but the agreements1 or the ulterior consequences to which those agreements lead1 may be of very different degrees of importance4 ,if1 for instance1 we only compare animals according to their color1 and class those together which are colored alike1 we form the general conceptions of a white animal1 a black animal1 etc41 which are conceptions legitimately formed2 and if an induction were to be attempted concerning the causes of the colors of animals1 this comparison would be the proper and necessary preparation for such an induction1 but would not help us toward a knowledge of the laws of any other of the properties of animals2 while if1 with ,cuvier1 we compare and class them according to the structure of the skeleton1 or1 with ,blainville1 according to the nature of their outward integuments1 the agreements and differences which are observable in these respects are not only of much greater importance in themselves1 but are marks of agreements and differences in many other important particulars of the structure and mode of life of the animals4 ,if1 therefore1 the study of their structure and habits be our object1 the conceptions generated by these last comparisons are far more 8appropriate0 than those generated by the former4 ,nothing1 other than this1 can be meant by the appropriateness of a conception4 ,when ,dr4 ,whewell says that the ancients1 or the school-men1 or any modern inquirers1 missed discovering the real law of a phenomenon because they applied to it an inappropriate instead of an appropriate conception2 he can only mean that in comparing various instances of the phenomenon1 to ascertain in what those instances agreed1 they missed the important points of agreement2 and fastened upon such as were either imaginary1 and not agreements at all1 or1 if real agreements1 were comparatively trifling1 and had no connection with the phenomenon1 the law of which was sought4 ,aristotle1 philosophizing on the subject of motion1 remarked that certain motions apparently take place spontaneously2 bodies fall to the ground1 flame ascends1 bubbles of air rise in water1 etc42 and these he called natural motions2 while others not only never take place without external incitement1 but even when such incitement is applied1 tend spontaneously to cease2 which1 to distinguish them from the former1 he called violent motions4 ,now1 in comparing the so-called natural motions with one another1 it appeared to ,aristotle that they agreed in one circumstance1 namely1 that the body which moved 7or seemed to move7 spontaneously1 was moving toward its own place2 meaning thereby the place from whence it originally came1 or the place where a great quantity of matter similar to itself was assembled4 ,in the other class of motions1 as when bodies are thrown up in the air1 they are1 on the contrary1 moving from their own place4 ,now1 this conception of a body moving toward its own place may justly be considered inappropriate2 because1 though it expresses a circumstance really found in some of the most familiar instances of motion apparently spontaneous1 yet1 first1 there are many other cases of such motion1 in which that circumstance is absent2 the motion1 for instance1 of the earth and planets4 ,secondly1 even when it is present1 the motion1 on closer examination1 would often be seen not to be spontaneous2 as1 when air rises in water1 it does not rise by its own nature1 but is pushed up by the superior weight of the water which presses upon it4 ,finally1 there are many cases in which the spontaneous motion takes place in the contrary direction to what the theory considers as the body's own place2 for instance1 when a fog rises from a lake1 or when water dries up4 ,the agreement1 therefore1 which ,aristotle selected as his principle of classification1 did not extend to all cases of the phenomenon he wanted to study1 spontaneous motion2 while it did include cases of the absence of the phenomenon1 cases of motion not spontaneous4 ,the conception was hence 8inappropriate40 ,we may add that1 in the case in question1 no conception would be appropriate2 there is no agreement which runs through all the cases of spontaneous or apparently spontaneous motion and no others2 they can not be brought under one law2 it is a case of ,plurality of ,causes47#bji7 #e4 ,so much for the first of ,dr4 ,whewell's conditions1 that conceptions must be appropriate4 ,the second is1 that they shall be 8clear30 and let us consider what this implies4 ,unless the conception corresponds to a real agreement1 it has a worse defect than that of not being clear3 it is not applicable to the case at all4 ,among the phenomena1 therefore1 which we are attempting to connect by means of the conception1 we must suppose that there really is an agreement1 and that the conception is a conception of that agreement4 ,in order1 then1 that it may be clear1 the only requisite is1 that we shall know exactly in what the agreement consists2 that it shall have been carefully observed1 and accurately remembered4 ,we are said not to have a clear conception of the resemblance among a set of objects1 when we have only a general feeling that they resemble1 without having analyzed their resemblance1 or perceived in what points it consists1 and fixed in our memory an exact recollection of those points4 ,this want of clearness1 or1 as it may be otherwise called1 this vagueness in the general conception1 may be owing either to our having no accurate knowledge of the objects themselves1 or merely to our not having carefully compared them4 ,thus a person may have no clear idea of a ship because he has never seen one1 or because he remembers but little1 and that faintly1 of what he has seen4 ,or he may have a perfect knowledge and remembrance of many ships of various kinds1 frigates among the rest1 but he may have no clear but only a confused idea of a frigate1 because he has never been told1 and has not compared them sufficiently to have remarked and remembered1 in what particular points a frigate differs from some other kind of ship4 ,it is not1 however1 necessary1 in order to have clear ideas1 that we should know all the common properties of the things which we class together4 ,that would be to have our conception of the class complete as well as clear4 ,it is sufficient if we never class things together without knowing exactly why we do so--without having ascertained exactly what agreements we are about to include in our conception2 and if1 after having thus fixed our conception1 we never vary from it1 never include in the class any thing which has not those common properties1 nor exclude from it any thing which has4 ,a clear conception means a determinate conception2 one which does not fluctuate1 which is not one thing to-day and another to-morrow1 but remains fixed and invariable1 except when1 from the progress of our knowledge1 or the correction of some error1 we consciously add to it or alter it4 ,a person of clear ideas is a person who always knows in virtue of what properties his classes are constituted2 what attributes are connoted by his general names4 ,the principal requisites1 therefore1 of clear conceptions1 are habits of attentive observation1 an extensive experience1 and a memory which receives and retains an exact image of what is observed4 ,and in proportion as any one has the habit of observing minutely and comparing carefully a particular class of phenomena1 and an accurate memory for the results of the observation and comparison1 so will his conceptions of that class of phenomena be clear2 provided he has the indispensable habit 7naturally1 however1 resulting from those other endowments71 of never using general names without a precise connotation4 ,as the clearness of our conceptions chiefly depends on the carefulness and accuracy of our observing and comparing faculties1 so their appropriateness1 or rather the chance we have of hitting upon the appropriate conception in any case1 mainly depends on the activity of the same faculties4 ,he who by habit1 grounded on sufficient natural aptitude1 has acquired a readiness in accurately observing and comparing phenomena1 will perceive so many more agreements1 and will perceive them so much more rapidly than other people1 that the chances are much greater of his perceiving1 in any instance1 the agreement on which the important consequences depend4 #f4 ,it is of so much importance that the part of the process of investigating truth1 discussed in this chapter1 should be rightly understood1 that ,i think it is desirable to restate the results we have arrived at1 in a somewhat different mode of expression4 ,we can not ascertain general truths1 that is1 truths applicable to classes1 unless we have formed the classes in such a manner that general truths can be affirmed of them4 ,in the formation of any class1 there is involved a conception of it as a class1 that is1 a conception of certain circumstances as being those which characterize the class1 and distinguish the objects composing it from all other things4 ,when we know exactly what these circumstances are1 we have a clear idea 7or conception7 of the class1 and of the meaning of the general name which designates it4 ,the primary condition implied in having this clear idea1 is that the class be really a class2 that it correspond to a real distinction2 that the things it includes really do agree with one another in certain particulars1 and differ1 in those same particulars1 from all other things4 ,a person without clear ideas is one who habitually classes together1 under the same general names1 things which have no common properties1 or none which are not possessed also by other things2 or who1 if the usage of other people prevents him from actually misclassing things1 is unable to state to himself the common properties in virtue of which he classes them rightly4 ,but is it not the sole requisite of classification that the classes should be real classes1 framed by a legitimate mental process8 ,some modes of classing things are more valuable than others for human uses1 whether of speculation or of practice2 and our classifications are not well made1 unless the things which they bring together not only agree with each other in something which distinguishes them from all other things1 but agree with each other and differ from other things in the very circumstances which are of primary importance for the purpose 7theoretical or practical7 which we have in view1 and which constitutes the problem before us4 ,in other words1 our conceptions1 though they may be clear1 are not appropriate for our purpose1 unless the properties we comprise in them are those which will help us toward what we wish to understand--i4e41 either those which go deepest into the nature of the things1 if our object be to understand that1 or those which are most closely connected with the particular property which we are endeavoring to investigate4 ,we can not1 therefore1 frame good general conceptions beforehand4 ,that the conception we have obtained is the one we want1 can only be known when we have done the work for the sake of which we wanted it2 when we completely understand the general character of the phenomena1 or the conditions of the particular property with which we concern ourselves4 ,general conceptions formed without this thorough knowledge1 are ,bacon's 8notiones temer rebus abstract40 ,yet such premature conceptions we must be continually making up1 in our progress to something better4 ,they are an impediment to the progress of knowledge1 only when they are permanently acquiesced in4 ,when it has become our habit to group things in wrong classes--in groups which either are not really classes1 having no distinctive points of agreement 7absence of clear ideas71 or which are not classes of which any thing important to our purpose can be predicated 7absence of appropriate ideas72 and when1 in the belief that these badly made classes are those sanctioned by nature1 we refuse to exchange them for others1 and can not or will not make up our general conceptions from any other elements2 in that case all the evils which ,bacon ascribes to his 8notiones temer abstract0 really occur4 ,this was what the ancients did in physics1 and what the world in general does in morals and politics to the present day4 ,it would thus1 in my view of the matter1 be an inaccurate mode of expression to say1 that obtaining appropriate conceptions is a condition precedent to generalization4 ,throughout the whole process of comparing phenomena with one another for the purpose of generalization1 the mind is trying to make up a conception2 but the conception which it is trying to make up is that of the really important point of agreement in the phenomena4 ,as we obtain more knowledge of the phenomena themselves1 and of the conditions on which their important properties depend1 our views on this subject naturally alter2 and thus we advance from a less to a more 8appropriate0 general conception1 in the progress of our investigations4 ,we ought not1 at the same time1 to forget that the really important agreement can not always be discovered by mere comparison of the very phenomena in question1 without the aid of a conception acquired elsewhere2 as in the case1 so often referred to1 of the planetary orbits4 ,the search for the agreement of a set of phenomena is in truth very similar to the search for a lost or hidden object4 ,at first we place ourselves in a sufficiently commanding position1 and cast our eyes round us1 and if we can see the object it is well2 if not1 we ask ourselves mentally what are the places in which it may be hid1 in order that we may there search for it3 and so on1 until we imagine the place where it really is4 ,and here too we require to have had a previous conception1 or knowledge1 of those different places4 ,as in this familiar process1 so in the philosophical operation which it illustrates1 we first endeavor to find the lost object or recognize the common attribute1 without conjecturally invoking the aid of any previously acquired conception1 or1 in other words1 of any hypothesis4 ,having failed in this1 we call upon our imagination for some hypothesis of a possible place1 or a possible point of resemblance1 and then look to see whether the facts agree with the conjecture4 ,for such cases something more is required than a mind accustomed to accurate observation and comparison4 ,it must be a mind stored with general conceptions1 previously acquired1 of the sorts which bear affinity to the subject of the particular inquiry4 ,and much will also depend on the natural strength and acquired culture of what has been termed the scientific imagination2 on the faculty possessed of mentally arranging known elements into new combinations1 such as have not yet been observed in nature1 though not contradictory to any known laws4 ,but the variety of intellectual habits1 the purposes which they serve1 and the modes in which they may be fostered and cultivated1 are considerations belonging to the ,art of ,education3 a subject far wider than ,logic1 and which this treatise does not profess to discuss4 ,here1 therefore1 the present chapter may properly close4 ,chapter ,,iii4 ,of ,naming1 ,as ,subsidiary ,to ,induction4 #a4 ,it does not belong to the present undertaking to dwell on the importance of language as a medium of human intercourse1 whether for purposes of sympathy or of information4 ,nor does our design admit of more than a passing allusion to that great property of names1 on which their functions as an intellectual instrument are1 in reality1 ultimately dependent2 their potency as a means of forming1 and of riveting1 associations among our other ideas2 a subject on which an able thinker7#baj7 has thus written3 8,names are impressions of sense1 and as such take the strongest hold on the mind1 and of all other impressions can be most easily recalled and retained in view4 ,they therefore serve to give a point of attachment to all the more volatile objects of thought and feeling4 ,impressions that when passed might be dissipated forever1 are1 by their connection with language1 always within reach4 ,thoughts1 of themselves1 are perpetually slipping out of the field of immediate mental vision2 but the name abides with us1 and the utterance of it restores them in a moment4 ,words are the custodiers of every product of mind less impressive than themselves4 ,all extensions of human knowledge1 all new generalizations1 are fixed and spread1 even unintentionally1 by the use of words4 ,the child growing up learns1 along with the vocables of his mother-tongue1 that things which he would have believed to be different are1 in important points1 the same4 ,without any formal instruction1 the language in which we grow up teaches us all the common philosophy of the age4 ,it directs us to observe and know things which we should have overlooked2 it supplies us with classifications ready made1 by which things are arranged 7as far as the light of by-gone generations admits7 with the objects to which they bear the greatest total resemblance4 ,the number of general names in a language1 and the degree of generality of those names1 afford a test of the knowledge of the era1 and of the intellectual insight which is the birthright of any one born into it40 ,it is not1 however1 of the functions of ,names1 considered generally1 that we have here to treat1 but only of the manner and degree in which they are directly instrumental to the investigation of truth2 in other words1 to the process of induction4 #b4 ,observation and ,abstraction1 the operations which formed the subject of the two foregoing chapters1 are conditions indispensable to induction2 there can be no induction where they are not4 ,it has been imagined that ,naming is also a condition equally indispensable4 ,there are thinkers who have held that language is not solely1 according to a phrase generally current1 an instrument of thought1 but the instrument2 that names1 or something equivalent to them1 some species of artificial signs1 are necessary to reasoning2 that there could be no inference1 and consequently no induction1 without them4 ,but if the nature of reasoning was correctly explained in the earlier part of the present work1 this opinion must be held to be an exaggeration1 though of an important truth4 ,if reasoning be from particulars to particulars1 and if it consist in recognizing one fact as a mark of another1 or a mark of a mark of another1 nothing is required to render reasoning possible1 except senses and association2 senses to perceive that two facts are conjoined2 association1 as the law by which one of those two facts raises up the idea of the other47#baa7 ,for these mental phenomena1 as well as for the belief or expectation which follows1 and by which we recognize as having taken place1 or as about to take place1 that of which we have perceived a mark1 there is evidently no need of language4 ,and this inference of one particular fact from another is a case of induction4 ,it is of this sort of induction that brutes are capable2 it is in this shape that uncultivated minds make almost all their inductions1 and that we all do so in the cases in which familiar experience forces our conclusions upon us without any active process of inquiry on our part1 and in which the belief or expectation follows the suggestion of the evidence with the promptitude and certainty of an instinct47#bab7 #c4 ,but though inference of an inductive character is possible without the use of signs1 it could never1 without them1 be carried much beyond the very simple cases which we have just described1 and which form1 in all probability1 the limit of the reasonings of those animals to whom conventional language is unknown4 ,without language1 or something equivalent to it1 there could only be as much reasoning from experience as can take place without the aid of general propositions4 ,now1 though in strictness we may reason from past experience to a fresh individual case without the intermediate stage of a general proposition1 yet without general propositions we should seldom remember what past experience we have had1 and scarcely ever what conclusions that experience will warrant4 ,the division of the inductive process into two parts1 the first ascertaining what is a mark of the given fact1 the second whether in the new case that mark exists1 is natural1 and scientifically indispensable4 ,it is1 indeed1 in a majority of cases1 rendered necessary by mere distance of time4 ,the experience by which we are to guide our judgments may be other people's experience1 little of which can be communicated to us otherwise than by language2 when it is our own1 it is generally experience long past2 unless1 therefore1 it were recorded by means of artificial signs1 little of it 7except in cases involving our intenser sensations or emotions1 or the subjects of our daily and hourly contemplation7 would be retained in the memory4 ,it is hardly necessary to add1 that when the inductive inference is of any but the most direct and obvious nature--when it requires several observations or experiments1 in varying circumstances1 and the comparison of one of these with another--it is impossible to proceed a step1 without the artificial memory which words bestow4 ,without words1 we should1 if we had often seen ,a and ,b in immediate and obvious conjunction1 expect ,b whenever we saw ,a2 but to discover their conjunction when not obvious1 or to determine whether it is really constant or only casual1 and whether there is reason to expect it under any given change of circumstances1 is a process far too complex to be performed without some contrivance to make our remembrance of our own mental operations accurate4 ,now1 language is such a contrivance4 ,when that instrument is called to our aid1 the difficulty is reduced to that of making our remembrance of the meaning of words accurate4 ,this being secured1 whatever passes through our minds may be remembered accurately1 by putting it carefully into words1 and committing the words either to writing or to memory4 ,the function of ,naming1 and particularly of ,general ,names1 in ,induction1 may be recapitulated as follows4 ,every inductive inference which is good at all1 is good for a whole class of cases2 and1 that the inference may have any better warrant of its correctness than the mere clinging together of two ideas1 a process of experimentation and comparison is necessary2 in which the whole class of cases must be brought to view1 and some uniformity in the course of nature evolved and ascertained1 since the existence of such a uniformity is required as a justification for drawing the inference in even a single case4 ,this uniformity1 therefore1 may be ascertained once for all2 and if1 being ascertained1 it can be remembered1 it will serve as a formula for making1 in particular cases1 all such inferences as the previous experience will warrant4 ,but we can only secure its being remembered1 or give ourselves even a chance of carrying in our memory any considerable number of such uniformities1 by registering them through the medium of permanent signs2 which 7being1 from the nature of the case1 signs not of an individual fact1 but of a uniformity1 that is1 of an indefinite number of facts similar to one another7 are general signs2 universals2 general names1 and general propositions4 #d4 ,and here ,i can not omit to notice an oversight committed by some eminent thinkers2 who have said that the cause of our using general names is the infinite multitude of individual objects1 which1 making it impossible to have a name for each1 compels us to make one name serve for many4 ,this is a very limited view of the function of general names4 ,even if there were a name for every individual object1 we should require general names as much as we now do4 ,without them we could not express the result of a single comparison1 nor record any one of the uniformities existing in nature2 and should be hardly better off in respect to ,induction than if we had no names at all4 ,with none but names of individuals 7or1 in other words1 proper names71 we might1 by pronouncing the name1 suggest the idea of the object1 but we could not assert any proposition2 except the unmeaning ones formed by predicating two proper names one of another4 ,it is only by means of general names that we can convey any information1 predicate any attribute1 even of an individual1 much more of a class4 ,rigorously speaking1 we could get on without any other general names than the abstract names of attributes2 all our propositions might be of the form 8such an individual object possesses such an attribute10 or 8such an attribute is always 7or never7 conjoined with such another attribute40 ,in fact1 however1 mankind have always given general names to objects as well as attributes1 and indeed before attributes3 but the general names given to objects imply attributes1 derive their whole meaning from attributes2 and are chiefly useful as the language by means of which we predicate the attributes which they connote4 ,it remains to be considered what principles are to be adhered to in giving general names1 so that these names1 and the general propositions in which they fill a place1 may conduce most to the purposes of ,induction4 ,chapter ,,iv4 ,of ,the ,requisites ,of ,a ,philosophical ,language1 ,and ,the ,principles ,of ,definition4 #a4 ,in order that we may possess a language perfectly suitable for the investigation and expression of general truths1 there are two principal1 and several minor requisites4 ,the first is1 that every general name should have a meaning1 steadily fixed1 and precisely determined4 ,when1 by the fulfillment of this condition1 such names as we possess are fitted for the due performance of their functions1 the next requisite1 and the second in order of importance1 is that we should possess a name wherever one is needed2 wherever there is any thing to be designated by it1 which it is of importance to express4 ,the former of these requisites is that to which our attention will be exclusively directed in the present chapter4 #b4 ,every general name1 then1 must have a certain and knowable meaning4 ,now the meaning 7as has so often been explained7 of a general connotative name1 resides in the connotation2 in the attribute on account of which1 and to express which1 the name is given4 ,thus1 the name animal being given to all things which possess the attributes of sensation and voluntary motion1 the word connotes those attributes exclusively1 and they constitute the whole of its meaning4 ,if the name be abstract1 its denotation is the same with the connotation of the corresponding concrete2 it designates directly the attribute1 which the concrete term implies4 ,to give a precise meaning to general names is1 then1 to fix with steadiness the attribute or attributes connoted by each concrete general name1 and denoted by the corresponding abstract4 ,since abstract names1 in the order of their creation1 do not precede but follow concrete ones1 as is proved by the etymological fact that they are almost always derived from them2 we may consider their meaning as determined by1 and dependent on1 the meaning of their concrete2 and thus the problem of giving a distinct meaning to general language1 is all included in that of giving a precise connotation to all concrete general names4 ,this is not difficult in the case of new names2 of the technical terms created by scientific inquirers for the purposes of science or art4 ,but when a name is in common use1 the difficulty is greater2 the problem in this case not being that of choosing a convenient connotation for the name1 but of ascertaining and fixing the connotation with which it is already used4 ,that this can ever be a matter of doubt1 is a sort of paradox4 ,but the vulgar 7including in that term all who have not accurate habits of thought7 seldom know exactly what assertion they intend to make1 what common property they mean to express1 when they apply the same name to a number of different things4 ,all which the name expresses with them1 when they predicate it of an object1 is a confused feeling of resemblance between that object and some of the other things which they have been accustomed to denote by the name4 ,they have applied the name ,stone to various objects previously seen2 they see a new object1 which appears to them somewhat like the former1 and they call it a stone1 without asking themselves in what respect it is like1 or what mode or degree of resemblance the best authorities1 or even they themselves1 require as a warrant for using the name4 ,this rough general impression of resemblance is1 however1 made up of particular circumstances of resemblance2 and into these it is the business of the logician to analyze it2 to ascertain what points of resemblance among the different things commonly called by the name1 have produced in the common mind this vague feeling of likeness2 have given to the things the similarity of aspect1 which has made them a class1 and has caused the same name to be bestowed upon them4 ,but though general names are imposed by the vulgar without any more definite connotation than that of a vague resemblance2 general propositions come in time to be made1 in which predicates are applied to those names1 that is1 general assertions are made concerning the whole of the things which are denoted by the name4 ,and since by each of these propositions some attribute1 more or less precisely conceived1 is of course predicated1 the ideas of these various attributes thus become associated with the name1 and in a sort of uncertain way it comes to connote them2 there is a hesitation to apply the name in any new case in which any of the attributes familiarly predicated of the class do not exist4 ,and thus1 to common minds1 the propositions which they are in the habit of hearing or uttering concerning a class make up in a loose way a sort of connotation for the class name4 ,let us take1 for instance1 the word ,civilized4 ,how few could be found1 even among the most educated persons1 who would undertake to say exactly what the term ,civilized connotes4 ,yet there is a feeling in the minds of all who use it1 that they are using it with a meaning2 and this meaning is made up1 in a confused manner1 of every thing which they have heard or read that civilized men or civilized communities are1 or may be expected to be4 ,it is at this stage1 probably1 in the progress of a concrete name1 that the corresponding abstract name generally comes into use4 ,under the notion that the concrete name must of course convey a meaning1 or1 in other words1 that there is some property common to all things which it denotes1 people give a name to this common property2 from the concrete ,civilized1 they form the abstract ,civilization4 ,but since most people have never compared the different things which are called by the concrete name1 in such a manner as to ascertain what properties these things have in common1 or whether they have any2 each is thrown back upon the marks by which he himself has been accustomed to be guided in his application of the term2 and these1 being merely vague hearsays and current phrases1 are not the same in any two persons1 nor in the same person at different times4 ,hence the word 7as ,civilization1 for example7 which professes to be the designation of the unknown common property1 conveys scarcely to any two minds the same idea4 ,no two persons agree in the things they predicate of it2 and when it is itself predicated of any thing1 no other person knows1 nor does the speaker himself know with precision1 what he means to assert4 ,many other words which could be named1 as the word honor1 or the word gentleman1 exemplify this uncertainty still more strikingly4 ,it needs scarcely be observed1 that general propositions of which no one can tell exactly what they assert1 can not possibly have been brought to the test of a correct induction4 ,whether a name is to be used as an instrument of thinking1 or as a means of communicating the result of thought1 it is imperative to determine exactly the attribute or attributes which it is to express2 to give it1 in short1 a fixed and ascertained connotation4 #c4 ,it would1 however1 be a complete misunderstanding of the proper office of a logician in dealing with terms already in use1 if we were to think that because a name has not at present an ascertained connotation1 it is competent to any one to give it such a connotation at his own choice4 ,the meaning of a term actually in use is not an arbitrary quantity to be fixed1 but an unknown quantity to be sought4 ,in the first place1 it is obviously desirable to avail ourselves1 as far as possible1 of the associations already connected with the name2 not enjoining the employment of it in a manner which conflicts with all previous habits1 and especially not so as to require the rupture of those strongest of all associations between names1 which are created by familiarity with propositions in which they are predicated of one another4 ,a philosopher would have little chance of having his example followed1 if he were to give such a meaning to his terms as should require us to call the ,north ,american ,indians a civilized people1 or the higher classes in ,europe savages2 or to say that civilized people live by hunting1 and savages by agriculture4 ,were there no other reason1 the extreme difficulty of effecting so complete a revolution in speech would be more than a sufficient one4 ,the endeavor should be1 that all generally received propositions into which the term enters1 should be at least as true after its meaning is fixed1 as they were before2 and that the concrete name1 therefore1 should not receive such a connotation as shall prevent it from denoting things which1 in common language1 it is currently affirmed of4 ,the fixed and precise connotation which it receives should not be in deviation from1 but in agreement 7as far as it goes7 with1 the vague and fluctuating connotation which the term already had4 ,to fix the connotation of a concrete name1 or the denotation of the corresponding abstract1 is to define the name4 ,when this can be done without rendering any received assertions inadmissible1 the name can be defined in accordance with its received use1 which is vulgarly called defining not the name but the thing4 ,what is meant by the improper expression of defining a thing 7or rather a class of things--for nobody talks of defining an individual71 is to define the name1 subject to the condition that it shall denote those things4 ,this1 of course1 supposes a comparison of the things1 feature by feature and property by property1 to ascertain what attributes they agree in2 and not unfrequently an operation strictly inductive1 for the purpose of ascertaining some unobvious agreement1 which is the cause of the obvious agreements4 ,for1 in order to give a connotation to a name1 consistently with its denoting certain objects1 we have to make our selection from among the various attributes in which those objects agree4 ,to ascertain in what they do agree is1 therefore1 the first logical operation requisite4 ,when this has been done as far as is necessary or practicable1 the question arises1 which of these common attributes shall be selected to be associated with the name4 ,for if the class which the name denotes be a ,kind1 the common properties are innumerable2 and even if not1 they are often extremely numerous4 ,our choice is first limited by the preference to be given to properties which are well known1 and familiarly predicated of the class2 but even these are often too numerous to be all included in the definition1 and1 besides1 the properties most generally known may not be those which serve best to mark out the class from all others4 ,we should therefore select from among the common properties 7if among them any such are to be found7 those on which it has been ascertained by experience1 or proved by deduction1 that many others depend2 or at least which are sure marks of them1 and from whence1 therefore1 many others will follow by inference4 ,we thus see that to frame a good definition of a name already in use1 is not a matter of choice but of discussion1 and discussion not merely respecting the usage of language1 but respecting the properties of things1 and even the origin of those properties4 ,and hence every enlargement of our knowledge of the objects to which the name is applied1 is liable to suggest an improvement in the definition4 ,it is impossible to frame a perfect set of definitions on any subject1 until the theory of the subject is perfect2 and as science makes progress1 its definitions are also progressive4 #d4 ,the discussion of ,definitions1 in so far as it does not turn on the use of words but on the properties of things1 ,dr4 ,whewell calls the ,explication of ,conceptions4 ,the act of ascertaining1 better than before1 in what particulars any phenomena which are classed together agree1 he calls in his technical phraseology1 unfolding the general conception in virtue of which they are so classed4 ,making allowance for what appears to me the darkening and misleading tendency of this mode of expression1 several of his remarks are so much to the purpose1 that ,i shall take the liberty of transcribing them4 ,he observes17#bac7 that many of the controversies which have had an important share in the formation of the existing body of science1 have 8assumed the form of a battle of ,definitions4 ,for example1 the inquiry concerning the laws of falling bodies led to the question whether the proper definition of a uniform force is that it generates a velocity proportional to the space from rest1 or to the time4 ,the controversy of the vis viva was what was the proper definition of the measure of force4 ,a principal question in the classification of minerals is1 what is the definition of a mineral species4 ,physiologists have endeavored to throw light on their subject by defining organization1 or some similar term40 ,questions of the same nature were long open and are not yet completely closed1 respecting the definitions of ,specific ,heat1 ,latent ,heat1 ,chemical ,combination1 and ,solution4 8,it is very important for us to observe1 that these controversies have never been questions of insulated and arbitrary definitions1 as men seem often tempted to imagine them to have been4 ,in all cases there is a tacit assumption of some proposition which is to be expressed by means of the definition1 and which gives it its importance4 ,the dispute concerning the definition thus acquires a real value1 and becomes a question concerning true and false4 ,thus1 in the discussion of the question1 ,what is a uniform force8 it was taken for granted that gravity is a uniform force4 ,in the debate of the vis viva1 it was assumed that in the mutual action of bodies the whole effect of the force is unchanged4 ,in the zoological definition of species 7that it consists of individuals which have1 or may have1 sprung from the same parents71 it is presumed that individuals so related resemble each other more than those which are excluded by such a definition2 or1 perhaps1 that species so defined have permanent and definite differences4 ,a definition of organization1 or of some other term which was not employed to express some principle1 would be of no value4 8,the establishment1 therefore1 of a right definition of a term1 may be a useful step in the explication of our conceptions2 but this will be the case then only when we have under our consideration some proposition in which the term is employed4 ,for then the question really is1 how the conception shall be understood and defined in order that the proposition may be true4 8,to unfold our conceptions by means of definitions has never been serviceable to science1 except when it has been associated with an immediate use of the definitions4 ,the endeavor to define a ,uniform ,force was combined with the assertion that gravity is a uniform force2 the attempt to define ,accelerating ,force was immediately followed by the doctrine that accelerating forces may be compounded2 the process of defining ,momentum was connected with the principle that momenta gained and lost are equal2 naturalists would have given in vain the definition of ,species which we have quoted1 if they had not also given the characters of species so separated4444 ,definition may be the best mode of explaining our conception1 but that which alone makes it worth while to explain it in any mode1 is the opportunity of using it in the expression of truth4 ,when a definition is propounded to us as a useful step in knowledge1 we are always entitled to ask what principle it serves to enunciate40 ,in giving1 then1 an exact connotation to the phrase1 8a uniform force10 the condition was understood1 that the phrase should continue to denote gravity4 ,the discussion1 therefore1 respecting the definition1 resolved itself into this question1 ,what is there of a uniform nature in the motions produced by gravity8 ,by observations and comparisons1 it was found that what was uniform in those motions was the ratio of the velocity acquired to the time elapsed2 equal velocities being added in equal times4 ,a uniform force1 therefore1 was defined a force which adds equal velocities in equal times4 ,so1 again1 in defining momentum4 ,it was already a received doctrine that1 when two objects impinge upon one another1 the momentum lost by the one is equal to that gained by the other4 ,this proposition it was deemed necessary to preserve1 not from the motive 7which operates in many other cases7 that it was firmly fixed in popular belief2 for the proposition in question had never been heard of by any but the scientifically instructed4 ,but it was felt to contain a truth2 even a superficial observation of the phenomena left no doubt that in the propagation of motion from one body to another1 there was something of which the one body gained precisely what the other lost2 and the word momentum had been invented to express this unknown something4 ,the settlement1 therefore1 of the definition of momentum1 involved the determination of the question1 ,what is that of which a body1 when it sets another body in motion1 loses exactly as much as it communicates8 ,and when experiment had shown that this something was the product of the velocity of the body by its mass1 or quantity of matter1 this became the definition of momentum4 ,the following remarks17#bad7 therefore1 are perfectly just3 8,the business of definition is part of the business of discovery4444 ,to define1 so that our definition shall have any scientific value1 requires no small portion of that sagacity by which truth is detected4444 ,when it has been clearly seen what ought to be our definition1 it must be pretty well known what truth we have to state4 ,the definition1 as well as the discovery1 supposes a decided step in our knowledge to have been made4 ,the writers on ,logic1 in the ,middle ,ages1 made ,definition the last stage in the progress of knowledge2 and in this arrangement at least1 the history of science1 and the philosophy derived from the history1 confirm their speculative views40 ,for in order to judge finally how the name which denotes a class may best be defined1 we must know all the properties common to the class1 and all the relations of causation or dependence among those properties4 ,if the properties which are fittest to be selected as marks of other common properties are also obvious and familiar1 and especially if they bear a great part in producing that general air of resemblance which was the original inducement to the formation of the class1 the definition will then be most felicitous4 ,but it is often necessary to define the class by some property not familiarly known1 provided that property be the best mark of those which are known4 ,m4 ,de ,blainville1 for instance1 founded his definition of life on the process of decomposition and recomposition which incessantly takes place in every living body1 so that the particles composing it are never for two instants the same4 ,this is by no means one of the most obvious properties of living bodies2 it might escape altogether the notice of an unscientific observer4 ,yet great authorities 7independently of ,m4 ,de ,blainville1 who is himself a first-rate authority7 have thought that no other property so well answers the conditions required for the definition4 #e4 ,having laid down the principles which ought for the most part to be observed in attempting to give a precise connotation to a term in use1 ,i must now add1 that it is not always practicable to adhere to those principles1 and that even when practicable1 it is occasionally not desirable4 ,cases in which it is impossible to comply with all the conditions of a precise definition of a name in agreement with usage1 occur very frequently4 ,there is often no one connotation capable of being given to a word1 so that it shall still denote every thing it is accustomed to denote2 or that all the propositions into which it is accustomed to enter1 and which have any foundation in truth1 shall remain true4 ,independently of accidental ambiguities1 in which the different meanings have no connection with one another2 it continually happens that a word is used in two or more senses derived from each other1 but yet radically distinct4 ,so long as a term is vague1 that is1 so long as its connotation is not ascertained and permanently fixed1 it is constantly liable to be applied by extension from one thing to another1 until it reaches things which have little1 or even no1 resemblance to those which were first designated by it4 8,suppose10 says ,dugald ,stewart1 in his ,philosophical ,essays17#bae7 8that the letters ,a1 ,b1 ,c1 ,d1 ,e1 denote a series of objects2 that ,a possesses some one quality in common with ,b2 ,b a quality in common with ,c2 ,c a quality in common with ,d2 ,d a quality in common with ,e2 while at the same time1 no quality can be found which belongs in common to any three objects in the series4 ,is it not conceivable1 that the affinity between ,a and ,b may produce a transference of the name of the first to the second2 and that1 in consequence of the other affinities which connect the remaining objects together1 the same name may pass in succession from ,b to ,c2 from ,c to ,d2 and from ,d to ,e8 ,in this manner1 a common appellation will arise between ,a and ,e1 although the two objects may1 in their nature and properties1 be so widely distant from each other1 that no stretch of imagination can conceive how the thoughts were led from the former to the latter4 ,the transitions1 nevertheless1 may have been all so easy and gradual1 that1 were they successfully detected by the fortunate ingenuity of a theorist1 we should instantly recognize1 not only the verisimilitude1 but the truth of the conjecture3 in the same way as we admit1 with the confidence of intuitive conviction1 the certainty of the well-known etymological process which connects the ,latin preposition e or ex with the ,english substantive stranger1 the moment that the intermediate links of the chain are submitted to our examination407#baf7 ,the applications which a word acquires by this gradual extension of it from one set of objects to another1 ,stewart1 adopting an expression from ,mr4 ,payne ,knight1 calls its transitive applications2 and after briefly illustrating such of them as are the result of local or casual associations1 he proceeds as follows37#bag7 8,but although by far the greater part of the transitive or derivative applications of words depend on casual and unaccountable caprices of the feelings or the fancy1 there are certain cases in which they open a very interesting field of philosophical speculation4 ,such are those1 in which an analogous transference of the corresponding term may be remarked universally1 or very generally1 in other languages2 and in which1 of course1 the uniformity of the result must be ascribed to the essential principles of the human frame4 ,even in such cases1 however1 it will by no means be always found1 on examination1 that the various applications of the same term have arisen from any common quality or qualities in the objects to which they relate4 ,in the greater number of instances1 they may be traced to some natural and universal associations of ideas1 founded in the common faculties1 common organs1 and common condition of the human race4444 ,according to the different degrees of intimacy and strength in the associations on which the transitions of language are founded1 very different effects may be expected to arise4 ,where the association is slight and casual1 the several meanings will remain distinct from each other1 and will often1 in process of time1 assume the appearance of capricious varieties in the use of the same arbitrary sign4 ,where the association is so natural and habitual as to become virtually indissoluble1 the transitive meanings will coalesce in one complex conception2 and every new transition will become a more comprehensive generalization of the term in question40 ,i solicit particular attention to the law of mind expressed in the last sentence1 and which is the source of the perplexity so often experienced in detecting these transitions of meaning4 ,ignorance of that law is the shoal on which some of the most powerful intellects which have adorned the human race have been stranded4 ,the inquiries of ,plato into the definitions of some of the most general terms of moral speculation are characterized by ,bacon as a far nearer approach to a true inductive method than is elsewhere to be found among the ancients1 and are1 indeed1 almost perfect examples of the preparatory process of comparison and abstraction2 but1 from being unaware of the law just mentioned1 he often wasted the powers of this great logical instrument on inquiries in which it could realize no result1 since the phenomena1 whose common properties he so elaborately endeavored to detect1 had not really any common properties4 ,bacon himself fell into the same error in his speculations on the nature of heat1 in which he evidently confounded under the name hot1 classes of phenomena which have no property in common4 ,stewart certainly overstates the matter when he speaks of 8a prejudice which has descended to modern times from the scholastic ages1 that when a word admits of a variety of significations1 these different significations must all be species of the same genus1 and must consequently include some essential idea common to every individual to which the generic term can be applied207#bah7 for both ,aristotle and his followers were well aware that there are such things as ambiguities of language1 and delighted in distinguishing them4 ,but they never suspected ambiguity in the cases where 7as ,stewart remarks7 the association on which the transition of meaning was founded is so natural and habitual1 that the two meanings blend together in the mind1 and a real transition becomes an apparent generalization4 ,accordingly they wasted infinite pains in endeavoring to find a definition which would serve for several distinct meanings at once2 as in an instance noticed by ,stewart himself1 that of 8causation2 the ambiguity of the word which1 in the ,greek language corresponds to the ,english word cause1 having suggested to them the vain attempt of tracing the common idea which1 in the case of any effect1 belongs to the efficient1 to the matter1 to the form1 and to the end4 ,the idle generalities0 7he adds7 8we meet with in other philosophers1 about the ideas of the good1 the fit1 and the becoming1 have taken their rise from the same undue influence of popular epithets on the speculations of the learned407#bai7 ,among the words which have undergone so many successive transitions of meaning that every trace of a property common to all the things they are applied to1 or at least common and also peculiar to those things1 has been lost1 ,stewart considers the word ,beautiful to be one4 ,and 7without attempting to decide a question which in no respect belongs to logic7 ,i can not but feel1 with him1 considerable doubt whether the word beautiful connotes the same property when we speak of a beautiful color1 a beautiful face1 a beautiful scene1 a beautiful character1 and a beautiful poem4 ,the word was doubtless extended from one of these objects to another on account of a resemblance between them1 or1 more probably1 between the emotions they excited2 and1 by this progressive extension1 it has at last reached things very remote from those objects of sight to which there is no doubt that it was first appropriated2 and it is at least questionable whether there is now any property common to all the things which1 consistently with usage1 may be called beautiful1 except the property of agreeableness1 which the term certainly does connote1 but which can not be all that people usually intend to express by it1 since there are many agreeable things which are never called beautiful4 ,if such be the case1 it is impossible to give to the word ,beautiful any fixed connotation1 such that it shall denote all the objects which in common use it now denotes1 but no others4 ,a fixed connotation1 however1 it ought to have2 for1 so long as it has not1 it is unfit to be used as a scientific term1 and is a perpetual source of false analogies and erroneous generalizations4 ,this1 then1 constitutes a case in exemplification of our remark1 that even when there is a property common to all the things denoted by a name1 to erect that property into the definition and exclusive connotation of the name is not always desirable4 ,the various things called beautiful unquestionably resemble one another in being agreeable2 but to make this the definition of beauty1 and so extend the word ,beautiful to all agreeable things1 would be to drop altogether a portion of meaning which the word really1 though indistinctly1 conveys1 and to do what depends on us toward causing those qualities of the objects which the word previously1 though vaguely1 pointed at1 to be overlooked and forgotten4 ,it is better1 in such a case1 to give a fixed connotation to the term by restricting1 than by extending its use2 rather excluding from the epithet ,beautiful some things to which it is commonly considered applicable1 than leaving out of its connotation any of the qualities by which1 though occasionally lost sight of1 the general mind may have been habitually guided in the commonest and most interesting applications of the term4 ,for there is no question that when people call any thing beautiful1 they think they are asserting more than that it is merely agreeable4 ,they think they are ascribing a peculiar sort of agreeableness1 analogous to that which they find in some other of the things to which they are accustomed to apply the same name4 ,if1 therefore1 there be any peculiar sort of agreeableness which is common though not to all1 yet to the principal things which are called beautiful1 it is better to limit the denotation of the term to those things1 than to leave that kind of quality without a term to connote it1 and thereby divert attention from its peculiarities4 #f4 ,the last remark exemplifies a rule of terminology1 which is of great importance1 and which has hardly yet been recognized as a rule1 but by a few thinkers of the present century4 ,in attempting to rectify the use of a vague term by giving it a fixed connotation1 we must take care not to discard 7unless advisedly1 and on the ground of a deeper knowledge of the subject7 any portion of the connotation which the word1 in however indistinct a manner1 previously carried with it4 ,for otherwise language loses one of its inherent and most valuable properties1 that of being the conservator of ancient experience2 the keeper-alive of those thoughts and observations of former ages1 which may be alien to the tendencies of the passing time4 ,this function of language is so often overlooked or undervalued1 that a few observations on it appear to be extremely required4 ,even when the connotation of a term has been accurately fixed1 and still more if it has been left in the state of a vague unanalyzed feeling of resemblance2 there is a constant tendency in the word1 through familiar use1 to part with a portion of its connotation4 ,it is a well-known law of the mind1 that a word originally associated with a very complex cluster of ideas1 is far from calling up all those ideas in the mind1 every time the word is used2 it calls up only one or two1 from which the mind runs on by fresh associations to another set of ideas1 without waiting for the suggestion of the remainder of the complex cluster4 ,if this were not the case1 processes of thought could not take place with any thing like the rapidity which we know they possess4 ,very often1 indeed1 when we are employing a word in our mental operations1 we are so far from waiting until the complex idea which corresponds to the meaning of the word is consciously brought before us in all its parts1 that we run on to new trains of ideas by the other associations which the mere word excites1 without having realized in our imagination any part whatever of the meaning2 thus using the word1 and even using it well and accurately1 and carrying on important processes of reasoning by means of it1 in an almost mechanical manner2 so much so1 that some metaphysicians1 generalizing from an extreme case1 have fancied that all reasoning is but the mechanical use of a set of terms according to a certain form4 ,we may discuss and settle the most important interests of towns or nations1 by the application of general theorems or practical maxims previously laid down1 without having had consciously suggested to us1 once in the whole process1 the houses and green fields1 the thronged market-places and domestic hearths1 of which not only those towns and nations consist1 but which the words town and nation confessedly mean4 ,since1 then1 general names come in this manner to be used 7and even to do a portion of their work well7 without suggesting to the mind the whole of their meaning1 and often with the suggestion of a very small1 or no part at all of that meaning2 we can not wonder that words so used come in time to be no longer capable of suggesting any other of the ideas appropriated to them1 than those with which the association is most immediate and strongest1 or most kept up by the incidents of life2 the remainder being lost altogether2 unless the mind1 by often consciously dwelling on them1 keeps up the association4 ,words naturally retain much more of their meaning to persons of active imagination1 who habitually represent to themselves things in the concrete1 with the detail which belongs to them in the actual world4 ,to minds of a different description1 the only antidote to this corruption of language is predication4 ,the habit of predicating of the name1 all the various properties which it originally connoted1 keeps up the association between the name and those properties4 ,but in order that it may do so1 it is necessary that the predicates should themselves retain their association with the properties which they severally connote4 ,for the propositions can not keep the meaning of the words alive1 if the meaning of the propositions themselves should die4 ,and nothing is more common than for propositions to be mechanically repeated1 mechanically retained in the memory1 and their truth undoubtingly assented to and relied on1 while yet they carry no meaning distinctly home to the mind2 and while the matter of fact or law of nature which they originally expressed is as much lost sight of1 and practically disregarded1 as if it never had been heard of at all4 ,in those subjects which are at the same time familiar and complicated1 and especially in those which are so in as great a degree as moral and social subjects are1 it is a matter of common remark how many important propositions are believed and repeated from habit1 while no account could be given1 and no sense is practically manifested1 of the truths which they convey4 ,hence it is1 that the traditional maxims of old experience1 though seldom questioned1 have often so little effect on the conduct of life2 because their meaning is never1 by most persons1 really felt1 until personal experience has brought it home4 ,and thus also it is that so many doctrines of religion1 ethics1 and even politics1 so full of meaning and reality to first converts1 have manifested 7after the association of that meaning with the verbal formulas has ceased to be kept up by the controversies which accompanied their first introduction7 a tendency to degenerate rapidly into lifeless dogmas2 which tendency1 all the efforts of an education expressly and skillfully directed to keeping the meaning alive1 are barely sufficient to counteract4 ,considering1 then1 that the human mind1 in different generations1 occupies itself with different things1 and in one age is led by the circumstances which surround it to fix more of its attention upon one of the properties of a thing1 in another age upon another2 it is natural and inevitable that in every age a certain portion of our recorded and traditional knowledge1 not being continually suggested by the pursuits and inquiries with which mankind are at that time engrossed1 should fall asleep1 as it were1 and fade from the memory4 ,it would be in danger of being totally lost1 if the propositions or formulas1 the results of the previous experience1 did not remain1 as forms of words it may be1 but of words that once really conveyed1 and are still supposed to convey1 a meaning3 which meaning1 though suspended1 may be historically traced1 and when suggested1 may be recognized by minds of the necessary endowments as being still matter of fact1 or truth4 ,while the formulas remain1 the meaning may at any time revive2 and as1 on the one hand1 the formulas progressively lose the meaning they were intended to convey1 so1 on the other1 when this forgetfulness has reached its height and begun to produce obvious consequences1 minds arise which from the contemplation of the formulas rediscover the truth1 when truth it was1 which was contained in them1 and announce it again to mankind1 not as a discovery1 but as the meaning of that which they have been taught1 and still profess to believe4 ,thus there is a perpetual oscillation in spiritual truths1 and in spiritual doctrines of any significance1 even when not truths4 ,their meaning is almost always in a process either of being lost or of being recovered4 ,whoever has attended to the history of the more serious convictions of mankind--of the opinions by which the general conduct of their lives is1 or as they conceive ought to be1 more especially regulated--is aware that even when recognizing verbally the same doctrines1 they attach to them at different periods a greater or a less quantity1 and even a different kind of meaning4 ,the words in their original acceptation connoted1 and the propositions expressed1 a complication of outward facts and inward feelings1 to different portions of which the general mind is more particularly alive in different generations of mankind4 ,to common minds1 only that portion of the meaning is in each generation suggested1 of which that generation possesses the counterpart in its own habitual experience4 ,but the words and propositions lie ready to suggest to any mind duly prepared the remainder of the meaning4 ,such individual minds are almost always to be found2 and the lost meaning1 revived by them1 again by degrees works its way into the general mind4 ,the arrival of this salutary reaction may1 however1 be materially retarded by the shallow conceptions and incautious proceedings of mere logicians4 ,it sometimes happens that toward the close of the downward period1 when the words have lost part of their significance1 and have not yet begun to recover it1 persons arise whose leading and favorite idea is the importance of clear conceptions and precise thought1 and the necessity1 therefore1 of definite language4 ,these persons1 in examining the old formulas1 easily perceive that words are used in them without a meaning2 and if they are not the sort of persons who are capable of rediscovering the lost signification1 they naturally enough dismiss the formula1 and define the name without reference to it4 ,in so doing they fasten down the name to what it connotes in common use at the time when it conveys the smallest quantity of meaning2 and introduce the practice of employing it1 consistently and uniformly1 according to that connotation4 ,the word in this way acquires an extent of denotation far beyond what it had before2 it becomes extended to many things to which it was previously1 in appearance capriciously1 refused4 ,of the propositions in which it was formerly used1 those which were true in virtue of the forgotten part of its meaning are now1 by the clearer light which the definition diffuses1 seen not to be true according to the definition2 which1 however1 is the recognized and sufficiently correct expression of all that is perceived to be in the mind of any one by whom the term is used at the present day4 ,the ancient formulas are consequently treated as prejudices2 and people are no longer taught as before1 though not to understand them1 yet to believe that there is truth in them4 ,they no longer remain in the general mind surrounded by respect1 and ready at any time to suggest their original meaning4 ,whatever truths they contain are not only1 in these circumstances1 rediscovered far more slowly1 but1 when rediscovered1 the prejudice with which novelties are regarded is now1 in some degree at least1 against them1 instead of being on their side4 ,an example may make these remarks more intelligible4 ,in all ages1 except where moral speculation has been silenced by outward compulsion1 or where the feelings which prompt to it still continue to be satisfied by the traditional doctrines of an established faith1 one of the subjects which have most occupied the minds of thinking persons is the inquiry1 ,what is virtue8 or1 ,what is a virtuous character8 ,among the different theories on the subject which have1 at different times1 grown up and obtained partial currency1 every one of which reflected as in the clearest mirror the express image of the age which gave it birth2 there was one1 according to which virtue consists in a correct calculation of our own personal interests1 either in this world only1 or also in another4 ,to make this theory plausible1 it was of course necessary that the only beneficial actions which people in general were accustomed to see1 or were therefore accustomed to praise1 should be such as were1 or at least might without contradicting obvious facts be supposed to be1 the result of a prudential regard to self-interest2 so that the words really connoted no more1 in common acceptation1 than was set down in the definition4 ,suppose1 now1 that the partisans of this theory had contrived to introduce a consistent and undeviating use of the term according to this definition4 ,suppose that they had seriously endeavored1 and had succeeded in the endeavor1 to banish the word disinterestedness from the language2 had obtained the disuse of all expressions attaching odium to selfishness or commendation to self-sacrifice1 or which implied generosity or kindness to be any thing but doing a benefit in order to receive a greater personal advantage in return4 ,need we say that this abrogation of the old formulas for the sake of preserving clear ideas and consistency of thought1 would have been a great evil8 while the very inconsistency incurred by the co-existence of the formulas with philosophical opinions which seemed to condemn them as absurdities1 operated as a stimulus to the re-examination of the subject and thus the very doctrines originating in the oblivion into which a part of the truth had fallen1 were rendered indirectly1 but powerfully1 instrumental to its revival4 ,the doctrine of the ,coleridge school1 that the language of any people among whom culture is of old date1 is a sacred deposit1 the property of all ages1 and which no one age should consider itself empowered to alter--borders indeed1 as thus expressed1 on an extravagance2 but it is grounded on a truth1 frequently overlooked by that class of logicians who think more of having a clear than of having a comprehensive meaning2 and who perceive that every age is adding to the truths which it has received from its predecessors1 but fail to see that a counter process of losing truths already possessed1 is also constantly going on1 and requiring the most sedulous attention to counteract it4 ,language is the depository of the accumulated body of experience to which all former ages have contributed their part1 and which is the inheritance of all yet to come4 ,we have no right to prevent ourselves from transmitting to posterity a larger portion of this inheritance than we may ourselves have profited by4 ,however much we may be able to improve on the conclusions of our forefathers1 we ought to be careful not inadvertently to let any of their premises slip through our fingers4 ,it may be good to alter the meaning of a word1 but it is bad to let any part of the meaning drop4 ,whoever seeks to introduce a more correct use of a term with which important associations are connected1 should be required to possess an accurate acquaintance with the history of the particular word1 and of the opinions which in different stages of its progress it served to express4 ,to be qualified to define the name1 we must know all that has ever been known of the properties of the class of objects which are1 or originally were1 denoted by it4 ,for if we give it a meaning according to which any proposition will be false which has ever been generally held to be true1 it is incumbent on us to be sure that we know and have considered all which those who believed the proposition understood by it4 ,chapter ,v4 ,on ,the ,natural ,history ,of ,the ,variations ,in ,the ,meaning ,of ,terms4 #a4 ,it is not only in the mode which has now been pointed out1 namely by gradual inattention to a portion of the ideas conveyed1 that words in common use are liable to shift their connotation4 ,the truth is1 that the connotation of such words is perpetually varying2 as might be expected from the manner in which words in common use acquire their connotation4 ,a technical term1 invented for purposes of art or science1 has1 from the first1 the connotation given to it by its inventor2 but a name which is in every one's mouth before any one thinks of defining it1 derives its connotation only from the circumstances which are habitually brought to mind when it is pronounced4 ,among these circumstances1 the properties common to the things denoted by the name1 have naturally a principal place2 and would have the sole place1 if language were regulated by convention rather than by custom and accident4 ,but besides these common properties1 which if they exist are certainly present whenever the name is employed1 any other circumstance may casually be found along with it1 so frequently as to become associated with it in the same manner1 and as strongly1 as the common properties themselves4 ,in proportion as this association forms itself1 people give up using the name in cases in which those casual circumstances do not exist4 ,they prefer using some other name1 or the same name with some adjunct1 rather than employ an expression which will call up an idea they do not want to excite4 ,the circumstance originally casual1 thus becomes regularly a part of the connotation of the word4 ,it is this continual incorporation of circumstances originally accidental1 into the permanent signification of words1 which is the cause that there are so few exact synonyms4 ,it is this also which renders the dictionary meaning of a word1 by universal remark so imperfect an exponent of its real meaning4 ,the dictionary meaning is marked out in a broad1 blunt way1 and probably includes all that was originally necessary for the correct employment of the term2 but in process of time so many collateral associations adhere to words1 that whoever should attempt to use them with no other guide than the dictionary1 would confound a thousand nice distinctions and subtle shades of meaning which dictionaries take no account of2 as we notice in the use of a language in conversation or writing by a foreigner not thoroughly master of it4 ,the history of a word1 by showing the causes which determine its use1 is in these cases a better guide to its employment than any definition2 for definitions can only show its meaning at the particular time1 or at most the series of its successive meanings1 but its history may show the law by which the succession was produced4 ,the word gentleman1 for instance1 to the correct employment of which a dictionary would be no guide1 originally meant simply a man born in a certain rank4 ,from this it came by degrees to connote all such qualities or adventitious circumstances as were usually found to belong to persons of that rank4 ,this consideration at once explains why in one of its vulgar acceptations it means any one who lives without labor1 in another without manual labor1 and in its more elevated signification it has in every age signified the conduct1 character1 habits1 and outward appearance1 in whomsoever found1 which1 according to the ideas of that age1 belonged or were expected to belong to persons born and educated in a high social position4 ,it continually happens that of two words1 whose dictionary meanings are either the same or very slightly different1 one will be the proper word to use in one set of circumstances1 another in another1 without its being possible to show how the custom of so employing them originally grew up4 ,the accident that one of the words was used and not the other on a particular occasion or in a particular social circle1 will be sufficient to produce so strong an association between the word and some specialty of circumstances1 that mankind abandon the use of it in any other case1 and the specialty becomes part of its signification4 ,the tide of custom first drifts the word on the shore of a particular meaning1 then retires and leaves it there4 ,an instance in point is the remarkable change which1 in the ,english language at least1 has taken place in the signification of the word loyalty4 ,that word originally meant in ,english1 as it still means in the language from whence it came1 fair1 open dealing1 and fidelity to engagements2 in that sense the quality it expressed was part of the ideal chivalrous or knightly character4 ,by what process1 in ,england1 the term became restricted to the single case of fidelity to the throne1 ,i am not sufficiently versed in the history of courtly language to be able to pronounce4 ,the interval between a loyal chevalier and a loyal subject is certainly great4 ,i can only suppose that the word was1 at some period1 the favorite term at court to express fidelity to the oath of allegiance2 until at length those who wished to speak of any other1 and as it was probably deemed1 inferior sort of fidelity1 either did not venture to use so dignified a term1 or found it convenient to employ some other in order to avoid being misunderstood4 #b4 ,cases are not unfrequent in which a circumstance1 at first casually incorporated into the connotation of a word which originally had no reference to it1 in time wholly supersedes the original meaning1 and becomes not merely a part of the connotation1 but the whole of it4 ,this is exemplified in the word pagan1 paganus2 which originally1 as its etymology imports1 was equivalent to villager2 the inhabitant of a pagus1 or village4 ,at a particular era in the extension of ,christianity over the ,roman empire1 the adherents of the old religion1 and the villagers or country people1 were nearly the same body of individuals1 the inhabitants of the towns having been earliest converted2 as in our own day1 and at all times1 the greater activity of social intercourse renders them the earliest recipients of new opinions and modes1 while old habits and prejudices linger longest among the country people2 not to mention that the towns were more immediately under the direct influence of the ,government1 which at that time had embraced ,christianity4 ,from this casual coincidence1 the word paganus carried with it1 and began more and more steadily to suggest1 the idea of a worshiper of the ancient divinities2 until at length it suggested that idea so forcibly that people who did not desire to suggest the idea avoided using the word4 ,but when paganus had come to connote heathenism1 the very unimportant circumstance1 with reference to that fact1 of the place of residence1 was soon disregarded in the employment of the word4 ,as there was seldom any occasion for making separate assertions respecting heathens who lived in the country1 there was no need for a separate word to denote them2 and pagan came not only to mean heathen1 but to mean that exclusively4 ,a case still more familiar to most readers is that of the word villain or villein4 ,this term1 as every body knows1 had in the ,middle ,ages a connotation as strictly defined as a word could have1 being the proper legal designation for those persons who were the subjects of the less onerous forms of feudal bondage4 ,the scorn of the semi-barbarous military aristocracy for these their abject dependants1 rendered the act of likening any person to this class of people a mark of the greatest contumely2 the same scorn led them to ascribe to the same people all manner of hateful qualities1 which doubtless also1 in the degrading situation in which they were held1 were often not unjustly imputed to them4 ,these circumstances combined to attach to the term villain ideas of crime and guilt1 in so forcible a manner that the application of the epithet even to those to whom it legally belonged became an affront1 and was abstained from whenever no affront was intended4 ,from that time guilt was part of the connotation2 and soon became the whole of it1 since mankind were not prompted by any urgent motive to continue making a distinction in their language between bad men of servile station and bad men of any other rank in life4 ,these and similar instances in which the original signification of a term is totally lost--another and an entirely distinct meaning being first ingrafted upon the former1 and finally substituted for it--afford examples of the double movement which is always taking place in language3 two counter-movements1 one of ,generalization1 by which words are perpetually losing portions of their connotation1 and becoming of less meaning and more general acceptation2 the other of ,specialization1 by which other1 or even these same words1 are continually taking on fresh connotation2 acquiring additional meaning by being restricted in their employment to a part only of the occasions on which they might properly be used before4 ,this double movement is of sufficient importance in the natural history of language 7to which natural history the artificial modifications ought always to have some degree of reference71 to justify our dwelling a little longer on the nature of the twofold phenomenon1 and the causes to which it owes its existence4 #c4 ,to begin with the movement of generalization4 ,it might seem unnecessary to dwell on the changes in the meaning of names which take place merely from their being used ignorantly1 by persons who1 not having properly mastered the received connotation of a word1 apply it in a looser and wider sense than belongs to it4 ,this1 however1 is a real source of alterations in the language2 for when a word1 from being often employed in cases where one of the qualities which it connotes does not exist1 ceases to suggest that quality with certainty1 then even those who are under no mistake as to the proper meaning of the word1 prefer expressing that meaning in some other way1 and leave the original word to its fate4 ,the word ',squire1 as standing for an owner of a landed estate2 ,parson1 as denoting not the rector of the parish1 but clergymen in general2 ,artist1 to denote only a painter or sculptor2 are cases in point4 ,such cases give a clear insight into the process of the degeneration of languages in periods of history when literary culture was suspended2 and we are now in danger of experiencing a similar evil through the superficial extension of the same culture4 ,so many persons without any thing deserving the name of education have become writers by profession1 that written language may almost be said to be principally wielded by persons ignorant of the proper use of the instrument1 and who are spoiling it more and more for those who understand it4 ,vulgarisms1 which creep in nobody knows how1 are daily depriving the ,english language of valuable modes of expressing thought4 ,to take a present instance3 the verb transpire formerly conveyed very expressively its correct meaning1 viz41 to become known through unnoticed channels--to exhale1 as it were1 into publicity through invisible pores1 like a vapor or gas disengaging itself4 ,but of late a practice has commenced of employing this word1 for the sake of finery1 as a mere synonym of to happen3 8the events which have transpired in the ,crimea10 meaning the incidents of the war4 ,this vile specimen of bad ,english is already seen in the dispatches of noblemen and viceroys2 and the time is apparently not far distant when nobody will understand the word if used in its proper sense4 ,in other cases it is not the love of finery1 but simple want of education1 which makes writers employ words in senses unknown to genuine ,english4 ,the use of 8aggravating0 for 8provoking10 in my boyhood a vulgarism of the nursery1 has crept into almost all newspapers1 and into many books2 and when the word is used in its proper sense1 as when writers on criminal law speak of aggravating and extenuating circumstances1 their meaning1 it is probable1 is already misunderstood4 ,it is a great error to think that these corruptions of language do no harm4 ,those who are struggling with the difficulty 7and who know by experience how great it already is7 of expressing one's self clearly with precision1 find their resources continually narrowed by illiterate writers1 who seize and twist from its purpose some form of speech which once served to convey briefly and compactly an unambiguous meaning4 ,it would hardly be believed how often a writer is compelled to a circumlocution by the single vulgarism1 introduced during the last few years1 of using the word alone as an adverb1 only not being fine enough for the rhetoric of ambitious ignorance4 ,a man will say 8to which ,i am not alone bound by honor but also by law10 unaware that what he has unintentionally said is1 that he is not alone bound1 some other person being bound with him4 ,formerly1 if any one said1 8,i am not alone responsible for this10 he was understood to mean 7what alone his words mean in correct ,english71 that he is not the sole person responsible2 but if he now used such an expression1 the reader would be confused between that and two other meanings3 that he is not only responsible but something more2 or that he is responsible not only for this but for something besides4 ,the time is coming when ,tennyson's none could not say1 8,i will not die alone10 lest she should be supposed to mean that she would not only die but do something else4 ,the blunder of writing predicate for predict has become so widely diffused that it bids fair to render one of the most useful terms in the scientific vocabulary of ,logic unintelligible4 ,the mathematical and logical term 8to eliminate0 is undergoing a similar destruction4 ,all who are acquainted either with the proper use of the word or with its etymology know that to eliminate a thing is to thrust it out3 but those who know nothing about it1 except that it is a fine-looking phrase1 use it in a sense precisely the reverse1 to denote1 not turning any thing out1 but bringing it in4 ,they talk of eliminating some truth1 or other useful result1 from a mass of details47#bbj7 ,a similar permanent deterioration in the language is in danger of being produced by the blunders of translators4 ,the writers of telegrams1 and the foreign correspondents of newspapers1 have gone on so long translating demander by 8to demand10 without a suspicion that it means only to ask1 that 7the context generally showing that nothing else is meant7 ,english readers are gradually associating the ,english word demand with simple asking1 thus leaving the language without a term to express a demand in its proper sense4 ,in like manner1 8transaction10 the ,french word for a compromise1 is translated into the ,english word transaction2 while1 curiously enough1 the inverse change is taking place in ,france1 where the word 8compromis0 has lately begun to be used for expressing the same idea4 ,if this continues1 the two countries will have exchanged phrases4 ,independently1 however1 of the generalization of names through their ignorant misuse1 there is a tendency in the same direction consistently with a perfect knowledge of their meaning2 arising from the fact1 that the number of things known to us1 and of which we feel a desire to speak1 multiply faster than the names for them4 ,except on subjects for which there has been constructed a scientific terminology1 with which unscientific persons do not meddle1 great difficulty is generally found in bringing a new name into use2 and independently of that difficulty1 it is natural to prefer giving to a new object a name which at least expresses its resemblance to something already known1 since by predicating of it a name entirely new we at first convey no information4 ,in this manner the name of a species often becomes the name of a genus2 as salt1 for example1 or oil2 the former of which words originally denoted only the muriate of soda1 the latter1 as its etymology indicates1 only olive-oil2 but which now denote large and diversified classes of substances resembling these in some of their qualities1 and connote only those common qualities1 instead of the whole of the distinctive properties of olive-oil and sea-salt4 ,the words glass and soap are used by modern chemists in a similar manner1 to denote genera of which the substances vulgarly so called are single species4 ,and it often happens1 as in those instances1 that the term keeps its special signification in addition to its more general one1 and becomes ambiguous1 that is1 two names instead of one4 ,these changes1 by which words in ordinary use become more and more generalized1 and less and less expressive1 take place in a still greater degree with the words which express the complicated phenomena of mind and society4 ,historians1 travelers1 and in general those who speak or write concerning moral and social phenomena with which they are not familiarly acquainted1 are the great agents in this modification of language4 ,the vocabulary of all except unusually instructed as well as thinking persons1 is1 on such subjects1 eminently scanty4 ,they have a certain small set of words to which they are accustomed1 and which they employ to express phenomena the most heterogeneous1 because they have never sufficiently analyzed the facts to which those words correspond in their own country1 to have attached perfectly definite ideas to the words4 ,the first ,english conquerors of ,bengal1 for example1 carried with them the phrase landed proprietor into a country where the rights of individuals over the soil were extremely different in degree1 and even in nature1 from those recognized in ,england4 ,applying the term with all its ,english associations in such a state of things2 to one who had only a limited right they gave an absolute right1 from another because he had not an absolute right they took away all right1 drove whole classes of people to ruin and despair1 filled the country with banditti1 created a feeling that nothing was secure1 and produced1 with the best intentions1 a disorganization of society which had not been produced in that country by the most ruthless of its barbarian invaders4 ,yet the usage of persons capable of so gross a misapprehension determines the meaning of language2 and the words they thus misuse grow in generality1 until the instructed are obliged to acquiesce2 and to employ those words 7first freeing them from vagueness by giving them a definite connotation7 as generic terms1 subdividing the genera into species4 #d4 ,while the more rapid growth of ideas than of names thus creates a perpetual necessity for making the same names serve1 even if imperfectly1 on a greater number of occasions2 a counter-operation is going on1 by which names become on the contrary restricted to fewer occasions1 by taking on1 as it were1 additional connotation1 from circumstances not originally included in the meaning1 but which have become connected with it in the mind by some accidental cause4 ,we have seen above1 in the words pagan and villain1 remarkable examples of the specialization of the meaning of words from casual associations1 as well as of the generalization of it in a new direction1 which often follows4 ,similar specializations are of frequent occurrence in the history even of scientific nomenclature4 8,it is by no means uncommon10 says ,dr4 ,paris1 in his ,pharmacologia17#bba7 8to find a word which is used to express general characters subsequently become the name of a specific substance in which such characters are predominant2 and we shall find that some important anomalies in nomenclature may be thus explained4 ,the term 1 from which the word ,arsenic is derived1 was an ancient epithet applied to those natural substances which possessed strong and acrimonious properties2 and as the poisonous quality of arsenic was found to be remarkably powerful1 the term was especially applied to ,orpiment1 the form in which this metal most usually occurred4 ,so the term ,verbena 7quasi ,herbena7 originally denoted all those herbs that were held sacred on account of their being employed in the rites of sacrifice1 as we learn from the poets2 but as one herb was usually adopted upon these occasions1 the word ,verbena came to denote that particular herb only1 and it is transmitted to us to this day under the same title1 viz41 ,verbena or ,vervain1 and indeed until lately it enjoyed the medical reputation which its sacred origin conferred upon it1 for it was worn suspended around the neck as an amulet4 ,vitriol1 in the original application of the word1 denoted any crystalline body with a certain degree of transparency 7vitrum72 it is hardly necessary to observe that the term is now appropriated to a particular species3 in the same manner1 ,bark1 which is a general term1 is applied to express one genus1 and by way of eminence it has the article ,the prefixed1 as ,the bark2 the same observation will apply to the word ,opium1 which1 in its primitive sense1 signifies any juice 71 ,succus71 while it now only denotes one species1 viz41 that of the poppy4 ,so1 again1 ,elaterium was used by ,hippocrates to signify various internal applications1 especially purgatives1 of a violent and drastic nature 7from the word 1 agito1 moveo1 stimulo71 but by succeeding authors it was exclusively applied to denote the active matter which subsides from the juice of the wild cucumber4 ,the word ,fecula1 again1 originally meant to imply any substance which was derived by spontaneous subsidence from a liquid 7from fx1 the grounds or settlement of any liquor72 afterward it was applied to ,starch1 which is deposited in this manner by agitating the flour of wheat in water2 and1 lastly1 it has been applied to a peculiar vegetable principle1 which1 like starch1 is insoluble in cold1 but completely soluble in boiling water1 with which it forms a gelatinous solution4 ,this indefinite meaning of the word fecula has created numerous mistakes in pharmaceutic chemistry2 ,elaterium1 for instance1 is said to be fecula1 and1 in the original sense of the word1 it is properly so called1 inasmuch as it is procured from a vegetable juice by spontaneous subsidence1 but in the limited and modern acceptation of the term it conveys an erroneous idea2 for instead of the active principle of the juice residing in fecula1 it is a peculiar proximate principle1 sui generis1 to which ,i have ventured to bestow the name of ,elatin4 ,for the same reason1 much doubt and obscurity involve the meaning of the word ,extract1 because it is applied generally to any substance obtained by the evaporation of a vegetable solution1 and specifically to a peculiar proximate principle1 possessed of certain characters1 by which it is distinguished from every other elementary body40 ,a generic term is always liable to become thus limited to a single species1 or even individual1 if people have occasion to think and speak of that individual or species much oftener than of any thing else which is contained in the genus4 ,thus by cattle1 a stage-coachman will understand horses2 beasts1 in the language of agriculturists1 stands for oxen2 and birds1 with some sportsmen1 for partridges only4 ,the law of language which operates in these trivial instances is the very same in conformity to which the terms 1 ,deus1 and ,god1 were adopted from ,polytheism by ,christianity1 to express the single object of its own adoration4 ,almost all the terminology of the ,christian ,church is made up of words originally used in a much more general acceptation3 ,ecclesia1 ,assembly2 ,bishop1 ,episcopus1 ,overseer2 ,priest1 ,presbyter1 ,elder2 ,deacon1 ,diaconus1 ,administrator2 ,sacrament1 a vow of allegiance2 ,evangelium1 good tidings2 and some words1 as ,minister1 are still used both in the general and in the limited sense4 ,it would be interesting to trace the progress by which author came1 in its most familiar sense1 to signify a writer1 and 1 or maker1 a poet4 ,of the incorporation into the meaning of a term1 of circumstances accidentally connected with it at some particular period1 as in the case of ,pagan1 instances might easily be multiplied4 ,physician 71 or naturalist7 became1 in ,england1 synonymous with a healer of diseases1 because until a comparatively late period medical practitioners were the only naturalists4 ,clerc1 or clericus1 a scholar1 came to signify an ecclesiastic1 because the clergy were for many centuries the only scholars4 ,of all ideas1 however1 the most liable to cling by association to any thing with which they have ever been connected by proximity1 are those of our pleasures and pains1 or of the things which we habitually contemplate as sources of our pleasures or pains4 ,the additional connotation1 therefore1 which a word soonest and most readily takes on1 is that of agreeableness or painfulness1 in their various kinds and degrees2 of being a good or bad thing2 desirable or to be avoided2 an object of hatred1 of dread1 contempt1 admiration1 hope1 or love4 ,accordingly there is hardly a single name1 expressive of any moral or social fact calculated to call forth strong affections either of a favorable or of a hostile nature1 which does not carry with it decidedly and irresistibly a connotation of those strong affections1 or1 at the least1 of approbation or censure2 insomuch that to employ those names in conjunction with others by which the contrary sentiments were expressed1 would produce the effect of a paradox1 or even a contradiction in terms4 ,the baneful influence of a connotation thus acquired1 on the prevailing habits of thought1 especially in morals and politics1 has been well pointed out on many occasions by ,bentham4 ,it gives rise to the fallacy of 8question-begging names40 ,the very property which we are inquiring whether a thing possesses or not1 has become so associated with the name of the thing as to be part of its meaning1 insomuch that by merely uttering the name we assume the point which was to be made out2 one of the most frequent sources of apparently self-evident propositions4 ,without any further multiplication of examples to illustrate the changes which usage is continually making in the signification of terms1 ,i shall add1 as a practical rule1 that the logician1 not being able to prevent such transformations1 should submit to them with a good grace when they are irrevocably effected1 and if a definition is necessary1 define the word according to its new meaning2 retaining the former as a second signification1 if it is needed1 and if there is any chance of being able to preserve it either in the language of philosophy or in common use4 ,logicians can not make the meaning of any but scientific terms2 that of all other words is made by the collective human race4 ,but logicians can ascertain clearly what it is which1 working obscurely1 has guided the general mind to a particular employment of a name2 and when they have found this1 they can clothe it in such distinct and permanent terms1 that mankind shall see the meaning which before they only felt1 and shall not suffer it to be afterward forgotten or misapprehended4 ,chapter ,,vi4 ,the ,principles ,of ,a ,philosophical ,language ,further ,considered4 #a4 ,we have1 thus far1 considered only one of the requisites of a language adapted for the investigation of truth2 that its terms shall each of them convey a determinate and unmistakable meaning4 ,there are1 however1 as we have already remarked1 other requisites2 some of them important only in the second degree1 but one which is fundamental1 and barely yields in point of importance1 if it yields at all1 to the quality which we have already discussed at so much length4 ,that the language may be fitted for its purposes1 not only should every word perfectly express its meaning1 but there should be no important meaning without its word4 ,whatever we have occasion to think of often1 and for scientific purposes1 ought to have a name appropriated to it4 ,this requisite of philosophical language may be considered under three different heads2 that number of separate conditions being involved in it4 #b4 ,first1 there ought to be all such names1 as are needful for making such a record of individual observations that the words of the record shall exactly show what fact it is which has been observed4 ,in other words1 there should be an accurate ,descriptive ,terminology4 ,the only things which we can observe directly being our own sensations1 or other feelings1 a complete descriptive language would be one in which there should be a name for every variety of elementary sensation or feeling4 ,combinations of sensations or feelings may always be described1 if we have a name for each of the elementary feelings which compose them2 but brevity of description1 and clearness 7which often depends very much on brevity71 are greatly promoted by giving distinctive names not to the elements alone1 but also to all combinations which are of frequent recurrence4 ,on this occasion ,i can not do better than quote from ,dr4 ,whewell7#bbb7 some of the excellent remarks which he has made on this important branch of our subject4 8,the meaning of descriptive technical terms can be fixed in the first instance only by convention1 and can be made intelligible only by presenting to the senses that which the terms are to signify4 ,the knowledge of a color by its name can only be taught through the eye4 ,no description can convey to a hearer what we mean by apple-green or ,french gray4 ,it might1 perhaps1 be supposed that1 in the first example1 the term apple1 referring to so familiar an object1 sufficiently suggests the color intended4 ,but it may easily be seen that this is not true2 for apples are of many different hues of green1 and it is only by a conventional selection that we can appropriate the term to one special shade4 ,when this appropriation is once made1 the term refers to the sensation1 and not to the parts of the term2 for these enter into the compound merely as a help to the memory1 whether the suggestion be a natural connection as in #8apple-green1' or a casual one as in #8,french gray4' ,in order to derive due advantage from technical terms of the kind1 they must be associated immediately with the perception to which they belong2 and not connected with it through the vague usages of common language4 ,the memory must retain the sensation2 and the technical word must be understood as directly as the most familiar word1 and more distinctly4 ,when we find such terms as tin-white or pinchbeck-brown1 the metallic color so denoted ought to start up in our memory without delay or search4 8,this1 which it is most important to recollect with respect to the simpler properties of bodies1 as color and form1 is no less true with respect to more compound notions4 ,in all cases the term is fixed to a peculiar meaning by convention2 and the student1 in order to use the word1 must be completely familiar with the convention1 so that he has no need to frame conjectures from the word itself4 ,such conjectures would always be insecure1 and often erroneous4 ,thus the term papilionaceous applied to a flower is employed to indicate1 not only a resemblance to a butterfly1 but a resemblance arising from five petals of a certain-peculiar shape and arrangement2 and even if the resemblance were much stronger than it is in such cases1 yet1 if it were produced in a different way1 as1 for example1 by one petal1 or two only1 instead of a #8standard1' two #8wings1' and a #8keel' consisting of two parts more or less united into one1 we should be no longer justified in speaking of it as a #8papilionaceous' flower40 ,when1 however1 the thing named is1 as in this last case1 a combination of simple sensations1 it is not necessary1 in order to learn the meaning of the word1 that the student should refer back to the sensations themselves2 it may be communicated to him through the medium of other words2 the terms1 in short1 may be defined4 ,but the names of elementary sensations1 or elementary feelings of any sort1 can not be defined2 nor is there any mode of making their signification known but by making the learner experience the sensation1 or referring him1 through some known mark1 to his remembrance of having experienced it before4 ,hence it is only the impressions on the outward senses1 or those inward feelings which are connected in a very obvious and uniform manner with outward objects1 that are really susceptible of an exact descriptive language4 ,the countless variety of sensations which arise1 for instance1 from disease1 or from peculiar physiological states1 it would be in vain to attempt to name2 for as no one can judge whether the sensation ,i have is the same with his1 the name can not have1 to us two1 real community of meaning4 ,the same may be said1 to a considerable extent1 of purely mental feelings4 ,but in some of the sciences which are conversant with external objects1 it is scarcely possible to surpass the perfection to which this quality of a philosophical language has been carried4 8,the formation7#bbc7 of an exact and extensive descriptive language for botany has been executed with a degree of skill and felicity1 which1 before it was attained1 could hardly have been dreamed of as attainable4 ,every part of a plant has been named2 and the form of every part1 even the most minute1 has had a large assemblage of descriptive terms appropriated to it1 by means of which the botanist can convey and receive knowledge of form and structure1 as exactly as if each minute part were presented to him vastly magnified4 ,this acquisition was part of the ,linnan reform4444 #8,tournefort1' says ,decandolle1 #8appears to have been the first who really perceived the utility of fixing the sense of terms in such a way as always to employ the same word in the same sense1 and always to express the same idea by the same words2 but it was ,linnus who really created and fixed this botanical language1 and this is his fairest claim to glory1 for by this fixation of language he has shed clearness and precision over all parts of the science4' 8,it is not necessary here to give any detailed account of the terms of botany4 ,the fundamental ones have been gradually introduced1 as the parts of plants were more carefully and minutely examined4 ,thus the flower was necessarily distinguished into the calyx1 the corolla1 the stamens1 and the pistils2 the sections of the corolla were termed petals by ,columna2 those of the calyx were called sepals by ,necker4 ,sometimes terms of greater generality were devised2 as perianth1 to include the calyx and corolla1 whether one or both of these were present2 pericarp1 for the part inclosing the grain1 of whatever kind it be1 fruit1 nut1 pod1 etc4 ,and it may easily be imagined1 that descriptive terms may1 by definition and combination1 become very numerous and distinct4 ,thus leaves may be called pinnatifid1 pinnatipartite1 pinnatisect1 pinnatilobate1 palmatifid1 palmatipartite1 etc41 and each of these words designates different combinations of the modes and extent of the divisions of the leaf with the divisions of its outline4 ,in some cases1 arbitrary numerical relations are introduced into the definition3 thus1 a leaf is called bilobate1 when it is divided into two parts by a notch2 but if the notch go to the middle of its length1 it is bifid2 if it go near the base of the leaf1 it is bipartite2 if to the base1 it is bisect4 ,thus1 too1 a pod of a cruciferous plant is a siliqua1 if it is four times as long as it is broad1 but if it be shorter than this it is a silicula4 ,such terms being established1 the form of the very complex leaf or frond of a fern 7,hymenophyllum ,wilsoni7 is exactly conveyed by the following phrase3 #8fronds rigid pinnate1 pinn recurved subunilateral1 pinnatifid1 the segments linear undivided or bifid1 spinuloso-serrate4' 8,other characters1 as well as form1 are conveyed with the like precision3 ,color by means of a classified scale of colors4444 ,this was done with most precision by ,werner1 and his scale of colors is still the most usual standard of naturalists4 ,werner also introduced a more exact terminology with regard to other characters which are important in mineralogy1 as lustre1 hardness4 ,but ,mohs improved upon this step by giving a numerical scale of hardness1 in which talc is #a1 gypsum #b1 calc spar #c1 and so on4444 ,some properties1 as specific gravity1 by their definition give at once a numerical measure2 and others1 as crystalline form1 require a very considerable array of mathematical calculation and reasoning1 to point out their relations and gradations40 #c4 ,thus far of ,descriptive ,terminology1 or of the language requisite for placing on record our observation of individual instances4 ,but when we proceed from this to ,induction1 or rather to that comparison of observed instances which is the preparatory step toward it1 we stand in need of an additional and a different sort of general names4 ,whenever1 for purposes of ,induction1 we find it necessary to introduce 7in ,dr4 ,whewell's phraseology7 some new general conception2 that is1 whenever the comparison of a set of phenomena leads to the recognition in them of some common circumstance1 which1 our attention not having been directed to it on any former occasion1 is to us a new phenomenon2 it is of importance that this new conception1 or this new result of abstraction1 should have a name appropriated to it2 especially if the circumstance it involves be one which leads to many consequences1 or which is likely to be found also in other classes of phenomena4 ,no doubt1 in most cases of the kind1 the meaning might be conveyed by joining together several words already in use4 ,but when a thing has to be often spoken of1 there are more reasons than the saving of time and space1 for speaking of it in the most concise manner possible4 ,what darkness would be spread over geometrical demonstrations1 if wherever the word circle is used1 the definition of a circle were inserted instead of it4 ,in mathematics and its applications1 where the nature of the processes demands that the attention should be strongly concentrated1 but does not require that it should be widely diffused1 the importance of concentration also in the expressions has always been duly felt2 and a mathematician no sooner finds that he shall often have occasion to speak of the same two things together1 than he at once creates a term to express them whenever combined3 just as1 in his algebraical operations1 he substitutes for 7am bn7 p_/q1 or for a_/b b_/c c_/d etc41 the single letter ,p1 ,q1 or ,s2 not solely to shorten his symbolical expressions1 but to simplify the purely intellectual part of his operations1 by enabling the mind to give its exclusive attention to the relation between the quantity ,s and the other quantities which enter into the equation1 without being distracted by thinking unnecessarily of the parts of which ,s is itself composed4 ,but there is another reason1 in addition to that of promoting perspicuity1 for giving a brief and compact name to each of the more considerable results of abstraction which are obtained in the course of our intellectual phenomena4 ,by naming them1 we fix our attention upon them2 we keep them more constantly before the mind4 ,the names are remembered1 and being remembered1 suggest their definition2 while if instead of specific and characteristic names1 the meaning had been expressed by putting together a number of other names1 that particular combination of words already in common use for other purposes would have had nothing to make itself remembered by4 ,if we want to render a particular combination of ideas permanent in the mind1 there is nothing which clinches it like a name specially devoted to express it4 ,if mathematicians had been obliged to speak of 8that to which a quantity1 in increasing or diminishing1 is always approaching nearer1 so that the difference becomes less than any assignable quantity1 but to which it never becomes exactly equal10 instead of expressing all this by the simple phrase1 8the limit of a quantity10 we should probably have long remained without most of the important truths which have been discovered by means of the relation between quantities of various kinds and their limits4 ,if instead of speaking of momentum1 it had been necessary to say1 8the product of the number of units of velocity in the velocity by the number of units of mass in the mass10 many of the dynamical truths now apprehended by means of this complex idea would probably have escaped notice1 for want of recalling the idea itself with sufficient readiness and familiarity4 ,and on subjects less remote from the topics of popular discussion1 whoever wishes to draw attention to some new or unfamiliar distinction among things1 will find no way so sure as to invent or select suitable names for the express purpose of marking it4 ,a volume devoted to explaining what the writer means by civilization1 does not raise so vivid a conception of it as the single expression1 that ,civilization is a different thing from ,cultivation2 the compactness of that brief designation for the contrasted quality being an equivalent for a long discussion4 ,so1 if we would impress forcibly upon the understanding and memory the distinction between the two different conceptions of a representative government1 we can not more effectually do so than by saying that ,delegation is not ,representation4 ,hardly any original thoughts on mental or social subjects ever make their way among mankind1 or assume their proper importance in the minds even of their inventors1 until aptly-selected words or phrases have1 as it were1 nailed them down and held them fast4 #d4 ,of the three essential parts of a philosophical language1 we have now mentioned two3 a terminology suited for describing with precision the individual facts observed2 and a name for every common property of any importance or interest1 which we detect by comparing those facts2 including 7as the concretes corresponding to those abstract terms7 names for the classes which we artificially construct in virtue of those properties1 or as many of them1 at least1 as we have frequent occasion to predicate any thing of4 ,but there is a sort of classes1 for the recognition of which no such elaborate process is necessary2 because each of them is marked out from all others not by some one property1 the detection of which may depend on a difficult act of abstraction1 but by its properties generally4 ,i mean1 the ,kinds of things1 in the sense which1 in this treatise1 has been specially attached to that term4 ,by a ,kind1 it will be remembered1 we mean one of those classes which are distinguished from all others not by one or a few definite properties1 but by an unknown multitude of them2 the combination of properties on which the class is grounded1 being a mere index to an indefinite number of other distinctive attributes4 ,the class horse is a ,kind1 because the things which agree in possessing the characters by which we recognize a horse1 agree in a great number of other properties1 as we know1 and1 it can not be doubted1 in many more than we know4 ,animal1 again1 is a ,kind1 because no definition that could be given of the name animal could either exhaust the properties common to all animals1 or supply premises from which the remainder of those properties could be inferred4 ,but a combination of properties which does not give evidence of the existence of any other independent peculiarities1 does not constitute a ,kind4 ,white horse1 therefore1 is not a ,kind2 because horses which agree in whiteness1 do not agree in any thing else1 except the qualities common to all horses1 and whatever may be the causes or effects of that particular color4 ,on the principle that there should be a name for every thing which we have frequent occasion to make assertions about1 there ought evidently to be a name for every ,kind2 for as it is the very meaning of a ,kind that the individuals composing it have an indefinite multitude of properties in common1 it follows that1 if not with our present knowledge1 yet with that which we may hereafter acquire1 the ,kind is a subject to which there will have to be applied many predicates4 ,the third component element of a philosophical language1 therefore1 is that there shall be a name for every ,kind4 ,in other words1 there must not only be a terminology1 but also a nomenclature4 ,the words ,nomenclature and ,terminology are employed by most authors almost indiscriminately2 ,dr4 ,whewell being1 as far as ,i am aware1 the first writer who has regularly assigned to the two words different meanings4 ,the distinction1 however1 which he has drawn between them being real and important1 his example is likely to be followed2 and 7as is apt to be the case when such innovations in language are felicitously made7 a vague sense of the distinction is found to have influenced the employment of the terms in common practice1 before the expediency had been pointed out of discriminating them philosophically4 ,every one would say that the reform effected by ,lavoisier and ,guyton-,morveau in the language of chemistry consisted in the introduction of a new nomenclature1 not of a new terminology4 ,linear1 lanceolate1 oval1 or oblong1 serrated1 dentate1 or crenate leaves1 are expressions forming part of the terminology of botany1 while the names 8,viola odorata10 and 8,ulex ,europus10 belong to its nomenclature4 ,a nomenclature may be defined1 the collection of the names of all the ,kinds with which any branch of knowledge is conversant2 or more properly1 of all the lowest ,kinds1 or infirm species--those which may be subdivided indeed1 but not into ,kinds1 and which generally accord with what in natural history are termed simply species4 ,science possesses two splendid examples of a systematic nomenclature2 that of plants and animals1 constructed by ,linnus and his successors1 and that of chemistry1 which we owe to the illustrious group of chemists who flourished in ,france toward the close of the eighteenth century4 ,in these two departments1 not only has every known species1 or lowest ,kind1 a name assigned to it1 but when new lowest ,kinds are discovered1 names are at once given to them on a uniform principle4 ,in other sciences the nomenclature is not at present constructed on any system1 either because the species to be named are not numerous enough to require one 7as in geometry1 for example71 or because no one has yet suggested a suitable principle for such a system1 as in mineralogy2 in which the want of a scientifically constructed nomenclature is now the principal cause which retards the progress of the science4 #e4 ,a word which carries on its face that it belongs to a nomenclature1 seems at first sight to differ from other concrete general names in this--that its meaning does not reside in its connotation1 in the attributes implied in it1 but in its denotation1 that is1 in the particular group of things which it is appointed to designate2 and can not1 therefore1 be unfolded by means of a definition1 but must be made known in another way4 ,this opinion1 however1 appears to me erroneous4 ,words belonging to a nomenclature differ1 ,i conceive1 from other words mainly in this1 that besides the ordinary connotation1 they have a peculiar one of their own3 besides connoting certain attributes1 they also connote that those attributes are distinctive of a ,kind4 ,the term 8peroxide of iron10 for example1 belonging by its form to the systematic nomenclature of chemistry1 bears on its face that it is the name of a peculiar ,kind of substance4 ,it moreover connotes1 like the name of any other class1 some portion of the properties common to the class2 in this instance the property of being a compound of iron and the largest dose of oxygen with which iron will combine4 ,these two things1 the fact of being such a compound1 and the fact of being a ,kind1 constitute the connotation of the name peroxide of iron4 ,when we say of the substance before us1 that it is the peroxide of iron1 we thereby assert1 first1 that it is a compound of iron and a maximum of oxygen1 and next1 that the substance so composed is a peculiar ,kind of substance4 ,now1 this second part of the connotation of any word belonging to a nomenclature is as essential a portion of its meaning as the first part1 while the definition only declares the first2 and hence the appearance that the signification of such terms can not be conveyed by a definition3 which appearance1 however1 is fallacious4 ,the name ,viola odorata denotes a ,kind1 of which a certain number of characters1 sufficient to distinguish it1 are enunciated in botanical works4 ,this enumeration of characters is surely1 as in other cases1 a definition of the name4 ,no1 say some1 it is not a definition1 for the name ,viola odorata does not mean those characters2 it means that particular group of plants1 and the characters are selected from among a much greater number1 merely as marks by which to recognize the group4 ,but to this ,i reply1 that the name does not mean that group1 for it would be applied to that group no longer than while the group is believed to be an infima species2 if it were to be discovered that several distinct ,kinds have been confounded under this one name1 no one would any longer apply the name ,viola odorata to the whole of the group1 but would apply it1 if retained at all1 to one only of the ,kinds retained therein4 ,what is imperative1 therefore1 is not that the name shall denote one particular collection of objects1 but that it shall denote a ,kind1 and a lowest ,kind4 ,the form of the name declares that1 happen what will1 it is to denote an infima species2 and that1 therefore1 the properties which it connotes1 and which are expressed in the definition1 are to be connoted by it no longer than while we continue to believe that those properties1 when found together1 indicate a ,kind1 and that the whole of them are found in no more than one ,kind4 ,with the addition of this peculiar connotation1 implied in the form of every word which belongs to a systematic nomenclature2 the set of characters which is employed to discriminate each ,kind from all other ,kinds 7and which is a real definition7 constitutes as completely as in any other case the whole meaning of the term4 ,it is no objection to say that 7as is often the case in natural history7 the set of characters may be changed1 and another substituted as being better suited for the purpose of distinction1 while the word1 still continuing to denote the same group or things1 is not considered to have changed its meaning4 ,for this is no more than may happen in the case of any other general name3 we may1 in reforming its connotation1 leave its denotation untouched2 and it is generally desirable to do so4 ,the connotation1 however1 is not the less for this the real meaning1 for we at once apply the name wherever the characters set down in the definition are found2 and that which exclusively guides us in applying the term1 must constitute its signification4 ,if we find1 contrary to our previous belief1 that the characters are not peculiar to one species1 we cease to use the term co-extensively with the characters2 but then it is because the other portion of the connotation fails2 the condition that the class must be a ,kind4 ,the connotation1 therefore1 is still the meaning2 the set of descriptive characters is a true definition2 and the meaning is unfolded1 not indeed 7as in other cases7 by the definition alone1 but by the definition and the form of the word taken together4 #f4 ,we have now analyzed what is implied in the two principal requisites of a philosophical language2 first1 precision1 or definiteness2 and1 secondly1 completeness4 ,any further remarks on the mode of constructing a nomenclature must be deferred until we treat of ,classification2 the mode of naming the ,kinds of things being necessarily subordinate to the mode of arranging those ,kinds into larger classes4 ,with respect to the minor requisites of terminology1 some of them are well stated and illustrated in the 8,aphorisms concerning the ,language of ,science10 included in ,dr4 ,whewell's ,philosophy of the ,inductive ,sciences4 ,these1 as being of secondary importance in the peculiar point of view of ,logic1 ,i shall not further refer to1 but shall confine my observations to one more quality1 which1 next to the two already treated of1 appears to be the most valuable which the language of science can possess4 ,of this quality a general notion may be conveyed by the following aphorism3 ,whenever the nature of the subject permits our reasoning processes to be1 without danger1 carried on mechanically1 the language should be constructed on as mechanical principles as possible2 while1 in the contrary case1 it should be so constructed that there shall be the greatest possible obstacles to a merely mechanical use of it4 ,i am aware that this maxim requires much explanation1 which ,i shall at once proceed to give4 ,at first1 as to what is meant by using a language mechanically4 ,the complete or extreme case of the mechanical use of language1 is when it is used without any consciousness of a meaning1 and with only the consciousness of using certain visible or audible marks in conformity to technical rules previously laid down4 ,this extreme case is nowhere realized except in the figures of arithmetic1 and still more the symbols of algebra1 a language unique in its kind1 and approaching as nearly to perfection1 for the purposes to which it is destined1 as can1 perhaps1 be said of any creation of the human mind4 ,its perfection consists in the completeness of its adaptation to a purely mechanical use4 ,the symbols are mere counters1 without even the semblance of a meaning apart from the convention which is renewed each time they are employed1 and which is altered at each renewal1 the same symbol a or x being used on different occasions to represent things which 7except that1 like all things1 they are susceptible of being numbered7 have no property in common4 ,there is nothing1 therefore1 to distract the mind from the set of mechanical operations which are to be performed upon the symbols1 such as squaring both sides of the equation1 multiplying or dividing them by the same or by equivalent symbols1 and so forth4 ,each of these operations1 it is true1 corresponds to a syllogism2 represents one step of a ratiocination relating not to the symbols1 but to the things signified by them4 ,but as it has been found practicable to frame a technical form1 by conforming to which we can make sure of finding the conclusion of the ratiocination1 our end can be completely attained without our ever thinking of any thing but the symbols4 ,being thus intended to work merely as mechanism1 they have the qualities which mechanism ought to have4 ,they are of the least possible bulk1 so that they take up scarcely any room1 and waste no time in their manipulation2 they are compact1 and fit so closely together that the eye can take in the whole at once of almost every operation which they are employed to perform4 ,these admirable properties of the symbolical language of mathematics have made so strong an impression on the minds of many thinkers1 as to have led them to consider the symbolical language in question as the ideal type of philosophical language generally2 to think that names in general1 or 7as they are fond of calling them7 signs1 are fitted for the purposes of thought in proportion as they can be made to approximate to the compactness1 the entire unmeaningness1 and the capability of being used as counters without a thought of what they represent1 which are characteristic of the a and b1 the x and y1 of algebra4 ,this notion has led to sanguine views of the acceleration of the progress of science by means which1 ,i conceive1 can not possibly conduce to that end1 and forms part of that exaggerated estimate of the influence of signs1 which has contributed in no small degree to prevent the real laws of our intellectual operations from being rightly understood4 ,in the first place1 a set of signs by which we reason without consciousness of their meaning1 can be serviceable1 at most1 only in our deductive operations4 ,in our direct inductions we can not for a moment dispense with a distinct mental image of the phenomena1 since the whole operation turns on a perception of the particulars in which those phenomena agree and differ4 ,but1 further1 this reasoning by counters is only suitable to a very limited portion even of our deductive processes4 ,in our reasonings respecting numbers1 the only general principles which we ever have occasion to introduce are these1 ,things which are equal to the same thing are equal to one another1 and ,the sums or differences of equal things are equal2 with their various corollaries4 ,not only can no hesitation ever arise respecting the applicability of these principles1 since they are true of all magnitudes whatever2 but every possible application of which they are susceptible1 may be reduced to a technical rule2 and such1 in fact1 the rules of the calculus are4 ,but if the symbols represent any other things than mere numbers1 let us say even straight or curve lines1 we have then to apply theorems of geometry not true of all lines without exception1 and to select those which are true of the lines we are reasoning about4 ,and how can we do this unless we keep completely in mind what particular lines these are8 ,since additional geometrical truths may be introduced into the ratiocination in any stage of its progress1 we can not suffer ourselves1 during even the smallest part of it1 to use the names mechanically 7as we use algebraical symbols7 without an image annexed to them4 ,it is only after ascertaining that the solution of a question concerning lines can be made to depend on a previous question concerning numbers1 or1 in other words1 after the question has been 7to speak technically7 reduced to an equation1 that the unmeaning signs become available1 and that the nature of the facts themselves to which the investigation relates can be dismissed from the mind4 ,up to the establishment of the equation1 the language in which mathematicians carry on their reasoning does not differ in character from that employed by close reasoners on any other kind of subject4 ,i do not deny that every correct ratiocination1 when thrown into the syllogistic shape1 is conclusive from the mere form of the expression1 provided none of the terms used be ambiguous2 and this is one of the circumstances which have led some writers to think that if all names were so judiciously constructed and so carefully defined as not to admit of any ambiguity1 the improvement thus made in language would not only give to the conclusions of every deductive science the same certainty with those of mathematics1 but would reduce all reasonings to the application of a technical form1 and enable their conclusiveness to be rationally assented to after a merely mechanical process1 as is undoubtedly the case in algebra4 ,but1 if we except geometry1 the conclusions of which are already as certain and exact as they can be made1 there is no science but that of number1 in which the practical validity of a reasoning can be apparent to any person who has looked only at the reasoning itself4 ,whoever has assented to what was said in the last ,book concerning the case of the ,composition of ,causes1 and the still stronger case of the entire supersession of one set of laws by another1 is aware that geometry and algebra are the only sciences of which the propositions are categorically true2 the general propositions of all other sciences are true only hypothetically1 supposing that no counteracting cause happens to interfere4 ,a conclusion1 therefore1 however correctly deduced1 in point of form1 from admitted laws of nature1 will have no other than an hypothetical certainty4 ,at every step we must assure ourselves that no other law of nature has superseded1 or intermingled its operation with1 those which are the premises of the reasoning2 and how can this be done by merely looking at the words8 ,we must not only be constantly thinking of the phenomena themselves1 but we must be constantly studying them2 making ourselves acquainted with the peculiarities of every case to which we attempt to apply our general principles4 ,the algebraic notation1 considered as a philosophical language1 is perfect in its adaptation to the subjects for which it is commonly employed1 namely those of which the investigations have already been reduced to the ascertainment of a relation between numbers4 ,but1 admirable as it is for its own purpose1 the properties by which it is rendered such are so far from constituting it the ideal model of philosophical language in general1 that the more nearly the language of any other branch of science approaches to it1 the less fit that language is for its own proper functions4 ,on all other subjects1 instead of contrivances to prevent our attention from being distracted by thinking of the meaning of our signs1 we ought to wish for contrivances to make it impossible that we should ever lose sight of that meaning even for an instant4 ,with this view1 as much meaning as possible should be thrown into the formation of the word itself2 the aids of derivation and analogy being made available to keep alive a consciousness of all that is signified by it4 ,in this respect those languages have an immense advantage which form their compounds and derivatives from native roots1 like the ,german1 and not from those of a foreign or dead language1 as is so much the case with ,english1 ,french1 and ,italian2 and the best are those which form them according to fixed analogies1 corresponding to the relations between the ideas to be expressed4 ,all languages do this more or less1 but especially1 among modern ,european languages1 the ,german2 while even that is inferior to the ,greek1 in which the relation between the meaning of a derivative word and that of its primitive is in general clearly marked by its mode of formation1 except in the case of words compounded with prepositions1 which are often1 in both those languages1 extremely anomalous4 ,but all that can be done1 by the mode of constructing words1 to prevent them from degenerating into sounds passing through the mind without any distinct apprehension of what they signify1 is far too little for the necessity of the case4 ,words1 however well constructed originally1 are always tending1 like coins1 to have their inscription worn off by passing from hand to hand2 and the only possible mode of reviving it is to be ever stamping it afresh1 by living in the habitual contemplation of the phenomena themselves1 and not resting in our familiarity with the words that express them4 ,if any one1 having possessed himself of the laws of phenomena as recorded in words1 whether delivered to him originally by others1 or even found out by himself1 is content from thenceforth to live among these formul1 to think exclusively of them1 and of applying them to cases as they arise1 without keeping up his acquaintance with the realities from which these laws were collected--not only will he continually fail in his practical efforts1 because he will apply his formul without duly considering whether1 in this case and in that1 other laws of nature do not modify or supersede them2 but the formul themselves will progressively lose their meaning to him1 and he will cease at last even to be capable of recognizing with certainty whether a case falls within the contemplation of his formula or not4 ,it is1 in short1 as necessary1 on all subjects not mathematical1 that the things on which we reason should be conceived by us in the concrete1 and 8clothed in circumstances10 as it is in algebra that we should keep all individualizing peculiarities sedulously out of view4 ,with this remark we close our observations on the ,philosophy of ,language4 ,chapter ,,vii4 ,of ,classification1 ,as ,subsidiary ,to ,induction4 #a4 ,there is1 as has been frequently remarked in this work1 a classification of things1 which is inseparable from the fact of giving them general names4 ,every name which connotes an attribute1 divides1 by that very fact1 all things whatever into two classes1 those which have the attribute and those which have it not2 those of which the name can be predicated1 and those of which it can not4 ,and the division thus made is not merely a division of such things as actually exist1 or are known to exist1 but of all such as may hereafter be discovered1 and even of all which can be imagined4 ,on this kind of ,classification we have nothing to add to what has previously been said4 ,the ,classification which requires to be discussed as a separate act of the mind1 is altogether different4 ,in the one1 the arrangement of objects in groups1 and distribution of them into compartments1 is a mere incidental effect consequent on the use of names given for another purpose1 namely that of simply expressing some of their qualities4 ,in the other1 the arrangement and distribution are the main object1 and the naming is secondary to1 and purposely conforms itself to1 instead of governing1 that more important operation4 ,classification1 thus regarded1 is a contrivance for the best possible ordering of the ideas of objects in our minds2 for causing the ideas to accompany or succeed one another in such a way as shall give us the greatest command over our knowledge already acquired1 and lead most directly to the acquisition of more4 ,the general problem of ,classification1 in reference to these purposes1 may be stated as follows3 ,to provide that things shall be thought of in such groups1 and those groups in such an order1 as will best conduce to the remembrance and to the ascertainment of their laws4 ,classification thus considered1 differs from classification in the wider sense1 in having reference to real objects exclusively1 and not to all that are imaginable3 its object being the due co-ordination in our minds of those things only1 with the properties of which we have actually occasion to make ourselves acquainted4 ,but1 on the other hand1 it embraces all really existing objects4 ,we can not constitute any one class properly1 except in reference to a general division of the whole of nature2 we can not determine the group in which any one object can most conveniently be placed1 without taking into consideration all the varieties of existing objects1 all at least which have any degree of affinity with it4 ,no one family of plants or animals could have been rationally constituted1 except as part of a systematic arrangement of all plants or animals2 nor could such a general arrangement have been properly made1 without first determining the exact place of plants and animals in a general division of nature4 #b4 ,there is no property of objects which may not be taken1 if we please1 as the foundation for a classification or mental grouping of those objects2 and in our first attempts we are likely to select for that purpose properties which are simple1 easily conceived1 and perceptible on a first view1 without any previous process of thought4 ,thus ,tournefort's arrangement of plants was founded on the shape and divisions of the corolla2 and that which is commonly called the ,linnan 7though ,linnus also suggested another and more scientific arrangement7 was grounded chiefly on the number of the stamens and pistils4 ,but these classifications1 which are at first recommended by the facility they afford of ascertaining to what class any individual belongs1 are seldom much adapted to the ends of that ,classification which is the subject of our present remarks4 ,the ,linnan arrangement answers the purpose of making us think together of all those kinds of plants which possess the same number of stamens and pistils2 but to think of them in that manner is of little use1 since we seldom have any thing to affirm in common of the plants which have a given number of stamens and pistils4 ,if plants of the class ,pentandria1 order ,monogynia1 agreed in any other properties1 the habit of thinking and speaking of the plants under a common designation would conduce to our remembering those common properties so far as they were ascertained1 and would dispose us to be on the lookout for such of them as were not yet known4 ,but since this is not the case1 the only purpose of thought which the ,linnan classification serves is that of causing us to remember1 better than we should otherwise have done1 the exact number of stamens and pistils of every species of plants4 ,now1 as this property is of little importance or interest1 the remembering it with any particular accuracy is of no moment4 ,and1 inasmuch as1 by habitually thinking of plants in those groups1 we are prevented from habitually thinking of them in groups which have a greater number of properties in common1 the effect of such a classification1 when systematically adhered to1 upon our habits of thought1 must be regarded as mischievous4 ,the ends of scientific classification are best answered1 when the objects are formed into groups respecting which a greater number of general propositions can be made1 and those propositions more important1 than could be made respecting any other groups into which the same things could be distributed4 ,the properties1 therefore1 according to which objects are classified1 should1 if possible1 be those which are causes of many other properties2 or1 at any rate1 which are sure marks of them4 ,causes are preferable1 both as being the surest and most direct of marks1 and as being themselves the properties on which it is of most use that our attention should be strongly fixed4 ,but the property which is the cause of the chief peculiarities of a class1 is unfortunately seldom fitted to serve also as the diagnostic of the class4 ,instead of the cause1 we must generally select some of its more prominent effects1 which may serve as marks of the other effects and of the cause4 ,a classification thus formed is properly scientific or philosophical1 and is commonly called a ,natural1 in contradistinction to a ,technical or ,artificial1 classification or arrangement4 ,the phrase ,natural ,classification seems most peculiarly appropriate to such arrangements as correspond1 in the groups which they form1 to the spontaneous tendencies of the mind1 by placing together the objects most similar in their general aspect2 in opposition to those technical systems which1 arranging things according to their agreement in some circumstance arbitrarily selected1 often throw into the same group objects which in the general aggregate of their properties present no resemblance1 and into different and remote groups1 others which have the closest similarity4 ,it is one of the most valid recommendations of any classification to the character of a scientific one1 that it shall be a natural classification in this sense also2 for the test of its scientific character is the number and importance of the properties which can be asserted in common of all objects included in a group2 and properties on which the general aspect of the things depends are1 if only on that ground1 important1 as well as1 in most cases1 numerous4 ,but1 though a strong recommendation1 this circumstance is not a sine qua non2 since the most obvious properties of things may be of trifling importance compared with others that are not obvious4 ,i have seen it mentioned as a great absurdity in the ,linnan classification1 that it places 7which by-the-way it does not7 the violet by the side of the oak2 it certainly dissevers natural affinities1 and brings together things quite as unlike as the oak and the violet are4 ,but the difference1 apparently so wide1 which renders the juxtaposition of those two vegetables so suitable an illustration of a bad arrangement1 depends1 to the common eye1 mainly on mere size and texture2 now if we made it our study to adopt the classification which would involve the least peril of similar rapprochements1 we should return to the obsolete division into trees1 shrubs1 and herbs1 which though of primary importance with regard to mere general aspect1 yet 7compared even with so petty and unobvious a distinction as that into dicotyledons and monocotyledons7 answers to so few differences in the other properties of plants1 that a classification founded on it 7independently of the indistinctness of the lines of demarcation7 would be as completely artificial and technical as the ,linnan4 ,our natural groups1 therefore1 must often be founded not on the obvious but on the unobvious properties of things1 when these are of greater importance4 ,but in such cases it is essential that there should be some other property or set of properties1 more readily recognizable by the observer1 which co-exist with1 and may be received as marks of1 the properties which are the real groundwork of the classification4 ,a natural arrangement1 for example1 of animals1 must be founded in the main on their internal structure1 but 7as ,m4 ,comte remarks7 it would be absurd that we should not be able to determine the genus and species of an animal without first killing it4 ,on this ground1 the preference1 among zoological classifications1 is probably due to that of ,m4 ,de ,blainville1 founded on the differences in the external integuments2 differences which correspond1 much more accurately than might be supposed1 to the really important varieties1 both in the other parts of the structure1 and in the habits and history of the animals4 ,this shows1 more strongly than ever1 how extensive a knowledge of the properties of objects is necessary for making a good classification of them4 ,and as it is one of the uses of such a classification that by drawing attention to the properties on which it is founded1 and which1 if the classification be good1 are marks of many others1 it facilitates the discovery of those others2 we see in what manner our knowledge of things1 and our classification of them1 tend mutually and indefinitely to the improvement of each other4 ,we said just now that the classification of objects should follow those of their properties which indicate not only the most numerous1 but also the most important peculiarities4 ,what is here meant by importance8 ,it has reference to the particular end in view2 and the same objects1 therefore1 may admit with propriety of several different classifications4 ,each science or art forms its classification of things according to the properties which fall within its special cognizance1 or of which it must take account in order to accomplish its peculiar practical end4 ,a farmer does not divide plants1 like a botanist1 into dicotyledonous and monocotyledonous1 but into useful plants and weeds4 ,a geologist divides fossils1 not like a zoologist1 into families corresponding to those of living species1 but into fossils of the paleozoic1 mesozoic1 and tertiary periods1 above the coal and below the coal1 etc4 ,whales are or are not fish according to the purpose for which we are considering them4 8,if we are speaking of the internal structure and physiology of the animal1 we must not call them fish2 for in these respects they deviate widely from fishes2 they have warm blood1 and produce and suckle their young as land quadrupeds do4 ,but this would not prevent our speaking of the whale-fishery1 and calling such animals fish on all occasions connected with this employment2 for the relations thus arising depend upon the animal's living in the water1 and being caught in a manner similar to other fishes4 ,a plea that human laws which mention fish do not apply to whales1 would be rejected at once by an intelligent judge407#bbd7 ,these different classifications are all good1 for the purposes of their own particular departments of knowledge or practice4 ,but when we are studying objects not for any special practical end1 but for the sake of extending our knowledge of the whole of their properties and relations1 we must consider as the most important attributes those which contribute most1 either by themselves or by their effects1 to render the things like one another1 and unlike other things2 which give to the class composed of them the most marked individuality2 which fill1 as it were1 the largest space in their existence1 and would most impress the attention of a spectator who knew all their properties but was not specially interested in any4 ,classes formed on this principle may be called1 in a more emphatic manner than any others1 natural groups4 #c4 ,on the subject of these groups ,dr4 ,whewell lays down a theory1 grounded on an important truth1 which he has1 in some respects1 expressed and illustrated very felicitously1 but also1 as it appears to me1 with some admixture of error4 ,it will be advantageous1 for both these reasons1 to extract the statement of his doctrine in the very words he has used4 8,natural groups10 according to this theory17#bbe7 are 8given by ,type1 not by ,definition40 ,and this consideration accounts for that 8indefiniteness and indecision which we frequently find in the descriptions of such groups1 and which must appear so strange and inconsistent to any one who does not suppose these descriptions to assume any deeper ground of connection than an arbitrary choice of the botanist4 ,thus in the family of the rose-tree1 we are told that the ovules are very rarely erect1 the stigmata usually simple4 ,of what use1 it might be asked1 can such loose accounts be8 ,to which the answer is1 that they are not inserted in order to distinguish the species1 but in order to describe the family1 and the total relations of the ovules and the stigmata of the family are better known by this general statement4 ,a similar observation may be made with regard to the ,anomalies of each group1 which occur so commonly1 that ,dr4 ,lindley1 in his ,introduction to the ,natural ,system of ,botany1 makes the #8,anomalies' an article in each family4 ,thus1 part of the character of the ,rosace is1 that they have alternate stipulate leaves1 and that the albumen is obliterated2 but yet in ,lowea1 one of the genera of this family1 the stipul are absent2 and the albumen is present in another1 ,neillia4 ,this implies1 as we have already seen1 that the artificial character 7or diagnosis1 as ,mr4 ,lindley calls it7 is imperfect4 ,it is1 though very nearly1 yet not exactly1 commensurate with the natural group2 and hence in certain cases this character is made to yield to the general weight of natural affinities4 8,these views--of classes determined by characters which can not be expressed in words--of propositions which state1 not what happens in all cases1 but only usually--of particulars which are included in a class1 though they transgress the definition of it1 may probably surprise the reader4 ,they are so contrary to many of the received opinions respecting the use of definitions1 and the nature of scientific propositions1 that they will probably appear to many persons highly illogical and unphilosophical4 ,but a disposition to such a judgment arises in a great measure from this1 that the mathematical and mathematico-physical sciences have1 in a great degree1 determined men's views of the general nature and form of scientific truth2 while ,natural ,history has not yet had time or opportunity to exert its due influence upon the current habits of philosophizing4 ,the apparent indefiniteness and inconsistency of the classifications and definitions of ,natural ,history belongs1 in a far higher degree1 to all other except mathematical speculations2 and the modes in which approximations to exact distinctions and general truths have been made in ,natural ,history1 may be worthy our attention1 even for the light they throw upon the best modes of pursuing truth of all kinds4 8,though in a ,natural group of objects a definition can no longer be of any use as a regulative principle1 classes are not therefore left quite loose1 without any certain standard or guide4 ,the class is steadily fixed1 though not precisely limited2 it is given1 though not circumscribed2 it is determined1 not by a boundary-line without1 but by a central point within2 not by what it strictly excludes1 but by what it eminently includes2 by an example1 not by a precept2 in short1 instead of a ,definition we have a ,type for our director4 8,a ,type is an example of any class1 for instance a species of a genus1 which is considered as eminently possessing the character of the class4 ,all the species which have a greater affinity with this type-species than with any others1 form the genus1 and are arranged about it1 deviating from it in various directions and different degrees4 ,thus a genus may consist of several species which approach very near the type1 and of which the claim to a place with it is obvious2 while there may be other species which straggle farther from this central knot1 and which yet are clearly more connected with it than with any other4 ,and even if there should be some species of which the place is dubious1 and which appear to be equally bound to two generic types1 it is easily seen that this would not destroy the reality of the generic groups1 any more than the scattered trees of the intervening plain prevent our speaking intelligibly of the distinct forests of two separate hills4 8,the type-species of every genus1 the type-genus of every family1 is then1 one which possesses all the characters and properties of the genus in a marked and prominent manner4 ,the type of the ,rose family has alternate stipulate leaves1 wants the albumen1 has the ovules not erect1 has the stigmata simple1 and besides these features1 which distinguish it from the exceptions or varieties of its class1 it has the features which make it prominent in its class4 ,it is one of those which possess clearly several leading attributes2 and thus1 though we can not say of any one genus that it must be the type of the family1 or of any one species that it must be the type of the genus1 we are still not wholly to seek2 the type must be connected by many affinities with most of the others of its group2 it must be near the centre of the crowd1 and not one of the stragglers40 ,in this passage 7the latter part of which especially ,i can not help noticing as an admirable example of philosophic style7 ,dr4 ,whewell has stated very clearly and forcibly1 but 7,i think7 without making all necessary distinctions1 one of the principles of a ,natural ,classification4 ,what this principle is1 what are its limits1 and in what manner he seems to me to have overstepped them1 will appear when we have laid down another rule of ,natural ,arrangement1 which appears to me still more fundamental4 #d4 ,the reader is by this time familiar with the general truth 7which ,i restate so often on account of the great confusion in which it is commonly involved71 that there are in nature distinctions of ,kind2 distinctions not consisting in a given number of definite properties plus the effects which follow from those properties1 but running through the whole nature1 through the attributes generally1 of the things so distinguished4 ,our knowledge of the properties of a ,kind is never complete4 ,we are always discovering1 and expecting to discover1 new ones4 ,where the distinction between two classes of things is not one of ,kind1 we expect to find their properties alike1 except where there is some reason for their being different4 ,on the contrary1 when the distinction is in ,kind1 we expect to find the properties different unless there be some cause for their being the same4 ,all knowledge of a ,kind must be obtained by observation and experiment upon the ,kind itself2 no inference respecting its properties from the properties of things not connected with it by ,kind1 goes for more than the sort of presumption usually characterized as an analogy1 and generally in one of its fainter degrees4 ,since the common properties of a true ,kind1 and consequently the general assertions which can be made respecting it1 or which are certain to be made hereafter as our knowledge extends1 are indefinite and inexhaustible2 and since the very first principle of natural classification is that of forming the classes so that the objects composing each may have the greatest number of properties in common2 this principle prescribes that every such classification shall recognize and adopt into itself all distinctions of ,kind1 which exist among the objects it professes to classify4 ,to pass over any distinctions of ,kind1 and substitute definite distinctions1 which1 however considerable they may be1 do not point to ulterior unknown differences1 would be to replace classes with more by classes with fewer attributes in common2 and would be subversive of the ,natural ,method of ,classification4 ,accordingly all natural arrangements1 whether the reality of the distinction of ,kinds was felt or not by their framers1 have been led1 by the mere pursuit of their own proper end1 to conform themselves to the distinctions of ,kind1 so far as these have been ascertained at the time4 ,the species of ,plants are not only real ,kinds1 but are probably1 all of them1 real lowest ,kinds1 ,infim ,species2 which1 if we were to subdivide1 as of course it is open to us to do1 into sub-classes1 the subdivision would necessarily be founded on definite distinctions1 not pointing 7apart from what may be known of their causes or effects7 to any difference beyond themselves4 ,in so far as a natural classification is grounded on real ,kinds1 its groups are certainly not conventional3 it is perfectly true that they do not depend upon an arbitrary choice of the naturalist4 ,but it does not follow1 nor1 ,i conceive1 is it true1 that these classes are determined by a type1 and not by characters4 ,to determine them by a type would be as sure a way of missing the ,kind1 as if we were to select a set of characters arbitrarily4 ,they are determined by characters1 but these are not arbitrary4 ,the problem is1 to find a few definite characters which point to the multitude of indefinite ones4 ,kinds are ,classes between which there is an impassable barrier2 and what we have to seek is1 marks whereby we may determine on which side of the barrier an object takes its place4 ,the characters which will best do this should be chosen3 if they are also important in themselves1 so much the better4 ,when we have selected the characters1 we parcel out the objects according to those characters1 and not1 ,i conceive1 according to resemblance to a type4 ,we do not compose the species ,ranunculus acris1 of all plants which bear a satisfactory degree of resemblance to a model buttercup1 but of those which possess certain characters selected as marks by which we might recognize the possibility of a common parentage2 and the enumeration of those characters is the definition of the species4 ,the question next arises1 whether1 as all ,kinds must have a place among the classes1 so all the classes in a natural arrangement must be ,kinds8 ,and to this ,i answer1 certainly not4 ,the distinctions of ,kinds are not numerous enough to make up the whole of a classification4 ,very few of the genera of plants1 or even of the families1 can be pronounced with certainty to be ,kinds4 ,the great distinctions of ,vascular and ,cellular1 ,dicotyledonous or ,exogenous and ,monocotyledonous or ,endogenous plants1 are perhaps differences of kind2 the lines of demarcation which divide those classes seem 7though even on this ,i would not pronounce positively7 to go through the whole nature of the plants4 ,but the different species of a genus1 or genera of a family1 usually have in common only a limited number of characters4 ,a ,rose does not seem to differ from a ,rubus1 or the ,umbellifer from the ,ranunculace1 in much else than the characters botanically assigned to those genera or those families4 ,unenumerated differences certainly do exist in some cases2 there are families of plants which have peculiarities of chemical composition1 or yield products having peculiar effects on the animal economy4 ,the ,crucifer and ,fungi contain an unusual proportion of nitrogen2 the ,labiat are the chief sources of essential oils1 the ,solane are very commonly narcotic1 etc4 ,in these and similar cases there are possibly distinctions of ,kind2 but it is by no means indispensable that there should be4 ,genera and ,families may be eminently natural1 though marked out from one another by properties limited in number2 provided those properties are important1 and the objects contained in each genus or family resemble each other more than they resemble any thing which is excluded from the genus or family4 ,after the recognition and definition1 then1 of the infim species1 the next step is to arrange those infim species into larger groups3 making these groups correspond to ,kinds wherever it is possible1 but in most cases without any such guidance4 ,and in doing this it is true that we are naturally and properly guided1 in most cases at least1 by resemblance to a type4 ,we form our groups round certain selected ,kinds1 each of which serves as a sort of exemplar of its group4 ,but though the groups are suggested by types1 ,i can not think that a group when formed is determined by the type2 that in deciding whether a species belongs to the group1 a reference is made to the type1 and not to the characters2 that the characters 8can not be expressed in words40 ,this assertion is inconsistent with ,dr4 ,whewell's own statement of the fundamental principle of classification1 namely1 that 8general assertions shall be possible40 ,if the class did not possess any characters in common1 what general assertions would be possible respecting it8 ,except that they all resemble each other more than they resemble any thing else1 nothing whatever could be predicated of the class4 ,the truth is1 on the contrary1 that every genus or family is framed with distinct reference to certain characters1 and is composed1 first and principally1 of species which agree in possessing all those characters4 ,to these are added1 as a sort of appendix1 such other species1 generally in small number1 as possess nearly all the properties selected2 wanting some of them one property1 some another1 and which1 while they agree with the rest almost as much as these agree with one another1 do not resemble in an equal degree any other group4 ,our conception of the class continues to be grounded on the characters2 and the class might be defined1 those things which either possess that set of characters1 or resemble the things that do so1 more than they resemble any thing else4 ,and this resemblance itself is not1 like resemblance between simple sensations1 an ultimate fact1 unsusceptible of analysis4 ,even the inferior degree of resemblance is created by the possession of common characters4 ,whatever resembles the genus ,rose more than it resembles any other genus1 does so because it possesses a greater number of the characters of that genus than of the characters of any other genus4 ,nor can there be any real difficulty in representing1 by an enumeration of characters1 the nature and degree of the resemblance which is strictly sufficient to include any object in the class4 ,there are always some properties common to all things which are included4 ,others there often are1 to which some things1 which are nevertheless included1 are exceptions4 ,but the objects which are exceptions to one character are not exceptions to another2 the resemblance which fails in some particulars must be made up for in others4 ,the class1 therefore1 is constituted by the possession of all the characters which are universal1 and most of those which admit of exceptions4 ,if a plant had the ovules erect1 the stigmata divided1 possessed the albumen1 and was without stipules1 it possibly would not be classed among the ,rosace4 ,but it may want any one1 or more than one of these characters1 and not be excluded4 ,the ends of a scientific classification are better answered by including it4 ,since it agrees so nearly1 in its known properties1 with the sum of the characters of the class1 it is likely to resemble that class more than any other in those of its properties which are still undiscovered4 ,not only1 therefore1 are natural groups1 no less than any artificial classes1 determined by characters2 they are constituted in contemplation of1 and by reason of1 characters4 ,but it is in contemplation not of those characters only which are rigorously common to all the objects included in the group1 but of the entire body of characters1 all of which are found in most of those objects1 and most of them in all4 ,and hence our conception of the class1 the image in our minds which is representative of it1 is that of a specimen complete in all the characters2 most naturally a specimen which1 by possessing them all in the greatest degree in which they are ever found1 is the best fitted to exhibit clearly1 and in a marked manner1 what they are4 ,it is by a mental reference to this standard1 not instead of1 but in illustration of1 the definition of the class1 that we usually and advantageously determine whether any individual or species belongs to the class or not4 ,and this1 as it seems to me1 is the amount of truth contained in the doctrine of ,types4 ,we shall see presently that where the classification is made for the express purpose of a special inductive inquiry1 it is not optional1 but necessary for fulfilling the conditions of a correct ,inductive ,method1 that we should establish a type-species or genus1 namely1 the one which exhibits in the most eminent degree the particular phenomenon under investigation4 ,but of this hereafter4 ,it remains1 for completing the theory of natural groups1 that a few words should be said on the principles of the nomenclature adapted to them4 #e4 ,a ,nomenclature in science is1 as we have said1 a system of the names of ,kinds4 ,these names1 like other class-names1 are defined by the enumeration of the characters distinctive of the class4 ,the only merit which a set of names can have beyond this1 is to convey1 by the mode of their construction1 as much information as possible3 so that a person who knows the thing1 may receive all the assistance which the name can give in remembering what he knows2 while he who knows it not1 may receive as much knowledge respecting it as the case admits of1 by merely being told its name4 ,there are two modes of giving to the name of a ,kind this sort of significance4 ,the best1 but which unfortunately is seldom practicable1 is when the word can be made to indicate1 by its formation1 the very properties which it is designed to connote4 ,the name of a ,kind does not1 of course1 connote all the properties of the ,kind1 since these are inexhaustible1 but such of them as are sufficient to distinguish it2 such as are sure marks of all the rest4 ,now1 it is very rarely that one property1 or even any two or three properties1 can answer this purpose4 ,to distinguish the common daisy from all other species of plants would require the specification of many characters4 ,and a name can not1 without being too cumbrous for use1 give indication1 by its etymology or mode of construction1 of more than a very small number of these4 ,the possibility1 therefore1 of an ideally perfect ,nomenclature1 is probably confined to the one case in which we are happily in possession of something approaching to it--the ,nomenclature of elementary ,chemistry4 ,the substances1 whether simple or compound1 with which chemistry is conversant1 are ,kinds1 and1 as such1 the properties which distinguish each of them from the rest are innumerable2 but in the case of compound substances 7the simple ones are not numerous enough to require a systematic nomenclature71 there is one property1 the chemical composition1 which is of itself sufficient to distinguish the ,kind2 and is 7with certain reservations not yet thoroughly understood7 a sure mark of all the other properties of the compound4 ,all that was needful1 therefore1 was to make the name of every compound express1 on the first hearing1 its chemical composition2 that is1 to form the name of the compound1 in some uniform manner1 from the names of the simple substances which enter into it as elements4 ,this was done1 most skillfully and successfully1 by the ,french chemists1 though their nomenclature has become inadequate to the convenient expression of the very complicated compounds now known to chemists4 ,the only thing left unexpressed by them was the exact proportion in which the elements were combined2 and even this1 since the establishment of the atomic theory1 it has been found possible to express by a simple adaptation of their phraseology4 ,but where the characters which must be taken into consideration1 in order sufficiently to designate the ,kind1 are too numerous to be all signified in the derivation of the name1 and where no one of them is of such preponderant importance as to justify its being singled out to be so indicated1 we may avail ourselves of a subsidiary resource4 ,though we can not indicate the distinctive properties of the ,kind1 we may indicate its nearest natural affinities1 by incorporating into its name the name of the proximate natural group of which it is one of the species4 ,on this principle is founded the admirable binary nomenclature of botany and zoology4 ,in this nomenclature the name of every species consists of the name of the genus1 or natural group next above it1 with a word added to distinguish the particular species4 ,the last portion of the compound name is sometimes taken from some one of the peculiarities in which that species differs from others of the genus2 as ,clematis integrifolia1 ,potentilla alba1 ,viola palustris1 ,artemisia vulgaris2 sometimes from a circumstance of an historical nature1 as ,narcissus poeticus1 ,potentilla tormentilla 7indicating that the plant is that which was formerly known by the latter name71 ,exacum ,candollii 7from the fact that ,de ,candolle was its first discoverer72 and sometimes the word is purely conventional1 as ,thlaspi bursapastoris1 ,ranunculus thora2 it is of little consequence which2 since the second1 or1 as it is usually called1 the specific name1 could at most express1 independently of convention1 no more than a very small portion of the connotation of the term4 ,but by adding to this the name of the superior genus1 we may make the best amends we can for the impossibility of so contriving the name as to express all the distinctive characters of the ,kind4 ,we make it1 at all events1 express as many of those characters as are common to the proximate natural group in which the ,kind is included4 ,if even those common characters are so numerous or so little familiar as to require a further extension of the same resource1 we might1 instead of a binary1 adopt a ternary nomenclature1 employing not only the name of the genus1 but that of the next natural group in order of generality above the genus1 commonly called the ,family4 ,this was done in the mineralogical nomenclature proposed by ,professor ,mohs4 8,the names framed by him were not composed of two1 but of three elements1 designating respectively the ,species1 the ,genus1 and the ,order2 thus he has such species as ,rhombohedral ,lime ,haloide1 ,octohedral ,fluor ,haloide1 ,prismatic ,hal ,baryte407#bbf7 ,the binary construction1 however1 has been found sufficient in botany and zoology1 the only sciences in which this general principle has hitherto been successfully adopted in the construction of a nomenclature4 ,besides the advantage which this principle of nomenclature possesses1 in giving to the names of species the greatest quantity of independent significance which the circumstances of the case admit of1 it answers the further end of immensely economizing the use of names1 and preventing an otherwise intolerable burden on the memory4 ,when the names of species become extremely numerous1 some artifice 7as ,dr4 ,whewell7#bbg7 observes7 becomes absolutely necessary to make it possible to recollect or apply them4 8,the known species of plants1 for example1 were ten thousand in the time of ,linnus1 and are now probably sixty thousand4 ,it would be useless to endeavor to frame and employ separate names for each of these species4 ,the division of the objects into a subordinated system of classification enables us to introduce a ,nomenclature which does not require this enormous number of names4 ,each of the genera has its name1 and the species are marked by the addition of some epithet to the name of the genus4 ,in this manner about seventeen hundred generic names1 with a moderate number of specific names1 were found by ,linnus sufficient to designate with precision all the species of vegetables known at his time40 ,and though the number of generic names has since greatly increased1 it has not increased in any thing like the proportion of the multiplication of known species4 ,chapter ,,viii4 ,of ,classification ,by ,series4 #a4 ,thus far1 we have considered the principles of scientific classification so far only as relates to the formation of natural groups2 and at this point most of those who have attempted a theory of natural arrangement1 including1 among the rest1 ,dr4 ,whewell1 have stopped4 ,there remains1 however1 another1 and a not less important portion of the theory1 which has not yet1 as far as ,i am aware1 been systematically treated of by any writer except ,m4 ,comte4 ,this is1 the arrangement of the natural groups into a natural series47#bbh7 ,the end of ,classification1 as an instrument for the investigation of nature1 is 7as before stated7 to make us think of those objects together which have the greatest number of important common properties2 and which1 therefore1 we have oftenest occasion1 in the course of our inductions1 for taking into joint consideration4 ,our ideas of objects are thus brought into the order most conducive to the successful prosecution of inductive inquiries generally4 ,but when the purpose is to facilitate some particular inductive inquiry1 more is required4 ,to be instrumental to that purpose1 the classification must bring those objects together1 the simultaneous contemplation of which is likely to throw most light upon the particular subject4 ,that subject being the laws of some phenomenon or some set of connected phenomena2 the very phenomenon or set of phenomena in question must be chosen as the groundwork of the classification4 ,the requisites of a classification intended to facilitate the study of a particular phenomenon1 are1 first to bring into one class all ,kinds of things which exhibit that phenomenon1 in whatever variety of forms or degrees2 and1 secondly1 to arrange those ,kinds in a series according to the degree in which they exhibit it1 beginning with those which exhibit most of it1 and terminating with those which exhibit least4 ,the principal example1 as yet1 of such a classification1 is afforded by comparative anatomy and physiology1 from which1 therefore1 our illustrations shall be taken4 #b4 ,the object being supposed to be1 the investigation of the laws of animal life2 the first step1 after forming the most distinct conception of the phenomenon itself1 possible in the existing state of our knowledge1 is to erect into one great class 7that of animals7 all the known ,kinds of beings where that phenomenon presents itself2 in however various combinations with other properties1 and in however different degrees4 ,as some of these ,kinds manifest the general phenomenon of animal life in a very high degree1 and others in an insignificant degree1 barely sufficient for recognition2 we must1 in the next place1 arrange the various ,kinds in a series1 following one another according to the degrees in which they severally exhibit the phenomenon2 beginning therefore with man1 and ending with the most imperfect kinds of zoophytes4 ,this is merely saying that we should put the instances1 from which the law is to be inductively collected1 into the order which is implied in one of the four ,methods of ,experimental ,inquiry discussed in the preceding ,book2 the fourth ,method1 that of ,concomitant ,variations4 ,as formerly remarked1 this is often the only method to which recourse can be had1 with assurance of a true conclusion1 in cases in which we have but limited means of effecting1 by artificial experiments1 a separation of circumstances usually conjoined4 ,the principle of the method is1 that facts which increase or diminish together1 and disappear together1 are either cause and effect1 or effects of a common cause4 ,when it has been ascertained that this relation really subsists between the variations1 a connection between the facts themselves may be confidently laid down1 either as a law of nature or only as an empirical law1 according to circumstances4 ,that the application of this ,method must be preceded by the formation of such a series as we have described1 is too obvious to need being pointed out2 and the mere arrangement of a set of objects in a series1 according to the degrees in which they exhibit some fact of which we are seeking the law1 is too naturally suggested by the necessities of our inductive operations1 to require any lengthened illustration here4 ,but there are cases in which the arrangement required for the special purpose becomes the determining principle of the classification of the same objects for general purposes4 ,this will naturally and properly happen1 when those laws of the objects which are sought in the special inquiry enact so principal a part in the general character and history of those objects--exercise so much influence in determining all the phenomena of which they are either the agents or the theatre--that all other differences existing among the objects are fittingly regarded as mere modifications of the one phenomenon sought2 effects determined by the co-operation of some incidental circumstance with the laws of that phenomenon4 ,thus in the case of animated beings1 the differences between one class of animals and another may reasonably be considered as mere modifications of the general phenomenon1 animal life2 modifications arising either from the different degrees in which that phenomenon is manifested in different animals1 or from the intermixture of the effects of incidental causes peculiar to the nature of each1 with the effects produced by the general laws of life2 those laws still exercising a predominant influence over the result4 ,such being the case1 no other inductive inquiry respecting animals can be successfully carried on1 except in subordination to the great inquiry into the universal laws of animal life2 and the classification of animals best suited to that one purpose1 is the most suitable to all the other purposes of zoological science4 #c4 ,to establish a classification of this sort1 or even to apprehend it when established1 requires the power of recognizing the essential similarity of a phenomenon1 in its minuter degrees and obscurer forms1 with what is called the same phenomenon in the greatest perfection of its development2 that is1 of identifying with each other all phenomena which differ only in degree1 and in properties which we suppose to be caused by difference of degree4 ,in order to recognize this identity1 or1 in other words1 this exact similarity of quality1 the assumption of a type-species is indispensable4 ,we must consider as the type of the class1 that among the ,kinds included in it1 which exhibits the properties constitutive of the class1 in the highest degree2 conceiving the other varieties as instances of degeneracy1 as it were1 from that type2 deviations from it by inferior intensity of the characteristic property or properties4 ,for every phenomenon is best studied 7cteris paribus7 where it exists in the greatest intensity4 ,it is there that the effects which either depend on it1 or depend on the same causes with it1 will also exist in the greatest degree4 ,it is there1 consequently1 and only there1 that those effects of it1 or joint effects with it1 can become fully known to us1 so that we may learn to recognize their smaller degrees1 or even their mere rudiments1 in cases in which the direct study would have been difficult or even impossible4 ,not to mention that the phenomenon in its higher degrees may be attended by effects or collateral circumstances which in its smaller degrees do not occur at all1 requiring for their production in any sensible amount a greater degree of intensity of the cause than is there met with4 ,in man1 for example 7the species in which both the phenomenon of animal and that of organic life exist in the highest degree71 many subordinate phenomena develop themselves in the course of his animated existence1 which the inferior varieties of animals do not show4 ,the knowledge of these properties may nevertheless be of great avail toward the discovery of the conditions and laws of the general phenomenon of life1 which is common to man with those inferior animals4 ,and they are1 even1 rightly considered as properties of animated nature itself2 because they may evidently be affiliated to the general laws of animated nature2 because we may fairly presume that some rudiments or feeble degrees of those properties would be recognized in all animals by more perfect organs1 or even by more perfect instruments1 than ours2 and because those may be correctly termed properties of a class1 which a thing exhibits exactly in proportion as it belongs to the class1 that is1 in proportion as it possesses the main attributes constitutive of the class4 #d4 ,it remains to consider how the internal distribution of the series may most properly take place2 in what manner it should be divided into ,orders1 ,families1 and ,genera4 ,the main principle of division must of course be natural affinity2 the classes formed must be natural groups2 and the formation of these has already been sufficiently treated of4 ,but the principles of natural grouping must be applied in subordination to the principle of a natural series4 ,the groups must not be so constituted as to place in the same group things which ought to occupy different points of the general scale4 ,the precaution necessary to be observed for this purpose is1 that the primary divisions must be grounded not on all distinctions indiscriminately1 but on those which correspond to variations in the degree of the main phenomenon4 ,the series of ,animated ,nature should be broken into parts at the points where the variation in the degree of intensity of the main phenomenon 7as marked by its principal characters1 ,sensation1 ,thought1 ,voluntary ,motion1 etc47 begins to be attended by conspicuous changes in the miscellaneous properties of the animal4 ,such well-marked changes take place1 for example1 where the class ,mammalia ends2 at the points where ,fishes are separated from ,insects1 ,insects from ,mollusca1 etc4 ,when so formed1 the primary natural groups will compose the series by mere juxtaposition1 without redistribution2 each of them corresponding to a definite portion of the scale4 ,in like manner each family should1 if possible1 be so subdivided1 that one portion of it shall stand higher and the other lower1 though of course contiguous1 in the general scale2 and only when this is impossible is it allowable to ground the remaining subdivisions on characters having no determinable connection with the main phenomenon4 ,where the principal phenomenon so far transcends in importance all other properties on which a classification could be grounded1 as it does in the case of animated existence1 any considerable deviation from the rule last laid down is in general sufficiently guarded against by the first principle of a natural arrangement1 that of forming the groups according to the most important characters4 ,all attempts at a scientific classification of animals1 since first their anatomy and physiology were successfully studied1 have been framed with a certain degree of instinctive reference to a natural series1 and have accorded in many more points than they have differed1 with the classification which would most naturally have been grounded on such a series4 ,but the accordance has not always been complete2 and it still is often a matter of discussion1 which of several classifications best accords with the true scale of intensity of the main phenomenon4 ,cuvier1 for example1 has been justly criticised for having formed his natural groups1 with an undue degree of reference to the mode of alimentation1 a circumstance directly connected only with organic life1 and not leading to the arrangement most appropriate for the purposes of an investigation of the laws of animal life1 since both carnivorous and herbivorous or frugivorous animals are found at almost every degree in the scale of animal perfection4 ,blainville's classification has been considered by high authorities to be free from this defect2 as representing correctly1 by the mere order of the principal groups1 the successive degeneracy of animal nature from its highest to its most imperfect exemplification4 #e4 ,a classification of any large portion of the field of nature in conformity to the foregoing principles1 has hitherto been found practicable only in one great instance1 that of animals4 ,in the case even of vegetables1 the natural arrangement has not been carried beyond the formation of natural groups4 ,naturalists have found1 and probably will continue to find it impossible to form those groups into any series1 the terms of which correspond to real gradations in the phenomenon of vegetative or organic life4 ,such a difference of degree may be traced between the class of ,vascular ,plants and that of ,cellular1 which includes lichens1 alg1 and other substances whose organization is simpler and more rudimentary than that of the higher order of vegetables1 and which therefore approach nearer to mere inorganic nature4 ,but when we rise much above this point1 we do not find any sufficient difference in the degree in which different plants possess the properties of organization and life4 ,the dicotyledons are of more complex structure1 and somewhat more perfect organization1 than the monocotyledons2 and some dicotyledonous families1 such as the ,composit1 are rather more complex in their organization than the rest4 ,but the differences are not of a marked character1 and do not promise to throw any particular light upon the conditions and laws of vegetable life and development4 ,if they did1 the classification of vegetables would have to be made1 like that of animals1 with reference to the scale or series indicated4 ,although the scientific arrangements of organic nature afford as yet the only complete example of the true principles of rational classification1 whether as to the formation of groups or of series1 those principles are applicable to all cases in which mankind are called upon to bring the various parts of any extensive subject into mental co-ordination4 ,they are as much to the point when objects are to be classed for purposes of art or business1 as for those of science4 ,the proper arrangement1 for example1 of a code of laws1 depends on the same scientific conditions as the classifications in natural history2 nor could there be a better preparatory discipline for that important function1 than the study of the principles of a natural arrangement1 not only in the abstract1 but in their actual application to the class of phenomena for which they were first elaborated1 and which are still the best school for learning their use4 ,of this the great authority on codification1 ,bentham1 was perfectly aware2 and his early ,fragment on ,government1 the admirable introduction to a series of writings unequaled in their department1 contains clear and just views 7as far as they go7 on the meaning of a natural arrangement1 such as could scarcely have occurred to any one who lived anterior to the age of ,linnus and ,bernard de ,jussieu4 ,book ,v4 ,,on ,,fallacies4 8,errare non modo affirmando et negando1 sed etiam sentiendo1 et in tacit hominum cogitatione contingit40--,,hobbes1 ,computatio sive ,logica1 chap4 v4 8,il leur semble qu'il n'y a qu' douter par fantaisie1 et qu'il n'y a qu' dire en gnral que notre nature est infirme2 que notre esprit est plein d'aveuglement3 qu'il faut avoir un grand soin de se dfaire de ses prjugs1 et autres choses semblables4 ,ils pensent que cela suffit pour ne plus se laisser sduire ses sens1 et pour ne plus se tromper du tout4 ,il ne suffit pas de dire que l'esprit est foible1 il faut lui faire sentir ses foiblesses4 ,ce n'est pas assez de dire qu'il est sujet l'erreur1 il faut lui dcouvrir en quoi consistent ses erreurs40--,,malebranche1 ,recherche de la ,vrit4 ,chapter ,i4 ,of ,fallacies ,in ,general4 #a4 ,it is a maxim of the school-men1 that 8contrariorum eadem est scientia30 we never really know what a thing is1 unless we are also able to give a sufficient account of its opposite4 ,conformably to this maxim1 one considerable section1 in most treatises on ,logic1 is devoted to the subject of ,fallacies2 and the practice is too well worthy of observance1 to allow of our departing from it4 ,the philosophy of reasoning1 to be complete1 ought to comprise the theory of bad as well as of good reasoning4 ,we have endeavored to ascertain the principles by which the sufficiency of any proof can be tested1 and by which the nature and amount of evidence needful to prove any given conclusion can be determined beforehand4 ,if these principles were adhered to1 then although the number and value of the truths ascertained would be limited by the opportunities1 or by the industry1 ingenuity1 and patience1 of the individual inquirer1 at least error would not be embraced instead of truth4 ,but the general consent of mankind1 founded on their experience1 vouches for their being far indeed from even this negative kind of perfection in the employment of their reasoning powers4 ,in the conduct of life--in the practical business of mankind--wrong inferences1 incorrect interpretations of experience1 unless after much culture of the thinking faculty1 are absolutely inevitable2 and with most people1 after the highest degree of culture they ever attain1 such erroneous inferences1 producing corresponding errors in conduct1 are lamentably frequent4 ,even in the speculations to which eminent intellects have systematically devoted themselves1 and in reference to which the collective mind of the scientific world is always at hand to aid the efforts and correct the aberrations of individuals1 it is only from the more perfect sciences1 from those of which the subject-matter is the least complicated1 that opinions not resting on a correct induction have at length1 generally speaking1 been expelled4 ,in the departments of inquiry relating to the more complex phenomena of nature1 and especially those of which the subject is man1 whether as a moral and intellectual1 a social1 or even as a physical being2 the diversity of opinions still prevalent among instructed persons1 and the equal confidence with which those of the most contrary ways of thinking cling to their respective tenets1 are proof not only that right modes of philosophizing are not yet generally adopted on those subjects1 but that wrong ones are2 that inquirers have not only in general missed the truth1 but have often embraced error2 that even the most cultivated portion of our species have not yet learned to abstain from drawing conclusions which the evidence does not warrant4 ,the only complete safeguard against reasoning ill1 is the habit of reasoning well2 familiarity with the principles of correct reasoning1 and practice in applying those principles4 ,it is1 however1 not unimportant to consider what are the most common modes of bad reasoning2 by what appearances the mind is most likely to be seduced from the observance of true principles of induction2 what1 in short1 are the most common and most dangerous varieties of ,apparent ,evidence1 whereby persons are misled into opinions for which there does not exist evidence really conclusive4 ,a catalogue of the varieties of apparent evidence which are not real evidence1 is an enumeration of ,fallacies4 ,without such an enumeration1 therefore1 the present work would be wanting in an essential point4 ,and while writers who included in their theory of reasoning nothing more than ratiocination1 have in consistency with this limitation1 confined their remarks to the fallacies which have their seat in that portion of the process of investigation2 we1 who profess to treat of the whole process1 must add to our directions for performing it rightly1 warnings against performing it wrongly in any of its parts3 whether the ratiocinative or the experimental portion of it be in fault1 or the fault lie in dispensing with ratiocination and induction altogether4 #b4 ,in considering the sources of unfounded inference1 it is unnecessary to reckon the errors which arise1 not from a wrong method1 nor even from ignorance of the right one1 but from a casual lapse1 through hurry or inattention1 in the application of the true principles of induction4 ,such errors1 like the accidental mistakes in casting up a sum1 do not call for philosophical analysis or classification2 theoretical considerations can throw no light upon the means of avoiding them4 ,in the present treatise our attention is required1 not to mere inexpertness in performing the operation in the right way 7the only remedies for which are increased attention and more sedulous practice71 but to the modes of performing it in a way fundamentally wrong2 the conditions under which the human mind persuades itself that it has sufficient grounds for a conclusion which it has not arrived at by any of the legitimate methods of induction--which it has not1 even carelessly or overhastily1 endeavored to test by those legitimate methods4 #c4 ,there is another branch of what may be called the ,philosophy of ,error1 which must be mentioned here1 though only to be excluded from our subject4 ,the sources of erroneous opinions are twofold1 moral and intellectual4 ,of these1 the moral do not fall within the compass of this work4 ,they may be classed under two general heads3 ,indifference to the attainment of truth1 and ,bias2 of which last the most common case is that in which we are biased by our wishes2 but the liability is almost as great to the undue adoption of a conclusion which is disagreeable to us1 as of one which is agreeable1 if it be of a nature to bring into action any of the stronger passions4 ,persons of timid character are the more predisposed to believe any statement1 the more it is calculated to alarm them4 ,indeed it is a psychological law1 deducible from the most general laws of the mental constitution of man1 that any strong passion renders us credulous as to the existence of objects suitable to excite it4 ,but the moral causes of opinions1 though with most persons the most powerful of all1 are but remote causes2 they do not act directly1 but by means of the intellectual causes2 to which they bear the same relation that the circumstances called1 in the theory of medicine1 predisposing causes1 bear to exciting causes4 ,indifference to truth can not1 in and by itself1 produce erroneous belief2 it operates by preventing the mind from collecting the proper evidences1 or from applying to them the test of a legitimate and rigid induction2 by which omission it is exposed unprotected to the influence of any species of apparent evidence which offers itself spontaneously1 or which is elicited by that smaller quantity of trouble which the mind may be willing to take4 ,as little is ,bias a direct source of wrong conclusions4 ,we can not believe a proposition only by wishing1 or only by dreading1 to believe it4 ,the most violent inclination to find a set of propositions true1 will not enable the weakest of mankind to believe them without a vestige of intellectual grounds--without any1 even apparent1 evidence4 ,it acts indirectly1 by placing the intellectual grounds of belief in an incomplete or distorted shape before his eyes4 ,it makes him shrink from the irksome labor of a rigorous induction1 when he has a misgiving that its result may be disagreeable2 and in such examination as he does institute1 it makes him exert that which is in a certain measure voluntary1 his attention1 unfairly1 giving a larger share of it to the evidence which seems favorable to the desired conclusion1 a smaller to that which seems unfavorable4 ,it operates1 too1 by making him look out eagerly for reasons1 or apparent reasons1 to support opinions which are conformable1 or resist those which are repugnant1 to his interests or feelings2 and when the interests or feelings are common to great numbers of persons1 reasons are accepted and pass current1 which would not for a moment be listened to in that character if the conclusion had nothing more powerful than its reasons to speak in its behalf4 ,the natural or acquired partialities of mankind are continually throwing up philosophical theories1 the sole recommendation of which consists in the premises they afford for proving cherished doctrines1 or justifying favorite feelings2 and when any one of these theories has been so thoroughly discredited as no longer to serve the purpose1 another is always ready to take its place4 ,this propensity1 when exercised in favor of any widely-spread persuasion or sentiment1 is often decorated with complimentary epithets2 and the contrary habit of keeping the judgment in complete subordination to evidence1 is stigmatized by various hard names1 as skepticism1 immorality1 coldness1 hard-heartedness1 and similar expressions according to the nature of the case4 ,but though the opinions of the generality of mankind1 when not dependent on mere habit and inculcation1 have their root much more in the inclinations than in the intellect1 it is a necessary condition to the triumph of the moral bias that it should first pervert the understanding4 ,every erroneous inference1 though originating in moral causes1 involves the intellectual operation of admitting insufficient evidence as sufficient2 and whoever was on his guard against all kinds of inconclusive evidence which can be mistaken for conclusive1 would be in no danger of being led into error even by the strongest bias4 ,there are minds so strongly fortified on the intellectual side1 that they could not blind themselves to the light of truth1 however really desirous of doing so2 they could not1 with all the inclination in the world1 pass off upon themselves bad arguments for good ones4 ,if the sophistry of the intellect could be rendered impossible1 that of the feelings1 having no instrument to work with1 would be powerless4 ,a comprehensive classification of all those things which1 not being evidence1 are liable to appear such to the understanding1 will1 therefore1 of itself include all errors of judgment arising from moral causes1 to the exclusion only of errors of practice committed against better knowledge4 ,to examine1 then1 the various kinds of apparent evidence which are not evidence at all1 and of apparently conclusive evidence which do not really amount to conclusiveness1 is the object of that part of our inquiry into which we are about to enter4 ,the subject is not beyond the compass of classification and comprehensive survey4 ,the things1 indeed1 which are not evidence of any given conclusion1 are manifestly endless1 and this negative property1 having no dependence on any positive ones1 can not be made the groundwork of a real classification4 ,but the things which1 not being evidence1 are susceptible of being mistaken for it1 are capable of a classification having reference to the positive property which they possess of appearing to be evidence4 ,we may arrange them1 at our choice1 on either of two principles2 according to the cause which makes them appear to be evidence1 not being so2 or according to the particular kind of evidence which they simulate4 ,the ,classification of ,fallacies which will be attempted in the ensuing chapter1 is founded on these considerations jointly4 ,chapter ,,ii4 ,classification ,of ,fallacies4 #a4 ,in attempting to establish certain general distinctions which shall mark out from one another the various kinds of ,fallacious ,evidence1 we propose to ourselves an altogether different aim from that of several eminent thinkers1 who have given1 under the name of ,political or other ,fallacies1 a mere enumeration of a certain number of erroneous opinions2 false general propositions which happen to be often met with2 loci communes of bad arguments on some particular subject4 ,logic is not concerned with the false opinions which people happen to entertain1 but with the manner in which they come to entertain them4 ,the question is not1 what facts have at any time been erroneously supposed to be proof of certain other facts1 but what property in the facts it was which led any one to this mistaken supposition4 ,when a fact is supposed1 though incorrectly1 to be evidentiary of1 or a mark of1 some other fact1 there must be a cause of the error2 the supposed evidentiary fact must be connected in some particular manner with the fact of which it is deemed evidentiary--must stand in some particular relation to it1 without which relation it would not be regarded in that light4 ,the relation may either be one resulting from the simple contemplation of the two facts side by side with one another1 or it may depend on some process of mind1 by which a previous association has been established between them4 ,some peculiarity of relation1 however1 there must be2 the fact which can1 even by the wildest aberration1 be supposed to prove another fact1 must stand in some special position with regard to it2 and if we could ascertain and define that special position1 we should perceive the origin of the error4 ,we can not regard one fact as evidentiary of another1 unless we believe that the two are always1 or in the majority of cases1 conjoined4 ,if we believe ,a to be evidentiary of ,b1 if when we see ,a we are inclined to infer ,b from it1 the reason is because we believe that wherever ,a is1 ,b also either always or for the most part exists1 either as an antecedent1 a consequent1 or a concomitant4 ,if when we see ,a we are inclined not to expect ,b--if we believe ,a to be evidentiary of the absence of ,b--it is because we believe that where ,a is1 ,b either is never1 or at least seldom1 found4 ,erroneous conclusions1 in short1 no less than correct conclusions1 have an invariable relation to a general formula1 either expressed or tacitly implied4 ,when we infer some fact from some other fact which does not really prove it1 we either have admitted1 or1 if we maintained consistency1 ought to admit1 some groundless general proposition respecting the conjunction of the two phenomena4 ,for every property1 therefore1 in facts1 or in our mode of considering facts1 which leads us to believe that they are habitually conjoined when they are not1 or that they are not when in reality they are1 there is a corresponding kind of ,fallacy2 and an enumeration of fallacies would consist in a specification of those properties in facts1 and those peculiarities in our mode of considering them1 which give rise to this erroneous opinion4 #b4 ,to begin1 then2 the supposed connection1 or repugnance1 between the two facts1 may either be a conclusion from evidence 7that is1 from some other proposition or propositions71 or may be admitted without any such ground2 admitted1 as the phrase is1 on its own evidence2 embraced as self-evident1 as an axiomatic truth4 ,this gives rise to the first great distinction1 that between ,fallacies of ,inference and ,fallacies of ,simple ,inspection4 ,in the latter division must be included not only all cases in which a proposition is believed and held for true1 literally without any extrinsic evidence1 either of specific experience or general reasoning2 but those more frequent cases in which simple inspection creates a presumption in favor of a proposition2 not sufficient for belief1 but sufficient to cause the strict principles of a regular induction to be dispensed with1 and creating a predisposition to believe it on evidence which would be seen to be insufficient if no such presumption existed4 ,this class1 comprehending the whole of what may be termed ,natural ,prejudices1 and which ,i shall call indiscriminately ,fallacies of ,simple ,inspection or ,fallacies a priori1 shall be placed at the head of our list4 ,fallacies of ,inference1 or erroneous conclusions from supposed evidence1 must be subdivided according to the nature of the apparent evidence from which the conclusions are drawn2 or 7what is the same thing7 according to the particular kind of sound argument which the fallacy in question simulates4 ,but there is a distinction to be first drawn1 which does not answer to any of the divisions of sound arguments1 but arises out of the nature of bad ones4 ,we may know exactly what our evidence is1 and yet draw a false conclusion from it2 we may conceive precisely what our premises are1 what alleged matters of fact1 or general principles1 are the foundation of our inference2 and yet1 because the premises are false1 or because we have inferred from them what they will not support1 our conclusion may be erroneous4 ,but a case1 perhaps even more frequent1 is that in which the error arises from not conceiving our premises with due clearness1 that is 7as shown in the preceding ,book7#bbi771 with due fixity3 forming one conception of our evidence when we collect or receive it1 and another when we make use of it2 or unadvisedly1 and in general unconsciously1 substituting1 as we proceed1 different premises in the place of those with which we set out1 or a different conclusion for that which we undertook to prove4 ,this gives existence to a class of fallacies which may be justly termed 7in a phrase borrowed from ,bentham7 ,fallacies of ,confusion2 comprehending1 among others1 all those which have their source in language1 whether arising from the vagueness or ambiguity of our terms1 or from casual associations with them4 ,when the fallacy is not one of ,confusion1 that is1 when the proposition believed1 and the evidence on which it is believed1 are steadily apprehended and unambiguously expressed1 there remain to be made two cross divisions4 ,the ,apparent ,evidence may be either particular facts1 or foregone generalizations2 that is1 the process may simulate either simple ,induction or ,deduction2 and again1 the evidence1 whether consisting of supposed facts or of general propositions1 may be false in itself1 or1 being true1 may fail to bear out the conclusion attempted to be founded on it4 ,this gives us first1 ,fallacies of ,induction and ,fallacies of ,deduction1 and then a subdivision of each of these1 according as the supposed evidence is false1 or true but inconclusive4 ,fallacies of ,induction1 where the facts on which the induction proceeds are erroneous1 may be termed ,fallacies of ,observation4 ,the term is not strictly accurate1 or1 rather1 not accurately co-extensive with the class of fallacies which ,i propose to designate by it4 ,induction is not always grounded on facts immediately observed1 but sometimes on facts inferred2 and when these last are erroneous1 the error may not be1 in the literal sense of the term1 an instance of bad observation1 but of bad inference4 ,it will be convenient1 however1 to make only one class of all the inductions of which the error lies in not sufficiently ascertaining the facts on which the theory is grounded2 whether the cause of failure be malobservation1 or simple non-observation1 and whether the malobservation be direct1 or by means of intermediate marks which do not prove what they are supposed to prove4 ,and in the absence of any comprehensive term to denote the ascertainment1 by whatever means1 of the facts on which an induction is grounded1 ,i will venture to retain for this class of fallacies1 under the explanation now given1 the title of ,fallacies of ,observation4 ,the other class of inductive fallacies1 in which the facts are correct1 but the conclusion not warranted by them1 are properly denominated ,fallacies of ,generalization2 and these1 again1 fall into various subordinate classes or natural groups1 some of which will be enumerated in their proper place4 ,when we now turn to ,fallacies of ,deduction1 namely those modes of incorrect argumentation in which the premises1 or some of them1 are general propositions1 and the argument a ratiocination2 we may of course subdivide these also into two species similar to the two preceding1 namely1 those which proceed on false premises1 and those of which the premises1 though true1 do not support the conclusion4 ,but of these species1 the first must necessarily fall under some one of the heads already enumerated4 ,for the error must be either in those premises which are general propositions1 or in those which assert individual facts4 ,in the former case it is an ,inductive ,fallacy1 of one or the other class2 in the latter it is a ,fallacy of ,observation2 unless1 in either case1 the erroneous premise has been assumed on simple inspection1 in which case the fallacy is a priori4 ,or1 finally1 the premises1 of whichever kind they are1 may never have been conceived in so distinct a manner as to produce any clear consciousness by what means they were arrived at2 as in the case of what is called reasoning in a circle2 and then the fallacy is one of ,confusion4 ,there remain1 therefore1 as the only class of fallacies having properly their seat in deduction1 those in which the premises of the ratiocination do not bear out its conclusion2 the various cases1 in short1 of vicious argumentation1 provided against by the rules of the syllogism4 ,we shall call these1 ,fallacies of ,ratiocination4 #c4 ,we must not1 however1 expect to find that men's actual errors always1 or even commonly1 fall so unmistakably under some one of these classes1 as to be incapable of being referred to any other4 ,erroneous arguments do not admit of such a sharply cut division as valid arguments do4 ,an argument fully stated1 with all its steps distinctly set out1 in language not susceptible of misunderstanding1 must1 if it be erroneous1 be so in some one of these five modes unequivocally2 or indeed of the first four1 since the fifth1 on such a supposition1 would vanish4 ,but it is not in the nature of bad reasoning to express itself thus unambiguously4 ,when a sophist1 whether he is imposing on himself or attempting to impose on others1 can be constrained to throw his sophistry into so distinct a form1 it needs1 in a large proportion of cases1 no further exposure4 ,in all arguments1 everywhere but in the schools1 some of the links are suppressed2 a fortiori when the arguer either intends to deceive1 or is a lame and inexpert thinker1 little accustomed to bring his reasoning processes to any test2 and it is in those steps of the reasoning which are made in this tacit and half-conscious1 or even wholly unconscious manner1 that the error oftenest lurks4 ,in order to detect the fallacy1 the proposition thus silently assumed must be supplied2 but the reasoner1 most likely1 has never really asked himself what he was assuming2 his confuter1 unless permitted to extort it from him by the ,socratic mode of interrogation1 must himself judge what the suppressed premise ought to be in order to support the conclusion4 ,and hence1 in the words of ,archbishop ,whately1 8it must be often a matter of doubt1 or1 rather1 of arbitrary choice1 not only to which genus each kind of fallacy should be referred1 but even to which kind to refer any one individual fallacy2 for since1 in any course of argument1 one premise is usually suppressed1 it frequently happens in the case of a fallacy1 that the hearers are left to the alternative of supplying either a premise which is not true1 or else1 one which does not prove the conclusion2 e4g41 if a man expatiates on the distress of the country1 and thence argues that the government is tyrannical1 we must suppose him to assume either that #8every distressed country is under a tyranny1' which is a manifest falsehood1 or merely that #8every country under a tyranny is distressed1' which1 however true1 proves nothing1 the middle term being undistributed40 ,the former would be ranked1 in our distribution1 among fallacies of generalization1 the latter among those of ratiocination4 8,which are we to suppose the speaker meant us to understand8 ,surely0 7if he understood himself7 8just whichever each of his hearers might happen to prefer3 some might assent to the false premise2 others allow the unsound syllogism40 ,almost all fallacies1 therefore1 might in strictness be brought under our fifth class1 ,fallacies of ,confusion4 ,a fallacy can seldom be absolutely referred to any of the other classes2 we can only say1 that if all the links were filled up which should be capable of being supplied in a valid argument1 it would either stand thus 7forming a fallacy of one class71 or thus 7a fallacy of another72 or at furthest we may say1 that the conclusion is most likely to have originated in a fallacy of such and such a class4 ,thus1 in the illustration just quoted1 the error committed may be traced with most probability to a fallacy of generalization2 that of mistaking an uncertain mark1 or piece of evidence1 for a certain one2 concluding from an effect to some one of its possible causes1 when there are others which would have been equally capable of producing it4 ,yet1 though the five classes run into each other1 and a particular error often seems to be arbitrarily assigned to one of them rather than to any of the rest1 there is considerable use in so distinguishing them4 ,we shall find it convenient to set apart1 as ,fallacies of ,confusion1 those of which confusion is the most obvious characteristic2 in which no other cause can be assigned for the mistake committed1 than neglect or inability to state the question properly1 and to apprehend the evidence with definiteness and precision4 ,in the remaining four classes ,i shall place not only the cases in which the evidence is clearly seen to be what it is1 and yet a wrong conclusion drawn from it1 but also those in which1 although there be confusion1 the confusion is not the sole cause of the error1 but there is some shadow of a ground for it in the nature of the evidence itself4 ,and in distributing these cases of partial confusion among the four classes1 ,i shall1 when there can be any hesitation as to the precise seat of the fallacy1 suppose it to be in that part of the process in which1 from the nature of the case1 and the tendencies of the human mind1 an error would in the particular circumstances be the most probable4 ,after these observations we shall proceed1 without further preamble1 to consider the five classes in their order4 ,chapter ,,iii4 ,fallacies ,of ,simple ,inspection2 ,or ,a ,priori ,fallacies4 #a4 ,the tribe of errors of which we are to treat in the first instance1 are those in which no actual inference takes place at all2 the proposition 7it can not in such cases be called a conclusion7 being embraced1 not as proved1 but as requiring no proof2 as a self-evident truth2 or else as having such intrinsic verisimilitude1 that external evidence not in itself amounting to proof1 is sufficient in aid of the antecedent presumption4 ,an attempt to treat this subject comprehensively would be a transgression of the bounds prescribed to this work1 since it would necessitate the inquiry which1 more than any other1 is the grand question of what is called metaphysics1 viz41 ,what are the propositions which may reasonably be received without proof8 ,that there must be some such propositions all are agreed1 since there can not be an infinite series of proof1 a chain suspended from nothing4 ,but to determine what these propositions are1 is the opus magnum of the more recondite mental philosophy4 ,two principal divisions of opinion on the subject have divided the schools of philosophy from its first dawn4 ,the one recognizes no ultimate premises but the facts of our subjective consciousness2 our sensations1 emotions1 intellectual states of mind1 and volitions4 ,these1 and whatever by strict rules of induction can be derived from these1 it is possible1 according to this theory1 for us to know2 of all else we must remain in ignorance4 ,the opposite school hold that there are other existences1 suggested indeed to our minds by these subjective phenomena1 but not inferable from them1 by any process either of deduction or of induction2 which1 however1 we must1 by the constitution of our mental nature1 recognize as realities2 and realities1 too1 of a higher order than the phenomena of our consciousness1 being the efficient causes and necessary substrata of all ,phenomena4 ,among these entities they reckon ,substances1 whether matter or spirit2 from the dust under our feet to the soul1 and from that to ,deity4 ,all these1 according to them1 are preternatural or supernatural beings1 having no likeness in experience1 though experience is entirely a manifestation of their agency4 ,their existence1 together with more or less of the laws to which they conform in their operations1 are1 on this theory1 apprehended and recognized as real by the mind itself intuitively2 experience 7whether in the form of sensation or of mental feeling7 having no other part in the matter than as affording facts which are consistent with these necessary postulates of reason1 and which are explained and accounted for by them4 ,as it is foreign to the purpose of the present treatise to decide between these conflicting theories1 we are precluded from inquiring into the existence1 or defining the extent and limits1 of knowledge a priori1 and from characterizing the kind of correct assumption which the fallacy of incorrect assumption1 now under consideration1 simulates4 ,yet since it is allowed on both sides that such assumptions are often made improperly1 we may find it practicable1 without entering into the ultimate metaphysical grounds of the discussion1 to state some speculative propositions1 and suggest some practical cautions1 respecting the forms in which such unwarranted assumptions are most likely to be made4 #b4 ,in the cases in which1 according to the thinkers of the ontological school1 the mind apprehends1 by intuition1 things1 and the laws of things1 not cognizable by our sensitive faculty2 those intuitive1 or supposed intuitive1 perceptions are undistinguishable from what the opposite school are accustomed to call ideas of the mind4 ,when they themselves say that they perceive the things by an immediate act of a faculty given for that purpose by their ,creator1 it would be said of them by their opponents that they find an idea or conception in their own minds1 and from the idea or conception1 infer the existence of a corresponding objective reality4 ,nor would this be an unfair statement1 but a mere version into other words of the account given by many of themselves2 and one to which the more clear-sighted of them might1 and generally do1 without hesitation1 subscribe4 ,since1 therefore1 in the cases which lay the strongest claims to be examples of knowledge a priori1 the mind proceeds from the idea of a thing to the reality of the thing itself1 we can not be surprised by finding that illicit assumptions a priori consist in doing the same thing erroneously2 in mistaking subjective facts for objective1 laws of the percipient mind for laws of the perceived object1 properties of the ideas or conceptions for properties of the things conceived4 ,accordingly1 a large proportion of the erroneous thinking which exists in the world proceeds on a tacit assumption1 that the same order must obtain among the objects in nature which obtains among our ideas of them4 ,that if we always think of two things together1 the two things must always exist together4 ,that if one thing makes us think of another as preceding or following it1 that other must precede it or follow it in actual fact4 ,and conversely1 that when we can not conceive two things together they can not exist together1 and that their combination may1 without further evidence1 be rejected from the list of possible occurrences4 ,few persons1 ,i am inclined to think1 have reflected on the great extent to which this fallacy has prevailed1 and prevails1 in the actual beliefs and actions of mankind4 ,for a first illustration of it we may refer to a large class of popular superstitions4 ,if any one will examine in what circumstances most of those things agree1 which in different ages and by different portions of the human race have been considered as omens or prognostics of some interesting event1 whether calamitous or fortunate2 they will be found very generally characterized by this peculiarity1 that they cause the mind to think of that1 of which they are therefore supposed to forbode the actual occurrence4 8,talk of the devil and he will appear10 has passed into a proverb4 ,talk of the devil1 that is1 raise the idea1 and the reality will follow4 ,in times when the appearance of that personage in a visible form was thought to be no unfrequent occurrence1 it has doubtless often happened to persons of vivid imagination and susceptible nerves1 that talking of the devil has caused them to fancy they saw him2 as even in our more incredulous days1 listening to ghost stories predisposes us to see ghosts2 and thus1 as a prop to the a priori fallacy1 there might come to be added an auxiliary fallacy of malobservation1 with one of false generalization grounded on it4 ,fallacies of different orders often herd or cluster together in this fashion1 one smoothing the way for another4 ,but the origin of the superstition is evidently that which we have assigned4 ,in like manner1 it has been universally considered unlucky to speak of misfortune4 ,the day on which any calamity happened has been considered an unfortunate day1 and there has been a feeling everywhere1 and in some nations a religious obligation1 against transacting any important business on that day4 ,for on such a day our thoughts are likely to be of misfortune4 ,for a similar reason1 any untoward occurrence in commencing an undertaking has been considered ominous of failure2 and often1 doubtless1 has really contributed to it by putting the persons engaged in the enterprise more or less out of spirits2 but the belief has equally prevailed where the disagreeable circumstance was1 independently of superstition1 too insignificant to depress the spirits by any influence of its own4 ,all know the story of ,csar's accidentally stumbling in the act of landing on the ,african coast2 and the presence of mind with which he converted the direful presage into a favorable one by exclaiming1 8,africa1 ,i embrace thee40 ,such omens1 it is true1 were often conceived as warnings of the future1 given by a friendly or a hostile deity2 but this very superstition grew out of a pre-existing tendency2 the god was supposed to send1 as an indication of what was to come1 something which people were already disposed to consider in that light4 ,so in the case of lucky or unlucky names4 ,herodotus tells us how the ,greeks1 on the way to ,mycale1 were encouraged in their enterprise by the arrival of a deputation from ,samos1 one of the members of which was named ,hegesistratus1 the leader of armies4 ,cases may be pointed out in which something which could have no real effect but to make persons think of misfortune1 was regarded not merely as a prognostic1 but as something approaching to an actual cause of it4 ,the of the ,greeks1 and favete linguis1 or bona verba quso1 of the ,romans1 evince the care with which they endeavored to repress the utterance of any word expressive or suggestive of ill fortune2 not from notions of delicate politeness1 to which their general mode of conduct and feeling had very little reference1 but from bona fide alarm lest the event so suggested to the imagination should in fact occur4 ,some vestige of a similar superstition has been known to exist among uneducated persons even in our own day3 it is thought an unchristian thing to talk of1 or suppose1 the death of any person while he is alive4 ,it is known how careful the ,romans were to avoid1 by an indirect mode of speech1 the utterance of any word directly expressive of death or other calamity2 how instead of mortuus est they said vixit2 and 8be the event fortunate or otherwise0 instead of adverse4 ,the name ,maleventum1 of which ,salmasius so sagaciously detected the ,thessalian origin 71 71 they changed into the highly propitious denomination1 ,beneventum2 ,egesta into ,segesta2 and ,epidamnus1 a name so interesting in its associations to the reader of ,thucydides1 they exchanged for ,dyrrhachium1 to escape the perils of a word suggestive of damnum or detriment4 8,if a hare cross the highway10 says ,sir ,thomas ,browne17#bcj7 8there are few above threescore that are not perplexed thereat2 which notwithstanding is but an augurial terror1 according to that received expression1 ,inauspicatum dat iter oblatus lepus4 ,and the ground of the conceit was probably no greater than this1 that a fearful animal passing by us portended unto us something to be feared2 as upon the like consideration the meeting of a fox presaged some future imposture40 ,such superstitions as these last must be the result of study2 they are too recondite for natural or spontaneous growth4 ,but when the attempt was once made to construct a science of predictions1 any association1 though ever so faint or remote1 by which an object could be connected in however far-fetched a manner with ideas either of prosperity or of danger and misfortune1 was enough to determine its being classed among good or evil omens4 ,an example of rather a different kind from any of these1 but falling under the same principle1 is the famous attempt on which so much labor and ingenuity were expended by the alchemists1 to make gold potable4 ,the motive to this was a conceit that potable gold could be no other than the universal medicine2 and why gold8 ,because it was so precious4 ,it must have all marvelous properties as a physical substance1 because the mind was already accustomed to marvel at it4 ,from a similar feeling1 8every substance10 says ,dr4 ,paris17#bca7 8whose origin is involved in mystery1 has at different times been eagerly applied to the purposes of medicine4 ,not long since1 one of those showers which are now known to consist of the excrements of insects1 fell in the north of ,italy2 the inhabitants regarded it as manna1 or some supernatural panacea1 and they swallowed it with such avidity1 that it was only by extreme address that a small quantity was obtained for a chemical examination40 ,the superstition1 in this instance1 though doubtless partly of a religious character1 probably in part also arose from the prejudice that a wonderful thing must of course have wonderful properties4 #c4 ,the instances of a priori fallacy which we have hitherto cited belong to the class of vulgar errors1 and do not now1 nor in any but a rude age ever could1 impose upon minds of any considerable attainments4 ,but those to which we are about to proceed1 have been1 and still are1 all but universally prevalent among thinkers4 ,the same disposition to give objectivity to a law of the mind--to suppose that what is true of our ideas of things must be true of the things themselves--exhibits itself in many of the most accredited modes of philosophical investigation1 both on physical and on metaphysical subjects4 ,in one of its most undisguised manifestations1 it embodies itself in two maxims1 which lay claim to axiomatic truth3 ,things which we can not think of together1 can not co-exist2 and ,things which we can not help thinking of together1 must co-exist4 ,i am not sure that the maxims were ever expressed in these precise words1 but the history both of philosophy and of popular opinions abounds with exemplifications of both forms of the doctrine4 ,to begin with the latter of them3 ,things which we can not think of except together1 must exist together4 ,this is assumed in the generally received and accredited mode of reasoning which concludes that ,a must accompany ,b in point of fact1 because 8it is involved in the idea40 ,such thinkers do not reflect that the idea1 being a result of abstraction1 ought to conform to the facts1 and can not make the facts conform to it4 ,the argument is at most admissible as an appeal to authority2 a surmise1 that what is now part of the idea1 must1 before it became so1 have been found by previous inquirers in the facts4 ,nevertheless1 the philosopher who more than all others made professions of rejecting authority1 ,descartes1 constructed his system on this very basis4 ,his favorite device for arriving at truth1 even in regard to outward things1 was by looking into his own mind for it4 8,credidi me10 says his celebrated maxim1 8pro regul generali sumere posse1 omne id quod vald dilucid et distinct concipiebam1 verum esse20 whatever can be very clearly conceived must certainly exist2 that is1 as he afterward explains it1 if the idea includes existence4 ,and on this ground he infers that geometrical figures really exist1 because they can be distinctly conceived4 ,whenever existence is 8involved in an idea10 a thing conformable to the idea must really exist2 which is as much as to say1 whatever the idea contains must have its equivalent in the thing2 and what we are not able to leave out of the idea can not be absent from the reality47#bcb7 ,this assumption pervades the philosophy not only of ,descartes1 but of all the thinkers who received their impulse mainly from him1 in particular the two most remarkable among them1 ,spinoza and ,leibnitz1 from whom the modern ,german metaphysical philosophy is essentially an emanation4 ,i am indeed disposed to think that the fallacy now under consideration has been the cause of two-thirds of the bad philosophy1 and especially of the bad metaphysics1 which the human mind has never ceased to produce4 ,our general ideas contain nothing but what has been put into them1 either by our passive experience1 or by our active habits of thought2 and the metaphysicians in all ages1 who have attempted to construct the laws of the universe by reasoning from our supposed necessities of thought1 have always proceeded1 and only could proceed1 by laboriously finding in their own minds what they themselves had formerly put there1 and evolving from their ideas of things what they had first involved in those ideas4 ,in this way all deeply-rooted opinions and feelings are enabled to create apparent demonstrations of their truth and reasonableness1 as it were1 out of their own substance4 ,the other form of the fallacy3 ,things which we can not think of together can not exist together--including as one of its branches1 that what we can not think of as existing can not exist at all--may thus be briefly expressed3 ,whatever is inconceivable must be false4 ,against this prevalent doctrine ,i have sufficiently argued in a former ,book17#bcc7 and nothing is required in this place but examples4 ,it was long held that ,antipodes were impossible because of the difficulty which was found in conceiving persons with their heads in the same direction as our feet4 ,and it was one of the received arguments against the ,copernican system1 that we can not conceive so great a void space as that system supposes to exist in the celestial regions4 ,when men's imaginations had always been used to conceive the stars as firmly set in solid spheres1 they naturally found much difficulty in imagining them in so different1 and1 as it doubtless appeared to them1 so precarious a situation4 ,but they had no right to mistake the limitation 7whether natural1 or1 as it in fact proved1 only artificial7 of their own faculties1 for an inherent limitation of the possible modes of existence in the universe4 ,it may be said in objection1 that the error in these cases was in the minor premise1 not the major2 an error of fact1 not of principle2 that it did not consist in supposing that what is inconceivable can not be true1 but in supposing antipodes to be inconceivable1 when present experience proves that they can be conceived4 ,even if this objection were allowed1 and the proposition that what is inconceivable can not be true were suffered to remain unquestioned as a speculative truth1 it would be a truth on which no practical consequence could ever be founded1 since1 on this showing1 it is impossible to affirm of any proposition1 not being a contradiction in terms1 that it is inconceivable4 ,antipodes were really1 not fictitiously1 inconceivable to our ancestors3 they are indeed conceivable to us2 and as the limits of our power of conception have been so largely extended1 by the extension of our experience and the more varied exercise of our imagination1 so may posterity find many combinations perfectly conceivable to them which are inconceivable to us4 ,but1 as beings of limited experience1 we must always and necessarily have limited conceptive powers2 while it does not by any means follow that the same limitation obtains in the possibilities of ,nature1 nor even in her actual manifestations4 ,rather more than a century and a half ago it was a scientific maxim1 disputed by no one1 and which no one deemed to require any proof1 that 8a thing can not act where it is not407#bcd7 ,with this weapon the ,cartesians waged a formidable war against the theory of gravitation1 which1 according to them1 involving so obvious an absurdity1 must be rejected in limine3 the sun could not possibly act upon the earth1 not being there4 ,it was not surprising that the adherents of the old systems of astronomy should urge this objection against the new2 but the false assumption imposed equally on ,newton himself1 who1 in order to turn the edge of the objection1 imagined a subtle ether which filled up the space between the sun and the earth1 and by its intermediate agency was the proximate cause of the phenomena of gravitation4 8,it is inconceivable10 said ,newton1 in one of his letters to ,dr4 ,bentley17#bce7 8that inanimate brute matter should1 without the mediation of something else1 which is not material1 operate upon and affect other matter without mutual contact4444 ,that gravity should be innate1 inherent1 and essential to matter1 so that one body may act on another1 at a distance1 through a vacuum1 without the mediation of any thing else1 by and through which their action and force may be conveyed from one to another1 is to me so great an absurdity1 that ,i believe no man1 who in philosophical matters has a competent faculty of thinking1 can ever fall into it40 ,this passage should be hung up in the cabinet of every cultivator of science who is ever tempted to pronounce a fact impossible because it appears to him inconceivable4 ,in our own day one would be more tempted1 though with equal injustice1 to reverse the concluding observation1 and consider the seeing any absurdity at all in a thing so simple and natural1 to be what really marks the absence of 8a competent faculty of thinking40 ,no one now feels any difficulty in conceiving gravity to be1 as much as any other property is1 8inherent and essential to matter10 nor finds the comprehension of it facilitated in the smallest degree by the supposition of an ether 7though some recent inquirers do give this as an explanation of it72 nor thinks it at all incredible that the celestial bodies can and do act where they1 in actual bodily presence1 are not4 ,to us it is not more wonderful that bodies should act upon one another 8without mutual contact10 than that they should do so when in contact2 we are familiar with both these facts1 and we find them equally inexplicable1 but equally easy to believe4 ,to ,newton1 the one1 because his imagination was familiar with it1 appeared natural and a matter of course1 while the other1 for the contrary reason1 seemed too absurd to be credited4 ,it is strange that any one1 after such a warning1 should rely implicitly on the evidence a priori of such propositions as these1 that matter can not think2 that space1 or extension1 is infinite2 that nothing can be made out of nothing 7ex nihilo nihil fit74 ,whether these propositions are true or not this is not the place to determine1 nor even whether the questions are soluble by the human faculties4 ,but such doctrines are no more self-evident truths1 than the ancient maxim that a thing can not act where it is not1 which probably is not now believed by any educated person in ,europe47#bcf7 ,matter can not think2 why8 because we can not conceive thought to be annexed to any arrangement of material particles4 ,space is infinite1 because having never known any part of it which had not other parts beyond it1 we can not conceive an absolute termination4 ,ex nihilo nihil fit1 because having never known any physical product without a pre-existing physical material1 we can not1 or think we can not1 imagine a creation out of nothing4 ,but these things may in themselves be as conceivable as gravitation without an intervening medium1 which ,newton thought too great an absurdity for any person of a competent faculty of philosophical thinking to admit3 and even supposing them not conceivable1 this1 for aught we know1 may be merely one of the limitations of our very limited minds1 and not in nature at all4 ,no writer has more directly identified himself with the fallacy now under consideration1 or has embodied it in more distinct terms1 than ,leibnitz4 ,in his view1 unless a thing was not merely conceivable1 but even explainable1 it could not exist in nature4 ,all natural phenomena1 according to him1 must be susceptible of being accounted for a priori4 ,the only facts of which no explanation could be given but the will of ,god1 were miracles properly so called4 8,je reconnais10 says he17#bcg7 8qu'il n'est pas permis de nier ce qu'on n'entend pas2 mais j'ajoute qu'on a droit de nier 7au moins dans l'ordre naturel7 ce que absolument n'est point intelligible ni explicable4 ,je soutiens aussi 444 qu'enfin la conception des cratures n'est pas la mesure du pouvoir de ,dieu1 mais que leur conceptivit1 ou force de concevoir1 est la mesure du pouvoir de la nature1 tout ce qui est conforme l'ordre naturel pouvant tre conu ou entendu par quelque crature40 ,not content with assuming that nothing can be true which we are unable to conceive1 scientific inquirers have frequently given a still further extension to the doctrine1 and held that1 even of things not altogether inconceivable1 that which we can conceive with the greatest ease is likeliest to be true4 ,it was long an admitted axiom1 and is not yet entirely discredited1 that 8nature always acts by the simplest means10 i4e41 by those which are most easily conceivable47#bch7 ,a large proportion of all the errors ever committed in the investigation of the laws of nature1 have arisen from the assumption that the most familiar explanation or hypothesis must be the truest4 ,one of the most instructive facts in scientific history is the pertinacity with which the human mind clung to the belief that the heavenly bodies must move in circles1 or be carried round by the revolution of spheres2 merely because those were in themselves the simplest suppositions3 though1 to make them accord with the facts which were ever contradicting them more and more1 it became necessary to add sphere to sphere and circle to circle1 until the original simplicity was converted into almost inextricable complication4 #d4 ,we pass to another a priori fallacy or natural prejudice1 allied to the former1 and originating1 as that does1 in the tendency to presume an exact correspondence between the laws of the mind and those of things external to it4 ,the fallacy may be enunciated in this general form--,whatever can be thought of apart exists apart3 and its most remarkable manifestation consists in the personification of abstractions4 ,mankind in all ages have had a strong propensity to conclude that wherever there is a name1 there must be a distinguishable separate entity corresponding to the name2 and every complex idea which the mind has formed for itself by operating upon its conceptions of individual things1 was considered to have an outward objective reality answering to it4 ,fate1 ,chance1 ,nature1 ,time1 ,space1 were real beings1 nay1 even gods4 ,if the analysis of qualities in the earlier part of this work be correct1 names of qualities and names of substances stand for the very same sets of facts or phenomena2 whiteness and a white thing are only different phrases1 required by convenience for speaking of the same external fact under different relations4 ,not such1 however1 was the notion which this verbal distinction suggested of old1 either to the vulgar or to the scientific4 ,whiteness was an entity1 inhering or sticking in the white substance3 and so of all other qualities4 ,so far was this carried1 that even concrete general terms were supposed to be1 not names of indefinite numbers of individual substances1 but names of a peculiar kind of entities termed ,universal ,substances4 ,because we can think and speak of man in general1 that is1 of all persons in so far as possessing the common attributes of the species1 without fastening our thoughts permanently on some one individual person2 therefore man in general was supposed to be1 not an aggregate of individual persons1 but an abstract or universal man1 distinct from these4 ,it may be imagined what havoc metaphysicians trained in these habits made with philosophy1 when they came to the largest generalizations of all4 ,substanti ,secund of any kind were bad enough1 but such ,substanti ,secund as 1 for example1 and 1 standing for peculiar entities supposed to be inherent in all things which exist1 or in all which are said to be one1 were enough to put an end to all intelligible discussion2 especially since1 with a just perception that the truths which philosophy pursues are general truths1 it was soon laid down that these general substances were the only subjects of science1 being immutable1 while individual substances cognizable by the senses1 being in a perpetual flux1 could not be the subject of real knowledge4 ,this misapprehension of the import of general language constitutes ,mysticism1 a word so much oftener written and spoken than understood4 ,whether in the ,vedas1 in the ,platonists1 or in the ,hegelians1 mysticism is neither more nor less than ascribing objective existence to the subjective creations of our own faculties1 to ideas or feelings of the mind2 and believing that by watching and contemplating these ideas of its own making1 it can read in them what takes place in the world without4 #e4 ,proceeding with the enumeration of a priori fallacies1 and endeavoring to arrange them with as much reference as possible to their natural affinities1 we come to another1 which is also nearly allied to the fallacy preceding the last1 standing in the same relation to one variety of it as the fallacy last mentioned does to the other4 ,this1 too1 represents nature as under incapacities corresponding to those of our intellect2 but instead of only asserting that nature can not do a thing because we can not conceive it done1 goes the still greater length of averring that nature does a particular thing1 on the sole ground that we can see no reason why she should not4 ,absurd as this seems when so plainly stated1 it is a received principle among scientific authorities for demonstrating a priori the laws of physical phenomena4 ,a phenomenon must follow a certain law1 because we see no reason why it should deviate from that law in one way rather than in another4 ,this is called the ,principle of the ,sufficient ,reason27#bci7 and by means of it philosophers often flatter themselves that they are able to establish1 without any appeal to experience1 the most general truths of experimental physics4 ,take1 for example1 two of the most elementary of all laws1 the law of inertia and the first law of motion4 ,a body at rest can not1 it is affirmed1 begin to move unless acted upon by some external force2 because1 if it did1 it must either move up or down1 forward or backward1 and so forth2 but if no outward force acts upon it1 there can be no reason for its moving up rather than down1 or down rather than up1 etc41 ergo1 it will not move at all4 ,this reasoning ,i conceive to be entirely fallacious1 as indeed ,dr4 ,brown1 in his treatise on ,cause and ,effect1 has shown with great acuteness and justness of thought4 ,we have before remarked1 that almost every fallacy may be referred to different genera by different modes of filling up the suppressed steps2 and this particular one may1 at our option1 be brought under petitio principii4 ,it supposes that nothing can be a 8sufficient reason0 for a body's moving in one particular direction1 except some external force4 ,but this is the very thing to be proved4 ,why not some internal force8 ,why not the law of the thing's own nature8 ,since these philosophers think it necessary to prove the law of inertia1 they of course do not suppose it to be self-evident2 they must1 therefore1 be of opinion that previously to all proof1 the supposition of a body's moving by internal impulse is an admissible hypothesis2 but if so1 why is not the hypothesis also admissible1 that the internal impulse acts naturally in some one particular direction1 not in another8 ,if spontaneous motion might have been the law of matter1 why not spontaneous motion toward the sun1 toward the earth1 or toward the zenith8 ,why not1 as the ancients supposed1 toward a particular place in the universe1 appropriated to each particular kind of substance8 ,surely it is not allowable to say that spontaneity of motion is credible in itself1 but not credible if supposed to take place in any determinate direction4 ,indeed1 if any one chose to assert that all bodies when uncontrolled set out in a direct line toward the ,north ,pole1 he might equally prove his point by the principle of the ,sufficient ,reason4 ,by what right is it assumed that a state of rest is the particular state which can not be deviated from without special cause8 ,why not a state of motion1 and of some particular sort of motion8 ,why may we not say that the natural state of a horse left to himself is to amble1 because otherwise he must either trot1 gallop1 or stand still1 and because we know no reason why he should do one of these rather than another8 ,if this is to be called an unfair use of the 8sufficient reason10 and the other a fair one1 there must be a tacit assumption that a state of rest is more natural to a horse than a state of ambling4 ,if this means that it is the state which the animal will assume when left to himself1 that is the very point to be proved2 and if it does not mean this1 it can only mean that a state of rest is the simplest state1 and therefore the most likely to prevail in nature1 which is one of the fallacies or natural prejudices we have already examined4 ,so again of the ,first ,law of ,motion2 that a body once moving will1 if left to itself1 continue to move uniformly in a straight line4 ,an attempt is made to prove this law by saying1 that if not1 the body must deviate either to the right or to the left1 and that there is no reason why it should do one more than the other4 ,but who could know1 antecedently to experience1 whether there was a reason or not8 ,might it not be the nature of bodies1 or of some particular bodies1 to deviate toward the right8 or if the supposition is preferred1 toward the east1 or south8 ,it was long thought that bodies1 terrestrial ones at least1 had a natural tendency to deflect downward2 and there is no shadow of any thing objectionable in the supposition1 except that it is not true4 ,the pretended proof of the law of motion is even more manifestly untenable than that of the law of inertia1 for it is flagrantly inconsistent2 it assumes that the continuance of motion in the direction first taken is more natural than deviation either to the right or to the left1 but denies that one of these can possibly be more natural than the other4 ,all these fancies of the possibility of knowing what is natural or not natural by any other means than experience1 are1 in truth1 entirely futile4 ,the real and only proof of the laws of motion1 or of any other law of the universe1 is experience2 it is simply that no other suppositions explain or are consistent with the facts of universal nature4 ,geometers have1 in all ages1 been open to the imputation of endeavoring to prove the most general facts of the outward world by sophistical reasoning1 in order to avoid appeals to the senses4 ,archimedes1 says ,professor ,playfair17#bdj7 established some of the elementary propositions of statics by a process in which he 8borrows no principle from experiment1 but establishes his conclusion entirely by reasoning a priori4 ,he assumes1 indeed1 that equal bodies1 at the ends of the equal arms of a lever1 will balance one another2 and also that a cylinder or parallelopiped of homogeneous matter1 will be balanced about its centre of magnitude4 ,these1 however1 are not inferences from experience2 they are1 properly speaking1 conclusions deduced from the principle of the ,sufficient ,reason40 ,and to this day there are few geometers who would not think it far more scientific to establish these or any other premises in this way1 than to rest their evidence on that familiar experience which in the case in question might have been so safely appealed to4 #f4 ,another natural prejudice1 of most extensive prevalence1 and which had a great share in producing the errors fallen into by the ancients in their physical inquiries1 was this3 ,that the differences in nature must correspond to our received distinctions3 that effects which we are accustomed1 in popular language1 to call by different names1 and arrange in different classes1 must be of different natures1 and have different causes4 ,this prejudice1 so evidently of the same origin with those already treated of1 marks more especially the earliest stage of science1 when it has not yet broken loose from the trammels of every-day phraseology4 ,the extraordinary prevalence of the fallacy among the ,greek philosophers may be accounted for by their generally knowing no other language than their own2 from which it was a consequence that their ideas followed the accidental or arbitrary combinations of that language1 more completely than can happen among the moderns to any but illiterate persons4 ,they had great difficulty in distinguishing between things which their language confounded1 or in putting mentally together things which it distinguished2 and could hardly combine the objects in nature1 into any classes but those which were made for them by the popular phrases of their own country2 or at least could not help fancying those classes to be natural and all others arbitrary and artificial4 ,accordingly1 scientific investigation among the ,greek schools of speculation and their followers in the ,middle ,ages1 was little more than a mere sifting and analyzing of the notions attached to common language4 ,they thought that by determining the meaning of words1 they could become acquainted with facts4 8,they took for granted10 says ,dr4 ,whewell17#bda7 8that philosophy must result from the relations of those notions which are involved in the common use of language1 and they proceeded to seek it by studying such notions40 ,in his next chapter1 ,dr4 ,whewell has so well illustrated and exemplified this error1 that ,i shall take the liberty of quoting him at some length4 8,the propensity to seek for principles in the common usages of language may be discerned at a very early period4 ,thus we have an example of it in a saying which is reported of ,thales1 the founder of ,greek philosophy4 ,when he was asked1 #8,what is the greatest thing8' he replied #8,place2 for all other things are in the world1 but the world is in it4' ,in ,aristotle we have the consummation of this mode of speculation4 ,the usual point from which he starts in his inquiries is1 that we say thus or thus in common language4 ,thus1 when he has to discuss the question whether there be1 in any part of the universe1 a void1 or space in which there is nothing1 he inquires first in how many senses we say that one thing is in another4 ,he enumerates many of these2 we say the part is in the whole1 as the finger is in the hand2 again we say1 the species is in the genus1 as man is included in animal2 again1 the government of ,greece is in the king2 and various other senses are described and exemplified1 but of all these the most proper is when we say a thing is in a vessel1 and generally in place4 ,he next examines what place is1 and comes to this conclusion1 that #8if about a body there be another body including it1 it is in place1 and if not1 not4' ,a body moves when it changes its place2 but he adds1 that if water be in a vessel1 the vessel being at rest1 the parts of the water may still move1 for they are included by each other2 so that while the whole does not change its place1 the parts may change their place in a circular order4 ,proceeding then to the question of a void1 he as usual examines the different senses in which the term is used1 and adopts as the most proper1 place without matter1 with no useful result4 8,again1 in a question concerning mechanical action1 he says1 #8,when a man moves a stone by pushing it with a stick1 we say both that the man moves the stone1 and that the stick moves the stone1 but the latter more properly4' 8,again1 we find the ,greek philosophers applying themselves to extract their dogmas from the most general and abstract notions which they could detect2 for example1 from the conception of the ,universe as ,one or as ,many things4 ,they tried to determine how far we may1 or must1 combine with these conceptions that of a whole1 of parts1 of number1 of limits1 of place1 of beginning or end1 of full or void1 of rest or motion1 of cause and effect1 and the like4 ,the analysis of such conceptions with such a view1 occupies1 for instance1 almost the whole of ,aristotle's ,treatise on the ,heavens40 ,the following paragraph merits particular attention3 8,another mode of reasoning1 very widely applied in these attempts1 was the doctrine of contrarieties1 in which it was assumed that adjectives or substances which are in common language1 or in some abstract mode of conception1 opposed to each other1 must point at some fundamental antithesis in nature1 which it is important to study4 ,thus ,aristotle says that the ,pythagoreans1 from the contrasts which number suggests1 collected ten principles--,limited and ,unlimited1 ,odd and ,even1 ,one and ,many1 ,right and ,left1 ,male and ,female1 ,rest and ,motion1 ,straight and ,curved1 ,light and ,darkness1 ,good and ,evil1 ,square and ,oblong4444 ,aristotle himself deduced the doctrine of four elements and other dogmas by oppositions of the same kind40 ,of the manner in which1 from premises obtained in this way1 the ancients attempted to deduce laws of nature1 an example is given in the same work a few pages further on4 8,aristotle decides that there is no void on such arguments as this4 ,in a void there could be no difference of up and down2 for as in nothing there are no differences1 so there are none in a privation or negation2 but a void is merely a privation or negation of matter2 therefore1 in a void1 bodies could not move up and down1 which it is in their nature to do4 ,it is easily seen0 7,dr4 ,whewell very justly adds7 8that such a mode of reasoning elevates the familiar forms of language1 and the intellectual connections of terms1 to a supremacy over facts2 making truth depend upon whether terms are or are not privative1 and whether we say that bodies fall naturally40 ,the propensity to assume that the same relations obtain between objects themselves1 which obtain between our ideas of them1 is here seen in the extreme stage of its development4 ,for the mode of philosophizing1 exemplified in the foregoing instances1 assumes no less than that the proper way of arriving at knowledge of nature1 is to study nature itself subjectively2 to apply our observation and analysis not to the facts1 but to the common notions entertained of the facts4 ,many other equally striking examples may be given of the tendency to assume that things which for the convenience of common life are placed in different classes1 must differ in every respect4 ,of this nature was the universal and deeply-rooted prejudice of antiquity and the ,middle ,ages1 that celestial and terrestrial phenomena must be essentially different1 and could in no manner or degree depend on the same laws4 ,of the same kind1 also1 was the prejudice against which ,bacon contended1 that nothing produced by nature could be successfully imitated by man3 8,calorem solis et ignis toto genere differre2 ne scilicet homines putent se per opera ignis1 aliquid simile iis qu in ,natura fiunt1 educere et formare posse20 and again1 8,compositionem tantum opus ,hominis1 ,mistionem vero opus solius ,natur esse3 ne scilicet homines sperent aliquam ex arte ,corporum naturalium generationem aut transformationem407#bdb7 ,the grand distinction in the ancient scientific speculations1 between natural and violent motions1 though not without a plausible foundation in the appearances themselves1 was doubtless greatly recommended to adoption by its conformity to this prejudice4 #g4 ,from the fundamental error of the scientific inquirers of antiquity1 we pass1 by a natural association1 to a scarcely less fundamental one of their great rival and successor1 ,bacon4 ,it has excited the surprise of philosophers that the detailed system of inductive logic1 which this extraordinary man labored to construct1 has been turned to so little direct use by subsequent inquirers1 having neither continued1 except in a few of its generalities1 to be recognized as a theory1 nor having conducted in practice to any great scientific results4 ,but this1 though not unfrequently remarked1 has scarcely received any plausible explanation2 and some1 indeed1 have preferred to assert that all rules of induction are useless1 rather than suppose that ,bacon's rules are grounded on an insufficient analysis of the inductive process4 ,such1 however1 will be seen to be the fact1 as soon as it is considered1 that ,bacon entirely overlooked ,plurality of ,causes4 ,all his rules tacitly imply the assumption1 so contrary to all we now know of nature1 that a phenomenon can not have more than one cause4 ,when he is inquiring into what he terms the forma calidi aut frigidi1 gravis aut levis1 sicci aut humidi1 and the like1 he never for an instant doubts that there is some one thing1 some invariable condition or set of conditions1 which is present in all cases of heat1 or cold1 or whatever other phenomenon he is considering2 the only difficulty being to find what it is2 which accordingly he tries to do by a process of elimination1 rejecting or excluding1 by negative instances1 whatever is not the forma or cause1 in order to arrive at what is4 ,but1 that this forma or cause is one thing1 and that it is the same in all hot objects1 he has no more doubt of1 than another person has that there is always some cause or other4 ,in the present state of knowledge it could not be necessary1 even if we had not already treated so fully of the question1 to point out how widely this supposition is at variance with the truth4 ,it is particularly unfortunate for ,bacon that1 falling into this error1 he should have fixed almost exclusively upon a class of inquiries in which it was especially fatal2 namely1 inquiries into the causes of the sensible qualities of objects4 ,for his assumption1 groundless in every case1 is false in a peculiar degree with respect to those sensible qualities4 ,in regard to scarcely any of them has it been found possible to trace any unity of cause1 any set of conditions invariably accompanying the quality4 ,the conjunctions of such qualities with one another constitute the variety of ,kinds1 in which1 as already remarked1 it has not been found possible to trace any law4 ,bacon was seeking for what did not exist4 ,the phenomenon of which he sought for the one cause has oftenest no cause at all1 and when it has1 depends 7as far as hitherto ascertained7 on an unassignable variety of distinct causes4 ,and on this rock every one must split1 who represents to himself as the first and fundamental problem of science to ascertain what is the cause of a given effect1 rather than what are the effects of a given cause4 ,it was shown1 in an early stage of our inquiry into the nature of ,induction17#bdc7 how much more ample are the resources which science commands for the latter than for the former inquiry1 since it is upon the latter only that we can throw any direct light by means of experiment2 the power of artificially producing an effect1 implying a previous knowledge of at least one of its causes4 ,if we discover the causes of effects1 it is generally by having previously discovered the effects of causes2 the greatest skill in devising crucial instances for the former purpose may only end1 as ,bacon's physical inquiries did1 in no result at all4 ,was it that his eagerness to acquire the power of producing for man's benefit effects of practical importance to human life1 rendering him impatient of pursuing that end by a circuitous route1 made even him1 the champion of experiment1 prefer the direct mode1 though one of mere observation1 to the indirect1 in which alone experiment was possible8 ,or had even ,bacon not entirely cleared his mind from the notion of the ancients1 that 8rerum cognoscere causas0 was the sole object of philosophy1 and that to inquire into the effects of things belonged to servile and mechanical arts8 ,it is worth remarking that1 while the only efficient mode of cultivating speculative science was missed from an undue contempt of manual operations1 the false speculative views thus engendered gave in their turn a false direction to such practical and mechanical aims as were suffered to exist4 ,the assumption universal among the ancients and in the ,middle ,ages1 that there were principles of heat and cold1 dryness and moisture1 etc41 led directly to a belief in alchemy2 in a transmutation of substances1 a change from one ,kind into another4 ,why should it not be possible to make gold8 ,each of the characteristic properties of gold has its forma1 its essence1 its set of conditions1 which if we could discover1 and learn how to realize1 we could superinduce that particular property upon any other substance1 upon wood1 or iron1 or lime1 or clay4 ,if1 then1 we could effect this with respect to every one of the essential properties of the precious metal1 we should have converted the other substance into gold4 ,nor did this1 if once the premises were granted1 appear to transcend the real powers of mankind4 ,for daily experience showed that almost every one of the distinctive sensible properties of any object1 its consistence1 its color1 its taste1 its smell1 its shape1 admitted of being totally changed by fire1 or water1 or some other chemical agent4 ,the form of all those qualities seeming1 therefore1 to be within human power either to produce or to annihilate1 not only did the transmutation of substances appear abstractedly possible1 but the employment of the power1 at our choice1 for practical ends1 seemed by no means hopeless47#bdd7 ,a prejudice1 universal in the ancient world1 and from which ,bacon was so far from being free1 that it pervaded and vitiated the whole practical part of his system of logic1 may with good reason be ranked high in the order of ,fallacies of which we are now treating4 #h4 ,there remains one a priori fallacy or natural prejudice1 the most deeply-rooted1 perhaps1 of all which we have enumerated2 one which not only reigned supreme in the ancient world1 but still possesses almost undisputed dominion over many of the most cultivated minds2 and some of the most remarkable of the numerous instances by which ,i shall think it necessary to exemplify it1 will be taken from recent thinkers4 ,this is1 that the conditions of a phenomenon must1 or at least probably will1 resemble the phenomenon itself4 ,conformably to what we have before remarked to be of frequent occurrence1 this fallacy might without much impropriety have been placed in a different class1 among ,fallacies of ,generalization2 for experience does afford a certain degree of countenance to the assumption4 ,the cause does1 in very many cases1 resemble its effect2 like produces like4 ,many phenomena have a direct tendency to perpetuate their own existence1 or to give rise to other phenomena similar to themselves4 ,not to mention forms actually moulded on one another1 as impressions on wax and the like1 in which the closest resemblance between the effect and its cause is the very law of the phenomenon2 all motion tends to continue itself1 with its own velocity1 and in its own original direction2 and the motion of one body tends to set others in motion1 which is indeed the most common of the modes in which the motions of bodies originate4 ,we need scarcely refer to contagion1 fermentation1 and the like2 or to the production of effects by the growth or expansion of a germ or rudiment resembling on a smaller scale the completed phenomenon1 as in the growth of a plant or animal from an embryo1 that embryo itself deriving its origin from another plant or animal of the same kind4 ,again1 the thoughts or reminiscences1 which are effects of our past sensations1 resemble those sensations2 feelings produce similar feelings by way of sympathy2 acts produce similar acts by involuntary or voluntary imitation4 ,with so many appearances in its favor1 no wonder if a presumption naturally grew up1 that causes must necessarily resemble their effects1 and that like could only be produced by like4 ,this principle of fallacy has usually presided over the fantastical attempts to influence the course of nature by conjectural means1 the choice of which was not directed by previous observation and experiment4 ,the guess almost always fixed upon some means which possessed features of real or apparent resemblance to the end in view4 ,if a charm was wanted1 as by ,ovid's ,medea1 to prolong life1 all long-lived animals1 or what were esteemed such1 were collected and brewed into a broth3 nec defuit illic ,squamea ,cinyphii tenuis membrana chelydri ,vivacisque jecur cervi3 quibus insuper addit ,ora caputque novem cornicis scula pass4 ,a similar notion was embodied in the celebrated medical theory called the 8,doctrine of ,signatures10 8which is no less10 says ,dr4 ,paris17#bde7 8than a belief that every natural substance which possesses any medicinal virtue indicates by an obvious and well-marked external character the disease for which it is a remedy1 or the object for which it should be employed40 ,this outward character was generally some feature of resemblance1 real or fantastical1 either to the effect it was supposed to produce1 or to the phenomenon over which its power was thought to be exercised4 8,thus the lungs of a fox must be a specific for asthma1 because that animal is remarkable for its strong powers of respiration4 ,turmeric has a brilliant yellow color1 which indicates that it has the power of curing the jaundice2 for the same reason1 poppies must relieve diseases of the head2 ,agaricus those of the bladder2 ,cassia fistula the affections of the intestines1 and ,aristolochia the disorders of the uterus3 the polished surface and stony hardness which so eminently characterize the seeds of the ,lithospermum officinale 7common gromwell7 were deemed a certain indication of their efficacy in calculous and gravelly disorders2 for a similar reason1 the roots of the ,saxifraga granulata 7white saxifrage7 gained reputation in the cure of the same disease2 and the ,euphrasia 7eye-bright7 acquired fame1 as an application in complaints of the eye1 because it exhibits a black spot in its corolla resembling the pupil4 ,the blood-stone1 the ,heliotropium of the ancients1 from the occasional small specks or points of a blood-red color exhibited on its green surface1 is even at this very day employed in many parts of ,england and ,scotland to stop a bleeding from the nose2 and nettle tea continues a popular remedy for the cure of ,urticaria4 ,it is also asserted that some substances bear the signatures of the humors1 as the petals of the red rose that of the blood1 and the roots of rhubarb and the flowers of saffron that of the bile40 ,the early speculations respecting the chemical composition of bodies were rendered abortive by no circumstance more than by their invariably taking for granted that the properties of the elements must resemble those of the compounds which were formed from them4 ,to descend to more modern instances2 it was long thought1 and was stoutly maintained by the ,cartesians and even by ,leibnitz against the ,newtonian system 7nor did ,newton himself1 as we have seen1 contest the assumption1 but eluded it by an arbitrary hypothesis71 that nothing 7of a physical nature at least7 could account for motion1 except previous motion2 the impulse or impact of some other body4 ,it was very long before the scientific world could prevail upon itself to admit attraction and repulsion 7i4e41 spontaneous tendencies of particles to approach or recede from one another7 as ultimate laws1 no more requiring to be accounted for than impulse itself1 if indeed the latter were not1 in truth1 resolvable into the former4 ,from the same source arose the innumerable hypotheses devised to explain those classes of motion which appeared more mysterious than others because there was no obvious mode of attributing them to impulse1 as for example the voluntary motions of the human body4 ,such were the interminable systems of vibrations propagated along the nerves1 or animal spirits rushing up and down between the muscles and the brain2 which1 if the facts could have been proved1 would have been an important addition to our knowledge of physiological laws2 but the mere invention1 or arbitrary supposition of them1 could not unless by the strongest delusion be supposed to render the phenomena of animal life more comprehensible1 or less mysterious4 ,nothing1 however1 seemed satisfactory1 but to make out that motion was caused by motion2 by something like itself4 ,if it was not one kind of motion1 it must be another4 ,in like manner it was supposed that the physical qualities of objects must arise from some similar quality1 or perhaps only some quality bearing the same name1 in the particles or atoms of which the objects were composed2 that a sharp taste1 for example1 must arise from sharp particles4 ,and reversing the inference1 the effects produced by a phenomenon must1 it was supposed1 resemble in their physical attributes the phenomenon itself4 ,the influences of the planets were supposed to be analogous to their visible peculiarities3 ,mars1 being of a red color1 portended fire and slaughter2 and the like4 ,passing from physics to metaphysics1 we may notice among the most remarkable fruits of this a priori fallacy two closely analogous theories1 employed in ancient and modern times to bridge over the chasm between the world of mind and that of matter2 the species sensibiles of the ,epicureans1 and the modern doctrine of perception by means of ideas4 ,these theories are indeed1 probably1 indebted for their existence not solely to the fallacy in question1 but to that fallacy combined with another natural prejudice already adverted to1 that a thing can not act where it is not4 ,in both doctrines it is assumed that the phenomenon which takes place in us when we see or touch an object1 and which we regard as an effect of that object1 or rather of its presence to our organs1 must of necessity resemble very closely the outward object itself4 ,to fulfill this condition1 the ,epicureans supposed that objects were constantly projecting in all directions impalpable images of themselves1 which entered at the eyes and penetrated to the mind2 while modern metaphysicians1 though they rejected this hypothesis1 agreed in deeming it necessary to suppose that not the thing itself1 but a mental image or representation of it1 was the direct object of perception4 ,dr4 ,reid had to employ a world of argument and illustration to familiarize people with the truth1 that the sensations or impressions on our minds need not necessarily be copies of1 or bear any resemblance to1 the causes which produce them2 in opposition to the natural prejudice which led people to assimilate the action of bodies upon our senses1 and through them upon our minds1 to the transfer of a given form from one object to another by actual moulding4 ,the works of ,dr4 ,reid are even now the most effectual course of study for detaching the mind from the prejudice of which this was an example4 ,and the value of the service which he thus rendered to popular philosophy is not much diminished1 although we may hold1 with ,brown1 that he went too far in imputing the 8ideal theory0 as an actual tenet1 to the generality of the philosophers who preceded him1 and especially to ,locke and ,hume2 for if they did not themselves consciously fall into the error1 unquestionably they often led their readers into it4 ,the prejudice1 that the conditions of a phenomenon must resemble the phenomenon1 is occasionally exaggerated1 at least verbally1 into a still more palpable absurdity2 the conditions of the thing are spoken of as if they were the very thing itself4 ,in ,bacon's model inquiry1 which occupies so great a space in the ,novum ,organum1 the inquisitio in formam calidi1 the conclusion which he favors is that heat is a kind of motion2 meaning of course not the feeling of heat1 but the conditions of the feeling2 meaning1 therefore1 only that wherever there is heat1 there must first be a particular kind of motion2 but he makes no distinction in his language between these two ideas1 expressing himself as if heat1 and the conditions of heat1 were one and the same thing4 ,so the elder ,darwin1 in the beginning of his ,zoonomia1 says1 8,the word idea has various meanings in the writers of metaphysics2 it is here used simply for those notions of external things which our organs of sense bring us acquainted with originally0 7thus far the proposition1 though vague1 is unexceptionable in meaning71 8and is defined a contraction1 a motion1 or configuration1 of the fibres which constitute the immediate organ of sense40 ,our notions1 a configuration of the fibres6 ,what kind of logician must he be who thinks that a phenomenon is defined to be the condition on which he supposes it to depend8 ,accordingly he says soon after1 not that our ideas are caused by1 or consequent on1 certain organic phenomena1 but 8our ideas are animal motions of the organs of sense40 ,and this confusion runs through the four volumes of the ,zoonomia2 the reader never knows whether the writer is speaking of the effect1 or of its supposed cause2 of the idea1 a state of mental consciousness1 or of the state of the nerves and brain which he considers it to presuppose4 ,i have given a variety of instances in which the natural prejudice1 that causes and their effects must resemble one another1 has operated in practice so as to give rise to serious errors4 ,i shall now go further1 and produce from writings even of the present or very recent times1 instances in which this prejudice is laid down as an established principle4 ,m4 ,victor ,cousin1 in the last of his celebrated lectures on ,locke1 enunciates the maxim in the following unqualified terms3 8,tout ce qui est vrai de l'effet1 est vrai de la cause40 ,a doctrine to which1 unless in some peculiar and technical meaning of the words cause and effect1 it is not to be imagined that any person would literally adhere2 but he who could so write must be far enough from seeing that the very reverse might be the effect2 that there is nothing impossible in the supposition that no one property which is true of the effect might be true of the cause4 ,without going quite so far in point of expression1 ,coleridge1 in his ,biographia ,literaria17#bdf7 affirms as an 8evident truth10 that 8the law of causality holds only between homogeneous things1 i4e41 things having some common property10 and therefore 8can not extend from one world into another1 its opposite20 hence1 as mind and matter have no common property1 mind can not act upon matter1 nor matter upon mind4 ,what is this but the a priori fallacy of which we are speaking8 ,the doctrine1 like many others of ,coleridge1 is taken from ,spinoza1 in the first book of whose ,ethica 7,de ,deo7 it stands as the ,third ,proposition1 8,qu res nihil commune inter se habent1 earum una alterius causa esse non potest10 and is there proved from two so-called axioms1 equally gratuitous with itself2 but ,spinoza ever systematically consistent1 pursued the doctrine to its inevitable consequence1 the materiality of ,god4 ,the same conception of impossibility led the ingenious and subtle mind of ,leibnitz to his celebrated doctrine of a pre-established harmony4 ,he1 too1 thought that mind could not act upon matter1 nor matter upon mind1 and that the two1 therefore1 must have been arranged by their ,maker like two clocks1 which1 though unconnected with one another1 strike simultaneously1 and always point to the same hour4 ,malebranche's equally famous theory of ,occasional ,causes was another form of the same conception2 instead of supposing the clocks originally arranged to strike together1 he held that when the one strikes1 ,god interposes1 and makes the other strike in correspondence with it4 ,descartes1 in like manner1 whose works are a rich mine of almost every description of a priori fallacy1 says that the ,efficient ,cause must at least have all the perfections of the effect1 and for this singular reason3 8,si enim ponamus aliquid in ide reperiri quod non fuerit in ejus caus1 hoc igitur habet a nihilo20 of which it is scarcely a parody to say1 that if there be pepper in the soup there must be pepper in the cook who made it1 since otherwise the pepper would be without a cause4 ,a similar fallacy is committed by ,cicero1 in his second book ,de ,finibus1 where1 speaking in his own person against the ,epicureans1 he charges them with inconsistency in saying that the pleasures of the mind had their origin from those of the body1 and yet that the former were more valuable1 as if the effect could surpass the cause4 8,animi voluptas oritur propter voluptatem corporis1 et major est animi voluptas quam corporis8 ita fit ut gratulator1 ltior sit quam is cui gratulatur40 ,even that1 surely1 is not an impossibility2 a person's good fortune has often given more pleasure to others than it gave to the person himself4 ,descartes1 with no less readiness1 applies the same principle the converse way1 and infers the nature of the effects from the assumption that they must1 in this or that property or in all their properties1 resemble their cause4 ,to this class belong his speculations1 and those of so many others after him1 tending to infer the order of the universe1 not from observation1 but by a priori reasoning from supposed qualities of the ,godhead4 ,this sort of inference was probably never carried to a greater length than it was in one particular instance by ,descartes1 when1 as a proof of one of his physical principles1 that the quantity of motion in the universe is invariable1 he had recourse to the immutability of the ,divine ,nature4 ,reasoning of a very similar character is1 however1 nearly as common now as it was in his time1 and does duty largely as a means of fencing off disagreeable conclusions4 ,writers have not yet ceased to oppose the theory of divine benevolence to the evidence of physical facts1 to the principle of population for example4 ,and people seem in general to think that they have used a very powerful argument1 when they have said1 that to suppose some proposition true1 would be a reflection on the goodness or wisdom of the ,deity4 ,put into the simplest possible terms1 their argument is1 8,if it had depended on me1 ,i would not have made the proposition true1 therefore it is not true40 ,put into other words1 it stands thus3 8,god is perfect1 therefore 7what ,i think7 perfection must obtain in nature40 ,but since in reality every one feels that nature is very far from perfect1 the doctrine is never applied consistently4 ,it furnishes an argument which 7like many others of a similar character7 people like to appeal to when it makes for their own side4 ,nobody is convinced by it1 but each appears to think that it puts religion on his side of the question1 and that it is a useful weapon of offense for wounding an adversary4 ,although several other varieties of a priori fallacy might probably be added to those here specified1 these are all against which it seems necessary to give any special caution4 ,our object is to open1 without attempting or affecting to exhaust1 the subject4 ,having illustrated1 therefore1 this first class of ,fallacies at sufficient length1 ,i shall proceed to the second4 ,chapter ,,iv4 ,fallacies ,of ,observation4 #a4 ,from the ,fallacies which are properly ,prejudices1 or presumptions antecedent to1 and superseding1 proof1 we pass to those which lie in the incorrect performance of the proving process4 ,and as ,proof1 in its widest extent1 embraces one or more1 or all1 of three processes1 ,observation1 ,generalization1 and ,deduction1 we shall consider in their order the errors capable of being committed in these three operations4 ,and first1 of the first mentioned4 ,a fallacy of misobservation may be either negative or positive2 either ,non-observation or ,mal-observation4 ,it is non-observation1 when all the error consists in overlooking1 or neglecting1 facts or particulars which ought to have been observed4 ,it is mal-observation1 when something is not simply unseen1 but seen wrong2 when the fact or phenomenon1 instead of being recognized for what it is in reality1 is mistaken for something else4 #b4 ,non-observation may either take place by overlooking instances1 or by overlooking some of the circumstances of a given instance4 ,if we were to conclude that a fortune-teller was a true prophet1 from not adverting to the cases in which his predictions had been falsified by the event1 this would be non-observation of instances2 but if we overlooked or remained ignorant of the fact that in cases where the predictions had been fulfilled1 he had been in collusion with some one who had given him the information on which they were grounded1 this would be non-observation of circumstances4 ,the former case1 in so far as the act of induction from insufficient evidence is concerned1 does not fall under this second class of ,fallacies1 but under the third1 ,fallacies of ,generalization4 ,in every such case1 however1 there are two defects or errors instead of one2 there is the error of treating the insufficient evidence as if it were sufficient1 which is a ,fallacy of the third class2 and there is the insufficiency itself2 the not having better evidence2 which1 when such evidence1 or1 in other words1 when other instances1 were to be had1 is ,non-observation2 and the erroneous inference1 so far as it is to be attributed to this cause1 is a ,fallacy of the second class4 ,it belongs not to our purpose to treat of non-observation as arising from casual inattention1 from general slovenliness of mental habits1 want of due practice in the use of the observing faculties1 or insufficient interest in the subject4 ,the question pertinent to logic is--,granting the want of complete competency in the observer1 on what point is that insufficiency on his part likely to lead him wrong8 or rather1 what sorts of instances1 or of circumstances in any given instance1 are most likely to escape the notice of observers generally2 of mankind at large4 #c4 ,first1 then1 it is evident that when the instances on one side of a question are more likely to be remembered and recorded than those on the other2 especially if there be any strong motive to preserve the memory of the first1 but not of the latter2 these last are likely to be overlooked1 and escape the observation of the mass of mankind4 ,this is the recognized explanation of the credit given1 in spite of reason and evidence1 to many classes of impostors2 to quack-doctors1 and fortune-tellers in all ages2 to the 8cunning man0 of modern times1 and the oracles of old4 ,few have considered the extent to which this fallacy operates in practice1 even in the teeth of the most palpable negative evidence4 ,a striking example of it is the faith which the uneducated portion of the agricultural classes1 in this and other countries1 continue to repose in the prophecies as to weather supplied by almanac-makers2 though every season affords to them numerous cases of completely erroneous prediction2 but as every season also furnishes some cases in which the prediction is fulfilled1 this is enough to keep up the credit of the prophet1 with people who do not reflect on the number of instances requisite for what we have called1 in our inductive terminology1 the ,elimination of ,chance2 since a certain number of casual coincidences not only may but will happen1 between any two unconnected events4 ,coleridge1 in one of the essays in the ,friend1 has illustrated the matter we are now considering1 in discussing the origin of a proverb1 8which1 differently worded1 is to be found in all the languages of ,europe10 viz41 8,fortune favors fools40 ,he ascribes it partly to the 8tendency to exaggerate all effects that seem disproportionate to their visible cause1 and all circumstances that are in any way strongly contrasted with our notions of the persons under them40 ,omitting some explanations which would refer the error to mal-observation1 or to the other species of non-observation 7that of circumstances71 ,i take up the quotation further on4 8,unforeseen coincidences may have greatly helped a man1 yet if they have done for him only what possibly from his own abilities he might have effected for himself1 his good luck will excite less attention1 and the instances be less remembered4 ,that clever men should attain their objects seems natural1 and we neglect the circumstances that perhaps produced that success of themselves without the intervention of skill or foresight2 but we dwell on the fact and remember it1 as something strange1 when the same happens to a weak or ignorant man4 ,so too1 though the latter should fail in his undertakings from concurrences that might have happened to the wisest man1 yet his failure being no more than might have been expected and accounted for from his folly1 it lays no hold on our attention1 but fleets away among the other undistinguished waves in which the stream of ordinary life murmurs by us1 and is forgotten4 ,had it been as true as it was notoriously false1 that those all-embracing discoveries1 which have shed a dawn of science on the art of chemistry1 and give no obscure promise of some one great constitutive law1 in the light of which dwell dominion and the power of prophecy2 if these discoveries1 instead of having been1 as they really were1 preconcerted by meditation1 and evolved out of his own intellect1 had occurred by a set of lucky accidents to the illustrious father and founder of philosophic alchemy2 if they had presented themselves to ,professor ,davy exclusively in consequence of his luck in possessing a particular galvanic battery2 if this battery1 as far as ,davy was concerned1 had itself been an accident1 and not 7as in point of fact it was7 desired and obtained by him for the purpose of insuring the testimony of experience to his principles1 and in order to bind down material nature under the inquisition of reason1 and force from her1 as by torture1 unequivocal answers to prepared and preconceived questions--yet still they would not have been talked of or described as instances of luck1 but as the natural results of his admitted genius and known skill4 ,but should an accident have disclosed similar discoveries to a mechanic at ,birmingham or ,sheffield1 and if the man should grow rich in consequence1 and partly by the envy of his neighbors and partly with good reason1 be considered by them as a man below par in the general powers of his understanding2 then1 #8,oh1 what a lucky fellow6 ,well1 ,fortune does favor fools--that's for certain6 ,it is always so6' ,and forthwith the exclaimer relates half a dozen similar instances4 ,thus accumulating the one sort of facts and never collecting the other1 we do1 as poets in their diction1 and quacks of all denominations do in their reasoning1 put a part for the whole40 ,this passage very happily sets forth the manner in which1 under the loose mode of induction which proceeds per enumerationem simplicem1 not seeking for instances of such a kind as to be decisive of the question1 but generalizing from any which occur1 or rather which are remembered1 opinions grow up with the apparent sanction of experience1 which have no foundation in the laws of nature at all4 8,itaque recte respondit ille0 7we may say with ,bacon7#bdg771 8qui cum suspensa tabula in templo ei monstraretur eorum1 qui vota solverant1 quod naufragii periculo elapsi sint1 atque interrogando premeretur1 anne tum quidem ,deorum numen agnosceret1 qusivit denuo1 ,at ubi sunt illi depicti qui post vota nuncupata perierunt8 ,eadem ratio est fere omnis superstitionis1 ut in ,astrologicis1 in ,somniis1 ,ominibus1 ,nemesibus1 et hujusmodi2 in quibus1 homines delectati hujusmodi vanitatibus1 advertunt eventus1 ubi implentur2 ast ubi fallunt1 licet multo frequentius1 tamen negligunt1 et prtereunt40 ,and he proceeds to say that1 independently of the love of the marvelous1 or any other bias in the inclinations1 there is a natural tendency in the intellect itself to this kind of fallacy2 since the mind is more moved by affirmative instances1 though negative ones are of most use in philosophy3 8,is tamen humano intellectui error est proprius et perpetuus1 ut magis moveatur et excitetur ,affirmativis quam ,negativis2 cum rite et ordine quum se utrique prbere debeat2 quin contra1 in omni ,axiomate vero constituendo1 major vis est instanti negativ40 ,but the greatest of all causes of non-observation is a preconceived opinion4 ,this it is which1 in all ages1 has made the whole race of mankind1 and every separate section of it1 for the most part unobservant of all facts1 however abundant1 even when passing under their own eyes1 which are contradictory to any first appearance1 or any received tenet4 ,it is worth while to recall occasionally to the oblivious memory of mankind some of the striking instances in which opinions that the simplest experiment would have shown to be erroneous1 continued to be entertained because nobody ever thought of trying that experiment4 ,one of the most remarkable of these was exhibited in the ,copernican controversy4 ,the opponents of ,copernicus argued that the earth did not move1 because if it did1 a stone let fall from the top of a high tower would not reach the ground at the foot of the tower1 but at a little distance from it1 in a contrary direction to the earth's course2 in the same manner 7said they7 as1 if a ball is let drop from the mast-head while the ship is in full sail1 it does not fall exactly at the foot of the mast1 but nearer to the stern of the vessel4 ,the ,copernicans would have silenced these objectors at once if they had tried dropping a ball from the mast-head1 since they would have found that it does fall exactly at the foot1 as the theory requires2 but no2 they admitted the spurious fact1 and struggled vainly to make out a difference between the two cases4 8,the ball was no part of the ship--and the motion forward was not natural1 either to the ship or to the ball4 ,the stone1 on the other hand1 let fall from the top of the tower1 was a part of the earth2 and therefore1 the diurnal and annular revolutions which were natural to the earth1 were also natural to the stone2 the stone would1 therefore1 retain the same motion with the tower1 and strike the ground precisely at the bottom of it407#bdh7 ,other examples1 scarcely less striking1 are recorded by ,dr4 ,whewell17#bdi7 where imaginary laws of nature have continued to be received as real1 merely because no person had steadily looked at facts which almost every one had the opportunity of observing4 8,a vague and loose mode of looking at facts very easily observable1 left men for a long time under the belief that a body ten times as heavy as another falls ten times as fast2 that objects immersed in water are always magnified1 without regard to the form of the surface2 that the magnet exerts an irresistible force2 that crystal is always found associated with ice2 and the like4 ,these and many others are examples how blind and careless man can be even in observation of the plainest and commonest appearances2 and they show us that the mere faculties of perception1 although constantly exercised upon innumerable objects1 may long fail in leading to any exact knowledge40 ,if even on physical facts1 and these of the most obvious character1 the observing faculties of mankind can be to this degree the passive slaves of their preconceived impressions1 we need not be surprised that this should be so lamentably true as all experience attests it to be1 on things more nearly connected with their stronger feelings--on moral1 social1 and religious subjects4 ,the information which an ordinary traveler brings back from a foreign country1 as the result of the evidence of his senses1 is almost always such as exactly confirms the opinions with which he set out4 ,he has had eyes and ears for such things only as he expected to see4 ,men read the sacred books of their religion1 and pass unobserved therein multitudes of things utterly irreconcilable with even their own notions of moral excellence4 ,with the same authorities before them1 different historians1 alike innocent of intentional misrepresentation1 see only what is favorable to ,protestants or ,catholics1 royalists or republicans1 ,charles ,i4 or ,cromwell2 while others1 having set out with the preconception that extremes must be in the wrong1 are incapable of seeing truth and justice when these are wholly on one side4 ,the influence of a preconceived theory is well exemplified in the superstitions of barbarians respecting the virtues of medicaments and charms4 ,the negroes1 among whom coral1 as of old among ourselves1 is worn as an amulet1 affirm1 according to ,dr4 ,paris17#bej7 that its color 8is always affected by the state of health of the wearer1 it becoming paler in disease40 ,on a matter open to universal observation1 a general proposition which has not the smallest vestige of truth is received as a result of experience2 the preconceived opinion preventing1 it would seem1 any observation whatever on the subject4 #d4 ,for illustration of the first species of non-observation1 that of ,instances1 what has now been stated may suffice4 ,but there may also be non-observation of some material circumstances1 in instances which have not been altogether overlooked--nay1 which may be the very instances on which the whole superstructure of a theory has been founded4 ,as1 in the cases hitherto examined1 a general proposition was too rashly adopted1 on the evidence of particulars1 true indeed1 but insufficient to support it2 so in the cases to which we now turn1 the particulars themselves have been imperfectly observed1 and the singular propositions on which the generalization is grounded1 or some at least of those singular propositions1 are false4 ,such1 for instance1 was one of the mistakes committed in the celebrated phlogistic theory2 a doctrine which accounted for combustion by the extrication of a substance called phlogiston1 supposed to be contained in all combustible matter4 ,the hypothesis accorded tolerably well with superficial appearances2 the ascent of flame naturally suggests the escape of a substance2 and the visible residuum of ashes1 in bulk and weight1 generally falls extremely short of the combustible material4 ,the error was1 non-observation of an important portion of the actual residue1 namely1 the gaseous products of combustion4 ,when these were at last noticed and brought into account1 it appeared to be a universal law1 that all substances gain instead of losing weight by undergoing combustion2 and after the usual attempt to accommodate the old theory to the new fact by means of an arbitrary hypothesis 7that phlogiston had the quality of positive levity instead of gravity71 chemists were conducted to the true explanation1 namely1 that instead of a substance separated1 there was1 on the contrary1 a substance absorbed4 ,many of the absurd practices which have been deemed to possess medicinal efficacy1 have been indebted for their reputation to non-observance of some accompanying circumstance which was the real agent in the cures ascribed to them4 ,thus1 of the sympathetic powder of ,sir ,kenelm ,digby3 8,whenever any wound had been inflicted1 this powder was applied to the weapon that had inflicted it1 which was1 moreover1 covered with ointment1 and dressed two or three times a day4 ,the wound itself1 in the mean time1 was directed to be brought together1 and carefully bound up with clean linen rags1 but1 above all1 to be let alone for seven days1 at the end of which period the bandages were removed1 when the wound was generally found perfectly united4 ,the triumph of the cure was decreed to the mysterious agency of the sympathetic powder which had been so assiduously applied to the weapon1 whereas it is hardly necessary to observe that the promptness of the cure depended on the total exclusion of air from the wound1 and upon the sanative operations of nature not having received any disturbance from the officious interference of art4 ,the result1 beyond all doubt1 furnished the first hint which led surgeons to the improved practice of healing wounds by what is technically called the first intention407#bea7 8,in all records10 adds ,dr4 ,paris1 of 8extraordinary cures performed by mysterious agents1 there is a great desire to conceal the remedies and other curative means which were simultaneously administered with them2 thus ,oribasius commends in high terms a necklace of ,pony root for the cure of epilepsy2 but we learn that he always took care to accompany its use with copious evacuations1 although he assigns to them no share of credit in the cure4 ,in later times we have a good specimen of this species of deception1 presented to us in a work on scrofula by ,mr4 ,morley1 written1 as we are informed1 for the sole purpose of restoring the much-injured character and use of the ,vervain2 in which the author directs the root of this plant to be tied with a yard of white satin ribbon around the neck1 where it is to remain until the patient is cured2 but mark--during this interval he calls to his aid the most active medicines in the materia medica407#beb7 ,in other cases1 the cures really produced by rest1 regimen1 and amusement have been ascribed to the medicinal1 or occasionally to the supernatural1 means which were put in requisition4 8,the celebrated ,john ,wesley1 while he commemorates the triumph of sulphur and supplication over his bodily infirmity1 forgets to appreciate the resuscitating influence of four months' repose from his apostolic labors2 and such is the disposition of the human mind to place confidence in the operation of mysterious agents1 that we find him more disposed to attribute his cure to a brown paper plaster of egg and brimstone1 than to ,dr4 ,fothergill's salutary prescription of country air1 rest1 asses' milk1 and horse exercise407#bec7 ,in the following example1 the circumstance overlooked was of a somewhat different character4 8,when the yellow fever raged in ,america1 the practitioners trusted exclusively to the copious use of mercury2 at first this plan was deemed so universally efficacious1 that1 in the enthusiasm of the moment1 it was triumphantly proclaimed that death never took place after the mercury had evinced its effect upon the system3 all this was very true1 but it furnished no proof of the efficacy of that metal1 since the disease in its aggravated form was so rapid in its career1 that it swept away its victims long before the system could be brought under mercurial influence1 while in its milder shape it passed off equally well without any assistance from art407#bed7 ,in these examples the circumstance overlooked was cognizable by the senses4 ,in other cases1 it is one the knowledge of which could only be arrived at by reasoning2 but the fallacy may still be classed under the head to which1 for want of a more appropriate name1 we have given the appellation ,fallacies of ,non-observation4 ,it is not the nature of the faculties which ought to have been employed1 but the non-employment of them1 which constitutes this ,natural ,order of ,fallacies4 ,wherever the error is negative1 not positive2 wherever it consists especially in overlooking1 in being ignorant or unmindful of some fact which1 if known and attended to1 would have made a difference in the conclusion arrived at2 the error is properly placed in the ,class which we are considering4 ,in this ,class1 there is not1 as in all other fallacies there is1 a positive misestimate of evidence actually had4 ,the conclusion would be just1 if the portion which is seen of the case were the whole of it2 but there is another portion overlooked1 which vitiates the result4 ,for instance1 there is a remarkable doctrine which has occasionally found a vent in the public speeches of unwise legislators1 but which only in one instance that ,i am aware of has received the sanction of a philosophical writer1 namely1 ,m4 ,cousin1 who in his preface to the ,gorgias of ,plato1 contending that punishment must have some other and higher justification than the prevention of crime1 makes use of this argument--that if punishment were only for the sake of example1 it would be indifferent whether we punished the innocent or the guilty1 since the punishment1 considered as an example1 is equally efficacious in either case4 ,now we must1 in order to go along with this reasoning1 suppose1 that the person who feels himself under temptation1 observing somebody punished1 concludes himself to be in danger of being punished likewise1 and is terrified accordingly4 ,but it is forgotten that if the person punished is supposed to be innocent1 or even if there be any doubt of his guilt1 the spectator will reflect that his own danger1 whatever it may be1 is not contingent on his guiltiness1 but threatens him equally if he remains innocent1 and how1 therefore1 is he deterred from guilt by the apprehension of such punishment8 ,m4 ,cousin supposes that people will be dissuaded from guilt by whatever renders the condition of the guilty more perilous1 forgetting that the condition of the innocent 7also one of the elements in the calculation7 is1 in the case supposed1 made perilous in precisely an equal degree4 ,this is a fallacy of overlooking2 or of non-observation1 within the intent of our classification4 ,fallacies of this description are the great stumbling-block to correct thinking in political economy4 ,the economical workings of society afford numerous cases in which the effects of a cause consist of two sets of phenomena3 the one immediate1 concentrated1 obvious to all eyes1 and passing1 in common apprehension1 for the whole effect2 the other widely diffused1 or lying deeper under the surface1 and which is exactly contrary to the former4 ,take1 for instance1 the common notion so plausible at the first glance1 of the encouragement given to industry by lavish expenditure4 ,a1 who spends his whole income1 and even his capital1 in expensive living1 is supposed to give great employment to labor4 ,b1 who lives on a small portion1 and invests the remainder in the funds1 is thought to give little or no employment4 ,for every body sees the gains which are made by ,a's tradesmen1 servants1 and others1 while his money is spending4 ,b's savings1 on the contrary1 pass into the hands of the person whose stock he purchased1 who with it pays a debt he owed to some banker1 who lends it again to some merchant or manufacturer2 and the capital being laid out in hiring spinners and weavers1 or carriers and the crews of merchant vessels1 not only gives immediate employment to at least as much industry as ,a employs during the whole of his career1 but coming back with increase by the sale of the goods which have been manufactured or imported1 forms a fund for the employment of the same and perhaps a greater quantity of labor in perpetuity4 ,but the observer does not see1 and therefore does not consider1 what becomes of ,b's money2 he does see what is done with ,a's2 he observes the amount of industry which ,a's profusion feeds2 he observes not the far greater quantity which it prevents from being fed2 and thence the prejudice1 universal to the time of ,adam ,smith1 that prodigality encourages industry1 and parsimony is a discouragement to it4 ,the common argument against free trade was a fallacy of the same nature4 ,the purchaser of ,british silk encourages ,british industry2 the purchaser of ,lyons silk encourages only ,french2 the former conduct is patriotic1 the latter ought to be prevented by law4 ,the circumstance is overlooked1 that the purchaser of any foreign commodity necessarily causes1 directly or indirectly1 the export of an equivalent value of some article of home production 7beyond what would otherwise be exported71 either to the same foreign country or to some other2 which fact1 though from the complication of the circumstances it can not always be verified by specific observation1 no observation can possibly be brought to contradict1 while the evidence of reasoning on which it rests is irrefragable4 ,the fallacy is1 therefore1 the same as in the preceding case1 that of seeing a part only of the phenomena1 and imagining that part to be the whole2 and may be ranked among ,fallacies of ,non-observation4 #e4 ,to complete the examination of the second of our five classes1 we have now to speak of ,mal-observation2 in which the error does not lie in the fact that something is unseen1 but that something seen is seen wrong4 ,perception being infallible evidence of whatever is really perceived1 the error now under consideration can be committed no otherwise than by mistaking for conception what is1 in fact1 inference4 ,we have formerly shown how intimately the two are blended in almost every thing which is called observation1 and still more in every ,description47#bee7 ,what is actually on any occasion perceived by our senses being so minute in amount1 and generally so unimportant a portion of the state of facts which we wish to ascertain or to communicate2 it would be absurd to say that either in our observations1 or in conveying their result to others1 we ought not to mingle inference with fact2 all that can be said is1 that when we do so we ought to be aware of what we are doing1 and to know what part of the assertion rests on consciousness1 and is therefore indisputable1 what part on inference1 and is therefore questionable4 ,one of the most celebrated examples of a universal error produced by mistaking an inference for the direct evidence of the senses1 was the resistance made1 on the ground of common sense1 to the ,copernican system4 ,people fancied they saw the sun rise and set1 the stars revolve in circles round the pole4 ,we now know that they saw no such thing2 what they really saw was a set of appearances1 equally reconcilable with the theory they held and with a totally different one4 ,it seems strange that such an instance as this of the testimony of the senses pleaded with the most entire conviction in favor of something which was a mere inference of the judgment1 and1 as it turned out1 a false inference1 should not have opened the eyes of the bigots of common sense1 and inspired them with a more modest distrust of the competency of mere ignorance to judge the conclusions of cultivated thought4 ,in proportion to any person's deficiency of knowledge and mental cultivation is1 generally1 his inability to discriminate between his inferences and the perceptions on which they were grounded4 ,many a marvelous tale1 many a scandalous anecdote1 owes its origin to this incapacity4 ,the narrator relates1 not what he saw or heard1 but the impression which he derived from what he saw or heard1 and of which perhaps the greater part consisted of inference1 though the whole is related1 not as inference but as matter of fact4 ,the difficulty of inducing witnesses to restrain within any moderate limits the intermixture of their inferences with the narrative of their perceptions1 is well known to experienced cross-examiners2 and still more is this the case when ignorant persons attempt to describe any natural phenomenon4 8,the simplest narrative10 says ,dugald ,stewart17#bef7 8of the most illiterate observer involves more or less of hypothesis2 nay1 in general1 it will be found that1 in proportion to his ignorance1 the greater is the number of conjectural principles involved in his statements4 ,a village apothecary 7and1 if possible1 in a still greater degree1 an experienced nurse7 is seldom able to describe the plainest case1 without employing a phraseology of which every word is a theory3 whereas a simple and genuine specification of the phenomena which mark a particular disease2 a specification unsophisticated by fancy1 or by preconceived opinions1 may be regarded as unequivocal evidence of a mind trained by long and successful study to the most difficult of all arts1 that of the faithful interpretation of nature40 ,the universality of the confusion between perceptions and the inferences drawn from them1 and the rarity of the power to discriminate the one from the other1 ceases to surprise us when we consider that in the far greater number of instances the actual perceptions of our senses are of no importance or interest to us except as marks from which we infer something beyond them4 ,it is not the color and superficial extension perceived by the eye that are important to us1 but the object1 of which those visible appearances testify the presence2 and where the sensation itself is indifferent1 as it generally is1 we have no motive to attend particularly to it1 but acquire a habit of passing it over without distinct consciousness1 and going on at once to the inference4 ,so that to know what the sensation actually was1 is a study in itself1 to which painters1 for example1 have to train themselves by special and long-continued discipline and application4 ,in things farther removed from the dominion of the outward senses1 no one who has not great experience in psychological analysis is competent to break this intense association2 and when such analytic habits do not exist in the requisite degree1 it is hardly possible to mention any of the habitual judgments of mankind on subjects of a high degree of abstraction1 from the being of a ,god and the immortality of the soul down to the multiplication table1 which are not1 or have not been1 considered as matter of direct intuition4 ,so strong is the tendency to ascribe an intuitive character to judgments which are mere inferences1 and often false ones4 ,no one can doubt that many a deluded visionary has actually believed that he was directly inspired from ,heaven1 and that the ,almighty had conversed with him face to face2 which yet was only1 on his part1 a conclusion drawn from appearances to his senses1 or feelings in his internal consciousness1 which afforded no warrant for any such belief4 ,a caution1 therefore1 against this class of errors1 is not only needful but indispensable2 though to determine whether1 on any of the great questions of metaphysics1 such errors are actually committed1 belongs not to this place1 but1 as ,i have so often said1 to a different science4 ,chapter ,v4 ,fallacies ,of ,generalization4 #a4 ,the class of ,fallacies of which we are now to speak1 is the most extensive of all2 embracing a greater number and variety of unfounded inferences than any of the other classes1 and which it is even more difficult to reduce to sub-classes or species4 ,if the attempt made in the preceding books to define the principles of well-grounded generalization has been successful1 all generalizations not conformable to those principles might1 in a certain sense1 be brought under the present class2 when1 however1 the rules are known and kept in view1 but a casual lapse committed in the application of them1 this is a blunder1 not a fallacy4 ,to entitle an error of generalization to the latter epithet1 it must be committed on principle2 there must lie in it some erroneous general conception of the inductive process2 the legitimate mode of drawing conclusions from observation and experiment must be fundamentally misconceived4 ,without attempting any thing so chimerical as an exhaustive classification of all the misconceptions which can exist on the subject1 let us content ourselves with noting1 among the cautions which might be suggested1 a few of the most useful and needful4 #b4 ,in the first place1 there are certain kinds of generalization which1 if the principles already laid down be correct1 must be groundless2 experience can not afford the necessary conditions for establishing them by a correct induction4 ,such1 for instance1 are all inferences from the order of nature existing on the earth1 or in the solar system1 to that which may exist in remote parts of the universe2 where the phenomena1 for aught we know1 may be entirely different1 or may succeed one another according to different laws1 or even according to no fixed law at all4 ,such1 again1 in matters dependent on causation1 are all universal negatives1 all propositions that assert impossibility4 ,the non-existence of any given phenomenon1 however uniformly experience may as yet have testified to the fact1 proves at most that no cause1 adequate to its production1 has yet manifested itself2 but that no such causes exist in nature can only be inferred if we are so foolish as to suppose that we know all the forces in nature4 ,the supposition would at least be premature while our acquaintance with some even of those which we do know is so extremely recent4 ,and however much our knowledge of nature may hereafter be extended1 it is not easy to see how that knowledge could ever be complete1 or how1 if it were1 we could ever be assured of its being so4 ,the only laws of nature which afford sufficient warrant for attributing impossibility 7even with reference to the existing order of nature1 and to our own region of the universe7 are1 first1 those of number and extension1 which are paramount to the laws of the succession of phenomena1 and not exposed to the agency of counteracting causes2 and1 secondly1 the universal law of causality itself4 ,that no valuation in any effect or consequent will take place while the whole of the antecedents remain the same1 may be affirmed with full assurance4 ,but1 that the addition of some new antecedent might not entirely alter and subvert the accustomed consequent1 or that antecedents competent to do this do not exist in nature1 we are in no case empowered positively to conclude4 #c4 ,it is next to be remarked that all generalizations which profess1 like the theories of ,thales1 ,democritus1 and others of the early ,greek speculators1 to resolve all things into some one element1 or like many modern theories1 to resolve phenomena radically different into the same1 are necessarily false4 ,by radically different phenomena ,i mean impressions on our senses which differ in quality1 and not merely in degree4 ,on this subject what appeared necessary was said in the chapter on the ,limits to the ,explanation of ,laws of ,nature2 but as the fallacy is even in our own times a common one1 ,i shall touch on it somewhat further in this place4 ,when we say that the force which retains the planets in their orbits is resolved into gravity1 or that the force which makes substances combine chemically is resolved into electricity1 we assert in the one case what is1 and in the other case what might1 and probably will ultimately1 be a legitimate result of induction4 ,in both these cases motion is resolved into motion4 ,the assertion is1 that a case of motion1 which was supposed to be special1 and to follow a distinct law of its own1 conforms to and is included in the general law which regulates another class of motions4 ,but1 from these and similar generalizations1 countenance and currency have been given to attempts to resolve1 not motion into motion1 but heat into motion1 light into motion1 sensation itself into motion2 states of consciousness into states of the nervous system1 as in the ruder forms of the materialist philosophy2 vital phenomena into mechanical or chemical processes1 as in some schools of physiology4 ,now ,i am far from pretending that it may not be capable of proof1 or that it is not an important addition to our knowledge if proved1 that certain motions in the particles of bodies are the conditions of the production of heat or light2 that certain assignable physical modifications of the nerves may be the conditions not only of our sensations or emotions1 but even of our thoughts2 that certain mechanical and chemical conditions may1 in the order of nature1 be sufficient to determine to action the physiological laws of life4 ,all ,i insist upon1 in common with every thinker who entertains any clear idea of the logic of science1 is1 that it shall not be supposed that by proving these things one step would be made toward a real explanation of heat1 light1 or sensation2 or that the generic peculiarity of those phenomena can be in the least degree evaded by any such discoveries1 however well established4 ,let it be shown1 for instance1 that the most complex series of physical causes and effects succeed one another in the eye and in the brain to produce a sensation of color2 rays falling on the eye1 refracted1 converging1 crossing one another1 making an inverted image on the retina1 and after this a motion--let it be a vibration1 or a rush of nervous fluid1 or whatever else you are pleased to suppose1 along the optic nerve--a propagation of this motion to the brain itself1 and as many more different motions as you choose2 still1 at the end of these motions1 there is something which is not motion1 there is a feeling or sensation of color4 ,whatever number of motions we may be able to interpolate1 and whether they be real or imaginary1 we shall still find1 at the end of the series1 a motion antecedent and a color consequent4 ,the mode in which any one of the motions produces the next1 may possibly be susceptible of explanation by some general law of motion3 but the mode in which the last motion produces the sensation of color1 can not be explained by any law of motion2 it is the law of color3 which is1 and must always remain1 a peculiar thing4 ,where our consciousness recognizes between two phenomena an inherent distinction2 where we are sensible of a difference which is not merely of degree1 and feel that no adding one of the phenomena to itself would produce the other2 any theory which attempts to bring either under the laws of the other must be false2 though a theory which merely treats the one as a cause or condition of the other1 may possibly be true4 #d4 ,among the remaining forms of erroneous generalization1 several of those most worthy of and most requiring notice have fallen under our examination in former places1 where1 in investigating the rules of correct induction1 we have had occasion to advert to the distinction between it and some common mode of the incorrect4 ,in this number is what ,i have formerly called the natural ,induction of uninquiring minds1 the induction of the ancients1 which proceeds per enumerationem simplicem3 8,this1 that1 and the other ,a are ,b1 ,i can not think of any ,a which is not ,b1 therefore every ,a is ,b40 ,as a final condemnation of this rude and slovenly mode of generalization1 ,i will quote ,bacon's emphatic denunciation of it2 the most important part1 as ,i have more than once ventured to assert1 of the permanent service rendered by him to philosophy4 8,inductio qu procedit per enumerationem simplicem1 res puerilis est1 et precario concludit0 7concludes only by your leave1 or provisionally71 8et periculo exponitur ab instanti contradictori1 et plerumque secundum pauciora quam par est1 et ex his tantummodo qu prsto sunt pronunciat4 ,at ,inductio qu ad inventionem et demonstrationem ,scientiarum et ,artium erit utilis1 ,naturam separare debet1 per rejectiones et exclusiones debitas2 ac deinde post negativas tot quot sufficiunt1 super affirmativas concludere40 ,i have already said that the mode of ,simple ,enumeration is still the common and received method of ,induction in whatever relates to man and society4 ,of this a very few instances1 more by way of memento than of instruction1 may suffice4 ,what1 for example1 is to be thought of all the 8common-sense0 maxims for which the following may serve as the universal formula1 8,whatsoever has never been1 will never be40 ,as for example3 negroes have never been as civilized as whites sometimes are1 therefore it is impossible they should be so4 ,women1 as a class1 are supposed not to have hitherto been equal in intellect to men1 therefore they are necessarily inferior4 ,society can not prosper without this or the other institution2 e4g41 in ,aristotle's time1 without slavery2 in later times1 without an established priesthood1 without artificial distinctions of rank1 etc4 ,one poor person in a thousand1 educated1 while the nine hundred and ninety-nine remain uneducated1 has usually aimed at raising himself out of his class1 therefore education makes people dissatisfied with the condition of a laborer4 ,bookish men1 taken from speculative pursuits and set to work on something they know nothing about1 have generally been found or thought to do it ill2 therefore philosophers are unfit for business1 etc41 etc4 ,all these are inductions by simple enumeration4 ,reasons having some reference to the canons of scientific investigation have been attempted to be given1 however unsuccessfully1 for some of these propositions2 but to the multitude of those who parrot them1 the enumeratio simplex1 ex his tantummodo qu prsto sunt pronuncians1 is the sole evidence4 ,their fallacy consists in this1 that they are inductions without elimination3 there has been no real comparison of instances1 nor even ascertainment of the material facts in any given instance4 ,there is also the further error1 of forgetting that such generalizations1 even if well established1 could not be ultimate truths1 but must be results of laws much more elementary2 and therefore1 until deduced from such1 could at most be admitted as empirical laws1 holding good within the limits of space and time by which the particular observations that suggested the generalization were bounded4 ,this error1 of placing mere empirical laws1 and laws in which there is no direct evidence of causation1 on the same footing of certainty as laws of cause and effect1 an error which is at the root of perhaps the greater number of bad inductions1 is exemplified only in its grossest form in the kind of generalizations to which we have now referred4 ,these1 indeed1 do not possess even the degree of evidence which pertains to a well-ascertained empirical law2 but admit of refutation on the empirical ground itself1 without ascending to casual laws4 ,a little reflection1 indeed1 will show that mere negations can only form the ground of the lowest and least valuable kind of empirical law4 ,a phenomenon has never been noticed2 this only proves that the conditions of that phenomenon have not yet occurred in experience1 but does not prove that they may not occur hereafter4 ,there is a better kind of empirical law than this1 namely1 when a phenomenon which is observed presents within the limits of observation a series of gradations1 in which a regularity1 or something like a mathematical law1 is perceptible2 from which1 therefore1 something may be rationally presumed as to those terms of the series which are beyond the limits of observation4 ,but in negation there are no gradations1 and no series2 the generalizations1 therefore1 which deny the possibility of any given condition of man and society merely because it has never yet been witnessed1 can not possess this higher degree of validity even as empirical laws4 ,what is more1 the minuter examination which that higher order of empirical laws presupposes1 being applied to the subject-matter of these1 not only does not confirm but actually refutes them4 ,for in reality the past history of ,man and ,society1 instead of exhibiting them as immovable1 unchangeable1 incapable of ever presenting new phenomena1 shows them1 on the contrary1 to be1 in many most important particulars1 not only changeable1 but actually undergoing a progressive change4 ,the empirical law1 therefore1 best expressive1 in most cases1 of the genuine result of observation1 would be1 not that such and such a phenomenon will continue unchanged1 but that it will continue to change in some particular manner4 ,accordingly1 while almost all generalizations relating to ,man and ,society1 antecedent to the last fifty or sixty years1 have erred in the gross way which we have attempted to characterize1 namely1 by implicitly assuming that nature and society will forever revolve in the same orbit1 and exhibit essentially the same phenomena2 which is also the vulgar error of the ostentatiously practical1 the votaries of so-called common sense1 in our day1 especially in ,great ,britain2 the more thinking minds of the present age1 having applied a more minute analysis to the past records of our race1 have for the most part adopted a contrary opinion1 that the human species is in a state of necessary progression1 and that from the terms of the series which are past we may infer positively those which are yet to come4 ,of this doctrine1 considered as a philosophical tenet1 we shall have occasion to speak more fully in the concluding ,book4 ,if not1 in all its forms1 free from error1 it is at least free from the gross and error which we previously exemplified4 ,but1 in all except the most eminently philosophical minds1 it is infected with precisely the same kind of fallacy as that is4 ,for we must remember that even this other and better generalization1 the progressive change in the condition of the human species1 is1 after all1 but an empirical law2 to which1 too1 it is not difficult to point out exceedingly large exceptions2 and even if these could be got rid of1 either by disputing the facts or by explaining and limiting the theory1 the general objection remains valid against the supposed law1 as applicable to any other than what1 in our third book1 were termed ,adjacent ,cases4 ,for not only is it no ultimate1 but not even a causal law4 ,changes do indeed take place in human affairs1 but every one of those changes depends on determinate causes2 the 8progressiveness of the species0 is not a cause1 but a summary expression for the general result of all the causes4 ,so soon as1 by a quite different sort of induction1 it shall be ascertained what causes have produced these successive changes1 from the beginning of history1 in so far as they have really taken place1 and by what causes of a contrary tendency they have been occasionally checked or entirely counteracted1 we may then be prepared to predict the future with reasonable foresight2 we may be in possession of the real law of the future2 and may be able to declare on what circumstances the continuance of the same onward movement will eventually depend4 ,but this it is the error of many of the more advanced thinkers1 in the present age1 to overlook2 and to imagine that the empirical law collected from a mere comparison of the condition of our species at different past times1 is a real law1 is the law of its changes1 not only past but also to come4 ,the truth is1 that the causes on which the phenomena of the moral world depend1 are in every age1 and almost in every country1 combined in some different proportion2 so that it is scarcely to be expected that the general result of them all should conform very closely1 in its details at least1 to any uniformly progressive series4 ,and all generalizations which affirm that mankind have a tendency to grow better or worse1 richer or poorer1 more cultivated or more barbarous1 that population increases faster than subsistence1 or subsistence than population1 that inequality of fortune has a tendency to increase or to break down1 and the like1 propositions of considerable value as empirical laws within certain 7but generally rather narrow7 limits1 are in reality true or false according to times and circumstances4 ,what we have said of empirical generalizations from times past to times still to come1 holds equally true of similar generalizations from present times to times past2 when persons whose acquaintance with moral and social facts is confined to their own age1 take the men and the things of that age for the type of men and things in general1 and apply without scruple to the interpretation of the events of history1 the empirical laws which represent sufficiently for daily guidance the common phenomena of human nature at that time and in that particular state of society4 ,if examples are wanted1 almost every historical work1 until a very recent period1 abounded in them4 ,the same may be said of those who generalize empirically from the people of their own country to the people of other countries1 as if human beings felt1 judged1 and acted everywhere in the same manner4 #e4 ,in the foregoing instances1 the distinction is confounded between empirical laws1 which express merely the customary order of the succession of effects1 and the laws of causation on which the effects depend4 ,there may1 however1 be incorrect generalization when this mistake is not committed2 when the investigation takes its proper direction1 that of causes1 and the result erroneously obtained purports to be a really causal law4 ,the most vulgar form of this fallacy is that which is commonly called post hoc1 ergo propter hoc1 or1 cum hoc1 ergo propter hoc4 ,as when it was inferred that ,england owed her industrial pre-eminence to her restrictions on commerce2 as when the old school of financiers1 and some speculative writers1 maintained that the national debt was one of the causes of national prosperity2 as when the excellence of the ,church1 of the ,houses of ,lords and ,commons1 of the procedure of the law courts1 etc41 were inferred from the mere fact that the country had prospered under them4 ,in such cases as these1 if it can be rendered probable by other evidence that the supposed causes have some tendency to produce the effect ascribed to them1 the fact of its having been produced1 though only in one instance1 is of some value as a verification by specific experience2 but in itself it goes scarcely any way at all toward establishing such a tendency1 since1 admitting the effect1 a hundred other antecedents could show an equally strong title of that kind to be considered as the cause4 ,in these examples we see bad generalization a posteriori1 or empiricism properly so called2 causation inferred from casual conjunction1 without either due elimination1 or any presumption arising from known properties of the supposed agent4 ,but bad generalization a priori is fully as common2 which is properly called false theory2 conclusions drawn1 by way of deduction1 from properties of some one agent which is known or supposed to be present1 all other co-existing agents being overlooked4 ,as the former is the error of sheer ignorance1 so the latter is especially that of semi-instructed minds2 and is mainly committed in attempting to explain complicated phenomena by a simpler theory than their nature admits of4 ,as when one school of physicians sought for the universal principle of all disease in 8lentor and morbid viscidity of the blood10 and imputing most bodily derangements to mechanical obstructions1 thought to cure them by mechanical remedies27#beg7 while another1 the chemical school1 8acknowledged no source of disease but the presence of some hostile acid or alkali1 or some deranged condition in the chemical composition of the fluid or solid parts10 and conceived1 therefore1 that 8all remedies must act by producing chemical changes in the body40 ,we find ,tournefort busily engaged in testing every vegetable juice1 in order to discover in it some traces of an acid or alkaline ingredient1 which might confer upon it medicinal activity4 ,the fatal errors into which such an hypothesis was liable to betray the practitioner1 received an awful illustration in the history of the memorable fever that raged at ,leyden in the year #afii1 and which consigned two-thirds of the population of that city to an untimely grave2 an event which in a great measure depended upon the ,professor ,sylvius de la ,boe1 who having just embraced the chemical doctrines of ,van ,helmont1 assigned the origin of the distemper to a prevailing acid1 and declared that its cure could alone only be effected by the copious administration of absorbent and testaceous medicines47#beh7 ,these aberrations in medical theory have their exact parallels in politics4 ,all the doctrines which ascribe absolute goodness to particular forms of government1 particular social arrangements1 and even to particular modes of education1 without reference to the state of civilization and the various distinguishing characters of the society for which they are intended1 are open to the same objection--that of assuming one class of influencing circumstances to be the paramount rulers of phenomena which depend in an equal or greater degree on many others4 ,but on these considerations it is the less necessary that we should now dwell1 as they will occupy our attention more largely in the concluding ,book4 #f4 ,the last of the modes of erroneous generalization to which ,i shall advert1 is that to which we may give the name of ,false ,analogies4 ,this ,fallacy stands distinguished from those already treated of by the peculiarity that it does not even simulate a complete and conclusive induction1 but consists in the misapplication of an argument which is at best only admissible as an inconclusive presumption1 where real proof is unattainable4 ,an argument from analogy1 is an inference that what is true in a certain case is true in a case known to be somewhat similar1 but not known to be exactly parallel1 that is1 to be similar in all the material circumstances4 ,an object has the property ,b3 another object is not known to have that property1 but resembles the first in a property ,a1 not known to be connected with ,b2 and the conclusion to which the analogy points1 is that this object has the property ,b also4 ,as1 for example1 that the planets are inhabited1 because the earth is so4 ,the planets resemble the earth in describing elliptical orbits round the sun1 in being attracted by it and by one another1 in being nearly spherical1 revolving on their axes1 etc42 and1 as we have now reason to believe from the revelations of the spectroscope1 are composed1 in great part at least1 of similar materials2 but it is not known that any of these properties1 or all of them together1 are the conditions on which the possession of inhabitants is dependent1 or are marks of those conditions4 ,nevertheless1 so long as we do not know what the conditions are1 they may be connected by some law of nature with those common properties2 and to the extent of that possibility the planets are more likely to be inhabited than if they did not resemble the earth at all4 ,this non-assignable and generally small increase of probability1 beyond what would otherwise exist1 is all the evidence which a conclusion can derive from analogy4 ,for if we have the slightest reason to suppose any real connection between the two properties ,a and ,b1 the argument is no longer one of analogy4 ,if it had been ascertained 7,i purposely put an absurd supposition7 that there was a connection by causation between the fact of revolving on an axis and the existence of animated beings1 or if there were any reasonable ground for even suspecting such a connection1 a probability would arise of the existence of inhabitants in the planets1 which might be of any degree of strength1 up to a complete induction2 but we should then infer the fact from the ascertained or presumed law of causation1 and not from the analogy of the earth4 ,the name analogy1 however1 is sometimes employed by extension to denote those arguments of an inductive character but not amounting to a real induction1 which are employed to strengthen the argument drawn from a simple resemblance4 ,though ,a1 the property common to the two cases1 can not be shown to be the cause or effect of ,b1 the analogical reasoner will endeavor to show that there is some less close degree of connection between them2 that ,a is one of a set of conditions from which1 when all united1 ,b would result2 or is an occasional effect of some cause which has been known also to produce ,b2 and the like4 ,any of which things1 if shown1 would render the existence of ,b by so much more probable1 than if there had not been even that amount of known connection between ,b and ,a4 ,now an error or fallacy of analogy may occur in two ways4 ,sometimes it consists in employing an argument of either of the above kinds with correctness indeed1 but overrating its probative force4 ,this very common aberration is sometimes supposed to be particularly incident to persons distinguished for their imagination2 but in reality it is the characteristic intellectual vice of those whose imaginations are barren1 either from want of exercise1 natural defect1 or the narrowness of their range of ideas4 ,to such minds objects present themselves clothed in but few properties2 and as1 therefore1 few analogies between one object and another occur to them1 they almost invariably overrate the degree of importance of those few3 while one whose fancy takes a wider range1 perceives and remembers so many analogies tending to conflicting conclusions1 that he is much less likely to lay undue stress on any of them4 ,we always find that those are the greatest slaves to metaphorical language who have but one set of metaphors4 ,but this is only one of the modes of error in the employment of arguments of analogy4 ,there is another1 more properly deserving the name of fallacy2 namely1 when resemblance in one point is inferred from resemblance in another point1 though there is not only no evidence to connect the two circumstances by way of causation1 but the evidence tends positively to disconnect them4 ,this is properly the ,fallacy of ,false ,analogies4 ,as a first instance1 we may cite that favorite argument in defense of absolute power1 drawn from the analogy of paternal government in a family1 which government1 however much in need of control1 is not and can not be controlled by the children themselves1 while they remain children4 ,paternal government1 says the argument1 works well2 therefore1 despotic government in a state will work well4 ,i waive1 as not pertinent in this place1 all that could be said in qualification of the alleged excellence of paternal government4 ,however this might be1 the argument from the family to the state would not the less proceed on a false analogy2 implying that the beneficial working of parental government depends1 in the family1 on the only point which it has in common with political despotism1 namely1 irresponsibility4 ,whereas it depends1 when real1 not on that but on two other circumstances of the case1 the affection of the parent for the children1 and the superiority of the parent in wisdom and experience2 neither of which properties can be reckoned on1 or are at all likely to exist1 between a political despot and his subjects2 and when either of these circumstances fails even in the family1 and the influence of the irresponsibility is allowed to work uncorrected1 the result is any thing but good government4 ,this1 therefore1 is a false analogy4 ,another example is the not uncommon dictum that bodies politic have youth1 maturity1 old age1 and death1 like bodies natural2 that after a certain duration of prosperity1 they tend spontaneously to decay4 ,this also is a false analogy1 because the decay of the vital powers in an animated body can be distinctly traced to the natural progress of those very changes of structure which1 in their earlier stages1 constitutes its growth to maturity2 while in the body politic the progress of those changes can not1 generally speaking1 have any effect but the still further continuance of growth3 it is the stoppage of that progress1 and the commencement of retrogression1 that alone would constitute decay4 ,bodies politic die1 but it is of disease1 or violent death2 they have no old age4 ,the following sentence from ,hooker's ,ecclesiastical ,polity is an instance of a false analogy from physical bodies to what are called bodies politic4 8,as there could be in natural bodies no motion of any thing unless there were some which moveth all things1 and continueth immovable2 even so in politic societies there must be some unpunishable1 or else no man shall suffer punishment40 ,there is a double fallacy here1 for not only the analogy1 but the premise from which it is drawn1 is untenable4 ,the notion that there must be something immovable which moves all other things1 is the old scholastic error of a primum mobile4 ,the following instance ,i quote from ,archbishop ,whately's ,rhetoric3 8,it would be admitted that a great and permanent diminution in the quantity of some useful commodity1 such as corn1 or coal1 or iron1 throughout the world1 would be a serious and lasting loss2 and again1 that if the fields and coal-mines yielded regularly double quantities1 with the same labor1 we should be so much the richer2 hence it might be inferred1 that if the quantity of gold and silver in the world were diminished one-half1 or were doubled1 like results would follow2 the utility of these metals1 for the purposes of coin1 being very great4 ,now there are many points of resemblance and many of difference1 between the precious metals on the one hand1 and corn1 coal1 etc41 on the other2 but the important circumstance to the supposed argument is1 that the utility of gold and silver 7as coin1 which is far the chief7 depends on their value1 which is regulated by their scarcity2 or rather1 to speak strictly1 by the difficulty of obtaining them2 whereas1 if corn and coal were ten times as abundant 7i4e41 more easily obtained71 a bushel of either would still be as useful as now4 ,but if it were twice as easy to procure gold as it is1 a sovereign would be twice as large2 if only half as easy1 it would be of the size of a half-sovereign1 and this 7besides the trifling circumstance of the cheapness or dearness of gold ornaments7 would be all the difference4 ,the analogy1 therefore1 fails in the point essential to the argument40 ,the same author notices1 after ,bishop ,copleston1 the case of ,false ,analogy which consists in inferring from the similarity in many respects between the metropolis of a country and the heart of the animal body1 that the increased size of the metropolis is a disease4 ,some of the false analogies on which systems of physics were confidently grounded in the time of the ,greek philosophers1 are such as we now call fanciful1 not that the resemblances are not often real1 but that it is long since any one has been inclined to draw from them the inferences which were then drawn4 ,such1 for instance1 are the curious speculations of the ,pythagoreans on the subject of numbers4 ,finding that the distances of the planets bore1 or seemed to bear1 to one another a proportion not varying much from that of the divisions of the monochord1 they inferred from it the existence of an inaudible music1 that of the spheres2 as if the music of a harp had depended solely on the numerical proportions1 and not on the material1 nor even on the existence of any material1 any strings at all4 ,it has been similarly imagined that certain combinations of numbers1 which were found to prevail in some natural phenomena1 must run through the whole of nature3 as that there must be four elements1 because there are four possible combinations of hot and cold1 wet and dry2 that there must be seven planets1 because there were seven metals1 and even because there were seven days of the week4 ,kepler himself thought that there could be only six planets1 because there were only five regular solids4 ,with these we may class the reasonings1 so common in the speculations of the ancients1 founded on a supposed perfection in nature2 meaning by nature the customary order of events as they take place of themselves without human interference4 ,this also is a rude guess at an analogy supposed to pervade all phenomena1 however dissimilar4 ,since what was thought to be perfection appeared to obtain in some phenomena1 it was inferred 7in opposition to the plainest evidence7 to obtain in all4 8,we always suppose that which is better to take place in nature1 if it be possible10 says ,aristotle2 and the vaguest and most heterogeneous qualities being confounded together under the notion of being better1 there was no limit to the wildness of the inferences4 ,thus1 because the heavenly bodies were 8perfect10 they must move in circles and uniformly4 ,for 8they0 7the ,pythagoreans7 8would not allow10 says ,geminus17#bei7 8of any such disorder among divine and eternal things1 as that they should sometimes move quicker and sometimes slower1 and sometimes stand still2 for no one would tolerate such anomaly in the movements even of a man1 who was decent and orderly4 ,the occasions of life1 however1 are often reasons for men going quicker or slower2 but in the incorruptible nature of the stars1 it is not possible that any cause can be alleged of quickness or slowness40 ,it is seeking an argument of analogy very far1 to suppose that the stars must observe the rules of decorum in gait and carriage prescribed for themselves by the long-bearded philosophers satirized by ,lucian4 ,as late as the ,copernican controversy it was urged as an argument in favor of the true theory of the solar system1 that it placed the fire1 the noblest element1 in the centre of the universe4 ,this was a remnant of the notion that the order of nature must be perfect1 and that perfection consisted in conformity to rules of precedency in dignity1 either real or conventional4 ,again1 reverting to numbers3 certain numbers were perfect1 therefore those numbers must obtain in the great phenomena of nature4 ,six was a perfect number1 that is1 equal to the sum of all its factors2 an additional reason why there must be exactly six planets4 ,the ,pythagoreans1 on the other hand1 attributed perfection to the number ten2 but agreed in thinking that the perfect number must be somehow realized in the heavens2 and knowing only of nine heavenly bodies1 to make up the enumeration1 they asserted 8that there was an antichthon1 or counter-earth1 on the other side of the sun1 invisible to us407#bfj7 ,even ,huygens was persuaded that when the number of the heavenly bodies had reached twelve1 it could not admit of any further increase4 ,creative power could not go beyond that sacred number4 ,some curious instances of false analogy are to be found in the arguments of the ,stoics to prove the equality of all crimes1 and the equal wretchedness of all who had not realized their idea of perfect virtue4 ,cicero1 toward the end of his ,fourth ,book1 ,de ,finibus1 states some of these as follows3 8,ut1 inquit1 in fidibus plurimis1 si nulla earum ita contenta numeris sit1 ut concentum servare possit1 omnes que incontent sunt2 sic peccata1 quia discrepant1 que discrepant2 paria sunt igitur40 ,to which ,cicero himself aptly answers1 8que contingit omnibus fidibus1 ut incontent sint2 illud non continuo1 ut que incontent40 ,the ,stoic resumes3 8,ut enim1 inquit1 gubernator que peccat1 si palearum navem evertit1 et si auri2 item que peccat qui parentem1 et qui servum1 injuri verberat20 assuming1 that because the magnitude of the interest at stake makes no difference in the mere defect of skill1 it can make none in the moral defect3 a false analogy4 ,again1 8,quis ignorat1 si plures ex alto emergere velint1 propius fore eos quidem ad respirandum1 qui ad summam jam aquam appropinquant1 sed nihilo magis respirare posse1 quam eos1 qui sunt in profundo8 ,nihil ergo adjuvat procedere1 et progredi in virtute1 quominus miserrimus sit1 antequam ad eam pervenerit1 quoniam in aqu nihil adjuvat3 et quoniam catuli1 qui jam despecturi sunt1 cci que1 et ii qui modo nati2 ,platonem quoque necesse est1 quoniam nondum videbat sapientiam1 que ccum animo1 ac ,phalarim fuisse40 ,cicero1 in his own person1 combats these false analogies by other analogies tending to an opposite conclusion4 8,ista similia non sunt1 ,cato4444 ,illa sunt similia2 hebes acies est cuipiam oculorum3 corpore alius languescit3 hi curatione adhibit levantur in dies3 alter valet plus quotidie3 alter videt4 ,hi similes sunt omnibus1 qui virtuti student2 levantur vitiis1 levantur erroribus40 #g4 ,in these and all other arguments drawn from remote analogies1 and from metaphors1 which are cases of analogy1 it is apparent 7especially when we consider the extreme facility of raising up contrary analogies and conflicting metaphors7 that1 so far from the metaphor or analogy proving any thing1 the applicability of the metaphor is the very thing to be made out4 ,it has to be shown that in the two cases asserted to be analogous1 the same law is really operating2 that between the known resemblance and the inferred one there is some connection by means of causation4 ,cicero and ,cato might have bandied opposite analogies forever2 it rested with each of them to prove by just induction1 or at least to render probable1 that the case resembled the one set of analogous cases and not the other1 in the circumstances on which the disputed question really hinged4 ,metaphors1 for the most part1 therefore1 assume the proposition which they are brought to prove3 their use is1 to aid the apprehension of it2 to make clearly and vividly comprehended what it is that the person who employs the metaphor is proposing to make out2 and sometimes also1 by what media he proposes to do so4 ,for an apt metaphor1 though it can not prove1 often suggests the proof4 ,for instance1 when ,d',alembert 7,i believe7 remarked that in certain governments only two creatures find their way to the highest places1 the eagle and the serpent1 the metaphor not only conveys with great vividness the assertion intended1 but contributes toward substantiating it1 by suggesting1 in a lively manner1 the means by which the two opposite characters thus typified effect their rise4 ,when it is said that a certain person misunderstands another because the lesser of two objects can not comprehend the greater1 the application of what is true in the literal sense of the word comprehend1 to its metaphorical sense1 points to the fact which is the ground and justification of the assertion1 viz41 that one mind can not thoroughly understand another unless it can contain it in itself1 that is1 unless it possesses all that is contained in the other4 ,when it is urged as an argument for education1 that if the soil is left uncultivated1 weeds will spring up1 the metaphor1 though no proof1 but a statement of the thing to be proved1 states it in terms which1 by suggesting a parallel case1 put the mind upon the track of the real proof4 ,for1 the reason why weeds grow in an uncultivated soil1 is that the seeds of worthless products exist everywhere1 and can germinate and grow in almost all circumstances1 while the reverse is the case with those which are valuable2 and this being equally true of mental products1 this mode of conveying an argument1 independently of its rhetorical advantages1 has a logical value2 since it not only suggests the grounds of the conclusion1 but points to another case in which those grounds have been found1 or at least deemed to be1 sufficient4 ,on the other hand1 when ,bacon1 who is equally conspicuous in the use and abuse of figurative illustration1 says that the stream of time has brought down to us only the least valuable part of the writings of the ancients1 as a river carries froth and straws floating on its surface1 while more weighty objects sink to the bottom2 this1 even if the assertion illustrated by it were true1 would be no good illustration1 there being no parity of cause4 ,the levity by which substances float on a stream1 and the levity which is synonymous with worthlessness1 have nothing in common except the name2 and 7to show how little value there is in the metaphor7 we need only change the word into buoyancy1 to turn the semblance of argument involved in ,bacon's illustration against himself4 ,a metaphor1 then1 is not to be considered as an argument1 but as an assertion that an argument exists2 that a parity subsists between the case from which the metaphor is drawn and that to which it is applied4 ,this parity may exist though the two cases be apparently very remote from one another2 the only resemblance existing between them may be a resemblance of relations1 an analogy in ,ferguson's and ,archbishop ,whately's sense3 as in the preceding instance1 in which an illustration from agriculture was applied to mental cultivation4 #h4 ,to terminate the subject of ,fallacies of ,generalization1 it remains to be said1 that the most fertile source of them is bad classification3 bringing together in one group1 and under one name1 things which have no common properties1 or none but such as are too unimportant to allow general propositions of any considerable value to be made respecting the class4 ,the misleading effect is greatest1 when a word which in common use expresses some definite fact1 is extended by slight links of connection to cases in which that fact does not exist1 but some other or others1 only slightly resembling it4 ,thus ,bacon17#bfa7 in speaking of the ,idola or ,fallacies arising from notions temere et inqualiter rebus abstract1 exemplifies them by the notion of ,humidum or ,wet1 so familiar in the physics of antiquity and of the ,middle ,ages4 8,invenietur verbum istud1 ,humidum1 nihil aliud quam nota confusa diversarum actionum1 qu nullam constantiam aut reductionem patiuntur4 ,significat enim1 et quod circa aliud corpus facile se circumfundit2 et quod in se est indeterminabile1 nec consistere potest2 et quod facile cedit undique2 et quod facile se dividit et dispergit2 et quod facile se unit et colligit2 et quod facile fluit1 et in motu ponitur2 et quod alteri corpori facile adhret1 idque madefacit2 et quod facile reducitur in liquidum1 sive colliquatur1 cum antea consisteret4 ,itaque quum ad hujus nominis prdicationem et impositionem ventum sit2 si alia accipias1 flamma humida est2 si alia accipias1 aer humidus non est2 si alia1 pulvis minutus humidus est2 si alia1 vitrum humidum est3 ut facile appareat1 istam notionem ex aqu tantum1 et communibus et vulgaribus liquoribus1 absque ull debit verificatione1 temere abstractam esse40 ,bacon himself is not exempt from a similar accusation when inquiring into the nature of heat3 where he occasionally proceeds like one who1 seeking for the cause of hardness1 after examining that quality in iron1 flint1 and diamond1 should expect to find that it is something which can be traced also in hard water1 a hard knot1 and a hard heart4 ,the word in the ,greek philosophy1 and the words ,generation and ,corruption1 both then and long afterward1 denoted such a multitude of heterogeneous phenomena1 that any attempt at philosophizing in which those words were used was almost as necessarily abortive as if the word hard had been taken to denote a class including all the things mentioned above4 1 for instance1 which properly signified motion1 was taken to denote not only all motion but even all change3 being recognized as one of the modes of 4 ,the effect was1 to connect with every form of or change1 ideas drawn from motion in the proper and literal sense1 and which had no real connection with any other kind of than that4 ,aristotle and ,plato labored under a continual embarrassment from this misuse of terms4 ,but if we proceed further in this direction we shall encroach upon the ,fallacy of ,ambiguity1 which belongs to a different class1 the last in order of our classification1 ,fallacies of ,confusion4 ,chapter ,,vi4 ,fallacies ,of ,ratiocination4 #a4 ,we have now1 in our progress through the classes of ,fallacies1 arrived at those to which1 in the common books of logic1 the appellation is in general exclusively appropriated2 those which have their seat in the ratiocinative or deductive part of the investigation of truth4 ,of these fallacies it is the less necessary for us to insist at any length1 as they have been most satisfactorily treated in a work familiar to almost all1 in this country at least1 who feel any interest in these speculations1 ,archbishop ,whately's ,logic4 ,against the more obvious forms of this class of fallacies1 the rules of the syllogism are a complete protection4 ,not 7as we have so often said7 that ratiocination can not be good unless it be in the form of a syllogism2 but that1 by showing it in that form1 we are sure to discover if it be bad1 or at least if it contain any fallacy of this class4 #b4 ,among ,fallacies of ,ratiocination1 we ought perhaps to include the errors committed in processes which have the appearance only1 not the reality1 of an inference from premises2 the fallacies connected with the conversion and quipollency of propositions4 ,i believe errors of this description to be far more frequently committed than is generally supposed1 or than their extreme obviousness might seem to admit of4 ,for example1 the simple conversion of a universal affirmative proposition1 ,all ,a are ,b1 therefore all ,b are ,a1 ,i take to be a very common form of error3 though committed1 like many other fallacies1 oftener in the silence of thought than in express words1 for it can scarcely be clearly enunciated without being detected4 ,and so with another form of fallacy1 not substantially different from the preceding3 the erroneous conversion of an hypothetical proposition4 ,the proper converse of an hypothetical proposition is this3 ,if the consequent be false1 the antecedent is false2 but this1 ,if the consequent be true1 the antecedent is true1 by no means holds good1 but is an error corresponding to the simple conversion of a universal affirmative4 ,yet hardly any thing is more common than for people1 in their private thoughts1 to draw this inference4 ,as when the conclusion is accepted1 which it so often is1 for proof of the premises4 ,that the premises can not be true if the conclusion is false1 is the unexceptionable foundation of the legitimate mode of reasoning called reductio ad absurdum4 ,but people continually think and express themselves1 as if they also believed that the premises can not be false if the conclusion is true4 ,the truth1 or supposed truth1 of the inferences which follow from a doctrine1 often enables it to find acceptance in spite of gross absurdities in it4 ,how many philosophical systems which had scarcely any intrinsic recommendation1 have been received by thoughtful men because they were supposed to lend additional support to religion1 morality1 some favorite view of politics1 or some other cherished persuasion3 not merely because their wishes were thereby enlisted on its side1 but because its leading to what they deemed sound conclusions appeared to them a strong presumption in favor of its truth3 though the presumption1 when viewed in its true light1 amounted only to the absence of that particular evidence of falsehood1 which would have resulted from its leading by correct inference to something already known to be false4 ,again1 the very frequent error in conduct1 of mistaking reverse of wrong for right1 is the practical form of a logical error with respect to the ,opposition of ,propositions4 ,it is committed for want of the habit of distinguishing the contrary of a proposition from the contradictory of it1 and of attending to the logical canon1 that contrary propositions1 though they can not both be true1 may both be false4 ,if the error were to express itself in words1 it would run distinctly counter to this canon4 ,it generally1 however1 does not so express itself1 and to compel it to do so is the most effectual method of detecting and exposing it4 #c4 ,among ,fallacies of ,ratiocination are to be ranked1 in the first place1 all the cases of vicious syllogism laid down in the books4 ,these generally resolve themselves into having more than three terms to the syllogism1 either avowedly1 or in the covert mode of an undistributed middle term1 or an illicit process of one of the two extremes4 ,it is not1 indeed1 very easy fully to convict an argument of falling under any one of these vicious cases in particular2 for the reason already more than once referred to1 that the premises are seldom formally set out3 if they were1 the fallacy would impose upon nobody2 and while they are not1 it is almost always to a certain degree optional in what manner the suppressed link shall be filled up4 ,the rules of the syllogism are rules for compelling a person to be aware of the whole of what he must undertake to defend if he persists in maintaining his conclusion4 ,he has it almost always in his power to make his syllogism good by introducing a false premise2 and hence it is scarcely ever possible decidedly to affirm that any argument involves a bad syllogism3 but this detracts nothing from the value of the syllogistic rules1 since it is by them that a reasoner is compelled distinctly to make his election what premises he is prepared to maintain4 ,the election made1 there is generally so little difficulty in seeing whether the conclusion follows from the premises set out1 that we might without much logical impropriety have merged this fourth class of fallacies in the fifth1 or ,fallacies of ,confusion4 #d4 ,perhaps1 however1 the commonest1 and certainly the most dangerous fallacies of this class1 are those which do not lie in a single syllogism1 but slip in between one syllogism and another in a chain of argument1 and are committed by changing the premises4 ,a proposition is proved1 or an acknowledged truth laid down1 in the first part of an argumentation1 and in the second a further argument is founded not on the same proposition1 but on some other1 resembling it sufficiently to be mistaken for it4 ,instances of this fallacy will be found in almost all the argumentative discourses of unprecise thinkers2 and we need only here advert to one of the obscurer forms of it1 recognized by the school-men as the fallacy dicto secundum quid ad dictum simpliciter4 ,this is committed when1 in the premises1 a proposition is asserted with a qualification1 and the qualification lost sight of in the conclusion2 or oftener1 when a limitation or condition1 though not asserted1 is necessary to the truth of the proposition1 but is forgotten when that proposition comes to be employed as a premise4 ,many of the bad arguments in vogue belong to this class of error4 ,the premise is some admitted truth1 some common maxim1 the reasons or evidence for which have been forgotten1 or are not thought of at the time1 but if they had been thought of would have shown the necessity of so limiting the premise that it would no longer have supported the conclusion drawn from it4 ,of this nature is the fallacy in what is called1 by ,adam ,smith and others1 the ,mercantile ,theory in ,political ,economy4 ,that theory sets out from the common maxim1 that whatever brings in money enriches2 or that every one is rich in proportion to the quantity of money he obtains4 ,from this it is concluded that the value of any branch of trade1 or of the trade of the country altogether1 consists in the balance of money it brings in2 that any trade which carries more money out of the country than it draws into it is a losing trade2 that therefore money should be attracted into the country and kept there1 by prohibitions and bounties2 and a train of similar corollaries4 ,all for want of reflecting that if the riches of an individual are in proportion to the quantity of money he can command1 it is because that is the measure of his power of purchasing money's worth2 and is therefore subject to the proviso that he is not debarred from employing his money in such purchases4 ,the premise1 therefore1 is only true secundum quid2 but the theory assumes it to be true absolutely1 and infers that increase of money is increase of riches1 even when produced by means subversive of the condition under which alone money can be riches4 ,a second instance is1 the argument by which it used to be contended1 before the commutation of tithe1 that tithes fell on the landlord1 and were a deduction from rent2 because the rent of tithe-free land was always higher than that of land of the same quality1 and the same advantages of situation1 subject to tithe4 ,whether it be true or not that a tithe falls on rent1 a treatise on ,logic is not the place to examine2 but it is certain that this is no proof of it4 ,whether the proposition be true or false1 tithe-free land must1 by the necessity of the case1 pay a higher rent4 ,for if tithes do not fall on rent1 it must be because they fall on the consumer2 because they raise the price of agricultural produce4 ,but if the produce be raised in price1 the farmer of tithe-free as well as the farmer of tithed land gets the benefit4 ,to the latter the rise is but a compensation for the tithe he pays2 to the first1 who pays none1 it is clear gain1 and therefore enables him1 and if there be freedom of competition1 forces him1 to pay so much more rent to his landlord4 ,the question remains1 to what class of fallacies this belongs4 ,the premise is1 that the owner of tithed land receives less rent than the owner of tithe-free land2 the conclusion is1 that therefore he receives less than he himself would receive if tithe were abolished4 ,but the premise is only true conditionally2 the owner of tithed land receives less than what the owner of tithe-free land is enabled to receive when other lands are tithed2 while the conclusion is applied to a state of circumstances in which that condition fails1 and in which1 by consequence1 the premise will not be true4 ,the fallacy1 therefore1 is dicto secundum quid ad dictum simpliciter4 ,a third example is the opposition sometimes made to legitimate interferences of government in the economical affairs of society1 grounded on a misapplication of the maxim1 that an individual is a better judge than the government of what is for his own pecuniary interest4 ,this objection was urged to ,mr4 ,wakefield's principle of colonization2 the concentration of the settlers1 by fixing such a price on unoccupied land as may preserve the most desirable proportion between the quantity of land in culture and the laboring population4 ,against this it was argued1 that if individuals found it for their advantage to occupy extensive tracts of land1 they1 being better judges of their own interest than the legislature 7which can only proceed on general rules71 ought not to be restrained from doing so4 ,but in this argument it was forgotten that the fact of a person's taking a large tract of land is evidence only that it is his interest to take as much as other people1 but not that it might not be for his interest to content himself with less1 if he could be assured that other people would do so too2 an assurance which nothing but a government regulation can give4 ,if all other people took much1 and he only a little1 he would reap none of the advantages derived from the concentration of the population and the consequent possibility of procuring labor for hire1 but would have placed himself1 without equivalent1 in a situation of voluntary inferiority4 ,the proposition1 therefore1 that the quantity of land which people will take when left to themselves is that which is most for their interest to take1 is true only secundum quid3 it is only their interest while they have no guarantee for the conduct of one another4 ,but the arrangement disregards the limitation1 and takes the proposition for true simpliciter4 ,one of the conditions oftenest dropped1 when what would otherwise be a true proposition is employed as a premise for proving others1 is the condition of time4 ,it is a principle of political economy that prices1 profits1 wages1 etc41 8always find their level20 but this is often interpreted as if it meant that they are always1 or generally1 at their level1 while the truth is1 as ,coleridge epigrammatically expresses it1 that they are always finding their level1 8which might be taken as a paraphrase or ironical definition of a storm40 ,under the same head of fallacy 7 dicto secundum quid ad dictum simpliciter7 might be placed all the errors which are vulgarly called misapplications of abstract truths2 that is1 where a principle1 true 7as the common expression is7 in the abstract1 that is1 all modifying causes being supposed absent1 is reasoned on as if it were true absolutely1 and no modifying circumstance could ever by possibility exist4 ,this very common form of error it is not requisite that we should exemplify here1 as it will be particularly treated of hereafter in its application to the subjects on which it is most frequent and most fatal1 those of politics and society47#bfb7 ,chapter ,,vii4 ,fallacies ,of ,confusion4 #a4 ,under this fifth and last class it is convenient to arrange all those fallacies in which the source of error is not so much a false estimate of the probative force of known evidence1 as an indistinct1 indefinite1 and fluctuating conception of what the evidence is4 ,at the head of these stands that multitudinous body of fallacious reasonings in which the source of error is the ambiguity of terms3 when something which is true if a word be used in a particular sense1 is reasoned on as if it were true in another sense4 ,in such a case there is not a mal-estimation of evidence1 because there is not properly any evidence to the point at all2 there is evidence1 but to a different point1 which from a confused apprehension of the meaning of the terms used1 is supposed to be the same4 ,this error will naturally be oftener committed in our ratiocinations than in our direct inductions1 because in the former we are deciphering our own or other people's notes1 while in the latter we have the things themselves present1 either to the senses or to the memory4 ,except1 indeed1 when the induction is not from individual cases to a generality1 but from generalities to a still higher generalization2 in that case the fallacy of ambiguity may affect the inductive process as well as the ratiocinative4 ,it occurs in ratiocination in two ways3 when the middle term is ambiguous1 or when one of the terms of the syllogism is taken in one sense in the premises1 and in another sense in the conclusion4 ,some good exemplifications of this fallacy are given by ,archbishop ,whately4 8,one case10 says he1 8which may be regarded as coming under the head of ,ambiguous ,middle1 is 7what ,i believe logical writers mean by #8,fallacia ,figur ,dictionis'7 the fallacy built on the grammatical structure of language1 from men's usually taking for granted that paronymous 7or conjugate7 words1 i4e41 those belonging to each other1 as the substantive1 adjective1 verb1 etc41 of the same root1 have a precisely corresponding meaning2 which is by no means universally the case4 ,such a fallacy could not indeed be even exhibited in strict logical form1 which would preclude even the attempt at it1 since it has two middle terms in sound as well as sense4 ,but nothing is more common in practice than to vary continually the terms employed1 with a view to grammatical convenience2 nor is there any thing unfair in such a practice1 as long as the meaning is preserved unaltered2 e4g41 #8murder should be punished with death2 this man is a murderer1 therefore he deserves to die1' etc4 ,here we proceed on the assumption 7in this case just7 that to commit murder1 and to be a murderer--to deserve death1 and to be one who ought to die1 are1 respectively1 equivalent expressions2 and it would frequently prove a heavy inconvenience to be debarred this kind of liberty2 but the abuse of it gives rise to the ,fallacy in question2 e4g41 projectors are unfit to be trusted2 this man has formed a project1 therefore he is unfit to be trusted3 here the sophist proceeds on the hypothesis that he who forms a project must be a projector3 whereas the bad sense that commonly attaches to the latter word1 is not at all implied in the former4 ,this fallacy may often be considered as lying not in the ,middle1 but in one of the terms of the ,conclusion2 so that the conclusion drawn shall not be1 in reality1 at all warranted by the premises1 though it will appear to be so1 by means of the grammatical affinity of the words2 e4g41 to be acquainted with the guilty is a presumption of guilt2 this man is so acquainted1 therefore we may presume that he is guilty3 this argument proceeds on the supposition of an exact correspondence between presume and presumption1 which1 however1 does not really exist2 for #8presumption' is commonly used to express a kind of slight suspicion2 whereas1 #8to presume' amounts to actual belief4 ,there are innumerable instances of a non-correspondence in paronymous words1 similar to that above instanced2 as between art and artful1 design and designing1 faith and faithful1 etc42 and the more slight the variation of the meaning1 the more likely is the fallacy to be successful2 for when the words have become so widely removed in sense as #8pity' and #8pitiful1' every one would perceive such a fallacy1 nor would it be employed but in jest47#bfc7 8,the present ,fallacy is nearly allied to1 or rather1 perhaps1 may be regarded as a branch of1 that founded on etymology--viz41 when a term is used1 at one time in its customary1 and at another in its etymological sense4 ,perhaps no example of this can be found that is more extensively and mischievously employed than in the case of the word representative3 assuming that its right meaning must correspond exactly with the strict and original sense of the verb #8represent1' the sophist persuades the multitude that a member of the ,house of ,commons is bound to be guided in all points by the opinion of his constituents2 and1 in short1 to be merely their spokesman2 whereas law and custom1 which in this case may be considered as fixing the meaning of the term1 require no such thing1 but enjoin the representative to act according to the best of his own judgment1 and on his own responsibility40 ,the following are instances of great practical importance1 in which arguments are habitually founded on a verbal ambiguity4 ,the mercantile public are frequently led into this fallacy by the phrase 8scarcity of money40 ,in the language of commerce1 8money0 has two meanings3 currency1 or the circulating medium2 and capital seeking investment1 especially investment on loan4 ,in this last sense the word is used when the 8money market0 is spoken of1 and when the 8value of money0 is said to be high or low1 the rate of interest being meant4 ,the consequence of this ambiguity is1 that as soon as scarcity of money in the latter of these senses begins to be felt--as soon as there is difficulty of obtaining loans1 and the rate of interest is high--it is concluded that this must arise from causes acting upon the quantity of money in the other and more popular sense2 that the circulating medium must have diminished in quantity1 or ought to be increased4 ,i am aware that1 independently of the double meaning of the term1 there are in the facts themselves some peculiarities1 giving an apparent support to this error2 but the ambiguity of the language stands on the very threshold of the subject1 and intercepts all attempts to throw light upon it4 ,another ambiguous expression which continually meets us in the political controversies of the present time1 especially in those which relate to organic changes1 is the phrase 8influence of property0--which is sometimes used for the influence of respect for superior intelligence or gratitude for the kind offices which persons of large property have it so much in their power to bestow2 at other times for the influence of fear2 fear of the worst sort of power1 which large property also gives to its possessor1 the power of doing mischief to dependents4 ,to confound these two1 is the standing fallacy of ambiguity brought against those who seek to purify the electoral system from corruption and intimidation4 ,persuasive influence1 acting through the conscience of the voter1 and carrying his heart and mind with it1 is beneficial--therefore 7it is pretended7 coercive influence1 which compels him to forget that he is a moral agent1 or to act in opposition to his moral convictions1 ought not to be placed under restraint4 ,another word which is often turned into an instrument of the fallacy of ambiguity1 is ,theory4 ,in its most proper acceptation1 theory means the completed result of philosophical induction from experience4 ,in that sense1 there are erroneous as well as true theories1 for induction may be incorrectly performed1 but theory of some sort is the necessary result of knowing any thing of a subject1 and having put one's knowledge into the form of general propositions for the guidance of practice4 ,in this1 the proper sense of the word1 ,theory is the explanation of practice4 ,in another and a more vulgar sense1 theory means any mere fiction of the imagination1 endeavoring to conceive how a thing may possibly have been produced1 instead of examining how it was produced4 ,in this sense only are theory and theorists unsafe guides2 but because of this1 ridicule or discredit is attempted to be attached to theory in its proper sense1 that is1 to legitimate generalization1 the end and aim of all philosophy2 and a conclusion is represented as worthless1 just because that has been done which1 if done correctly1 constitutes the highest worth that a principle for the guidance of practice can possess1 namely1 to comprehend in a few words the real law on which a phenomenon depends1 or some property or relation which is universally true of it4 8,the ,church0 is sometimes understood to mean the clergy alone1 sometimes the whole body of believers1 or at least of communicants4 ,the declamations respecting the inviolability of church property are indebted for the greater part of their apparent force to this ambiguity4 ,the clergy1 being called the church1 are supposed to be the real owners of what is called church property2 whereas they are in truth only the managing members of a much larger body of proprietors1 and enjoy on their own part a mere usufruct1 not extending beyond a life interest4 ,the following is a ,stoical argument taken from ,cicero1 ,de ,finibus1 book the third3 8,quod est bonum1 omne laudabile est4 ,quod autem laudabile est1 omne honestum est4 ,bonum igitur quod est1 honestum est40 ,here the ambiguous word is laudabile1 which in the minor premise means any thing which mankind are accustomed1 on good grounds1 to admire or value2 as beauty1 for instance1 or good fortune3 but in the major1 it denotes exclusively moral qualities4 ,in much the same manner the ,stoics endeavored logically to justify as philosophical truths1 their figurative and rhetorical expressions of ethical sentiment3 as that the virtuous man is alone free1 alone beautiful1 alone a king1 etc4 ,whoever has virtue has ,good 7because it has been previously determined not to call any thing else good72 but1 again1 ,good necessarily includes freedom1 beauty1 and even kingship1 all these being good things2 therefore whoever has virtue has all these4 ,the following is an argument of ,descartes to prove1 in his a priori manner1 the being of a ,god4 ,the conception1 says he1 of an infinite ,being proves the real existence of such a being4 ,for if there is not really any such being1 ,i must have made the conception2 but if ,i could make it1 ,i can also unmake it2 which evidently is not true2 therefore there must be1 externally to myself1 an archetype1 from which the conception was derived4 ,in this argument 7which1 it may be observed1 would equally prove the real existence of ghosts and of witches7 the ambiguity is in the pronoun ,i1 by which1 in one place1 is to be understood my will1 in another the laws of my nature4 ,if the conception1 existing as it does in my mind1 had no original without1 the conclusion would unquestionably follow that ,i made it2 that is1 the laws of my nature must have somehow evolved it3 but that my will made it1 would not follow4 ,now when ,descartes afterward adds that ,i can not unmake the conception1 he means that ,i can not get rid of it by an act of my will3 which is true1 but is not the proposition required4 ,i can as much unmake this conception as ,i can any other3 no conception which ,i have once had1 can ,i ever dismiss by mere volition2 but what some of the laws of my nature have produced1 other laws1 or those same laws in other circumstances1 may1 and often do1 subsequently efface4 ,analogous to this are some of the ambiguities in the free-will controversy2 which1 as they will come under special consideration in the concluding ,book1 ,i only mention memori caus4 ,in that discussion1 too1 the word ,i is often shifted from one meaning to another1 at one time standing for my volitions1 at another time for the actions which are the consequences of them1 or the mental dispositions from which they proceed4 ,the latter ambiguity is exemplified in an argument of ,coleridge 7in his ,aids to ,reflection71 in support of the freedom of the will4 ,it is not true1 he says1 that a man is governed by motives2 8the man makes the motive1 not the motive the man20 the proof being that 8what is a strong motive to one man is no motive at all to another40 ,the premise is true1 but only amounts to this1 that different persons have different degrees of susceptibility to the same motive2 as they have also to the same intoxicating liquid1 which1 however1 does not prove that they are free to be drunk or not drunk1 whatever quantity of the fluid they may drink4 ,what is proved is1 that certain mental conditions in the person himself must co-operate1 in the production of the act1 with the external inducement2 but those mental conditions also are the effect of causes2 and there is nothing in the argument to prove that they can arise without a cause--that a spontaneous determination of the will1 without any cause at all1 ever takes place1 as the free-will doctrine supposes4 ,the double use1 in the free-will controversy1 of the word ,necessity1 which sometimes stands only for ,certainty1 at other times for ,compulsion2 sometimes for what can not be prevented1 at other times only for what we have reason to be assured will not2 we shall have occasion hereafter to pursue to some of its ulterior consequences4 ,a most important ambiguity1 both in common and in metaphysical language1 is thus pointed out by ,archbishop ,whately in the ,appendix to his ,logic3 8,same 7as well as ,one1 ,identical1 and other words derived from them7 is used frequently in a sense very different from its primary one1 as applicable to a single object2 being employed to denote great similarity4 ,when several objects are undistinguishably alike1 one single description will apply equally to any of them2 and thence they are said to be all of one and the same nature1 appearance1 etc4 ,as1 e4g41 when we say #8this house is built of the same stone with such another1' we only mean that the stones are undistinguishable in their qualities2 not that the one building was pulled down1 and the other constructed with the materials4 ,whereas sameness1 in the primary sense1 does not even necessarily imply similarity2 for if we say of any man that he is greatly altered since such a time1 we understand1 and indeed imply by the very expression1 that he is one person1 though different in several qualities4 ,it is worth observing also1 that ,same1 in the secondary sense1 admits1 according to popular usage1 of degrees3 we speak of two things being nearly the same1 but not entirely3 personal identity does not admit of degrees4 ,nothing1 perhaps1 has contributed more to the error of ,realism than inattention to this ambiguity4 ,when several persons are said to have one and the same opinion1 thought1 or idea1 many men1 overlooking the true simple statement of the case1 which is1 that they are all thinking alike1 look for something more abstruse and mystical1 and imagine there must be some ,one ,thing1 in the primary sense1 though not an individual which is present at once in the mind of each of these persons2 and thence readily sprung ,plato's theory of ,ideas1 each of which was1 according to him1 one real1 eternal object1 existing entire and complete in each of the individual objects that are known by one name40 ,it is1 indeed1 not a matter of inference1 but of authentic history1 that ,plato's doctrine of ,ideas1 and the ,aristotelian doctrine 7in this respect similar to the ,platonic7 of substantial forms and second substances1 grew up in the precise way here pointed out2 from the supposed necessity of finding1 in things which were said to have the same nature1 or the same qualities1 something which was the same in the very sense in which a man is the same as himself4 ,all the idle speculations respecting 1 1 1 and similar abstractions1 so common in the ancient and in some modern schools of thought1 sprang from the same source4 ,the ,aristotelian logicians saw1 however1 one case of the ambiguity1 and provided against it with their peculiar felicity in the invention of technical language1 when they distinguished things which differed both specie and numero1 from those which differed numero tantum1 that is1 which were exactly alike 7in some particular respect at least7 but were distinct individuals4 ,an extension of this distinction to the two meanings of the word ,same1 namely1 things which are the same specie tantum1 and a thing which is the same numero as well as specie1 would have prevented the confusion which has been a source of so much darkness and such an abundance of positive error in metaphysical philosophy4 ,one of the most singular examples of the length to which a thinker of eminence may be led away by an ambiguity of language1 is afforded by this very case4 ,i refer to the famous argument by which ,bishop ,berkeley flattered himself that he had forever put an end to 8skepticism1 atheism1 and irreligion40 ,it is briefly as follows3 ,i thought of a thing yesterday2 ,i ceased to think of it2 ,i think of it again to-day4 ,i had1 therefore1 in my mind yesterday an idea of the object2 ,i have also an idea of it to-day2 this idea is evidently not another1 but the very same idea4 ,yet an intervening time elapsed in which ,i had it not4 ,where was the idea during this interval8 ,it must have been somewhere2 it did not cease to exist2 otherwise the idea ,i had yesterday could not be the same idea2 no more than the man ,i see alive to-day can be the same whom ,i saw yesterday if the man has died in the mean while4 ,now an idea can not be conceived to exist anywhere except in a mind2 and hence there must exist a ,universal ,mind1 in which all ideas have their permanent residence during the intervals of their conscious presence in our own minds4 ,it is evident that ,berkeley here confounded sameness numero with sameness specie1 that is1 with exact resemblance1 and assumed the former where there was only the latter2 not perceiving that when we say we have the same thought to-day which we had yesterday1 we do not mean the same individual thought1 but a thought exactly similar3 as we say that we have the same illness which we had last year1 meaning only the same sort of illness4 ,in one remarkable instance the scientific world was divided into two furiously hostile parties by an ambiguity of language affecting a branch of science which1 more completely than most others1 enjoys the advantage of a precise and well-defined terminology4 ,i refer to the famous dispute respecting the vis viva1 the history of which is given at large in ,professor ,playfair's ,dissertation4 ,the question was1 whether the force of a moving body was proportional 7its mass being given7 to its velocity simply1 or to the square of its velocity3 and the ambiguity was in the word ,force4 8,one of the effects10 says ,playfair1 8produced by a moving body is proportional to the square of the velocity1 while another is proportional to the velocity simply30 from whence clearer thinkers were subsequently led to establish a double measure of the efficiency of a moving power1 one being called vis viva1 and the other momentum4 ,about the facts1 both parties were from the first agreed3 the only question was1 with which of the two effects the term force should be1 or could most conveniently be1 associated4 ,but the disputants were by no means aware that this was all2 they thought that force was one thing1 the production of effects another2 and the question1 by which set of effects the force which produced both the one and the other should be measured1 was supposed to be a question not of terminology1 but of fact4 ,the ambiguity of the word ,infinite is the real fallacy in the amusing logical puzzle of ,achilles and the ,tortoise1 a puzzle which has been too hard for the ingenuity or patience of many philosophers1 and which no less a thinker than ,sir ,william ,hamilton considered as insoluble2 as a sound argument1 though leading to a palpable falsehood4 ,the fallacy1 as ,hobbes hinted1 lies in the tacit assumption that whatever is infinitely divisible is infinite2 but the following solution 7to the invention of which ,i have no claim7 is more precise and satisfactory4 ,the argument is1 let ,achilles run ten times as fast as the tortoise1 yet if the tortoise has the start1 ,achilles will never overtake him4 ,for suppose them to be at first separated by an interval of a thousand feet3 when ,achilles has run these thousand feet1 the tortoise will have got on a hundred2 when ,achilles has run those hundred1 the tortoise will have run ten1 and so on forever3 therefore ,achilles may run forever without overtaking the tortoise4 ,now the 8forever10 in the conclusion1 means1 for any length of time that can be supposed2 but in the premises1 8ever0 does not mean any length of time2 it means any number of subdivisions of time4 ,it means that we may divide a thousand feet by ten1 and that quotient again by ten1 and so on as often as we please2 that there never needs be an end to the subdivisions of the distance1 nor consequently to those of the time in which it is performed4 ,but an unlimited number of subdivisions may be made of that which is itself limited4 ,the argument proves no other infinity of duration than may be embraced within five minutes4 ,as long as the five minutes are not expired1 what remains of them may be divided by ten1 and again by ten1 as often as we like1 which is perfectly compatible with their being only five minutes altogether4 ,it proves1 in short1 that to pass through this finite space requires a time which is infinitely divisible1 but not an infinite time2 the confounding of which distinction ,hobbes had already seen to be the gist of the fallacy4 ,the following ambiguities of the word right 7in addition to the obvious and familiar one of a right and the adjective right7 are extracted from a forgotten paper of my own1 in a periodical3 8,speaking morally1 you are said to have a right to do a thing1 if all persons are morally bound not to hinder you from doing it4 ,but1 in another sense1 to have a right to do a thing is the opposite of having no right to do it1 i4e41 of being under a moral obligation to forbear doing it4 ,in this sense1 to say that you have a right to do a thing1 means that you may do it without any breach of duty on your part2 that other persons not only ought not to hinder you1 but have no cause to think worse of you for doing it4 ,this is a perfectly distinct proposition from the preceding4 ,the right which you have by virtue of a duty incumbent upon other persons1 is obviously quite a different thing from a right consisting in the absence of any duty incumbent upon yourself4 ,yet the two things are perpetually confounded4 ,thus1 a man will say he has a right to publish his opinions2 which may be true in this sense1 that it would be a breach of duty in any other person to interfere and prevent the publication3 but he assumes thereupon that1 in publishing his opinions1 he himself violates no duty2 which may either be true or false1 depending1 as it does1 on his having taken due pains to satisfy himself1 first1 that the opinions are true1 and next1 that their publication in this manner1 and at this particular juncture1 will probably be beneficial to the interests of truth on the whole4 8,the second ambiguity is that of confounding a right of any kind1 with a right to enforce that right by resisting or punishing a violation of it4 ,people will say1 for example1 that they have a right to good government1 which is undeniably true1 it being the moral duty of their governors to govern them well4 ,but in granting this1 you are supposed to have admitted their right or liberty to turn out their governors1 and perhaps to punish them1 for having failed in the performance of this duty2 which1 far from being the same thing1 is by no means universally true1 but depends on an immense number of varying circumstances10 requiring to be conscientiously weighed before adopting or acting on such a resolution4 ,this last example is 7like others which have been cited7 a case of fallacy within fallacy2 it involves not only the second of the two ambiguities pointed out1 but the first likewise4 ,one not unusual form of the ,fallacy of ,ambiguous ,terms is known technically as the ,fallacy of ,composition and ,division2 when the same term is collective in the premises1 distributive in the conclusion1 or vic versa2 or when the middle term is collective in one premise1 distributive in the other4 ,as if one were to say 7,i quote from ,archbishop ,whately71 8,all the angles of a triangle are equal to two right angles3 ,a ,b ,c is an angle of a triangle2 therefore ,a ,b ,c is equal to two right angles4444 ,there is no fallacy more common1 or more likely to deceive1 than the one now before us4 ,the form in which it is most usually employed is to establish some truth1 separately1 concerning each single member of a certain class1 and thence to infer the same of the whole collectively40 ,as in the argument one sometimes hears1 to prove that the world could do without great men4 ,if ,columbus 7it is said7 had never lived1 ,america would still have been discovered1 at most only a few years later2 if ,newton had never lived1 some other person would have discovered the law of gravitation2 and so forth4 ,most true3 these things would have been done1 but in all probability not till some one had again been found with the qualities of ,columbus or ,newton4 ,because any one great man might have had his place supplied by other great men1 the argument concludes that all great men could have been dispensed with4 ,the term 8great men0 is distributive in the premises and collective in the conclusion4 8,such also is the fallacy which probably operates on most adventurers in lotteries2 e4g41 #8the gaining of a high prize is no uncommon occurrence2 and what is no uncommon occurrence may reasonably be expected2 therefore the gaining of a high prize may reasonably be expected2' the conclusion1 when applied to the individual 7as in practice it is71 must be understood in the sense of #8reasonably expected by a certain individual2' therefore for the major premise to be true1 the middle term must be understood to mean1 #8no uncommon occurrence to some one particular person2' whereas for the minor 7which has been placed first7 to be true1 you must understand it of #8no uncommon occurrence to some one or other2' and thus you will have the ,fallacy of ,composition4 8,this is a ,fallacy with which men are extremely apt to deceive themselves2 for when a multitude of particulars are presented to the mind1 many are too weak or too indolent to take a comprehensive view of them1 but confine their attention to each single point1 by turns2 and then decide1 infer1 and act accordingly2 e4g41 the imprudent spendthrift1 finding that he is able to afford this1 or that1 or the other expense1 forgets that all of them together will ruin him40 ,the debauchee destroys his health by successive acts of intemperance1 because no one of those acts would be of itself sufficient to do him any serious harm4 ,a sick person reasons with himself1 8one1 and another1 and another1 of my symptoms do not prove that ,i have a fatal disease20 and practically concludes that all taken together do not prove it4 #b4 ,we have now sufficiently exemplified one of the principal ,genera in this ,order of ,fallacies2 where1 the source of error being the ambiguity of terms1 the premises are verbally what is required to support the conclusion1 but not really so4 ,in the second great ,fallacy of ,confusion they are neither verbally nor really sufficient1 though1 from their multiplicity and confused arrangement1 and still oftener from defect of memory1 they are not seen to be what they are4 ,the fallacy ,i mean is that of ,petitio ,principii1 or begging the question2 including the more complex and not uncommon variety of it1 which is termed ,reasoning in a ,circle4 ,petitio ,principii1 as defined by ,archbishop ,whately1 is the fallacy 8in which the premise either appears manifestly to be the same as the conclusion1 or is actually proved from the conclusion1 or is such as would naturally and properly so be proved40 ,by the last clause ,i presume is meant1 that it is not susceptible of any other proof2 for otherwise1 there would be no fallacy4 ,to deduce from a proposition propositions from which it would itself more naturally be deduced1 is often an allowable deviation from the usual didactic order2 or at most1 what1 by an adaptation of a phrase familiar to mathematicians1 may be called a logical inelegance47#bfd7 ,the employment of a proposition to prove that on which it is itself dependent for proof1 by no means implies the degree of mental imbecility which might at first be supposed4 ,the difficulty of comprehending how this fallacy could possibly be committed1 disappears when we reflect that all persons1 even the instructed1 hold a great number of opinions without exactly recollecting how they came by them4 ,believing that they have at some former time verified them by sufficient evidence1 but having forgotten what the evidence was1 they may easily be betrayed into deducing from them the very propositions which are alone capable of serving as premises for their establishment4 8,as if10 says ,archbishop ,whately1 8one should attempt to prove the being of a ,god from the authority of ,holy ,writ20 which might easily happen to one with whom both doctrines1 as fundamental tenets of his religious creed1 stand on the same ground of familiar and traditional belief4 ,arguing in a circle1 however1 is a stronger case of the fallacy1 and implies more than the mere passive reception of a premise by one who does not remember how it is to be proved4 ,it implies an actual attempt to prove two propositions reciprocally from one another2 and is seldom resorted to1 at least in express terms1 by any person in his own speculations1 but is committed by those who1 being hard pressed by an adversary1 are forced into giving reasons for an opinion of which1 when they began to argue1 they had not sufficiently considered the grounds4 ,as in the following example from ,archbishop ,whately3 8,some mechanicians attempt to prove 7what they ought to lay down as a probable but doubtful hypothesis77#bfe7 that every particle of matter gravitates equally3 #8why8' #8because those bodies which contain more particles ever gravitate more strongly1 i4e41 are heavier3' #8but 7it may be urged7 those which are heaviest are not always more bulky2' #8no1 but they contain more particles1 though more closely condensed3' #8how do you know that8' #8because they are heavier3' #8how does that prove it8' #8because all particles of matter gravitating equally1 that mass which is specifically the heavier must needs have the more of them in the same space4'0 ,it appears to me that the fallacious reasoner1 in his private thoughts1 would not be likely to proceed beyond the first step4 ,he would acquiesce in the sufficiency of the reason first given1 8bodies which contain more particles are heavier40 ,it is when he finds this questioned1 and is called upon to prove it1 without knowing how1 that he tries to establish his premise by supposing proved what he is attempting to prove by it4 ,the most effectual way1 in fact1 of exposing a petitio principii1 when circumstances allow of it1 is by challenging the reasoner to prove his premises2 which if he attempts to do1 he is necessarily driven into arguing in a circle4 ,it is not uncommon1 however1 for thinkers1 and those not of the lowest description1 to be led even in their own thoughts1 not indeed into formally proving each of two propositions from the other1 but into admitting propositions which can only be so proved4 ,in the preceding example the two together form a complete and consistent1 though hypothetical1 explanation of the facts concerned4 ,and the tendency to mistake mutual coherency for truth--to trust one's safety to a strong chain though it has no point of support--is at the bottom of much which1 when reduced to the strict forms of argumentation1 can exhibit itself no otherwise than as reasoning in a circle4 ,all experience bears testimony to the enthralling effect of neat concatenation in a system of doctrines1 and the difficulty with which people admit the persuasion that any thing which holds so well together can possibly fall4 ,since every case where a conclusion which can only be proved from certain premises is used for the proof of those premises1 is a case of petitio principii1 that fallacy includes a very great proportion of all incorrect reasoning4 ,it is necessary1 for completing our view of the fallacy1 to exemplify some of the disguises under which it is accustomed to mask itself1 and to escape exposure4 ,a proposition would not be admitted by any person in his senses as a corollary from itself1 unless it were expressed in language which made it seem different4 ,one of the commonest modes of so expressing it1 is to present the proposition itself in abstract terms1 as a proof of the same proposition expressed in concrete language4 ,this is a very frequent mode1 not only of pretended proof1 but of pretended explanation2 and is parodied when ,molire 7,le ,malade ,imaginaire7 makes one of his absurd physicians say1 ,mihi a docto doctore1 ,demandatur causam et rationem quare ,opium facit dormire4 ,a quoi respondeo1 ,quia est in eo ,virtus dormitiva1 ,cujus est natura ,sensus assoupire4 ,the words ,nature and ,essence are grand instruments of this mode of begging the question1 as in the well-known argument of the scholastic theologians1 that the mind thinks always1 because the essence of the mind is to think4 ,locke had to point out1 that if by essence is here meant some property which must manifest itself by actual exercise at all times1 the premise is a direct assumption of the conclusion2 while if it only means that to think is the distinctive property of a mind1 there is no connection between the premise and the conclusion1 since it is not necessary that a distinctive property should be perpetually in action4 ,the following is one of the modes in which these abstract terms1 ,nature and ,essence1 are used as instruments of this fallacy4 ,some particular properties of a thing are selected1 more or less arbitrarily1 to be termed its nature or essence2 and when this has been done1 these properties are supposed to be invested with a kind of indefeasibleness2 to have become paramount to all the other properties of the thing1 and incapable of being prevailed over or counteracted by them4 ,as when ,aristotle1 in a passage already cited1 8decides that there is no void on such arguments as this3 in a void there could be no difference of up and down2 for as in nothing there are no differences1 so there are none in a privation or negation2 but a void is merely a privation or negation of matter2 therefore1 in a void1 bodies could not move up and down1 which it is in their nature to do407#bff7 ,in other words1 it is in the nature of bodies to move up and down1 ergo any physical fact which supposes them not so to move1 can not be authentic4 ,this mode of reasoning1 by which a bad generalization is made to overrule all facts which contradict it1 is ,petitio ,principii in one of its most palpable forms4 ,none of the modes of assuming what should be proved are in more frequent use than what are termed by ,bentham 8question-begging appellatives20 names which beg the question under the disguise of stating it4 ,the most potent of these are such as have a laudatory or vituperative character4 ,for instance1 in politics1 the word ,innovation4 ,the dictionary meaning of this term being merely 8a change to something new10 it is difficult for the defenders even of the most salutary improvement to deny that it is an innovation2 yet the word having acquired in common usage a vituperative connotation in addition to its dictionary meaning1 the admission is always construed as a large concession to the disadvantage of the thing proposed4 ,the following passage from the argument in refutation of the ,epicureans1 in the second book of ,cicero1 8,de ,finibus10 affords a fine example of this sort of fallacy3 8,et quidem illud ipsum non nimium probo 7et tantum patior7 philosophum loqui de cupiditatibus finiendis4 ,an potest cupiditas finiri8 tollenda est1 atque extrahenda radicitus4 ,quis est enim1 in quo sit cupiditas1 quin recte cupidus dici possit8 ,ergo et avarus erit1 sed finite3 adulter1 verum habebit modum3 et luxuriosus eodem modo4 ,qualis ista philosophia est1 qu non interitum afferat pravitatis1 sed sit contenta mediocritate vitiorum80 ,the question was1 whether certain desires1 when kept within bounds1 are vices or not2 and the argument decides the point by applying to them a word 7cupiditas7 which implies vice4 ,it is shown1 however1 in the remarks which follow1 that ,cicero did not intend this as a serious argument1 but as a criticism on what he deemed an inappropriate expression4 8,rem ipsam prorsus probo3 elegantiam desidero4 ,appellet hc desideria natur2 cupiditatis nomen servet alio10 etc4 ,but many persons1 both ancient and modern1 have employed this1 or something equivalent to it1 as a real and conclusive argument4 ,we may remark that the passage respecting cupiditas and cupidus is also an example of another fallacy already noticed1 that of ,paronymous ,terms4 ,many more of the arguments of the ancient moralists1 and especially of the ,stoics1 fall within the definition of ,petitio ,principii4 ,in the 8,de ,finibus10 for example1 which ,i continue to quote as being probably the best extant exemplification at once of the doctrines and the methods of the schools of philosophy existing at that time2 of what value as arguments are such pleas as those of ,cato in the third book3 ,that if virtue were not happiness1 it could not be a thing to boast of3 ,that if death or pain were evils1 it would be impossible not to fear them1 and it could not1 therefore1 be laudable to despise them1 etc4 ,in one way of viewing these arguments1 they may be regarded as appeals to the authority of the general sentiment of mankind which had stamped its approval upon certain actions and characters by the phrases referred to2 but that such could have been the meaning intended is very unlikely1 considering the contempt of the ancient philosophers for vulgar opinion4 ,in any other sense they are clear cases of ,petitio ,principii1 since the word laudable1 and the idea of boasting1 imply principles of conduct2 and practical maxims can only be proved from speculative truths1 namely1 from the properties of the subject-matter1 and can not1 therefore1 be employed to prove those properties4 ,as well might it be argued that a government is good because we ought to support it1 or that there is a ,god because it is our duty to pray to him4 ,it is assumed by all the disputants in the 8,de ,finibus0 as the foundation of the inquiry into the summum bonum1 that 8sapiens semper beatus est40 ,not simply that wisdom gives the best chance of happiness1 or that wisdom consists in knowing what happiness is1 and by what things it is promoted2 these propositions would not have been enough for them2 but that the sage always is1 and must of necessity be1 happy4 ,the idea that wisdom could be consistent with unhappiness1 was always rejected as inadmissible3 the reason assigned by one of the interlocutors1 near the beginning of the third book1 being1 that if the wise could be unhappy1 there was little use in pursuing wisdom4 ,but by unhappiness they did not mean pain or suffering2 to that it was granted that the wisest person was liable in common with others3 he was happy1 because in possessing wisdom he had the most valuable of all possessions1 the most to be sought and prized of all things1 and to possess the most valuable thing was to be the most happy4 ,by laying it down1 therefore1 at the commencement of the inquiry1 that the sage must be happy1 the disputed question respecting the summum bonum was in fact begged2 with the further assumption1 that pain and suffering1 so far as they can co-exist with wisdom1 are not unhappiness1 and are no evil4 ,the following are additional instances of ,petitio ,principii1 under more or less of disguise4 ,plato1 in the ,sophistes1 attempts to prove that things may exist which are incorporeal1 by the argument that justice and wisdom are incorporeal1 and justice and wisdom must be something4 ,here1 if by something be meant1 as ,plato did in fact mean1 a thing capable of existing in and by itself1 and not as a quality of some other thing1 he begs the question in asserting that justice and wisdom must be something2 if he means any thing else1 his conclusion is not proved4 ,this fallacy might also be classed under ambiguous middle-term2 something1 in the one premise1 meaning some substance1 in the other merely some object of thought1 whether substance or attribute4 ,it was formerly an argument employed in proof of what is now no longer a popular doctrine1 the infinite divisibility of matter1 that every portion of matter however small1 must at least have an upper and an under surface4 ,those who used this argument did not see that it assumed the very point in dispute1 the impossibility of arriving at a minimum of thickness2 for if there be a minimum1 its upper and under surface will of course be one2 it will be itself a surface1 and no more4 ,the argument owes its very considerable plausibility to this1 that the premise does actually seem more obvious than the conclusion1 though really identical with it4 ,as expressed in the premise1 the proposition appeals directly and in concrete language to the incapacity of the human imagination for conceiving a minimum4 ,viewed in this light1 it becomes a case of the a priori fallacy or natural prejudice1 that whatever can not be conceived can not exist4 ,every fallacy of ,confusion 7it is almost unnecessary to repeat7 will1 if cleared up1 become a fallacy of some other sort2 and it will be found of deductive or ratiocinative fallacies generally1 that when they mislead1 there is mostly1 as in this case1 a fallacy of some other description lurking under them1 by virtue of which chiefly it is that the verbal juggle1 which is the outside or body of this kind of fallacy1 passes undetected4 ,euler's ,algebra1 a book otherwise of great merit1 but full1 to overflowing1 of logical errors in respect to the foundation of the science1 contains the following argument to prove that minus multiplied by minus gives plus1 a doctrine the opprobrium of all mere mathematicians1 and which ,euler had not a glimpse of the true method of proving4 ,he says minus multiplied by minus can not give minus2 for minus multiplied by plus gives minus1 and minus multiplied by minus can not give the same product as minus multiplied by plus4 ,now one is obliged to ask1 why minus multiplied by minus must give any product at all8 and if it does1 why its product can not be the same as that of minus multiplied by plus8 for this would seem1 at the first glance1 not more absurd than that minus by minus should give the same as plus by plus1 the proposition which ,euler prefers to it4 ,the premise requires proof1 as much as the conclusion2 nor can it be proved1 except by that more comprehensive view of the nature of multiplication1 and of algebraic processes in general1 which would also supply a far better proof of the mysterious doctrine which ,euler is here endeavoring to demonstrate4 ,a striking instance of reasoning in a circle is that of some ethical writers1 who first take for their standard of moral truth what1 being the general1 they deem to be the natural or instinctive sentiments and perceptions of mankind1 and then explain away the numerous instances of divergence from their assumed standard1 by representing them as cases in which the perceptions are unhealthy4 ,some particular mode of conduct or feeling is affirmed to be unnatural2 why8 because it is abhorrent to the universal and natural sentiments of mankind4 ,finding no such sentiment in yourself1 you question the fact2 and the answer is 7if your antagonist is polite71 that you are an exception1 a peculiar case4 ,but neither 7say you7 do ,i find in the people of some other country1 or of some former age1 any such feeling of abhorrence2 8ay1 but their feelings were sophisticated and unhealthy40 ,one of the most notable specimens of reasoning in a circle is the doctrine of ,hobbes1 ,rousseau1 and others1 which rests the obligations by which human beings are bound as members of society1 on a supposed social compact4 ,i waive the consideration of the fictitious nature of the compact itself2 but when ,hobbes1 through the whole ,leviathan1 elaborately deduces the obligation of obeying the sovereign1 not from the necessity or utility of doing so1 but from a promise supposed to have been made by our ancestors1 on renouncing savage life and agreeing to establish political society1 it is impossible not to retort by the question1 ,why are we bound to keep a promise made for us by others8 or why bound to keep a promise at all8 ,no satisfactory ground can be assigned for the obligation1 except the mischievous consequences of the absence of faith and mutual confidence among mankind4 ,we are1 therefore1 brought round to the interests of society1 as the ultimate ground of the obligation of a promise2 and yet those interests are not admitted to be a sufficient justification for the existence of government and law4 ,without a promise it is thought that we should not be bound to that which is implied in all modes of living in society1 namely1 to yield a general obedience to the laws therein established2 and so necessary is the promise deemed1 that if none has actually been made1 some additional safety is supposed to be given to the foundations of society by feigning one4 #c4 ,two principal subdivisions of the class of ,fallacies of ,confusion having been disposed of2 there remains a third1 in which the confusion is not1 as in the ,fallacy of ,ambiguity1 in misconceiving the import of the premises1 nor1 as in ,petitio ,principii1 in forgetting what the premises are1 but in mistaking the conclusion which is to be proved4 ,this is the fallacy of ,ignoratio ,elenchi1 in the widest sense of the phrase2 also called by ,archbishop ,whately the ,fallacy of ,irrelevant ,conclusion4 ,his examples and remarks are highly worthy of citation4 8,various kinds of propositions are1 according to the occasion1 substituted for the one of which proof is required2 sometimes the particular for the universal2 sometimes a proposition with different terms2 and various are the contrivances employed to effect and to conceal this substitution1 and to make the conclusion which the sophist has drawn1 answer practically the same purpose as the one he ought to have established4 ,we say1 #8practically the same purpose1' because it will very often happen that some emotion will be excited1 some sentiment impressed on the mind 7by a dexterous employment of this fallacy71 such as shall bring men into the disposition requisite for your purpose2 though they may not have assented to1 or even stated distinctly in their own minds1 the proposition which it was your business to establish4 ,thus if a sophist has to defend one who has been guilty of some serious offense1 which he wishes to extenuate1 though he is unable distinctly to prove that it is not such1 yet if he can succeed in making the audience laugh at some casual matter1 he has gained practically the same point4 ,so also if any one has pointed out the extenuating circumstances in some particular case of offense1 so as to show that it differs widely from the generality of the same class1 the sophist1 if he finds himself unable to disprove these circumstances1 may do away the force of them1 by simply referring the action to that very class1 which no one can deny that it belongs to1 and the very name of which will excite a feeling of disgust sufficient to counteract the extenuation2 e4g41 let it be a case of peculation1 and that many mitigating circumstances have been brought forward which can not be denied2 the sophistical opponent will reply1 #8,well1 but after all1 the man is a rogue1 and there is an end of it2' now in reality this was 7by hypothesis7 never the question2 and the mere assertion of what was never denied ought not1 in fairness1 to be regarded as decisive2 but1 practically1 the odiousness of the word1 arising in great measure from the association of those very circumstances which belong to most of the class1 but which we have supposed to be absent in this particular instance1 excites precisely that feeling of disgust which1 in effect1 destroys the force of the defense4 ,in like manner we may refer to this head all cases of improper appeal to the passions1 and every thing else which is mentioned by ,aristotle as extraneous to the matter in hand 7 740 ,again1 8instead of proving that #8this prisoner has committed an atrocious fraud1' you prove that the fraud he is accused of is atrocious2 instead of proving 7as in the well-known tale of ,cyrus and the two coats7 that the taller boy had a right to force the other boy to exchange coats with him1 you prove that the exchange would have been advantageous to both2 instead of proving that the poor ought to be relieved in this way rather than in that1 you prove that the poor ought to be relieved2 instead of proving that the irrational agent--whether a brute or a madman--can never be deterred from any act by apprehension of punishment 7as1 for instance1 a dog from sheep-biting1 by fear of being beaten71 you prove that the beating of one dog does not operate as an example to other dogs1 etc4 8,it is evident that ,ignoratio ,elenchi may be employed as well for the apparent refutation of your opponent's proposition1 as for the apparent establishment of your own2 for it is substantially the same thing1 to prove what was not denied or to disprove what was not asserted4 ,the latter practice is not less common1 and it is more offensive1 because it frequently amounts to a personal affront1 in attributing to a person opinions1 etc41 which he perhaps holds in abhorrence4 ,thus1 when in a discussion one party vindicates1 on the ground of general expediency1 a particular instance of resistance to government in a case of intolerable oppression1 the opponent may gravely maintain1 #8that we ought not to do evil that good may come2' a proposition which of course had never been denied1 the point in dispute being1 #8whether resistance in this particular case were doing evil or not4' ,or again1 by way of disproving the assertion of the right of private judgment in religion1 one may hear a grave argument to prove that #8it is impossible every one can be right in his judgment4'0 ,the works of controversial writers are seldom free from this fallacy4 ,the attempts1 for instance1 to disprove the population doctrines of ,malthus1 have been mostly cases of ignoratio elenchi4 ,malthus has been supposed to be refuted if it could be shown that in some countries or ages population has been nearly stationary2 as if he had asserted that population always increases in a given ratio1 or had not expressly declared that it increases only in so far as it is not restrained by prudence1 or kept down by poverty and disease4 ,or1 perhaps1 a collection of facts is produced to prove that in some one country the people are better off with a dense population than they are in another country with a thin one2 or that the people have become more numerous and better off at the same time4 ,as if the assertion were that a dense population could not possibly be well off2 as if it were not part of the very doctrine1 and essential to it1 that where there is a more abundant production there may be a greater population without any increase of poverty1 or even with a diminution of it4 ,the favorite argument against ,berkeley's theory of the non-existence of matter1 and the most popularly effective1 next to a 8grin07#bfg7--;an argument1 moreover1 which is not confined to 8coxcombs10 nor to men like ,samuel ,johnson1 whose greatly overrated ability certainly did not lie in the direction of metaphysical speculation1 but is the stock argument of the ,scotch school of metaphysicians--is a palpable ,ignoratio ,elenchi4 ,the argument is perhaps as frequently expressed by gesture as by words1 and one of its commonest forms consists in knocking a stick against the ground4 ,this short and easy confutation overlooks the fact1 that in denying matter1 ,berkeley did not deny any thing to which our senses bear witness1 and therefore can not be answered by any appeal to them4 ,his skepticism related to the supposed substratum1 or hidden cause of the appearances perceived by our senses2 the evidence of which1 whatever may be thought of its conclusiveness1 is certainly not the evidence of sense4 ,and it will always remain a signal proof of the want of metaphysical profundity of ,reid1 ,stewart1 and1 ,i am sorry to add1 of ,brown1 that they should have persisted in asserting that ,berkeley1 if he believed his own doctrine1 was bound to walk into the kennel1 or run his head against a post4 ,as if persons who do not recognize an occult cause of their sensations could not possibly believe that a fixed order subsists among the sensations themselves4 ,such a want of comprehension of the distinction between a thing and its sensible manifestation1 or1 in metaphysical language1 between the noumenon and the phenomenon1 would be impossible to even the dullest disciple of ,kant or ,coleridge4 ,it would be easy to add a greater number of examples of this fallacy1 as well as of the others which ,i have attempted to characterize4 ,but a more copious exemplification does not seem to be necessary2 and the intelligent reader will have little difficulty in adding to the catalogue from his own reading and experience4 ,we shall1 therefore1 here close our exposition of the general principles of logic1 and proceed to the supplementary inquiry which is necessary to complete our design4 ,book ,,vi4 ,,on ,,the ,,logic ,,of ,,the ,,moral ,,sciences4 8,si l'homme peut prdire1 avec une assurance presque entire1 les phnomnes dont il connat les lois2 si lors mme qu'elles lui sont inconnues1 il peut1 d'aprs l'exprience1 prvoir avec une grande probabilit les vnements de l'avenir2 pourquoi regarderait-on comme une entreprise chimrique1 celle de tracer avec quelque vraisemblance le tableau des destines futures de l'espce humaine1 d'aprs les rsultats de son histoire8 ,le seul fondement de croyance dans les sciences naturelles1 est cette ide1 que les lois gnrales1 connues ou ignores1 qui rglent les phnomnes de l'univers1 sont ncessaires et constantes2 et par quelle raison ce principe serait-il moins vrai pour le dveloppement des facults intellectuelles et morales de l'homme1 que pour les autres oprations de la nature8 ,enfin1 puisque des opinions formes d'aprs l'exprience 444 sont la seule rgle de la conduite des hommes les plus sages1 pourquoi interdirait-on au philosophe d'appuyer ses conjectures sur cette mme base1 pourvu qu'il ne leur attribue pas une certitude suprieure celle qui peut natre du nombre1 de la constance1 de l'exactitude des observations80--,,condorcet1 ,esquisse d'un ,tableau ,historique des ,progrs de l',esprit ,humain4 ,chapter ,i4 ,introductory ,remarks4 #a4 ,principles of ,evidence and ,theories of ,method are not to be constructed a priori4 ,the laws of our rational faculty1 like those of every other natural agency1 are only learned by seeing the agent at work4 ,the earlier achievements of science were made without the conscious observance of any ,scientific ,method2 and we should never have known by what process truth is to be ascertained1 if we had not previously ascertained many truths4 ,but it was only the easier problems which could be thus resolved3 natural sagacity1 when it tried its strength against the more difficult ones1 either failed altogether1 or1 if it succeeded here and there in obtaining a solution1 had no sure means of convincing others that its solution was correct4 ,in scientific investigation1 as in all other works of human skill1 the way of obtaining the end is seen as it were instinctively by superior minds in some comparatively simple case1 and is then1 by judicious generalization1 adapted to the variety of complex cases4 ,we learn to do a thing in difficult circumstances1 by attending to the manner in which we have spontaneously done the same thing in easier ones4 ,this truth is exemplified by the history of the various branches of knowledge which have successively1 in the ascending order of their complication1 assumed the character of sciences2 and will doubtless receive fresh confirmation from those of which the final scientific constitution is yet to come1 and which are still abandoned to the uncertainties of vague and popular discussion4 ,although several other sciences have emerged from this state at a comparatively recent date1 none now remain in it except those which relate to man himself1 the most complex and most difficult subject of study on which the human mind can be engaged4 ,concerning the physical nature of man1 as an organized being--though there is still much uncertainty and much controversy1 which can only be terminated by the general acknowledgment and employment of stricter rules of induction than are commonly recognized--there is1 however1 a considerable body of truths which all who have attended to the subject consider to be fully established2 nor is there now any radical imperfection in the method observed in the department of science by its most distinguished modern teachers4 ,but the laws of ,mind1 and1 in even a greater degree1 those of ,society1 are so far from having attained a similar state of even partial recognition1 that it is still a controversy whether they are capable of becoming subjects of science in the strict sense of the term3 and among those who are agreed on this point1 there reigns the most irreconcilable diversity on almost every other4 ,here1 therefore1 if anywhere1 the principles laid down in the preceding ,books may be expected to be useful4 ,if on matters so much the most important with which human intellect can occupy itself a more general agreement is ever to exist among thinkers2 if what has been pronounced 8the proper study of mankind0 is not destined to remain the only subject which ,philosophy can not succeed in rescuing from ,empiricism2 the same process through which the laws of many simpler phenomena have by general acknowledgment been placed beyond dispute1 must be consciously and deliberately applied to those more difficult inquiries4 ,if there are some subjects on which the results obtained have finally received the unanimous assent of all who have attended to the proof1 and others on which mankind have not yet been equally successful2 on which the most sagacious minds have occupied themselves from the earliest date1 and have never succeeded in establishing any considerable body of truths1 so as to be beyond denial or doubt2 it is by generalizing the methods successfully followed in the former inquiries1 and adapting them to the latter1 that we may hope to remove this blot on the face of science4 ,the remaining chapters are an endeavor to facilitate this most desirable object4 #b4 ,in attempting this1 ,i am not unmindful how little can be done toward it in a mere treatise on ,logic1 or how vague and unsatisfactory all precepts of ,method must necessarily appear when not practically exemplified in the establishment of a body of doctrine4 ,doubtless1 the most effectual mode of showing how the sciences of ,ethics and ,politics may be constructed would be to construct them3 a task which1 it needs scarcely be said1 ,i am not about to undertake4 ,but even if there were no other examples1 the memorable one of ,bacon would be sufficient to demonstrate1 that it is sometimes both possible and useful to point out the way1 though without being one's self prepared to adventure far into it4 ,and if more were to be attempted1 this at least is not a proper place for the attempt4 ,in substance1 whatever can be done in a work like this for the ,logic of the ,moral ,sciences1 has been or ought to have been accomplished in the five preceding ,books2 to which the present can be only a kind of supplement or appendix1 since the methods of investigation applicable to moral and social science must have been already described1 if ,i have succeeded in enumerating and characterizing those of science in general4 ,it remains1 however1 to examine which of those methods are more especially suited to the various branches of moral inquiry2 under what peculiar facilities or difficulties they are there employed2 how far the unsatisfactory state of those inquiries is owing to a wrong choice of methods1 how far to want of skill in the application of right ones2 and what degree of ultimate success may be attained or hoped for by a better choice or more careful employment of logical processes appropriate to the case4 ,in other words1 whether moral sciences exist1 or can exist2 to what degree of perfection they are susceptible of being carried2 and by what selection or adaptation of the methods brought to view in the previous part of this work that degree of perfection is attainable4 ,at the threshold of this inquiry we are met by an objection1 which1 if not removed1 would be fatal to the attempt to treat human conduct as a subject of science4 ,are the actions of human beings1 like all other natural events1 subject to invariable laws8 ,does that constancy of causation1 which is the foundation of every scientific theory of successive phenomena1 really obtain among them8 ,this is often denied2 and for the sake of systematic completeness1 if not from any very urgent practical necessity1 the question should receive a deliberate answer in this place4 ,we shall devote to the subject a chapter apart4 ,chapter ,,ii4 ,of ,liberty ,and ,necessity4 #a4 ,the question1 whether the law of causality applies in the same strict sense to human actions as to other phenomena1 is the celebrated controversy concerning the freedom of the will2 which1 from at least as far back as the time of ,pelagius1 has divided both the philosophical and the religious world4 ,the affirmative opinion is commonly called the doctrine of ,necessity1 as asserting human volitions and actions to be necessary and inevitable4 ,the negative maintains that the will is not determined1 like other phenomena1 by antecedents1 but determines itself2 that our volitions are not1 properly speaking1 the effects of causes1 or at least have no causes which they uniformly and implicitly obey4 ,i have already made it sufficiently apparent that the former of these opinions is that which ,i consider the true one2 but the misleading terms in which it is often expressed1 and the indistinct manner in which it is usually apprehended1 have both obstructed its reception1 and perverted its influence when received4 ,the metaphysical theory of free-will1 as held by philosophers 7for the practical feeling of it1 common in a greater or less degree to all mankind1 is in no way inconsistent with the contrary theory71 was invented because the supposed alternative of admitting human actions to be necessary was deemed inconsistent with every one's instinctive consciousness1 as well as humiliating to the pride and even degrading to the moral nature of man4 ,nor do ,i deny that the doctrine1 as sometimes held1 is open to these imputations2 for the misapprehension in which ,i shall be able to show that they originate1 unfortunately is not confined to the opponents of the doctrine1 but is participated in by many1 perhaps we might say by most1 of its supporters4 #b4 ,correctly conceived1 the doctrine called ,philosophical ,necessity is simply this3 that1 given the motives which are present to an individual's mind1 and given likewise the character and disposition of the individual1 the manner in which he will act might be unerringly inferred2 that if we knew the person thoroughly1 and knew all the inducements which are acting upon him1 we could foretell his conduct with as much certainty as we can predict any physical event4 ,this proposition ,i take to be a mere interpretation of universal experience1 a statement in words of what every one is internally convinced of4 ,no one who believed that he knew thoroughly the circumstances of any case1 and the characters of the different persons concerned1 would hesitate to foretell how all of them would act4 ,whatever degree of doubt he may in fact feel1 arises from the uncertainty whether he really knows the circumstances1 or the character of some one or other of the persons1 with the degree of accuracy required2 but by no means from thinking that if he did know these things1 there could be any uncertainty what the conduct would be4 ,nor does this full assurance conflict in the smallest degree with what is called our feeling of freedom4 ,we do not feel ourselves the less free1 because those to whom we are intimately known are well assured how we shall will to act in a particular case4 ,we often1 on the contrary1 regard the doubt what our conduct will be1 as a mark of ignorance of our character1 and sometimes even resent it as an imputation4 ,the religious metaphysicians who have asserted the freedom of the will1 have always maintained it to be consistent with divine foreknowledge of our actions3 and if with divine1 then with any other foreknowledge4 ,we may be free1 and yet another may have reason to be perfectly certain what use we shall make of our freedom4 ,it is not1 therefore1 the doctrine that our volitions and actions are invariable consequents of our antecedent states of mind1 that is either contradicted by our consciousness1 or felt to be degrading4 ,but the doctrine of causation1 when considered as obtaining between our volitions and their antecedents1 is almost universally conceived as involving more than this4 ,many do not believe1 and very few practically feel1 that there is nothing in causation but invariable1 certain1 and unconditional sequence4 ,there are few to whom mere constancy of succession appears a sufficiently stringent bond of union for so peculiar a relation as that of cause and effect4 ,even if the reason repudiates1 the imagination retains1 the feeling of some more intimate connection1 of some peculiar tie1 or mysterious constraint exercised by the antecedent over the consequent4 ,now this it is which1 considered as applying to the human will1 conflicts with our consciousness1 and revolts our feelings4 ,we are certain that1 in the case of our volitions1 there is not this mysterious constraint4 ,we know that we are not compelled1 as by a magical spell1 to obey any particular motive4 ,we feel1 that if we wished to prove that we have the power of resisting the motive1 we could do so 7that wish being1 it needs scarcely be observed1 a new antecedent72 and it would be humiliating to our pride1 and 7what is of more importance7 paralyzing to our desire of excellence1 if we thought otherwise4 ,but neither is any such mysterious compulsion now supposed1 by the best philosophical authorities1 to be exercised by any other cause over its effect4 ,those who think that causes draw their effects after them by a mystical tie1 are right in believing that the relation between volitions and their antecedents is of another nature4 ,but they should go farther1 and admit that this is also true of all other effects and their antecedents4 ,if such a tie is considered to be involved in the word ,necessity1 the doctrine is not true of human actions2 but neither is it then true of inanimate objects4 ,it would be more correct to say that matter is not bound by necessity1 than that mind is so4 ,that the free-will metaphysicians1 being mostly of the school which rejects ,hume's and ,brown's analysis of ,cause and ,effect1 should miss their way for want of the light which that analysis affords1 can not surprise us4 ,the wonder is1 that the necessitarians1 who usually admit that philosophical theory1 should in practice equally lose sight of it4 ,the very same misconception of the doctrine called ,philosophical ,necessity1 which prevents the opposite party from recognizing its truth1 ,i believe to exist more or less obscurely in the minds of most necessitarians1 however they may in words disavow it4 ,i am much mistaken if they habitually feel that the necessity which they recognize in actions is but uniformity of order1 and capability of being predicted4 ,they have a feeling as if there were at bottom a stronger tie between the volitions and their causes2 as if1 when they asserted that the will is governed by the balance of motives1 they meant something more cogent than if they had only said1 that whoever knew the motives1 and our habitual susceptibilities to them1 could predict how we should will to act4 ,they commit1 in opposition to their own scientific system1 the very same mistake which their adversaries commit in obedience to theirs2 and in consequence do really in some instances suffer those depressing consequences which their opponents erroneously impute to the doctrine itself4 #c4 ,i am inclined to think that this error is almost wholly an effect of the associations with a word1 and that it would be prevented1 by forbearing to employ1 for the expression of the simple fact of causation1 so extremely inappropriate a term as ,necessity4 ,that word1 in its other acceptations1 involves much more than mere uniformity of sequence3 it implies irresistibleness4 ,applied to the will1 it only means that1 the given cause will be followed by the effect1 subject to all possibilities of counteraction by other causes2 but in common use it stands for the operation of those causes exclusively which are supposed too powerful to be counteracted at all4 ,when we say that all human actions take place of necessity1 we only mean that they will certainly happen if nothing prevents2 when we say that dying of want1 to those who can not get food1 is a necessity1 we mean that it will certainly happen whatever may be done to prevent it4 ,the application of the same term to the agencies on which human actions depend1 as is used to express those agencies of nature which are really uncontrollable1 can not fail1 when habitual1 to create a feeling of uncontrollableness in the former also4 ,this1 however1 is a mere illusion4 ,there are physical sequences which we call necessary1 as death for want of food or air2 there are others which1 though as much cases of causation as the former1 are not said to be necessary1 as death from poison1 which an antidote1 or the use of the stomach-pump1 will sometimes avert4 ,it is apt to be forgotten by people's feelings1 even if remembered by their understandings1 that human actions are in this last predicament3 they are never 7except in some cases of mania7 ruled by any one motive with such absolute sway that there is no room for the influence of any other4 ,the causes1 therefore1 on which action depends1 are never uncontrollable2 and any given effect is only necessary provided that the causes tending to produce it are not controlled4 ,that whatever happens1 could not have happened otherwise1 unless something had taken place which was capable of preventing it1 no one surely needs hesitate to admit4 ,but to call this by the name ,necessity is to use the term in a sense so different from its primitive and familiar meaning1 from that which it bears in the common occasions of life1 as to amount almost to a play upon words4 ,the associations derived from the ordinary sense of the term will adhere to it in spite of all we can do2 and though the doctrine of ,necessity1 as stated by most who hold it1 is very remote from fatalism1 it is probable that most necessitarians are fatalists1 more or less1 in their feelings4 ,a fatalist believes1 or half believes 7for nobody is a consistent fatalist71 not only that whatever is about to happen will be the infallible result of the causes which produce it 7which is the true necessitarian doctrine71 but moreover that there is no use in struggling against it2 that it will happen1 however we may strive to prevent it4 ,now1 a necessitarian1 believing that our actions follow from our characters1 and that our characters follow from our organization1 our education1 and our circumstances1 is apt to be1 with more or less of consciousness on his part1 a fatalist as to his own actions1 and to believe that his nature is such1 or that his education and circumstances have so moulded his character1 that nothing can now prevent him from feeling and acting in a particular way1 or at least that no effort of his own can hinder it4 ,in the words of the sect which in our own day has most perseveringly inculcated and most perversely misunderstood this great doctrine1 his character is formed for him1 and not by him2 therefore his wishing that it had been formed differently is of no use2 he has no power to alter it4 ,but this is a grand error4 ,he has1 to a certain extent1 a power to alter his character4 ,its being1 in the ultimate resort1 formed for him1 is not inconsistent with its being1 in part1 formed by him as one of the intermediate agents4 ,his character is formed by his circumstances 7including among these his particular organization72 but his own desire to mould it in a particular way1 is one of those circumstances1 and by no means one of the least influential4 ,we can not1 indeed1 directly will to be different from what we are4 ,but neither did those who are supposed to have formed our characters directly will that we should be what we are4 ,their will had no direct power except over their own actions4 ,they made us what they did make us1 by willing1 not the end1 but the requisite means2 and we1 when our habits are not too inveterate1 can1 by similarly willing the requisite means1 make ourselves different4 ,if they could place us under the influence of certain circumstances1 we1 in like manner1 can place ourselves under the influence of other circumstances4 ,we are exactly as capable of making our own character1 if we will1 as others are of making it for us4 ,yes 7answers the ,owenite71 but these words1 8if we will10 surrender the whole point3 since the will to alter our own character is given us1 not by any efforts of ours1 but by circumstances which we can not help1 it comes to us either from external causes1 or not at all4 ,most true3 if the ,owenite stops here1 he is in a position from which nothing can expel him4 ,our character is formed by us as well as for us2 but the wish which induces us to attempt to form it is formed for us2 and how8 ,not1 in general1 by our organization1 nor wholly by our education1 but by our experience2 experience of the painful consequences of the character we previously had2 or by some strong feeling of admiration or aspiration1 accidentally aroused4 ,but to think that we have no power of altering our character1 and to think that we shall not use our power unless we desire to use it1 are very different things1 and have a very different effect on the mind4 ,a person who does not wish to alter his character1 can not be the person who is supposed to feel discouraged or paralyzed by thinking himself unable to do it4 ,the depressing effect of the fatalist doctrine can only be felt where there is a wish to do what that doctrine represents as impossible4 ,it is of no consequence what we think forms our character1 when we have no desire of our own about forming it2 but it is of great consequence that we should not be prevented from forming such a desire by thinking the attainment impracticable1 and that if we have the desire1 we should know that the work is not so irrevocably done as to be incapable of being altered4 ,and indeed1 if we examine closely1 we shall find that this feeling1 of our being able to modify our own character if we wish1 is itself the feeling of moral freedom which we are conscious of4 ,a person feels morally free who feels that his habits or his temptations are not his masters1 but he theirs2 who1 even in yielding to them1 knows that he could resist2 that were he desirous of altogether throwing them off1 there would not be required for that purpose a stronger desire than he knows himself to be capable of feeling4 ,it is of course necessary1 to render our consciousness of freedom complete1 that we should have succeeded in making our character all we have hitherto attempted to make it2 for if we have wished and not attained1 we have1 to that extent1 not power over our own character2 we are not free4 ,or at least1 we must feel that our wish1 if not strong enough to alter our character1 is strong enough to conquer our character when the two are brought into conflict in any particular case of conduct4 ,and hence it is said with truth1 that none but a person of confirmed virtue is completely free4 ,the application of so improper a term as ,necessity to the doctrine of cause and effect in the matter of human character1 seems to me one of the most signal instances in philosophy of the abuse of terms1 and its practical consequences one of the most striking examples of the power of language over our associations4 ,the subject will never be generally understood until that objectionable term is dropped4 ,the free-will doctrine1 by keeping in view precisely that portion of the truth which the word ,necessity puts out of sight1 namely the power of the mind to co-operate in the formation of its own character1 has given to its adherents a practical feeling much nearer to the truth than has generally 7,i believe7 existed in the minds of necessitarians4 ,the latter may have had a stronger sense of the importance of what human beings can do to shape the characters of one another2 but the free-will doctrine has1 ,i believe1 fostered in its supporters a much stronger spirit of self-culture4 #d4 ,there is still one fact which requires to be noticed 7in addition to the existence of a power of self-formation7 before the doctrine of the causation of human actions can be freed from the confusion and misapprehensions which surround it in many minds4 ,when the will is said to be determined by motives1 a motive does not mean always1 or solely1 the anticipation of a pleasure or of a pain4 ,i shall not here inquire whether it be true that1 in the commencement1 all our voluntary actions are mere means consciously employed to obtain some pleasure or avoid some pain4 ,it is at least certain that we gradually1 through the influence of association1 come to desire the means without thinking of the end2 the action itself becomes an object of desire1 and is performed without reference to any motive beyond itself4 ,thus far1 it may still be objected that1 the action having through association become pleasurable1 we are1 as much as before1 moved to act by the anticipation of a pleasure1 namely1 the pleasure of the action itself4 ,but granting this1 the matter does not end here4 ,as we proceed in the formation of habits1 and become accustomed to will a particular act or a particular course of conduct because it is pleasurable1 we at last continue to will it without any reference to its being pleasurable4 ,although1 from some change in us or in our circumstances1 we have ceased to find any pleasure in the action1 or perhaps to anticipate any pleasure as the consequence of it1 we still continue to desire the action1 and consequently to do it4 ,in this manner it is that habits of hurtful excess continue to be practiced although they have ceased to be pleasurable2 and in this manner also it is that the habit of willing to persevere in the course which he has chosen1 does not desert the moral hero1 even when the reward1 however real1 which he doubtless receives from the consciousness of well-doing1 is any thing but an equivalent for the sufferings he undergoes1 or the wishes which he may have to renounce4 ,a habit of willing is commonly called a purpose2 and among the causes of our volitions1 and of the actions which flow from them1 must be reckoned not only likings and aversions1 but also purposes4 ,it is only when our purposes have become independent of the feelings of pain or pleasure from which they originally took their rise1 that we are said to have a confirmed character4 8,a character10 says ,novalis1 8is a completely fashioned will30 and the will1 once so fashioned1 may be steady and constant1 when the passive susceptibilities of pleasure and pain are greatly weakened or materially changed4 ,with the corrections and explanations now given1 the doctrine of the causation of our volitions by motives1 and of motives by the desirable objects offered to us1 combined with our particular susceptibilities of desire1 may be considered1 ,i hope1 as sufficiently established for the purposes of this treatise47#bfh7 ,chapter ,,iii4 ,that ,there ,is1 ,or ,may ,be1 ,a ,science ,of ,human ,nature4 #a4 ,it is a common notion1 or at least it is implied in many common modes of speech1 that the thoughts1 feelings1 and actions of sentient beings are not a subject of science1 in the same strict sense in which this is true of the objects of outward nature4 ,this notion seems to involve some confusion of ideas1 which it is necessary to begin by clearing up4 ,any facts are fitted1 in themselves1 to be a subject of science which follow one another according to constant laws1 although those laws may not have been discovered1 nor even be discoverable by our existing resources4 ,take1 for instance1 the most familiar class of meteorological phenomena1 those of rain and sunshine4 ,scientific inquiry has not yet succeeded in ascertaining the order of antecedence and consequence among these phenomena1 so as to be able1 at least in our regions of the earth1 to predict them with certainty1 or even with any high degree of probability4 ,yet no one doubts that the phenomena depend on laws1 and that these must be derivative laws resulting from known ultimate laws1 those of heat1 electricity1 vaporization1 and elastic fluids4 ,nor can it be doubted that if we were acquainted with all the antecedent circumstances1 we could1 even from those more general laws1 predict 7saving difficulties of calculation7 the state of the weather at any future time4 ,meteorology1 therefore1 not only has in itself every natural requisite for being1 but actually is1 a science2 though1 from the difficulty of observing the facts on which the phenomena depend 7a difficulty inherent in the peculiar nature of those phenomena71 the science is extremely imperfect2 and were it perfect1 might probably be of little avail in practice1 since the data requisite for applying its principles to particular instances would rarely be procurable4 ,a case may be conceived1 of an intermediate character1 between the perfection of science and this its extreme imperfection4 ,it may happen that the greater causes1 those on which the principal part of the phenomena depends1 are within the reach of observation and measurement2 so that if no other causes intervened1 a complete explanation could be given not only of the phenomena in general1 but of all the variations and modifications which it admits of4 ,but inasmuch as other1 perhaps many other causes1 separately insignificant in their effects1 co-operate or conflict in many or in all cases with those greater causes1 the effect1 accordingly1 presents more or less of aberration from what would be produced by the greater causes alone4 ,now if these minor causes are not so constantly accessible1 or not accessible at all1 to accurate observation1 the principal mass of the effect may still1 as before1 be accounted for1 and even predicted2 but there will be variations and modifications which we shall not be competent to explain thoroughly1 and our predictions will not be fulfilled accurately1 but only approximately4 ,it is thus1 for example1 with the theory of the tides4 ,no one doubts that ,tidology 7as ,dr4 ,whewell proposes to call it7 is really a science4 ,as much of the phenomena as depends on the attraction of the sun and moon is completely understood1 and may1 in any1 even unknown1 part of the earth's surface1 be foretold with certainty2 and the far greater part of the phenomena depends on those causes4 ,but circumstances of a local or casual nature1 such as the configuration of the bottom of the ocean1 the degree of confinement from shores1 the direction of the wind1 etc41 influence1 in many or in all places1 the height and time of the tide2 and a portion of these circumstances being either not accurately knowable1 not precisely measurable1 or not capable of being certainly foreseen1 the tide in known places commonly varies from the calculated result of general principles by some difference that we can not explain1 and in unknown ones may vary from it by a difference that we are not able to foresee or conjecture4 ,nevertheless1 not only is it certain that these variations depend on causes1 and follow their causes by laws of unerring uniformity2 not only1 therefore1 is tidology a science1 like meteorology1 but it is1 what hitherto at least meteorology is not1 a science largely available in practice4 ,general laws may be laid down respecting the tides1 predictions may be founded on those laws1 and the result will in the main1 though often not with complete accuracy1 correspond to the predictions4 ,and this is what is or ought to be meant by those who speak of sciences which are not exact sciences4 ,astronomy was once a science1 without being an exact science4 ,it could not become exact until not only the general course of the planetary motions1 but the perturbations also1 were accounted for1 and referred to their causes4 ,it has become an exact science1 because its phenomena have been brought under laws comprehending the whole of the causes by which the phenomena are influenced1 whether in a great or only in a trifling degree1 whether in all or only in some cases1 and assigning to each of those causes the share of effect which really belongs to it4 ,but in the theory of the tides the only laws as yet accurately ascertained are those of the causes which affect the phenomenon in all cases1 and in a considerable degree2 while others which affect it in some cases only1 or1 if in all1 only in a slight degree1 have not been sufficiently ascertained and studied to enable us to lay down their laws2 still less to deduce the completed law of the phenomenon1 by compounding the effects of the greater with those of the minor causes4 ,tidology1 therefore1 is not yet an exact science2 not from any inherent incapacity of being so1 but from the difficulty of ascertaining with complete precision the real derivative uniformities4 ,by combining1 however1 the exact laws of the greater causes1 and of such of the minor ones as are sufficiently known1 with such empirical laws or such approximate generalizations respecting the miscellaneous variations as can be obtained by specific observation1 we can lay down general propositions which will be true in the main1 and on which1 with allowance for the degree of their probable inaccuracy1 we may safely ground our expectations and our conduct4 #b4 ,the science of human nature is of this description4 ,it falls far short of the standard of exactness now realized in ,astronomy2 but there is no reason that it should not be as much a science as ,tidology is1 or as ,astronomy was when its calculations had only mastered the main phenomena1 but not the perturbations4 ,the phenomena with which this science is conversant being the thoughts1 feelings1 and actions of human beings1 it would have attained the ideal perfection of a science if it enabled us to foretell how an individual would think1 feel1 or act throughout life1 with the same certainty with which astronomy enables us to predict the places and the occultations of the heavenly bodies4 ,it needs scarcely be stated that nothing approaching to this can be done4 ,the actions of individuals could not be predicted with scientific accuracy1 were it only because we can not foresee the whole of the circumstances in which those individuals will be placed4 ,but further1 even in any given combination of 7present7 circumstances1 no assertion1 which is both precise and universally true1 can be made respecting the manner in which human beings will think1 feel1 or act4 ,this is not1 however1 because every person's modes of thinking1 feeling1 and acting do not depend on causes2 nor can we doubt that if1 in the case of any individual1 our data could be complete1 we even now know enough of the ultimate laws by which mental phenomena are determined1 to enable us in many cases to predict1 with tolerable certainty1 what1 in the greater number of supposable combinations of circumstances1 his conduct or sentiments would be4 ,but the impressions and actions of human beings are not solely the result of their present circumstances1 but the joint result of those circumstances and of the characters of the individuals2 and the agencies which determine human character are so numerous and diversified 7nothing which has happened to the person throughout life being without its portion of influence71 that in the aggregate they are never in any two cases exactly similar4 ,hence1 even if our science of human nature were theoretically perfect1 that is1 if we could calculate any character as we can calculate the orbit of any planet1 from given data2 still1 as the data are never all given1 nor ever precisely alike in different cases1 we could neither make positive predictions1 nor lay down universal propositions4 ,inasmuch1 however1 as many of those effects which it is of most importance to render amenable to human foresight and control are determined1 like the tides1 in an incomparably greater degree by general causes1 than by all partial causes taken together2 depending in the main on those circumstances and qualities which are common to all mankind1 or at least to large bodies of them1 and only in a small degree on the idiosyncrasies of organization or the peculiar history of individuals2 it is evidently possible with regard to all such effects1 to make predictions which will almost always be verified1 and general propositions which are almost always true4 ,and whenever it is sufficient to know how the great majority of the human race1 or of some nation or class of persons1 will think1 feel1 and act1 these propositions are equivalent to universal ones4 ,for the purposes of political and social science this is sufficient4 ,as we formerly remarked17#bfi7 an approximate generalization is1 in social inquiries1 for most practical purposes equivalent to an exact one2 that which is only probable when asserted of individual human beings indiscriminately selected1 being certain when affirmed of the character and collective conduct of masses4 ,it is no disparagement1 therefore1 to the science of ,human ,nature1 that those of its general propositions which descend sufficiently into detail to serve as a foundation for predicting phenomena in the concrete1 are for the most part only approximately true4 ,but in order to give a genuinely scientific character to the study1 it is indispensable that these approximate generalizations1 which in themselves would amount only to the lowest kind of empirical laws1 should be connected deductively with the laws of nature from which they result2 should be resolved into the properties of the causes on which the phenomena depend4 ,in other words1 the science of ,human ,nature may be said to exist in proportion as the approximate truths1 which compose a practical knowledge of mankind1 can be exhibited as corollaries from the universal laws of human nature on which they rest2 whereby the proper limits of those approximate truths would be shown1 and we should be enabled to deduce others for any new state of circumstances1 in anticipation of specific experience4 ,the proposition now stated is the text on which the two succeeding chapters will furnish the comment4 ,chapter ,,iv4 ,of ,the ,laws ,of ,mind4 #a4 ,what the ,mind is1 as well as what ,matter is1 or any other question respecting ,things in themselves1 as distinguished from their sensible manifestations1 it would be foreign to the purposes of this treatise to consider4 ,here1 as throughout our inquiry1 we shall keep clear of all speculations respecting the mind's own nature1 and shall understand by the laws of mind those of mental ,phenomena2 of the various feelings or states of consciousness of sentient beings4 ,these1 according to the classification we have uniformly followed1 consist of ,thoughts1 ,emotions1 ,volitions1 and ,sensations2 the last being as truly states of ,mind as the three former4 ,it is usual1 indeed1 to speak of sensations as states of body1 not of mind4 ,but this is the common confusion1 of giving one and the same name to a phenomenon and to the approximate cause or conditions of the phenomenon4 ,the immediate antecedent of a sensation is a state of body1 but the sensation itself is a state of mind4 ,if the word ,mind means any thing1 it means that which feels4 ,whatever opinion we hold respecting the fundamental identity or diversity of matter and mind1 in any case the distinction between mental and physical facts1 between the internal and the external world1 will always remain1 as a matter of classification2 and in that classification1 sensations1 like all other feelings1 must be ranked as mental phenomena4 ,the mechanism of their production1 both in the body itself and in what is called outward nature1 is all that can with any propriety be classed as physical4 ,the phenomena of mind1 then1 are the various feelings of our nature1 both those improperly called physical and those peculiarly designated as mental2 and by the laws of mind1 ,i mean the laws according to which those feelings generate one another4 #b4 ,all states of mind are immediately caused either by other states of mind1 or by states of body4 ,when a state of mind is produced by a state of mind1 ,i call the law concerned in the case a law of ,mind4 ,when a state of mind is produced directly by a state of body1 the law is a law of ,body1 and belongs to physical science4 ,with regard to those states of mind which are called sensations1 all are agreed that these have for their immediate antecedents1 states of body4 ,every sensation has for its proximate cause some affection of the portion of our frame called the nervous system1 whether this affection originates in the action of some external object1 or in some pathological condition of the nervous organization itself4 ,the laws of this portion of our nature--the varieties of our sensations1 and the physical conditions on which they proximately depend--manifestly belong to the province of ,physiology4 ,whether the remainder of our mental states are similarly dependent on physical conditions1 is one of the vexat questiones in the science of human nature4 ,it is still disputed whether our thoughts1 emotions1 and volitions are generated through the intervention of material mechanism2 whether we have organs of thought and of emotion1 in the same sense in which we have organs of sensation4 ,many eminent physiologists hold the affirmative4 ,these contend that a thought 7for example7 is as much the result of nervous agency1 as a sensation2 that some particular state of our nervous system1 in particular of that central portion of it called the brain1 invariably precedes1 and is presupposed by1 every state of our consciousness4 ,according to this theory1 one state of mind is never really produced by another3 all are produced by states of body4 ,when one thought seems to call up another by association1 it is not really a thought which recalls a thought2 the association did not exist between the two thoughts1 but between the two states of the brain or nerves which preceded the thoughts3 one of those states recalls the other1 each being attended in its passage by the particular state of consciousness which is consequent on it4 ,on this theory the uniformities of succession among states of mind would be mere derivative uniformities1 resulting from the laws of succession of the bodily states which cause them4 ,there would be no original mental laws1 no ,laws of ,mind in the sense in which ,i use the term1 at all2 and mental science would be a mere branch1 though the highest and most recondite branch1 of the science of physiology4 ,m4 ,comte1 accordingly1 claims the scientific cognizance of moral and intellectual phenomena exclusively for physiologists2 and not only denies to ,psychology1 or ,mental ,philosophy properly so called1 the character of a science1 but places it1 in the chimerical nature of its objects and pretensions1 almost on a par with astrology4 ,but1 after all has been said which can be said1 it remains incontestable that there exist uniformities of succession among states of mind1 and that these can be ascertained by observation and experiment4 ,further1 that every mental state has a nervous state for its immediate antecedent and proximate cause1 though extremely probable1 can not hitherto be said to be proved1 in the conclusive manner in which this can be proved of sensations2 and even were it certain1 yet every one must admit that we are wholly ignorant of the characteristics of these nervous states2 we know not1 and at present have no means of knowing1 in what respect one of them differs from another2 and our only mode of studying their successions or co-existences must be by observing the successions and co-existences of the mental states1 of which they are supposed to be the generators or causes4 ,the successions1 therefore1 which obtain among mental phenomena1 do not admit of being deduced from the physiological laws of our nervous organization2 and all real knowledge of them must continue1 for a long time at least1 if not always1 to be sought in the direct study1 by observation and experiment1 of the mental successions themselves4 ,since1 therefore1 the order of our mental phenomena must be studied in those phenomena1 and not inferred from the laws of any phenomena more general1 there is a distinct and separate ,science of ,mind4 ,the relations1 indeed1 of that science to the science of physiology must never be overlooked or undervalued4 ,it must by no means be forgotten that the laws of mind may be derivative laws resulting from laws of animal life1 and that their truth1 therefore1 may ultimately depend on physical conditions2 and the influence of physiological states or physiological changes in altering or counteracting the mental successions1 is one of the most important departments of psychological study4 ,but1 on the other hand1 to reject the resource of psychological analysis1 and construct the theory of the mind solely on such data as physiology at present affords1 seems to me as great an error in principle1 and an even more serious one in practice4 ,imperfect as is the science of mind1 ,i do not scruple to affirm that it is in a considerably more advanced state than the portion of physiology which corresponds to it2 and to discard the former for the latter appears1 to me an infringement of the true canons of inductive philosophy1 which must produce1 and which does produce1 erroneous conclusions in some very important departments of the science of human nature4 #c4 ,the subject1 then1 of ,psychology is the uniformities of succession1 the laws1 whether ultimate or derivative1 according to which one mental state succeeds another2 is caused by1 or at least1 is caused to follow1 another4 ,of these laws some are general1 others more special4 ,the following are examples of the most general laws3 ,first4 ,whenever any state of consciousness has once been excited in us1 no matter by what cause1 an inferior degree of the same state of consciousness1 a state of consciousness resembling the former1 but inferior in intensity1 is capable of being reproduced in us1 without the presence of any such cause as excited it at first4 ,thus1 if we have once seen or touched an object1 we can afterward think of the object though it be absent from our sight or from our touch4 ,if we have been joyful or grieved at some event1 we can think of or remember our past joy or grief1 though no new event of a happy or painful nature has taken place4 ,when a poet has put together a mental picture of an imaginary object1 a ,castle of ,indolence1 a ,una1 or a ,hamlet1 he can afterward think of the ideal object he has created1 without any fresh act of intellectual combination4 ,this law is expressed by saying1 in the language of ,hume1 that every mental impression has its idea4 ,secondly4 ,these ideas1 or secondary mental states1 are excited by our impressions1 or by other ideas1 according to certain laws which are called ,laws of ,association4 ,of these laws the first is1 that similar ideas tend to excite one another4 ,the second is1 that when two impressions have been frequently experienced 7or even thought of7 either simultaneously or in immediate succession1 then whenever one of these impressions1 or the idea of it1 recurs1 it tends to excite the idea of the other4 ,the third law is1 that greater intensity in either or both of the impressions is equivalent1 in rendering them excitable by one another1 to a greater frequency of conjunction4 ,these are the laws of ideas1 on which ,i shall not enlarge in this place1 but refer the reader to works professedly psychological1 in particular to ,mr4 ,james ,mill's ,analysis of the ,phenomena of the ,human ,mind1 where the principal laws of association1 along with many of their applications1 are copiously exemplified1 and with a masterly hand47#bgj7 ,these simple or elementary ,laws of ,mind have been ascertained by the ordinary methods of experimental inquiry2 nor could they have been ascertained in any other manner4 ,but a certain number of elementary laws having thus been obtained1 it is a fair subject of scientific inquiry how far those laws can be made to go in explaining the actual phenomena4 ,it is obvious that complex laws of thought and feeling not only may1 but must1 be generated from these simple laws4 ,and it is to be remarked1 that the case is not always one of ,composition of ,causes3 the effect of concurring causes is not always precisely the sum of the effects of those causes when separate1 nor even always an effect of the same kind with them4 ,reverting to the distinction which occupies so prominent a place in the theory of induction1 the laws of the phenomena of mind are sometimes analogous to mechanical1 but sometimes also to chemical laws4 ,when many impressions or ideas are operating in the mind together1 there sometimes takes place a process of a similar kind to chemical combination4 ,when impressions have been so often experienced in conjunction1 that each of them calls up readily and instantaneously the ideas of the whole group1 those ideas sometimes melt and coalesce into one another1 and appear not several ideas1 but one2 in the same manner as1 when the seven prismatic colors are presented to the eye in rapid succession1 the sensation produced is that of white4 ,but as in this last case it is correct to say that the seven colors when they rapidly follow one another generate white1 but not that they actually are white2 so it appears to me that the ,complex ,idea1 formed by the blending together of several simpler ones1 should1 when it really appears simple 7that is1 when the separate elements are not consciously distinguishable in it71 be said to result from1 or be generated by1 the simple ideas1 not to consist of them4 ,our idea of an orange really consists of the simple ideas of a certain color1 a certain form1 a certain taste and smell1 etc41 because we can1 by interrogating our consciousness1 perceive all these elements in the idea4 ,but we can not perceive1 in so apparently simple a feeling as our perception of the shape of an object by the eye1 all that multitude of ideas derived from other senses1 without which it is well ascertained that no such visual perception would ever have had existence2 nor1 in our idea of ,extension1 can we discover those elementary ideas of resistance1 derived from our muscular frame1 in which it has been conclusively shown that the idea originates4 ,these1 therefore1 are cases of mental chemistry2 in which it is proper to say that the simple ideas generate1 rather than that they compose1 the complex ones4 ,with respect to all the other constituents of the mind1 its beliefs1 its abstruser conceptions1 its sentiments1 emotions1 and volitions1 there are some 7among whom are ,hartley and the author of the ,analysis7 who think that the whole of these are generated from simple ideas of sensation1 by a chemistry similar to that which we have just exemplified4 ,these philosophers have made out a great part of their case1 but ,i am not satisfied that they have established the whole of it4 ,they have shown that there is such a thing as mental chemistry2 that the heterogeneous nature of a feeling ,a1 considered in relation to ,b and ,c1 is no conclusive argument against its being generated from ,b and ,c4 ,having proved this1 they proceed to show1 that where ,a is found1 ,b and ,c were1 or may have been present1 and why1 therefore1 they ask1 should not ,a have been generated from ,b and ,c8 ,but even if this evidence were carried to the highest degree of completeness which it admits of2 if it were shown 7which hitherto it has not1 in all cases1 been7 that certain groups of associated ideas not only might have been1 but actually were1 present whenever the more recondite mental feeling was experienced2 this would amount only to the ,method of ,agreement1 and could not prove causation until confirmed by the more conclusive evidence of the ,method of ,difference4 ,if the question be whether ,belief is a mere case of close association of ideas1 it would be necessary to examine experimentally if it be true that any ideas whatever1 provided they are associated with the required degree of closeness1 give rise to belief4 ,if the inquiry be into the origin of moral feelings1 the feeling for example of moral reprobation1 it is necessary to compare all the varieties of actions or states of mind which are ever morally disapproved1 and see whether in all these cases it can be shown1 or reasonably surmised1 that the action or state of mind had become connected by association1 in the disapproving mind1 with some particular class of hateful or disgusting ideas2 and the method employed is1 thus far1 that of ,agreement4 ,but this is not enough4 ,supposing this proved1 we must try further by the ,method of ,difference1 whether this particular kind of hateful or disgusting ideas1 when it becomes associated with an action previously indifferent1 will render that action a subject of moral disapproval4 ,if this question can be answered in the affirmative1 it is shown to be a law of the human mind1 that an association of that particular description is the generating cause of moral reprobation4 ,that all this is the case has been rendered extremely probable1 but the experiments have not been tried with the degree of precision necessary for a complete and absolutely conclusive induction47#bga7 ,it is further to be remembered1 that even if all which this theory of mental phenomena contends for could be proved1 we should not be the more enabled to resolve the laws of the more complex feelings into those of the simpler ones4 ,the generation of one class of mental phenomena from another1 whenever it can be made out1 is a highly interesting fact in psychological chemistry2 but it no more supersedes the necessity of an experimental study of the generated phenomenon1 than a knowledge of the properties of oxygen and sulphur enables us to deduce those of sulphuric acid without specific observation and experiment4 ,whatever1 therefore1 may be the final issue of the attempt to account for the origin of our judgments1 our desires1 or our volitions1 from simpler mental phenomena1 it is not the less imperative to ascertain the sequences of the complex phenomena themselves1 by special study in conformity to the canons of ,induction4 ,thus1 in respect to ,belief1 psychologists will always have to inquire what beliefs we have by direct consciousness1 and according to what laws one belief produces another2 what are the laws in virtue of which one thing is recognized by the mind1 either rightly or erroneously1 as evidence of another thing4 ,in regard to ,desire1 they will have to examine what objects we desire naturally1 and by what causes we are made to desire things originally indifferent1 or even disagreeable to us2 and so forth4 ,it may be remarked that the general laws of association prevail among these more intricate states of mind1 in the same manner as among the simpler ones4 ,a desire1 an emotion1 an idea of the higher order of abstraction1 even our judgments and volitions1 when they have become habitual1 are called up by association1 according to precisely the same laws as our simple ideas4 #d4 ,in the course of these inquiries1 it will be natural and necessary to examine how far the production of one state of mind by another is influenced by any assignable state of body4 ,the commonest observation shows that different minds are susceptible in very different degrees to the action of the same psychological causes4 ,the idea1 for example1 of a given desirable object will excite in different minds very different degrees of intensity of desire4 ,the same subject of meditation1 presented to different minds1 will excite in them very unequal degrees of intellectual action4 ,these differences of mental susceptibility in different individuals may be1 first1 original and ultimate facts2 or1 secondly1 they may be consequences of the previous mental history of those individuals2 or1 thirdly and lastly1 they may depend on varieties of physical organization4 ,that the previous mental history of the individuals must have some share in producing or in modifying the whole of their mental character1 is an inevitable consequence of the laws of mind2 but that differences of bodily structure also co-operate1 is the opinion of all physiologists1 confirmed by common experience4 ,it is to be regretted that hitherto this experience1 being accepted in the gross1 without due analysis1 has been made the groundwork of empirical generalizations most detrimental to the progress of real knowledge4 ,it is certain that the natural differences which really exist in the mental predispositions or susceptibilities of different persons are often not unconnected with diversities in their organic constitution4 ,but it does not therefore follow that these organic differences must in all cases influence the mental phenomena directly and immediately4 ,they often affect them through the medium of their psychological causes4 ,for example1 the idea of some particular pleasure may excite in different persons1 even independently of habit or education1 very different strengths of desire1 and this may be the effect of their different degrees or kinds of nervous susceptibility2 but these organic differences1 we must remember1 will render the pleasurable sensation itself more intense in one of these persons than in the other2 so that the idea of the pleasure will also be an intenser feeling1 and will1 by the operation of mere mental laws1 excite an intenser desire1 without its being necessary to suppose that the desire itself is directly influenced by the physical peculiarity4 ,as in this1 so in many cases1 such differences in the kind or in the intensity of the physical sensations as must necessarily result from differences of bodily organization1 will of themselves account for many differences not only in the degree1 but even in the kind1 of the other mental phenomena4 ,so true is this1 that even different qualities of mind1 different types of mental character1 will naturally be produced by mere differences of intensity in the sensations generally2 as is well pointed out in the able essay on ,dr4 ,priestley1 by ,mr4 ,martineau1 mentioned in a former chapter3 8,the sensations which form the elements of all knowledge are received either simultaneously or successively3 when several are received simultaneously1 as the smell1 the taste1 the color1 the form1 etc41 of a fruit1 their association together constitutes our idea of an object2 when received successively1 their association makes up the idea of an event4 ,any thing1 then1 which favors the associations of synchronous ideas will tend to produce a knowledge of objects1 a perception of qualities2 while any thing which favors association in the successive order1 will tend to produce a knowledge of events1 of the order of occurrences1 and of the connection of cause and effect3 in other words1 in the one case a perceptive mind1 with a discriminate feeling of the pleasurable and painful properties of things1 a sense of the grand and the beautiful will be the result3 in the other1 a mind attentive to the movements and phenomena1 a ratiocinative and philosophic intellect4 ,now it is an acknowledged principle1 that all sensations experienced during the presence of any vivid impression become strongly associated with it1 and with each other2 and does it not follow that the synchronous feelings of a sensitive constitution 7i4e41 the one which has vivid impressions7 will be more intimately blended than in a differently formed mind8 ,if this suggestion has any foundation in truth1 it leads to an inference not unimportant2 that where nature has endowed an individual with great original susceptibility1 he will probably be distinguished by fondness for natural history1 a relish for the beautiful and great1 and moral enthusiasm2 where there is but a mediocrity of sensibility1 a love of science1 of abstract truth1 with a deficiency of taste and of fervor1 is likely to be the result40 ,we see from this example1 that when the general laws of mind are more accurately known1 and1 above all1 more skillfully applied to the detailed explanation of mental peculiarities1 they will account for many more of those peculiarities than is ordinarily supposed4 ,unfortunately the reaction of the last and present generation against the philosophy of the eighteenth century has produced a very general neglect of this great department of analytical inquiry2 of which1 consequently1 the recent progress has been by no means proportional to its early promise4 ,the majority of those who speculate on human nature prefer dogmatically to assume that the mental differences which they perceive1 or think they perceive1 among human beings1 are ultimate facts1 incapable of being either explained or altered1 rather than take the trouble of fitting themselves1 by the requisite processes of thought1 for referring those mental differences to the outward causes by which they are for the most part produced1 and on the removal of which they would cease to exist4 ,the ,german school of metaphysical speculation1 which has not yet lost its temporary predominance in ,european thought1 has had this among many other injurious influences2 and at the opposite extreme of the psychological scale1 no writer1 either of early or of recent date1 is chargeable in a higher degree with this aberration from the true scientific spirit1 than ,m4 ,comte4 ,it is certain that1 in human beings at least1 differences in education and in outward circumstances are capable of affording an adequate explanation of by far the greatest portion of character2 and that the remainder may be in great part accounted for by physical differences in the sensations produced in different individuals by the same external or internal cause4 ,there are1 however1 some mental facts which do not seem to admit of these modes of explanation4 ,such1 to take the strongest case1 are the various instincts of animals1 and the portion of human nature which corresponds to those instincts4 ,no mode has been suggested1 even by way of hypothesis1 in which these can receive any satisfactory1 or even plausible1 explanation from psychological causes alone2 and there is great reason to think that they have as positive1 and even as direct and immediate1 a connection with physical conditions of the brain and nerves as any of our mere sensations have4 ,a supposition which 7it is perhaps not superfluous to add7 in no way conflicts with the indisputable fact that these instincts may be modified to any extent1 or entirely conquered1 in human beings1 and to no inconsiderable extent even in some of the domesticated animals1 by other mental influences1 and by education4 ,whether organic causes exercise a direct influence over any other classes of mental phenomena1 is hitherto as far from being ascertained as is the precise nature of the organic conditions even in the case of instincts4 ,the physiology1 however1 of the brain and nervous system is in a state of such rapid advance1 and is continually bringing forth such new and interesting results1 that if there be really a connection between mental peculiarities and any varieties cognizable by our senses in the structure of the cerebral and nervous apparatus1 the nature of that connection is now in a fair way of being found out4 ,the latest discoveries in cerebral physiology appear to have proved that any such connection which may exist is of a radically different character from that contended for by ,gall and his followers1 and that1 whatever may hereafter be found to be the true theory of the subject1 phrenology at least is untenable4 ,chapter ,v4 ,of ,ethology1 ,or ,the ,science ,of ,the ,formation ,of ,character4 #a4 ,the laws of mind as characterized in the preceding chapter1 compose the universal or abstract portion of the philosophy of human nature2 and all the truths of common experience1 constituting a practical knowledge of mankind1 must1 to the extent to which they are truths1 be results or consequences of these4 ,such familiar maxims1 when collected a posteriori from observation of life1 occupy among the truths of the science the place of what1 in our analysis of ,induction1 have so often been spoken of under the title of ,empirical ,laws4 ,an ,empirical ,law 7it will be remembered7 is a uniformity1 whether of succession or of co-existence1 which holds true in all instances within our limits of observation1 but is not of a nature to afford any assurance that it would hold beyond those limits2 either because the consequent is not really the effect of the antecedent1 but forms part along with it of a chain of effects flowing from prior causes not yet ascertained1 or because there is ground to believe that the sequence 7though a case of causation7 is resolvable into simpler sequences1 and1 depending therefore on a concurrence of several natural agencies1 is exposed to an unknown multitude of possibilities of counteraction4 ,in other words1 an empirical law is a generalization1 of which1 not content with finding it true1 we are obliged to ask1 why is it true8 knowing that its truth is not absolute1 but dependent on some more general conditions1 and that it can only be relied on in so far as there is ground of assurance that those conditions are realized4 ,now1 the observations concerning human affairs collected from common experience are precisely of this nature4 ,even if they were universally and exactly true within the bounds of experience1 which they never are1 still they are not the ultimate laws of human action2 they are not the principles of human nature1 but results of those principles under the circumstances in which mankind have happened to be placed4 ,when the ,psalmist 8said in his haste that all men are liars10 he enunciated what in some ages and countries is borne out by ample experience2 but it is not a law of man's nature to lie2 though it is one of the consequences of the laws of human nature1 that lying is nearly universal when certain external circumstances exist universally1 especially circumstances productive of habitual distrust and fear4 ,when the character of the old is asserted to be cautious1 and of the young impetuous1 this1 again1 is but an empirical law2 for it is not because of their youth that the young are impetuous1 nor because of their age that the old are cautious4 ,it is chiefly1 if not wholly1 because the old1 during their many years of life1 have generally had much experience of its various evils1 and having suffered or seen others suffer much from incautious exposure to them1 have acquired associations favorable to circumspection2 while the young1 as well from the absence of similar experience as from the greater strength of the inclinations which urge them to enterprise1 engage themselves in it more readily4 ,here1 then1 is the explanation of the empirical law2 here are the conditions which ultimately determine whether the law holds good or not4 ,if an old man has not been oftener than most young men in contact with danger and difficulty1 he will be equally incautious2 if a youth has not stronger inclinations than an old man1 he probably will be as little enterprising4 ,the empirical law derives whatever truth it has from the causal laws of which it is a consequence4 ,if we know those laws1 we know what are the limits to the derivative law2 while1 if we have not yet accounted for the empirical law--if it rests only on observation--there is no safety in applying it far beyond the limits of time1 place1 and circumstance in which the observations were made4 ,the really scientific truths1 then1 are not these empirical laws1 but the causal laws which explain them4 ,the empirical laws of those phenomena which depend on known causes1 and of which a general theory can therefore be constructed1 have1 whatever may be their value in practice1 no other function in science than that of verifying the conclusions of theory4 ,still more must this be the case when most of the empirical laws amount1 even within the limits of observation1 only to approximate generalizations4 #b4 ,this1 however1 is not1 so much as is sometimes supposed1 a peculiarity of the sciences called moral4 ,it is only in the simplest branches of science that empirical laws are ever exactly true2 and not always in those4 ,astronomy1 for example1 is the simplest of all the sciences which explain1 in the concrete1 the actual course of natural events4 ,the causes or forces on which astronomical phenomena depend1 are fewer in number than those which determine any other of the great phenomena of nature4 ,accordingly1 as each effect results from the conflict of but few causes1 a great degree of regularity and uniformity might be expected to exist among the effects2 and such is really the case3 they have a fixed order1 and return in cycles4 ,but propositions which should express1 with absolute correctness1 all the successive positions of a planet until the cycle is completed1 would be of almost unmanageable complexity1 and could be obtained from theory alone4 ,the generalizations which can be collected on the subject from direct observation1 even such as ,kepler's law1 are mere approximations2 the planets1 owing to their perturbations by one another1 do not move in exact ellipses4 ,thus even in astronomy1 perfect exactness in the mere empirical laws is not to be looked for2 much less1 then1 in more complex subjects of inquiry4 ,the same example shows how little can be inferred against the universality or even the simplicity of the ultimate laws1 from the impossibility of establishing any but approximate empirical laws of the effects4 ,the laws of causation according to which a class of phenomena are produced may be very few and simple1 and yet the effects themselves may be so various and complicated that it shall be impossible to trace any regularity whatever completely through them4 ,for the phenomena in question may be of an eminently modifiable character2 insomuch that innumerable circumstances are capable of influencing the effect1 although they may all do it according to a very small number of laws4 ,suppose that all which passes in the mind of man is determined by a few simple laws2 still1 if those laws be such that there is not one of the facts surrounding a human being1 or of the events which happen to him1 that does not influence in some mode or degree his subsequent mental history1 and if the circumstances of different human beings are extremely different1 it will be no wonder if very few propositions can be made respecting the details of their conduct or feelings1 which will be true of all mankind4 ,now1 without deciding whether the ultimate laws of our mental nature are few or many1 it is at least certain that they are of the above description4 ,it is certain that our mental states1 and our mental capacities and susceptibilities1 are modified1 either for a time or permanently1 by every thing which happens to us in life4 ,considering1 therefore1 how much these modifying causes differ in the case of any two individuals1 it would be unreasonable to expect that the empirical laws of the human mind1 the generalizations which can be made respecting the feelings or actions of mankind without reference to the causes that determine them1 should be any thing but approximate generalizations4 ,they are the common wisdom of common life1 and as such are invaluable2 especially as they are mostly to be applied to cases not very dissimilar to those from which they were collected4 ,but when maxims of this sort1 collected from ,englishmen1 come to be applied to ,frenchmen1 or when those collected from the present day are applied to past or future generations1 they are apt to be very much at fault4 ,unless we have resolved the empirical law into the laws of the causes on which it depends1 and ascertained that those causes extend to the case which we have in view1 there can be no reliance placed in our inferences4 ,for every individual is surrounded by circumstances different from those of every other individual2 every nation or generation of mankind from every other nation or generation3 and none of these differences are without their influence in forming a different type of character4 ,there is1 indeed1 also a certain general resemblance2 but peculiarities of circumstances are continually constituting exceptions even to the propositions which are true in the great majority of cases4 ,although1 however1 there is scarcely any mode of feeling or conduct which is1 in the absolute sense1 common to all mankind2 and though the generalizations which assert that any given variety of conduct or feeling will be found universally 7however nearly they may approximate to truth within given limits of observation71 will be considered as scientific propositions by no one who is at all familiar with scientific investigation2 yet all modes of feeling and conduct met with among mankind have causes which produce them2 and in the propositions which assign those causes will be found the explanation of the empirical laws1 and the limiting principle of our reliance on them4 ,human beings do not all feel and act alike in the same circumstances2 but it is possible to determine what makes one person1 in a given position1 feel or act in one way1 another in another2 how any given mode of feeling and conduct1 compatible with the general laws 7physical and mental7 of human nature1 has been1 or may be1 formed4 ,in other words1 mankind have not one universal character1 but there exist universal laws of the ,formation of ,character4 ,and since it is by these laws1 combined with the facts of each particular case1 that the whole of the phenomena of human action and feeling are produced1 it is on these that every rational attempt to construct the science of human nature in the concrete1 and for practical purposes1 must proceed4 #c4 ,the laws1 then1 of the formation of character being the principal object of scientific inquiry into human nature1 it remains to determine the method of investigation best fitted for ascertaining them4 ,and the logical principles according to which this question is to be decided1 must be those which preside over every other attempt to investigate the laws of very complex phenomena4 ,for it is evident that both the character of any human being1 and the aggregate of the circumstances by which that character has been formed1 are facts of a high order of complexity4 ,now to such cases we have seen that the ,deductive ,method1 setting out from general laws1 and verifying their consequences by specific experience1 is alone applicable4 ,the grounds of this great logical doctrine have formerly been stated2 and its truth will derive additional support from a brief examination of the specialties of the present case4 ,there are only two modes in which laws of nature can be ascertained--deductively and experimentally2 including under the denomination of experimental inquiry1 observation as well as artificial experiment4 ,are the laws of the formation of character susceptible of a satisfactory investigation by the method of experimentation8 ,evidently not2 because1 even if we suppose unlimited power of varying the experiment 7which is abstractedly possible1 though no one but an ,oriental despot has that power1 or1 if he had1 would probably be disposed to exercise it71 a still more essential condition is wanting--the power of performing any of the experiments with scientific accuracy4 ,the instances requisite for the prosecution of a directly experimental inquiry into the formation of character1 would be a number of human beings to bring up and educate1 from infancy to mature age4 ,and to perform any one of these experiments with scientific propriety1 it would be necessary to know and record every sensation or impression received by the young pupil from a period long before it could speak2 including its own notions respecting the sources of all those sensations and impressions4 ,it is not only impossible to do this completely1 but even to do so much of it as should constitute a tolerable approximation4 ,one apparently trivial circumstance which eluded our vigilance might let in a train of impressions and associations sufficient to vitiate the experiment as an authentic exhibition of the effects flowing from given causes4 ,no one who has sufficiently reflected on education is ignorant of this truth2 and whoever has not1 will find it most instructively illustrated in the writings of ,rousseau and ,helvetius on that great subject4 ,under this impossibility of studying the laws of the formation of character by experiments purposely contrived to elucidate them1 there remains the resource of simple observation4 ,but if it be impossible to ascertain the influencing circumstances with any approach to completeness even when we have the shaping of them ourselves1 much more impossible is it when the cases are further removed from our observation1 and altogether out of our control4 ,consider the difficulty of the very first step--of ascertaining what actually is the character of the individual1 in each particular case that we examine4 ,there is hardly any person living concerning some essential part of whose character there are not differences of opinion even among his intimate acquaintances2 and a single action1 or conduct continued only for a short time1 goes a very little way toward ascertaining it4 ,we can only make our observations in a rough way and en masse2 not attempting to ascertain completely in any given instance1 what character has been formed1 and still less by what causes2 but only observing in what state of previous circumstances it is found that certain marked mental qualities or deficiencies oftenest exist4 ,these conclusions1 besides that they are mere approximate generalizations1 deserve no reliance1 even as such1 unless the instances are sufficiently numerous to eliminate not only chance1 but every assignable circumstance in which a number of the cases examined may happen to have resembled one another4 ,so numerous and various1 too1 are the circumstances which form individual character1 that the consequence of any particular combination is hardly ever some definite and strongly marked character1 always found where that combination exists1 and not otherwise4 ,what is obtained1 even after the most extensive and accurate observation1 is merely a comparative result2 as1 for example1 that in a given number of ,frenchmen1 taken indiscriminately1 there will be found more persons of a particular mental tendency1 and fewer of the contrary tendency1 than among an equal number of ,italians or ,english1 similarly taken2 or thus3 of a hundred ,frenchmen and an equal number of ,englishmen1 fairly selected1 and arranged according to the degree in which they possess a particular mental characteristic1 each number1 #a1 #b1 #c1 etc41 of the one series1 will be found to possess more of that characteristic than the corresponding number of the other4 ,since1 therefore1 the comparison is not one of kinds1 but of ratios and degrees2 and since1 in proportion as the differences are slight1 it requires a greater number of instances to eliminate chance1 it can not often happen to any one to know a sufficient number of cases with the accuracy requisite for making the sort of comparison last mentioned2 less than which1 however1 would not constitute a real induction4 ,accordingly1 there is hardly one current opinion respecting the characters of nations1 classes1 or descriptions of persons1 which is universally acknowledged as indisputable47#bgb7 ,and finally1 if we could even obtain by way of experiment a much more satisfactory assurance of these generalizations than is really possible1 they would still be only empirical laws4 ,they would show1 indeed1 that there was some connection between the type of character formed and the circumstances existing in the case2 but not what the precise connection was1 nor to which of the peculiarities of those circumstances the effect was really owing4 ,they could only1 therefore1 be received as results of causation1 requiring to be resolved into the general laws of the causes3 until the determination of which1 we could not judge within what limits the derivative laws might serve as presumptions in cases yet unknown1 or even be depended on as permanent in the very cases from which they were collected4 ,the ,french people had1 or were supposed to have1 a certain national character2 but they drive out their royal family and aristocracy1 alter their institutions1 pass through a series of extraordinary events for the greater part of a century1 and at the end of that time their character is found to have undergone important changes4 ,a long list of mental and moral differences are observed1 or supposed to exist between men and women2 but at some future and1 it may be hoped1 not distant period1 equal freedom and an equally independent social position come to be possessed by both1 and their differences of character are either removed or totally altered4 ,but if the differences which we think we observe between ,french and ,english1 or between men and women1 can be connected with more general laws2 if they be such as might be expected to be produced by the differences of government1 former customs1 and physical peculiarities in the two nations1 and by the diversities of education1 occupations1 personal independence1 and social privileges1 and whatever original differences there may be in bodily strength and nervous sensibility between the two sexes2 then1 indeed1 the coincidence of the two kinds of evidence justifies us in believing that we have both reasoned rightly and observed rightly4 ,our observation1 though not sufficient as proof1 is ample as verification4 ,and having ascertained not only the empirical laws1 but the causes1 of the peculiarities1 we need be under no difficulty in judging how far they may be expected to be permanent1 or by what circumstances they would be modified or destroyed4 #d4 ,since then it is impossible to obtain really accurate propositions respecting the formation of character from observation and experiment alone1 we are driven perforce to that which1 even if it had not been the indispensable1 would have been the most perfect1 mode of investigation1 and which it is one of the principal aims of philosophy to extend2 namely1 that which tries its experiments not on the complex facts1 but on the simple ones of which they are compounded2 and after ascertaining the laws of the causes1 the composition of which gives rise to the complex phenomena1 then considers whether these will not explain and account for the approximate generalizations which have been framed empirically respecting the sequences of those complex phenomena4 ,the laws of the formation of character are1 in short1 derivative laws1 resulting from the general laws of mind1 and are to be obtained by deducing them from those general laws by supposing any given set of circumstances1 and then considering what1 according to the laws of mind1 will be the influence of those circumstances on the formation of character4 ,a science is thus formed1 to which ,i would propose to give the name of ,ethology1 or the ,science of ,character1 from 1 a word more nearly corresponding to the term 8character0 as ,i here use it1 than any other word in the same language4 ,the name is perhaps etymologically applicable to the entire science of our mental and moral nature2 but if1 as is usual and convenient1 we employ the name ,psychology for the science of the elementary laws of mind1 ,ethology will serve for the ulterior science which determines the kind of character produced in conformity to those general laws by any set of circumstances1 physical and moral4 ,according to this definition1 ,ethology is the science which corresponds to the art of education in the widest sense of the term1 including the formation of national or collective character as well as individual4 ,it would indeed be vain to expect 7however completely the laws of the formation of character might be ascertained7 that we could know so accurately the circumstances of any given case as to be able positively to predict the character that would be produced in that case4 ,but we must remember that a degree of knowledge far short of the power of actual prediction is often of much practical value4 ,there may be great power of influencing phenomena1 with a very imperfect knowledge of the causes by which they are in any given instance determined4 ,it is enough that we know that certain means have a tendency to produce a given effect1 and that others have a tendency to frustrate it4 ,when the circumstances of an individual or of a nation are in any considerable degree under our control1 we may1 by our knowledge of tendencies1 be enabled to shape those circumstances in a manner much more favorable to the ends we desire1 than the shape which they would of themselves assume4 ,this is the limit of our power2 but within this limit the power is a most important one4 ,this science of ,ethology may be called the ,exact ,science of ,human ,nature2 for its truths are not1 like the empirical laws which depend on them1 approximate generalizations1 but real laws4 ,it is1 however 7as in all cases of complex phenomena71 necessary to the exactness of the propositions1 that they should be hypothetical only1 and affirm tendencies1 not facts4 ,they must not assert that something will always1 or certainly1 happen2 but only that such and such will be the effect of a given cause1 so far as it operates uncounteracted4 ,it is a scientific proposition1 that bodily strength tends to make men courageous2 not that it always makes them so3 that an interest on one side of a question tends to bias the judgment2 not that it invariably does so3 that experience tends to give wisdom2 not that such is always its effect4 ,these propositions1 being assertive only of tendencies1 are not the less universally true because the tendencies may be frustrated4 #e4 ,while1 on the one hand1 ,psychology is altogether1 or principally1 a science of observation and experiment1 ,ethology1 as ,i have conceived it1 is1 as ,i have already remarked1 altogether deductive4 ,the one ascertains the simple laws of ,mind in general1 the other traces their operation in complex combinations of circumstances4 ,ethology stands to ,psychology in a relation very similar to that in which the various branches of natural philosophy stand to mechanics4 ,the principles of ,ethology are properly the middle principles1 the axiomata media 7as ,bacon would have said7 of the science of mind3 as distinguished1 on the one hand1 from the empirical laws resulting from simple observation1 and1 on the other1 from the highest generalizations4 ,and this seems a suitable place for a logical remark1 which1 though of general application1 is of peculiar importance in reference to the present subject4 ,bacon has judiciously observed that the axiomata media of every science principally constitute its value4 ,the lowest generalizations1 until explained by and resolved into the middle principles of which they are the consequences1 have only the imperfect accuracy of empirical laws2 while the most general laws are too general1 and include too few circumstances1 to give sufficient indication of what happens in individual cases1 where the circumstances are almost always immensely numerous4 ,in the importance1 therefore1 which ,bacon assigns1 in every science1 to the middle principles1 it is impossible not to agree with him4 ,but ,i conceive him to have been radically wrong in his doctrine respecting the mode in which these axiomata media should be arrived at2 though there is no one proposition laid down in his works for which he has been more extravagantly eulogized4 ,he enunciates as a universal rule that induction should proceed from the lowest to the middle principles1 and from those to the highest1 never reversing that order1 and1 consequently1 leaving no room for the discovery of new principles by way of deduction at all4 ,it is not to be conceived that a man of his sagacity could have fallen into this mistake if there had existed in his time1 among the sciences which treat of successive phenomena1 one single instance of a deductive science1 such as mechanics1 astronomy1 optics1 acoustics1 etc41 now are4 ,in those sciences it is evident that the higher and middle principles are by no means derived from the lowest1 but the reverse4 ,in some of them the very highest generalizations were those earliest ascertained with any scientific exactness2 as1 for example 7in mechanics71 the laws of motion4 ,those general laws had not1 indeed1 at first the acknowledged universality which they acquired after having been successfully employed to explain many classes of phenomena to which they were not originally seen to be applicable2 as when the laws of motion were employed1 in conjunction with other laws1 to explain deductively the celestial phenomena4 ,still1 the fact remains1 that the propositions which were afterward recognized as the most general truths of the science were1 of all its accurate generalizations1 those earliest arrived at4 ,bacon's greatest merit can not therefore consist1 as we are so often told that it did1 in exploding the vicious method pursued by the ancients of flying to the highest generalizations first1 and deducing the middle principles from them2 since this is neither a vicious nor an exploded1 but the universally accredited method of modern science1 and that to which it owes its greatest triumphs4 ,the error of ancient speculation did not consist in making the largest generalizations first1 but in making them without the aid or warrant of rigorous inductive methods1 and applying them deductively without the needful use of that important part of the ,deductive ,method termed ,verification4 ,the order in which truths of the various degrees of generality should be ascertained can not1 ,i apprehend1 be prescribed by any unbending rule4 ,i know of no maxim which can be laid down on the subject1 but to obtain those first in respect to which the conditions of a real induction can be first and most completely realized4 ,now1 wherever our means of investigation can reach causes1 without stopping at the empirical laws of the effects1 the simplest cases1 being those in which fewest causes are simultaneously concerned1 will be most amenable to the inductive process2 and these are the cases which elicit laws of the greatest comprehensiveness4 ,in every science1 therefore1 which has reached the stage at which it becomes a science of causes1 it will be usual as well as desirable first to obtain the highest generalizations1 and then deduce the more special ones from them4 ,nor can ,i discover any foundation for the ,baconian maxim1 so much extolled by subsequent writers1 except this3 ,that before we attempt to explain deductively from more general laws any new class of phenomena1 it is desirable to have gone as far as is practicable in ascertaining the empirical laws of those phenomena2 so as to compare the results of deduction1 not with one individual instance after another1 but with general propositions expressive of the points of agreement which have been found among many instances4 ,for if ,newton had been obliged to verify the theory of gravitation1 not by deducing from it ,kepler's laws1 but by deducing all the observed planetary positions which had served ,kepler to establish those laws1 the ,newtonian theory would probably never have emerged from the state of an hypothesis47#bgc7 ,the applicability of these remarks to the special case under consideration can not admit of question4 ,the science of the formation of character is a science of causes4 ,the subject is one to which those among the canons of induction1 by which laws of causation are ascertained1 can be rigorously applied4 ,it is1 therefore1 both natural and advisable to ascertain the simplest1 which are necessarily the most general1 laws of causation first1 and to deduce the middle principles from them4 ,in other words1 ,ethology1 the deductive science1 is a system of corollaries from ,psychology1 the experimental science4 #f4 ,of these1 the earlier alone has been1 as yet1 really conceived or studied as a science2 the other1 ,ethology1 is still to be created4 ,but its creation has at length become practicable4 ,the empirical laws1 destined to verify its deductions1 have been formed in abundance by every successive age of humanity2 and the premises for the deductions are now sufficiently complete4 ,excepting the degree of uncertainty which still exists as to the extent of the natural differences of individual minds1 and the physical circumstances on which these may be dependent 7considerations which are of secondary importance when we are considering mankind in the average1 or en masse71 ,i believe most competent judges will agree that the general laws of the different constituent elements of human nature are even now sufficiently understood to render it possible for a competent thinker to deduce from those laws1 with a considerable approach to certainty1 the particular type of character which would be formed in mankind generally by any assumed set of circumstances4 ,a science of ,ethology1 founded on the laws of ,psychology1 is therefore possible2 though little has yet been done1 and that little not at all systematically1 toward forming it4 ,the progress of this important but most imperfect science will depend on a double process3 first1 that of deducing theoretically the ethological consequences of particular circumstances of position1 and comparing them with the recognized results of common experience2 and1 secondly1 the reverse operation2 increased study of the various types of human nature that are to be found in the world2 conducted by persons not only capable of analyzing and recording the circumstances in which these types severally prevail1 but also sufficiently acquainted with psychological laws to be able to explain and account for the characteristics of the type1 by the peculiarities of the circumstances3 the residuum alone1 when there proves to be any1 being set down to the account of congenital predispositions4 ,for the experimental or a posteriori part of this process1 the materials are continually accumulating by the observation of mankind4 ,so far as thought is concerned1 the great problem of ,ethology is to deduce the requisite middle principles from the general laws of ,psychology4 ,the subject to be studied is1 the origin and sources of all those qualities in human beings which are interesting to us1 either as facts to be produced1 to be avoided1 or merely to be understood2 and the object is1 to determine1 from the general laws of mind1 combined with the general position of our species in the universe1 what actual or possible combinations of circumstances are capable of promoting or of preventing the production of those qualities4 ,a science which possesses middle principles of this kind1 arranged in the order1 not of causes1 but of the effects which it is desirable to produce or to prevent1 is duly prepared to be the foundation of the corresponding ,art4 ,and when ,ethology shall be thus prepared1 practical education will be the mere transformation of those principles into a parallel system of precepts1 and the adaptation of these to the sum total of the individual circumstances which exist in each particular case4 ,it is hardly necessary again to repeat that1 as in every other deductive science1 verification a posteriori must proceed pari passu with deduction a priori4 ,the inference given by theory as to the type of character which would be formed by any given circumstances must be tested by specific experience of those circumstances whenever obtainable2 and the conclusions of the science as a whole must undergo a perpetual verification and correction from the general remarks afforded by common experience respecting human nature in our own age1 and by history respecting times gone by4 ,the conclusions of theory can not be trusted1 unless confirmed by observation2 nor those of observation1 unless they can be affiliated to theory1 by deducing them from the laws of human nature1 and from a close analysis of the circumstances of the particular situation4 ,it is the accordance of these two kinds of evidence separately taken--the consilience of a priori reasoning and specific experience--which forms the only sufficient ground for the principles of any science so 8immersed in matter10 dealing with such complex and concrete phenomena1 as ,ethology4 ,chapter ,,vi4 ,general ,considerations ,on ,the ,social ,science4 #a4 ,next after the science of individual man comes the science of man in society--of the actions of collective masses of mankind1 and the various phenomena which constitute social life4 ,if the formation of individual character is already a complex subject of study1 this subject must be1 in appearance at least1 still more complex2 because the number of concurrent causes1 all exercising more or less influence on the total effect1 is greater1 in the proportion in which a nation1 or the species at large1 exposes a larger surface to the operation of agents1 psychological and physical1 than any single individual4 ,if it was necessary to prove1 in opposition to an existing prejudice1 that the simpler of the two is capable of being a subject of science1 the prejudice is likely to be yet stronger against the possibility of giving a scientific character to the study of ,politics1 and of the phenomena of ,society4 ,it is1 accordingly1 but of yesterday that the conception of a political or social science has existed anywhere but in the mind of here and there an insulated thinker1 generally very ill prepared for its realization3 though the subject itself has of all others engaged the most general attention1 and been a theme of interested and earnest discussions1 almost from the beginning of recorded time4 ,the condition1 indeed1 of politics as a branch of knowledge was1 until very lately1 and has scarcely even yet ceased to be1 that which ,bacon animadverted on1 as the natural state of the sciences while their cultivation is abandoned to practitioners2 not being carried on as a branch of speculative inquiry1 but only with a view to the exigencies of daily practice1 and the fructifera experimenta1 therefore1 being aimed at1 almost to the exclusion of the lucifera4 ,such was medical investigation1 before physiology and natural history began to be cultivated as branches of general knowledge4 ,the only questions examined were1 what diet is wholesome1 or what medicine will cure some given disease2 without any previous systematic inquiry into the laws of nutrition1 and of the healthy and morbid action of the different organs1 on which laws the effect of any diet or medicine must evidently depend4 ,and in politics the questions which engaged general attention were similar3 ,is such an enactment1 or such a form of government1 beneficial or the reverse--either universally1 or to some particular community8 without any previous inquiry into the general conditions by which the operation of legislative measures1 or the effects produced by forms of government1 are determined4 ,students in politics thus attempted to study the pathology and therapeutics of the social body1 before they had laid the necessary foundation in its physiology2 to cure disease without understanding the laws of health4 ,and the result was such as it must always be when persons1 even of ability1 attempt to deal with the complex questions of a science before its simpler and more elementary truths have been established4 ,no wonder that1 when the phenomena of society have so rarely been contemplated in the point of view characteristic of science1 the philosophy of society should have made little progress2 should contain few general propositions sufficiently precise and certain for common inquirers to recognize in them a scientific character4 ,the vulgar notion accordingly is1 that all pretension to lay down general truths on politics and society is quackery2 that no universality and no certainty are attainable in such matters4 ,what partly excuses this common notion is1 that it is really not without foundation in one particular sense4 ,a large proportion of those who have laid claim to the character of philosophic politicians have attempted not to ascertain universal sequences1 but to frame universal precepts4 ,they have imagined some one form of government1 or system of laws1 to fit all cases--a pretension well meriting the ridicule with which it is treated by practitioners1 and wholly unsupported by the analogy of the art to which1 from the nature of its subject1 that of politics must be the most nearly allied4 ,no one now supposes it possible that one remedy can cure all diseases1 or even the same disease in all constitutions and habits of body4 ,it is not necessary even to the perfection of a science1 that the corresponding art should possess universal1 or even general1 rules4 ,the phenomena of society might not only be completely dependent on known causes1 but the mode of action of all those causes might be reducible to laws of considerable simplicity1 and yet no two cases might admit of being treated in precisely the same manner4 ,so great might be the variety of circumstances on which the results in different cases depend1 that the art might not have a single general precept to give1 except that of watching the circumstances of the particular case1 and adapting our measures to the effects which1 according to the principles of the science1 result from those circumstances4 ,but although1 in so complicated a class of subjects1 it is impossible to lay down practical maxims of universal application1 it does not follow that the phenomena do not conform to universal laws4 #b4 ,all phenomena of society are phenomena of human nature1 generated by the action of outward circumstances upon masses of human beings2 and if1 therefore1 the phenomena of human thought1 feeling1 and action are subject to fixed laws1 the phenomena of society can not but conform to fixed laws1 the consequence of the preceding4 ,there is1 indeed1 no hope that these laws1 though our knowledge of them were as certain and as complete as it is in astronomy1 would enable us to predict the history of society1 like that of the celestial appearances1 for thousands of years to come4 ,but the difference of certainty is not in the laws themselves1 it is in the data to which these laws are to be applied4 ,in astronomy the causes influencing the result are few1 and change little1 and that little according to known laws2 we can ascertain what they are now1 and thence determine what they will be at any epoch of a distant future4 ,the data1 therefore1 in astronomy are as certain as the laws themselves4 ,the circumstances1 on the contrary1 which influence the condition and progress of society are innumerable1 and perpetually changing2 and though they all change in obedience to causes1 and therefore to laws1 the multitude of the causes is so great as to defy our limited powers of calculation4 ,not to say that the impossibility of applying precise numbers to facts of such a description would set an impassable limit to the possibility of calculating them beforehand1 even if the powers of the human intellect were otherwise adequate to the task4 ,but1 as before remarked1 an amount of knowledge quite insufficient for prediction1 may be most valuable for guidance4 ,the science of society would have attained a very high point of perfection if it enabled us1 in any given condition of social affairs1 in the condition1 for instance1 of ,europe or any ,european country at the present time1 to understand by what causes it had1 in any and every particular1 been made what it was2 whether it was tending to any1 and to what1 changes2 what effects each feature of its existing state was likely to produce in the future2 and by what means any of those effects might be prevented1 modified1 or accelerated1 or a different class of effects superinduced4 ,there is nothing chimerical in the hope that general laws1 sufficient to enable us to answer these various questions for any country or time with the individual circumstances of which we are well acquainted1 do really admit of being ascertained2 and that the other branches of human knowledge1 which this undertaking presupposes1 are so far advanced that the time is ripe for its commencement4 ,such is the object of the ,social ,science4 ,that the nature of what ,i consider the true method of the science may be made more palpable1 by first showing what that method is not1 it will be expedient to characterize briefly two radical misconceptions of the proper mode of philosophizing on society and government1 one or other of which is1 either explicitly or more often unconsciously1 entertained by almost all who have meditated or argued respecting the logic of politics1 since the notion of treating it by strict rules1 and on ,baconian principles1 has been current among the more advanced thinkers4 ,these erroneous methods1 if the word method can be applied to erroneous tendencies arising from the absence of any sufficiently distinct conception of method1 may be termed the ,experimental1 or ,chemical1 mode of investigation1 and the ,abstract1 or ,geometrical1 mode4 ,we shall begin with the former4 ,chapter ,,vii4 ,of ,the ,chemical1 ,or ,experimental1 ,method ,in ,the ,social ,science4 #a4 ,the laws of the phenomena of society are1 and can be1 nothing but the laws of the actions and passions of human beings united together in the social state4 ,men1 however1 in a state of society are still men2 their actions and passions are obedient to the laws of individual human nature4 ,men are not1 when brought together1 converted into another kind of substance1 with different properties2 as hydrogen and oxygen are different from water1 or as hydrogen1 oxygen1 carbon1 and azote1 are different from nerves1 muscles1 and tendons4 ,human beings in society have no properties but those which are derived from1 and may be resolved into1 the laws of the nature of individual man4 ,in social phenomena the ,composition of ,causes is the universal law4 ,now1 the method of philosophizing which may be termed chemical overlooks this fact1 and proceeds as if the nature of man as an individual were not concerned at all1 or were concerned in a very inferior degree1 in the operations of human beings in society4 ,all reasoning in political or social affairs1 grounded on principles of human nature1 is objected to by reasoners of this sort1 under such names as 8abstract theory40 ,for the direction of their opinions and conduct1 they profess to demand1 in all cases without exception1 specific experience4 ,this mode of thinking is not only general with practitioners in politics1 and with that very numerous class who 7on a subject which no one1 however ignorant1 thinks himself incompetent to discuss7 profess to guide themselves by common sense rather than by science2 but is often countenanced by persons with greater pretensions to instruction--persons who1 having sufficient acquaintance with books and with the current ideas to have heard that ,bacon taught mankind to follow experience1 and to ground their conclusions on facts instead of metaphysical dogmas1 think that1 by treating political facts in as directly experimental a method as chemical facts1 they are showing themselves true ,baconians1 and proving their adversaries to be mere syllogizers and school-men4 ,as1 however1 the notion of the applicability of experimental methods to political philosophy can not co-exist with any just conception of these methods themselves1 the kind of arguments from experience which the chemical theory brings forth as its fruits 7and which form the staple1 in this country especially1 of parliamentary and hustings oratory71 are such as1 at no time since ,bacon1 would have been admitted to be valid in chemistry itself1 or in any other branch of experimental science4 ,they are such as these3 that the prohibition of foreign commodities must conduce to national wealth1 because ,england has flourished under it1 or because countries in general which have adopted it have flourished2 that our laws1 or our internal administration1 or our constitution1 are excellent for a similar reason2 and the eternal arguments from historical examples1 from ,athens or ,rome1 from the fires in ,smithfield or the ,french ,revolution4 ,i will not waste time in contending against modes of argumentation which no person with the smallest practice in estimating evidence could possibly be betrayed into2 which draw conclusions of general application from a single unanalyzed instance1 or arbitrarily refer an effect to some one among its antecedents1 without any process of elimination or comparison of instances4 ,it is a rule both of justice and of good sense to grapple not with the absurdest1 but with the most reasonable form of a wrong opinion4 ,we shall suppose our inquirer acquainted with the true conditions of experimental investigation1 and competent in point of acquirements for realizing them1 so far as they can be realized4 ,he shall know as much of the facts of history as mere erudition can teach--as much as can be proved by testimony1 without the assistance of any theory2 and if those mere facts1 properly collated1 can fulfill the conditions of a real induction1 he shall be qualified for the task4 ,but that no such attempt can have the smallest chance of success1 has been abundantly shown in the tenth chapter of the ,third ,book47#bgd7 ,we there examined whether effects which depend on a complication of causes can be made the subject of a true induction by observation and experiment2 and concluded1 on the most convincing grounds1 that they can not4 ,since1 of all effects1 none depend on so great a complication of causes as social phenomena1 we might leave our case to rest in safety on that previous showing4 ,but a logical principle as yet so little familiar to the ordinary run of thinkers1 requires to be insisted on more than once1 in order to make the due impression2 and the present being the case which of all others exemplifies it the most strongly1 there will be advantage in re-stating the grounds of the general maxim1 as applied to the specialties of the class of inquiries now under consideration4 #b4 ,the first difficulty which meets us in the attempt to apply experimental methods for ascertaining the laws of social phenomena1 is that we are without the means of making artificial experiments4 ,even if we could contrive experiments at leisure1 and try them without limit1 we should do so under immense disadvantage2 both from the impossibility of ascertaining and taking note of all the facts of each case1 and because 7those facts being in a perpetual state of change71 before sufficient time had elapsed to ascertain the result of the experiment1 some material circumstances would always have ceased to be the same4 ,but it is unnecessary to consider the logical objections which would exist to the conclusiveness of our experiments1 since we palpably never have the power of trying any4 ,we can only watch those which nature produces1 or which are produced for other reasons4 ,we can not adapt our logical means to our wants1 by varying the circumstances as the exigencies of elimination may require4 ,if the spontaneous instances1 formed by contemporary events and by the successions of phenomena recorded in history1 afford a sufficient variation of circumstances1 an induction from specific experience is attainable2 otherwise not4 ,the question to be resolved is1 therefore1 whether the requisites for induction respecting the causes of political effects or the properties of political agents1 are to be met with in history8 including under the term1 contemporary history4 ,and in order to give fixity to our conceptions1 it will be advisable to suppose this question asked in reference to some special subject of political inquiry or controversy2 such as that frequent topic of debate in the present century1 the operation of restrictive and prohibitory commercial legislation upon national wealth4 ,let this1 then1 be the scientific question to be investigated by specific experience4 #c4 ,in order to apply to the case the most perfect of the methods of experimental inquiry1 the ,method of ,difference1 we require to find two instances which tally in every particular except the one which is the subject of inquiry4 ,if two nations can be found which are alike in all natural advantages and disadvantages2 whose people resemble each other in every quality1 physical and moral1 spontaneous and acquired2 whose habits1 usages1 opinions1 laws1 and institutions are the same in all respects1 except that one of them has a more protective tariff1 or in other respects interferes more with the freedom of industry2 if one of these nations is found to be rich and the other poor1 or one richer than the other1 this will be an experimentum crucis3 a real proof by experience1 which of the two systems is most favorable to national riches4 ,but the supposition that two such instances can be met with is manifestly absurd4 ,nor is such a concurrence even abstractedly possible4 ,two nations which agreed in every thing except their commercial policy would agree also in that4 ,differences of legislation are not inherent and ultimate diversities2 are not properties of ,kinds4 ,they are effects of pre-existing causes4 ,if the two nations differ in this portion of their institutions1 it is from some difference in their position1 and thence in their apparent interests1 or in some portion or other of their opinions1 habits1 and tendencies2 which opens a view of further differences without any assignable limit1 capable of operating on their industrial prosperity1 as well as on every other feature of their condition1 in more ways than can be enumerated or imagined4 ,there is thus a demonstrated impossibility of obtaining1 in the investigations of the social science1 the conditions required for the most conclusive form of inquiry by specific experience4 ,in the absence of the direct1 we may next try1 as in other cases1 the supplementary resource1 called in a former place the ,indirect ,method of ,difference2 which1 instead of two instances differing in nothing but the presence or absence of a given circumstance1 compares two classes of instances respectively agreeing in nothing but the presence of a circumstance on the one side and its absence on the other4 ,to choose the most advantageous case conceivable 7a case far too advantageous to be ever obtained71 suppose that we compare one nation which has a restrictive policy with two or more nations agreeing in nothing but in permitting free trade4 ,we need not now suppose that either of these nations agrees with the first in all its circumstances2 one may agree with it in some of its circumstances1 and another in the remainder4 ,and it may be argued1 that if these nations remain poorer than the restrictive nation1 it can not be for want either of the first or of the second set of circumstances1 but it must be for want of the protective system4 ,if 7we might say7 the restrictive nation had prospered from the one set of causes1 the first of the free-trade nations would have prospered equally2 if by reason of the other1 the second would2 but neither has2 therefore the prosperity was owing to the restrictions4 ,this will be allowed to be a very favorable specimen of an argument from specific experience in politics1 and if this be inconclusive1 it would not be easy to find another preferable to it4 ,yet1 that it is inconclusive1 scarcely requires to be pointed out4 ,why must the prosperous nation have prospered from one cause exclusively8 ,national prosperity is always the collective result of a multitude of favorable circumstances2 and of these1 the restrictive nation may unite a greater number than either of the others1 though it may have all of those circumstances in common with either one or the other of them4 ,its prosperity may be partly owing to circumstances common to it with one of those nations1 and partly with the other1 while they1 having each of them only half the number of favorable circumstances1 have remained inferior4 ,so that the closest imitation which can be made1 in the social science1 of a legitimate induction from direct experience1 gives but a specious semblance of conclusiveness1 without any real value4 #d4 ,the ,method of ,difference in either of its forms being thus completely out of the question1 there remains the ,method of ,agreement4 ,but we are already aware of how little value this method is1 in cases admitting ,plurality of ,causes2 and social phenomena are those in which the plurality prevails in the utmost possible extent4 ,suppose that the observer makes the luckiest hit which could be given by any conceivable combination of chances2 that he finds two nations which agree in no circumstance whatever1 except in having a restrictive system1 and in being prosperous2 or a number of nations1 all prosperous1 which have no antecedent circumstances common to them all but that of having a restrictive policy4 ,it is unnecessary to go into the consideration of the impossibility of ascertaining from history1 or even from contemporary observation1 that such is really the fact2 that the nations agree in no other circumstance capable of influencing the case4 ,let us suppose this impossibility vanquished1 and the fact ascertained that they agree only in a restrictive system as an antecedent1 and industrial prosperity as a consequent4 ,what degree of presumption does this raise that the restrictive system caused the prosperity8 ,one so trifling as to be equivalent to none at all4 ,that some one antecedent is the cause of a given effect1 because all other antecedents have been found capable of being eliminated1 is a just inference1 only if the effect can have but one cause4 ,if it admits of several1 nothing is more natural than that each of these should separately admit of being eliminated4 ,now1 in the case of political phenomena1 the supposition of unity of cause is not only wide of the truth1 but at an immeasurable distance from it4 ,the causes of every social phenomenon which we are particularly interested about1 security1 wealth1 freedom1 good government1 public virtue1 general intelligence1 or their opposites1 are infinitely numerous1 especially the external or remote causes1 which alone are1 for the most part1 accessible to direct observation4 ,no one cause suffices of itself to produce any of these phenomena2 while there are countless causes which have some influence over them1 and may co-operate either in their production or in their prevention4 ,from the mere fact1 therefore1 of our having been able to eliminate some circumstance1 we can by no means infer that this circumstance was not instrumental to the effect in some of the very instances from which we have eliminated it4 ,we can conclude that the effect is sometimes produced without it2 but not that1 when present1 it does not contribute its share4 ,similar objections will be found to apply to the ,method of ,concomitant ,variations4 ,if the causes which act upon the state of any society produced effects differing from one another in kind2 if wealth depended on one cause1 peace on another1 a third made people virtuous1 a fourth intelligent2 we might1 though unable to sever the causes from one another1 refer to each of them that property of the effect which waxed as it waxed1 and which waned as it waned4 ,but every attribute of the social body is influenced by innumerable causes2 and such is the mutual action of the co-existing elements of society1 that whatever affects any one of the more important of them1 will by that alone1 if it does not affect the others directly1 affect them indirectly4 ,the effects1 therefore1 of different agents not being different in quality1 while the quantity of each is the mixed result of all the agents1 the variations of the aggregate can not bear a uniform proportion to those of any one of its component parts4 #e4 ,there remains the ,method of ,residues2 which appears1 on the first view1 less foreign to this kind of inquiry than the three other methods1 because it only requires that we should accurately note the circumstances of some one country1 or state of society4 ,making allowance1 thereupon1 for the effect of all causes whose tendencies are known1 the residue which those causes are inadequate to explain may plausibly be imputed to the remainder of the circumstances which are known to have existed in the case4 ,something similar to this is the method which ,coleridge7#bge7 describes himself as having followed in his political essays in the ,morning ,post4 8,on every great occurrence ,i endeavored to discover in past history the event that most nearly resembled it4 ,i procured1 whenever it was possible1 the contemporary historians1 memorialists1 and pamphleteers4 ,then fairly subtracting the points of difference from those of likeness1 as the balance favored the former or the latter1 ,i conjectured that the result would be the same or different4 ,as1 for instance1 in the series of essays entitled #8,a ,comparison of ,france under ,napoleon with ,rome under the first ,csars1' and in those which followed1 #8on the probable final restoration of the ,bourbons4' ,the same plan ,i pursued at the commencement of the ,spanish ,revolution1 and with the same success1 taking the war of the ,united ,provinces with ,philip ,,ii4 as the groundwork of the comparison40 ,in this inquiry he no doubt employed the ,method of ,residues2 for1 in 8subtracting the points of difference from those of likeness10 he doubtless weighed1 and did not content himself with numbering1 them3 he doubtless took those points of agreement only which he presumed from their own nature to be capable of influencing the effect1 and1 allowing for that influence1 concluded that the remainder of the result would be referable to the points of difference4 ,whatever may be the efficacy of this method1 it is1 as we long ago remarked1 not a method of pure observation and experiment2 it concludes1 not from a comparison of instances1 but from the comparison of an instance with the result of a previous deduction4 ,applied to social phenomena1 it presupposes that the causes from which part of the effect proceeded are already known2 and as we have shown that these can not have been known by specific experience1 they must have been learned by deduction from principles of human nature2 experience being called in only as a supplementary resource1 to determine the causes which produced an unexplained residue4 ,but if the principles of human nature may be had recourse to for the establishment of some political truths1 they may for all4 ,if it be admissible to say1 ,england must have prospered by reason of the prohibitory system1 because after allowing for all the other tendencies which have been operating1 there is a portion of prosperity still to be accounted for2 it must be admissible to go to the same source for the effect of the prohibitory system1 and examine what account the laws of human motives and actions will enable us to give of its tendencies4 ,nor1 in fact1 will the experimental argument amount to any thing1 except in verification of a conclusion drawn from those general laws4 ,for we may subtract the effect of one1 two1 three1 or four causes1 but we shall never succeed in subtracting the effect of all causes except one2 while it would be a curious instance of the dangers of too much caution if1 to avoid depending on a priori reasoning concerning the effect of a single cause1 we should oblige ourselves to depend on as many separate a priori reasonings as there are causes operating concurrently with that particular cause in some given instance4 ,we have now sufficiently characterized the gross misconception of the mode of investigation proper to political phenomena1 which ,i have termed the ,chemical ,method4 ,so lengthened a discussion would not have been necessary1 if the claim to decide authoritatively on political doctrines were confined to persons who had competently studied any one of the higher departments of physical science4 ,but since the generality of those who reason on political subjects1 satisfactorily to themselves and to a more or less numerous body of admirers1 know nothing whatever of the methods of physical investigation beyond a few precepts which they continue to parrot after ,bacon1 being entirely unaware that ,bacon's conception of scientific inquiry has done its work1 and that science has now advanced into a higher stage1 there are probably many to whom such remarks as the foregoing may still be useful4 ,in an age in which chemistry itself1 when attempting to deal with the more complex chemical sequences--those of the animal or even the vegetable organism--has found it necessary to become1 and has succeeded in becoming1 a ,deductive ,science1 it is not to be apprehended that any person of scientific habits1 who has kept pace with the general progress of the knowledge of nature1 can be in danger of applying the methods of elementary chemistry to explore the sequences of the most complex order of phenomena in existence4 ,chapter ,,viii4 ,of ,the ,geometrical1 ,or ,abstract1 ,method4 #a4 ,the misconception discussed in the preceding chapter is1 as we said1 chiefly committed by persons not much accustomed to scientific investigation3 practitioners in politics1 who rather employ the commonplaces of philosophy to justify their practice than seek to guide their practice by philosophic principles2 or imperfectly educated persons1 who1 in ignorance of the careful selection and elaborate comparison of instances required for the formation of a sound theory1 attempt to found one upon a few coincidences which they have casually noticed4 ,the erroneous method of which we are now to treat is1 on the contrary1 peculiar to thinking and studious minds4 ,it never could have suggested itself but to persons of some familiarity with the nature of scientific research2 who1 being aware of the impossibility of establishing1 by casual observation or direct experimentation1 a true theory of sequences so complex as are those of the social phenomena1 have recourse to the simpler laws which are immediately operative in those phenomena1 and which are no other than the laws of the nature of the human beings therein concerned1 ,these thinkers perceive 7what the partisans of the chemical or experimental theory do not7 that the science of society must necessarily be deductive4 ,but1 from an insufficient consideration of the specific nature of the subject-matter--and often because 7their own scientific education having stopped short in too early a stage7 geometry stands in their minds as the type of all deductive science--it is to geometry1 rather than to astronomy and natural philosophy1 that they unconsciously assimilate the deductive science of society4 ,among the differences between geometry 7a science of co-existent facts1 altogether independent of the laws of the succession of phenomena71 and those physical ,sciences of ,causation which have been rendered deductive1 the following is one of the most conspicuous3 ,that geometry affords no room for what so constantly occurs in mechanics and its applications1 the case of conflicting forces2 of causes which counteract or modify one another4 ,in mechanics we continually find two or more moving forces producing1 not motion1 but rest2 or motion in a different direction from that which would have been produced by either of the generating forces4 ,it is true that the effect of the joint forces is the same when they act simultaneously1 as if they had acted one after another1 or by turns2 and it is in this that the difference between mechanical and chemical laws consists4 ,but still the effects1 whether produced by successive or by simultaneous action1 do1 wholly or in part1 cancel one another3 what the one force does1 the other1 partly1 or altogether undoes4 ,there is no similar state of things in geometry4 ,the result which follows from one geometrical principle has nothing that conflicts with the result which follows from another4 ,what is proved true from one geometrical theorem1 what would be true if no other geometrical principles existed1 can not be altered and made no longer true by reason of some other geometrical principle4 ,what is once proved true is true in all cases1 whatever supposition may be made in regard to any other matter4 ,now a conception similar to this last would appear to have been formed of the social science1 in the minds of the earlier of those who have attempted to cultivate it by a deductive method4 ,mechanics would be a science very similar to geometry1 if every motion resulted from one force alone1 and not from a conflict of forces4 ,in the geometrical theory of society1 it seems to be supposed that this is really the case with the social phenomena2 that each of them results always from only one force1 one single property of human nature4 ,at the point which we have now reached1 it can not be necessary to say any thing either in proof or in illustration of the assertion that such is not the true character of the social phenomena4 ,there is not1 among these most complex and 7for that reason7 most modifiable of all phenomena1 any one over which innumerable forces do not exercise influence2 which does not depend on a conjunction of very many causes4 ,we have not1 therefore1 to prove the notion in question to be an error1 but to prove that the error has been committed2 that so mistaken a conception of the mode in which the phenomena of society are produced has actually been ascertained4 #b4 ,one numerous division of the reasoners who have treated social facts according to geometrical methods1 not admitting any modification of one law by another1 must for the present be left out of consideration1 because in them this error is complicated with1 and is the effect of1 another fundamental misconception1 of which we have already taken some notice1 and which will be further treated of before we conclude4 ,i speak of those who deduce political conclusions not from laws of nature1 not from sequences of phenomena1 real or imaginary1 but from unbending practical maxims4 ,such1 for example1 are all who found their theory of politics on what is called abstract right1 that is to say1 on universal precepts2 a pretension of which we have already noticed the chimerical nature4 ,such1 in like manner1 are those who make the assumption of a social contract1 or any other kind of original obligation1 and apply it to particular cases by mere interpretation4 ,but in this the fundamental error is the attempt to treat an art like a science1 and to have a deductive art2 the irrationality of which will be shown in a future chapter4 ,it will be proper to take our exemplification of the geometrical theory from those thinkers who have avoided this additional error1 and who entertain1 so far1 a juster idea of the nature of political inquiry4 ,we may cite1 in the first instance1 those who assume as the principle of their political philosophy that government is founded on fear2 that the dread of each other is the one motive by which human beings were originally brought into a state of society1 and are still held in it4 ,some of the earlier scientific inquirers into politics1 in particular ,hobbes1 assumed this proposition1 not by implication1 but avowedly1 as the foundation of their doctrine1 and attempted to build a complete philosophy of politics thereupon4 ,it is true that ,hobbes did not find this one maxim sufficient to carry him through the whole of his subject1 but was obliged to eke it out by the double sophism of an original contract4 ,i call this a double sophism2 first1 as passing off a fiction for a fact1 and1 secondly1 assuming a practical principle1 or precept1 as the basis of a theory2 which is a petitio principii1 since 7as we noticed in treating of that ,fallacy7 every rule of conduct1 even though it be so binding a one as the observance of a promise1 must rest its own foundations on the theory of the subject2 and the theory1 therefore1 can not rest upon it4 #c4 ,passing over less important instances1 ,i shall come at once to the most remarkable example afforded by our own times of the geometrical method in politics2 emanating from persons who are well aware of the distinction between science and art2 who knew that rules of conduct must follow1 not precede1 the ascertainment of laws of nature1 and that the latter1 not the former1 is the legitimate field for the application of the deductive method4 ,i allude to the interest-philosophy of the ,bentham school4 ,the profound and original thinkers who are commonly known under this description1 founded their general theory of government on one comprehensive premise1 namely1 that men's actions are always determined by their interests4 ,there is an ambiguity in this last expression2 for1 as the same philosophers1 especially ,bentham1 gave the name of an interest to any thing which a person likes1 the proposition may be understood to mean only this1 that men's actions are always determined by their wishes4 ,in this sense1 however1 it would not bear out any of the consequences which these writers drew from it2 and the word1 therefore1 in their political reasonings1 must be understood to mean 7which is also the explanation they themselves1 on such occasions gave of it7 what is commonly termed private1 or worldly1 interest4 ,taking the doctrine1 then1 in this sense1 an objection presents itself in limine which might be deemed a fatal one1 namely1 that so sweeping a proposition is far from being universally true4 ,human beings are not governed in all their actions by their worldly interests4 ,this1 however1 is by no means so conclusive an objection as it at first appears2 because in politics we are for the most part concerned with the conduct1 not of individual persons1 but either of a series of persons 7as a succession of kings71 or a body or mass of persons1 as a nation1 an aristocracy1 or a representative assembly4 ,and whatever is true of a large majority of mankind1 may without much error be taken for true of any succession of persons1 considered as a whole1 or of any collection of persons in which the act of the majority becomes the act of the whole body4 ,although1 therefore1 the maxim is sometimes expressed in a manner unnecessarily paradoxical1 the consequences drawn from it will hold equally good if the assertion be limited as follows3 ,any succession of persons1 or the majority of any body of persons1 will be governed in the bulk of their conduct by their personal interests4 ,we are bound to allow to this school of thinkers the benefit of this more rational statement of their fundamental maxim1 which is also in strict conformity to the explanations which1 when considered to be called for1 have been given by themselves4 ,the theory goes on to infer1 quite correctly1 that if the actions of mankind are determined in the main by their selfish interests1 the only rulers who will govern according to the interest of the governed1 are those whose selfish interests are in accordance with it4 ,and to this is added a third proposition1 namely1 that no rulers have their selfish interest identical with that of the governed1 unless it be rendered so by accountability1 that is1 by dependence on the will of the governed4 ,in other words 7and as the result of the whole71 that the desire of retaining or the fear of losing their power1 and whatever is thereon consequent1 is the sole motive which can be relied on for producing on the part of rulers a course of conduct in accordance with the general interest4 ,we have thus a fundamental theorem of political science1 consisting of three syllogisms1 and depending chiefly on two general premises1 in each of which a certain effect is considered as determined only by one cause1 not by a concurrence of causes4 ,in the one1 it is assumed that the actions of average rulers are determined solely by self-interest2 in the other1 that the sense of identity of interest with the governed1 is produced and producible by no other cause than responsibility4 ,neither of these propositions is by any means true2 the last is extremely wide of the truth4 ,it is not true that the actions even of average rulers are wholly1 or any thing approaching to wholly1 determined by their personal interest1 or even by their own opinion of their personal interest4 ,i do not speak of the influence of a sense of duty1 or feelings of philanthropy1 motives never to be mainly relied on1 though 7except in countries or during periods of great moral debasement7 they influence almost all rulers in some degree1 and some rulers in a very great degree4 ,but ,i insist only on what is true of all rulers1 viz41 that the character and course of their actions is largely influenced 7independently of personal calculation7 by the habitual sentiments and feelings1 the general modes of thinking and acting1 which prevail throughout the community of which they are members2 as well as by the feelings1 habits1 and modes of thought which characterize the particular class in that community to which they themselves belong4 ,and no one will understand or be able to decipher their system of conduct1 who does not take all these things into account4 ,they are also much influenced by the maxims and traditions which have descended to them from other rulers1 their predecessors2 which maxims and traditions have been known to retain an ascendancy during long periods1 even in opposition to the private interests of the rulers for the time being4 ,i put aside the influence of other less general causes4 ,although1 therefore1 the private interest of the rulers or of the ruling class is a very powerful force1 constantly in action1 and exercising the most important influence upon their conduct1 there is also1 in what they do1 a large portion which that private interest by no means affords a sufficient explanation of2 and even the particulars which constitute the goodness or badness of their government1 are in some1 and no small degree1 influenced by those among the circumstances acting upon them1 which can not1 with any propriety1 be included in the term self-interest4 ,turning now to the other proposition1 that responsibility to the governed is the only cause capable of producing in the rulers a sense of identity of interest with the community1 this is still less admissible as a universal truth1 than even the former4 ,i am not speaking of perfect identity of interest1 which is an impracticable chimera2 which1 most assuredly1 responsibility to the people does not give4 ,i speak of identity in essentials2 and the essentials are different at different places and times4 ,there are a large number of cases in which those things which it is most for the general interest that the rulers should do1 are also those which they are prompted to do by their strongest personal interest1 the consolidation of their power4 ,the suppression1 for instance1 of anarchy and resistance to law--the complete establishment of the authority of the central government1 in a state of society like that of ,europe in the ,middle ,ages--is one of the strongest interests of the people1 and also of the rulers simply because they are the rulers2 and responsibility on their part could not strengthen1 though in many conceivable ways it might weaken1 the motives prompting them to pursue this object4 ,during the greater part1 of the reign of ,queen ,elizabeth1 and of many other monarchs who might be named1 the sense of identity of interest between the sovereign and the majority of the people was probably stronger than it usually is in responsible governments2 every thing that the people had most at heart1 the monarch had at heart too4 ,had ,peter the ,great1 or the rugged savages whom he began to civilize1 the truest inclination toward the things which were for the real interest of those savages8 ,i am not here attempting to establish a theory of government1 and am not called upon to determine the proportional weight which ought to be given to the circumstances which this school of geometrical politicians left out of their system1 and those which they took into it4 ,i am only concerned to show that their method was unscientific2 not to measure the amount of error which may have affected their practical conclusions4 ,it is but justice to them1 however1 to remark1 that their mistake was not so much one of substance as of form1 and consisted in presenting in a systematic shape1 and as the scientific treatment of a great philosophical question1 what should have passed for that which it really was1 the mere polemics of the day4 ,although the actions of rulers are by no means wholly determined by their selfish interests1 it is chiefly as a security against those selfish interests that constitutional checks are required2 and for that purpose such checks1 in ,england1 and the other nations of modern ,europe1 can in no manner be dispensed with4 ,it is likewise true1 that in these same nations1 and in the present age1 responsibility to the governed is the only means practically available to create a feeling of identity of interest1 in the cases1 and on the points1 where that feeling does not sufficiently exist4 ,to all this1 and to the arguments which may be founded on it in favor of measures for the correction of our representative system1 ,i have nothing to object2 but ,i confess my regret1 that the small though highly important portion of the philosophy of government1 which was wanted for the immediate purpose of serving the cause of parliamentary reform1 should have been held forth by thinkers of such eminence as a complete theory4 ,it is not to be imagined possible1 nor is it true in point of fact1 that these philosophers regarded the few premises of their theory as including all that is required for explaining social phenomena1 or for determining the choice of forms of government and measures of legislation and administration4 ,they were too highly instructed1 of too comprehensive intellect1 and some of them of too sober and practical a character1 for such an error4 ,they would have applied1 and did apply1 their principles with innumerable allowances4 ,but it is not allowances that are wanted4 ,there is little chance of making due amends in the superstructure of a theory for the want of sufficient breadth in its foundations4 ,it is unphilosophical to construct a science out of a few of the agencies by which the phenomena are determined1 and leave the rest to the routine of practice or the sagacity of conjecture4 ,we either ought not to pretend to scientific forms1 or we ought to study all the determining agencies equally1 and endeavor1 so far as it can be done1 to include all of them within the pale of the science2 else we shall infallibly bestow a disproportionate attention upon those which our theory takes into account1 while we misestimate the rest1 and probably underrate their importance4 ,that the deductions should be from the whole and not from a part only of the laws of nature that are concerned1 would be desirable even if those omitted were so insignificant in comparison with the others1 that they might1 for most purposes and on most occasions1 be left out of the account4 ,but this is far indeed from being true in the social science4 ,the phenomena of society do not depend1 in essentials1 on some one agency or law of human nature1 with only inconsiderable modifications from others4 ,the whole of the qualities of human nature influence those phenomena1 and there is not one which influences them in a small degree4 ,there is not one1 the removal or any great alteration of which would not materially affect the whole aspect of society1 and change more or less the sequences of social phenomena generally4 ,the theory which has been the subject of these remarks is1 in this country at least1 the principal contemporary example of what ,i have styled the geometrical method of philosophizing in the social science2 and our examination of it has1 for this reason1 been more detailed than would otherwise have been suitable to a work like the present4 ,having now sufficiently illustrated the two erroneous methods1 we shall pass without further preliminary to the true method2 that which proceeds 7conformably to the practice of the more complex physical sciences7 deductively indeed1 but by deduction from many1 not from one or a very few1 original premises2 considering each effect as 7what it really is7 an aggregate result of many causes1 operating sometimes through the same1 sometimes through different mental agencies1 or laws of human nature4 ,chapter ,,ix4 ,of ,the ,physical1 ,or ,concrete ,deductive1 ,method4 #a4 ,after what has been said to illustrate the nature of the inquiry into social phenomena1 the general character of the method proper to that inquiry is sufficiently evident1 and needs only to be recapitulated1 not proved4 ,however complex the phenomena1 all their sequences and co-existences result from the laws of the separate elements4 ,the effect produced1 in social phenomena1 by any complex set of circumstances1 amounts precisely to the sum of the effects of the circumstances taken singly2 and the complexity does not arise from the number of the laws themselves1 which is not remarkably great1 but from the extraordinary number and variety of the data or elements--of the agents which1 in obedience to that small number of laws1 co-operate toward the effect4 ,the ,social ,science1 therefore 7which1 by a convenient barbarism1 has been termed ,sociology71 is a deductive science2 not1 indeed1 after the model of geometry1 but after that of the more complex physical sciences4 ,it infers the law of each effect from the laws of causation on which that effect depends2 not1 however1 from the law merely of one cause1 as in the geometrical method1 but by considering all the causes which conjunctly influence the effect1 and compounding their laws with one another4 ,its method1 in short1 is the ,concrete ,deductive ,method3 that of which astronomy furnishes the most perfect1 natural philosophy a somewhat less perfect1 example1 and the employment of which1 with the adaptations and precautions required by the subject1 is beginning to regenerate physiology4 ,nor does it admit of doubt1 that similar adaptations and precautions are indispensable in sociology4 ,in applying to that most complex of all studies what is demonstrably the sole method capable of throwing the light of science even upon phenomena of a far inferior degree of complication1 we ought to be aware that the same superior complexity which renders the instrument of ,deduction more necessary1 renders it also more precarious2 and we must be prepared to meet1 by appropriate contrivances1 this increase of difficulty4 ,the actions and feelings of human beings in the social state1 are1 no doubt1 entirely governed by psychological and ethological laws3 whatever influence any cause exercises upon the social phenomena1 it exercises through those laws4 ,supposing therefore the laws of human actions and feelings to be sufficiently known1 there is no extraordinary difficulty in determining from those laws1 the nature of the social effects which any given cause tends to produce4 ,but when the question is that of compounding several tendencies together1 and computing the aggregate result of many co-existent causes2 and especially when1 by attempting to predict what will actually occur in a given case1 we incur the obligation of estimating and compounding the influences of all the causes which happen to exist in that case1 we attempt a task to proceed far in which1 surpasses the compass of the human faculties4 ,if all the resources of science are not sufficient to enable us to calculate1 a priori1 with complete precision1 the mutual action of three bodies gravitating toward one another1 it may be judged with what prospect of success we should endeavor to calculate the result of the conflicting tendencies which are acting in a thousand different directions and promoting a thousand different changes at a given instant in a given society2 although we might and ought to be able1 from the laws of human nature1 to distinguish correctly enough the tendencies themselves1 so far as they depend on causes accessible to our observation2 and to determine the direction which each of them1 if acting alone1 would impress upon society1 as well as1 in a general way at least1 to pronounce that some of these tendencies are more powerful than others4 ,but1 without dissembling the necessary imperfections of the a priori method when applied to such a subject1 neither ought we1 on the other hand2 to exaggerate them4 ,the same objections which apply to the ,method of ,deduction in this its most difficult employment1 apply to it1 as we formerly showed17#bgf7 in its easiest2 and would even there have been insuperable1 if there had not existed1 as was then fully explained1 an appropriate remedy4 ,this remedy consists in the process which1 under the name of ,verification1 we have characterized as the third essential constituent part of the ,deductive ,method2 that of collating the conclusions of the ratiocination either with the concrete phenomena themselves1 or1 when such are obtainable1 with their empirical laws4 ,the ground of confidence in any concrete deductive science is not the a priori reasoning itself1 but the accordance between its results and those of observation a posteriori4 ,either of these processes1 apart from the other1 diminishes in value as the subject increases in complication1 and this is in so rapid a ratio as soon to become entirely worthless2 but the reliance to be placed in the concurrence of the two sorts of evidence1 not only does not diminish in any thing like the same proportion1 but is not necessarily much diminished at all4 ,nothing more results than a disturbance in the order of precedency of the two processes1 sometimes amounting to its actual inversion3 insomuch that instead of deducing our conclusions by reasoning1 and verifying them by observation1 we in some cases begin by obtaining them provisionally from specific experience1 and afterward connect them with the principles of human nature by a priori reasonings1 which reasonings are thus a real ,verification4 ,the only thinker who1 with a competent knowledge of scientific methods in general1 has attempted to characterize the ,method of ,sociology1 ,m4 ,comte1 considers this inverse order as inseparably inherent in the nature of sociological speculation4 ,he looks upon the social science as essentially consisting of generalizations from history1 verified1 not originally suggested1 by deduction from the laws of human nature4 ,though there is a truth contained in this opinion1 of which ,i shall presently endeavor to show the importance1 ,i can not but think that this truth is enunciated in too unlimited a manner1 and that there is considerable scope in sociological inquiry for the direct1 as well as for the inverse1 ,deductive ,method4 ,it will1 in fact1 be shown in the next chapter1 that there is a kind of sociological inquiries to which1 from their prodigious complication1 the method of direct deduction is altogether inapplicable1 while by a happy compensation it is precisely in these cases that we are able to obtain the best empirical laws3 to these inquiries1 therefore1 the ,inverse ,method is exclusively adapted4 ,but there are also1 as will presently appear1 other cases in which it is impossible to obtain from direct observation any thing worthy the name of an empirical law2 and it fortunately happens that these are the very cases in which the ,direct ,method is least affected by the objection which undoubtedly must always affect it in a certain degree4 ,we shall begin1 then1 by looking at the ,social ,science as a science of direct ,deduction1 and considering what can be accomplished in it1 and under what limitations1 by that mode of investigation4 ,we shall1 then1 in a separate chapter1 examine and endeavor to characterize the inverse process4 #b4 ,it is evident1 in the first place1 that ,sociology1 considered as a system of deductions a priori1 can not be a science of positive predictions1 but only of tendencies4 ,we may be able to conclude1 from the laws of human nature applied to the circumstances of a given state of society1 that a particular cause will operate in a certain manner unless counteracted2 but we can never be assured to what extent or amount it will so operate1 or affirm with certainty that it will not be counteracted2 because we can seldom know1 even approximately1 all the agencies which may co-exist with it1 and still less calculate the 8collective result0 of so many combined elements4 ,the remark1 however1 must here be once more repeated1 that knowledge insufficient for prediction may be most valuable for guidance4 ,it is not necessary for the wise conduct of the affairs of society1 no more than of any one's private concerns1 that we should be able to foresee infallibly the results of what we do4 ,we must seek our objects by means which may perhaps be defeated1 and take precautions against dangers which possibly may never be realized4 ,the aim of practical politics is to surround any given society with the greatest possible number of circumstances of which the tendencies are beneficial1 and to remove or counteract1 as far as practicable1 those of which the tendencies are injurious4 ,a knowledge of the tendencies only1 though without the power of accurately predicting their conjunct result1 gives us to a considerable extent this power4 ,it would1 however1 be an error to suppose that even with respect to tendencies we could arrive in this manner at any great number of propositions which will be true in all societies without exception4 ,such a supposition would be inconsistent with the eminently modifiable nature of the social phenomena1 and the multitude and variety of the circumstances by which they are modified--circumstances never the same1 or even nearly the same1 in two different societies1 or in two different periods of the same society4 ,this would not be so serious an obstacle if1 though the causes acting upon society in general are numerous1 those which influence any one feature of society were limited in number2 for we might then insulate any particular social phenomenon1 and investigate its laws without disturbance from the rest4 ,but the truth is the very opposite of this4 ,whatever affects1 in an appreciable degree1 any one element of the social state1 affects through it all the other elements4 ,the mode of production of all social phenomena is one great case of ,intermixture of ,laws4 ,we can never either understand in theory or command in practice the condition of a society in any one respect1 without taking into consideration its condition in all other respects4 ,there is no social phenomenon which is not more or less influenced by every other part of the condition of the same society1 and therefore by every cause which is influencing any other of the contemporaneous social phenomena4 ,there is1 in short1 what physiologists term a consensus1 similar to that existing among the various organs and functions of the physical frame of man and the more perfect animals2 and constituting one of the many analogies which have rendered universal such expressions as the 8body politic0 and 8body natural40 ,it follows from this consensus1 that unless two societies could be alike in all the circumstances which surround and influence them 7which would imply their being alike in their previous history71 no portion whatever of the phenomena will1 unless by accident1 precisely correspond2 no one cause will produce exactly the same effects in both4 ,every cause1 as its effect spreads through society1 comes somewhere in contact with different sets of agencies1 and thus has its effects on some of the social phenomena differently modified2 and these differences1 by their reaction1 produce a difference even in those of the effects which would otherwise have been the same4 ,we can never1 therefore1 affirm with certainty that a cause which has a particular tendency in one people or in one age will have exactly the same tendency in another1 without referring back to our premises1 and performing over again for the second age or nation1 that analysis of the whole of its influencing circumstances which we had already performed for the first4 ,the deductive science of society will not lay down a theorem1 asserting in a universal manner the effect of any cause2 but will rather teach us how to frame the proper theorem for the circumstances of any given case4 ,it will not give the laws of society in general1 but the means of determining the phenomena of any given society from the particular elements or data of that society4 ,all the general propositions which can be framed by the deductive science1 are therefore1 in the strictest sense of the word1 hypothetical4 ,they are grounded on some suppositious set of circumstances1 and declare how some given cause would operate in those circumstances1 supposing that no others were combined with them4 ,if the set of circumstances supposed have been copied from those of any existing society1 the conclusions will be true of that society1 provided1 and in as far as1 the effect of those circumstances shall not be modified by others which have not been taken into the account4 ,if we desire a nearer approach to concrete truth1 we can only aim at it by taking1 or endeavoring to take1 a greater number of individualizing circumstances into the computation4 ,considering1 however1 in how accelerating a ratio the uncertainty of our conclusions increases as we attempt to take the effect of a greater number of concurrent causes into our calculations1 the hypothetical combinations of circumstances on which we construct the general theorems of the science1 can not be made very complex1 without so rapidly accumulating a liability to error as must soon deprive our conclusions of all value4 ,this mode of inquiry1 considered as a means of obtaining general propositions1 must1 therefore1 on pain of frivolity1 be limited to those classes of social facts which1 though influenced like the rest by all sociological agents1 are under the immediate influence1 principally at least1 of a few only4 #c4 ,notwithstanding the universal consensus of the social phenomena1 whereby nothing which takes place in any part of the operations of society is without its share of influence on every other part2 and notwithstanding the paramount ascendancy which the general state of civilization and social progress in any given society must hence exercise over all the partial and subordinate phenomena2 it is not the less true that different species of social facts are in the main dependent1 immediately and in the first resort1 on different kinds of causes2 and therefore not only may with advantage1 but must1 be studied apart3 just as in the natural body we study separately the physiology and pathology of each of the principal organs and tissues1 though every one is acted upon by the state of all the others2 and though the peculiar constitution and general state of health of the organism co-operates with1 and often preponderates over1 the local causes1 in determining the state of any particular organ4 ,on these considerations is grounded the existence of distinct and separate1 though not independent1 branches or departments of sociological speculation4 ,there is1 for example1 one large class of social phenomena in which the immediately determining causes are principally those which act through the desire of wealth1 and in which the psychological law mainly concerned is the familiar one1 that a greater gain is preferred to a smaller4 ,i mean1 of course1 that portion of the phenomena of society which emanate from the industrial1 or productive1 operations of mankind2 and from those of their acts through which the distribution of the products of those industrial operations takes place1 in so far as not effected by force1 or modified by voluntary gift4 ,by reasoning from that one law of human nature1 and from the principal outward circumstances 7whether universal or confined to particular states of society7 which operate upon the human mind through that law1 we may be enabled to explain and predict this portion of the phenomena of society1 so far as they depend on that class of circumstances only2 overlooking the influence of any other of the circumstances of society2 and therefore neither tracing back the circumstances which we do take into account1 to their possible origin in some other facts in the social state1 nor making allowance for the manner in which any of those other circumstances may interfere with1 and counteract or modify1 the effect of the former4 ,a department of science may thus be constructed1 which has received the name of ,political ,economy4 ,the motive which suggests the separation of this portion of the social phenomena from the rest1 and the creation of a distinct branch of science relating to them is--that they do mainly depend1 at least in the first resort1 on one class of circumstances only2 and that even when other circumstances interfere1 the ascertainment of the effect due to the one class of circumstances alone1 is a sufficiently intricate and difficult business to make it expedient to perform it once for all1 and then allow for the effect of the modifying circumstances2 especially as certain fixed combinations of the former are apt to recur often1 in conjunction with ever-varying circumstances of the latter class4 ,political ,economy1 as ,i have said on another occasion1 concerns itself only with 8such of the phenomena of the social state as take place in consequence of the pursuit of wealth4 ,it makes entire abstraction of every other human passion or motive2 except those which may be regarded as perpetually antagonizing principles to the desire of wealth1 namely1 aversion to labor1 and desire of the present enjoyment of costly indulgences4 ,these it takes1 to a certain extent1 into its calculations1 because these do not merely1 like our other desires1 occasionally conflict with the pursuit of wealth1 but accompany it always as a drag or impediment1 and are therefore inseparably mixed up in the consideration of it4 ,political ,economy considers mankind as occupied solely in acquiring and consuming wealth2 and aims at showing what is the course of action into which mankind1 living in a state of society1 would be impelled1 if that motive1 except in the degree in which it is checked by the two perpetual counter-motives above adverted to1 were absolute ruler of all their actions4 ,under the influence of this desire1 it shows mankind accumulating wealth1 and employing that wealth in the production of other wealth2 sanctioning by mutual agreement the institution of property2 establishing laws to prevent individuals from encroaching upon the property of others by force or fraud2 adopting various contrivances for increasing the productiveness of their labor2 settling the division of the produce by agreement1 under the influence of competition 7competition itself being governed by certain laws1 which laws are therefore the ultimate regulators of the division of the produce72 and employing certain expedients 7as money1 credit1 etc47 to facilitate the distribution4 ,all these operations1 though many of them are really the result of a plurality of motives1 are considered by political economy as flowing solely from the desire of wealth4 ,the science then proceeds to investigate the laws which govern these several operations1 under the supposition that man is a being who is determined1 by the necessity of his nature1 to prefer a greater portion of wealth to a smaller1 in all cases1 without any other exception than that constituted by the two counter-motives already specified4 ,not that any political economist was ever so absurd as to suppose that mankind are really thus constituted1 but because this is the mode in which science must necessarily proceed4 ,when an effect depends on a concurrence of causes1 these causes must be studied one at a time1 and their laws separately investigated1 if we wish1 through the causes1 to obtain the power of either predicting or controlling the effect2 since the law of the effect is compounded of the laws of all the causes which determine it4 ,the law of the centripetal and that of the projectile force must have been known1 before the motions of the earth and planets could be explained1 or many of them predicted4 ,the same is the case with the conduct of man in society4 ,in order to judge how he will act under the variety of desires and aversions which are concurrently operating upon him1 we must know how he would act under the exclusive influence of each one in particular4 ,there is1 perhaps1 no action of a man's life in which he is neither under the immediate nor under the remote influence of any impulse but the mere desire of wealth4 ,with respect to those parts of human conduct of which wealth is not even the principal object1 to these political economy does not pretend that its conclusions are applicable4 ,but there are also certain departments of human affairs1 in which the acquisition of wealth is the main and acknowledged end4 ,it is only of these that political economy takes notice4 ,the manner in which it necessarily proceeds is that of treating the main and acknowledged end as if it were the sole end2 which1 of all hypotheses equally simple1 is the nearest to the truth4 ,the political economist inquires1 what are the actions which would be produced by this desire1 if within the departments in question it were unimpeded by any other4 ,in this way a nearer approximation is obtained than would otherwise be practicable to the real order of human affairs in those departments4 ,this approximation has then to be corrected by making proper allowance for the effects of any impulses of a different description1 which can be shown to interfere with the result in any particular case4 ,only in a few of the most striking cases 7such as the important one of the principle of population7 are these corrections interpolated into the expositions of political economy itself2 the strictness of purely scientific arrangement being thereby somewhat departed from1 for the sake of practical utility4 ,so far as it is known1 or may be presumed1 that the conduct of mankind in the pursuit of wealth is under the collateral influence of any other of the properties of our nature than the desire of obtaining the greatest quantity of wealth with the least labor and self-denial1 the conclusions of political economy will so far fail of being applicable to the explanation or prediction of real events1 until they are modified by a correct allowance for the degree of influence exercised by the other cause407#bgg7 ,extensive and important practical guidance may be derived1 in any given state of society1 from general propositions such as those above indicated2 even though the modifying influence of the miscellaneous causes which the theory does not take into account1 as well as the effect of the general social changes in progress1 be provisionally overlooked4 ,and though it has been a very common error of political economists to draw conclusions from the elements of one state of society1 and apply them to other states in which many of the elements are not the same1 it is even then not difficult1 by tracing back the demonstrations1 and introducing the new premises in their proper places1 to make the same general course of argument which served for the one case1 serve for the others too4 ,for example1 it has been greatly the custom of ,english political economists to discuss the laws of the distribution of the produce of industry1 on a supposition which is scarcely realized anywhere out of ,england and ,scotland1 namely1 that the produce is 8shared among three classes1 altogether distinct from one another1 laborers1 capitalists1 and landlords2 and that all these are free agents1 permitted in law and in fact to set upon their labor1 their capital1 and their land1 whatever price they are able to get for it4 ,the conclusions of the science1 being all adapted to a society thus constituted1 require to be revised whenever they are applied to any other4 ,they are inapplicable where the only capitalists are the landlords1 and the laborers are their property1 as in slave countries4 ,they are inapplicable where the almost universal landlord is the state1 as in ,india4 ,they are inapplicable where the agricultural laborer is generally the owner both of the land itself and of the capital1 as frequently in ,france1 or of the capital only1 as in ,ireland40 ,but though it may often be very justly objected to the existing race of political economists 8that they attempt to construct a permanent fabric out of transitory materials2 that they take for granted the immutability of arrangements of society1 many of which are in their nature fluctuating or progressive1 and enunciate with as little qualification as if they were universal and absolute truths1 propositions which are perhaps applicable to no state of society except the particular one in which the writer happened to live20 this does not take away the value of the propositions1 considered with reference to the state of society from which they were drawn4 ,and even as applicable to other states of society1 8it must not be supposed that the science is so incomplete and unsatisfactory as this might seem to prove4 ,though many of its conclusions are only locally true1 its method of investigation is applicable universally2 and as whoever has solved a certain number of algebraic equations1 can without difficulty solve all others of the same kind1 so whoever knows the political economy of ,england1 or even of ,yorkshire1 knows that of all nations1 actual or possible1 provided he have good sense enough not to expect the same conclusion to issue from varying premises40 ,whoever has mastered with the degree of precision which is attainable the laws which1 under free competition1 determine the rent1 profits1 and wages1 received by landlords1 capitalists1 and laborers1 in a state of society in which the three classes are completely separate1 will have no difficulty in determining the very different laws which regulate the distribution of the produce among the classes interested in it in any of the states of cultivation and landed property set forth in the foregoing extract47#bgh7 #d4 ,i would not here undertake to decide what other hypothetical or abstract sciences similar to ,political ,economy1 may admit of being carved out of the general body of the social science2 what other portions of the social phenomena are in a sufficiently close and complete dependence1 in the first resort1 on a peculiar class of causes1 to make it convenient to create a preliminary science of those causes2 postponing the consideration of the causes which act through them1 or in concurrence with them1 to a later period of the inquiry4 ,there is1 however1 among these separate departments one which can not be passed over in silence1 being of a more comprehensive and commanding character than any of the other branches into which the social science may admit of being divided4 ,like them1 it is directly conversant with the causes of only one class of social facts1 but a class which exercises1 immediately or remotely1 a paramount influence over the test4 ,i allude to what may be termed ,political ,ethology1 or the theory of the causes which determine the type of character belonging to a people or to an age4 ,of all the subordinate branches of the social science1 this is the most completely in its infancy4 ,the causes of national character are scarcely at all understood1 and the effect of institutions or social arrangements upon the character of the people is generally that portion of their effects which is least attended to1 and least comprehended4 ,nor is this wonderful1 when we consider the infant state of the science of ,ethology itself1 from whence the laws must be drawn1 of which the truths of political ethology can be but results and exemplifications4 ,yet1 to whoever well considers the matter1 it must appear that the laws of national 7or collective7 character are by far the most important class of sociological laws4 ,in the first place1 the character which is formed by any state of social circumstances is in itself the most interesting phenomenon which that state of society can possibly present4 ,secondly1 it is also a fact which enters largely into the production of all the other phenomena4 ,and above all1 the character1 that is1 the opinions1 feelings1 and habits1 of the people1 though greatly the results of the state of society which precedes them1 are also greatly the causes of the state of society which follows them2 and are the power by which all those of the circumstances of society which are artificial1 laws and customs for instance1 are altogether moulded3 customs evidently1 laws no less really1 either by the direct influence of public sentiment upon the ruling powers1 or by the effect which the state of national opinion and feeling has in determining the form of government and shaping the character of the governors4 ,as might be expected1 the most imperfect part of those branches of social inquiry which have been cultivated as separate sciences1 is the theory of the manner in which their conclusions are affected by ethological considerations4 ,the omission is no defect in them as abstract or hypothetical sciences1 but it vitiates them in their practical application as branches of a comprehensive social science4 ,in political economy1 for instance1 empirical laws of human nature are tacitly assumed by ,english thinkers1 which are calculated only for ,great ,britain and the ,united ,states4 ,among other things1 an intensity of competition is constantly supposed1 which1 as a general mercantile fact1 exists in no country in the world except those two4 ,an ,english political economist1 like his countrymen in general1 has seldom learned that it is possible that men1 in conducting the business of selling their goods over a counter1 should care more about their ease or their vanity than about their pecuniary gain4 ,yet those who know the habits of the continent of ,europe are aware how apparently small a motive often outweighs the desire of money getting1 even in the operations which have money getting for their direct object4 ,the more highly the science of ethology is cultivated1 and the better the diversities of individual and national character are understood1 the smaller1 probably1 will the number of propositions become1 which it will be considered safe to build on as universal principles of human nature4 ,these considerations show that the process of dividing off the social science into compartments1 in order that each may be studied separately1 and its conclusions afterward corrected for practice by the modifications supplied by the others1 must be subject to at least one important limitation4 ,those portions alone of the social phenomena can with advantage be made the subjects1 even provisionally1 of distinct branches of science1 into which the diversities of character between different nations or different times enter as influencing causes only in a secondary degree4 ,those phenomena1 on the contrary1 with which the influences of the ethological state of the people are mixed up at every step 7so that the connection of effects and causes can not be even rudely marked out without taking those influences into consideration7 could not with any advantage1 nor without great disadvantage1 be treated independently of political ethology1 nor1 therefore1 of all the circumstances by which the qualities of a people are influenced4 ,for this reason 7as well as for others which will hereafter appear7 there can be no separate ,science of ,government2 that being the fact which1 of all others1 is most mixed up1 both as cause and effect1 with the qualities of the particular people or of the particular age4 ,all questions respecting the tendencies of forms of government must stand part of the general science of society1 not of any separate branch of it4 ,this general ,science of ,society1 as distinguished from the separate departments of the science 7each of which asserts its conclusions only conditionally1 subject to the paramount control of the laws of the general science7 now remains to be characterized4 ,and as will be shown presently1 nothing of a really scientific character is here possible1 except by the inverse deductive method4 ,but before we quit the subject of those sociological speculations which proceed by way of direct deduction1 we must examine in what relation they stand to that indispensable element in all deductive sciences1 ,verification by ,specific ,experience--comparison between the conclusions of reasoning and the results of observation4 #e4 ,we have seen that1 in most deductive sciences1 and among the rest in ,ethology itself1 which is the immediate foundation of the ,social ,science1 a preliminary work of preparation is performed on the observed facts1 to fit them for being rapidly and accurately collated 7sometimes even for being collated at all7 with the conclusions of theory4 ,this preparatory treatment consists in finding general propositions which express concisely what is common to large classes of observed facts2 and these are called the empirical laws of the phenomena4 ,we have1 therefore1 to inquire1 whether any similar preparatory process can be performed on the facts of the social science2 whether there are any empirical laws in history or statistics4 ,in statistics1 it is evident that empirical laws may sometimes be traced2 and the tracing them forms an important part of that system of indirect observation on which we must often rely for the data of the ,deductive ,science4 ,the process of the science consists in inferring effects from their causes2 but we have often no means of observing the causes1 except through the medium of their effects4 ,in such cases the deductive science is unable to predict the effects1 for want of the necessary data2 it can determine what causes are capable of producing any given effect1 but not with what frequency and in what quantities those causes exist4 ,an instance in point is afforded by a newspaper now lying before me4 ,a statement was furnished by one of the official assignees in bankruptcy showing among the various bankruptcies which it had been his duty to investigate1 in how many cases the losses had been caused by misconduct of different kinds1 and in how many by unavoidable misfortunes4 ,the result was1 that the number of failures caused by misconduct greatly preponderated over those arising from all other causes whatever4 ,nothing but specific experience could have given sufficient ground for a conclusion to this purport4 ,to collect1 therefore1 such empirical laws 7which are never more than approximate generalizations7 from direct observation1 is an important part of the process of sociological inquiry4 ,the experimental process is not here to be regarded as a distinct road to the truth1 but as a means 7happening accidentally to be the only1 or the best1 available7 for obtaining the necessary data for the deductive science4 ,when the immediate causes of social facts are not open to direct observation1 the empirical law of the effects gives us the empirical law 7which in that case is all that we can obtain7 of the causes likewise4 ,but those immediate causes depend on remote causes2 and the empirical law1 obtained by this indirect mode of observation1 can only be relied on as applicable to unobserved cases1 so long as there is reason to think that no change has taken place in any of the remote causes on which the immediate causes depend4 ,in making use1 therefore1 of even the best statistical generalizations for the purpose of inferring 7though it be only conjecturally7 that the same empirical laws will hold in any new case1 it is necessary that we be well acquainted with the remoter causes1 in order that we may avoid applying the empirical law to cases which differ in any of the circumstances on which the truth of the law ultimately depends4 ,and thus1 even where conclusions derived from specific observation are available for practical inferences in new cases1 it is necessary that the deductive science should stand sentinel over the whole process2 that it should be constantly referred to1 and its sanction obtained to every inference4 ,the same thing holds true of all generalizations which can be grounded on history4 ,not only there are such generalizations1 but it will presently be shown that the general science of society1 which inquires into the laws of succession and co-existence of the great facts constituting the state of society and civilization at any time1 can proceed in no other manner than by making such generalizations--afterward to be confirmed by connecting them with the psychological and ethological laws on which they must really depend4 #f4 ,but 7reserving this question for its proper place7 in those more special inquiries which form the subject of the separate branches of the social science1 this twofold logical process and reciprocal verification is not possible2 specific experience affords nothing amounting to empirical laws4 ,this is particularly the case where the object is to determine the effect of any one social cause among a great number acting simultaneously2 the effect1 for example1 of corn laws1 or of a prohibitive commercial system generally4 ,though it may be perfectly certain1 from theory1 what kind of effects corn laws must produce1 and in what general direction their influence must tell upon industrial prosperity1 their effect is yet of necessity so much disguised by the similar or contrary effects of other influencing agents1 that specific experience can at most only show that on the average of some great number of instances1 the cases where there were corn laws exhibited the effect in a greater degree than those where there were not4 ,now the number of instances necessary to exhaust the whole round of combinations of the various influential circumstances1 and thus afford a fair average1 never can be obtained4 ,not only we can never learn with sufficient authenticity the facts of so many instances1 but the world itself does not afford them in sufficient numbers1 within the limits of the given state of society and civilization which such inquiries always presuppose4 ,having thus no previous empirical generalizations with which to collate the conclusions of theory1 the only mode of direct verification which remains is to compare those conclusions with the result of an individual experiment or instance4 ,but here the difficulty is equally great4 ,for in order to verify a theory by an experiment1 the circumstances of the experiment must be exactly the same with those contemplated in the theory4 ,but in social phenomena the circumstances of no two cases are exactly alike4 ,a trial of corn laws in another country1 or in a former generation1 would go a very little way toward verifying a conclusion drawn respecting their effect in this generation and in this country4 ,it thus happens1 in most cases1 that the only individual instance really fitted to verify the predictions of theory is the very instance for which the predictions were made2 and the verification comes too late to be of any avail for practical guidance4 ,although1 however1 direct verification is impossible1 there is an indirect verification1 which is scarcely of less value1 and which is always practicable4 ,the conclusion drawn as to the individual case can only be directly verified in that case2 but it is verified indirectly1 by the verification of other conclusions1 drawn in other individual cases from the same laws4 ,the experience which comes too late to verify the particular proposition to which it refers1 is not too late to help toward verifying the general sufficiency of the theory4 ,the test of the degree in which the science affords safe ground for predicting 7and consequently for practically dealing with7 what has not yet happened1 is the degree in which it would have enabled us to predict what has actually occurred4 ,before our theory of the influence of a particular cause1 in a given state of circumstances1 can be entirely trusted1 we must be able to explain and account for the existing state of all that portion of the social phenomena which that cause has a tendency to influence4 ,if1 for instance1 we would apply our speculations in political economy to the prediction or guidance of the phenomena of any country1 we must be able to explain all the mercantile or industrial facts of a general character1 appertaining to the present state of that country2 to point out causes sufficient to account for all of them1 and prove1 or show good ground for supposing1 that these causes have really existed4 ,if we can not do this1 it is a proof either that the facts which ought to be taken into account are not yet completely known to us1 or that although we know the facts1 we are not masters of a sufficiently perfect theory to enable us to assign their consequences4 ,in either case we are not1 in the present state of our knowledge1 fully competent to draw conclusions1 speculative or practical1 for that country4 ,in like manner1 if we would attempt to judge of the effect which any political institution would have1 supposing that it could be introduced into any given country1 we must be able to show that the existing state of the practical government of that country1 and of whatever else depends thereon1 together with the particular character and tendencies of the people1 and their state in respect to the various elements of social well-being1 are such as the institutions they have lived under1 in conjunction with the other circumstances of their nature or of their position1 were calculated to produce4 ,to prove1 in short1 that our science1 and our knowledge of the particular case1 render us competent to predict the future1 we must show that they would have enabled us to predict the present and the past4 ,if there be any thing which we could not have predicted1 this constitutes a residual phenomenon1 requiring further study for the purpose of explanation2 and we must either search among the circumstances of the particular case until we find one which1 on the principles of our existing theory1 accounts for the unexplained phenomenon1 or we must turn back1 and seek the explanation by an extension and improvement of the theory itself4 ,chapter ,x4 ,of ,the ,inverse ,deductive1 ,or ,historical1 ,method4 #a4 ,there are two kinds of sociological inquiry4 ,in the first kind1 the question proposed is1 what effect will follow from a given cause1 a certain general condition of social circumstances being presupposed4 ,as1 for example1 what would be the effect of imposing or of repealing corn laws1 of abolishing monarchy or introducing universal suffrage1 in the present condition of society and civilization in any ,european country1 or under any other given supposition with regard to the circumstances of society in general1 without reference to the changes which might take place1 or which may already be in progress1 in those circumstances4 ,but there is also a second inquiry1 namely1 what are the laws which determine those general circumstances themselves4 ,in this last the question is1 not what will be the effect of a given cause in a certain state of society1 but what are the causes which produce1 and the phenomena which characterize1 states of society generally4 ,in the solution of this question consists the general ,science of ,society2 by which the conclusions of the other and more special kind of inquiry must be limited and controlled4 #b4 ,in order to conceive correctly the scope of this general science1 and distinguish it from the subordinate departments of sociological speculation1 it is necessary to fix the ideas attached to the phrase1 8,a ,state of ,society40 ,what is called a state of society1 is the simultaneous state of all the greater social facts or phenomena4 ,such are3 the degree of knowledge1 and of intellectual and moral culture1 existing in the community1 and in every class of it2 the state of industry1 of wealth and its distribution2 the habitual occupations of the community2 their division into classes1 and the relations of those classes to one another2 the common beliefs which they entertain on all the subjects most important to mankind1 and the degree of assurance with which those beliefs are held2 their tastes1 and the character and degree of their sthetic development2 their form of government1 and the more important of their laws and customs4 ,the condition of all these things1 and of many more which will readily suggest themselves1 constitute the state of society1 or the state of civilization1 at any given time4 ,when states of society1 and the causes which produce them1 are spoken of as a subject of science1 it is implied that there exists a natural correlation among these different elements2 that not every variety of combination of these general social facts is possible1 but only certain combinations2 that1 in short1 there exist ,uniformities of ,co-existence between the states of the various social phenomena4 ,and such is the truth2 as is indeed a necessary consequence of the influence exercised by every one of those phenomena over every other4 ,it is a fact implied in the consensus of the various parts of the social body4 ,states of society are like different constitutions or different ages in the physical frame2 they are conditions not of one or a few organs or functions1 but of the whole organism4 ,accordingly1 the information which we possess respecting past ages1 and respecting the various states of society now existing in different regions of the earth1 does1 when duly analyzed1 exhibit uniformities4 ,it is found that when one of the features of society is in a particular state1 a state of many other features1 more or less precisely determinate1 always or usually co-exists with it4 ,but the uniformities of co-existence obtaining among phenomena which are effects of causes1 must 7as we have so often observed7 be corollaries from the laws of causation by which these phenomena are really determined4 ,the mutual correlation between the different elements of each state of society1 is1 therefore1 a derivative law1 resulting from the laws which regulate the succession between one state of society and another2 for the proximate cause of every state of society is the state of society immediately preceding it4 ,the fundamental problem1 therefore1 of the social science1 is to find the laws according to which any state of society produces the state which succeeds it and takes its place4 ,this opens the great and vexed question of the progressiveness of man and society2 an idea involved in every just conception of social phenomena as the subject of a science4 #c4 ,it is one of the characters1 not absolutely peculiar to the sciences of human nature and society1 but belonging to them in a peculiar degree1 to be conversant with a subject-matter whose properties are changeable4 ,i do not mean changeable from day to day1 but from age to age2 so that not only the qualities of individuals vary1 but those of the majority are not the same in one age as in another4 ,the principal cause of this peculiarity is the extensive and constant reaction of the effects upon their causes4 ,the circumstances in which mankind are placed1 operating according to their own laws and to the laws of human nature1 form the characters of the human beings2 but the human beings1 in their turn1 mould and shape the circumstances for themselves and for those who come after them4 ,from this reciprocal action there must necessarily result either a cycle or a progress4 ,in astronomy also1 every fact is at once effect and cause2 the successive positions of the various heavenly bodies produce changes both in the direction and in the intensity of the forces by which those positions are determined4 ,but in the case of the solar system1 these mutual actions bring around again1 after a certain number of changes1 the former state of circumstances2 which1 of course1 leads to the perpetual recurrence of the same series in an unvarying order4 ,those bodies1 in short1 revolve in orbits3 but there are 7or1 conformably to the laws of astronomy1 there might be7 others which1 instead of an orbit1 describe a trajectory--a course not returning into itself4 ,one or other of these must be the type to which human affairs must conform4 ,one of the thinkers who earliest conceived the succession of historical events as subject to fixed laws1 and endeavored to discover these laws by an analytical survey of history1 ,vico1 the celebrated author of the ,scienza ,nuova1 adopted the former of these opinions4 ,he conceived the phenomena of human society as revolving in an orbit2 as going through periodically the same series of changes4 ,though there were not wanting circumstances tending to give some plausibility to this view1 it would not bear a close scrutiny3 and those who have succeeded ,vico in this kind of speculations have universally adopted the idea of a trajectory or progress1 in lieu of an orbit or cycle4 ,the words ,progress and ,progressiveness are not here to be understood as synonymous with improvement and tendency to improvement4 ,it is conceivable that the laws of human nature might determine1 and even necessitate1 a certain series of changes in man and society1 which might not in every case1 or which might not on the whole1 be improvements4 ,it is my belief1 indeed1 that the general tendency is1 and will continue to be1 saving occasional and temporary exceptions1 one of improvement2 a tendency toward a better and happier state4 ,this1 however1 is not a question of the method of the social science1 but a theorem of the science itself4 ,for our purpose it is sufficient that there is a progressive change both in the character of the human race and in their outward circumstances1 so far as moulded by themselves2 that in each successive age the principal phenomena of society are different from what they were in the age preceding1 and still more different from any previous age3 the periods which most distinctly mark these successive changes being intervals of one generation1 during which a new set of human beings have been educated1 have grown up from childhood1 and taken possession of society4 ,the progressiveness of the human race is the foundation on which a method of philosophizing in the social science has been of late years erected1 far superior to either of the two modes which had previously been prevalent1 the chemical or experimental1 and the geometrical modes4 ,this method1 which is now generally adopted by the most advanced thinkers on the ,continent1 consists in attempting1 by a study and analysis of the general facts of history1 to discover 7what these philosophers term7 the law of progress3 which law1 once ascertained1 must according to them enable us to predict future events1 just as after a few terms of an infinite series in algebra we are able to detect the principle1 of regularity in their formation1 and to predict the rest of the series to any number of terms we please4 ,the principal aim of historical speculation in ,france1 of late years1 has been to ascertain this law4 ,but while ,i gladly acknowledge the great services which have been rendered to historical knowledge by this school1 ,i can not but deem them to be mostly chargeable with a fundamental misconception of the true method of social philosophy4 ,the misconception consists in supposing that the order of succession which we may be able to trace among the different states of society and civilization which history presents to us1 even if that order were more rigidly uniform than it has yet been proved to be1 could ever amount to a law of nature4 ,it can only be an empirical law4 ,the succession of states of the human mind and of human society can not have an independent law of its own2 it must depend on the psychological and ethological laws which govern the action of circumstances on men and of men on circumstances4 ,it is conceivable that those laws might be such1 and the general circumstances of the human race such1 as to determine the successive transformations of man and society to one given and unvarying order4 ,but even if the case were so1 it can not be the ultimate aim of science to discover an empirical law4 ,until that law could be connected with the psychological and ethological laws on which it must depend1 and1 by the consilience of deduction a priori with historical evidence1 could be converted from an empirical law into a scientific one1 it could not be relied on for the prediction of future events1 beyond1 at most1 strictly adjacent cases4 ,m4 ,comte alone1 among the new historical school1 has seen the necessity of thus connecting all our generalizations from history with the laws of human nature4 #d4 ,but1 while it is an imperative rule never to introduce any generalization from history into the social science unless sufficient grounds can be pointed out for it in human nature1 ,i do not think any one will contend that it would have been possible1 setting out from the principles of human nature and from the general circumstances of the position of our species1 to determine a priori the order in which human development must take place1 and to predict1 consequently1 the general facts of history up to the present time4 ,after the first few terms of the series1 the influence exercised1 over each generation by the generations which preceded it1 becomes1 7as is well observed by the writer last referred to7 more and more preponderant over all other influences2 until at length what we now are and do1 is in a very small degree the result of the universal circumstances of the human race1 or even of our own circumstances acting through the original qualities of our species1 but mainly of the qualities produced in us by the whole previous history of humanity4 ,so long a series of actions and reactions between ,circumstances and ,man1 each successive term being composed of an ever greater number and variety of parts1 could not possibly be computed by human faculties from the elementary laws which produce it4 ,the mere length of the series would be a sufficient obstacle1 since a slight error in any one of the terms would augment in rapid progression at every subsequent step4 ,if1 therefore1 the series of the effects themselves did not1 when examined as a whole1 manifest any regularity1 we should in vain attempt to construct a general science of society4 ,we must in that case have contented ourselves with that subordinate order of sociological speculation formerly noticed1 namely1 with endeavoring to ascertain what would be the effect of the introduction of any new cause1 in a state of society supposed to be fixed--a knowledge sufficient for the more common exigencies of daily political practice1 but liable to fail in all cases in which the progressive movement of society is one of the influencing elements2 and therefore more precarious in proportion as the case is more important4 ,but since both the natural varieties of mankind1 and the original diversities of local circumstances1 are much less considerable than the points of agreement1 there will naturally be a certain degree of uniformity in the progressive development of the species and of its works4 ,and this uniformity tends to become greater1 not less1 as society advances2 since the evolution of each people1 which is at first determined exclusively by the nature and circumstances of that people1 is gradually brought under the influence 7which becomes stronger as civilization advances7 of the other nations of the earth1 and of the circumstances by which they have been influenced4 ,history accordingly does1 when judiciously examined1 afford ,empirical ,laws of ,society4 ,and the problem of general sociology is to ascertain these1 and connect them with the laws of human nature1 by deductions showing that such were the derivative laws naturally to be expected as the consequences of those ultimate ones4 ,it is1 indeed1 hardly ever possible1 even after history has suggested the derivative law1 to demonstrate a priori that such was the only order of succession or of co-existence in which the effects could1 consistently with the laws of human nature1 have been produced4 ,we can at most make out that there were strong a priori reasons for expecting it1 and that no other order of succession or co-existence would have been so likely to result from the nature of man and the general circumstances of his position4 ,often we can not do even this2 we can not even show that what did take place was probable a priori1 but only that it was possible4 ,this1 however--which1 in the ,inverse ,deductive ,method that we are now characterizing1 is a real process of verification--is as indispensable1 as verification by specific experience has been shown to be1 where the conclusion is originally obtained by the direct way of deduction4 ,the empirical laws must be the result of but a few instances1 since few nations have ever attained at all1 and still fewer by their own independent development1 a high stage of social progress4 ,if1 therefore1 even one or two of these few instances be insufficiently known1 or imperfectly analyzed into their elements1 and therefore not adequately compared with other instances1 nothing is more probable than that a wrong empirical law will emerge instead of the right one4 ,accordingly1 the most erroneous generalizations are continually made from the course of history2 not only in this country1 where history can not yet be said to be at all cultivated as a science1 but in other countries where it is so cultivated1 and by persons well versed in it4 ,the only check or corrective is1 constant verification by psychological and ethological laws4 ,we may add to this1 that no one but a person competently skilled in those laws is capable of preparing the materials for historical generalization1 by analyzing the facts of history1 or even by observing the social phenomena of his own time4 ,no other will be aware of the comparative importance of different facts1 nor consequently know what facts to look for1 or to observe2 still less will he be capable of estimating the evidence of facts which1 as is the case with most1 can not be ascertained by direct observation or learned from testimony1 but must be inferred from marks4 #e4 ,the ,empirical ,laws of ,society are of two kinds2 some are uniformities of co-existence1 some of succession4 ,according as the science is occupied in ascertaining and verifying the former sort of uniformities or the latter1 ,m4 ,comte gives it the title of ,social ,statics1 or of ,social ,dynamics2 conformably to the distinction in mechanics between the conditions of equilibrium and those of movement2 or in biology1 between the laws of organization and those of life4 ,the first branch of the science ascertains the conditions of stability in the social union2 the second1 the laws of progress4 ,social ,dynamics is the theory of ,society considered in a state of progressive movement2 while ,social ,statics is the theory of the consensus already spoken of as existing among the different parts of the social organism2 in other words1 the theory of the mutual actions and reactions of contemporaneous social phenomena2 making7#bgi7 provisionally1 as far as possible1 abstraction1 for scientific purposes1 of the fundamental movement which is at all times gradually modifying the whole of them4 8,in this first point of view1 the provisions of sociology will enable us to infer one from another 7subject to ulterior verification by direct observation7 the various characteristic marks of each distinct mode of social existence1 in a manner essentially analogous to what is now habitually practiced in the anatomy of the physical body4 ,this preliminary aspect1 therefore1 of political science1 of necessity supposes that 7contrary to the existing habits of philosophers7 each of the numerous elements of the social state1 ceasing to be looked at independently and absolutely1 shall be always and exclusively considered relatively to all the other elements1 with the whole of which it is united by mutual interdependence4 ,it would be superfluous to insist here upon the great and constant utility of this branch of sociological speculation4 ,it is1 in the first place1 the indispensable basis of the theory of social progress4 ,it may1 moreover1 be employed1 immediately1 and of itself1 to supply the place1 provisionally at least1 of direct observation1 which in many cases is not always practicable for some of the elements of society1 the real condition of which may1 however1 be sufficiently judged of by means of the relations which connect them with others previously known4 ,the history of the sciences may give us some notion of the habitual importance of this auxiliary resource1 by reminding us1 for example1 how the vulgar errors of mere erudition concerning the pretended acquirements of the ancient ,egyptians in the higher astronomy were irrevocably dissipated 7even before sentence had been passed on them by a sounder erudition7 from the single consideration of the inevitable connection between the general state of astronomy and that of abstract geometry1 then evidently in its infancy4 ,it would be easy to cite a multitude of analogous cases1 the character of which could admit of no dispute4 ,in order to avoid exaggeration1 however1 it should be remarked1 that these necessary relations among the different aspects of society can not1 from their very nature1 be so simple and precise that the results observed could only have arisen from some one mode of mutual co-ordination4 ,such a notion1 already too narrow in the science of life1 would be completely at variance with the still more complex nature of sociological speculations4 ,but the exact estimation of these limits of variation1 both in the healthy and in the morbid state1 constitutes1 at least as much as in the anatomy of the natural body1 an indispensable complement to every theory of ,sociological ,statics2 without which the indirect exploration above spoken of would often lead into error4 8,this is not the place for methodically demonstrating the existence of a necessary relation among all the possible aspects of the same social organism2 a point on which1 in principle at least1 there is now little difference of opinion among sound thinkers4 ,from whichever of the social elements we choose to set out1 we may easily recognize that it has always a connection1 more or less immediate1 with all the other elements1 even with those which at first sight appear the most independent of it4 ,the dynamical consideration of the progressive development of civilized humanity1 affords1 no doubt1 a still more efficacious means of effecting this interesting verification of the consensus of the social phenomena1 by displaying the manner in which every change in any one part1 operates immediately1 or very speedily1 upon all the rest4 ,but this indication may be preceded1 or at all events followed1 by a confirmation of a purely statical kind2 for1 in politics as in mechanics1 the communication of motion from one object to another proves a connection between them4 ,without descending to the minute interdependence of the different branches of any one science or art1 is it not evident that among the different sciences1 as well as among most of the arts1 there exists such a connection1 that if the state of any one well-marked division of them is sufficiently known to us1 we can with real scientific assurance infer1 from their necessary correlation1 the contemporaneous state of every one of the others8 ,by a further extension of this consideration1 we may conceive the necessary relation which exists between the condition of the sciences in general and that of the arts in general1 except that the mutual dependence is less intense in proportion as it is more indirect4 ,the same is the case1 when1 instead of considering the aggregate of the social phenomena in some one people1 we examine it simultaneously in different contemporaneous nations2 between which the perpetual reciprocity of influence1 especially in modern times1 can not be contested1 though the consensus must in this case be ordinarily of a less decided character1 and must decrease gradually with the affinity of the cases and the multiplicity of the points of contact1 so as at last1 in some cases1 to disappear almost entirely2 as for1 example1 between ,western ,europe and ,eastern ,asia1 of which the various general states of society appear to have been hitherto almost independent of one another40 ,these remarks are followed by illustrations of one of the most important1 and until lately1 most neglected1 of the general principles which1 in this division of the social science1 may be considered as established2 namely1 the necessary correlation between the form of government existing in any society and the contemporaneous state of civilization3 a natural law which stamps the endless discussions and innumerable theories respecting forms of government in the abstract1 as fruitless and worthless1 for any other purpose than as a preparatory treatment of materials to be afterward used for the construction of a better philosophy4 ,as already remarked1 one of the main results of the science of social statics would be to ascertain the requisites of stable political union4 ,there are some circumstances which1 being found in all societies without exception1 and in the greatest degree where the social union is most complete1 may be considered 7when psychological and ethological laws confirm the indication7 as conditions of the existence of the complex phenomena called a ,state4 ,for example1 no numerous society has ever been held together without laws1 or usages equivalent to them2 without tribunals1 and an organized force of some sort to execute their decisions4 ,there have always been public authorities whom1 with more or less strictness and in cases more or less accurately defined1 the rest of the community obeyed1 or according to general opinion were bound to obey4 ,by following out this course of inquiry we shall find a number of requisites1 which have been present in every society that has maintained a collective existence1 and on the cessation of which it has either merged in some other society1 or reconstructed itself on some new basis1 in which the conditions were conformed to4 ,although these results1 obtained by comparing different forms and states of society1 amount in themselves only to empirical laws2 some of them1 when once suggested1 are found to follow with so much probability from general laws of human nature1 that the consilience of the two processes raises the evidence to proof1 and the generalizations to the rank of scientific truths4 ,this seems to be affirmable 7for instance7 of the conclusions arrived at in the following passage1 extracted1 with some alterations1 from a criticism on the negative philosophy of the eighteenth century17#bhj7 and which ,i quote1 though 7as in some former instances7 from myself1 because ,i have no better way of illustrating the conception ,i have formed of the kind of theorems of which sociological statics would consist4 8,the very first element of the social union1 obedience to a government of some sort1 has not been found so easy a thing to establish in the world4 ,among a timid and spiritless race like the inhabitants of the vast plains of tropical countries1 passive obedience may be of natural growth2 though even there we doubt whether it has ever been found among any people with whom fatalism1 or in other words1 submission to the pressure of circumstances as a divine decree1 did not prevail as a religious doctrine4 ,but the difficulty of inducing a brave and warlike race to submit their individual arbitrium to any common umpire1 has always been felt to be so great1 that nothing short of supernatural power has been deemed adequate to overcome it2 and such tribes have always assigned to the first institution of civil society a divine origin4 ,so differently did those judge who knew savage men by actual experience1 from those who had no acquaintance with them except in the civilized state4 ,in modern ,europe itself1 after the fall of the ,roman empire1 to subdue the feudal anarchy and bring the whole people of any ,european nation into subjection to government 7though ,christianity in the most concentrated form of its influence was co-operating in the work7 required thrice as many centuries as have elapsed since that time4 8,now if these philosophers had known human nature under any other type than that of their own age1 and of the particular classes of society among whom they lived1 it would have occurred to them1 that wherever this habitual submission to law and government has been firmly and durably established1 and yet the vigor and manliness of character which resisted its establishment have been in any degree preserved1 certain requisites have existed1 certain conditions have been fulfilled1 of which the following may be regarded as the principal4 8,first3 there has existed1 for all who were accounted citizens--for all who were not slaves1 kept down by brute force--a system of education1 beginning with infancy and continued through life1 of which whatever else it might include1 one main and incessant ingredient was restraining discipline4 ,to train the human being in the habit1 and thence the power1 of subordinating his personal impulses and aims to what were considered the ends of society2 of adhering1 against all temptation1 to the course of conduct which those ends prescribed2 of controlling in himself all feelings which were liable to militate against those ends1 and encouraging all such as tended toward them2 this was the purpose1 to which every outward motive that the authority directing the system could command1 and every inward power or principle which its knowledge of human nature enabled it to evoke1 were endeavored to be rendered instrumental4 ,the entire civil and military policy of the ancient commonwealths was such a system of training2 in modern nations its place has been attempted to be supplied1 principally1 by religious teaching4 ,and whenever and in proportion as the strictness of the restraining discipline was relaxed1 the natural tendency of mankind to anarchy re-asserted itself2 the state became disorganized from within2 mutual conflict for selfish ends1 neutralized the energies which were required to keep up the contest against natural causes of evil2 and the nation1 after a longer or briefer interval of progressive decline1 became either the slave of a despotism1 or the prey of a foreign invader4 8,the second condition of permanent political society has been found to be1 the existence1 in some form or other1 of the feeling of allegiance or loyalty4 ,this feeling may vary in its objects1 and is not confined to any particular form of government2 but whether in a democracy or in a monarchy1 its essence is always the same2 viz41 that there be in the constitution of the state something which is settled1 something permanent1 and not to be called in question2 something which1 by general agreement1 has a right to be where it is1 and to be secure against disturbance1 whatever else may change4 ,this feeling may attach itself1 as among the ,jews 7and in most of the commonwealths of antiquity71 to a common ,god or gods1 the protectors and guardians of their state4 ,or it may attach itself to certain persons1 who are deemed to be1 whether by divine appointment1 by long prescription1 or by the general recognition of their superior capacity and worthiness1 the rightful guides and guardians of the rest4 ,or it may connect itself with laws2 with ancient liberties or ordinances4 ,or1 finally1 7and this is the only shape in which the feeling is likely to exist hereafter71 it may attach itself to the principles of individual freedom and political and social equality1 as realized in institutions which as yet exist nowhere1 or exist only in a rudimentary state4 ,but in all political societies which have had a durable existence1 there has been some fixed point3 something which people agreed in holding sacred2 which1 wherever freedom of discussion was a recognized principle1 it was of course lawful to contest in theory1 but which no one could either fear or hope to see shaken in practice2 which1 in short 7except perhaps during some temporary crisis71 was in the common estimation placed beyond discussion4 ,and the necessity of this may easily be made evident4 ,a state never is1 nor until mankind are vastly improved1 can hope to be1 for any long time exempt from internal dissension2 for there neither is nor has ever been any state of society in which collisions did not occur between the immediate interests and passions of powerful sections of the people4 ,what1 then1 enables nations to weather these storms1 and pass through turbulent times without any permanent weakening of the securities for peaceable existence8 ,precisely this--that however important the interests about which men fell out1 the conflict did not affect the fundamental principle of the system of social union which happened to exist2 nor threaten large portions of the community with the subversion of that on which they had built their calculations1 and with which their hopes and aims had become identified4 ,but when the questioning of these fundamental principles is 7not the occasional disease1 or salutary medicine1 but7 the habitual condition of the body politic1 and when all the violent animosities are called forth1 which spring naturally from such a situation1 the state is virtually in a position of civil war2 and can never long remain free from it in act and fact4 8,the third essential condition of stability in political society1 is a strong and active principle of cohesion among the members of the same community or state4 ,we need scarcely say that we do not mean nationality1 in the vulgar sense of the term2 a senseless antipathy to foreigners2 indifference to the general welfare of the human race1 or an unjust preference of the supposed interests of our own country2 a cherishing of bad peculiarities because they are national1 or a refusal to adopt what has been found good by other countries4 ,we mean a principle of sympathy1 not of hostility2 of union1 not of separation4 ,we mean a feeling of common interest among those who live under the same government1 and are contained within the same natural or historical boundaries4 ,we mean1 that one part of the community do not consider themselves as foreigners with regard to another part2 that they set a value on their connection--feel that they are one people1 that their lot is cast together1 that evil to any of their fellow-countrymen is evil to themselves1 and do not desire selfishly to free themselves from their share of any common inconvenience by severing the connection4 ,how strong this feeling was in those ancient commonwealths which attained any durable greatness1 every one knows4 ,how happily ,rome1 in spite of all her tyranny1 succeeded in establishing the feeling of a common country among the provinces of her vast and divided empire1 will appear when any one who has given due attention to the subject shall take the trouble to point it out4 ,in modern times the countries which have had that feeling in the strongest degree have been the most powerful countries3 ,england1 ,france1 and1 in proportion to their territory and resources1 ,holland and ,switzerland2 while ,england in her connection with ,ireland is one of the most signal examples of the consequences of its absence4 ,every ,italian knows why ,italy is under a foreign yoke2 every ,german knows what maintains despotism in the ,austrian empire27#bha7 the evils of ,spain flow as much from the absence of nationality among the ,spaniards themselves1 as from the presence of it in their relations with foreigners3 while the completest illustration of all is afforded by the republics of ,south ,america1 where the parts of one and the same state adhere so slightly together1 that no sooner does any province think itself aggrieved by the general government than it proclaims itself a separate nation40 #f4 ,while the derivative laws of social statics are ascertained by analyzing different states of society1 and comparing them with one another1 without regard to the order of their succession1 the consideration of the successive order is1 on the contrary1 predominant in the study of social dynamics1 of which the aim is to observe and explain the sequences of social conditions4 ,this branch of the social science would be as complete as it can be made1 if every one of the leading general circumstances of each generation were traced to its causes in the generation immediately preceding4 ,but the consensus is so complete 7especially in modern history71 that in the filiation of one generation and another1 it is the whole which produces the whole1 rather than any part a part4 ,little progress1 therefore1 can be made in establishing the filiation1 directly from laws of human nature1 without having first ascertained the immediate or derivative laws according to which social states generate one another as society advances2 the axiomata media of ,general ,sociology4 ,the empirical laws which are most readily obtained by generalization from history do not amount to this4 ,they are not the 8middle principles0 themselves1 but only evidence toward the establishment of such principles4 ,they consist of certain general tendencies which may be perceived in society2 a progressive increase of some social elements1 and diminution of others1 or a gradual change in the general character of certain elements4 ,it is easily seen1 for instance1 that as society advances1 mental tend more and more to prevail over bodily qualities1 and masses over individuals2 that the occupation of all that portion of mankind who are not under external restraint is at first chiefly military1 but society becomes progressively more and more engrossed with productive pursuits1 and the military spirit gradually gives way to the industrial2 to which many similar truths might be added4 ,and with generalizations of this description1 ordinary inquirers1 even of the historical school now predominant on the ,continent1 are satisfied4 ,but these and all such results are still at too great a distance from the elementary laws of human nature on which they depend--too many links intervene1 and the concurrence of causes at each link is far too complicated--to enable these propositions to be presented as direct corollaries from those elementary principles4 ,they have1 therefore1 in the minds of most inquirers1 remained in the state of empirical laws1 applicable only within the bounds of actual observation2 without any means of determining their real limits1 and of judging whether the changes which have hitherto been in progress are destined to continue indefinitely1 or to terminate1 or even to be reversed4 #g4 ,in order to obtain better empirical laws1 we must not rest satisfied with noting the progressive changes which manifest themselves in the separate elements of society1 and in which nothing is indicated but the relation of fragments of the effect to corresponding fragments of the cause4 ,it is necessary to combine the statical view of social phenomena with the dynamical1 considering not only the progressive changes of the different elements1 but the contemporaneous condition of each2 and thus obtain empirically the law of correspondence not only between the simultaneous states1 but between the simultaneous changes1 of those elements4 ,this law of correspondence it is1 which1 duly verified a priori1 would become the real scientific derivative law of the development of humanity and human affairs4 ,in the difficult process of observation and comparison which is here required1 it would evidently be a great assistance if it should happen to be the fact1 that some one element in the complex existence of social man is pre-eminent over all others as the prime agent of the social movement4 ,for we could then take the progress of that one element as the central chain1 to each successive link of which1 the corresponding links of all the other progressions being appended1 the succession of the facts would by this alone be presented in a kind of spontaneous order1 far more nearly approaching to the real order of their filiation than could be obtained by any other merely empirical process4 ,now1 the evidence of history and that of human nature combine1 by a striking instance of consilience1 to show that there really is one social element which is thus predominant1 and almost paramount1 among the agents of the social progression4 ,this is1 the state of the speculative faculties of mankind2 including the nature of the beliefs which by any means they have arrived at1 concerning themselves and the world by which they are surrounded4 ,it would be a great error1 and one very little likely to be committed1 to assert that speculation1 intellectual activity1 the pursuit of truth1 is among the more powerful propensities of human nature1 or holds a predominating place in the lives of any1 save decidedly exceptional1 individuals4 ,but1 notwithstanding the relative weakness of this principle among other sociological agents1 its influence is the main determining cause of the social progress2 all the other dispositions of our nature which contribute to that progress being dependent on it for the means of accomplishing their share of the work4 ,thus 7to take the most obvious case first71 the impelling force to most of the improvements effected in the arts of life1 is the desire of increased material comfort2 but as we can only act upon external objects in proportion to our knowledge of them1 the state of knowledge at any time is the limit of the industrial improvements possible at that time2 and the progress of industry must follow1 and depend on1 the progress of knowledge4 ,the same thing may be shown to be true1 though it is not quite so obvious1 of the progress of the fine arts4 ,further1 as the strongest propensities of uncultivated or half-cultivated human nature 7being the purely selfish ones1 and those of a sympathetic character which partake most of the nature of selfishness7 evidently tend in themselves to disunite mankind1 not to unite them--to make them rivals1 not confederates1 social existence is only possible by a disciplining of those more powerful propensities1 which consists in subordinating them to a common system of opinions4 ,the degree of this subordination is the measure of the completeness of the social union1 and the nature of the common opinions determines its kind4 ,but in order that mankind should conform their actions to any set of opinions1 these opinions must exist1 must be believed by them4 ,and thus1 the state of the speculative faculties1 the character of the propositions assented to by the intellect1 essentially determines the moral and political state of the community1 as we have already seen that it determines the physical4 ,these conclusions1 deduced from the laws of human nature1 are in entire accordance with the general facts of history4 ,every considerable change historically known to us in the condition of any portion of mankind1 when not brought about by external force1 has been preceded by a change1 of proportional extent1 in the state of their knowledge1 or in their prevalent beliefs4 ,as between any given state of speculation1 and the correlative state of every thing else1 it was almost always the former which first showed itself2 though the effects1 no doubt1 reacted potently upon the cause4 ,every considerable advance in material civilization has been preceded by an advance in knowledge3 and when any great social change has come to pass1 either in the way of gradual development or of sudden conflict1 it has had for its precursor a great change in the opinions and modes of thinking of society4 ,polytheism1 ,judaism1 ,christianity1 ,protestantism1 the critical philosophy of modern ,europe1 and its positive science--each of these has been a primary agent in making society what it was at each successive period1 while society was but secondarily instrumental in making them1 each of them 7so far as causes can be assigned for its existence7 being mainly an emanation not from the practical life of the period1 but from the previous state of belief and thought4 ,the weakness of the speculative propensity in mankind generally has not1 therefore1 prevented the progress of speculation from governing that of society at large2 it has only1 and too often1 prevented progress altogether1 where the intellectual progression has come to an early stand for want of sufficiently favorable circumstances4 ,from this accumulated evidence1 we are justified in concluding1 that the order of human progression in all respects will mainly depend on the order of progression in the intellectual convictions of mankind1 that is1 on the law of the successive transformations of human opinions4 ,the question remains1 whether this law can be determined2 at first from history as an empirical law1 then converted into a scientific theorem by deducing it a priori from the principles of human nature4 ,as the progress of knowledge and the changes in the opinions of mankind are very slow1 and manifest themselves in a well-defined manner only at long intervals1 it can not be expected that the general order of sequence should be discoverable from the examination of less than a very considerable part of the duration of the social progress4 ,it is necessary to take into consideration the whole of past time1 from the first recorded condition of the human race1 to the memorable phenomena of the last and present generations4 #h4 ,the investigation which ,i have thus endeavored to characterize1 has been systematically attempted1 up to the present time1 by ,m4 ,comte alone4 ,his work is hitherto the only known example of the study of social phenomena according to this conception of the ,historical ,method4 ,without discussing here the worth of his conclusions1 and especially of his predictions and recommendations with respect to the ,future of society1 which appear to me greatly inferior in value to his appreciation of the ,past1 ,i shall confine myself to mentioning one important generalization1 which ,m4 ,comte regards as the fundamental law of the progress of human knowledge4 ,speculation he conceives to have1 on every subject of human inquiry1 three successive stages2 in the first of which it tends to explain the phenomena by supernatural agencies1 in the second by metaphysical abstractions1 and in the third or final state confines itself to ascertaining their laws of succession and similitude4 ,this generalization appears to me to have that high degree of scientific evidence which is derived from the concurrence of the indications of history with the probabilities derived from the constitution of the human mind4 ,nor could it be easily conceived1 from the mere enunciation of such a proposition1 what a flood of light it lets in upon the whole course of history1 when its consequences are traced1 by connecting with each of the three states of human intellect which it distinguishes1 and with each successive modification of those three states1 the correlative condition of other social phenomena47#bhb7 ,but whatever decision competent judges may pronounce on the results arrived at by any individual inquirer1 the method now characterized is that by which the derivative laws of social order and of social progress must be sought4 ,by its aid we may hereafter succeed not only in looking far forward into the future history of the human race1 but in determining what artificial means may be used1 and to what extent1 to accelerate the natural progress in so far as it is beneficial2 to compensate for whatever may be its inherent inconveniences or disadvantages2 and to guard against the dangers or accidents to which our species is exposed from the necessary incidents of its progression4 ,such practical instructions1 founded on the highest branch of speculative sociology1 will form the noblest and most beneficial portion of the ,political ,art4 ,that of this science and art even the foundations are but beginning to be laid1 is sufficiently evident4 ,but the superior minds are fairly turning themselves toward that object4 ,it has become the aim of really scientific thinkers to connect by theories the facts of universal history3 it is acknowledged to be one of the requisites of a general system of social doctrine1 that it should explain1 so far as the data exist1 the main facts of history2 and a ,philosophy of ,history is generally admitted to be at once the verification1 and the initial form1 of the ,philosophy of the ,progress of ,society4 ,if the endeavors now making in all the more cultivated nations1 and beginning to be made even in ,england 7usually the last to enter into the general movement of the ,european mind7 for the construction of a ,philosophy of ,history1 shall be directed and controlled by those views of the nature of sociological evidence which ,i have 7very briefly and imperfectly7 attempted to characterize2 they can not fail to give birth to a sociological system widely removed from the vague and conjectural character of all former attempts1 and worthy to take its place1 at last1 among the sciences4 ,when this time shall come1 no important branch of human affairs will be any longer abandoned to empiricism and unscientific surmise3 the circle of human knowledge will be complete1 and it can only thereafter receive further enlargement by perpetual expansion from within4 ,chapter ,,xi4 ,additional ,elucidations ,of ,the ,science ,of ,history4 #a4 ,the doctrine which the preceding chapters were intended to enforce and elucidate--that the collective series of social phenomena1 in other words the course of history1 is subject to general laws1 which philosophy may possibly detect--has been familiar for generations to the scientific thinkers of the ,continent1 and has for the last quarter of a century passed out of their peculiar domain1 into that of newspapers and ordinary political discussion4 ,in our own country1 however1 at the time of the first publication of this ,treatise1 it was almost a novelty1 and the prevailing habits of thought on historical subjects were the very reverse of a preparation for it4 ,since then a great change has taken place1 and has been eminently promoted by the important work of ,mr4 ,buckle2 who1 with characteristic energy1 flung down this great principle1 together with many striking exemplifications of it1 into the arena of popular discussion1 to be fought over by a sort of combatants1 in the presence of a sort of spectators1 who would never even have been aware that there existed such a principle if they had been left to learn its existence from the speculations of pure science4 ,and hence has arisen a considerable amount of controversy1 tending not only to make the principle rapidly familiar to the majority of cultivated minds1 but also to clear it from the confusions and misunderstandings by which it was but natural that it should for a time be clouded1 and which impair the worth of the doctrine to those who accept it1 and are the stumbling-block of many who do not4 ,among the impediments to the general acknowledgment1 by thoughtful minds1 of the subjection of historical facts to scientific laws1 the most fundamental continues to be that which is grounded on the doctrine of ,free ,will1 or1 in other words1 on the denial that the law of invariable ,causation holds true of human volitions2 for if it does not1 the course of history1 being the result of human volitions1 can not be a subject of scientific laws1 since the volitions on which it depends can neither be foreseen1 nor reduced to any canon of regularity even after they have occurred4 ,i have discussed this question1 as far as seemed suitable to the occasion1 in a former chapter2 and ,i only think it necessary to repeat1 that the doctrine of the ,causation of human actions1 improperly called the doctrine of ,necessity1 affirms no mysterious nexus1 or overruling fatality3 it asserts only that men's actions are the joint result of the general laws and circumstances of human nature1 and of their own particular characters2 those characters again being the consequence of the natural and artificial circumstances that constituted their education1 among which circumstances must be reckoned their own conscious efforts4 ,any one who is willing to take 7if the expression may be permitted7 the trouble of thinking himself into the doctrine as thus stated1 will find it1 ,i believe1 not only a faithful interpretation of the universal experience of human conduct1 but a correct representation of the mode in which he himself1 in every particular case1 spontaneously interprets his own experience of that conduct4 ,but if this principle is true of individual man1 it must be true of collective man4 ,if it is the law of human life1 the law must be realized in history4 ,the experience of human affairs when looked at en masse1 must be in accordance with it if true1 or repugnant to it if false4 ,the support which this a posteriori verification affords to the law1 is the part of the case which has been most clearly and triumphantly brought out by ,mr4 ,buckle4 ,the facts of statistics1 since they have been made a subject of careful recordation and study1 have yielded conclusions1 some of which have been very startling to persons not accustomed to regard moral actions as subject to uniform laws4 ,the very events which in their own nature appear most capricious and uncertain1 and which in any individual case no attainable degree of knowledge would enable us to foresee1 occur1 when considerable numbers are taken into the account1 with a degree of regularity approaching to mathematical4 ,what act is there which all would consider as more completely dependent on individual character1 and on the exercise of individual free will1 than that of slaying a fellow-creature8 ,yet in any large country1 the number of murders1 in proportion to the population1 varies 7it has been found7 very little from one year to another1 and in its variations never deviates widely from a certain average4 ,what is still more remarkable1 there is a similar approach to constancy in the proportion of these murders annually committed with every particular kind of instrument4 ,there is a like approximation to identity1 as between one year and another1 in the comparative number of legitimate and of illegitimate births4 ,the same thing is found true of suicides1 accidents1 and all other social phenomena of which the registration is sufficiently perfect2 one of the most curiously illustrative examples being the fact1 ascertained by the registers of the ,london and ,paris post-offices1 that the number of letters posted which the writers have forgotten to direct1 is nearly the same1 in proportion to the whole number of letters posted1 in one year as in another4 8,year after year10 says ,mr4 ,buckle1 8the same proportion of letter-writers forget this simple act2 so that for each successive period we can actually foretell the number of persons whose memory will fail them in regard to this trifling1 and as it might appear1 accidental occurrence407#bhc7 ,this singular degree of regularity en masse1 combined with the extreme of irregularity in the cases composing the mass1 is a felicitous verification a posteriori of the law of causation in its application to human conduct4 ,assuming the truth of that law1 every human action1 every murder1 for instance1 is the concurrent result of two sets of causes4 ,on the one part1 the general circumstances of the country and its inhabitants2 the moral1 educational1 economical1 and other influences operating on the whole people1 and constituting what we term the state of civilization4 ,on the other part1 the great variety of influences special to the individual3 his temperament1 and other peculiarities of organization1 his parentage1 habitual associates1 temptations1 and so forth4 ,if we now take the whole of the instances which occur within a sufficiently large field to exhaust all the combinations of these special influences1 or1 in other words1 to eliminate chance2 and if all these instances have occurred within such narrow limits of time1 that no material change can have taken place in the general influences constituting the state of civilization of the country2 we may be certain1 that if human actions are governed by invariable laws1 the aggregate result will be something like a constant quantity4 ,the number of murders committed within that space and time1 being the effect partly of general causes which have not varied1 and partly of partial causes the whole round of whose variations has been included1 will be1 practically speaking1 invariable4 ,literally and mathematically invariable it is not1 and could not be expected to be3 because the period of a year is too short to include all the possible combinations of partial causes1 while it is1 at the same time1 sufficiently long to make it probable that in some years at least1 of every series1 there will have been introduced new influences of a more or less general character2 such as a more vigorous or a more relaxed police2 some temporary excitement from political or religious causes2 or some incident generally notorious1 of a nature to act morbidly on the imagination4 ,that in spite of these unavoidable imperfections in the data1 there should be so very trifling a margin of variation in the annual results1 is a brilliant continuation of the general theory4 #b4 ,the same considerations which thus strikingly corroborate the evidence of the doctrine1 that historical facts are the invariable effects of causes1 tend equally to clear that doctrine from various misapprehensions1 the existence of which has been put in evidence by the recent discussions4 ,some persons1 for instance1 seemingly imagine the doctrine to imply1 not merely that the total number of murders committed in a given space and time is entirely the effect of the general circumstances of society1 but that every particular murder is so too--that the individual murderer is1 so to speak1 a mere instrument in the hands of general causes that he himself has no option1 or1 if he has1 and chose to exercise it1 some one else would be necessitated to take his place2 that if any one of the actual murderers had abstained from the crime1 some person who would otherwise have remained innocent1 would have committed an extra murder to make up the average4 ,such a corollary would certainly convict any theory which necessarily led to it of absurdity4 ,it is obvious1 however1 that each particular murder depends1 not on the general state of society only1 but on that combined with causes special to the case1 which are generally much more powerful2 and if these special causes1 which have greater influence than the general ones in causing every particular murder1 have no influence on the number of murders in a given period1 it is because the field of observation is so extensive as to include all possible combinations of the special causes--all varieties of individual character and individual temptation compatible with the general state of society4 ,the collective experiment1 as it may be termed1 exactly separates the effect of the general from that of the special causes1 and shows the net result of the former2 but it declares nothing at all respecting the amount of influence of the special causes1 be it greater or smaller1 since the scale of the experiment extends to the number of cases within which the effects of the special causes balance one another1 and disappear in that of the general causes4 ,i will not pretend that all the defenders of the theory have always kept their language free from this same confusion1 and have shown no tendency to exalt the influence of general causes at the expense of special4 ,i am of opinion1 on the contrary1 that they have done so in a very great degree1 and by so doing have encumbered their theory with difficulties1 and laid it open to objections1 which do not necessarily affect it4 ,some1 for example 7among whom is ,mr4 ,buckle himself71 have inferred1 or allowed it to be supposed that they inferred1 from the regularity in the recurrence of events which depend on moral qualities1 that the moral qualities of mankind are little capable of being improved1 or are of little importance in the general progress of society1 compared with intellectual or economic causes4 ,but to draw this inference is to forget that the statistical tables1 from which the invariable averages are deduced1 were compiled from facts occurring within narrow geographical limits and in a small number of successive years2 that is1 from a field the whole of which was under the operation of the same general causes1 and during too short a time to allow of much change therein4 ,all moral causes but those common to the country generally1 have been eliminated by the great number of instances taken2 and those which are common to the whole country have not varied considerably1 in the short space of time comprised in the observations4 ,if we admit the supposition that they have varied2 if we compare one age with another1 or one country with another1 or even one part of a country with another1 differing in position and character as to the moral elements1 the crimes committed within a year give no longer the same1 but a widely different numerical aggregate4 ,and this can not but be the case3 for1 inasmuch as every single crime committed by an individual mainly depends on his moral qualities1 the crimes committed by the entire population of the country must depend in an equal degree on their collective moral qualities4 ,to render this element inoperative upon the large scale1 it would be necessary to suppose that the general moral average of mankind does not vary from country to country or from age to age2 which is not true1 and1 even if it were true1 could not possibly be proved by any existing statistics4 ,i do not on this account the less agree in the opinion of ,mr4 ,buckle1 that the intellectual element in mankind1 including in that expression the nature of their beliefs1 the amount of their knowledge1 and the development of their intelligence1 is the predominant circumstance in determining their progress4 ,but ,i am of this opinion1 not because ,i regard their moral or economical condition either as less powerful or less variable agencies1 but because these are in a great degree the consequences of the intellectual condition1 and are1 in all cases1 limited by it2 as was observed in the preceding chapter4 ,the intellectual changes are the most conspicuous agents in history1 not from their superior force1 considered in themselves1 but because practically they work with the united power belonging to all three47#bhd7 #c4 ,there is another distinction often neglected in the discussion of this subject1 which it is extremely important to observe4 ,the theory of the subjection of social progress to invariable laws1 is often held in conjunction with the doctrine1 that social progress can not be materially influenced by the exertions of individual persons1 or by the acts of governments4 ,but though these opinions are often held by the same persons1 they are two very different opinions1 and the confusion between them is the eternally recurring error of confounding ,causation with ,fatalism4 ,because whatever happens will be the effect of causes1 human volitions among the rest1 it does not follow that volitions1 even those of peculiar individuals1 are not of great efficacy as causes4 ,if any one in a storm at sea1 because about the same number of persons in every year perish by shipwreck1 should conclude that it was useless for him to attempt to save his own life1 we should call him a ,fatalist2 and should remind him that the efforts of shipwrecked persons to save their lives are so far from being immaterial1 that the average amount of those efforts is one of the causes on which the ascertained annual number of deaths by shipwreck depend4 ,however universal the laws of social development may be1 they can not be more universal or more rigorous than those of the physical agencies of nature2 yet human will can convert these into instruments of its designs1 and the extent to which it does so makes the chief difference between savages and the most highly civilized people4 ,human and social facts1 from their more complicated nature1 are not less1 but more1 modifiable than mechanical and chemical facts2 human agency1 therefore1 has still greater power over them4 ,and accordingly1 those who maintain that the evolution of society depends exclusively1 or almost exclusively1 on general causes1 always include among these the collective knowledge and intellectual development of the race4 ,but if of the race1 why not also of some powerful monarch or thinker1 or of the ruling portion of some political society1 acting through its government8 ,though the varieties of character among ordinary individuals neutralize one another on any large scale1 exceptional individuals in important positions do not in any given age neutralize one another2 there was not another ,themistocles1 or ,luther1 or ,julius ,csar1 of equal powers and contrary dispositions1 who exactly balanced the given ,themistocles1 ,luther1 and ,csar1 and prevented them from having any permanent effect4 ,moreover1 for aught that appears1 the volitions of exceptional persons1 or the opinions and purposes of the individuals who at some particular time compose a government1 may be indispensable links in the chain of causation by which even the general causes produce their effects2 and ,i believe this to be the only tenable form of the theory4 ,lord ,macaulay1 in a celebrated passage of one of his early essays 7let me add that it was one which he did not himself choose to reprint71 gives expression to the doctrine of the absolute inoperativeness of great men1 more unqualified1 ,i should think1 than has been given to it by any writer of equal abilities4 ,he compares them to persons who merely stand on a loftier height1 and thence receive the sun's rays a little earlier1 than the rest of the human race4 8,the sun illuminates the hills while it is still below the horizon1 and truth is discovered by the highest minds a little before it becomes manifest to the multitude4 ,this is the extent of their superiority4 ,they are the first to catch and reflect a light which1 without their assistance1 must in a short time be visible to those who lie far beneath them407#bhe7 ,if this metaphor is to be carried out1 it follows that if there had been no ,newton1 the world would not only have had the ,newtonian system1 but would have had it equally soon2 as the sun would have risen just as early to spectators in the plain if there had been no mountain at hand to catch still earlier rays4 ,and so it would be1 if truths1 like the sun1 rose by their own proper motion1 without human effort2 but not otherwise4 ,i believe that if ,newton had not lived1 the world must have waited for the ,newtonian philosophy until there had been another ,newton1 or his equivalent4 ,no ordinary man1 and no succession of ordinary men1 could have achieved it4 ,i will not go the length of saying that what ,newton did in a single life1 might not have been done in successive steps by some of those who followed him1 each singly inferior to him in genius4 ,but even the least of those steps required a man of great intellectual superiority4 ,eminent men do not merely see the coming light from the hill-top1 they mount on the hill-top and evoke it2 and if no one had ever ascended thither1 the light1 in many cases1 might never have risen upon the plain at all4 ,philosophy and religion are abundantly amenable to general causes2 yet few will doubt that1 had there been no ,socrates1 no ,plato1 and no ,aristotle1 there would have been no philosophy for the next two thousand years1 nor in all probability then2 and that if there had been no ,christ1 and no ,st4 ,paul1 there would have been no ,christianity4 ,the point in which1 above all1 the influence of remarkable individuals is decisive1 is in determining the celerity of the movement4 ,in most states of society it is the existence of great men which decides even whether there shall be any progress4 ,it is conceivable that ,greece1 or that ,christian ,europe1 might have been progressive in certain periods of their history through general causes only3 but if there had been no ,mohammed1 would ,arabia have produced ,avicenna or ,averroes1 or ,caliphs of ,bagdad or of ,cordova8 ,in determining1 however1 in what manner and order the progress of mankind shall take place if it take place at all1 much less depends on the character of individuals4 ,there is a sort of necessity established in this respect by the general laws of human nature--by the constitution of the human mind4 ,certain truths can not be discovered1 nor inventions made1 unless certain others have been made first2 certain social improvements1 from the nature of the case1 can only follow1 and not precede1 others4 ,the order of human progress1 therefore1 may to a certain extent have definite laws assigned to it3 while as to its celerity1 or even as to its taking place at all1 no generalization1 extending to the human species generally1 can possibly be made2 but only some very precarious approximate generalizations1 confined to the small portion of mankind in whom there has been any thing like consecutive progress within the historical period1 and deduced from their special position1 or collected from their particular history4 ,even looking to the manner of progress1 the order of succession of social states1 there is need of great flexibility in our generalizations4 ,the limits of variation in the possible development of social1 as of animal life1 are a subject of which little is yet understood1 and are one of the great problems in social science4 ,it is1 at all events1 a fact1 that different portions of mankind1 under the influence of different circumstances1 have developed themselves in a more or less different manner and into different forms2 and among these determining circumstances1 the individual character of their great speculative thinkers or practical organizers may well have been one4 ,who can tell how profoundly the whole subsequent history of ,china may have been influenced by the individuality of ,confucius8 and of ,sparta 7and hence of ,greece and the world7 by that of ,lycurgus8 ,concerning the nature and extent of what a great man under favorable circumstances can do for mankind1 as well as of what a government can do for a nation1 many different opinions are possible2 and every shade of opinion on these points is consistent with the fullest recognition that there are invariable laws of historical phenomena4 ,of course the degree of influence which has to be assigned to these more special agencies1 makes a great difference in the precision which can be given to the general laws1 and in the confidence with which predictions can be grounded on them4 ,whatever depends on the peculiarities of individuals1 combined with the accident of the positions they hold1 is necessarily incapable of being foreseen4 ,undoubtedly these casual combinations might be eliminated like any others1 by taking a sufficiently large cycle3 the peculiarities of a great historical character make their influence felt in history sometimes for several thousand years1 but it is highly probable that they will make no difference at all at the end of fifty millions4 ,since1 however1 we can not obtain an average of the vast length of time necessary to exhaust all the possible combinations of great men and circumstances1 as much of the law of evolution of human affairs as depends upon this average1 is and remains inaccessible to us2 and within the next thousand years1 which are of considerably more importance to us than the whole remainder of the fifty millions1 the favorable and unfavorable combinations which will occur will be to us purely accidental4 ,we can not foresee the advent of great men4 ,those who introduce new speculative thoughts or great practical conceptions into the world1 can not have their epoch fixed beforehand4 ,what science can do1 is this4 ,it can trace through past history the general causes which had brought mankind into that preliminary state which1 when the right sort of great man appeared1 rendered them accessible to his influence4 ,if this state continues1 experience renders it tolerably certain that in a longer or shorter period the great man will be produced2 provided that the general circumstances of the country and people are 7which very often they are not7 compatible with his existence2 of which point also1 science can in some measure judge4 ,it is in this manner that the results of progress1 except as to the celerity of their production1 can be1 to a certain extent1 reduced to regularity and law4 ,and the belief that they can be so1 is equally consistent with assigning very great1 or very little efficacy1 to the influence of exceptional men1 or of the acts of governments4 ,and the same may be said of all other accidents and disturbing causes4 #d4 ,it would nevertheless be a great error to assign only a trifling importance to the agency of eminent individuals1 or of governments4 ,it must not be concluded that the influence of either is small1 because they can not bestow what the general circumstances of society1 and the course of its previous history1 have not prepared it to receive4 ,neither thinkers nor governments effect all that they intend1 but in compensation they often produce important results which they did not in the least foresee4 ,great men1 and great actions1 are seldom wasted2 they send forth a thousand unseen influences1 more effective than those which are seen2 and though nine out of every ten things done1 with a good purpose1 by those who are in advance of their age1 produce no material effect1 the tenth thing produces effects twenty times as great as any one would have dreamed of predicting from it4 ,even the men who for want of sufficiently favorable circumstances left no impress at all upon their own age1 have often been of the greatest value to posterity4 ,who could appear to have lived more entirely in vain than some of the early heretics8 ,they were burned or massacred1 their writings extirpated1 their memory anathematized1 and their very names and existence left for seven or eight centuries in the obscurity of musty manuscripts--their history to be gathered1 perhaps1 only from the sentences by which they were condemned4 ,yet the memory of these men--men who resisted certain pretensions or certain dogmas of the ,church in the very age in which the unanimous assent of ,christendom was afterward claimed as having been given to them1 and asserted as the ground of their authority--broke the chain of tradition1 established a series of precedents for resistance1 inspired later ,reformers with the courage1 and armed them with the weapons1 which they needed when mankind were better prepared to follow their impulse4 ,to this example from men1 let us add another from governments4 ,the comparatively enlightened rule of which ,spain had the benefit during a considerable part of the eighteenth century1 did not correct the fundamental defects of the ,spanish people2 and in consequence1 though it did great temporary good1 so much of that good perished with it1 that it may plausibly be affirmed to have had no permanent effect4 ,the case has been cited as a proof how little governments can do in opposition to the causes which have determined the general character of the nation4 ,it does show how much there is which they can not do2 but not that they can do nothing4 ,compare what ,spain was at the beginning of that half-century of liberal government1 with what she had become at its close4 ,that period fairly let in the light of ,european thought upon the more educated classes2 and it never afterward ceased to go on spreading4 ,previous to that time the change was in an inverse direction2 culture1 light1 intellectual and even material activity1 were becoming extinguished4 ,was it nothing to arrest this downward and convert it into an upward course8 ,how much that ,charles the ,third and ,aranda could not do1 has been the ultimate consequence of what they did6 ,to that half-century ,spain owes that she has got rid of the ,inquisition1 that she has got rid of the monks1 that she now has parliaments and 7save in exceptional intervals7 a free press1 and the feelings of freedom and citizenship1 and is acquiring railroads and all the other constituents of material and economical progress4 ,in the ,spain which preceded that era1 there was not a single element at work which could have led to these results in any length of time1 if the country had continued to be governed as it was by the last princes of the ,austrian dynasty1 or if the ,bourbon rulers had been from the first what1 both in ,spain and in ,naples1 they afterward became4 ,and if a government can do much1 even when it seems to have done little1 in causing positive improvement1 still greater are the issues dependent on it in the way of warding off evils1 both internal and external1 which else would stop improvement altogether4 ,a good or a bad counselor1 in a single city at a particular crisis1 has affected the whole subsequent fate of the world4 ,it is as certain as any contingent judgment respecting historical events can be1 that if there had been no ,themistocles there would have been no victory of ,salamis2 and had there not1 where would have been all our civilization8 ,how different1 again1 would have been the issue if ,epaminondas1 or ,timoleon1 or even ,iphicrates1 instead of ,chares and ,lysicles1 had commanded at ,chroneia4 ,as is well said in the second of two ,essays on the ,study of ,history17#bhf7 in my judgment the soundest and most philosophical productions which the recent controversies on this subject have called forth1 historical science authorizes not absolute1 but only conditional predictions4 ,general causes count for much1 but individuals also 8produce great changes in history1 and color its whole complexion long after their death4444 ,no one can doubt that the ,roman republic would have subsided into a military despotism if ,julius ,csar had never lived0 7thus much was rendered practically certain by general causes72 8but is it at all clear that in that case ,gaul would ever have formed a province of the empire8 ,might not ,varus have lost his three legions on the banks of the ,rhone8 and might not that river have become the frontier instead of the ,rhine8 ,this might well have happened if ,csar and ,crassus had changed provinces2 and it is surely impossible to say that in such an event the venue 7as lawyers say7 of ,european civilization might not have been changed4 ,the ,norman ,conquest in the same way was as much the act of a single man1 as the writing of a newspaper article2 and knowing as we do the history of that man and his family1 we can retrospectively predict with all but infallible certainty1 that no other person0 7no other in that age1 ,i presume1 is meant7 8could have accomplished the enterprise4 ,if it had not been accomplished1 is there any ground to suppose that either our history or our national character would have been what they are80 ,as is most truly remarked by the same writer1 the whole stream of ,grecian history1 as cleared up by ,mr4 ,grote1 is one series of examples how often events on which the whole destiny of subsequent civilization turned1 were dependent on the personal character for good or evil of some one individual4 ,it must be said1 however1 that ,greece furnishes the most extreme example of this nature to be found in history1 and is a very exaggerated specimen of the general tendency4 ,it has happened only that once1 and will probably never happen again1 that the fortunes of mankind depended upon keeping a certain order of things in existence in a single town1 or a country scarcely larger than ,yorkshire2 capable of being ruined or saved by a hundred causes1 of very slight magnitude in comparison with the general tendencies of human affairs4 ,neither ordinary accidents1 nor the characters of individuals1 can ever again be so vitally important as they then were4 ,the longer our species lasts1 and the more civilized it becomes1 the more1 as ,comte remarks1 does the influence of past generations over the present1 and of mankind en masse over every individual in it1 predominate over other forces2 and though the course of affairs never ceases to be susceptible of alteration both by accidents and by personal qualities1 the increasing preponderance of the collective agency of the species over all minor causes1 is constantly bringing the general evolution of the race into something which deviates less from a certain and preappointed track4 ,historical science1 therefore1 is always becoming more possible2 not solely because it is better studied1 but because1 in every generation1 it becomes better adapted for study4 ,chapter ,,xii4 ,of ,the ,logic ,of ,practice1 ,or ,art2 ,including ,morality ,and ,policy4 #a4 ,in the preceding chapters we have endeavored to characterize the present state of those among the branches of knowledge called ,moral1 which are sciences in the only proper sense of the term1 that is1 inquiries into the course of nature4 ,it is customary1 however1 to include under the term moral knowledge1 and even 7though improperly7 under that of moral science1 an inquiry the results of which do not express themselves in the indicative1 but in the imperative mood1 or in periphrases equivalent to it2 what is called the knowledge of duties2 practical ethics1 or morality4 ,now1 the imperative mood is the characteristic of art1 as distinguished from science4 ,whatever speaks in rules1 or precepts1 not in assertions respecting matters of fact1 is art2 and ethics1 or morality1 is properly a portion of the art corresponding to the sciences of human nature and society47#bhg7 ,the ,method1 therefore1 of ,ethics1 can be no other than that of ,art1 or ,practice1 in general2 and the portion yet uncompleted of the task which we proposed to ourselves in the concluding ,book1 is to characterize the general ,method of ,art1 as distinguished from ,science4 #b4 ,in all branches of practical business there are cases in which individuals are bound to conform their practice to a pre-established rule1 while there are others in which it is part of their task to find or construct the rule by which they are to govern their conduct4 ,the first1 for example1 is the case of a judge1 under a definite written code4 ,the judge is not called upon to determine what course would be intrinsically the most advisable in the particular case in hand1 but only within what rule of law it falls2 what the legislature has ordained to be done in the kind of case1 and must therefore be presumed to have intended in the individual case4 ,the method must here be wholly and exclusively one of ratiocination1 or syllogism2 and the process is obviously1 what in our analysis of the syllogism we showed that all ratiocination is1 namely the interpretation of a formula4 ,in order that our illustration of the opposite case may be taken from the same class of subjects as the former1 we will suppose1 in contrast with the situation of the judge1 the position of the legislator4 ,as the judge has laws for his guidance1 so the legislator has rules1 and maxims of policy2 but it would be a manifest error to suppose that the legislator is bound by these maxims in the same manner as the judge is bound by the laws1 and that all he has to do is to argue down from them to the particular case1 as the judge does from the laws4 ,the legislator is bound to take into consideration the reasons or grounds of the maxim2 the judge has nothing to do with those of the law1 except so far as a consideration of them may throw light upon the intention of the law-maker1 where his words have left it doubtful4 ,to the judge1 the rule1 once positively ascertained1 is final2 but the legislator1 or other practitioner1 who goes by rules rather than by their reasons1 like the old-fashioned ,german tacticians who were vanquished by ,napoleon1 or the physician who preferred that his patients should die by rule rather than recover contrary to it1 is rightly judged to be a mere pedant1 and the slave of his formulas4 ,now1 the reasons of a maxim of policy1 or of any other rule of art1 can be no other than the theorems of the corresponding science4 ,the relation in which rules of art stand to doctrines of science may be thus characterized4 ,the art proposes to itself an end to be attained1 defines the end1 and hands it over to the science4 ,the science receives it1 considers it as a phenomenon or effect to be studied1 and having investigated its causes and conditions1 sends it back to art with a theorem of the combination of circumstances by which it could be produced4 ,art then examines these combinations of circumstances1 and according as any of them are or are not in human power1 pronounces the end attainable or not4 ,the only one of the premises1 therefore1 which ,art supplies1 is the original major premise1 which asserts that the attainment of the given end is desirable4 ,science then lends to ,art the proposition 7obtained by a series of inductions or of deductions7 that the performance of certain actions will attain the end4 ,from these premises ,art concludes that the performance of these actions is desirable1 and finding it also practicable1 converts the theorem into a rule or precept4 #c4 ,it deserves particular notice1 that the theorem or speculative truth is not ripe for being turned into a precept1 until the whole1 and not a part merely1 of the operation which belongs to science1 has been performed4 ,suppose that we have completed the scientific process only up to a certain point2 have discovered that a particular cause will produce the desired effect1 but have not ascertained all the negative conditions which are necessary1 that is1 all the circumstances which1 if present1 would prevent its production4 ,if1 in this imperfect state of the scientific theory1 we attempt to frame a rule of art1 we perform that operation prematurely4 ,whenever any counteracting cause1 overlooked by the theorem1 takes place1 the rule will be at fault2 we shall employ the means and the end will not follow4 ,no arguing from or about the rule itself will then help us through the difficulty2 there is nothing for it but to turn back and finish the scientific process which should have preceded the formation of the rule4 ,we must re-open the investigation to inquire into the remainder of the conditions on which the effect depends2 and only after we have ascertained the whole of these are we prepared to transform the completed law of the effect into a precept1 in which those circumstances or combinations of circumstances which the science exhibits as conditions are prescribed as means4 ,it is true that1 for the sake of convenience1 rules must be formed from something less than this ideally perfect theory3 in the first place1 because the theory can seldom be made ideally perfect2 and next1 because1 if all the counteracting contingencies1 whether of frequent or of rare occurrence1 were included1 the rules would be too cumbrous to be apprehended and remembered by ordinary capacities1 on the common occasions of life4 ,the rules of art do not attempt to comprise more conditions than require to be attended to in ordinary cases2 and are therefore always imperfect4 ,in the manual arts1 where the requisite conditions are not numerous1 and where those which the rules do not specify are generally either plain to common observation or speedily learned from practice1 rules may often be safely acted on by persons who know nothing more than the rule4 ,but in the complicated affairs of life1 and still more in those of states and societies1 rules can not be relied on1 without constantly referring back to the scientific laws on which they are founded4 ,to know what are the practical contingencies which require a modification of the rule1 or which are altogether exceptions to it1 is to know what combinations of circumstances would interfere with1 or entirely counteract1 the consequences of those laws2 and this can only be learned by a reference to the theoretic grounds of the rule4 ,by a wise practitioner1 therefore1 rules of conduct will only be considered as provisional4 ,being made for the most numerous cases1 or for those of most ordinary occurrence1 they point out the manner in which it will be least perilous to act1 where time or means do not exist for analyzing the actual circumstances of the case1 or where we can not trust our judgment in estimating them4 ,but they do not at all supersede the propriety of going through1 when circumstances permit1 the scientific process requisite for framing a rule from the data of the particular case before us4 ,at the same time1 the common rule may very properly serve as an admonition that a certain mode of action has been found by ourselves and others to be well adapted to the cases of most common occurrence2 so that if it be unsuitable to the case in hand1 the reason of its being so will be likely to arise from some unusual circumstance4 #d4 ,the error is therefore apparent of those who would deduce the line of conduct proper to particular cases from supposed universal practical maxims1 overlooking the necessity of constantly referring back to the principles of the speculative science1 in order to be sure of attaining even the specific end which the rules have in view4 ,how much greater still1 then1 must the error be1 of setting up such unbending principles1 not merely as universal rules for attaining a given end1 but as rules of conduct generally1 without regard to the possibility1 not only that some modifying cause may prevent the attainment of the given end by the means which the rule prescribes1 but that success itself may conflict with some other end1 which may possibly chance to be more desirable4 ,this is the habitual error of many of the political speculators whom ,i have characterized as the geometrical school2 especially in ,france1 where ratiocination from rules of practice forms the staple commodity of journalism and political oratory--a misapprehension of the functions of ,deduction which has brought much discredit1 in the estimation of other countries1 upon the spirit of generalization so honorably characteristic of the ,french mind4 ,the commonplaces of politics in ,france are large and sweeping practical maxims1 from which1 as ultimate premises1 men reason downward to particular applications2 and this they call being logical and consistent4 ,for instance1 they are perpetually arguing that such and such a measure ought to be adopted1 because it is a consequence of the principle on which the form of government is founded2 of the principle of legitimacy1 or the principle of the sovereignty of the people4 ,to which it may be answered1 that if these be really practical principles1 they must rest on speculative grounds2 the sovereignty of the people1 for example1 must be a right foundation for government1 because a government thus constituted tends to produce certain beneficial effects4 ,inasmuch1 however1 as no government produces all possible beneficial effects1 but all are attended with more or fewer inconveniences1 and since these can not usually be combated by means drawn from the very causes which produce them1 it would be often a much stronger recommendation of some practical arrangement1 that it does not follow from what is called the general principle of the government1 than that it does4 ,under a government of legitimacy1 the presumption is far rather in favor of institutions of popular origin2 and in a democracy1 in favor of arrangements tending to check the impetus of popular will4 ,the line of augmentation so commonly mistaken in ,france for political philosophy1 tends to the practical conclusion that we should exert our utmost efforts to aggravate1 instead of alleviating1 whatever are the characteristic imperfections of the system of institutions which we prefer1 or under which we happen to live4 #e4 ,the grounds1 then1 of every rule of art1 are to be found in the theorems of science4 ,an art1 or a body of art1 consists of the rules1 together with as much of the speculative propositions as comprises the justification of those rules4 ,the complete art of any matter includes a selection of such a portion from the science as is necessary to show on what conditions the effects1 which the art aims at producing1 depend4 ,and ,art in general1 consists of the truths of ,science1 arranged in the most convenient order for practice1 instead of the order which is the most convenient for thought4 ,science groups and arranges its truths1 so as to enable us to take in at one view as much as possible of the general order of the universe4 ,art1 though it must assume the same general laws1 follows them only into such of their detailed consequences as have led to the formation of rules of conduct2 and brings together from parts of the field of science most remote from one another1 the truths relating to the production of the different and heterogeneous conditions necessary to each effect which the exigencies of practical life require to be produced47#bhh7 ,science1 therefore1 following one cause to its various effects1 while art traces one effect to its multiplied and diversified causes and conditions1 there is need of a set of intermediate scientific truths1 derived from the higher generalities of science1 and destined to serve as the generalia or first principles of the various arts4 ,the scientific operation of framing these intermediate principles1 ,m4 ,comte characterizes as one of those results of philosophy which are reserved for futurity4 ,the only complete example which he points out as actually realized1 and which can be held up as a type to be imitated in more important matters1 is the general theory of the art of ,descriptive ,geometry1 as conceived by ,m4 ,monge4 ,it is not1 however1 difficult to understand what the nature of these intermediate principles must generally be4 ,after framing the most comprehensive possible conception of the end to be aimed at1 that is1 of the effect to be produced1 and determining in the same comprehensive manner the set of conditions on which that effect depends1 there remains to be taken1 a general survey of the resources which can be commanded for realizing this set of conditions2 and when the result of this survey has been embodied in the fewest and most extensive propositions possible1 those propositions will express the general relation between the available means and the end1 and will constitute the general scientific theory of the art1 from which its practical methods will follow as corollaries4 #f4 ,but though the reasonings which connect the end or purpose of every art with its means belong to the domain of ,science1 the definition of the end itself belongs exclusively to ,art1 and forms its peculiar province4 ,every art has one first principle1 or general major premise1 not borrowed from science2 that which enunciates the object aimed at1 and affirms it to be a desirable object4 ,the builder's art assumes that it is desirable to have buildings2 architecture1 as one of the fine arts1 that it is desirable to have them beautiful or imposing4 ,the hygienic and medical arts assume1 the one that the preservation of health1 the other that the cure of disease1 are fitting and desirable ends4 ,these are not propositions of science4 ,propositions of science assert a matter of fact3 an existence1 a co-existence1 a succession1 or a resemblance4 ,the propositions now spoken of do not assert that any thing is1 but enjoin or recommend that something should be4 ,they are a class by themselves4 ,a proposition of which the predicate is expressed by the words ought or should be1 is generically different from one which is expressed by is1 or will be4 ,it is true1 that in the largest sense of the words1 even these propositions assert something as a matter of fact4 ,the fact affirmed in them is1 that the conduct recommended excites in the speaker's mind the feeling of approbation4 ,this1 however1 does not go to the bottom of the matter2 for the speaker's approbation is no sufficient reason why other people should approve2 nor ought it to be a conclusive reason even with himself4 ,for the purposes of practice1 every one must be required to justify his approbation2 and for this there is need of general premises1 determining what are the proper objects of approbation1 and what the proper order of precedence among those objects4 ,these general premises1 together with the principal conclusions which may be deduced from them1 form 7or rather might form7 a body of doctrine1 which is properly the ,art of ,life1 in its three departments1 ,morality1 ,prudence or ,policy1 and sthetics2 the ,right1 the ,expedient1 and the ,beautiful or ,noble1 in human conduct and works4 ,to this art 7which1 in the main1 is unfortunately still to be created71 all other arts are subordinate2 since its principles are those which must determine whether the special aim of any particular art is worthy and desirable1 and what is its place in the scale of desirable things4 ,every art is thus a joint result of laws of nature disclosed by science1 and of the general principles of what has been called ,teleology1 or the ,doctrine of ,ends27#bhi7 which1 borrowing the language of the ,german metaphysicians1 may also be termed1 not improperly1 the principles of ,practical ,reason4 ,a scientific observer or reasoner1 merely as such1 is not an adviser for practice4 ,his part is only to show that certain consequences follow from certain causes1 and that to obtain certain ends1 certain means are the most effectual4 ,whether the ends themselves are such as ought to be pursued1 and if so1 in what cases and to how great a length1 it is no part of his business as a cultivator of science to decide1 and science alone will never qualify him for the decision4 ,in purely physical science1 there is not much temptation to assume this ulterior office2 but those who treat of human nature and society invariably claim it3 they always undertake to say1 not merely what is1 but what ought to be4 ,to entitle them to do this1 a complete doctrine of ,teleology is indispensable4 ,a scientific theory1 however perfect1 of the subject-matter1 considered merely as part of the order of nature1 can in no degree serve as a substitute4 ,in this respect the various subordinate arts afford a misleading analogy4 ,in them there is seldom any visible necessity for justifying the end1 since in general its desirableness is denied by nobody1 and it is only when the question of precedence is to be decided between that end and some other1 that the general principles of ,teleology have to be called in2 but a writer on ,morals and ,politics requires those principles at every step4 ,the most elaborate and well-digested exposition of the laws of succession and co-existence among mental or social phenomena1 and of their relation to one another as causes and effects1 will be of no avail toward the art of ,life or of ,society1 if the ends to be aimed at by that art are left to the vague suggestions of the intellectus sibi permissus1 or are taken for granted without analysis or questioning4 #g4 ,there is1 then1 a philosophia prima peculiar to ,art1 as there is one which belongs to ,science4 ,there are not only first principles of ,knowledge1 but first principles of ,conduct4 ,there must be some standard by which to determine the goodness or badness1 absolute and comparative1 of ends1 or objects of desire4 ,and whatever that standard is1 there can be but one2 for if there were several ultimate principles of conduct1 the same conduct might be approved by one of those principles and condemned by another2 and there would be needed some more general principle1 as umpire between them4 ,accordingly1 writers on ,moral ,philosophy have mostly felt the necessity not only of referring all rules of conduct1 and all judgments of praise and blame1 to principles1 but of referring them to some one principle2 some rule1 or standard1 with which all other rules of conduct were required to be consistent1 and from which by ultimate consequence they could all be deduced4 ,those who have dispensed with the assumption of such a universal standard1 have only been enabled to do so by supposing that a moral sense1 or instinct1 inherent in our constitution1 informs us1 both what principles of conduct we are bound to observe1 and also in what order these should be subordinated to one another4 ,the theory of the foundations of morality is a subject which it would be out of place1 in a work like this1 to discuss at large1 and which could not to any useful purpose be treated incidentally4 ,i shall content myself1 therefore1 with saying1 that the doctrine of intuitive moral principles1 even if true1 would provide only for that portion of the field of conduct which is properly called moral4 ,for the remainder of the practice of life some general principle1 or standard1 must still be sought2 and if that principle be rightly chosen1 it will be found1 ,i apprehend1 to serve quite as well for the ultimate principle of ,morality1 as for that of ,prudence1 ,policy1 or ,taste4 ,without attempting in this place to justify my opinion1 or even to define the kind of justification which it admits of1 ,i merely declare my conviction1 that the general principle to which all rules of practice ought to conform1 and the test by which they should be tried1 is that of conduciveness to the happiness of mankind1 or rather1 of all sentient beings2 in other words1 that the promotion of happiness is the ultimate principle of ,teleology47#bij7 ,i do not mean to assert that the promotion of happiness should be itself the end of all actions1 or even of all rules of action4 ,it is the justification1 and ought to be the controller1 of all ends1 but it is not itself the sole end4 ,there are many virtuous actions1 and even virtuous modes of action 7though the cases are1 ,i think1 less frequent than is often supposed71 by which happiness in the particular instance is sacrificed1 more pain being produced than pleasure4 ,but conduct of which this can be truly asserted1 admits of justification only because it can be shown that1 on the whole1 more happiness will exist in the world1 if feelings are cultivated which will make people1 in certain cases1 regardless of happiness4 ,i fully admit that this is true2 that the cultivation of an ideal nobleness of will and conduct should be to individual human beings an end1 to which the specific pursuit either of their own happiness or of that of others 7except so far as included in that idea7 should1 in any case of conflict1 give way4 ,but ,i hold that the very question1 what constitutes this elevation of character1 is itself to be decided by a reference to happiness as the standard4 ,the character itself should be1 to the individual1 a paramount end1 simply because the existence of this ideal nobleness of character1 or of a near approach to it1 in any abundance1 would go farther than all things else toward making human life happy1 both in the comparatively humble sense of pleasure and freedom from pain1 and in the higher meaning1 of rendering life1 not what it now is almost universally1 puerile and insignificant1 but such as human beings with highly developed faculties can care to have4 #h4 ,with these remarks we must close this summary view of the application of the general logic of scientific inquiry to the moral and social departments of science4 ,notwithstanding the extreme generality of the principles of method which ,i have laid down 7a generality which1 ,i trust1 is not1 in this instance1 synonymous with vagueness71 ,i have indulged the hope that to some of those on whom the task will devolve of bringing those most important of all sciences into a more satisfactory state1 these observations may be useful1 both in removing erroneous1 and in clearing up the true1 conceptions of the means by which1 on subjects of so high a degree of complication1 truth can be attained4 ,should this hope be realized1 what is probably destined to be the great intellectual achievement of the next two or three generations of ,european thinkers will have been in some degree forwarded4 ,,the ,,end4 ,,footnotes #a ,in the later editions of ,archbishop ,whately's 8,logic10 he states his meaning to be1 not that 8rules0 for the ascertainment of truths by inductive investigation can not be laid down1 or that they may not be 8of eminent service10 but that they 8must always be comparatively vague and general1 and incapable of being built up into a regular demonstrative theory like that of the ,syllogism40 7,book iv41 ch4 iv41 #c47 ,and he observes1 that to devise a system for this purpose1 capable of being 8brought into a scientific form10 would be an achievement which 8he must be more sanguine than scientific who expects40 7,book iv41 ch4 ii41 #d47 ,to effect this1 however1 being the express object of the portion of the present work which treats of ,induction1 the words in the text are no overstatement of the difference of opinion between ,archbishop ,whately and me on the subject4 #b ,now forming a chapter in his volume on 8,the ,philosophy of ,discovery40 #c ,archbishop ,whately4 #d ,i use these terms indiscriminately1 because1 for the purpose in view1 there is no need for making any distinction between them4 ,but metaphysicians usually restrict the name ,intuition to the direct knowledge we are supposed to have of things external to our minds1 and ,consciousness to our knowledge of our own mental phenomena4 #e ,this important theory has of late been called in question by a writer of deserved reputation1 ,mr4 ,samuel ,bailey2 but ,i do not conceive that the grounds on which it has been admitted as an established doctrine for a century past1 have been at all shaken by that gentleman's objections4 ,i have elsewhere said what appeared to me necessary in reply to his arguments4 7,westminster ,review for ,october1 #ahdb2 reprinted in 8,dissertations and ,discussions10 vol4 ii47 #f ,the view taken in the text1 of the definition and purpose of ,logic1 stands in marked opposition to that of the school of philosophy which1 in this country1 is represented by the writings of ,sir ,william ,hamilton and of his numerous pupils4 ,logic1 as this school conceives it1 is 8the ,science of the ,formal ,laws of ,thought20 a definition framed for the express purpose of excluding1 as irrelevant to ,logic1 whatever relates to ,belief and ,disbelief1 or to the pursuit of truth as such1 and restricting the science to that very limited portion of its total province1 which has reference to the conditions1 not of ,truth1 but of ,consistency4 ,what ,i have thought it useful to say in opposition to this limitation of the field of ,logic1 has been said at some length in a separate work1 first published in #ahfe1 and entitled 8,an ,examination of ,sir ,william ,hamilton's ,philosophy1 and of the ,principal ,philosophical ,questions discussed in his ,writings40 ,for the purposes of the present ,treatise1 ,i am content that the justification of the larger extension which ,i give to the domain of the science1 should rest on the sequel of the ,treatise itself4 ,some remarks on the relation which the ,logic of ,consistency bears to the ,logic of ,truth1 and on the place which that particular part occupies in the whole to which it belongs1 will be found in the present volume 7,book ,,ii41 chap4 iii41 #i74 #g ,computation or ,logic1 chap4 ii4 #h ,in the original 8had1 or had not40 ,these last words1 as involving a subtlety foreign to our present purpose1 ,i have forborne to quote4 #i ,vide infra1 note at the end of #c1 book ii41 chap4 ii4 #aj ,notare1 to mark2 connotare1 to mark along with2 to mark one thing with or in addition to another4 #aa ,archbishop ,whately1 who1 in the later editions of his ,elements of ,logic1 aided in reviving the important distinction treated of in the text1 proposes the term 8,attributive0 as a substitute for 8,connotative0 7p4 #bb1 #ith edit474 ,the expression is1 in itself1 appropriate2 but as it has not the advantage of being connected with any verb1 of so markedly distinctive a character as 8to connote10 it is not1 ,i think1 fitted to supply the place of the word ,connotative in scientific use4 #ab ,a writer who entitles his book ,philosophy2 or1 the ,science of ,truth1 charges me in his very first page 7referring at the foot of it to this passage7 with asserting that general names have properly no signification4 ,and he repeats this statement many times in the course of his volume1 with comments1 not at all flattering1 thereon4 ,it is well to be now and then reminded to how great a length perverse misquotation 7for1 strange as it appears1 ,i do not believe that the writer is dishonest7 can sometimes go4 ,it is a warning to readers when they see an author accused1 with volume and page referred to1 and the apparent guarantee of inverted commas1 of maintaining something more than commonly absurd1 not to give implicit credence to the assertion without verifying the reference4 #ac 8,take the familiar term ,stone4 ,it is applied to mineral and rocky materials1 to the kernels of fruit1 to the accumulations in the gall-bladder and in the kidney2 while it is refused to polished minerals 7called gems71 to rocks that have the cleavage suited for roofing 7slates71 and to baked clay 7bricks74 ,it occurs in the designation of the magnetic oxide of iron 7loadstone71 and not in speaking of other metallic ores4 ,such a term is wholly unfit for accurate reasoning1 unless hedged round on every occasion by other phrases2 as building stone1 precious stone1 gall-stone1 etc4 ,moreover1 the methods of definition are baffled for want of sufficient community to ground upon4 ,there is no quality uniformly present in the cases where it is applied1 and uniformly absent where it is not applied2 hence the definer would have to employ largely the license of striking off existing applications1 and taking in new ones40--,,bain1 ,logic1 ii41 #agb4 #ad ,before quitting the subject of connotative names1 it is proper to observe1 that the first writer who1 in our times1 has adopted from the schoolmen the word to connote1 ,mr4 ,james ,mill1 in his ,analysis of the ,phenomena of the ,human ,mind1 employs it in a signification different from that in which it is here used4 ,he uses the word in a sense co-extensive with its etymology1 applying it to every case in which a name1 while pointing directly to one thing 7which is consequently termed its signification71 includes also a tacit reference to some other thing4 ,in the case considered in the text1 that of concrete general names1 his language and mine are the converse of one another4 ,considering 7very justly7 the signification of the name to lie in the attribute1 he speaks of the word as noting the attribute1 and connoting the things possessing the attribute4 ,and he describes abstract names as being properly concrete names with their connotation dropped2 whereas1 in my view1 it is the denotation which would be said to be dropped1 what was previously connoted becoming the whole signification4 ,in adopting a phraseology at variance with that which so high an authority1 and one which ,i am less likely than any other person to undervalue1 has deliberately sanctioned1 ,i have been influenced by the urgent necessity for a term exclusively appropriated to express the manner in which a concrete general name serves to mark the attributes which are involved in its signification4 ,this necessity can scarcely be felt in its full force by any one who has not found by experience how vain is the attempt to communicate clear ideas on the philosophy of language without such a word4 ,it is hardly an exaggeration to say1 that some of the most prevalent of the errors with which logic has been infected1 and a large part of the cloudiness and confusion of ideas which have enveloped it1 would1 in all probability1 have been avoided1 if a term had been in common use to express exactly what ,i have signified by the term to connote4 ,and the schoolmen1 to whom we are indebted for the greater part of our logical language1 gave us this also1 and in this very sense4 ,for though some of their general expressions countenance the use of the word in the more extensive and vague acceptation in which it is taken by ,mr4 ,mill1 yet when they had to define it specifically as a technical term1 and to fix its meaning as such1 with that admirable precision which always characterizes their definitions1 they clearly explained that nothing was said to be connoted except forms1 which word may generally1 in their writings1 be understood as synonymous with attributes4 ,now1 if the word to connote1 so well suited to the purpose to which they applied it1 be diverted from that purpose by being taken to fulfill another1 for which it does not seem to me to be at all required2 ,i am unable to find any expression to replace it1 but such as are commonly employed in a sense so much more general1 that it would be useless attempting to associate them peculiarly with this precise idea4 ,such are the words1 to involve1 to imply1 etc4 ,by employing these1 ,i should fail of attaining the object for which alone the name is needed1 namely1 to distinguish this particular kind of involving and implying from all other kinds1 and to assure to it the degree of habitual attention which its importance demands4 #ae ,professor ,bain 7,logic1 i41 #ef7 thinks that negative names are not names of all things whatever except those denoted by the correlative positive name1 but only for all things of some particular class3 not-white1 for instance1 he deems not to be a name for every thing in nature except white things1 but only for every colored thing other than white4 ,in this case1 however1 as in all others1 the test of what a name denotes is what it can be predicated of3 and we can certainly predicate of a sound1 or a smell1 that it is not white4 ,the affirmation and the negation of the same attribute can not but divide the whole field of predication between them4 #af ,or rather1 all objects except itself and the percipient mind2 for1 as we shall see hereafter1 to ascribe any attribute to an object1 necessarily implies a mind to perceive it4 ,the simple and clear explanation given in the text1 of relation and relative names1 a subject so long the opprobrium of metaphysics1 was given 7as far as ,i know7 for the first time1 by ,mr4 ,james ,mill1 in his ,analysis of the ,phenomena of the ,human ,mind4 #ag ,on the preceding passage ,professor ,bain remarks 7,logic1 i41 #bfe73 8,the ,categories do not seem to have been intended as a classification of ,namable ,things1 in the sense of #8an enumeration of all kinds of ,things which are capable of being made predicates1 or of having any thing predicated of them4' ,they seem to have been rather intended as a generalization of predicates2 an analysis of the final import of predication4 ,viewed in this light1 they are not open to the objections offered by ,mr4 ,mill4 ,the proper question to ask is not--,in what ,category are we to place sensations or other feelings or states of mind8 but1 ,under what ,categories can we predicate regarding states of mind8 ,take1 for example1 ,hope4 ,when we say that it is a state of mind1 we predicate ,substance3 we may also describe how great it is 7,quantity71 what is the quality of it1 pleasurable or painful 7,quality71 what it has reference to 7,relation74 ,aristotle seems to have framed the ,categories on the plan--,here is an individual2 what is the final analysis of all that we can predicate about him80 ,this is doubtless a true statement of the leading idea in the classification4 ,the ,category was certainly understood by ,aristotle to be a general name for all possible answers to the question ,quid sit8 when asked respecting a concrete individual2 as the other ,categories are names comprehending all possible answers to the questions ,quantum sit8 ,quale sit8 etc4 ,in ,aristotle's conception1 therefore1 the ,categories may not have been a classification of ,things2 but they were soon converted into one by his ,scholastic followers1 who certainly regarded and treated them as a classification of ,things1 and carried them out as such1 dividing down the ,category ,substance as a naturalist might do1 into the different classes of physical or metaphysical objects as distinguished from attributes1 and the other ,categories into the principal varieties of quantity1 quality1 relation1 etc4 ,it is1 therefore1 a just subject of complaint against them1 that they had no ,category of ,feeling4 ,feeling is assuredly predicable as a summum genus1 of every particular kind of feeling1 for instance1 as in ,mr4 ,bain's example1 of ,hope3 but it can not be brought within any of the ,categories as interpreted either by ,aristotle or by his followers4 #ah ,philosophy of the ,inductive ,sciences1 vol4 i41 p4 #dj4 #ai ,discussions on ,philosophy1 etc4 ,appendix ,i41 pp4 #fdc1 #fdd4 #bj ,it is to be regretted that ,sir ,william ,hamilton1 though he often strenuously insists on this doctrine1 and though1 in the passage quoted1 he states it with a comprehensiveness and force which leave nothing to be desired1 did not consistently adhere to his own doctrine1 but maintained along with it opinions with which it is utterly irreconcilable4 ,see the third and other chapters of ,an ,examination of ,sir ,william ,hamilton's ,philosophy4 #ba 8,nous savons qu'il existe quelque chose hors de nous1 parceque nous ne pouvons expliquer nos perceptions sans les rattacher des causes distinctes de nous mmes2 nous savons de plus que ces causes1 dont nous ne connaissons pas d'ailleurs l'essence1 produisent les effets les plus variables1 les plus divers1 et mme les plus contraires1 selon qu'elles rencontrent telle nature ou telle disposition du sujet4 ,mais savons-nous quelque chose de plus8 et mme1 vu le caractre indtermin des causes que nous concevons dans les corps1 y a-t-il quelque chose de plus savoir8 ,y a-t-il lieu de nous enqurir si nous percevons les choses telles qu'elles sont8 ,non videmment4444 ,je ne dis pas que le problme est insoluble1 je dis qu'il est absurde et enferme une contradiction4 ,nous ne savons pas ce que ces causes sont en elles-mmes1 et la raison nous dfend de chercher le connatre3 mais il est bien vident priori1 qu'elles ne sont pas en elles-mmes ce qu'elles sont par rapport nous1 puisque la prsence du sujet modifie ncessairement leur action4 ,supprimez tout sujet sentant1 il est certain que ces causes agiraient encore puisqu'elles continueraient d'exister2 mais elles agiraient autrement2 elles seraient encore des qualits et des proprits1 mais qui ne ressembleraient rien de ce que nous connaissons4 ,le feu ne manifesterait plus aucune des proprits que nous lui connaissons3 que serait-il8 ,c'est ce que nous ne saurons jamais4 ,c'est d'ailleurs peut-tre un problme qui ne rpugne pas seulement la nature de notre esprit1 mais l'essence mme des choses4 ,quand mme en effet on supprimerait par le pense tous les sujets sentants1 il faudrait encore admettre que nul corps ne manifesterait ses proprits autrement qu'en relation avec un sujet quelconque1 et dans ce cas ses proprits ne seraient encore que relatives3 en sorte qu'il me parat fort raisonnable d'admettre que les proprits dtermines des corps n'existent pas indpendamment d'un sujet quelconque1 et que quand on demande si les proprits de la matiere sont telles que nous les percevons1 il faudrait voir auparavant si elles sont en tant que dtermines1 et dans quel sens il est vrai de dire qu'elles sont40--,cours d',histoire de la ,philosophie ,morale au #ahme sicle1 #hme leon4 #bb ,an attempt1 indeed1 has been made by ,reid and others1 to establish that although some of the properties we ascribe to objects exist only in our sensations1 others exist in the things themselves1 being such as can not possibly be copies of any impression upon the senses2 and they ask1 from what sensations our notions of extension and figure have been derived8 ,the gauntlet thrown down by ,reid was taken up by ,brown1 who1 applying greater powers of analysis than had previously been applied to the notions of extension and figure1 pointed out that the sensations from which those notions are derived1 are sensations of touch1 combined with sensations of a class previously too little adverted to by metaphysicians1 those which have their seat in our muscular frame4 ,his analysis1 which was adopted and followed up by ,james ,mill1 has been further and greatly improved upon in ,professor ,bain's profound work1 ,the ,senses and the ,intellect1 and in the chapters on 8,perception0 of a work of eminent analytic power1 ,mr4 ,herbert ,spencer's ,principles of ,psychology4 ,on this point ,m4 ,cousin may again be cited in favor of the better doctrine4 ,m4 ,cousin recognizes1 in opposition to ,reid1 the essential subjectivity of our conceptions of what are called the primary qualities of matter1 as extension1 solidity1 etc41 equally with those of color1 heat1 and the remainder of the so-called secondary qualities4--,cours1 ut supra1 #ime leon4 #bc ,this doctrine1 which is the most complete form of the philosophical theory known as the ,relativity of ,human ,knowledge1 has1 since the recent revival in this country of an active interest in metaphysical speculation1 been the subject of a greatly increased amount of discussion and controversy2 and dissentients have manifested themselves in considerably greater number than ,i had any knowledge of when the passage in the text was written4 ,the doctrine has been attacked from two sides4 ,some thinkers1 among whom are the late ,professor ,ferrier1 in his ,institutes of ,metaphysic1 and ,professor ,john ,grote1 in his ,exploratio ,philosophica1 appear to deny altogether the reality of ,noumena1 or ,things in themselves--of an unknowable substratum or support for the sensations which we experience1 and which1 according to the theory1 constitute all our knowledge of an external world4 ,it seems to me1 however1 that in ,professor ,grote's case at least1 the denial of ,noumena is only apparent1 and that he does not essentially differ from the other class of objectors1 including ,mr4 ,bailey in his valuable ,letters on the ,philosophy of the ,human ,mind1 and 7in spite of the striking passage quoted in the text7 also ,sir ,william ,hamilton1 who contend for a direct knowledge by the human mind of more than the sensations--of certain attributes or properties as they exist not in us1 but in the ,things themselves4 ,with the first of these opinions1 that which denies ,noumena1 ,i have1 as a metaphysician1 no quarrel2 but1 whether it be true or false1 it is irrelevant to ,logic4 ,and since all the forms of language are in contradiction to it1 nothing but confusion could result from its unnecessary introduction into a treatise1 every essential doctrine of which could stand equally well with the opposite and accredited opinion4 ,the other and rival doctrine1 that of a direct perception or intuitive knowledge of the outward object as it is in itself1 considered as distinct from the sensations we receive from it1 is of far greater practical moment4 ,but even this question1 depending on the nature and laws of ,intuitive ,knowledge1 is not within the province of ,logic4 ,for the grounds of my own opinion concerning it1 ,i must content myself with referring to a work already mentioned--,an ,examination of ,sir ,william ,hamilton's ,philosophy2 several chapters of which are devoted to a full discussion of the questions and theories relating to the supposed direct perception of external objects4 #bd ,professor ,bain 7,logic1 i41 #di7 defines attributes as 8points of community among classes40 ,this definition expresses well one point of view1 but is liable to the objection that it applies only to the attributes of classes2 though an object1 unique in its kind1 may be said to have attributes4 ,moreover1 the definition is not ultimate1 since the points of community themselves admit of1 and require1 further analysis2 and ,mr4 ,bain does analyze them into resemblances in the sensations1 or other states of consciousness excited by the object4 #be ,analysis of the ,human ,mind1 i41 #abf et seq4 #bf ,logic1 i41 #he4 #bg ,instead of ,universal and ,particular as applied to propositions1 ,professor ,bain proposes 7,logic1 i41 #ha7 the terms ,total and ,partial2 reserving the former pair of terms for their inductive meaning1 8the contrast between a general proposition and the particulars or individuals that we derive it from40 ,this change in nomenclature would be attended with the further advantage1 that ,singular propositions1 which in the ,syllogism follow the same rules as ,universal1 would be included along with them in the same class1 that of ,total predications4 ,it is not the ,subject's denoting many things or only one1 that is of importance in reasoning1 it is that the assertion is made of the whole or a part only of what the ,subject denotes4 ,the words ,universal and ,particular1 however1 are so familiar and so well understood in both the senses mentioned by ,mr4 ,bain1 that the double meaning does not produce any material inconvenience4 #bh ,it may1 however1 be considered as equivalent to a universal proposition with a different predicate1 viz43 8,all wine is good qu wine10 or 8is good in respect of the qualities which constitute it wine40 #bi ,logic1 i41 #hb4 #cj ,dr4 ,whewell 7,philosophy of ,discovery1 p4 #bdb7 questions this statement1 and asks1 8,are we to say that a mole can not dig the ground1 except he has an idea of the ground1 and of the snout and paws with which he digs it80 ,i do not know what passes in a mole's mind1 nor what amount of mental apprehension may or may not accompany his instinctive actions4 ,but a human being does not use a spade by instinct2 and he certainly could not use it unless he had knowledge of a spade1 and of the earth which he uses it upon4 #ca ,professor ,bain remarks1 in qualification of the statement in the text 7,logic1 i41 #ej71 that the word ,class has two meanings2 8the class definite1 and the class indefinite4 ,the class definite is an enumeration of actual individuals1 as the ,peers of the ,realm1 the oceans of the globe1 the known planets4444 ,the class indefinite is unenumerated4 ,such classes are stars1 planets1 gold-bearing rocks1 men1 poets1 virtuous4444 ,in this last acceptation of the word1 class name and general name are identical4 ,the class name denotes an indefinite number of individuals1 and connotes the points of community or likeness40 ,the theory controverted in the text1 tacitly supposes all classes to be definite4 ,i have assumed them to be indefinite2 because1 for the purposes of ,logic1 definite classes1 as such1 are almost useless2 though often serviceable as means of abridged expression4 7,vide infra1 book iii41 chap4 ii47 #cb 8,from hence also this may be deduced1 that the first truths were arbitrarily made by those that first of all imposed names upon things1 or received them from the imposition of others4 ,for it is true 7for example7 that man is a living creature1 but it is for this reason1 that it pleased men to impose both these names on the same thing40--,computation or ,logic1 chap4 iii41 sect4 #h4 #cc 8,men are subject to err not only in affirming and denying1 but also in perception1 and in silent cogitation4444 ,tacit errors1 or the errors of sense and cogitation1 are made by passing from one imagination to the imagination of another different thing2 or by feigning that to be past1 or future1 which never was1 nor ever shall be2 as when by seeing the image of the sun in water1 we imagine the sun itself to be there2 or by seeing swords1 that there has been1 or shall be1 fighting1 because it used to be so for the most part2 or when from promises we feign the mind of the promiser to be such and such2 or1 lastly1 when from any sign we vainly imagine something to be signified which is not4 ,and errors of this sort are common to all things that have sense40--,computation or ,logic1 chap4 v41 sect4 #a4 #cd ,chap4 iii41 sect #c4 #ce ,to the preceding statement it has been objected1 that 8we naturally construe the subject of a proposition in its extension1 and the predicate 7which therefore may be an adjective7 in its intension 7connotation73 and that consequently co-existence of attributes does not1 any more than the opposite theory of equation of groups1 correspond with the living processes of thought and language40 ,i acknowledge the distinction here drawn1 which1 indeed1 ,i had myself laid down and exemplified a few pages back 7p4 #gg74 ,but though it is true that we naturally 8construe the subject of a proposition in its extension10 this extension1 or in other words1 the extent of the class denoted by the name1 is not apprehended or indicated directly4 ,it is both apprehended and indicated solely through the attributes4 ,in the 8living processes of thought and language0 the extension1 though in this case really thought of 7which in the case of the predicate it is not71 is thought of only through the medium of what my acute and courteous critic terms the 8intension40 ,for further illustrations of this subject1 see ,examination of ,sir ,william ,hamilton's ,philosophy1 chap4 xxii4 #cf ,professor ,bain1 in his ,logic 7i41 #bef71 excludes ,existence from the list1 considering it as a mere name4 ,all propositions1 he says1 which predicate mere existence 8are more or less abbreviated1 or elliptical3 when fully expressed they fall under either co-existence or succession4 ,when we say there exists a conspiracy for a particular purpose1 we mean that at the present time a body of men have formed themselves into a society for a particular object2 which is a complex affirmation1 resolvable into propositions of co-existence and succession 7as causation74 ,the assertion that the dodo does not exist1 points to the fact that this animal1 once known in a certain place1 has disappeared or become extinct2 is no longer associated with the locality3 all which may be better stated without the use of the verb #8exist4' ,there is a debated question--,does an ether exist8 but the concrete form would be this--#8,are heat and light and other radiant influences propagated by an ethereal medium diffused in space2' which is a proposition of causation4 ,in like manner the question of the ,existence of a ,deity can not be discussed in that form4 ,it is properly a question as to the ,first ,cause of the ,universe1 and as to the continued exertion of that ,cause in providential superintendence40 7i41 #djg47 ,mr4 ,bain thinks it 8fictitious and unmeaning language0 to carry up the classification of ,nature to one summum genus1 ,being1 or that which ,exists2 since nothing can be perceived or apprehended but by way of contrast with something else 7of which important truth1 under the name of ,law of ,relativity1 he has been in our time the principal expounder and champion71 and we have no other class to oppose to ,being1 or fact to contrast with ,existence4 ,i accept fully ,mr4 ,bain's ,law of ,relativity1 but ,i do not understand by it that to enable us to apprehend or be conscious of any fact1 it is necessary that we should contrast it with some other positive fact4 ,the antithesis necessary to consciousness need not1 ,i conceive1 be an antithesis between two positives2 it may be between one positive and its negative4 ,hobbes was undoubtedly right when he said that a single sensation indefinitely prolonged would cease to be felt at all2 but simple intermission1 without other change1 would restore it to consciousness4 ,in order to be conscious of heat1 it is not necessary that we should pass to it from cold2 it suffices that we should pass to it from a state of no sensation1 or from a sensation of some other kind4 ,the relative opposite of ,being1 considered as a summum genus1 is ,nonentity1 or ,nothing2 and we have1 now and then1 occasion to consider and discuss things merely in contrast with ,nonentity4 ,i grant that the decision of questions of ,existence usually if not always depends on a previous question of either ,causation or ,co-existence4 ,but ,existence is nevertheless a different thing from ,causation or ,co-existence1 and can be predicated apart from them4 ,the meaning of the abstract name ,existence1 and the connotation of the concrete name ,being1 consist1 like the meaning of all other names1 in sensations or states of consciousness3 their peculiarity is that to exist1 is to excite1 or be capable of exciting1 any sensations or states of consciousness3 no matter what1 but it is indispensable that there should be some4 ,it was from overlooking this that ,hegel1 finding that ,being is an abstraction reached by thinking away all particular attributes1 arrived at the self-contradictory proposition on which he founded all his philosophy1 that ,being is the same as ,nothing4 ,it is really the name of ,something1 taken in the most comprehensive sense of the word4 #cg ,book iv41 chap4 vii4 #ch ,logic1 i41 #ajc-aje4 #ci ,the doctrines which prevented the real meaning of ,essences from being understood1 had not assumed so settled a shape in the time of ,aristotle and his immediate followers1 as was afterward given to them by the ,realists of the ,middle ,ages4 ,aristotle himself 7in his ,treatise on the ,categories7 expressly denies that the 1 or ,substanti ,secund1 inhere in a subject4 ,they are only1 he says1 predicated of it4 #dj ,the always acute and often profound author of ,an ,outline of ,sematology 7,mr4 ,b4 ,h4 ,smart7 justly says1 8,locke will be much more intelligible1 if1 in the majority of places1 we substitute #8the knowledge of' for what he calls #8the ,idea of'0 7p4 #aj74 ,among the many criticisms on ,locke's use of the word ,idea1 this is the one which1 as it appears to me1 most nearly hits the mark2 and ,i quote it for the additional reason that it precisely expresses the point of difference respecting the import of ,propositions1 between my view and what ,i have spoken of as the ,conceptualist view of them4 ,where a ,conceptualist says that a name or a proposition expresses our ,idea of a thing1 ,i should generally say 7instead of our ,idea7 our ,knowledge1 or ,belief1 concerning the thing itself4 #da ,this distinction corresponds to that which is drawn by ,kant and other metaphysicians between what they term analytic and synthetic1 judgments2 the former being those which can be evolved from the meaning of the terms used4 #db ,if we allow a differentia to what is not really a species4 ,for the distinction of ,kinds1 in the sense explained by us1 not being in any way applicable to attributes1 it of course follows that although attributes may be put into classes1 those classes can be admitted to be genera or species only by courtesy4 #dc ,professor ,bain1 in his ,logic1 takes a peculiar view of ,definition4 ,he holds 7i41 #ga7 with the present work1 that 8the definition in its full import1 is the sum of all the properties connoted by the name2 it exhausts the meaning of a word40 ,but he regards the meaning of a general name as including1 not indeed all the common properties of the class named1 but all of them that are ultimate properties1 not resolvable into one another4 8,the enumeration of the attributes of oxygen1 of gold1 of man1 should be an enumeration of the final 7so far as can be made out71 the underivable1 powers or functions of each10 and nothing less than this is a complete ,definition 7i41 #ge74 ,an independent property1 not derivable from other properties1 even if previously unknown1 yet as soon as discovered becomes1 according to him1 part of the meaning of the term1 and should be included in the definition4 8,when we are told that diamond1 which we know to be a transparent1 glittering1 hard1 and high-priced substance1 is composed of carbon1 and is combustible1 we must put these additional properties on the same level as the rest2 to us they are henceforth connoted by the name0 7i41 #gc74 ,consequently the propositions that diamond is composed of carbon1 and that it is combustible1 are regarded by ,mr4 ,bain as merely verbal propositions4 ,he carries this doctrine so far as to say that unless mortality can be shown to be a consequence of the ultimate laws of animal organization1 mortality is connoted by man1 and 8,man is ,mortal0 is a merely verbal proposition4 ,and one of the peculiarities 7,i think a disadvantageous peculiarity7 of his able and valuable treatise1 is the large number of propositions requiring proof1 and learned by experience1 which1 in conformity with this doctrine1 he considers as not real1 but verbal1 propositions4 ,the objection ,i have to this language is that it confounds1 or at least confuses1 a much more important distinction than that which it draws4 ,the only reason for dividing ,propositions into real and verbal1 is in order to discriminate propositions which convey information about facts1 from those which do not4 ,a proposition which affirms that an object has a given attribute1 while designating the object by a name which already signifies the attribute1 adds no information to that which was already possessed by all who understood the name4 ,but when this is said1 it is implied that1 by the signification of a name1 is meant the signification attached to it in the common usage of life4 ,i can not think we ought to say that the meaning of a word includes matters of fact which are unknown to every person who uses the word unless he has learned them by special study of a particular department of ,nature2 or that because a few persons are aware of these matters of fact1 the affirmation of them is a proposition conveying no information4 ,i hold that 7special scientific connotation apart7 a name means1 or connotes1 only the properties which it is a mark of in the general mind2 and that in the case of any additional properties1 however uniformly found to accompany these1 it remains possible that a thing which did not possess the properties might still be thought entitled to the name4 ,ruminant1 according to ,mr4 ,bain's use of language1 connotes cloven-hoofed1 since the two properties are always found together1 and no connection has ever been discovered between them3 but ruminant does not mean cloven-hoofed2 and were an animal to be discovered which chews the cud1 but has its feet undivided1 ,i venture to say that it would still be called ruminant4 #dd ,in the fuller discussion which ,archbishop ,whately has given to this subject in his later editions1 he almost ceases to regard the definitions of names and those of things as1 in any important sense1 distinct4 ,he seems 7#ith ed41 p4 #ade7 to limit the notion of a ,real ,definition to one which 8explains any thing more of the nature of the thing than is implied in the name20 7including under the word 8implied10 not only what the name connotes1 but every thing which can be deduced by reasoning from the attributes connoted74 ,even this1 as he adds1 is usually called not a ,definition1 but a ,description2 and 7as it seems to me7 rightly so called4 ,a ,description1 ,i conceive1 can only be ranked among ,definitions1 when taken 7as in the case of the zoological definition of man7 to fulfill the true office of a ,definition1 by declaring the connotation given to a word in some special use1 as a term of science or art3 which special connotation of course would not be expressed by the proper definition of the word in its ordinary employment4 ,mr4 ,de ,morgan1 exactly reversing the doctrine of ,archbishop ,whately1 understands by a ,real ,definition one which contains less than the ,nominal ,definition1 provided only that what it contains is sufficient for distinction4 8,by real definition ,i mean such an explanation of the word1 be it the whole of the meaning or only part1 as will be sufficient to separate the things contained under that word from all others4 ,thus the following1 ,i believe1 is a complete definition of an elephant3 ,an animal which naturally drinks by drawing the water into its nose1 and then spurting it into its mouth40--,formal ,logic1 p4 #cf4 ,mr4 ,de ,morgan's general proposition and his example are at variance2 for the peculiar mode of drinking of the elephant certainly forms no part of the meaning of the word elephant4 ,it could not be said1 because a person happened to be ignorant of this property1 that he did not know what an elephant means4 #de ,in the only attempt which1 so far as ,i know1 has been made to refute the preceding argumentation1 it is maintained that in the first form of the syllogism1 ,a dragon is a thing which breathes flame1 ,a dragon is a serpent1 ,therefore some serpent or serpents breathe flame1 8there is just as much truth in the conclusion as there is in the premises1 or rather1 no more in the latter than in the former4 ,if the general name serpent includes both real and imaginary serpents1 there is no falsity in the conclusion2 if not1 there is falsity in the minor premise40 ,let us1 then1 try to set out the syllogism on the hypothesis that the name serpent includes imaginary serpents4 ,we shall find that it is now necessary to alter the predicates2 for it can not be asserted that an imaginary creature breathes flame2 in predicating of it such a fact1 we assert by the most positive implication that it is real1 and not imaginary4 ,the conclusion must run thus1 8,some serpent or serpents either do or are imagined to breathe flame40 ,and to prove this conclusion by the instance of dragons1 the premises must be1 ,a dragon is imagined as breathing flame4 ,a dragon is a 7real or imaginary7 serpent3 from which it undoubtedly follows1 that there are serpents which are imagined to breathe flame2 but the major premise is not a definition1 nor part of a definition2 which is all that ,i am concerned to prove4 ,let us now examine the other assertion--that if the word serpent stands for none but real serpents1 the minor premise 7a dragon is a serpent7 is false4 ,this is exactly what ,i have myself said of the premise1 considered as a statement of fact3 but it is not false as part of the definition of a dragon2 and since the premises1 or one of them1 must be false 7the conclusion being so71 the real premise can not be the definition1 which is true1 but the statement of fact1 which is false4 #df 8,few people0 7,i have said in another place7 8have reflected how great a knowledge of ,things is required to enable a man to affirm that any given argument turns wholly upon words4 ,there is1 perhaps1 not one of the leading terms of philosophy which is not used in almost innumerable shades of meaning1 to express ideas more or less widely different from one another4 ,between two of these ideas a sagacious and penetrating mind will discern1 as it were intuitively1 an unobvious link of connection1 upon which1 though perhaps unable to give a logical account of it1 he will found a perfectly valid argument1 which his critic1 not having so keen an insight into the ,things1 will mistake for a fallacy turning on the double meaning of a term4 ,and the greater the genius of him who thus safely leaps over the chasm1 the greater will probably be the crowing and vainglory of the mere logician1 who1 hobbling after him1 evinces his own superior wisdom by pausing on its brink1 and giving up as desperate his proper business of bridging it over40 #dg ,the different cases of ,equipollency1 or 8,equivalent ,propositional ,forms10 are set forth with some fullness in ,professor ,bain's ,logic4 ,one of the commonest of these changes of expression1 that from affirming a proposition to denying its negative1 or vic versa1 ,mr4 ,bain designates1 very happily1 by the name ,obversion4 #dh ,as ,sir ,william ,hamilton has pointed out1 8,some ,a is not ,b0 may also be converted in the following form3 8,no ,b is some ,a40 ,some men are not negroes2 therefore1 ,no negroes are some men 7e4g41 ,europeans74 #di ,contraries3 ,all ,a is ,b ,no ,a is ,b ,subtraries3 ,some ,a is ,b ,some ,a is not ,b ,contradictories3 ,all ,a is ,b ,some ,a is not ,b ,also contradictories3 ,no ,a is ,b ,some ,a is ,b ,respectively subalternate3 ,all ,a is ,b and ,no ,a is ,b ,some ,a is ,b and ,some ,a is not ,b #ej ,professor ,bain denies the claim of ,singular ,propositions to be classed1 for the purposes of ratiocination1 with ,universal2 though they come within the designation which he himself proposes as an equivalent for ,universal1 that of ,total4 ,he would even1 to use his own expression1 banish them entirely from the syllogism4 ,he takes as an example1 ,socrates is wise1 ,socrates is poor1 therefore ,some poor men are wise1 or more properly 7as he observes7 8one poor man is wise40 8,now1 if wise1 poor1 and a man1 are attributes belonging to the meaning of the word ,socrates1 there is then no march of reasoning at all4 ,we have given in ,socrates1 inter alia1 the facts wise1 poor1 and a man1 and we merely repeat the concurrence which is selected from the whole aggregate of properties making up the whole1 ,socrates4 ,the case is one under the head #8,greater and ,less ,connotation' in ,equivalent ,propositional ,forms1 or ,immediate ,inference4 8,but the example in this form does not do justice to the syllogism of singulars4 ,we must suppose both propositions to be real1 the predicates being in no way involved in the subject4 ,thus ,socrates was the master of ,plato1 ,socrates fought at ,delium1 ,the master of ,plato fought at ,delium4 8,it may fairly be doubted whether the transitions1 in this instance1 are any thing more than equivalent forms4 ,for the proposition #8,socrates was the master of ,plato and fought at ,delium1' compounded out of the two premises1 is obviously nothing more than a grammatical abbreviation4 ,no one can say that there is here any change of meaning1 or any thing beyond a verbal modification of the original form4 ,the next step is1 #8,the master of ,plato fought at ,delium1' which is the previous statement cut down by the omission of ,socrates4 ,it contents itself with reproducing a part of the meaning1 or saying less than had been previously said4 ,the full equivalent of the affirmation is1 #8,the master of ,plato fought at ,delium1 and the master of ,plato was ,socrates3' the new form omits the last piece of information1 and gives only the first4 ,now1 we never consider that we have made a real inference1 a step in advance1 when we repeat less than we are entitled to say1 or drop from a complex statement some portion not desired at the moment4 ,such an operation keeps strictly within the domain of equivalence1 or ,immediate ,inference4 ,in no way1 therefore1 can a syllogism with two singular premises be viewed as a genuine syllogistic or deductive inference40 7,logic1 i41 #aei47 ,the first argument1 as will have been seen1 rests upon the supposition that the name ,socrates has a meaning2 that man1 wise1 and poor1 are parts of this meaning2 and that by predicating them of ,socrates we convey no information2 a view of the signification of names which1 for reasons already given 7,note to #d of the chapter on ,definition1 supra1 pp4 #aaj1 #aaa471 ,i can not admit1 and which1 as applied to the class of names which ,socrates belongs to1 is at war with ,mr4 ,bain's own definition of a ,proper ,name 7i41 #adh71 8a single meaningless mark or designation appropriated to the thing40 ,such names1 ,mr4 ,bain proceeded to say1 do not necessarily indicate even human beings3 much less then does the name ,socrates include the meaning of wise or poor4 ,otherwise it would follow that if ,socrates had grown rich1 or had lost his mental faculties by illness1 he would no longer have been called ,socrates4 ,the second part of ,mr4 ,bain's argument1 in which he contends that even when the premises convey real information1 the conclusion is merely the premises with a part left out1 is applicable1 if at all1 as much to universal propositions as to singular4 ,in every syllogism the conclusion contains less than is asserted in the two premises taken together4 ,suppose the syllogism to be ,all bees are intelligent1 ,all bees are insects1 therefore ,some insects are intelligent3 one might use the same liberty taken by ,mr4 ,bain1 of joining together the two premises as if they were one--8,all bees are insects and intelligent0--and might say that in omitting the middle term bees we make no real inference1 but merely reproduce part of what had been previously said4 ,mr4 ,bain's is really an objection to the syllogism itself1 or at all events to the third figure3 it has no special applicability to singular propositions4 #ea ,his conclusions are1 8,the first figure is suited to the discovery or proof of the properties of a thing2 the second to the discovery or proof of the distinctions between things2 the third to the discovery or proof of instances and exceptions2 the fourth to the discovery1 or exclusion1 of the different species of a genus40 ,the reference of syllogisms in the last three figures to the dictum de omni et nullo is1 in ,lambert's opinion1 strained and unnatural3 to each of the three belongs1 according to him1 a separate axiom1 co-ordinate and of equal authority with that dictum1 and to which he gives the names of dictum de diverso for the second figure1 dictum de exemplo for the third1 and dictum de reciproco for the fourth4 ,see part i41 or ,dianoiologie1 chap1 iv41 #bbi et seqq4 ,mr4 ,bailey 7,theory of ,reasoning1 #b;d ed41 pp4 #gj-gd7 takes a similar view of the subject4 #eb ,since this chapter was written1 two treatises have appeared 7or rather a treatise and a fragment of a treatise71 which aim at a further improvement in the theory of the forms of ratiocination3 ,mr4 ,de ,morgan's 8,formal ,logic2 or1 the ,calculus of ,inference1 ,necessary and ,probable20 and the 8,new ,analytic of ,logical ,forms10 attached as an ,appendix to ,sir ,william ,hamilton's ,discussions on ,philosophy1 and at greater length1 to his posthumous ,lectures on ,logic4 ,in ,mr4 ,de ,morgan's volume--abounding1 in its more popular parts1 with valuable observations felicitously expressed--the principal feature of originality is an attempt to bring within strict technical rules the cases in which a conclusion can be drawn from premises of a form usually classed as particular4 ,mr4 ,de ,morgan observes1 very justly1 that from the premises most ,bs are ,cs1 most ,bs are ,as1 it may be concluded with certainty that some ,as are ,cs1 since two portions of the class ,b1 each of them comprising more than half1 must necessarily in part consist of the same individuals4 ,following out this line of thought1 it is equally evident that if we knew exactly what proportion the 8most0 in each of the premises bear to the entire class ,b1 we could increase in a corresponding degree the definiteness of the conclusion4 ,thus if #fj per cent4 of ,b are included in ,c1 and #gj per cent4 in ,a1 #cj per cent4 at least must be common to both2 in other words1 the number of ,as which are ,cs1 and of ,cs which are ,as1 must be at least equal to #cj per cent4 of the class ,b4 ,proceeding on this conception of 8numerically definite propositions10 and extending it to such forms as these3--8#de ,xs 7or more7 are each of them one of #gj ,ys10 or 8#de ,xs 7or more7 are no one of them to be found among #gj ,ys10 and examining what inferences admit of being drawn from the various combinations which may be made of premises of this description1 ,mr4 ,de ,morgan establishes universal formul for such inferences2 creating for that purpose not only a new technical language1 but a formidable array of symbols analogous to those of algebra4 ,since it is undeniable that inferences1 in the cases examined by ,mr4 ,de ,morgan1 can legitimately be drawn1 and that the ordinary theory takes no account of them1 ,i will not say that it was not worth while to show in detail how these also could be reduced to formul as rigorous as those of ,aristotle4 ,what ,mr4 ,de ,morgan has done was worth doing once 7perhaps more than once1 as a school exercise72 but ,i question if its results are worth studying and mastering for any practical purpose4 ,the practical use of technical forms of reasoning is to bar out fallacies3 but the fallacies which require to be guarded against in ratiocination properly so called1 arise from the incautious use of the common forms of language2 and the logician must track the fallacy into that territory1 instead of waiting for it on a territory of his own4 ,while he remains among propositions which have acquired the numerical precision of the ,calculus of ,probabilities1 the enemy is left in possession of the only ground on which he can be formidable4 ,and since the propositions 7short of universal7 on which a thinker has to depend1 either for purposes of speculation or of practice1 do not1 except in a few peculiar cases1 admit of any numerical precision2 common reasoning can not be translated into ,mr4 ,de ,morgan's forms1 which therefore can not serve any purpose as a test of it4 ,sir ,william ,hamilton's theory of the 8quantification of the predicate0 may be described as follows3 8,logically0 7,i quote his words7 8we ought to take into account the quantity1 always understood in thought1 but usually1 for manifest reasons1 elided in its expression1 not only of the subject1 but also of the predicate of a judgment40 ,all ,a is ,b1 is equivalent to all ,a is some ,b4 ,no ,a is ,b1 to ,no ,a is any ,b4 ,some ,a is ,b1 is tantamount to some ,a is some ,b4 ,some ,a is not ,b1 to ,some ,a is not any ,b4 ,as in these forms of assertion the predicate is exactly co-extensive with the subject1 they all admit of simple conversion2 and by this we obtain two additional forms--,some ,b is all ,a1 and ,no ,b is some ,a4 ,we may also make the assertion ,all ,a is all ,b1 which will be true if the classes ,a and ,b are exactly co-extensive4 ,the last three forms1 though conveying real assertions1 have no place in the ordinary classification of ,propositions4 ,all propositions1 then1 being supposed to be translated into this language1 and written each in that one of the preceding forms which answers to its signification1 there emerges a new set of syllogistic rules1 materially different from the common ones4 ,a general view of the points of difference may be given in the words of ,sir ,w4 ,hamilton 7,discussions1 #b;d ed41 p4 #fea73 8,the revocation of the two terms of a ,proposition to their true relation2 a proposition being always an equation of its subject and its predicate4 8,the consequent reduction of the ,conversion of ,propositions from three species to one--that of ,simple ,conversion4 8,the reduction of all the ,general ,laws of ,categorical ,syllogisms to a single ,canon4 8,the evolution from that one canon of all the ,species and varieties of ,syllogisms4 8,the abrogation of all the ,special ,laws of ,syllogism4 8,a demonstration of the exclusive possibility of ,three ,syllogistic ,figures2 and 7on new grounds7 the scientific and final abolition of the ,fourth4 8,a manifestation that ,figure is an unessential variation in syllogistic form2 and the consequent absurdity of ,reducing the syllogisms of the other figures to the first4 8,an enouncement of one ,organic ,principle for each ,figure4 8,a determination of the true number of the ,legitimate ,moods2 with 8,their amplification in number 7thirty-six72 8,their numerical equality under all the figures2 and 8,their relative equivalence1 or virtual identity1 throughout every schematic difference4 8,that1 in the second and third figures1 the extremes holding both the same relation to the middle term1 there is not1 as in the first1 an opposition and subordination between a term major and a term minor1 mutually containing and contained1 in the counter wholes of ,extension and ,comprehension4 8,consequently1 in the second and third figures1 there is no determinate major and minor premises1 and there are two indifferent conclusions3 whereas in the first the premises are determinate1 and there is a single proximate conclusion40 ,this doctrine1 like that of ,mr4 ,de ,morgan previously noticed1 is a real addition to the syllogistic theory2 and has moreover this advantage over ,mr4 ,de ,morgan's 8numerically definite ,syllogism10 that the forms it supplies are really available as a test of the correctness of ratiocination2 since propositions in the common form may always have their predicates quantified1 and so be made amenable to ,sir ,w4 ,hamilton's rules4 ,considered1 however1 as a contribution to the ,science of ,logic1 that is1 to the analysis of the mental processes concerned in reasoning1 the new doctrine appears to me1 ,i confess1 not merely superfluous1 but erroneous2 since the form in which it clothes propositions does not1 like the ordinary form1 express what is in the mind of the speaker when he enunciates the proposition4 ,i can not think ,sir ,william ,hamilton right in maintaining that the quantity of the predicate is 8always understood in thought40 ,it is implied1 but is not present to the mind of the person who asserts the proposition4 ,the quantification of the predicate1 instead of being a means of bringing out more clearly the meaning of the proposition1 actually leads the mind out of the proposition1 into another order of ideas4 ,for when we say1 ,all men are mortal1 we simply mean to affirm the attribute mortality of all men2 without thinking at all of the class mortal in the concrete1 or troubling ourselves about whether it contains any other beings or not4 ,it is only for some artificial purpose that we ever look at the proposition in the aspect in which the predicate also is thought of as a class-name1 either including the subject only1 or the subject and something more4 7,see above1 p4 #gg1 #gh47 ,for a fuller discussion of this subject1 see the twenty-second chapter of a work already referred to1 8,an ,examination of ,sir ,william ,hamilton's ,philosophy40 #ec ,mr4 ,herbert ,spencer 7,principles of ,psychology1 pp4 #abe-g71 though his theory of the syllogism coincides with all that is essential of mine1 thinks it a logical fallacy to present the two axioms in the text1 as the regulating principles of syllogism4 ,he charges me with falling into the error pointed out by ,archbishop ,whately and myself1 of confounding exact likeness with literal identity2 and maintains1 that we ought not to say that ,socrates possesses the same attributes which are connoted by the word ,man1 but only that he possesses attributes exactly like them3 according to which phraseology1 ,socrates1 and the attribute mortality1 are not two things co-existing with the same thing1 as the axiom asserts1 but two things coexisting with two different things4 ,the question between ,mr4 ,spencer and me is merely one of language2 for neither of us 7if ,i understand ,mr4 ,spencer's opinions rightly7 believes an attribute to be a real thing1 possessed of objective existence2 we believe it to be a particular mode of naming our sensations1 or our expectations of sensation1 when looked at in their relation to an external object which excites them4 ,the question raised by ,mr4 ,spencer does not1 therefore1 concern the properties of any really existing thing1 but the comparative appropriateness1 for philosophical purposes1 of two different modes of using a name4 ,considered in this point of view1 the phraseology ,i have employed1 which is that commonly used by philosophers1 seems to me to be the best4 ,mr4 ,spencer is of opinion that because ,socrates and ,alcibiades are not the same man1 the attribute which constitutes them men should not be called the same attribute2 that because the humanity of one man and that of another express themselves to our senses not by the same individual sensations but by sensations exactly alike1 humanity ought to be regarded as a different attribute in every different man4 ,but on this showing1 the humanity even of any one man should be considered as different attributes now and half an hour hence2 for the sensations by which it will then manifest itself to my organs will not be a continuation of my present sensations1 but a repetition of them2 fresh sensations1 not identical with1 but only exactly like the present4 ,if every general conception1 instead of being 8the ,one in the ,many10 were considered to be as many different conceptions as there are things to which it is applicable1 there would be no such thing as general language4 ,a name would have no general meaning if man connoted one thing when predicated of ,john1 and another1 though closely resembling1 thing when predicated of ,william4 ,accordingly a recent pamphlet asserts the impossibility of general knowledge on this precise ground4 ,the meaning of any general name is some outward or inward phenomenon1 consisting1 in the last resort1 of feelings2 and these feelings1 if their continuity is for an instant broken1 are no longer the same feelings1 in the sense of individual identity4 ,what1 then1 is the common something which gives a meaning to the general name8 ,mr4 ,spencer can only say1 it is the similarity of the feelings2 and ,i rejoin1 the attribute is precisely that similarity4 ,the names of attributes are in their ultimate analysis names for the resemblances of our sensations 7or other feelings74 ,every general name1 whether abstract or concrete1 denotes or connotes one or more of those resemblances4 ,it will not1 probably1 be denied1 that if a hundred sensations are undistinguishably alike1 their resemblance ought to be spoken of as one resemblance1 and not a hundred resemblances which merely resemble one another4 ,the things compared are many1 but the something common to all of them must be conceived as one1 just as the name is conceived as one1 though corresponding to numerically different sensations of sound each time it is pronounced4 ,the general term man does not connote the sensations derived once from one man1 which1 once gone1 can no more occur again than the same flash of lightning4 ,it connotes the general type of the sensations derived always from all men1 and the power 7always thought of as one7 of producing sensations of that type4 ,and the axiom might be thus worded3 ,two types of sensation each of which co-exists with a third type1 co-exist with another2 or ,two powers each of which co-exists with a third power co-exist with one another4 ,mr4 ,spencer has misunderstood me in another particular4 ,he supposes that the co-existence spoken of in the axiom1 of two things with the same third thing1 means simultaneousness in time4 ,the co-existence meant is that of being jointly attributes of the same subject4 ,the attribute of being born without teeth1 and the attribute of having thirty-two teeth in mature age1 are in this sense co-existent1 both being attributes of man1 though ex vi termini never of the same man at the same time4 #ed ,supra1 p4 #ic4 #ee ,professor ,bain 7,logic1 i41 #aeg7 considers the axiom 7or rather axioms7 here proposed as a substitute for the dictum de omni1 to possess certain advantages1 but to be 8unworkable as a basis of the syllogism4 ,the fatal defect consists in this1 that it is ill-adapted to bring out the difference between total and partial coincidence of terms1 the observation of which is the essential precaution in syllogizing correctly4 ,if all the terms were co-extensive1 the axiom would flow on admirably2 ,a carries ,b1 all ,b and none but ,b2 ,b carries ,c in the same manner2 at once ,a carries ,c1 without limitation or reserve4 ,but in point of fact1 we know that while ,a carries ,b1 other things carry ,b also2 whence a process of limitation is required1 in transferring ,a to ,c through ,b4 ,a 7in common with other things7 carries ,b2 ,b 7in common with other things7 carries ,c2 whence ,a 7in common with other things7 carries ,c4 ,the axiom provides no means of making this limitation2 if we were to follow ,a literally1 we should be led to suppose ,a and ,c co-extensive3 for such is the only obvious meaning of #8the attribute ,a coincides with the attribute ,c4'0 ,it is certainly possible that a careless learner here and there may suppose that if ,a carries ,b1 it follows that ,b carries ,a4 ,but if any one is so incautious as to commit this mistake1 the very earliest lesson in the logic of inference1 the ,conversion of propositions1 will correct it4 ,the first of the two forms in which ,i have stated the axiom1 is in some degree open to ,mr4 ,bain's criticism3 when ,b is said to co-exist with ,a 7it must be by a lapsus calami that ,mr4 ,bain uses the word coincide71 it is possible1 in the absence of warning1 to suppose the meaning to be that the two things are only found together4 ,but this misinterpretation is excluded by the other1 or practical1 form of the maxim2 ,nota not est nota rei ipsius4 ,no one would be in any danger of inferring that because a is a mark of b1 b can never exist without a2 that because being in a confirmed consumption is a mark of being about to die1 no one dies who is not in a consumption2 that because being coal is a mark of having come out of the earth1 nothing can come out of the earth except coal4 ,ordinary knowledge of ,english seems a sufficient protection against these mistakes1 since in speaking of a mark of any thing we are never understood as implying reciprocity4 ,a more fundamental objection is stated by ,mr4 ,bain in a subsequent passage 7p4 #aeh74 8,the axiom does not accommodate itself to the type of ,deductive ,reasoning as contrasted with ,induction--the application of a general principle to a special case4 ,any thing that fails to make prominent this circumstance is not adapted as a foundation for the syllogism40 ,but though it may be proper to limit the term ,deduction to the application of a general principle to a special case1 it has never been held that ,ratiocination or ,syllogism is subject to the same limitation2 and the adoption of it would exclude a great amount of valid and conclusive syllogistic reasoning4 ,moreover1 if the dictum de omni makes prominent the fact of the application of a general principle to a particular case1 the axiom ,i propose makes prominent the condition which alone makes that application a real inference4 ,i conclude1 therefore1 that both forms have their value1 and their place in ,logic4 ,the dictum de omni should be retained as the fundamental axiom of the logic of mere consistency1 often called ,formal ,logic2 nor have ,i ever quarreled with the use of it in that character1 nor proposed to banish it from treatises on ,formal ,logic4 ,but the other is the proper axiom for the logic of the pursuit of truth by way of ,deduction2 and the recognition of it can alone show how it is possible that deductive reasoning can be a road to truth4 #ef ,logic1 p4 #bci 7#ith ed474 #eg ,it is hardly necessary to say1 that ,i am not contending for any such absurdity as that we actually 8ought to have known0 and considered the case of every individual man1 past1 present1 and future1 before affirming that all men are mortal3 although this interpretation has been1 strangely enough1 put upon the preceding observations4 ,there is no difference between me and ,archbishop ,whately1 or any other defender of the syllogism1 on the practical part of the matter2 ,i am only pointing out an inconsistency in the logical theory of it1 as conceived by almost all writers4 ,i do not say that a person who affirmed1 before the ,duke of ,wellington was born1 that all men are mortal1 knew that the ,duke of ,wellington was mortal2 but ,i do say that he asserted it2 and ,i ask for an explanation of the apparent logical fallacy1 of adducing in proof of the ,duke of ,wellington's mortality1 a general statement which presupposes it4 ,finding no sufficient resolution of this difficulty in any of the writers on ,logic1 ,i have attempted to supply one4 #eh ,the language of ratiocination would1 ,i think1 be brought into closer agreement with the real nature of the process1 if the general propositions employed in reasoning1 instead of being in the form ,all men are mortal1 or ,every man is mortal1 were expressed in the form ,any man is mortal4 ,this mode of expression1 exhibiting as the type of all reasoning from experience 8,the men ,a1 ,b1 ,c1 etc41 are so and so1 therefore any man is so and so10 would much better manifest the true idea--that inductive reasoning is always1 at bottom1 inference from particulars to particulars1 and that the whole function of general propositions in reasoning1 is to vouch for the legitimacy of such inferences4 #ei ,review of ,quetelet on ,probabilities1 ,essays1 p4 #cfg4 #fj ,philosophy of ,discovery1 p4 #bhi4 #fa ,theory of ,reasoning1 chap4 iv41 to which ,i may refer for an able statement and enforcement of the grounds of the doctrine4 #fb ,on a recent careful reperusal of ,berkeley's whole works1 ,i have been unable to find this doctrine in them4 ,sir ,john ,herschel probably meant that it is implied in ,berkeley's argument against abstract ideas4 ,but ,i can not find that ,berkeley saw the implication1 or had ever asked himself what bearing his argument had on the theory of the syllogism4 ,still less can ,i admit that the doctrine is 7as has been affirmed by one of my ablest and most candid critics7 8among the standing marks of what is called the empirical philosophy40 #fc ,logic1 book iv41 chap4 i41 sect4 #a4 #fd ,see the important chapter on ,belief1 in ,professor ,bain's great treatise1 ,the ,emotions and the ,will1 pp4 #eha-d4 #fe ,a writer in the 8,british ,quarterly ,review0 7,august1 #ahdf71 in a review of this treatise1 endeavors to show that there is no petitio principii in the syllogism1 by denying that the proposition1 ,all men are mortal1 asserts or assumes that ,socrates is mortal4 ,in support of this denial1 he argues that we may1 and in fact do1 admit the general proposition that all men are mortal1 without having particularly examined the case of ,socrates1 and even without knowing whether the individual so named is a man or something else4 ,but this of course was never denied4 ,that we can and do draw conclusions concerning cases specifically unknown to us1 is the datum from which all who discuss this subject must set out4 ,the question is1 in what terms the evidence1 or ground1 on which we draw these conclusions1 may best be designated--whether it is most correct to say1 that the unknown case is proved by known cases1 or that it is proved by a general proposition including both sets of cases1 the unknown and the known8 ,i contend for the former mode of expression4 ,i hold it an abuse of language to say1 that the proof that ,socrates is mortal1 is that all men are mortal4 ,turn it in what way we will1 this seems to me to be asserting that a thing is the proof of itself4 ,whoever pronounces the words1 ,all men are mortal1 has affirmed that ,socrates is mortal1 though he may never have heard of ,socrates2 for since ,socrates1 whether known to be so or not1 really is a man1 he is included in the words1 ,all men1 and in every assertion of which they are the subject4 ,if the reviewer does not see that there is a difficulty here1 ,i can only advise him to reconsider the subject until he does3 after which he will be a better judge of the success or failure of an attempt to remove the difficulty4 ,that he had reflected very little on the point when he wrote his remarks1 is shown by his oversight respecting the dictum de omni et nullo4 ,he acknowledges that this maxim as commonly expressed--8,whatever is true of a class1 is true of every thing included in the class10 is a mere identical proposition1 since the class is nothing but the things included in it4 ,but he thinks this defect would be cured by wording the maxim thus--8,whatever is true of a class1 is true of every thing which can be shown to be a member of the class30 as if a thing could 8be shown0 to be a member of the class without being one4 ,if a class means the sum of all the things included in the class1 the things which can 8be shown0 to be included in it are part of the sum1 and the dictum is as much an identical proposition with respect to them as to the rest4 ,one would almost imagine that1 in the reviewer's opinion1 things are not members of a class until they are called up publicly to take their place in it--that so long1 in fact1 as ,socrates is not known to be a man1 he is not a man1 and any assertion which can be made concerning men does not at all regard him1 nor is affected as to its truth or falsity by any thing in which he is concerned4 ,the difference between the reviewer's theory and mine may be thus stated4 ,both admit that when we say1 ,all men are mortal1 we make an assertion reaching beyond the sphere of our knowledge of individual cases2 and that when a new individual1 ,socrates1 is brought within the field of our knowledge by means of the minor premise1 we learn that we have already made an assertion respecting ,socrates without knowing it3 our own general formula being1 to that extent1 for the first time interpreted to us4 ,but according to the reviewer's theory1 the smaller assertion is proved by the larger3 while ,i contend1 that both assertions are proved together1 by the same evidence1 namely1 the grounds of experience on which the general assertion was made1 and by which it must be justified4 ,the reviewer says1 that if the major premise included the conclusion1 8we should be able to affirm the conclusion without the intervention of the minor premise2 but every one sees that that is impossible40 ,a similar argument is urged by ,mr4 ,de ,morgan 7,formal ,logic1 p4 #bei73 8,the whole objection tacitly assumes the superfluity of the minor2 that is1 tacitly assumes we know ,socrates 7,mr4 ,de ,morgan says #8,plato1' but to prevent confusion ,i have kept to my own exemplum47 to be a man as soon as we know him to be ,socrates40 ,the objection would be well grounded if the assertion that the major premise includes the conclusion1 meant that it individually specifies all it includes4 ,as1 however1 the only indication it gives is a description by marks1 we have still to compare any new individual with the marks2 and to show that this comparison has been made1 is the office of the minor4 ,but since1 by supposition1 the new individual has the marks1 whether we have ascertained him to have them or not2 if we have affirmed the major premise1 we have asserted him to be mortal4 ,now my position is that this assertion can not be a necessary part of the argument4 ,it can not be a necessary condition of reasoning that we should begin by making an assertion1 which is afterward to be employed in proving a part of itself4 ,i can conceive only one way out of this difficulty1 viz41 that what really forms the proof is the other part of the assertion3 the portion of it1 the truth of which has been ascertained previously3 and that the unproved part is bound up in one formula with the proved part in mere anticipation1 and as a memorandum of the nature of the conclusions which we are prepared to prove4 ,with respect to the minor premise in its formal shape1 the minor as it stands in the syllogism1 predicating of ,socrates a definite class name1 ,i readily admit that it is no more a necessary part of reasoning than the major4 ,when there is a major1 doing its work by means of a class name1 minors are needed to interpret it3 but reasoning can be carried on without either the one or the other4 ,they are not the conditions of reasoning1 but a precaution against erroneous reasoning4 ,the only minor premise necessary to reasoning in the example under consideration1 is1 ,socrates is like ,a1 ,b1 ,c1 and the other individuals who are known to have died4 ,and this is the only universal type of that step in the reasoning process which is represented by the minor4 ,experience1 however1 of the uncertainty of this loose mode of inference1 teaches the expediency of determining beforehand what kind of likeness to the cases observed1 is necessary to bring an unobserved case within the same predicate2 and the answer to this question is the major4 ,the minor then identifies the precise kind of likeness possessed by ,socrates1 as being the kind required by the formula4 ,thus the syllogistic major and the syllogistic minor start into existence together1 and are called forth by the same exigency4 ,when we conclude from personal experience without referring to any record--to any general theorems1 either written1 or traditional1 or mentally registered by ourselves as conclusions of our own drawing--we do not use1 in our thoughts1 either a major or a minor1 such as the syllogism puts into words4 ,when1 however1 we revise this rough inference from particulars to particulars1 and substitute a careful one1 the revision consists in selecting two syllogistic premises4 ,but this neither alters nor adds to the evidence we had before2 it only puts us in a better position for judging whether our inference from particulars to particulars is well grounded4 #ff ,infra1 book iii41 chap4 ii4 #fg ,infra1 book iii41 ch4 iv41 #c1 and elsewhere4 #fh ,it is justly remarked by ,professor ,bain 7,logic1 ii41 #acd7 that the word ,hypothesis is here used in a somewhat peculiar sense4 ,an hypothesis1 in science1 usually means a supposition not proved to be true1 but surmised to be so1 because if true it would account for certain known facts2 and the final result of the speculation may be to prove its truth4 ,the hypotheses spoken of in the text are of a different character2 they are known not to be literally true1 while as much of them as is true is not hypothetical1 but certain4 ,the two cases1 however1 resemble in the circumstance that in both we reason1 not from a truth1 but from an assumption1 and the truth therefore of the conclusions is conditional1 not categorical4 ,this suffices to justify1 in point of logical propriety1 ,stewart's use of the term4 ,it is of course needful to bear in mind that the hypothetical element in the definitions of geometry is the assumption that what is very nearly true is exactly so4 ,this unreal exactitude might be called a fiction1 as properly as an hypothesis2 but that appellation1 still more than the other1 would fail to point out the close relation which exists between the fictitious point or line and the points and lines of which we have experience4 #fi ,mechanical ,euclid1 pp4 #adi et seqq4 #gj ,we might1 it is true1 insert this property into the definition of parallel lines1 framing the definition so as to require1 both that when produced indefinitely they shall never meet1 and also that any straight line which intersects one of them shall1 if prolonged1 meet the other4 ,but by doing this we by no means get rid of the assumption2 we are still obliged to take for granted the geometrical truth1 that all straight lines in the same plane1 which have the former of these properties1 have also the latter4 ,for if it were possible that they should not1 that is1 if any straight lines in the same plane1 other than those which are parallel according to the definition1 had the property of never meeting although indefinitely produced1 the demonstrations of the subsequent portions of the theory of parallels could not be maintained4 #ga ,some persons find themselves prevented from believing that the axiom1 ,two straight lines can not inclose a space1 could ever become known to us through experience1 by a difficulty which may be stated as follows3 ,if the straight lines spoken of are those contemplated in the definition--lines absolutely without breadth and absolutely straight--that such are incapable of inclosing a space is not proved by experience1 for lines such as these do not present themselves in our experience4 ,if1 on the other hand1 the lines meant are such straight lines as we do meet with in experience1 lines straight enough for practical purposes1 but in reality slightly zigzag1 and with some1 however trifling1 breadth2 as applied to these lines the axiom is not true1 for two of them may1 and sometimes do1 inclose a small portion of space4 ,in neither case1 therefore1 does experience prove the axiom4 ,those who employ this argument to show that geometrical axioms can not be proved by induction1 show themselves unfamiliar with a common and perfectly valid mode of inductive proof2 proof by approximation4 ,though experience furnishes us with no lines so unimpeachably straight that two of them are incapable of inclosing the smallest space1 it presents us with gradations of lines possessing less and less either of breadth or of flexure1 of which series the straight line of the definition is the ideal limit4 ,and observation shows that just as much1 and as nearly1 as the straight lines of experience approximate to having no breadth or flexure1 so much and so nearly does the space-inclosing power of any two of them approach to zero4 ,the inference that if they had no breadth or flexure at all1 they would inclose no space at all1 is a correct inductive inference from these facts1 conformable to one of the four ,inductive ,methods hereinafter characterized1 the ,method of ,concomitant ,variations2 of which the mathematical ,doctrine of ,limits presents the extreme case4 #gb ,whewell's ,history of ,scientific ,ideas1 i41 #adj4 #gc ,dr4 ,whewell 7,philosophy of ,discovery1 p4 #bhi7 thinks it unreasonable to contend that we know by experience1 that our idea of a line exactly resembles a real line4 8,it does not appear10 he says1 8how we can compare our ideas with the realities1 since we know the realities only by our ideas40 ,we know the realities by our sensations4 ,dr4 ,whewell surely does not hold the 8doctrine of perception by means of ideas10 which ,reid gave himself so much trouble to refute4 ,if ,dr4 ,whewell doubts whether we compare our ideas with the corresponding sensations1 and assume that they resemble1 let me ask on what evidence do we judge that a portrait of a person not present is like the original4 ,surely because it is like our idea1 or mental image of the person1 and because our idea is like the man himself4 ,dr4 ,whewell also says1 that it does not appear why this resemblance of ideas to the sensations of which they are copies1 should be spoken of as if it were a peculiarity of one class of ideas1 those of space4 ,my reply is1 that ,i do not so speak of it4 ,the peculiarity ,i contend for is only one of degree4 ,all our ideas of sensation of course resemble the corresponding sensations1 but they do so with very different degrees of exactness and of reliability4 ,no one1 ,i presume1 can recall in imagination a color or an odor with the same distinctness and accuracy with which almost every one can mentally reproduce an image of a straight line or a triangle4 ,to the extent1 however1 of their capabilities of accuracy1 our recollections of colors or of odors may serve as subjects of experimentation1 as well as those of lines and spaces1 and may yield conclusions which will be true of their external prototypes4 ,a person in whom1 either from natural gift or from cultivation1 the impressions of color were peculiarly vivid and distinct1 if asked which of two blue flowers was of the darkest tinge1 though he might never have compared the two1 or even looked at them together1 might be able to give a confident answer on the faith of his distinct recollection of the colors2 that is1 he might examine his mental pictures1 and find there a property of the outward objects4 ,but in hardly any case except that of simple geometrical forms1 could this be done by mankind generally1 with a degree of assurance equal to that which is given by a contemplation of the objects themselves4 ,persons differ most widely in the precision of their recollection1 even of forms3 one person1 when he has looked any one in the face for half a minute1 can draw an accurate likeness of him from memory2 another may have seen him every day for six months1 and hardly know whether his nose is long or short4 ,but every body has a perfectly distinct mental image of a straight line1 a circle1 or a rectangle4 ,and every one concludes confidently from these mental images to the corresponding outward things4 ,the truth is1 that we may1 and continually do1 study nature in our recollections1 when the objects themselves are absent2 and in the case of geometrical forms we can perfectly1 but in most other cases only imperfectly1 trust our recollections4 #gd ,logic1 i41 #bbb4 #ge ,ibid41 #bbf4 #gf ,history of ,scientific ,ideas1 i41 #fe-fg4 #gg ,ibid41 i41 #fj4 #gh ,ibid41 #eh1 #ei4 #gi 8,if all mankind had spoken one language1 we can not doubt that there would have been a powerful1 perhaps a universal1 school of philosophers1 who would have believed in the inherent connection between names and things1 who would have taken the sound man to be the mode of agitating the air which is essentially communicative of the ideas of reason1 cookery1 bipedality1 etc40--,de ,morgan1 ,formal ,logic1 p4 #bdf4 #hj ,it would be difficult to name a man more remarkable at once for the greatness and the wide range of his mental accomplishments1 than ,leibnitz4 ,yet this eminent man gave as a reason for rejecting ,newton's scheme of the solar system1 that ,god could not make a body revolve round a distant centre1 unless either by some impelling mechanism1 or by miracle3 8,tout ce qui n'est pas explicable10 says he in a letter to the ,abb ,conti1 8par la nature des cratures1 est miraculeux4 ,il ne suffit pas de dire3 ,dieu a fait une telle loi de nature2 donc la chose est naturelle4 ,il faut que la loi soit excutable par les natures des cratures4 ,si ,dien donnait cette loi1 par exemple1 un corps libre1 de tourner l'entour d'un certain centre1 il faudrait ou qu'il y joignt d'autres corps qui par leur impulsion l'obligeassent de rester toujours dans son orbite circulaire1 ou qu'il mt un ange ses trousses1 ou enfin il faudrait qu'il y concourt extraordinairement2 car naturellement il s'cartera par la tangente40--,works of ,leibnitz1 ed4 ,dutens1 iii41 #ddf4 #ha ,novum ,organum ,renovatum1 pp4 #cb1 #cc4 #hb ,history of ,scientific ,ideas1 i41 #bfd4 #hc ,ibid41 i41 #bfc4 #hd ,ibid41 #bdj4 #he ,hist4 ,scientific ,ideas1 ii41 #be1 #bf4 #hf ,phil4 of ,disc41 p4 #cci4 #hg ,phil4 of ,disc41 p4 #cch4 #hh ,ibid41 p4 #dfc4 #hi ,phil4 of ,disc41 pp4 #dgb1 #dgc4 #ij ,the ,quarterly ,review for ,june1 #ahda1 contained an article of great ability on ,dr4 ,whewell's two great works 7since acknowledged and reprinted in ,sir ,john ,herschel's ,essays7 which maintains1 on the subject of axioms1 the doctrine advanced in the text1 that they are generalizations from experience1 and supports that opinion by a line of argument strikingly coinciding with mine4 ,when ,i state that the whole of the present chapter 7except the last four pages1 added in the fifth edition7 was written before ,i had seen the article 7the greater part1 indeed1 before it was published71 it is not my object to occupy the reader's attention with a matter so unimportant as the degree of originality which may or may not belong to any portion of my own speculations1 but to obtain for an opinion which is opposed to reigning doctrines1 the recommendation derived from a striking concurrence of sentiment between two inquirers entirely independent of one another4 ,i embrace the opportunity of citing from a writer of the extensive acquirements in physical and metaphysical knowledge and the capacity of systematic thought which the article evinces1 passages so remarkably in unison with my own views as the following3 8,the truths of geometry are summed up and embodied in its definitions and axioms4444 ,let us turn to the axioms1 and what do we find8 ,a string of propositions concerning magnitude in the abstract1 which are equally true of space1 time1 force1 number1 and every other magnitude susceptible of aggregation and subdivision4 ,such propositions1 where they are not mere definitions1 as some of them are1 carry their inductive origin on the face of their enunciation4444 ,those which declare that two straight lines can not inclose a space1 and that two straight lines which cut one another can not both be parallel to a third1 are in reality the only ones which express characteristic properties of space1 and these it will be worth while to consider more nearly4 ,now the only clear notion we can form of straightness is uniformity of direction1 for space in its ultimate analysis is nothing but an assemblage of distances and directions4 ,and 7not to dwell on the notion of continued contemplation1 i4e41 mental experience1 as included in the very idea of uniformity2 nor on that of transfer of the contemplating being from point to point1 and of experience1 during such transfer1 of the homogeneity of the interval passed over7 we can not even propose the proposition in an intelligible form to any one whose experience ever since he was born has not assured him of the fact4 ,the unity of direction1 or that we can not march from a given point by more than one path direct to the same object1 is matter of practical experience long before it can by possibility become matter of abstract thought4 ,we can not attempt mentally to exemplify the conditions of the assertion in an imaginary case opposed to it1 without violating our habitual recollection of this experience1 and defacing our mental picture of space as grounded on it4 ,what but experience1 we may ask1 can possibly assure us of the homogeneity of the parts of distance1 time1 force1 and measurable aggregates in general1 on which the truth of the other axioms depends8 ,as regards the latter axiom1 after what has been said it must be clear that the very same course of remarks equally applies to its case1 and that its truth is quite as much forced on the mind as that of the former by daily and hourly experience1 444 including always1 be it observed1 in our notion of experience1 that which is gained by contemplation of the inward picture which the mind forms to itself in any proposed case1 or which it arbitrarily selects as an example--such picture1 in virtue of the extreme simplicity of these primary relations1 being called up by the imagination with as much vividness and clearness as could be done by any external impression1 which is the only meaning we can attach to the word intuition1 as applied to such relations40 ,and again1 of the axioms of mechanics3 8,as we admit no such propositions1 other than as truths inductively collected from observation1 even in geometry itself1 it can hardly be expected that1 in a science of obviously contingent relations1 we should acquiesce in a contrary view4 ,let us take one of these axioms and examine its evidence3 for instance1 that equal forces perpendicularly applied at the opposite ends of equal arms of a straight lever will balance each other4 ,what but experience1 we may ask1 in the first place1 can possibly inform us that a force so applied will have any tendency to turn the lever on its centre at all8 or that force can be so transmitted along a rigid line perpendicular to its direction1 as to act elsewhere in space than along its own line of action8 ,surely this is so far from being self-evident that it has even a paradoxical appearance1 which is only to be removed by giving our lever thickness1 material composition1 and molecular powers4 ,again1 we conclude1 that the two forces1 being equal and applied under precisely similar circumstances1 must1 if they exert any effort at all to turn the lever1 exert equal and opposite efforts3 but what a priori reasoning can possibly assure us that they do act under precisely similar circumstances8 that points which differ in place are similarly circumstanced as regards the exertion of force8 that universal space may not have relations to universal force--or1 at all events1 that the organization of the material universe may not be such as to place that portion of space occupied by it in such relations to the forces exerted in it1 as may invalidate the absolute similarity of circumstances assumed8 ,or we may argue1 what have we to do with the notion of angular movement in the lever at all8 ,the case is one of rest1 and of quiescent destruction of force by force4 ,now how is this destruction effected8 ,assuredly by the counter-pressure which supports the fulcrum4 ,but would not this destruction equally arise1 and by the same amount of counteracting force1 if each force simply pressed its own half of the lever against the fulcrum8 ,and what can assure us that it is not so1 except removal of one or other force1 and consequent tilting of the lever8 ,the other fundamental axiom of statics1 that the pressure on the point of support is the sum of the weights 444 is merely a scientific transformation and more refined mode of stating a coarse and obvious result of universal experience1 viz41 that the weight of a rigid body is the same1 handle it or suspend it in what position or by what point we will1 and that whatever sustains it sustains its total weight4 ,assuredly1 as ,mr4 ,whewell justly remarks1 #8,no one probably ever made a trial for the purpose of showing that the pressure on the support is equal to the sum of the weights4' 444 ,but it is precisely because in every action of his life from earliest infancy he has been continually making the trial1 and seeing it made by every other living being about him1 that he never dreams of staking its result on one additional attempt made with scientific accuracy4 ,this would be as if a man should resolve to decide by experiment whether his eyes were useful for the purpose of seeing1 by hermetically sealing himself up for half an hour in a metal case40 ,on the 8paradox of universal propositions obtained by experience10 the same writer says3 8,if there be necessary and universal truths expressible in propositions of axiomatic simplicity and obviousness1 and having for their subject-matter the elements of all our experience and all our knowledge1 surely these are the truths which1 if experience suggest to us any truths at all1 it ought to suggest most readily1 clearly1 and unceasingly4 ,if it were a truth1 universal and necessary1 that a net is spread over the whole surface of every planetary globe1 we should not travel far on our own without getting entangled in its meshes1 and making the necessity of some means of extrication an axiom of locomotion4444 ,there is1 therefore1 nothing paradoxical1 but the reverse1 in our being led by observation to a recognition of such truths1 as general propositions1 co-extensive at least with all human experience4 ,that they pervade all the objects of experience1 must insure their continual suggestion by experience2 that they are true1 must insure that consistency of suggestion1 that iteration of uncontradicted assertion1 which commands implicit assent1 and removes all occasion of exception2 that they are simple1 and admit of no misunderstanding1 must secure their admission by every mind40 8,a truth1 necessary and universal1 relative to any object of our knowledge1 must verify itself in every instance where that object is before our contemplation1 and if at the same time it be simple and intelligible1 its verification must be obvious4 ,the sentiment of such a truth can not1 therefore1 but be present to our minds whenever that object is contemplated1 and must therefore make a part of the mental picture or idea of that object which we may on any occasion summon before our imagination4444 ,all propositions1 therefore1 become not only untrue but inconceivable1 if 444 axioms be violated in their enunciation40 ,another eminent mathematician had previously sanctioned by his authority the doctrine of the origin of geometrical axioms in experience4 8,geometry is thus founded likewise on observation2 but of a kind so familiar and obvious1 that the primary notions which it furnishes might seem intuitive40--,sir ,john ,leslie1 quoted by ,sir ,william ,hamilton1 ,discourses1 etc41 p4 #bgb4 #ia ,principles of ,psychology4 #ib ,mr4 ,spencer is mistaken in supposing me to claim any peculiar 8necessity0 for this axiom as compared with others4 ,i have corrected the expressions which led him into that misapprehension of my meaning4 #ic ,mr4 ,spencer1 in recently returning to the subject 7,principles of ,psychology1 new edition1 chap4 xii43 8,the ,test of ,relative ,validity071 makes two answers to the preceding remarks4 ,one is3 8,were an argument formed by repeating the same proposition over and over again1 it would be true that any intrinsic fallibility of the postulate would not make the conclusion more untrustworthy than the first step4 ,but an argument consists of unlike propositions4 ,now1 since ,mr4 ,mill's criticism on the ,universal ,postulate is that in some cases1 which he names1 it has proved to be an untrustworthy test2 it follows that in any argument consisting of heterogeneous propositions1 there is a risk1 increasing as the number of propositions increases1 that some one of them belongs to this class of cases1 and is wrongly accepted because of the inconceivableness of its negation40 ,no doubt3 but this supposes new premises to be taken in4 ,the point we are discussing is the fallibility not of the premises1 but of the reasoning1 as distinguished from the premises4 ,now the validity of the reasoning depends always upon the same axiom1 repeated 7in thought7 8over and over again10 viz41 that whatever has a mark1 has what it is a mark of4 ,even1 therefore1 on the assumption that this axiom rests ultimately on the ,universal ,postulate1 and that1 the ,postulate not being wholly trustworthy1 the axiom may be one of the cases of its failure2 all the risk there is of this is incurred at the very first step of the reasoning1 and is not added to1 however long may be the series of subsequent steps4 ,i am here arguing1 of course1 from ,mr4 ,spencer's point of view4 ,from my own the case is still clearer2 for1 in my view1 the truth that whatever has a mark has what it is a mark of1 is wholly trustworthy1 and derives none of its evidence from so very untrustworthy a test as the inconceivability of the negative4 ,mr4 ,spencer's second answer is valid up to a certain point2 it is1 that every prolongation of the process involves additional chances of casual error1 from carelessness in the reasoning operation4 ,this is an important consideration in the private speculations of an individual reasoner2 and even with respect to mankind at large1 it must be admitted that1 though mere oversights in the syllogistic process1 like errors of addition in an account1 are special to the individual1 and seldom escape detection1 confusion of thought produced 7for example7 by ambiguous terms has led whole nations or ages to accept fallacious reasoning as valid4 ,but this very fact points to causes of error so much more dangerous than the mere length of the process1 as quite to vitiate the doctrine that the 8test of the relative validities of conflicting conclusions0 is the number of times the fundamental postulate is involved4 ,on the contrary1 the subjects on which the trains of reasoning are longest1 and the assumption1 therefore1 oftenest repeated1 are in general those which are best fortified against the really formidable causes of fallacy2 as in the example already given of mathematics4 #id ,mr4 ,spencer makes a distinction between conceiving myself looking into darkness1 and conceiving that ,i am then and there looking into darkness4 ,to me it seems that this change of the expression to the form ,i am1 just marks the transition from conception to belief1 and that the phrase 8to conceive that ,i am10 or 8that any thing is10 is not consistent with using the word conceive in its rigorous sense4 #ie ,i have myself accepted the contest1 and fought it out on this battle-ground1 in the eleventh chapter of ,an ,examination of ,sir ,william ,hamilton's ,philosophy4 #if ,chap4 xi4 #ig ,in one of the three cases1 ,mr4 ,spencer1 to my no small surprise1 thinks that the belief of mankind 8can not be rightly said to have undergone0 the change ,i allege4 ,mr4 ,spencer himself still thinks we are unable to conceive gravitation acting through empty space4 8,if an astronomer avowed that he could conceive gravitative force as exercised through space absolutely void1 my private opinion would be that he mistook the nature of conception4 ,conception implies representation4 ,here the elements of the representation are the two bodies and an agency by which either affects the other4 ,to conceive this agency is to represent it in some terms derived from our experiences--that is1 from our sensations4 ,as this agency gives us no sensations1 we are obliged 7if we try to conceive it7 to use symbols idealized from our sensations--imponderable units forming a medium40 ,if ,mr4 ,spencer means that the action of gravitation gives us no sensations1 the assertion is one than which ,i have not seen1 in the writings of philosophers1 many more startling4 ,what other sensation do we need than the sensation of one body moving toward another8 8,the elements of the representation0 are not two bodies and an 8agency10 but two bodies and an effect2 viz41 the fact of their approaching one another4 ,if we are able to conceive a vacuum1 is there any difficulty in conceiving a body falling to the earth through it8 #ih ,discussions1 etc41 #b;d ed41 p4 #fbd4 #ii ,professor ,bain 7,logic1 i41 #af7 identifies the ,principle of ,contradiction with his ,law of ,relativity1 viz41 that 8every thing that can be thought of1 every affirmation that can be made1 has an opposite or counter notion or affirmation20 a proposition which is one of the general results of the whole body of human experience4 ,for further considerations respecting the axioms of ,contradiction and ,excluded ,middle1 see the twenty-first chapter of ,an ,examination of ,sir ,william ,hamilton's ,philosophy4 #ajj ,dr4 ,whewell thinks it improper to apply the term ,induction to any operation not terminating in the establishment of a general truth4 ,induction1 he says 7,philosophy of ,discovery1 p4 #bde71 8is not the same thing as experience and observation4 ,induction is experience or observation consciously looked at in a general form4 ,this consciousness and generality are necessary parts of that knowledge which is science40 ,and he objects 7p4 #bda7 to the mode in which the word ,induction is employed in this work1 as an undue extension of that term 8not only to the cases in which the general induction is consciously applied to a particular instance1 but to the cases in which the particular instance is dealt with by means of experience in that rude sense in which experience can be asserted of brutes1 and in which of course we can in no way imagine that the law is possessed or understood as a general proposition40 ,this use of the term he deems a 8confusion of knowledge with practical tendencies40 ,i disclaim1 as strongly as ,dr4 ,whewell can do1 the application of such terms as induction1 inference1 or reasoning1 to operations performed by mere instinct1 that is1 from an animal impulse1 without the exertion of any intelligence4 ,but ,i perceive no ground for confining the use of those terms to cases in which the inference is drawn in the forms and with the precautions required by scientific propriety4 ,to the idea of ,science1 an express recognition and distinct apprehension of general laws as such1 is essential3 but nine-tenths of the conclusions drawn from experience in the course of practical life1 are drawn without any such recognition3 they are direct inferences from known cases1 to a case supposed to be similar4 ,i have endeavored to show that this is not only as legitimate an operation1 but substantially the same operation1 as that of ascending from known cases to a general proposition2 except that the latter process has one great security for correctness which the former does not possess4 ,in science1 the inference must necessarily pass through the intermediate stage of a general proposition1 because ,science wants its conclusions for record1 and not for instantaneous use4 ,but the inferences drawn for the guidance of practical affairs1 by persons who would often be quite incapable of expressing in unexceptionable terms the corresponding generalizations1 may and frequently do exhibit intellectual powers quite equal to any which have ever been displayed in science2 and if these inferences are not inductive1 what are they8 ,the limitation imposed on the term by ,dr4 ,whewell seems perfectly arbitrary2 neither justified by any fundamental distinction between what he includes and what he desires to exclude1 nor sanctioned by usage1 at least from the time of ,reid and ,stewart1 the principal legislators 7as far as the ,english language is concerned7 of modern metaphysical terminology4 #aja ,supra1 p4 #ade4 #ajb ,novum ,organum ,renovatum1 pp4 #gb1 #gc4 #ajc ,novum ,organum ,renovatum1 p4 #cb4 #ajd ,cours de ,philosophie ,positive1 vol4 ii41 p4 #bjb4 #aje ,dr4 ,whewell1 in his reply1 contests the distinction here drawn1 and maintains1 that not only different descriptions1 but different explanations of a phenomenon1 may all be true4 ,of the three theories respecting the motions of the heavenly bodies1 he says 7,philosophy of ,discovery1 p4 #bca73 8,undoubtedly all these explanations may be true and consistent with each other1 and would be so if each had been followed out so as to show in what manner it could be made consistent with the facts4 ,and this was1 in reality1 in a great measure done4 ,the doctrine that the heavenly bodies were moved by vortices was successfully modified1 so that it came to coincide in its results with the doctrine of an inverse-quadratic centripetal force4444 ,when this point was reached1 the vortex was merely a machinery1 well or ill devised1 for producing such a centripetal force1 and therefore did not contradict the doctrine of a centripetal force4 ,newton himself does not appear to have been averse to explaining gravity by impulse4 ,so little is it true that if one theory be true the other must be false4 ,the attempt to explain gravity by the impulse of streams of particles flowing through the universe in all directions1 which ,i have mentioned in the ,philosophy1 is so far from being inconsistent with the ,newtonian theory1 that it is founded entirely upon it4 ,and even with regard to the doctrine1 that the heavenly bodies move by an inherent virtue2 if this doctrine had been maintained in any such way that it was brought to agree with the facts1 the inherent virtue must have had its laws determined2 and then it would have been found that the virtue had a reference to the central body2 and so1 the #8inherent virtue' must have coincided in its effect with the ,newtonian force2 and then1 the two explanations would agree1 except so far as the word #8inherent' was concerned4 ,and if such a part of an earlier theory as this word inherent indicates1 is found to be untenable1 it is of course rejected in the transition to later and more exact theories1 in ,inductions of this kind1 as well as in what ,mr4 ,mill calls ,descriptions4 ,there is1 therefore1 still no validity discoverable in the distinction which ,mr4 ,mill attempts to draw between descriptions like ,kepler's law of elliptical orbits1 and other examples of induction40 ,if the doctrine of vortices had meant1 not that vortices existed1 but only that the planets moved in the same manner as if they had been whirled by vortices2 if the hypothesis had been merely a mode of representing the facts1 not an attempt to account for them2 if1 in short1 it had been only a ,description2 it would1 no doubt1 have been reconcilable with the ,newtonian theory4 ,the vortices1 however1 were not a mere aid to conceiving the motions of the planets1 but a supposed physical agent1 actively impelling them2 a material fact1 which might be true or not true1 but could not be both true and not true4 ,according to ,descartes's theory it was true1 according to ,newton's it was not true4 ,dr4 ,whewell probably means that since the phrases1 centripetal and projectile force1 do not declare the nature but only the direction of the forces1 the ,newtonian theory does not absolutely contradict any hypothesis which may be framed respecting the mode of their production4 ,the ,newtonian theory1 regarded as a mere description of the planetary motions1 does not2 but the ,newtonian theory as an explanation of them does4 ,for in what does the explanation consist8 ,in ascribing those motions to a general law which obtains between all particles of matter1 and in identifying this with the law by which bodies fall to the ground4 ,if the planets are kept in their orbits by a force which draws the particles composing them toward every other particle of matter in the solar system1 they are not kept in those orbits by the impulsive force of certain streams of matter which whirl them round4 ,the one explanation absolutely excludes the other4 ,either the planets are not moved by vortices1 or they do not move by a law common to all matter4 ,it is impossible that both opinions can be true4 ,as well might it be said that there is no contradiction between the assertions1 that a man died because somebody killed him1 and that he died a natural death4 ,so1 again1 the theory that the planets move by a virtue inherent in their celestial nature1 is incompatible with either of the two others3 either that of their being moved by vortices1 or that which regards them as moving by a property which they have in common with the earth and all terrestrial bodies4 ,dr4 ,whewell says that the theory of an inherent virtue agrees with ,newton's when the word inherent is left out1 which of course it would be 7he says7 if 8found to be untenable40 ,but leave that out1 and where is the theory8 ,the word inherent is the theory4 ,when that is omitted1 there remains nothing except that the heavenly bodies move 8by a virtue10 i4e41 by a power of some sort2 or by virtue of their celestial nature1 which directly contradicts the doctrine that terrestrial bodies fall by the same law4 ,if ,dr4 ,whewell is not yet satisfied1 any other subject will serve equally well to test his doctrine4 ,he will hardly say that there is no contradiction between the emission theory and the undulatory theory of light2 or that there can be both one and two electricities2 or that the hypothesis of the production of the higher organic forms by development from the lower1 and the supposition of separate and successive acts of creation1 are quite reconcilable2 or that the theory that volcanoes are fed from a central fire1 and the doctrines which ascribe them to chemical action at a comparatively small depth below the earth's surface1 are consistent with one another1 and all true as far as they go4 ,if different explanations of the same fact can not both be true1 still less1 surely1 can different predictions4 ,dr4 ,whewell quarrels 7on what ground it is not necessary here to consider7 with the example ,i had chosen on this point1 and thinks an objection to an illustration a sufficient answer to a theory4 ,examples not liable to his objection are easily found1 if the proposition that conflicting predictions can not both be true1 can be made clearer by many examples4 ,suppose the phenomenon to be a newly-discovered comet1 and that one astronomer predicts its return once in every #cjj years--another once in every #djj3 can they both be right8 ,when ,columbus predicted that by sailing constantly westward he should in time return to the point from which he set out1 while others asserted that he could never do so except by turning back1 were both he and his opponents true prophets8 ,were the predictions which foretold the wonders of railways and steamships1 and those which averred that the ,atlantic could never be crossed by steam navigation1 nor a railway train propelled ten miles an hour1 both 7in ,dr4 ,whewell's words7 8true1 and consistent with one another80 ,dr4 ,whewell sees no distinction between holding contradictory opinions on a question of fact1 and merely employing different analogies to facilitate the conception of the same fact4 ,the case of different ,inductions belongs to the former class1 that of different ,descriptions to the latter4 #ajf ,phil4 of ,discov41 p4 #bef4 #ajg ,essays on the ,pursuit of ,truth4 #ajh ,in the first edition a note was appended at this place1 containing some criticism on ,archbishop ,whately's mode of conceiving the relation between ,syllogism and ,induction4 ,in a subsequent issue of his ,logic1 the ,archbishop made a reply to the criticism1 which induced me to cancel part of the note1 incorporating the remainder in the text4 ,in a still later edition1 the ,archbishop observes in a tone of something like disapprobation1 that the objections1 8doubtless from their being fully answered and found untenable1 were silently suppressed10 and that hence he might appear to some of his readers to be combating a shadow4 ,on this latter point1 the ,archbishop need give himself no uneasiness4 ,his readers1 ,i make bold to say1 will fully credit his mere affirmation that the objections have actually been made4 ,but as he seems to think that what he terms the suppression of the objections ought not to have been made 8silently10 ,i now break that silence1 and state exactly what it is that ,i suppressed1 and why4 ,i suppressed that alone which might be regarded as personal criticism on the ,archbishop4 ,i had imputed to him the having omitted to ask himself a particular question4 ,i found that he had asked himself the question1 and could give it an answer consistent with his own theory4 ,i had also1 within the compass of a parenthesis1 hazarded some remarks on certain general characteristics of ,archbishop ,whately as a philosopher4 ,these remarks1 though their tone1 ,i hope1 was neither disrespectful nor arrogant1 ,i felt1 on reconsideration1 that ,i was hardly entitled to make2 least of all1 when the instance which ,i had regarded as an illustration of them1 failed1 as ,i now saw1 to bear them out4 ,the real matter at the bottom of the whole dispute1 the different view we take of the function of the major premise1 remains exactly where it was2 and so far was ,i from thinking that my opinion had been fully 8answered0 and was 8untenable10 that in the same edition in which ,i canceled the note1 ,i not only enforced the opinion by further arguments1 but answered 7though without naming him7 those of the ,archbishop4 ,for not having made this statement before1 ,i do not think it needful to apologize4 ,it would be attaching very great importance to one's smallest sayings1 to think a formal retractation requisite every time that one falls into an error4 ,nor is ,archbishop ,whately's well-earned fame of so tender a quality as to require that in withdrawing a slight criticism on him ,i should have been bound to offer a public amende for having made it4 #aji ,but though it is a condition of the validity of every induction that there be uniformity in the course of nature1 it is not a necessary condition that the uniformity should pervade all nature4 ,it is enough that it pervades the particular class of phenomena to which the induction relates4 ,an induction concerning the motions of the planets1 or the properties of the magnet1 would not be vitiated though we were to suppose that wind and weather are the sport of chance1 provided it be assumed that astronomical and magnetic phenomena are under the dominion of general laws4 ,otherwise the early experience of mankind would have rested on a very weak foundation2 for in the infancy of science it could not be known that all phenomena are regular in their course4 ,neither would it be correct to say that every induction by which we infer any truth1 implies the general fact of uniformity as foreknown1 even in reference to the kind of phenomena concerned4 ,it implies1 either that this general fact is already known1 or that we may now know it3 as the conclusion1 the ,duke of ,wellington is mortal1 drawn from the instances ,a1 ,b1 and ,c1 implies either that we have already concluded all men to be mortal1 or that we are now entitled to do so from the same evidence4 ,a vast amount of confusion and paralogism respecting the grounds of ,induction would be dispelled by keeping in view these simple considerations4 #aaj ,infra1 chap4 xxi4 #aaa ,infra1 chap4 xxi41 xxii4 #aab ,in strictness1 wherever the present constitution of space exists2 which we have ample reason to believe that it does in the region of the fixed stars4 #aac ,dr4 ,whewell 7,phil4 of ,discov41 p4 #bdf7 will not allow these and similar erroneous judgments to be called inductions2 inasmuch as such superstitious fancies 8were not collected from the facts by seeking a law of their occurrence1 but were suggested by an imagination of the anger of superior powers1 shown by such deviations from the ordinary course of nature40 ,i conceive the question to be1 not in what manner these notions were at first suggested1 but by what evidence they have1 from time to time1 been supposed to be substantiated4 ,if the believers in these erroneous opinions had been put on their defense1 they would have referred to experience3 to the comet which preceded the assassination of ,julius ,csar1 or to oracles and other prophecies known to have been fulfilled4 ,it is by such appeals to facts that all analogous superstitions1 even in our day1 attempt to justify themselves2 the supposed evidence of experience is necessary to their hold on the mind4 ,i quite admit that the influence of such coincidences would not be what it is1 if strength were not lent to it by an antecedent presumption2 but this is not peculiar to such cases2 preconceived notions of probability form part of the explanation of many other cases of belief on insufficient evidence4 ,the a priori prejudice does not prevent the erroneous opinion from being sincerely regarded as a legitimate conclusion from experience2 though it improperly predisposes the mind to that interpretation of experience4 ,thus much in defense of the sort of examples objected to4 ,but it would be easy to produce instances1 equally adapted to the purpose1 and in which no antecedent prejudice is at all concerned4 8,for many ages10 says ,archbishop ,whately1 8all farmers and gardeners were firmly convinced--and convinced of their knowing it by experience--that the crops would never turn out good unless the seed were sown during the increase of the moon40 ,this was induction1 but bad induction2 just as a vicious syllogism is reasoning1 but bad reasoning4 #aad ,the assertion1 that any and every one of the conditions of a phenomenon may be and is1 on some occasions and for some purposes1 spoken of as the cause1 has been disputed by an intelligent reviewer of this work in the ,prospective ,review 7the predecessor of the justly esteemed ,national ,review71 who maintains that 8we always apply the word cause rather to that element in the antecedents which exercises force1 and which would tend at all times to produce the same or a similar effect to that which1 under certain conditions1 it would actually produce40 ,and he says1 that 8every one would feel0 the expression1 that the cause of a surprise was the sentinel's being off his post1 to be incorrect2 but that the 8allurement or force which drew him off his post1 might be so called1 because in doing so it removed a resisting power which would have prevented the surprise40 ,i can not think that it would be wrong to say1 that the event took place because the sentinel was absent1 and yet right to say that it took place because he was bribed to be absent4 ,since the only direct effect of the bribe was his absence1 the bribe could be called the remote cause of the surprise1 only on the supposition that the absence was the proximate cause2 nor does it seem to me that any one 7who had not a theory to support7 would use the one expression and reject the other4 ,the reviewer observes1 that when a person dies of poison1 his possession of bodily organs is a necessary condition1 but that no one would ever speak of it as the cause4 ,i admit the fact2 but ,i believe the reason to be1 that the occasion could never arise for so speaking of it2 for when in the inaccuracy of common discourse we are led to speak of some one condition of a phenomenon as its cause1 the condition so spoken of is always one which it is at least possible that the hearer may require to be informed of4 ,the possession of bodily organs is a known condition1 and to give that as the answer1 when asked the cause of a person's death1 would not supply the information sought4 ,once conceive that a doubt could exist as to his having bodily organs1 or that he were to be compared with some being who had them not1 and cases may be imagined in which it might be said that his possession of them was the cause of his death4 ,if ,faust and ,mephistopheles together took poison1 it might be said that ,faust died because he was a human being1 and had a body1 while ,mephistopheles survived because he was a spirit4 ,it is for the same reason that no one 7as the reviewer remarks7 8calls the cause of a leap1 the muscles or sinews of the body1 though they are necessary conditions2 nor the cause of a self-sacrifice1 the knowledge which was necessary for it2 nor the cause of writing a book1 that a man has time for it1 which is a necessary condition40 ,these conditions 7besides that they are antecedent states1 and not proximate antecedent events1 and are therefore never the conditions in closest apparent proximity to the effect7 are all of them so obviously implied1 that it is hardly possible there should exist that necessity for insisting on them1 which alone gives occasion for speaking of a single condition as if it were the cause4 ,wherever this necessity exists in regard to some one condition1 and does not exist in regard to any other1 ,i conceive that it is consistent with usage1 when scientific accuracy is not aimed at1 to apply the name cause to that one condition4 ,if the only condition which can be supposed to be unknown is a negative condition1 the negative condition may be spoken of as the cause4 ,it might be said that a person died for want of medical advice3 though this would not be likely to be said1 unless the person was already understood to be ill1 and in order to indicate that this negative circumstance was what made the illness fatal1 and not the weakness of his constitution1 or the original virulence of the disease4 ,it might be said that a person was drowned because he could not swim2 the positive condition1 namely1 that he fell into the water1 being already implied in the word drowned4 ,and here let me remark1 that his falling into the water is in this case the only positive condition3 all the conditions not expressly or virtually included in this 7as that he could not swim1 that nobody helped him1 and so forth7 are negative4 ,yet1 if it were simply said that the cause of a man's death was falling into the water1 there would be quite as great a sense of impropriety in the expression1 as there would be if it were said that the cause was his inability to swim2 because1 though the one condition is positive and the other negative1 it would be felt that neither of them was sufficient1 without the other1 to produce death4 ,with regard to the assertion that nothing is termed the cause1 except the element which exerts active force2 ,i waive the question as to the meaning of active force1 and accepting the phrase in its popular sense1 ,i revert to a former example1 and ,i ask1 would it be more agreeable to custom to say that a man fell because his foot slipped in climbing a ladder1 or that he fell because of his weight8 for his weight1 and not the motion of his foot1 was the active force which determined his fall4 ,if a person walking out in a frosty day1 stumbled and fell1 it might be said that he stumbled because the ground was slippery1 or because he was not sufficiently careful3 but few people1 ,i suppose1 would say1 that he stumbled because he walked4 ,yet the only active force concerned was that which he exerted in walking3 the others were mere negative conditions2 but they happened to be the only ones which there could be any necessity to state2 for he walked1 most likely1 in exactly his usual manner1 and the negative conditions made all the difference4 ,again1 if a person were asked why the army of ,xerxes defeated that of ,leonidas1 he would probably say1 because they were a thousand times the number2 but ,i do not think he would say1 it was because they fought1 though that was the element of active force4 ,to borrow another example1 used by ,mr4 ,grove and by ,mr4 ,baden ,powell1 the opening of flood-gates is said to be the cause of the flow of water2 yet the active force is exerted by the water itself1 and opening the flood-gates merely supplies a negative condition4 ,the reviewer adds1 8,there are some conditions absolutely passive1 and yet absolutely necessary to physical phenomena1 viz41 the relations of space and time2 and to these no one ever applies the word cause without being immediately arrested by those who hear him40 ,even from this statement ,i am compelled to dissent4 ,few persons would feel it incongruous to say 7for example7 that a secret became known because it was spoken of when ,a4 ,b4 was within hearing2 which is a condition of space3 or that the cause why one of two particular trees is taller than the other1 is that it has been longer planted2 which is a condition of time4 #aae ,there are a few exceptions2 for there are some properties of objects which seem to be purely preventive2 as the property of opaque bodies1 by which they intercept the passage of light4 ,this1 as far as we are able to understand it1 appears an instance not of one cause counteracting another by the same law whereby it produces its own effects1 but of an agency which manifests itself in no other way than in defeating the effects of another agency4 ,if we knew on what other relations to light1 or on what peculiarities of structure1 opacity depends1 we might find that this is only an apparent1 not a real1 exception to the general proposition in the text4 ,in any case it needs not affect the practical application4 ,the formula which includes all the negative conditions of an effect in the single one of the absence of counteracting causes1 is not violated by such cases as this2 though1 if all counteracting agencies were of this description1 there would be no purpose served by employing the formula4 #aaf ,i mean by this expression1 the ultimate laws of nature 7whatever they may be7 as distinguished from the derivative laws and from the collocations4 ,the diurnal revolution of the earth 7for example7 is not a part of the constitution of things1 because nothing can be so called which might possibly be terminated or altered by natural causes4 #aag ,i use the words 8straight line0 for brevity and simplicity4 ,in reality the line in question is not exactly straight1 for1 from the effect of refraction1 we actually see the sun for a short interval during which the opaque mass of the earth is interposed in a direct line between the sun and our eyes2 thus realizing1 though but to a limited extent1 the coveted desideratum of seeing round a corner4 #aah ,second ,burnett ,prize ,essay1 by ,principal ,tulloch1 p4 #be4 #aai ,letters on the ,philosophy of the ,human ,mind1 ,first ,series1 p4 #bai4 #abj ,essays1 pp4 #bjf-bjh4 #aba ,to the universality which mankind are agreed in ascribing to the ,law of ,causation1 there is one claim of exception1 one disputed case1 that of the ,human ,will2 the determinations of which1 a large class of metaphysicians are not willing to regard as following the causes called motives1 according to as strict laws as those which they suppose to exist in the world of mere matter4 ,this controverted point will undergo a special examination when we come to treat particularly of the ,logic of the ,moral ,sciences 7,book vi41 chap4 #b74 ,in the mean time1 ,i may remark that these metaphysicians1 who1 it must be observed1 ground the main part of their objection on the supposed repugnance of the doctrine in question to our consciousness1 seem to me to mistake the fact which consciousness testifies against4 ,what is really in contradiction to consciousness1 they would1 ,i think1 on strict self-examination1 find to be1 the application to human actions and volitions of the ideas involved in the common use of the term ,necessity2 which ,i agree with them in objecting to4 ,but if they would consider that by saying that a person's actions necessarily follow from his character1 all that is really meant 7for no more is meant in any case whatever of causation7 is that he invariably does act in conformity to his character1 and that any one who thoroughly knew his character could certainly predict how he would act in any supposable case2 they probably would not find this doctrine either contrary to their experience or revolting to their feelings4 ,and no more than this is contended for by any one but an ,asiatic fatalist4 #abb ,i believe1 however1 the accredited authorities do suppose that molecular motion1 equivalent in amount to that which will be manifested in the combustion of the coal1 is actually taking place during the whole of the long interval1 if not in the coal1 yet in the oxygen which will then combine with it4 ,but how purely hypothetical this supposition is1 need hardly be remarked2 ,i venture to say1 unnecessarily and extravagantly hypothetical4 #abc ,lectures on ,metaphysics1 vol4 ii41 ,lect4 xxxix41 pp4 #cia-b4 ,i regret that ,i can not invoke the authority of ,sir ,william ,hamilton in favor of my own opinions on ,causation1 as ,i can against the particular theory which ,i am now combating4 ,but that acute thinker has a theory of ,causation peculiar to himself1 which has never yet1 as far as ,i know1 been analytically examined1 but which1 ,i venture to think1 admits of as complete refutation as any one of the false or insufficient psychological theories which strew the ground in such numbers under his potent metaphysical scythe4 7,since examined and controverted in the sixteenth chapter of ,an ,examination of ,sir ,william ,hamilton's ,philosophy47 #abd ,unless we are to consider as such the following statement1 by one of the writers quoted in the text3 8,in the case of mental exertion1 the result to be accomplished is preconsidered or meditated1 and is therefore known a priori1 or before experience40--7,bowen's ,lowell ,lectures on the ,application of ,metaphysical and ,ethical ,science to the ,evidence of ,religion4 ,boston1 #ahdi47 ,this is merely saying that when we will a thing we have an idea of it4 ,but to have an idea of what we wish to happen1 does not imply a prophetic knowledge that it will happen4 ,perhaps it will be said that the first time we exerted our will1 when we had of course no experience of any of the powers residing in us1 we nevertheless must already have known that we possessed them1 since we can not will that which we do not believe to be in our power4 ,but the impossibility is perhaps in the words only1 and not in the facts2 for we may desire what we do not know to be in our power2 and finding by experience that our bodies move according to our desire1 we may then1 and only then1 pass into the more complicated mental state which is termed will4 ,after all1 even if we had an instinctive knowledge that our actions would follow our will1 this1 as ,brown remarks1 would prove nothing as to the nature of ,causation4 ,our knowing1 previous to experience1 that an antecedent will be followed by a certain consequent1 would not prove the relation between them to be any thing more than antecedence and consequence4 #abe ,reid's ,essays on the ,active ,powers1 ,essay iv41 chap4 #c4 #abf ,prospective ,review for ,february1 #ahej4 #abg ,vide supra1 p4 #agh1 note4 #abh ,westminster ,review for ,october1 #ahee4 #abi ,see the whole doctrine in ,aristotle de nim1 where the is treated as exactly equivalent to 4 #acj ,it deserves notice that the parts of nature which ,aristotle regards as representing evidence of design1 are the ,uniformities3 the phenomena in so far as reducible to law4 and satisfy him as explanations of the variable element in phenomena1 but their occurring according to a fixed rule can only1 to his conceptions1 be accounted for by an ,intelligent ,will4 ,the common1 or what may be called the instinctive1 religious interpretation of nature1 is the reverse of this4 ,the events in which men spontaneously see the hand of a supernatural being1 are those which can not1 as they think1 be reduced to a physical law4 ,what they can distinctly connect with physical causes1 and especially what they can predict1 though of course ascribed to an ,author of ,nature1 if they already recognize such an author1 might be conceived1 they think1 to arise from a blind fatality1 and in any case do not appear to them to bear so obviously the mark of a divine will4 ,and this distinction has been countenanced by eminent writers on ,natural ,theology1 in particular by ,dr4 ,chalmers1 who thinks that though design is present everywhere1 the irresistible evidence of it is to be found not in the laws of nature but in the collocations1 i4e41 in the part of nature in which it is impossible to trace any law4 ,a few properties of dead matter might1 he thinks1 conceivably account for the regular and invariable succession of effects and causes2 but that the different kinds of matter have been so placed as to promote beneficent ends1 is what he regards as the proof of a ,divine ,providence4 ,mr4 ,baden ,powell1 in his ,essay entitled 8,philosophy of ,creation10 has returned to the point of view of ,aristotle and the ancients1 and vigorously re-asserts the doctrine that the indication of design in the universe is not special adaptations1 but ,uniformity and ,law1 these being the evidences of mind1 and not what appears to us to be a provision for our uses4 ,while ,i decline to express any opinion here on this vexata qustio1 ,i ought not to mention ,mr4 ,powell's volume without the acknowledgment due to the philosophic spirit which pervades generally the three ,essays composing it1 forming in the case of one of them 7the 8,unity of ,worlds07 an honorable contrast with the other dissertations1 so far as they have come under my notice1 which have appeared on either side of that controversy4 #aca ,in the words of ,fontenelle1 another celebrated ,cartesian1 8les philosophes aussi bien que le peuple avaient cru que l'me et le corps agissaient rellement et physiquement l'un sur l'autre4 ,descartes vint1 qui prouva que leur nature ne permettait point cette sorte de communication vritable1 et qu'ils n'en pouvaient avoir qu'une apparente1 dont ,dieu tait le ,mdiateur40--7uvres de ,fontenelle1 ed4 #agfg1 tom4 v41 p4 #ecd47 #acb ,i omit1 for simplicity1 to take into account the effect1 in this latter case1 of the diminution of pressure1 in diminishing the flow of water through the drain2 which evidently in no way affects the truth or applicability of the principle1 since when the two causes act simultaneously the conditions of that diminution of pressure do not arise4 #acc ,professor ,bain adds several other well-established chemical generalizations3 8,the laws that simple substances exhibit the strongest affinities2 that compounds are more fusible than their elements2 that combination tends to a lower state of matter from gas down to solid20 and some general propositions concerning the circumstances which facilitate or resist chemical combination4 7,logic1 ii41 #bed47 #acd ,professor ,bain 7,logic1 ii41 #ci7 points out a class of cases1 other than that spoken of in the text1 which he thinks must be regarded as an exception to the ,composition of ,causes4 8,causes that merely make good the collocation for bringing a prime mover into action1 or that release a potential force1 do not follow any such rule4 ,one man may direct a gun upon a fort as well as three3 two sparks are not more effectual than one in exploding a barrel of gunpowder4 ,in medicine there is a certain dose that answers the end2 and adding to it does no more good40 ,i am not sure that these cases are really exceptions4 ,the law of ,composition of ,causes1 ,i think1 is really fulfilled1 and the appearance to the contrary is produced by attending to the remote instead of the immediate effect of the causes4 ,in the cases mentioned1 the immediate effect of the causes in action is a collocation1 and the duplication of the cause does double the quantity of collocation4 ,two men could raise the gun to the required angle twice as quickly as one1 though one is enough4 ,two sparks put two sets of particles of the gunpowder into the state of intestine motion which makes them explode1 though one is sufficient4 ,it is the collocation itself that does not1 by being doubled1 always double the effect2 because in many cases a certain collocation1 once obtained1 is all that is required for the production of the whole amount of effect which can be produced at all at the given time and place4 ,doubling the collocation with difference of time and place1 as by pointing two guns1 or exploding a second barrel after the first1 does double the effect4 ,this remark applies still more to ,mr4 ,bain's third example1 that of a double dose of medicine2 for a double dose of an aperient does purge more violently1 and a double dose of laudanum does produce longer and sounder sleep4 ,but a double purging1 or a double amount of narcotism1 may have remote effects different in kind from the effect of the smaller amount1 reducing the case to that of heteropathic laws1 discussed in the text4 #ace ,unless1 indeed1 the consequent was generated1 not by the antecedent1 but by the means employed to produce the antecedent4 ,as1 however1 these means are under our power1 there is so far a probability that they are also sufficiently within our knowledge to enable us to judge whether that could be the case or not4 #acf ,discourse on the ,study of ,natural ,philosophy1 p4 #agi4 #acg ,for this speculation1 as for many other of my scientific illustrations1 ,i am indebted to ,professor ,bain1 whose subsequent treatise on ,logic abounds with apt illustrations of all the inductive methods4 #ach ,this view of the necessary co-existence of opposite excitements involves a great extension of the original doctrine of two electricities4 ,the early theorists assumed that1 when amber was rubbed1 the amber was made positive and the rubber negative to the same degree2 but it never occurred to them to suppose that the existence of the amber charge was dependent on an opposite charge in the bodies with which the amber was contiguous1 while the existence of the negative charge on the rubber was equally dependent on a contrary state of the surfaces that might accidentally be confronted with it2 that1 in fact1 in a case of electrical excitement by friction1 four charges were the minimum that could exist4 ,but this double electrical action is essentially implied in the explanation now universally adopted in regard to the phenomena of the common electric machine4 #aci ,pp4 #aaj1 #aaa4 #adj ,infra1 book iv41 chap4 ii41 ,on ,abstraction4 #ada ,i must1 however1 remark1 that this example1 which seems to militate against the assertion we made of the comparative inapplicability of the ,method of ,difference to cases of pure observation1 is really one of those exceptions which1 according to a proverbial expression1 prove the general rule4 ,for in this case1 in which ,nature1 in her experiment1 seems to have imitated the type of the experiments made by man1 she has only succeeded in producing the likeness of man's most imperfect experiments2 namely1 those in which1 though he succeeds in producing the phenomenon1 he does so by employing complex means1 which he is unable perfectly to analyze1 and can form1 therefore1 no sufficient judgment what portion of the effects may be due1 not to the supposed cause1 but to some unknown agency of the means by which that cause was produced4 ,in the natural experiment which we are speaking of1 the means used was the clearing off a canopy of clouds2 and we certainly do not know sufficiently in what this process consists1 or on what it depends1 to be certain a priori that it might not operate upon the deposition of dew independently of any thermometric effect at the earth's surface4 ,even1 therefore1 in a case so favorable as this to ,nature's experimental talents1 her experiment is of little value except in corroboration of a conclusion already attained through other means4 #adb ,in his subsequent work1 ,outlines of ,astronomy 7 #egj71 ,sir ,john ,herschel suggests another possible explanation of the acceleration of the revolution of a comet4 #adc ,discourse1 pp4 #aef-h1 and #aga4 #add ,outlines of ,astronomy1 #hef4 #ade ,philosophy of ,discovery1 pp4 #bfc1 #bfd4 #adf ,see1 on this point1 the second chapter of the present book4 #adg ,ante1 chap4 vii41 #a4 #adh ,it seems hardly necessary to say that the word impinge1 as a general term to express collision of forces1 is here used by a figure of speech1 and not as expressive of any theory respecting the nature of force4 #adi ,essays on some ,unsettled ,questions of ,political ,economy1 ,essay ,v4 #aej ,it is justly remarked by ,professor ,bain1 that though the ,methods of ,agreement and ,difference are not applicable to these cases1 they are not wholly inaccessible to the ,method of ,concomitant ,variations4 8,if a cause happens to vary alone1 the effect will also vary alone3 a cause and effect may be thus singled out under the greatest complications4 ,thus1 when the appetite for food increases with the cold1 we have a strong evidence of connection between these two facts1 although other circumstances may operate in the same direction4 ,the assigning of the respective parts of the sun and moon in the action of the tides may be effected1 to a certain degree of exactness1 by the variations of the amount according to the positions of the two attractive bodies4 ,by a series of experiments of ,concomitant ,variations1 directed to ascertain the elimination of nitrogen from the human body under varieties of muscular exercise1 ,dr4 ,parkes obtained the remarkable conclusion1 that a muscle grows during exercise1 and loses bulk during the subsequent rest40 7,logic1 ii41 #hc47 ,it is1 no doubt1 often possible to single out the influencing causes from among a great number of mere concomitants1 by noting what are the antecedents1 a variation in which is followed by a variation in the effect4 ,but when there are many influencing causes1 no one of them greatly predominating over the rest1 and especially when some of these are continually changing1 it is scarcely ever possible to trace such a relation between the variations of the effect and those of any one cause as would enable us to assign to that cause its real share in the production of the effect4 #aea ,bain's ,logic1 ii41 #cfj4 #aeb ,what is said in the text on the applicability of the experimental methods to resolve particular questions of medical treatment1 does not detract from their efficacy in ascertaining the general laws of the animal or human system4 ,the functions1 for example1 of the different classes of nerves have been discovered1 and probably could only have been discovered1 by experiments on living animals4 ,observation and experiment are the ultimate basis of all knowledge3 from them we obtain the elementary laws of life1 as we obtain all other elementary truths4 ,it is in dealing with the complex combinations that the experimental methods are for the most part illusory1 and the deductive mode of investigation must be invoked to disentangle the complexity4 #aec ,professor ,bain1 though concurring generally in the views expressed in this chapter1 seems to estimate more highly than ,i do the scope for specific experimental evidence in politics4 7,logic1 ii41 #ccc-ccg47 ,there are1 it is true1 as he remarks 7p4 #ccf71 some cases 8when an agent suddenly introduced is almost instantaneously followed by some other changes1 as when the announcement of a diplomatic rupture between two nations is followed the same day by a derangement of the money-market40 ,but this experiment would be quite inconclusive merely as an experiment4 ,it can only serve1 as any experiment may1 to verify the conclusion of a deduction4 ,unless we already knew by our knowledge of the motives which act on business men1 that the prospect of war tends to derange the money-market1 we should never have been able to prove a connection between the two facts1 unless after having ascertained historically that the one followed the other in too great a number of instances to be consistent with their having been recorded with due precautions4 ,whoever has carefully examined any of the attempts continually made to prove economic doctrines by such a recital of instances1 knows well how futile they are4 ,it always turns out that the circumstances of scarcely any of the cases have been fully stated2 and that cases1 in equal or greater numbers1 have been omitted which would have tended to an opposite conclusion4 #aed ,vide ,memoir by ,thomas ,graham1 ,f4,r4,s41 ,master of the ,mint1 8,on ,liquid ,diffusion applied to ,analysis10 in the ,philosophical ,transactions for #ahfb1 reprinted in the ,journal of the ,chemical ,society1 and also separately as a pamphlet4 #aee ,it was an old generalization in surgery1 that tight bandaging had a tendency to prevent or dissipate local inflammation4 ,this sequence1 being1 in the progress of physiological knowledge1 resolved into more general laws1 led to the important surgical invention made by ,dr4 ,arnott1 the treatment of local inflammation and tumors by means of an equable pressure1 produced by a bladder partially filled with air4 ,the pressure1 by keeping back the blood from the part1 prevents the inflammation1 or the tumor1 from being nourished3 in the case of inflammation1 it removes the stimulus1 which the organ is unfit to receive2 in the case of tumors1 by keeping back the nutritive fluid1 it causes the absorption of matter to exceed the supply1 and the diseased mass is gradually absorbed and disappears4 #aef ,since acknowledged and reprinted in ,mr4 ,martineau's ,miscellanies4 #aeg ,dissertations and ,discussions1 vol4 i41 fourth paper4 #aeh ,written before the rise of the new views respecting the relation of heat to mechanical force2 but confirmed rather than contradicted by them4 #aei ,as is well remarked by ,professor ,bain1 in the very valuable chapter of his ,logic which treats of this subject 7ii41 #aba71 8scientific explanation and inductive generalization being the same thing1 the limits of ,explanation are the limits of ,induction10 and 8the limits to inductive generalization are the limits to the agreement or community of facts4 ,induction supposes similarity among phenomena2 and when such similarity is discovered1 it reduces the phenomena under a common statement4 ,the similarity of terrestrial gravity to celestial attraction enables the two to be expressed as one phenomenon4 ,the similarity between capillary attraction1 solution1 the operation of cements1 etc41 leads to their being regarded not as a plurality1 but as a unity1 a single causative link1 the operation of a single agency4444 ,if it be asked whether we can merge gravity itself in some still higher law1 the answer must depend upon the facts4 ,are there any other forces1 at present held distinct from gravity1 that we may hope to make fraternize with it1 so as to join in constituting a higher unity8 ,gravity is an attractive force2 and another great attractive force is cohesion1 or the force that binds together the atoms of solid matter4 ,might we1 then1 join these two in a still higher unity1 expressed under a more comprehensive law8 ,certainly we might1 but not to any advantage4 ,the two kinds of force agree in the one point1 attraction1 but they agree in no other2 indeed1 in the manner of the attraction1 they differ widely2 so widely that we should have to state totally distinct laws for each4 ,gravity is common to all matter1 and equal in amount in equal masses of matter1 whatever be the kind2 it follows the law of the diffusion of space from a point 7the inverse square of the distance72 it extends to distances unlimited2 it is indestructible and invariable4 ,cohesion is special for each separate substance2 it decreases according to distance much more rapidly than the inverse square1 vanishing entirely at very small distances4 ,two such forces have not sufficient kindred to be generalized into one force2 the generalization is only illusory2 the statement of the difference would still make two forces2 while the consideration of one would not in any way simplify the phenomena of the other1 as happened in the generalization of gravity itself40 ,to the impassable limit of the explanation of laws of nature1 set forth in the text1 must therefore be added a further limitation4 ,although1 when the phenomena to be explained are not1 in their own nature1 generically distinct1 the attempt to refer them to the same cause is scientifically legitimate2 yet to the success of the attempt it is indispensable that the cause should be shown to be capable of producing them according to the same law4 ,otherwise the unity of cause is a mere guess1 and the generalization only a nominal one1 which1 even if admitted1 would not diminish the number of ultimate laws of nature4 #afj ,cours de ,philosophie ,positive1 ii41 #fef4 #afa ,vide supra1 book iii41 chap4 xi4 #afb ,philosophy of ,discovery1 p4 #ahe et seq4 #afc ,comte1 ,philosophie ,positive1 ii41 #dcd-dcg4 #afd ,as an example of legitimate hypothesis according to the test here laid down1 has been justly cited that of ,broussais1 who1 proceeding on the very rational principle that every disease must originate in some definite part or other of the organism1 boldly assumed that certain fevers1 which not being known to be local were called constitutional1 had their origin in the mucous membrane of the alimentary canal4 ,the supposition was1 indeed1 as is now generally admitted1 erroneous2 but he was justified in making it1 since by deducing the consequences of the supposition1 and comparing them with the facts of those maladies1 he might be certain of disproving his hypothesis if it was ill founded1 and might expect that the comparison would materially aid him in framing another more conformable to the phenomena4 ,the doctrine now universally received that the earth is a natural magnet1 was originally an hypothesis of the celebrated ,gilbert4 ,another hypothesis1 to the legitimacy of which no objection can lie1 and which is well calculated to light the path of scientific inquiry1 is that suggested by several recent writers1 that the brain is a voltaic pile1 and that each of its pulsations is a discharge of electricity through the system4 ,it has been remarked that the sensation felt by the hand from the beating of a brain1 bears a strong resemblance to a voltaic shock4 ,and the hypothesis1 if followed to its consequences1 might afford a plausible explanation of many physiological facts1 while there is nothing to discourage the hope that we may in time sufficiently understand the conditions of voltaic phenomena to render the truth of the hypothesis amenable to observation and experiment4 ,the attempt to localize1 in different regions of the brain1 the physical organs of our different mental faculties and propensities1 was1 on the part of its original author1 a legitimate example of a scientific hypothesis2 and we ought not1 therefore1 to blame him for the extremely slight grounds on which he often proceeded1 in an operation which could only be tentative1 though we may regret that materials barely sufficient for a first rude hypothesis should have been hastily worked up into the vain semblance of a science4 ,if there be really a connection between the scale of mental endowments and the various degrees of complication in the cerebral system1 the nature of that connection was in no other way so likely to be brought to light as by framing1 in the first instance1 an hypothesis similar to that of ,gall4 ,but the verification of any such hypothesis is attended1 from the peculiar nature of the phenomena1 with difficulties which phrenologists have not shown themselves even competent to appreciate1 much less to overcome4 ,mr4 ,darwin's remarkable speculation on the ,origin of ,species is another unimpeachable example of a legitimate hypothesis4 ,what he terms 8natural selection0 is not only a vera causa1 but one proved to be capable of producing effects of the same kind with those which the hypothesis ascribes to it2 the question of possibility is entirely one of degree4 ,it is unreasonable to accuse ,mr4 ,darwin 7as has been done7 of violating the rules of ,induction4 ,the rules of ,induction are concerned with the conditions of ,proof4 ,mr4 ,darwin has never pretended that his doctrine was proved4 ,he was not bound by the rules of ,induction1 but by those of ,hypothesis4 ,and these last have seldom been more completely fulfilled4 ,he has opened a path of inquiry full of promise1 the results of which none can foresee4 ,and is it not a wonderful feat of scientific knowledge and ingenuity to have rendered so bold a suggestion1 which the first impulse of every one was to reject at once1 admissible and discussible1 even as a conjecture8 #afe ,whewell's ,phil4 of ,discovery1 pp4 #bge1 #bgf4 #aff ,what has most contributed to accredit the hypothesis of a physical medium for the conveyance of light1 is the certain fact that light travels 7which can not be proved of gravitation72 that its communication is not instantaneous1 but requires time2 and that it is intercepted 7which gravitation is not7 by intervening objects4 ,these are analogies between its phenomena and those of the mechanical motion of a solid or fluid substance4 ,but we are not entitled to assume that mechanical motion is the only power in nature capable of exhibiting those attributes4 #afg ,phil4 of ,discovery1 p4 #bgd4 #afh ,p4 #bga4 #afi ,p4 #bea and the whole of ,appendix ,g4 #agj ,in ,dr4 ,whewell's latest version of his theory 7,philosophy of ,discovery1 p4 #cca7 he makes a concession respecting the medium of the transmission of light1 which1 taken in conjunction with the rest of his doctrine on the subject1 is not1 ,i confess1 very intelligible to me1 but which goes far toward removing1 if it does not actually remove1 the whole of the difference between us4 ,he is contending1 against ,sir ,william ,hamilton1 that all matter has weight4 ,sir ,william1 in proof of the contrary1 cited the luminiferous ether1 and the calorific and electric fluids1 8which10 he said1 8we can neither denude of their character of substance1 nor clothe with the attribute of weight40 8,to which10 continues ,dr4 ,whewell1 8my reply is1 that precisely because ,i can not clothe these agents with the attribute of ,weight1 ,i do denude them of the character of ,substance4 ,they are not substances1 but agencies4 ,these ,imponderable ,agents are not properly called ,imponderable ,fluids4 ,this ,i conceive that ,i have proved40 ,nothing can be more philosophical4 ,but if the luminiferous ether is not matter1 and fluid matter1 too1 what is the meaning of its undulations8 ,can an agency undulate8 ,can there be alternate motion forward and backward of the particles of an agency8 ,and does not the whole mathematical theory of the undulations imply them to be material8 ,is it not a series of deductions from the known properties of elastic fluids8 ,this opinion of ,dr4 ,whewell reduces the undulations to a figure of speech1 and the undulatory theory to the proposition which all must admit1 that the transmission of light takes place according to laws which present a very striking and remarkable agreement with those of undulations4 ,if ,dr4 ,whewell is prepared to stand by this doctrine1 ,i have no difference with him on the subject4 #aga ,thus water1 of which eight-ninths in weight are oxygen1 dissolves most bodies which contain a high proportion of oxygen1 such as all the nitrates 7which have more oxygen than any others of the common salts71 most of the sulphates1 many of the carbonates1 etc4 ,again1 bodies largely composed of combustible elements1 like hydrogen and carbon1 are soluble in bodies of similar composition2 resin1 for instance1 will dissolve in alcohol1 tar in oil of turpentine4 ,this empirical generalization is far from being universally true2 no doubt because it is a remote1 and therefore easily defeated1 result of general laws too deep for us at present to penetrate2 but it will probably in time suggest processes of inquiry1 leading to the discovery of those laws4 #agb ,or1 according to ,laplace's theory1 the sun and the sun's rotation4 #agc ,supra1 book iii41 chap4 v41 #g4 #agd ,supra1 book iii41 chap4 x41 #b #age ,in the preceding discussion1 the mean is spoken of as if it were exactly the same thing with the average4 ,but the mean1 for purposes of inductive inquiry1 is not the average1 or arithmetical mean1 though in a familiar illustration of the theory the difference may be disregarded4 ,if the deviations on one side of the average are much more numerous than those on the other 7these last being fewer but greater71 the effect due to the invariable cause1 as distinct from the variable ones1 will not coincide with the average1 but will be either below or above the average1 the deviation being toward the side on which the greatest number of the instances are found4 ,this follows from a truth1 ascertained both inductively and deductively1 that small deviations from the true central point are greatly more frequent than large ones4 ,the mathematical law is1 8that the most probable determination of one or more invariable elements from observation is that in which the sum of the squares of the individual aberrations10 or deviations1 8shall be the least possible40 ,see this principle stated1 and its grounds popularly explained1 by ,sir ,john ,herschel1 in his review of ,quetelet on ,probabilities1 ,essays1 p4 #cie et seq4 #agf ,essai ,philosophique sur les ,probabilits1 fifth ,paris edition1 p4 #g4 #agg ,it even appears to me that the calculation of chances1 where there are no data grounded either on special experience or on special inference1 must1 in an immense majority of cases1 break down1 from sheer impossibility of assigning any principle by which to be guided in setting out the list of possibilities4 ,in the case of the colored balls we have no difficulty in making the enumeration1 because we ourselves determine what the possibilities shall be4 ,but suppose a case more analogous to those which occur in nature3 instead of three colors1 let there be in the box all possible colors1 we being supposed ignorant of the comparative frequency with which different colors occur in nature1 or in the productions of art4 ,how is the list of cases to be made out8 ,is every distinct shade to count as a color8 ,if so1 is the test to be a common eye1 or an educated eye--a painter's1 for instance8 ,on the answer to these questions would depend whether the chances against some particular color would be estimated at ten1 twenty1 or perhaps five hundred to one4 ,while if we knew from experience that the particular color occurs on an average a certain number of times in every hundred or thousand1 we should not require to know any thing either of the frequency or of the number of the other possibilities4 #agh ,prospective ,review for ,february1 #ahej4 #agi 8,if this be not so1 why do we feel so much more probability added by the first instance than by any single subsequent instance8 ,why1 except that the first instance gives us its possibility 7a cause adequate to it71 while every other only gives us the frequency of its conditions8 ,if no reference to a cause be supposed1 possibility would have no meaning2 yet it is clear that1 antecedent to its happening1 we might have supposed the event impossible1 i4e41 have believed that there was no physical energy really existing in the world equal to producing it4444 ,after the first time of happening1 which is1 then1 more important to the whole probability than any other single instance 7because proving the possibility71 the number of times becomes important as an index to the intensity or extent of the cause1 and its independence of any particular time4 ,if we took the case of a tremendous leap1 for instance1 and wished to form an estimate of the probability of its succeeding a certain number of times2 the first instance1 by showing its possibility 7before doubtful7 is of the most importance2 but every succeeding leap shows the power to be more perfectly under control1 greater and more invariable1 and so increases the probability2 and no one would think of reasoning in this case straight from one instance to the next1 without referring to the physical energy which each leap indicated4 ,is it not1 then1 clear that we do not ever0 7let us rather say1 that we do not in an advanced state of our knowledge7 8conclude directly from the happening of an event to the probability of its happening again2 but that we refer to the cause1 regarding the past cases as an index to the cause1 and the cause as our guide to the future80--,ibid4 #ahj ,the writer last quoted says that the valuation of chances by comparing the number of cases in which the event occurs with the number in which it does not occur1 8would generally be wholly erroneous10 and 8is not the true theory of probability40 ,it is at least that which forms the foundation of insurance1 and of all those calculations of chances in the business of life which experience so abundantly verifies4 ,the reason which the reviewer gives for rejecting the theory is1 that it 8would regard an event as certain which had hitherto never failed2 which is exceedingly far from the truth1 even for a very large number of constant successes40 ,this is not a defect in a particular theory1 but in any theory of chances4 ,no principle of evaluation can provide for such a case as that which the reviewer supposes4 ,if an event has never once failed1 in a number of trials sufficient to eliminate chance1 it really has all the certainty which can be given by an empirical law2 it is certain during the continuance of the same collocation of causes which existed during the observations4 ,if it ever fails1 it is in consequence of some change in that collocation4 ,now1 no theory of chances will enable us to infer the future probability of an event from the past1 if the causes in operation1 capable of influencing the event1 have intermediately undergone a change4 #aha ,pp4 #ah1 #ai4 ,the theorem is not stated by ,laplace in the exact terms in which ,i have stated it2 but the identity of import of the two modes of expression is easily demonstrable4 #ahb ,for a fuller treatment of the many interesting questions raised by the theory of probabilities1 ,i may now refer to a recent work by ,mr4 ,venn1 ,fellow of ,caius ,college1 ,cambridge1 8,the ,logic of ,chance20 one of the most thoughtful and philosophical treatises on any subject connected with ,logic and ,evidence which have been produced1 to my knowledge1 for many years4 ,some criticisms contained in it have been very useful to me in revising the corresponding chapters of the present work4 ,in several of ,mr4 ,venn's opinions1 however1 ,i do not agree4 ,what these are will be obvious to any reader of ,mr4 ,venn's work who is also a reader of this4 #ahc ,hartley's ,observations on ,man1 vol4 i41 p4 #af4 ,the passage is not in ,priestley's curtailed edition4 #ahd ,i am happy to be able to quote the following excellent passage from ,mr4 ,baden ,powell's ,essay on the ,inductive ,philosophy1 in confirmation1 both in regard to history and to doctrine1 of the statement made in the text4 ,speaking of the 8conviction of the universal and permanent uniformity of nature10 ,mr4 ,powell says 7pp4 #ih-ajj73 8,we may remark that this idea1 in its proper extent1 is by no means one of popular acceptance or natural growth4 ,just so far as the daily experience of every one goes1 so far indeed he comes to embrace a certain persuasion of this kind1 but merely to this limited extent1 that what is going on around him at present1 in his own narrow sphere of observation1 will go on in like manner in future4 ,the peasant believes that the sun which rose to-day will rise again to-morrow2 that the seed put into the ground will be followed in due time by the harvest this year as it was last year1 and the like2 but has no notion of such inferences in subjects beyond his immediate observation4 ,and it should be observed that each class of persons1 in admitting this belief within the limited range of his own experience1 though he doubt or deny it in every thing beyond1 is1 in fact1 bearing unconscious testimony to its universal truth4 ,nor1 again1 is it only among the most ignorant that this limitation is put upon the truth4 ,there is a very general propensity to believe that every thing beyond common experience1 or especially ascertained laws of nature1 is left to the dominion of chance or fate or arbitrary intervention2 and even to object to any attempted explanation by physical causes1 if conjecturally thrown out for an apparently unaccountable phenomenon4 8,the precise doctrine of the generalization of this idea of the uniformity of nature1 so far from being obvious1 natural1 or intuitive1 is utterly beyond the attainment of the many4 ,in all the extent of its universality it is characteristic of the philosopher4 ,it is clearly the result of philosophic cultivation and training1 and by no means the spontaneous offspring of any primary principle naturally inherent in the mind1 as some seem to believe4 ,it is no mere vague persuasion taken up without examination1 as a common prepossession to which we are always accustomed2 on the contrary1 all common prejudices and associations are against it4 ,it is pre-eminently an acquired idea4 ,it is not attained without deep study and reflection4 ,the best informed philosopher is the man who most firmly believes it1 even in opposition to received notions2 its acceptance depends on the extent and profoundness of his inductive studies40 #ahe ,supra1 book iii41 chap4 iii41 #a #ahf ,it deserves remark1 that these early generalizations did not1 like scientific inductions1 presuppose causation4 ,what they did presuppose1 was uniformity in physical facts4 ,but the observers were as ready to presume uniformity in the co-existence of facts as in the sequences4 ,on the other hand1 they never thought of assuming that this uniformity was a principle pervading all nature3 their generalizations did not imply that there was uniformity in every thing1 but only that as much uniformity as existed within their observation1 existed also beyond it4 ,the induction1 fire burns1 does not require for its validity that all nature should observe uniform laws1 but only that there should be uniformity in one particular class of natural phenomena2 the effects of fire on the senses and on combustible substances4 ,and uniformity to this extent was not assumed1 anterior to the experience1 but proved by the experience4 ,the same observed instances which proved the narrower truth1 proved as much of the wider one as corresponded to it4 ,it is from losing sight of this fact1 and considering the law of causation in its full extent as necessarily presupposed in the very earliest generalizations1 that persons have been led into the belief that the law of causation is known a priori1 and is not itself a conclusion from experience4 #ahg ,book ii41 chap4 iii4 #ahh ,one of the most rising thinkers of the new generation in ,france1 ,m4 ,taine 7who has given1 in the ,revue des ,deux ,mondes1 the most masterly analysis1 at least in one point of view1 ever made of the present work71 though he rejects1 on this and similar points of psychology1 the intuition theory in its ordinary form1 nevertheless assigns to the law of causation1 and to some other of the most universal laws1 that certainty beyond the bounds of human experience1 which ,i have not been able to accord to them4 ,he does this on the faith of our faculty of abstraction1 in which he seems to recognize an independent source of evidence1 not indeed disclosing truths not contained in our experience1 but affording an assurance which experience can not give1 of the universality of those which it does contain4 ,by abstraction ,m4 ,taine seems to think that we are able1 not merely to analyze that part of nature which we see1 and exhibit apart the elements which pervade it1 but to distinguish such of them as are elements of the system of nature considered as a whole1 not incidents belonging to our limited terrestrial experience4 ,i am not sure that ,i fully enter into ,m4 ,taine's meaning2 but ,i confess ,i do not see how any mere abstract conception1 elicited by our minds from our experience1 can be evidence of an objective fact in universal ,nature1 beyond what the experience itself bears witness of2 or how1 in the process of interpreting in general language the testimony of experience1 the limitations of the testimony itself can be cast off4 ,dr4 ,ward1 in an able article in the ,dublin ,review for ,october1 #ahga1 contends that the uniformity of nature can not be proved from experience1 but from 8transcendental considerations0 only1 and that1 consequently1 all physical science would be deprived of its basis1 if such transcendental proof were impossible4 ,when physical science is said to depend on the assumption that the course of nature is invariable1 all that is meant is that the conclusions of physical science are not known as absolute truths3 the truth of them is conditional on the uniformity of the course of nature2 and all that the most conclusive observations and experiments can prove1 is that the result arrived at will be true if1 and as long as1 the present laws of nature are valid4 ,but this is all the assurance we require for the guidance of our conduct4 ,dr4 ,ward himself does not think that his transcendental proofs make it practically greater2 for he believes1 as a ,catholic1 that the course of nature not only has been1 but frequently and even daily is1 suspended by supernatural intervention4 ,but though this conditional conclusiveness of the evidence of experience1 which is sufficient for the purposes of life1 is all that ,i was necessarily concerned to prove1 ,i have given reasons for thinking that the uniformity1 as itself a part of experience1 is sufficiently proved to justify undoubting reliance on it4 ,this ,dr4 ,ward contests1 for the following reasons3 ,first 7p4 #cae71 supposing it true that there has hitherto been no well authenticated case of a breach in the uniformity of nature2 8the number of natural agents constantly at work is incalculably large2 and the observed cases of uniformity in their action must be immeasurably fewer than one thousandth of the whole4 ,scientific men1 we assume for the moment1 have discovered that in a certain proportion of instances--immeasurably fewer than one thousandth of the whole--a certain fact has prevailed2 the fact of uniformity2 and they have not found a single instance in which that fact does not prevail4 ,are they justified1 we ask1 in inferring from these premises that the fact is universal8 ,surely the question answers itself4 ,let us make a very grotesque supposition1 in which1 however1 the conclusion would really be tried according to the arguments adduced4 ,in some desert of ,africa there is an enormous connected edifice1 surrounding some vast space1 in which dwell certain reasonable beings1 who are unable to leave the inclosure4 ,in this edifice are more than a thousand chambers1 which some years ago were entirely locked up1 and the keys no one knew where4 ,by constant diligence twenty-five keys have been found1 out of the whole number2 and the corresponding chambers1 situated promiscuously throughout the edifice1 have been opened4 ,each chamber1 when examined1 is found to be in the precise shape of a dodecahedron4 ,are the inhabitants justified on that account in holding with certitude that the remaining #ige chambers are built on the same plan80 ,not with perfect certitude1 but 7if the chambers to which the keys have been found are really 8situated promiscuously07 with so high a degree of probability that they would be justified in acting upon the presumption until an exception appeared4 ,dr4 ,ward's argument1 however1 does not touch mine as it stands in the text4 ,my argument is grounded on the fact that the uniformity of the course of nature as a whole1 is constituted by the uniform sequences of special effects from special natural agencies2 that the number of these natural agencies in the part of the universe known to us is not incalculable1 nor even extremely great2 that we have now reason to think that at least the far greater number of them1 if not separately1 at least in some of the combinations into which they enter1 have been made sufficiently amenable to observation1 to have enabled us actually to ascertain some of their fixed laws2 and that this amount of experience justifies the same degree of assurance that the course of nature is uniform throughout1 which we previously had of the uniformity of sequence among the phenomena best known to us4 ,this view of the subject1 if correct1 destroys the force of ,dr4 ,ward's first argument4 ,his second argument is1 that many or most persons1 both scientific and unscientific1 believe that there are well authenticated cases of breach in the uniformity of nature1 namely1 miracles4 ,neither does this consideration touch what ,i have said in the text4 ,i admit no other uniformity in the events of nature than the law of ,causation2 and 7as ,i have explained in the chapter of this volume which treats of the ,grounds of ,disbelief7 a miracle is no exception to that law4 ,in every case of alleged miracle1 a new antecedent is affirmed to exist2 a counteracting cause1 namely1 the volition of a supernatural being4 ,to all1 therefore1 to whom beings with superhuman power over nature are a vera causa1 a miracle is a case of the ,law of ,universal ,causation1 not a deviation from it4 ,dr4 ,ward's last1 and as he says1 strongest argument1 is the familiar one of ,reid1 ,stewart1 and their followers--that whatever knowledge experience gives us of the past and present1 it gives us none of the future4 ,i confess that ,i see no force whatever in this argument4 ,wherein does a future fact differ from a present or a past fact1 except in their merely momentary relation to the human beings at present in existence8 ,the answer made by ,priestley1 in his ,examination of ,reid1 seems to me sufficient1 viz41 that though we have had no experience of what is future1 we have had abundant experience of what was future4 ,the 8leap in the dark0 7as ,professor ,bain calls it7 from the past to the future1 is exactly as much in the dark and no more1 as the leap from a past which we have personally observed1 to a past which we have not4 ,i agree with ,mr4 ,bain in the opinion that the resemblance of what we have not experienced to what we have1 is1 by a law of our nature1 presumed through the mere energy of the idea1 before experience has proved it4 ,this psychological truth1 however1 is not1 as ,dr4 ,ward when criticising ,mr4 ,bain appears to think1 inconsistent with the logical truth that experience does prove it4 ,the proof comes after the presumption1 and consists in its invariable verification by experience when the experience arrives4 ,the fact which while it was future could not be observed1 having as yet no existence1 is always1 when it becomes present and can be observed1 found conformable to the past4 ,dr4 ,m',cosh maintains 7,examination of ,mr4 ,j4 ,s4 ,mill's ,philosophy1 p4 #beg7 that the uniformity of the course of nature is a different thing from the law of causation2 and while he allows that the former is only proved by a long continuance of experience1 and that it is not inconceivable nor necessarily incredible that there may be worlds in which it does not prevail1 he considers the law of causation to be known intuitively4 ,there is1 however1 no other uniformity in the events of nature than that which arises from the law of causation3 so long therefore as there remained any doubt that the course of nature was uniform throughout1 at least when not modified by the intervention of a new 7supernatural7 cause1 a doubt was necessarily implied1 not indeed of the reality of causation1 but of its universality4 ,if the uniformity of the course of nature has any exceptions--if any events succeed one another without fixed laws--to that extent the law of causation fails2 there are events which do not depend on causes4 #ahi ,book i41 chap4 vii4 #aij ,in some cases1 a ,kind is sufficiently identified by some one remarkable property3 but most commonly several are required2 each property considered singly1 being a joint property of that and of other ,kinds4 ,the color and brightness of the diamond are common to it with the paste from which false diamonds are made2 its octohedral form is common to it with alum1 and magnetic iron ore2 but the color and brightness and the form together1 identify its ,kind3 that is1 are a mark to us that it is combustible2 that when burned it produces carbonic acid2 that it can not be cut with any known substance2 together with many other ascertained properties1 and the fact that there exist an indefinite number still unascertained4 #aia ,this doctrine of course assumes that the allotropic forms of what is chemically the same substance are so many different ,kinds2 and such1 in the sense in which the word ,kind is used in this treatise1 they really are4 #aib ,professor ,bain 7,logic1 ii41 #ac7 mentions two empirical laws1 which he considers to be1 with the exception of the law connecting ,gravity with ,resistance to motion1 8the two most widely operating laws as yet discovered whereby two distinct properties are conjoined throughout substances generally40 ,the first is1 8a law connecting ,atomic ,weight and ,specific ,heat by an inverse proportion4 ,for equal weights of the simple bodies1 the atomic weight multiplied by a number expressing the specific heat1 gives a nearly uniform product4 ,the products1 for all the elements1 are near the constant number #f40 ,the other is a law which obtains 8between the specific gravity of substances in the gaseous state1 and the atomic weights4 ,the relationship of the two numbers is in some instances equality2 in other instances the one is a multiple of the other40 ,neither of these generalizations has the smallest appearance of being an ultimate law4 ,they point unmistakably to higher laws4 ,since the heat necessary to raise to a given temperature the same weight of different substances 7called their specific heat7 is inversely as their atomic weight1 that is1 directly as the number of atoms in a given weight of the substance1 it follows that a single atom of every substance requires the same amount of heat to raise it to a given temperature2 a most interesting and important law1 but a law of causation4 ,the other law mentioned by ,mr4 ,bain points to the conclusion1 that in the gaseous state all substances contain1 in the same space1 the same number of atoms2 which1 as the gaseous state suspends all cohesive force1 might naturally be expected1 though it could not have been positively assumed4 ,this law may also be a result of the mode of action of causes1 namely1 of molecular motions4 ,the cases in which one of the numbers is not identical with the other1 but a multiple of it1 may be explained on the nowise unlikely supposition1 that in our present estimate of the atomic weights of some substances1 we mistake two1 or three1 atoms for one1 or one for several4 #aic ,dr4 ,m',cosh 7p4 #cbd of his book7 considers the laws of the chemical composition of bodies as not coming under the principle of ,causation2 and thinks it an omission in this work not to have provided special canons for their investigation and proof4 ,but every case of chemical composition is1 as ,i have explained1 a case of causation4 ,when it is said that water is composed of hydrogen and oxygen1 the affirmation is that hydrogen and oxygen1 by the action on one another which they exert under certain conditions1 generate the properties of water4 ,the ,canons of ,induction1 therefore1 as laid down in this treatise1 are applicable to the case4 ,such special adaptations as the ,inductive methods may require in their application to chemistry1 or any other science1 are a proper subject for any one who treats of the logic of the special sciences1 as ,professor ,bain has done in the latter part of his work2 but they do not appertain to ,general ,logic4 ,dr4 ,m',cosh also complains 7p4 #cbe7 that ,i have given no canons for those sciences in which 8the end sought is not the discovery of ,causes or of ,composition1 but of ,classes2 that is1 ,natural ,classes40 ,such canons could be no other than the principles and rules of ,natural ,classification1 which ,i certainly thought that ,i had expounded at considerable length4 ,but this is far from the only instance in which ,dr4 ,m',cosh does not appear to be aware of the contents of the books he is criticising4 #aid ,mr4 ,de ,morgan1 in his ,formal ,logic1 makes the just remark1 that from two such premises as ,most ,a are ,b1 and ,most ,a are ,c1 we may infer with certainty that some ,b are ,c4 ,but this is the utmost limit of the conclusions which can be drawn from two approximate generalizations1 when the precise degree of their approximation to universality is unknown or undefined4 #aie ,rationale of ,judicial ,evidence1 vol4 iii41 p4 #bbd4 #aif ,the evaluation of the chances in this statement has been objected to by a mathematical friend4 ,the correct mode1 in his opinion1 of setting out the possibilities is as follows4 ,if the thing 7let us call it ,t7 which is both an ,a and a ,c1 is a ,b1 something is true which is only true twice in every thrice1 and something else which is only true thrice in every four times4 ,the first fact being true eight times in twelve1 and the second being true six times in every eight1 and consequently six times in those eight2 both facts will be true only six times in twelve4 ,on the other hand1 if ,t1 although it is both an ,a and a ,c1 is not a ,b1 something is true which is only true once in every thrice1 and something else which is only true once in every four times4 ,the former being true four times out of twelve1 and the latter once in every four1 and therefore once in those four2 both are only true in one case out of twelve4 ,so that ,t is a ,b six times in twelve1 and ,t is not a ,b1 only once3 making the comparative probabilities1 not eleven to one1 as ,i had previously made them1 but six to one4 ,in the last edition ,i accepted this reasoning as conclusive4 ,more attentive consideration1 however1 has convinced me that it contains a fallacy4 ,the objector argues1 that the fact of ,a's being a ,b is true eight times in twelve1 and the fact of ,c's being a ,b six times in eight1 and consequently six times in those eight2 both facts1 therefore1 are true only six times in every twelve4 ,that is1 he concludes that because among ,as taken indiscriminately only eight out of twelve are ,bs and the remaining four are not1 it must equally hold that four out of twelve are not ,bs when the twelve are taken from the select portion of ,as which are also ,cs4 ,and by this assumption he arrives at the strange result1 that there are fewer ,bs among things which are both ,as and ,cs than there are among either ,as or ,cs taken indiscriminately2 so that a thing which has both chances of being a ,b1 is less likely to be so than if it had only the one chance or only the other4 ,the objector 7as has been acutely remarked by another correspondent7 applies to the problem under consideration1 a mode of calculation only suited to the reverse problem4 ,had the question been--,if two of every three ,bs are ,as and three out of every four ,bs are ,cs1 how many ,bs will be both ,as and ,cs1 his reasoning would have been correct4 ,for the ,bs that are both ,as and ,cs must be fewer than either the ,bs that are ,as or the ,bs that are ,cs1 and to find their number we must abate either of these numbers in the ratio due to the other4 ,but when the problem is to find1 not how many ,bs are both ,as and ,cs1 but how many things that are both ,as and ,cs are ,bs1 it is evident that among these the proportion of ,bs must be not less1 but greater1 than among things which are only ,a1 or among things which are only ,b4 ,the true theory of the chances is best found by going back to the scientific grounds on which the proportions rest4 ,the degree of frequency of a coincidence depends on1 and is a measure of1 the frequency1 combined with the efficacy1 of the causes in operation that are favorable to it4 ,if out of every twelve ,as taken indiscriminately eight are ,bs and four are not1 it is implied that there are causes operating on ,a which tend to make it a ,b1 and that these causes are sufficiently constant and sufficiently powerful to succeed in eight out of twelve cases1 but fail in the remaining four4 ,so if of twelve ,cs1 nine are ,bs and three are not1 there must be causes of the same tendency operating on ,c1 which succeed in nine cases and fail in three4 ,now suppose twelve cases which are both ,as and ,cs4 ,the whole twelve are now under the operation of both sets of causes4 ,one set is sufficient to prevail in eight of the twelve cases1 the other in nine4 ,the analysis of the cases shows that six of the twelve will be ,bs through the operation of both sets of causes2 two more in virtue of the causes operating on ,a2 and three more through those operating on ,c1 and that there will be only one case in which all the causes will be inoperative4 ,the total number1 therefore1 which are ,bs will be eleven in twelve1 and the evaluation in the text is correct4 #aig ,supra1 book i41 chap4 v4 #aih ,supra1 book i41 chap4 v41 #a1 and book ii41 chap1 v41 #e4 #aii ,the axiom1 8,equals subtracted from equals leave equal differences10 may be demonstrated from the two axioms in the text4 ,if ,a a and ,b b1 ,a-,b a-b4 ,for if not1 let ,a-,b a-bc4 ,then since ,b b1 adding equals to equals1 ,a ac4 ,but ,a a4 ,therefore a ac1 which is impossible4 ,this proposition having been demonstrated1 we may1 by means of it1 demonstrate the following3 8,if equals be added to unequals1 the sums are unequal40 ,if ,a a and ,b not b1 ,a,b is not ab4 ,for suppose it to be so4 ,then1 since ,a a and ,a,b ab1 subtracting equals from equals1 ,b b2 which is contrary to the hypothesis4 ,so again1 it may be proved that two things1 one of which is equal and the other unequal to a third thing1 are unequal to one another4 ,if ,a a and ,a not ,b1 neither is a ,b4 ,for suppose it to be equal4 ,then since ,a a and a ,b1 and since things equal to the same thing are equal to one another ,a ,b2 which is contrary to the hypothesis4 #bjj ,geometers have usually preferred to define parallel lines by the property of being in the same plane and never meeting4 ,this1 however1 has rendered it necessary for them to assume1 as an additional axiom1 some other property of parallel lines2 and the unsatisfactory manner in which properties for that purpose have been selected by ,euclid and others has always been deemed the opprobrium of elementary geometry4 ,even as a verbal definition1 equidistance is a fitter property to characterize parallels by1 since it is the attribute really involved in the signification of the name4 ,if to be in the same plane and never to meet were all that is meant by being parallel1 we should feel no incongruity in speaking of a curve as parallel to its asymptote4 ,the meaning of parallel lines is1 lines which pursue exactly the same direction1 and which1 therefore1 neither draw nearer nor go farther from one another2 a conception suggested at once by the contemplation of nature4 ,that the lines will never meet is of course included in the more comprehensive proposition that they are everywhere equally distant4 ,and that any straight lines which are in the same plane and not equidistant will certainly meet1 may be demonstrated in the most rigorous manner from the fundamental property of straight lines assumed in the text1 viz41 that if they set out from the same point1 they diverge more and more without limit4 #bja ,philosophie ,positive1 iii41 #dad-daf4 #bjb ,see the two remarkable notes 7,a7 and 7,f71 appended to his ,inquiry into the ,relation of ,cause and ,effect4 #bjc ,supra1 p4 #dac4 #bjd ,a writer to whom ,i have several times referred1 gives as the definition of an impossibility1 that which there exists in the world no cause adequate to produce4 ,this definition does not take in such impossibilities as these--that two and two should make five2 that two straight lines should inclose a space2 or that any thing should begin to exist without a cause4 ,i can think of no definition of impossibility comprehensive enough to include all its varieties1 except the one which ,i have given3 viz41 ,an impossibility is that1 the truth of which would conflict with a complete induction1 that is1 with the most conclusive evidence which we possess of universal truth4 ,as to the reputed impossibilities which rest on no other grounds than our ignorance of any cause capable of producing the supposed effects2 very few of them are certainly impossible1 or permanently incredible4 ,the facts of traveling seventy miles an hour1 painless surgical operations1 and conversing by instantaneous signals between ,london and ,new ,york1 held a high place1 not many years ago1 among such impossibilities4 #bje ,not1 however1 as might at first sight appear1 #iii times as much4 ,a complete analysis of the cases shows that 7always assuming the veracity of the witness to be 7 in #aj1jjj drawings1 the drawing of ,no4 #gi will occur nine times1 and be announced incorrectly once2 the credibility1 therefore1 of the announcement of ,no4 #gi is 2 while the drawing of a white ball will occur nine times1 and be announced incorrectly #iii times4 ,the credibility1 therefore1 of the announcement of white is 1 and the ratio of the two #ajjh3aj2 the one announcement being thus only about a hundred times more credible than the other1 instead of #iii times4 #bjf ,supra1 book iii41 chap4 ii41 #c1 #d1 #e4 #bjg ,mr4 ,bailey has given the best statement of this theory4 8,the general name10 he says1 8raises up the image sometimes of one individual of the class formerly seen1 sometimes of another1 not unfrequently of many individuals in succession2 and it sometimes suggests an image made up of elements from several different objects1 by a latent process of which ,i am not conscious40 7,letters on the ,philosophy of the ,human ,mind1 #ast series1 letter #bb47 ,but ,mr4 ,bailey must allow that we carry on inductions and ratiocinations respecting the class1 by means of this idea or conception of some one individual in it4 ,this is all ,i require4 ,the name of a class calls up some idea1 through which we can1 to all intents and purposes1 think of the class as such1 and not solely of an individual member of it4 #bjh ,i have entered rather fully into this question in chap4 xvii4 of ,an ,examination of ,sir ,william ,hamilton's ,philosophy1 headed 8,the ,doctrine of ,concepts or ,general ,notions10 which contains my last views on the subject4 #bji ,other examples of inappropriate conceptions are given by ,dr4 ,whewell 7,phil4 ,ind4 ,sc4 ii41 #ahe7 as follows3 8,aristotle and his followers endeavored in vain to account for the mechanical relation of forces in the lever1 by applying the inappropriate geometrical conceptions of the properties of the circle3 they failed in explaining the form of the luminous spot made by the sun shining through a hole1 because they applied the inappropriate conception of a circular quality in the sun's light3 they speculated to no purpose about the elementary composition of bodies1 because they assumed the inappropriate conception of likeness between the elements and the compound1 instead of the genuine notion of elements merely determining the qualities of the compound40 ,but in these cases there is more than an inappropriate conception2 there is a false conception2 one which has no prototype in nature1 nothing corresponding to it in facts4 ,this is evident in the last two examples1 and is equally true in the first2 the 8properties of the circle0 which were referred to1 being purely fantastical4 ,there is1 therefore1 an error beyond the wrong choice of a principle of generalization2 there is a false assumption of matters of fact4 ,the attempt is made to resolve certain laws of nature into a more general law1 that law not being one which1 though real1 is inappropriate1 but one wholly imaginary4 #baj ,professor ,bain4 #baa ,this sentence having been erroneously understood as if ,i had meant to assert that belief is nothing but an irresistible association1 ,i think it necessary to observe that ,i express no theory respecting the ultimate analysis either of reasoning or of belief1 two of the most obscure points in analytical psychology4 ,i am speaking not of the powers themselves1 but of the previous conditions necessary to enable those powers to exert themselves3 of which conditions ,i am contending that language is not one1 senses and association being sufficient without it4 ,the irresistible association theory of belief1 and the difficulties connected with the subject1 have been discussed at length in the notes to the new edition of ,mr4 ,james ,mill's ,analysis of the ,phenomena of the ,human ,mind4 #bab ,mr4 ,bailey agrees with me in thinking that whenever 8from something actually present to my senses1 conjoined with past experience1 ,i feel satisfied that something has happened1 or will happen1 or is happening1 beyond the sphere of my personal observation10 ,i may with strict propriety be said to reason3 and of course to reason inductively1 for demonstrative reasoning is excluded by the circumstances of the case4 7,the ,theory of ,reasoning1 #b;d ed41 p4 #bg47 #bac ,novum ,organum ,renovatum1 pp4 #ce-cg4 #bad ,novum ,organum ,renovatum1 pp4 #ci1 #dj4 #bae ,p4 #bag1 #dto edition4 #baf 8,e1 ex1 extra1 extraneus1 tranger1 stranger40 ,another etymological example sometimes cited is the derivation of the ,english uncle from the ,latin avus4 ,it is scarcely possible for two words to bear fewer outward marks of relationship1 yet there is but one step between them1 avus1 avunculus1 uncle4 ,so pilgrim1 from ager3 per agrum1 peragrinus1 peregrinus1 pellegrino1 pilgrim4 ,professor ,bain gives some apt examples of these transitions of meaning4 8,the word #8damp' primarily signified moist1 humid1 wet4 ,but the property is often accompanied with the feeling of cold or chilliness1 and hence the idea of cold is strongly suggested by the word4 ,this is not all4 ,proceeding upon the superadded meaning1 we speak of damping a man's ardor1 a metaphor where the cooling is the only circumstance concerned2 we go on still further to designate the iron slide that shuts off the draft of a stove1 #8the damper1' the primary meaning being now entirely dropped4 #8,dry1' in like manner1 through signifying the absence of moisture1 water1 or liquidity1 is applied to sulphuric acid containing water1 although not thereby ceasing to be a moist1 wet1 or liquid substance40 ,so in the phrases1 dry sherry1 or ,champagne4 8#8,street1' originally a paved way1 with or without houses1 has been extended to roads lined with houses1 whether paved or unpaved4 #8,impertinent' signified at first irrelevant1 alien to the purpose in hand3 through which it has come to mean1 meddling1 intrusive1 unmannerly1 insolent40 7,logic1 ii41 #agc1 #agd47 #bag ,pp4 #bbf1 #bbg4 #bah ,essays1 p4 #bad4 #bai ,essays1 p4 #bae4 #bbj ,though no such evil consequences as take place in these instances are likely to arise from the modern freak of writing sanatory instead of sanitary1 it deserves notice as a charming specimen of pedantry ingrafted upon ignorance4 ,those who thus undertake to correct the spelling of the classical ,english writers1 are not aware that the meaning of sanatory1 if there were such a word in the language1 would have reference not to the preservation of health1 but to the cure of disease4 #bba ,historical ,introduction1 vol4 i41 pp4 #ff-fh4 #bbb ,history of ,scientific ,ideas1 ii41 #aaj1 #aaa4 #bbc ,history of ,scientific ,ideas1 ii41 #aaa-aac4 #bbd ,nov4 ,org4 ,renov41 pp4 #bhf1 #bhg4 #bbe ,history of ,scientific ,ideas1 ii41 #abj-abb4 #bbf ,nov4 ,org4 ,renov41 p4 #bgd4 #bbg ,hist4 ,sc4 ,id41 i4 #acc4 #bbh ,dr4 ,whewell1 in his reply 7,philosophy of ,discovery1 p4 #bgj7 says that he 8stopped short of1 or rather passed by1 the doctrine of a series of organized beings10 because he 8thought it bad and narrow philosophy40 ,if he did1 it was evidently without understanding this form of the doctrine2 for he proceeds to quote a passage from his 8,history10 in which the doctrine he condemns is designated as that of 8a mere linear progression in nature1 which would place each genus in contact only with the preceding and succeeding ones40 ,now the series treated of in the text agrees with this linear progression in nothing whatever but in being a progression4 #bbi ,supra1 p4 #acg4 #bcj ,vulgar ,errors1 book v41 chap4 #ba4 #bca ,pharmacologia1 ,historical ,introduction1 p4 #af4 #bcb ,the author of one of the ,bridgewater ,treatises has fallen1 as it seems to me1 into a similar fallacy when1 after arguing in rather a curious way to prove that matter may exist without any of the known properties of matter1 and may therefore be changeable1 he concludes that it can not be eternal1 because 8eternal 7passive7 existence necessarily involves incapability of change40 ,i believe it would be difficult to point out any other connection between the facts of eternity and unchangeableness1 than a strong association between the two ideas4 ,most of the a priori arguments1 both religious and anti-religious1 on the origin of things1 are fallacies drawn from the same source4 #bcc ,supra1 book ii41 chap4 v41 #f1 and chap4 vii41 #a1 #b1 #c1 #d4 ,see also ,examination of ,sir ,william ,hamilton's ,philosophy1 chap4 vi4 and elsewhere4 #bcd ,it seems that this doctrine was1 before the time ,i have mentioned1 disputed by some thinkers4 ,dr4 ,ward mentions ,scotus1 ,vasquez1 ,biel1 ,francis ,lugo1 and ,valentia4 #bce ,i quote this passage from ,playfair's celebrated ,dissertation on the ,progress of ,mathematical and ,physical ,science4 #bcf ,this statement ,i must now correct1 as too unqualified4 ,the maxim in question was maintained with full conviction by no less an authority than ,sir ,william ,hamilton4 ,see my ,examination1 chap4 xxiv4 #bcg ,nouveaux ,essais sur l',entendement ,humain--,avant-propos4 7uvres1 ,paris ed41 #ahdb1 vol4 i41 p4 #ai47 #bch ,this doctrine also was accepted as true1 and conclusions were grounded on it1 by ,sir ,william ,hamilton4 ,see ,examination1 chap4 xxiv4 #bci ,not that of ,leibnitz1 but the principle commonly appealed to under that name by mathematicians4 #bdj ,dissertation1 p4 #bg4 #bda ,hist4 ,ind4 ,sc41 ,book i41 chap4 i4 #bdb ,novum ,organum1 ,aph4 #ge4 #bdc ,supra1 book iii41 chap4 vii41 #d4 #bdd ,it is hardly needful to remark that nothing is here intended to be said against the possibility at some future period of making gold--by first discovering it to be a compound1 and putting together its different elements or ingredients4 ,but this is a totally different idea from that of the seekers of the grand arcanum4 #bde ,pharmacologia1 pp4 #dc-de4 #bdf ,vol4 i41 chap4 #h4 #bdg ,nov4 ,org41 ,aph4 #df4 #bdh ,playfair's ,dissertation1 sect4 #d4 #bdi ,nov4 ,org4 ,renov41 p4 #fa4 #bej ,pharmacologia1 p4 #ba4 #bea ,pharmacologia1 pp4 #bc1 #bd4 #beb ,ibid41 p4 #bh4 #bec ,ibid41 p4 #fb4 #bed ,ibid41 pp4 #fa1 #fb4 #bee ,supra1 p4 #dej4 #bef ,elements of the ,philosophy of the ,mind1 vol4 ii41 chap4 #d1 sect4 #e4 #beg 8,thus ,fourcroy10 says ,dr4 ,paris1 8explained the operation of mercury by its specific gravity1 and the advocates of this doctrine favored the general introduction of the preparations of iron1 especially in scirrhus of the spleen or liver1 upon the same hypothetical principle2 for1 say they1 whatever is most forcible in removing the obstruction must be the most proper instrument of cure3 such is steel1 which1 besides the attenuating power with which it is furnished1 has still a greater force in this case from the gravity of its particles1 which1 being seven times specifically heavier than any vegetable1 acts in proportion with a stronger impulse1 and therefore is a more powerful deobstruent4 ,this may be taken as a specimen of the style in which these mechanical physicians reasoned and practiced40--,pharmacologia1 pp4 #ch1 #ci4 #beh ,pharmacologia1 pp4 #ci1 #dj4 #bei ,i quote from ,dr4 ,whewell's ,hist4 ,ind4 ,sc41 #c;d ed41 i41 #abi4 #bfj ,hist4 ,ind4 ,sc41 i41 #eb4 #bfa ,nov4 ,org41 ,aph4 #fj4 #bfb 8,an advocate10 says ,mr4 ,de ,morgan 7,formal ,logic1 p4 #bgj71 8is sometimes guilty of the argument dicto secundum quid ad dictum simpliciter3 it is his business to do for his client all that his client might honestly do for himself4 ,is not the word in italics frequently omitted8 ,might any man honestly try to do for himself all that counsel frequently try to do for him8 ,we are often reminded of the two men who stole the leg of mutton2 one could swear he had not got it1 the other that he had not taken it4 ,the counsel is doing his duty by his client1 the client has left the matter to his counsel4 ,between the unexecuted intention of the client1 and the unintended execution of the counsel1 there may be a wrong done1 and1 if we are to believe the usual maxims1 no wrong-doer40 ,the same writer justly remarks 7p4 #bea7 that there is a converse fallacy1 dicto simpliciter ad dictum secundum quid1 called by the scholastic logicians fallacia accidentis2 and another which may be called dicto secundum quid ad dictum secundum alterum quid 7p4 #bfe74 ,for apt instances of both1 ,i must refer the reader to ,mr4 ,de ,morgan's able chapter on ,fallacies4 #bfc ,an example of this fallacy is the popular error that strong drink must be a cause of strength4 ,there is here fallacy within fallacy2 for granting that the words 8strong0 and 8strength0 were not 7as they are7 applied in a totally different sense to fermented liquors and to the human body1 there would still be involved the error of supposing that an effect must be like its cause2 that the conditions of a phenomenon are likely to resemble the phenomenon itself2 which we have already treated of as an a priori fallacy of the first rank4 ,as well might it be supposed that a strong poison will make the person who takes it strong4 #bfd ,in his later editions1 ,archbishop ,whately confines the name of ,petitio ,principii 8to those cases in which one of the premises either is manifestly the same in sense with the conclusion1 or is actually proved from it1 or is such as the persons you are addressing are not likely to know1 or to admit1 except as an inference from the conclusion2 as1 e4g41 if any one should infer the authenticity of a certain history1 from its recording such and such facts1 the reality of which rests on the evidence of that history40 #bfe ,no longer even a probable hypothesis1 since the establishment of the atomic theory2 it being now certain that the integral particles of different substances gravitate unequally4 ,it is true that these particles1 though real minima for the purposes of chemical combination1 may not be the ultimate particles of the substance2 and this doubt alone renders the hypothesis admissible1 even as an hypothesis4 #bff ,hist4 ,ind4 ,sc41 i41 #cd4 #bfg 8,and coxcombs vanquish ,berkeley with a grin40 #bfh ,some arguments and explanations1 supplementary to those in the text1 will be found in ,an ,examination of ,sir ,william ,hamilton's ,philosophy1 chap4 xxvi4 #bfi ,supra1 p4 #dbd4 #bgj ,when this chapter was written1 ,professor ,bain had not yet published even the first part 78,the ,senses and the ,intellect07 of his profound ,treatise on the ,mind4 ,in this the laws of association have been more comprehensively stated and more largely exemplified than by any previous writer2 and the work1 having been completed by the publication of 8,the ,emotions and the ,will10 may now be referred to as incomparably the most complete analytical exposition of the mental phenomena1 on the basis of a legitimate ,induction1 which has yet been produced4 ,more recently still1 ,mr4 ,bain has joined with me in appending to a new edition of the 8,analysis10 notes intended to bring up the analytic science of ,mind to its latest improvements4 ,many striking applications of the laws of association to the explanation of complex mental phenomena are also to be found in ,mr4 ,herbert ,spencer's 8,principles of ,psychology40 #bga ,in the case of the moral sentiments the place of direct experiment is to a considerable extent supplied by historical experience1 and we are able to trace with a tolerable approach to certainty the particular associations by which those sentiments are engendered4 ,this has been attempted1 so far as respects the sentiment of justice1 in a little work by the present author1 entitled ,utilitarianism4 #bgb ,the most favorable cases for making such approximate generalizations are what may be termed collective instances2 where we are fortunately enabled to see the whole class respecting which we are inquiring in action at once1 and1 from the qualities displayed by the collective body1 are able to judge what must be the qualities of the majority of the individuals composing it4 ,thus the character of a nation is shown in its acts as a nation2 not so much in the acts of its government1 for those are much influenced by other causes2 but in the current popular maxims1 and other marks of the general direction of public opinion2 in the character of the persons or writings that are held in permanent esteem or admiration2 in laws and institutions1 so far as they are the work of the nation itself1 or are acknowledged and supported by it2 and so forth4 ,but even here there is a large margin of doubt and uncertainty4 ,these things are liable to be influenced by many circumstances2 they are partially determined by the distinctive qualities of that nation or body of persons1 but partly also by external causes which would influence any other body of persons in the same manner4 ,in order1 therefore1 to make the experiment really complete1 we ought to be able to try it without variation upon other nations3 to try how ,englishmen would act or feel if placed in the same circumstances in which we have supposed ,frenchmen to be placed2 to apply1 in short1 the ,method of ,differences as well as that of ,agreement4 ,now these experiments we can not try1 nor even approximate to4 #bgc 8,to which10 says ,dr4 ,whewell1 8we may add1 that it is certain1 from the history of the subject1 that in that case the hypothesis would never have been framed at all40 ,dr4 ,whewell 7,philosophy of ,discovery1 pp4 #bgg-bhb7 defends ,bacon's rule against the preceding strictures4 ,but his defense consists only in asserting and exemplifying a proposition which ,i had myself stated1 viz41 that though the largest generalizations may be the earliest made1 they are not at first seen in their entire generality1 but acquire it by degrees1 as they are found to explain one class after another of phenomena4 ,the laws of motion1 for example1 were not known to extend to the celestial regions1 until the motions of the celestial bodies had been deduced from them4 ,this1 however1 does not in any way affect the fact1 that the middle principles of astronomy1 the central force1 for example1 and the law of the inverse square1 could not have been discovered1 if the laws of motion1 which are so much more universal1 had not been known first4 ,on ,bacon's system of step-by-step generalization1 it would be impossible in any science to ascend higher than the empirical laws2 a remark which ,dr4 ,whewell's own ,inductive ,tables1 referred to by him in support of his argument1 amply bear out4 #bgd ,supra1 page #cag to the end of the chapter4 #bge ,biographia ,literaria1 i41 #bad4 #bgf ,supra1 p4 #cba4 #bgg ,essays on some ,unsettled ,questions of ,political ,economy1 pp4 #acg-adj4 #bgh ,the quotations in this paragraph are from a paper written by the author1 and published in a periodical in #ahcd4 #bgi ,cours de ,philosophie ,positive1 iv41 #cbe-bi4 #bhj ,since reprinted entire in ,dissertations and ,discussions1 as the concluding paper of the first volume4 #bha ,written and first published in #ahdj4 #bhb ,this great generalization is often unfavorably criticised 7as by ,dr4 ,whewell1 for instance7 under a misapprehension of its real import4 ,the doctrine1 that the theological explanation of phenomena belongs only to the infancy of our knowledge of them1 ought not to be construed as if it was equivalent to the assertion1 that mankind1 as their knowledge advances1 will necessarily cease to believe in any kind of theology4 ,this was ,m4 ,comte's opinion2 but it is by no means implied in his fundamental theorem4 ,all that is implied is1 that in an advanced state of human knowledge1 no other ,ruler of the ,world will be acknowledged than one who rules by universal laws1 and does not at all1 or does not unless in very peculiar cases1 produce events by special interpositions4 ,originally all natural events were ascribed to such interpositions4 ,at present every educated person rejects this explanation in regard to all classes of phenomena of which the laws have been fully ascertained2 though some have not yet reached the point of referring all phenomena to the idea of ,law1 but believe that rain and sunshine1 famine and pestilence1 victory and defeat1 death and life1 are issues which the ,creator does not leave to the operation of his general laws1 but reserves to be decided by express acts of volition4 ,m4 ,comte's theory is the negation of this doctrine4 ,dr4 ,whewell equally misunderstands ,m4 ,comte's doctrine respecting the second or metaphysical stage of speculation4 ,m4 ,comte did not mean that 8discussions concerning ideas0 are limited to an early stage of inquiry1 and cease when science enters into the positive stage4 7,philosophy of ,discovery1 pp4 #bbf et seq47 ,in all ,m4 ,comte's speculations as much stress is laid on the process of clearing up our conceptions as on the ascertainment of facts4 ,when ,m4 ,comte speaks of the metaphysical stage of speculation1 he means the stage in which men speak of 8,nature0 and other abstractions as if they were active forces1 producing effects2 when ,nature is said to do this1 or forbid that2 when ,nature's horror of a vacuum1 ,nature's non-admission of a break1 ,nature's vis medicatrix1 were offered as explanations of phenomena2 when the qualities of things were mistaken for real entities dwelling in the things2 when the phenomena of living bodies were thought to be accounted for by being referred to a 8vital force20 when1 in short1 the abstract names of phenomena were mistaken for the causes of their existence4 ,in this sense of the word it can not be reasonably denied that the metaphysical explanation of phenomena1 equally with the theological1 gives way before the advance of real science4 ,that the final1 or positive stage1 as conceived by ,m4 ,comte1 has been equally misunderstood1 and that1 notwithstanding some expressions open to just criticism1 ,m4 ,comte never dreamed of denying the legitimacy of inquiry into all causes which are accessible to human investigation1 ,i have pointed out in a former place4 #bhc ,buckle's ,history of ,civilization1 i41 #cj4 #bhd ,i have been assured by an intimate friend of ,mr4 ,buckle that he would not have withheld his assent from these remarks1 and that he never intended to affirm or imply that mankind are not progressive in their moral as well as in their intellectual qualities4 8,in dealing with his problem1 he availed himself of the artifice resorted to by the ,political ,economist1 who leaves out of consideration the generous and benevolent sentiments1 and founds his science on the proposition that mankind are actuated by acquisitive propensities alone10 not because such is the fact1 but because it is necessary to begin by treating the principal influence as if it was the sole one1 and make the due corrections afterward4 8,he desired to make abstraction of the intellect as the determining and dynamical element of the progression1 eliminating the more dependent set of conditions1 and treating the more active one as if it were an entirely independent variable40 ,the same friend of ,mr4 ,buckle states that when he used expressions which seemed to exaggerate the influence of general at the expense of special causes1 and especially at the expense of the influence of individual minds1 ,mr4 ,buckle really intended no more than to affirm emphatically that the greatest men can not effect great changes in human affairs unless the general mind has been in some considerable degree prepared for them by the general circumstances of the age2 a truth which1 of course1 no one thinks of denying4 ,and there certainly are passages in ,mr4 ,buckle's writings which speak of the influence exercised by great individual intellects in as strong terms as could be desired4 #bhe ,essay on ,dryden1 in ,miscellaneous ,writings1 i41 #ahf4 #bhf ,in the ,cornhill ,magazine for ,june and ,july1 #ahfa4 #bhg ,it is almost superfluous to observe1 that there is another meaning of the word ,art1 in which it may be said to denote the poetical department or aspect of things in general1 in contradistinction to the scientific4 ,in the text1 the word is used in its older1 and ,i hope1 not yet obsolete sense4 #bhh ,professor ,bain and others call the selection from the truths of science made for the purposes of an art1 a ,practical ,science1 and confine the name ,art to the actual rules4 #bhi ,the word ,teleology is also1 but inconveniently and improperly1 employed by some writers as a name for the attempt to explain the phenomena of the universe from final causes4 #bij ,for an express discussion and vindication of this principle1 see the little volume entitled 8,utilitarianism40