,,university ,,manuals ,,edited ,,by ,,professor ,,knight ,,logic ,,inductive ,,and ,,deductive ,,published ,,may1 #ahic ,reprinted ,december1 #ahic ,november1 #ahid ,january1 #ahii ,august1 #aijd ,june1 #aiji ,september1 #aiab ,july1 #aiac ,january1 #aiae ,,logic ,,inductive ,,and ,,deductive ,,by ,,william ,,minto1 ,m4,a4 ,,hon4 ,,ll4,d4 ,,st4 ,,andrews ,,late ,,professor ,,of ,,logic ,,in ,,the ,,university ,,of ,,aberdeen ,,london ,,john ,,murray1 ,,albemarle ,,street1 ,w4 #aiae ,,preface4 ,in this little treatise two things are attempted that at first might appear incompatible4 ,one of them is to put the study of logical formulae on a historical basis4 ,strangely enough1 the scientific evolution of logical forms1 is a bit of history that still awaits the zeal and genius of some great scholar4 ,i have neither ambition nor qualification for such a magnum opus1 and my life is already more than half spent2 but the gap in evolutionary research is so obvious that doubtless some younger man is now at work in the field unknown to me4 ,all that ,i can hope to do is to act as a humble pioneer according to my imperfect lights4 ,even the little ,i have done represents work begun more than twenty years ago1 and continuously pursued for the last twelve years during a considerable portion of my time4 ,the other aim1 which might at first appear inconsistent with this1 is to increase the power of ,logic as a practical discipline4 ,the main purpose of this practical science1 or scientific art1 is conceived to be the organisation of reason against error1 and error in its various kinds is made the basis of the division of the subject4 ,to carry out this practical aim along with the historical one is not hopeless1 because throughout its long history ,logic has been a practical science2 and1 as ,i have tried to show at some length in introductory chapters1 has concerned itself at different periods with the risks of error peculiar to each4 ,to enumerate the various books1 ancient and modern1 to which ,i have been indebted1 would be a vain parade4 ,where ,i have consciously adopted any distinctive recent contribution to the long line of tradition1 ,i have made particular acknowledgment4 ,my greatest obligation is to my old professor1 ,alexander ,bain1 to whom ,i owe my first interest in the subject1 and more details than ,i can possibly separate from the general body of my knowledge4 ,w4 ,m4 ,,aberdeen1 ,january1 #ahic4 ,since these sentences were written1 the author of this book has died2 and ,professor ,minto's ,logic is his last contribution to the literature of his country4 ,it embodies a large part of his teaching in the philosophical class-room of his ,university1 and doubtless reflects the spirit of the whole of it4 ,scottish ,philosophy has lost in him one of its typical representatives1 and the ,university of the ,north one of its most stimulating teachers4 ,there have been few more distinguished men than ,william ,minto in the professoriate of ,aberdeen2 and the memory of what he was1 of his wide and varied learning1 his brilliant conversation1 his urbanity1 and his rare power of sympathy with men with whose opinions he did not agree1 will remain a possession to many who mourn his loss4 ,it will be something if this little book keeps his memory alive1 both amongst the students who owed so much to him1 and in the large circle of friends who used to feel the charm of his personality4 ,,william ,,knight4 ,,general ,,plan ,,of ,,the ,,series4 ,this ,series is primarily designed to aid the ,university ,extension ,movement throughout ,great ,britain and ,america1 and to supply the need so widely felt by students1 of ,text-books for study and reference1 in connexion with the authorised ,courses of ,lectures4 ,the ,manuals differ from those already in existence in that they are not intended for ,school use1 or for ,examination purposes2 and that their aim is to educate1 rather than to inform4 ,the statement of details is meant to illustrate the working of general laws1 and the development of principles2 while the historical evolution of the subject dealt with is kept in view1 along with its philosophical significance4 ,the remarkable success which has attended ,university ,extension in ,britain has been partly due to the combination of scientific treatment with popularity1 and to the union of simplicity with thoroughness4 ,this movement1 however1 can only reach those resident in the larger centres of population1 while all over the country there are thoughtful persons who desire the same kind of teaching4 ,it is for them also that this ,series is designed4 ,its aim is to supply the general reader with the same kind of teaching as is given in the ,lectures1 and to reflect the spirit which has characterised the movement1 viz41 the combination of principles with facts1 and of methods with results4 ,the ,manuals are also intended to be contributions to the ,literature of the ,subjects with which they respectively deal1 quite apart from ,university ,extension2 and some of them will be found to meet a general rather than a special want4 ,they will be issued simultaneously in ,england and ,america4 ,volumes dealing with separate sections of ,literature1 ,science1 ,philosophy1 ,history1 and ,art have been assigned to representative literary men1 to ,university ,professors1 or to ,extension ,lecturers connected with ,oxford1 ,cambridge1 ,london1 and the ,universities of ,scotland and ,ireland4 ,a list of the works in this ,series will be found at the end of the volume4 ,,contents4 ,,introduction4 ,i4 ,,page ,the ,origin and ,scope of ,logic1 #a ,,ii4 ,logic as a ,preventive of ,error or ,fallacy--,the ,inner ,sophist1 #ag ,,iii4 ,the ,axioms of ,dialectic and of ,syllogism1 #bi ,,book ,i4 ,,the ,,logic ,,of ,,consistency--,,syllogism ,,and ,,definition4 ,,part ,i4 ,,the ,,elements ,,of ,,propositions4 ,,chapter ,i4 ,general ,names and ,allied ,distinctions1 #dc ,,chapter ,,ii4 ,the ,syllogistic ,analysis of ,proposition1 into ,terms4 7#a7 ,the ,bare ,analytic ,forms4 7#b7 ,the ,practice of ,syllogistic ,analysis4 7#c7 ,some ,technical ,difficulties1 #fb ,,part ,,ii4 ,,definition4 ,,chapter ,i4 7#a7 ,imperfect ,understanding of ,words4 7#b7 ,verification of the ,meaning--,dialectic4 7#c7 ,fixation of the ,meaning--,division or ,classification1 ,definition1 ,naming1 #hb ,,chapter ,,ii4 ,the ,five ,predicables--,verbal and ,real ,predication1 #aje ,,chapter ,,iii4 ,aristotle's ,categories1 #aab ,,chapter ,,iv4 ,the ,controversy about ,universals--,difficulties concerning the ,relation of ,general ,names to ,thought and to ,reality1 #abj ,,part ,,iii4 ,,the ,,interpretation ,,of ,,propositions4 ,,chapter ,i4 ,theories of ,predication--,theories of ,judgment1 #aca ,,chapter ,,ii4 ,the ,opposition of ,propositions--,the ,interpretation of ,no1 #aci ,,chapter ,,iii4 ,the ,implication of ,propositions--,immediate ,formal ,inference --,eduction1 #adf ,,chapter ,,iv4 ,the ,counter-,implication of ,propositions1 #aef ,,part ,,iv4 ,,the ,,interdependence ,,of ,,propositions4 ,,chapter ,i4 ,the ,syllogism1 #afg ,,chapter ,,ii4 ,the ,figures and ,moods of the ,syllogism4 7#a7 ,the ,first ,figure4 7#b7 ,the ,minor ,figures and their ,reduction to the ,first4 7#c7 ,sorites1 #agc ,,chapter ,,iii4 ,the ,demonstration of the ,syllogistic ,moods--,the ,canons of the ,syllogism1 #ahe ,,chapter ,,iv4 ,the ,analysis of ,arguments into ,syllogistic ,forms1 #aif ,,chapter ,v4 ,enthymemes1 #bje ,,chapter ,,vi4 ,the ,utility of the ,syllogism1 #bji ,,chapter ,,vii4 ,conditional ,arguments--,hypothetical ,syllogism1 ,disjunctive ,syllogism and ,dilemma1 #bae ,,chapter ,,viii4 ,fallacies in ,deductive ,argument--,petitio ,principii and ,ignoratio ,elenchi1 #bbf ,,chapter ,,ix4 ,formal or ,aristotelian ,induction--,inductive ,argument--,the ,inductive ,syllogism1 #bce ,,book ,,ii4 ,,inductive ,,logic1 ,,or ,,the ,,logic ,,of ,,science4 ,introduction1 #bdc ,,chapter ,i4 ,the ,data of ,experience as ,grounds of ,inference or ,rational ,belief1 #bgc ,,chapter ,,ii4 ,ascertainment of ,simple ,facts in their ,order--,personal ,observation--,hearsay ,evidence--,method of ,testing ,traditional ,evidence1 #bhe ,,chapter ,,iii4 ,ascertainment of ,facts of ,causation4 7#a7 ,post ,hoc ,ergo ,propter ,hoc4 7#b7 ,meaning of ,cause--,methods of ,observation --,mill's ,experimental ,methods1 #bie ,,chapter ,,iv4 ,method of ,observation--,single ,difference4 7#a7 ,the ,principle of ,single ,difference4 7#b7 ,application of the ,principle1 #cjh ,,chapter ,v4 ,methods of ,observation--,elimination--,single ,agreement4 7#a7 ,the ,principle of ,elimination4 7#b7 ,the ,principle of ,single ,agreement4 7#c7 ,mill's ,joint ,method of ,agreement and ,difference1 #cah ,,chapter ,,vi4 ,methods of ,observation--,minor ,methods4 7#a7 ,concomitant ,variations4 7#b7 ,single ,residue1 #cbi ,,chapter ,,vii4 ,the ,method of ,explanation4 7#a7 ,the ,four ,stages of ,orderly ,procedure4 7#b7 ,obstacles to ,explanation--,plurality of ,causes and ,intermixture of ,effects4 7#c7 ,the ,proof of a ,hypothesis1 #ccd ,,chapter ,,viii4 ,supplementary ,methods of ,investigation4 7#a7 ,the ,maintenance of ,averages--,supplement to the ,method of ,difference4 7#b7 ,the ,presumption from ,extra-,casual ,coincidence1 #cea ,,chapter ,,ix4 ,probable ,inference to ,particulars--,the ,measurement of ,probability1 #cfb ,,chapter ,x4 ,inference from ,analogy1 #cfg ,,introduction4 ,i4--,,the ,,origin ,,and ,,scope ,,of ,,logic4 ,the question has sometimes been asked1 ,where should we begin in ,logic8 ,particularly within the present century has this difficulty been felt1 when the study of ,logic has been revived and made intricate by the different purposes of its cultivators4 ,where did the founder of ,logic begin8 ,where did ,aristotle begin8 ,this seems to be the simplest way of settling where we should begin1 for the system shaped by ,aristotle is still the trunk of the tree1 though there have been so many offshoots from the old stump and so many parasitic plants have wound themselves round it that ,logic is now almost as tangled a growth as the ,yews of ,borrowdale-- ,an intertwisted mass of fibres serpentine ,upcoiling and inveterately convolved4 ,it used to be said that ,logic had remained for two thousand years precisely as ,aristotle left it4 ,it was an example of a science or art perfected at one stroke by the genius of its first inventor4 ,the bewildered student must often wish that this were so3 it is only superficially true4 ,much of ,aristotle's nomenclature and his central formulae have been retained1 but they have been very variously supplemented and interpreted to very different purposes--often to no purpose at all4 ,the ,cambridge mathematician's boast about his new theorem--,the best of it all is that it can never by any possibility be made of the slightest use to anybody for anything--might be made with truth about many of the later developments of ,logic4 ,we may say the same1 indeed1 about the later developments of any subject that has been a playground for generation after generation of acute intellects1 happy in their own disinterested exercise4 ,educational subjects--subjects appropriated for the general schooling of young minds--are particularly apt to be developed out of the lines of their original intention4 ,so many influences conspire to pervert the original aim4 ,the convenience of the teacher1 the convenience of the learner1 the love of novelty1 the love of symmetry1 the love of subtlety2 easy-going indolence on the one hand and intellectual restlessness on the other--all these motives act from within on traditional matter without regard to any external purpose whatever4 ,thus in ,logic difficulties have been glossed over and simplified for the dull understanding1 while acute minds have revelled in variations and new and ingenious manipulations of the old formulae1 and in multiplication and more exact and symmetrical definition of the old distinctions4 ,to trace the evolution of the forms and theories of ,logic under these various influences during its periods of active development is a task more easily conceived than executed1 and one far above the ambition of an introductory treatise4 ,but it is well that even he who writes for beginners should recognise that the forms now commonly used have been evolved out of a simpler tradition4 ,without entering into the details of the process1 it is possible to indicate its main stages1 and thus furnish a clue out of the modern labyrinthine confusion of purposes4 ,how did the ,aristotelian ,logic originate8 ,its central feature is the syllogistic forms4 ,in what circumstances did ,aristotle invent these8 ,for what purpose8 ,what use did he contemplate for them8 ,in rightly understanding this1 we shall understand the original scope or province of ,logic1 and thus be in a position to understand more clearly how it has been modified1 contracted1 expanded1 and supplemented4 ,logic has always made high claims as the scientia scientiarum1 the science of sciences4 ,the builders of this ,tower of ,babel are threatened in these latter days with confusion of tongues4 ,we may escape this danger if we can recover the designs of the founder1 and of the master-builders who succeeded him4 ,aristotle's ,logic has been so long before the world in abstract isolation that we can hardly believe that its form was in any way determined by local accident4 ,a horror as of sacrilege is excited by the bare suggestion that the author of this grand and venerable work1 one of the most august monuments of transcendent intellect1 was in his day and generation only a pre-eminent tutor or schoolmaster1 and that his logical writings were designed for the accomplishment of his pupils in a special art in which every intellectually ambitious young ,athenian of the period aspired to excel4 ,yet such is the plain fact1 baldly stated4 ,aristotle's ,logic in its primary aim was as practical as a treatise on ,navigation1 or ,cavendish on ,whist4 ,the latter is the more exact of the two comparisons4 ,it was in effect in its various parts a series of handbooks for a temporarily fashionable intellectual game1 a peculiar mode of disputation or dialectic1#a the game of ,question and ,answer1 the game so fully illustrated in the ,dialogues of ,plato1 the game identified with the name of ,socrates4 ,we may lay stress1 if we like1 on the intellectuality of the game1 and the high topics on which it was exercised4 ,it was a game that could flourish only among a peculiarly intellectual people2 a people less acute would find little sport in it4 ,the ,athenians still take a singular delight in disputation4 ,you cannot visit ,athens without being struck by it4 ,you may still see groups formed round two protagonists in the cafes or the squares1 or among the ruins of the ,acropolis1 in a way to remind you of ,socrates and his friends4 ,they do not argue as ,gil ,blas and his ,hibernians did with heat and temper1 ending in blows4 ,they argue for the pure love of arguing1 the audience sitting or standing by to see fair play with the keenest enjoyment of intellectual thrust and parry4 ,no other people could argue like the ,greeks without coming to blows4 ,it is one of their characteristics now1 and so it was in old times two thousand years ago4 ,and about a century before ,aristotle reached manhood1 they had invented this peculiarly difficult and trying species of disputative pastime1 in which we find the genesis of ,aristotle's logical treatises4 ,to get a proper idea of this debate by ,question and ,answer1 which we may call ,socratic disputation after its most renowned master1 one must read some of the dialogues of ,plato4 ,i will indicate merely the skeleton of the game1 to show how happily it lent itself to ,aristotle's analysis of arguments and propositions4 ,a thesis or proposition is put up for debate1 e4g41 that knowledge is nothing else than sensible perception1#b that it is a greater evil to do wrong than to suffer wrong1#c that the love of gain is not reprehensible4#d ,there are two disputants1 but they do not speak on the question by turns1 so many minutes being allowed to each as in a modern encounter of wits4 ,one of the two1 who may be called the ,questioner1 is limited to asking questions1 the other1 the ,respondent1 is limited to answering4 ,further1 the ,respondent can answer only ,yes or ,no1 with perhaps a little explanation3 on his side the ,questioner must ask only questions that admit of the simple answer ,yes or ,no4 ,the ,questioner's business is to extract from the ,respondent admissions involving the opposite of what he has undertaken to maintain4 ,the ,questioner tries in short to make him contradict himself4 ,only a very stupid ,respondent would do this at once3 the ,questioner plies him with general principles1 analogies1 plain cases2 leads him on from admission to admission1 and then putting the admissions together convicts him out of his own mouth of inconsistency4#e ,now mark precisely where ,aristotle struck in with his invention of the ,syllogism1 the invention on which he prided himself as specially his own1 and the forms of which have clung to ,logic ever since1 even in the usage of those who deride ,aristotle's ,moods and ,figures as antiquated superstitions4 ,suppose yourself the ,questioner1 where did he profess to help you with his mechanism8 ,in effect1 as the word ,syllogism indicates1 it was when you had obtained a number of admissions1 and wished to reason them together1 to demonstrate how they bore upon the thesis in dispute1 how they hung together1 how they necessarily involved what you were contending for4 ,and the essence of his mechanism was the reduction of the admitted propositions to common terms1 and to certain types or forms which are manifestly equivalent or inter-dependent4 ,aristotle advised his pupils also in the tactics of the game1 but his grand invention was the form or type of admissions that you should strive to obtain1 and the effective manipulation of them when you had got them4 ,an example will show the nature of this help1 and what it was worth4 ,to bring the thing nearer home1 let us1 instead of an example from ,plato1 whose topics often seem artificial to us now1 take a thesis from last century1 a paradox still arguable1 ,mandeville's famous--some would say infamous--paradox that ,private ,vices are ,public ,benefits4 ,undertake to maintain this1 and you will have no difficulty in getting a respondent prepared to maintain the negative4 ,the plain men1 such as ,socrates cross-questioned1 would have declared at once that a vice is a vice1 and can never do any good to anybody4 ,your ,respondent denies your proposition simply3 he upholds that private vices never are public benefits1 and defies you to extract from him any admission inconsistent with this4 ,your task then is to lure him somehow into admitting that in some cases what is vicious in the individual may be of service to the ,state4 ,this is enough3 you are not concerned to establish that this holds of all private vices4 ,a single instance to the contrary is enough to break down his universal negative4 ,you cannot1 of course1 expect him to make the necessary admission in direct terms3 you must go round about4 ,you know1 perhaps1 that he has confidence in ,bishop ,butler as a moralist4 ,you try him with the saying3 ,to aim at public and private good are so far from being inconsistent that they mutually promote each other4 ,does he admit this8 ,perhaps he wants some little explanation or exemplification to enable him to grasp your meaning4 ,this was within the rules of the game4 ,you put cases to him1 asking for his ,yes or ,no to each4 ,suppose a man goes into ,parliament1 not out of any zeal for the public good1 but in pure vainglory1 or to serve his private ends1 is it possible for him to render the ,state good service8 ,or suppose a milk-seller takes great pains to keep his milk pure1 not because he cares for the public health1 but because it pays1 is this a benefit to the public8 ,let these questions be answered in the affirmative1 putting you in possession of the admission that some actions undertaken for private ends are of public advantage1 what must you extract besides to make good your position as against the ,respondent8 ,to see clearly at this stage what now is required1 though you have to reach it circuitously1 masking your approach under difference of language1 would clearly be an advantage4 ,this was the advantage that ,aristotle's method offered to supply4 ,a disputant familiar with his analysis would foresee at once that if he could get the ,respondent to admit that all actions undertaken for private ends are vicious1 the victory was his1 while nothing short of this would serve4 ,here my reader may interject that he could have seen this without any help from ,aristotle1 and that anybody may see it without knowing that what he has to do is1 in ,aristotelian language1 to construct a syllogism in ,bokardo4 ,i pass this over4 ,i am not concerned at this point to defend the utility of ,aristotle's method4 ,all that ,i want is to illustrate the kind of use that it was intended for4 ,perhaps if ,aristotle had not habituated men's minds to his analysis1 we should none of us have been able to discern coherence and detect incoherence as quickly and clearly as we do now4 ,but to return to our example4 ,as ,aristotle's pupil1 you would have seen at the stage we are speaking of that the establishment of your thesis must turn upon the definition of virtue and vice4 ,you must proceed1 therefore1 to cross-examine your ,respondent about this4 ,you are not allowed to ask him what he means by virtue1 or what he means by vice4 ,in accordance with the rules of the dialectic1 it is your business to propound definitions1 and demand his ,yes or ,no to them4 ,you ask him1 say1 whether he agrees with ,shaftesbury's definition of a virtuous action as an action undertaken purely for the good of others4 ,if he assents1 it follows that an action undertaken with any suspicion of a self-interested motive cannot be numbered among the virtues4 ,if he agrees1 further1 that every action must be either vicious or virtuous1 you have admissions sufficient to prove your original thesis4 ,all that you have now to do to make your triumph manifest1 is to display the admissions you have obtained in common terms4 ,some actions done with a self-interested motive are public benefits4 ,all actions done with a self-interested motive are private vices4 ,from these premisses it follows irresistibly that ,some private vices are public benefits4 ,this illustration may serve to show the kind of disputation for which ,aristotle's logic was designed1 and thus to make clear its primary uses and its limitations4 ,to realise its uses1 and judge whether there is anything analogous to them in modern needs1 conceive the chief things that it behoved ,questioner and ,respondent in this game to know4 ,all that a proposition necessarily implies2 all that two propositions put together imply2 on what conditions and to what extent one admission is inconsistent with another2 when one admission necessarily involves another2 when two necessarily involve a third4 ,and to these ends it was obviously necessary to have an exact understanding of the terms used1 so as to avoid the snares of ambiguous language4 ,that a ,syllogistic or ,logic of ,consistency should emerge out of ,yes-and-,no ,dialectic was natural4 ,things in this world come when they are wanted3 inventions are made on the spur of necessity4 ,it was above all necessary in this kind of debate to avoid contradicting yourself3 to maintain your consistency4 ,a clever interrogator spread out proposition after proposition before you and invited your assent1 choosing forms of words likely to catch your prejudices and lure you into self-contradiction4 ,an organon1 instrument1 or discipline calculated to protect you as ,respondent and guide you as ,questioner by making clear what an admission led to1 was urgently called for1 and when the game had been in high fashion for more than a century ,aristotle's genius devised what was wanted1 meeting at the same time1 no doubt1 collateral needs that had arisen from the application of ,dialectic to various kinds of subject-matter4 ,the thoroughness of ,aristotle's system was doubtless due partly to the searching character of the dialectic in which it had its birth4 ,no other mode of disputation makes such demands upon the disputant's intellectual agility and precision1 or is so well adapted to lay bare the skeleton of an argument4 ,the uses of ,aristotle's logical treatises remained when the fashion that had called them forth had passed4#f ,clear and consistent thinking1 a mastery of the perplexities and ambiguities of language1 power to detect identity of meaning under difference of expression1 a ready apprehension of all that a proposition implies1 all that may be educed or deduced from it--whatever helps to these ends must be of perpetual use4 ,to purge the understanding of those errors which lie in the confusion and perplexities of an inconsequent thinking1 is a modern description of the main scope of ,logic4#g ,it is a good description of the branch of ,logic that keeps closest to the ,aristotelian tradition4 ,the limitations as well as the uses of ,aristotle's logic may be traced to the circumstances of its origin4 ,both parties to the disputation1 ,questioner and ,respondent alike1 were mainly concerned with the inter-dependence of the propositions put forward4 ,once the ,respondent had given his assent to a question1 he was bound in consistency to all that it implied4 ,he must take all the consequences of his admission4 ,it might be true or it might be false as a matter of fact3 all the same he was bound by it3 its truth or falsehood was immaterial to his position as a disputant4 ,on the other hand1 the ,questioner could not go beyond the admissions of the ,respondent4 ,it has often been alleged as a defect in the ,syllogism that the conclusion does not go beyond the premisses1 and ingenious attempts have been made to show that it is really an advance upon the premisses4 ,but having regard to the primary use of the syllogism1 this was no defect1 but a necessary character of the relation4 ,the ,questioner could not in fairness assume more than had been granted by implication4 ,his advance could only be an argumentative advance3 if his conclusion contained a grain more than was contained in the premisses1 it was a sophistical trick1 and the ,respondent could draw back and withhold his assent4 ,he was bound in consistency to stand by his admissions2 he was not bound to go a fraction of an inch beyond them4 ,we thus see how vain it is to look to the ,aristotelian tradition for an organon of truth or a criterion of falsehood4 ,directly and primarily1 at least1 it was not so2 the circumstances of its origin gave it a different bent4 ,indirectly and secondarily1 no doubt1 it served this purpose1 inasmuch as truth was the aim of all serious thinkers who sought to clear their minds and the minds of others by ,dialectic4 ,but in actual debate truth was represented merely by the common-sense of the audience4 ,a dialectician who gained a triumph by outraging this1 however cleverly he might outwit his antagonist1 succeeded only in amusing his audience1 and dialecticians of the graver sort aimed at more serious uses and a more respectful homage1 and did their best to discountenance merely eristic disputation4 ,further1 it would be a mistake to conclude because ,aristotle's ,logic1 as an instrument of ,dialectic1 concerned itself with the syllogism of propositions rather than their truth1 that it was merely an art of quibbling4 ,on the contrary1 it was essentially the art of preventing and exposing quibbling4 ,it had its origin in quibbling1 no doubt1 inasmuch as what we should call verbal quibbling was of the essence of ,yes-and-,no ,dialectic1 and the main secret of its charm for an intellectual and disputatious people2 but it came into being as a safeguard against quibbling1 not a serviceable adjunct4 ,the mediaeval developments of ,logic retained and even exaggerated the syllogistic character of the original treatises4 ,interrogative dialectic had disappeared in the ,middle ,ages whether as a diversion or as a discipline3 but errors of inconsistency still remained the errors against which principally educated men needed a safeguard4 ,men had to keep their utterances in harmony with the dogmas of the ,church4 ,a clear hold of the exact implications of a proposition1 whether singly or in combination with other propositions1 was still an important practical need4 ,the ,inductive ,syllogism was not required1 and its treatment dwindled to insignificance in mediaeval text-books1 but the ,deductive ,syllogism and the formal apparatus for the definition of terms held the field4 ,it was when observation of ,nature and its laws became a paramount pursuit that the defects of ,syllogistic ,logic began to be felt4 ,errors against which this ,logic offered no protection then called for a safeguard--especially the errors to which men are liable in the investigation of cause and effect4 ,bring your thoughts into harmony one with another1 was the demand of ,aristotle's age4 ,bring your thoughts into harmony with authority1 was the demand of the ,middle ,ages4 ,bring them into harmony with fact1 was the requirement most keenly felt in more recent times4 ,it is in response to this demand that what is commonly but not very happily known as ,inductive ,logic has been formulated4 ,in obedience to custom1 ,i shall follow the now ordinary division of ,logic into ,deductive and ,inductive4 ,the titles are misleading in many ways1 but they are fixed by a weight of usage which it would be vain to try to unsettle4 ,both come charging down the stream of time each with its cohort of doctrines behind it1 borne forward with irresistible momentum4 ,the best way of preventing confusion now is to retain the established titles1 recognise that the doctrines behind each have a radically different aim or end1 and supply the interpretation of this end from history4 ,what they have in common may be described as the prevention of error1 the organisation of reason against error4 ,i have shown that owing to the bent impressed upon it by the circumstances of its origin1 the errors chiefly safeguarded by the ,aristotelian logic were the errors of inconsistency4 ,the other branch of ,logic1 commonly called ,induction1 was really a separate evolution1 having its origin in a different practical need4 ,the history of this ,i will trace separately after we have seen our way through the ,aristotelian tradition and its accretions4 ,the ,experimental ,methods are no less manifestly the germ1 the evolutionary centre or starting-point1 of the new ,logic than the ,syllogism is of the old1 and the main errors safeguarded are errors of fact and inference from fact4 ,at this stage it will be enough to indicate briefly the broad relations between ,deductive ,logic and ,inductive ,logic4 ,inductive ,logic1 as we now understand it--the ,logic of ,observation and ,explanation--was first formulated and articulated to a ,system of ,logic by ,j4 ,s4 ,mill4 ,it was he that added this wing to the old building4 ,but the need of it was clearly expressed as early as the thirteenth century4 ,roger ,bacon1 the ,franciscan friar 7#abad-abib71 and not his more illustrious namesake ,francis1 ,lord ,verulam1 was the real founder of ,inductive ,logic4 ,it is remarkable that the same century saw ,syllogistic ,logic advanced to its most complete development in the system of ,petrus ,hispanus1 a ,portuguese scholar who under the title of ,john ,,xxi4 filled the ,papal ,chair for eight months in #abgf-g4 ,a casual remark of ,roger ,bacon's in the course of his advocacy of ,experimental ,science in the ,opus ,majus draws a clear line between the two branches of ,logic4 ,there are1 he says1 two ways of knowing1 by ,argument and by ,experience4 ,argument concludes a question1 but it does not make us feel certain1 unless the truth be also found in experience4 ,on this basis the old ,logic may be clearly distinguished from the new1 taking as the general aim of ,logic the protection of the mind against the errors to which it is liable in the acquisition of knowledge4 ,all knowledge1 broadly speaking1 comes either from ,authority1 i4e41 by argument from accepted premisses1 or from ,experience4 ,if it comes from ,authority it comes through the medium of words3 if it comes from ,experience it comes through the senses4 ,in taking in knowledge through words we are liable to certain errors2 and in taking in knowledge through the senses we are liable to certain errors4 ,to protect against the one is the main end of ,deductive ,logic3 to protect against the other is the main end of ,inductive ,logic4 ,as a matter of fact the pith of treatises on ,deduction and ,induction is directed to those ends respectively1 the old meanings of ,deduction and ,induction as formal processes 7to be explained afterwards7 being virtually ignored4 ,there is thus no antagonism whatever between the two branches of ,logic4 ,they are directed to different ends4 ,the one is supplementary to the other4 ,the one cannot supersede the other4 ,aristotelian ,logic can never become superfluous as long as men are apt to be led astray by words4 ,its ultimate business is to safeguard in the interpretation of the tradition of language4 ,the mere syllogistic1 the bare forms of equivalent or consistent expression1 have a very limited utility1 as we shall see4 ,but by cogent sequence syllogism leads to proposition1 and proposition to term1 and term to a close study of the relations between words and thoughts and things4 ,footnote #a3 ,we know for certain--and it is one of the evidences of the importance attached to this trivial-looking pastime--that two of the great teacher's logical treatises1 the ,topics and the ,sophistical ,refutations1 were written especially for the guidance of ,questioners and ,respondents4 ,the one instructs the disputant how to qualify himself methodically for discussion before an ordinary audience1 when the admissions extracted from the respondent are matters of common belief1 the questioner's skill being directed to make it appear that the respondent's position is inconsistent with these4 ,the other is a systematic exposure of sophistical tricks1 mostly verbal quibbles1 whereby a delusive appearance of victory in debate may be obtained4 ,but in the concluding chapter of the ,elenchi1 where ,aristotle claims not only that his method is superior to the empirical methods of rival teachers1 but that it is entirely original1 it is the ,syllogism upon which he lays stress as his peculiar and chief invention4 ,the ,syllogism1 the pure forms of which are expounded in his ,prior ,analytics1 is really the centre of ,aristotle's logical system1 whether the propositions to which it is applied are matters of scientific truth as in the ,posterior ,analytics1 or matters of common opinion as in the ,topics4 ,the treatise on ,interpretation1 i4e41 the interpretation of the ,respondent's ,yes and ,no1 is preliminary to the ,syllogism1 the reasoning of the admissions together4 ,even in the half-grammatical half-logical treatise on the ,categories1 the author always keeps an eye on the ,syllogistic analysis4 ,footnote #b3 ,theaetetus1 #aea ,e4 ,footnote #c3 ,gorgias1 #dgc ,d4 ,footnote #d3 ,hipparchus1 #bbe ,a4 ,footnote #e3 ,in its leading and primary use1 this was a mode of debate1 a duel of wits1 in which two men engaged before an audience4 ,but the same form could be used1 and was used1 notably by ,socrates1 not in an eristic spirit but as a means of awakening people to the consequences of certain admissions or first principles1 and thus making vague knowledge explicit and clear4 ,the mind being detained on proposition after proposition as assent was given to it1 dialectic was a valuable instrument of instruction and exposition4 ,but whatever the purpose of the exercise1 controversial triumph1 or solid grounding in the first principles--the evolution of in-dwelling conceptions--the central interest lay in the syllogising or reasoning together of the separately assumed or admitted propositions4 ,footnote #f3 ,like every other fashion1 ,yes-and-,no ,dialectic had its period1 its rise and fall4 ,the invention of it is ascribed to ,zeno the ,eleatic1 the answering and questioning ,zeno1 who flourished about the middle of the fifth century ,b4,c4 ,socrates 7#dfi-cii7 was in his prime at the beginning of the great ,peloponnesian ,war when ,pericles died in #dbi4 ,in that year ,plato was born1 and lived to #cdg1 the olive groves of ,academe being established centre of his teaching from about #chf onwards4 ,aristotle 7#chd-cbb71 who was the tutor of ,alexander the ,great1 established his school at the ,lyceum when ,alexander became king in #ccf and set out on his career of conquest4 ,that ,yes-and-,no ,dialectic was then a prominent exercise1 his logical treatises everywhere bear witness4 ,the subsequent history of the game is obscure4 ,it is probable that ,aristotle's thorough exposition of its legitimate arts and illegitimate tricks helped to destroy its interest as an amusement4 ,footnote #g3 ,hamilton's ,lectures1 iii4 p4 #cg4 ,,ii4--,,logic ,,as ,a ,,preventive ,,of ,,error ,,or ,,fallacy4--,,the ,,inner ,,sophist4 ,why describe ,logic as a system of defence against error8 ,why say that its main end and aim is the organisation of reason against confusion and falsehood8 ,why not rather say1 as is now usual1 that its end is the attainment of truth8 ,does this not come to the same thing8 ,substantially1 the meaning is the same1 but the latter expression is more misleading4 ,to speak of ,logic as a body of rules for the investigation of truth has misled people into supposing that ,logic claims to be an art of ,discovery1 that it claims to lay down rules by simply observing which investigators may infallibly arrive at new truths4 ,now1 this does not hold even of the ,logic of ,induction1 still less of the older ,logic1 the precise relation of which to truth will become apparent as we proceed4 ,it is only by keeping men from going astray and by disabusing them when they think they have reached their destination that ,logic helps men on the road to truth4 ,truth often lies hid in the centre of a maze1 and logical rules only help the searcher onwards by giving him warning when he is on the wrong track and must try another4 ,it is the searcher's own impulse that carries him forward3 ,logic does not so much beckon him on to the right path as beckon him back from the wrong4 ,in laying down the conditions of correct interpretation1 of valid argument1 of trustworthy evidence1 of satisfactory explanation1 ,logic shows the inquirer how to test and purge his conclusions1 not how to reach them4 ,to discuss1 as is sometimes done1 whether ,fallacies lie within the proper sphere of ,logic1 is to obscure the real connexion between ,fallacies and ,logic4 ,it is the existence of ,fallacies that calls ,logic into existence2 as a practical science ,logic is needed as a protection against ,fallacies4 ,such historically is its origin4 ,we may1 if we like1 lay down an arbitrary rule that a treatise on ,logic should be content to expound the correct forms of interpretation and reasoning and should not concern itself with the wrong4 ,if we take this view we are bound to pronounce ,fallacies extra-logical4 ,but to do so is simply to cripple the usefulness of ,logic as a practical science4 ,the manipulation of the bare logical forms1 without reference to fallacious departures from them1 is no better than a nursery exercise4 ,every correct form in ,logic is laid down as a safeguard against some erroneous form to which men are prone1 whether in the interpretation of argument or the interpretation of experience1 and the statement and illustration of the typical forms of wrong procedure should accompany pari passu the exposition of the right procedure4 ,in accordance with this principle1 ,i shall deal with special fallacies1 special snares or pitfalls--misapprehension of words1 misinterpretation of propositions1 misunderstanding of arguments1 misconstruction of facts1 evidences1 or signs--each in connexion with its appropriate safeguard4 ,this seems to me the most profitable method4 ,but at this stage1 it may be worth while1 by way of emphasising the need for ,logic as a science of rational belief1 to take a survey of the most general tendencies to irrational belief1 the chief kinds of illusion or bias that are rooted in the human constitution4 ,we shall then better appreciate the magnitude of the task that ,logic attempts in seeking to protect reason against its own fallibility and the pressure of the various forces that would usurp its place4 ,it is a common notion that we need ,logic to protect us against the arts of the ,sophist1 the dishonest juggler with words and specious facts4 ,but in truth the ,inner ,sophist1 whose instruments are our own inborn propensities to error1 is a much more dangerous enemy4 ,for once that we are the victims of designing ,sophists1 we are nine times the victims of our own irrational impulses and prejudices4 ,men generally deceive themselves before they deceive others4 ,francis ,bacon drew attention to these inner perverting influences1 these universal sources of erroneous belief1 in his ,de ,augmentis and again in his ,novum ,organum1 under the designation of ,idola 7,greek3 eidola71 deceptive appearances of truth1 illusions4 ,his classification of ,idola--,idola ,tribus1 illusions common to all men1 illusions of the race2 ,idola ,specus1 personal illusions1 illusions peculiar to the den in which each man lives2 ,idola ,fori1 illusions of conversation1 vulgar prejudices embodied in words2 ,idola ,theatri1 illusions of illustrious doctrine1 illusions imposed by the dazzling authority of great names--is defective as a classification inasmuch as the first class includes all the others1 but like all his writings it is full of sagacious remarks and happy examples4 ,not for the sake of novelty1 but because it is well that matters so important should be presented from more than one point of view1 ,i shall follow a division adapted from the more scientific1 if less picturesque1 arrangement of ,professor ,bain1 in his chapter on the ,fallacious ,tendencies of the ,human ,mind4#a ,the illusions to which we are all subject may best be classified according to their origin in the depths of our nature4 ,let us try to realise how illusory beliefs arise4 ,what is a belief8 ,one of the uses of ,logic is to set us thinking about such simple terms4 ,an exhaustive analysis and definition of belief is one of the most difficult of psychological problems4 ,we cannot enter upon that3 let us be content with a few simple characters of belief4 ,first1 then1 belief is a state of mind4 ,second1 this state of mind is outward-pointing3 it has a reference beyond itself1 a reference to the order of things outside us4 ,in believing1 we hold that the world as it is1 has been1 or will be1 corresponds to our conceptions of it4 ,third1 belief is the guide of action3 it is in accordance with what we believe that we direct our activities4 ,if we want to know what a man really believes1 we look at his action4 ,this at least is the clue to what he believes at the moment4 ,i cannot1 a great orator once said1 read the minds of men4 ,this was received with ironical cheers4 ,no1 he retorted1 but ,i can construe their acts4 ,promoters of companies are expected to invest their own money as a guarantee of good faith4 ,if a man says he believes the world is coming to an end in a year1 and takes a lease of a house for fifteen years1 we conclude that his belief is not of the highest degree of strength4 ,the close connexion of belief with our activities1 enables us to understand how illusions1 false conceptions of reality1 arise4 ,the illusions of ,feeling and the illusions of ,custom are well understood1 but other sources of illusion1 which may be designated ,impatient ,impulse and ,happy ,exercise1 are less generally recognised4 ,an example or two will show what is meant4 ,we cannot understand the strength of these perverting influences till we realise them in our own case4 ,we detect them quickly enough in others4 ,seeing that in common speech the word illusion implies a degree of error amounting almost to insanity1 and the illusions we speak of are such as no man is ever quite free from1 it is perhaps less startling to use the word bias4 ,the ,bias of ,impatient ,impulse4 ,as a being formed for action1 not only does healthy man take a pleasure in action1 physical and mental1 for its own sake1 irrespective of consequences1 but he is so charged with energy that he cannot be comfortable unless it finds a free vent4 ,in proportion to the amount and excitability of his energy1 restraint1 obstruction1 delay is irksome1 and soon becomes a positive and intolerable pain4 ,any bar or impediment that gives us pause is hateful even to think of3 the mere prospect annoys and worries4 ,hence it arises that belief1 a feeling of being prepared for action1 a conviction that the way is clear before us for the free exercise of our activities1 is a very powerful and exhilarating feeling1 as much a necessity of happy existence as action itself4 ,we see this when we consider how depressing and uncomfortable a condition is the opposite state to belief1 namely1 doubt1 perplexity1 hesitation1 uncertainty as to our course4 ,and realising this1 we see how strong a bias we have in this fact of our nature1 this imperious inward necessity for action2 how it urges us to act without regard to consequences1 and to jump at beliefs without inquiry4 ,for1 unless inquiry itself is our business1 a self-sufficient occupation1 it means delay and obstruction4 ,this ultimate fact of our nature1 this natural inbred constitutional impatience1 explains more than half of the wrong beliefs that we form and persist in4 ,we must have a belief of some kind3 we cannot be happy till we get it1 and we take up with the first that seems to show the way clear4 ,it may be right or it may be wrong3 it is not1 of course1 necessarily always wrong3 but that1 so far as we are concerned1 is a matter of accident4 ,the pressing need for a belief of some sort1 upon which our energies may proceed in anticipation at least1 will not allow us to stop and inquire4 ,any course that offers a relief from doubt and hesitation1 any conviction that lets the will go free1 is eagerly embraced4 ,it may be thought that this can apply only to beliefs concerning the consequences of our own personal actions1 affairs in which we individually play a part4 ,it is from them1 no doubt1 that our nature takes this set3 but the habit once formed is extended to all sorts of matters in which we have no personal interest4 ,tell an ordinary ,englishman1 it has been wittily said1 that it is a question whether the planets are inhabited1 and he feels bound at once to have a confident opinion on the point4 ,the strength of the conviction bears no proportion to the amount of reason spent in reaching it1 unless it may be said that as a general rule the less a belief is reasoned the more confidently it is held4 ,a grocer1 writes ,mr4 ,bagehot in an acute essay on ,the ,emotion of ,conviction1#b has a full creed as to foreign policy1 a young lady a complete theory of the ,sacraments1 as to which neither has any doubt4 ,a girl in a country parsonage will be sure that ,paris never can be taken1 or that ,bismarck is a wretch4 ,an attitude of philosophic doubt1 of suspended judgment1 is repugnant to the natural man4 ,belief is an independent joy to him4 ,this bias works in all men4 ,while there is life1 there is pressure from within on belief1 tending to push reason aside4 ,the force of the pressure1 of course1 varies with individual temperament1 age1 and other circumstances4 ,the young are more credulous than the old1 as having greater energy3 they are apt1 as ,bacon puts it1 to be carried away by the sanguine element in their temperament4 ,shakespeare's ,laertes is a study of the impulsive temperament1 boldly contrasted with ,hamlet1 who has more discourse of reason4 ,when ,laertes hears that his father has been killed1 he hurries home1 collects a body of armed sympathisers1 bursts into the presence of the king1 and threatens with his vengeance--the wrong man4 ,he never pauses to make inquiry3 like ,hotspur he is a wasp-stung and impatient fool2 he must wreak his revenge on somebody1 and at once4 ,hamlet's father also has been murdered1 but his reason must be satisfied before he proceeds to his revenge1 and when doubtful proof is offered1 he waits for proof more relative4 ,bacon's ,idola ,tribus and ,dr4 ,bain's illustrations of incontinent energy1 are mostly examples of unreasoning intellectual activity1 hurried generalisations1 unsound and superficial analogies1 rash hypotheses4 ,bacon quotes the case of the sceptic in the temple of ,poseidon1 who1 when shown the offerings of those who had made vows in danger and been delivered1 and asked whether he did not now acknowledge the power of the god1 replied3 ,but where are they who made vows and yet perished8 ,this man answered rightly1 says ,bacon4 ,in dreams1 omens1 retributions1 and such like1 we are apt to remember when they come true and to forget the cases when they fail4 ,if we have seen but one man of a nation1 we are apt to conclude that all his countrymen are like him2 we cannot suspend our judgment till we have seen more4 ,confident belief1 as ,dr4 ,bain remarks1 is the primitive attitude of the human mind3 it is only by slow degrees that this is corrected by experience4 ,the old adage1 ,experience teaches fools1 has a meaning of its own1 but in one sense it is the reverse of the truth4 ,the mark of a fool is that he is not taught by experience1 and we are all more or less intractable pupils1 till our energies begin to fail4 ,the ,bias of ,happy ,exercise4 ,if an occupation is pleasant in itself1 if it fully satisfies our inner craving for action1 we are liable to be blinded thereby to its consequences4 ,happy exercise is the fool's ,paradise4 ,the fallacy lies not in being content with what provides a field for the full activity of our powers3 to be content in such a case may be the height of wisdom3 but the fallacy lies in claiming for our occupation results1 benefits1 utilities that do not really attend upon it4 ,thus we see subjects of study1 originally taken up for some purpose1 practical1 artistic1 or religious1 pursued into elaborate detail far beyond their original purpose1 and the highest value1 intellectual1 spiritual1 moral1 claimed for them by their votaries1 when in truth they merely serve to consume so much vacant energy1 and may be a sheer waste of time that ought to be otherwise employed4 ,but as ,i am in danger of myself furnishing an illustration of this bias--it is nowhere more prevalent than in philosophy--,i will pass to our next head4 ,the ,bias of the ,feelings4 ,this source of illusion is much more generally understood4 ,the blinding and perverting influence of passion on reason has been a favourite theme with moralists ever since man began to moralise1 and is acknowledged in many a popular proverb4 ,love is blind2 ,the wish is father to the thought2 ,some people's geese are all swans2 and so forth4 ,we need not dwell upon the illustration of it4 ,fear and ,sloth magnify dangers and difficulties2 ,affection can see no imperfection in its object3 in the eyes of ,jealousy a rival is a wretch4 ,from the nature of the case we are much more apt to see examples in others than in ourselves4 ,if the strength of this bias were properly understood by everybody1 the mistake would not so often be committed of suspecting bad faith1 conscious hypocrisy1 when people are found practising the grossest inconsistencies1 and shutting their eyes apparently in deliberate wilfulness to facts held under their very noses4 ,men are inclined to ascribe this human weakness to women4 ,reasoning from feeling is said to be feminine logic4 ,but it is a human weakness4 ,to take one very powerful feeling1 the feeling of self-love or self-interest--this operates in much more subtle ways than most people imagine1 in ways so subtle that the self-deceiver1 however honest1 would fail to be conscious of the influence if it were pointed out to him4 ,when the slothful man saith1 ,there is a lion in the path1 we can all detect the bias to his belief1 and so we can when the slothful student says that he will work hard to-morrow1 or next week1 or next month2 or when the disappointed man shows an exaggerated sense of the advantages of a successful rival or of his own disadvantages4 ,but self-interest works to bias belief in much less palpable ways than those4 ,it is this bias that accounts for the difficulty that men of antagonistic interests have in seeing the arguments or believing in the honesty of their opponents4 ,you shall find conferences held between capitalists and workmen in which the two sides1 both represented by men incapable of consciously dishonest action1 fail altogether to see the force of each other's arguments1 and are mutually astonished each at the other's blindness4 ,the ,bias of ,custom4 ,that custom1 habits of thought and practice1 affect belief1 is also generally acknowledged1 though the strength and wide reach of the bias is seldom realised4 ,very simple cases of unreasoning prejudice were adduced by ,locke1 who was the first to suggest a general explanation of them in the ,association of ,ideas 7,human ,understanding1 bk4 ii4 ch4 xxxiii474 ,there is1 for instance1 the fear that overcomes many people when alone in the dark4 ,in vain reason tells them that there is no real danger2 they have a certain tremor of apprehension that they cannot get rid of1 because darkness is inseparably connected in their minds with images of horror4 ,similarly we contract unreasonable dislikes to places where painful things have happened to us4 ,equally unreasoning1 if not unreasonable1 is our attachment to customary doctrines or practices1 and our invincible antipathy to those who do not observe them4 ,words are very common vehicles for the currency of this kind of prejudice1 good or bad meanings being attached to them by custom4 ,the power of words in this way is recognised in the proverb3 ,give a dog a bad name1 and then hang him4 ,these verbal prejudices are ,bacon's ,idola ,fori1 illusions of conversation4 ,each of us is brought up in a certain sect or party1 and accustomed to respect or dishonour certain sectarian or party names1 ,whig1 ,tory1 ,radical1 ,socialist1 ,evolutionist1 ,broad1 ,low1 or ,high ,church4 ,we may meet a man without knowing under what label he walks and be charmed with his company3 meet him again when his name is known1 and all is changed4 ,such errors are called ,fallacies of ,association to point to the psychological explanation4 ,this is that by force of association certain ideas are brought into the mind1 and that once they are there1 we cannot help giving them objective reality4 ,for example1 a doctor comes to examine a patient1 and finds certain symptoms4 ,he has lately seen or heard of many cases of influenza1 we shall say2 influenza is running in his head4 ,the idea once suggested has all the advantage of possession4 ,but why is it that a man cannot get rid of an idea8 ,why does it force itself upon him as a belief8 ,association1 custom1 explains how it got there1 but not why it persists in staying4 ,to explain this we must call in our first fallacious principle1 the ,impatience of ,doubt or ,delay1 the imperative inward need for a belief of some sort4 ,and this leads to another remark1 that though for convenience of exposition1 we separate these various influences1 they are not separated in practice4 ,they may and often do act all together1 the ,inner ,sophist concentrating his forces4 ,finally1 it may be asked whether1 seeing that illusions are the offspring of such highly respectable qualities as excess of energy1 excess of feeling1 excess of docility1 it is a good thing for man to be disillusioned4 ,the rose-colour that lies over the world for youth is projected from the abundant energy and feeling within3 disillusion comes with failing energies1 when hope is unwilling to be fed4 ,is it good then to be disillusioned8 ,the foregoing exposition would be egregiously wrong if the majority of mankind did not resent the intrusion of ,reason and its organising lieutenant ,logic4 ,but really there is no danger that this intrusion succeeds to the extent of paralysing action and destroying feeling1 and uprooting custom4 ,the utmost that ,logic can do is to modify the excess of these good qualities by setting forth the conditions of rational belief4 ,the student who masters those conditions will soon see the practical wisdom of applying his knowledge only in cases where the grounds of rational belief are within his reach4 ,to apply it to the consequences of every action would be to yield to that bias of incontinent activity which is1 perhaps1 our most fruitful source of error4 ,footnote #a3 ,bain's ,logic1 bk4 vi4 chap4 iii4 ,bacon intended his ,idola to bear the same relation to his ,novum ,organum that ,aristotle's ,fallacies or ,sophistical ,tricks bore to the old ,organum4 ,but in truth1 as ,i have already indicated1 what ,bacon classifies is our inbred tendencies to form idola or false images1 and it is these same tendencies that make us liable to the fallacies named by ,aristotle4 ,some of ,aristotle's1 as we shall see1 are fallacies of ,induction4 ,footnote #b3 ,bagehot's ,literary ,studies1 ii4 #dbg4 ,,iii4--,,the ,,axioms ,,of ,,dialectic ,,and ,,of ,,syllogism4 ,there are certain principles known as the ,laws of ,thought or the ,maxims of ,consistency4 ,they are variously expressed1 variously demonstrated1 and variously interpreted1 but in one form or another they are often said to be the foundation of all ,logic4 ,it is even said that all the doctrines of ,deductive or ,syllogistic ,logic may be educed from them4 ,let us take the most abstract expression of them1 and see how they originated4 ,three laws are commonly given1 named respectively the ,law of ,identity1 the ,law of ,contradiction and the ,law of ,excluded ,middle4 #a4 ,the ,law of ,identity4 ,a is ,a4 ,socrates is ,socrates4 ,guilt is guilt4 #b4 ,the ,law of ,contradiction4 ,a is not not-,a4 ,socrates is not other than ,socrates4 ,guilt is not other than guilt4 ,or ,a is not at once b and not-b4 ,socrates is not at once good and not-good4 ,guilt is not at once punishable and not-punishable4 #c4 ,the ,law of ,excluded ,middle4 ,everything is either ,a or not-,a2 or1 ,a is either b or not-b4 ,a given thing is either ,socrates or not-,socrates1 either guilty or not-guilty4 ,it must be one or the other3 no middle is possible4 ,why lay down principles so obvious1 in some interpretations1 and so manifestly sophistical in others8 ,the bare forms of modern ,logic have been reached by a process of attenuation from a passage in ,aristotle's ,metaphysics#a 7iii4 #c1 #d1 #ajje;b - #ajjh74 ,he is there laying down the first principle of demonstration1 which he takes to be that it is impossible that the same predicate can both belong1 and not belong1 to the same subject1 at the same time1 and in the same sense4#b ,that ,socrates knows grammar1 and does not know grammar--these two propositions cannot both be true at the same time1 and in the same sense4 ,two contraries cannot exist together in the same subject4 ,the double answer ,yes and ,no cannot be given to one and the same question understood in the same sense4 ,but why did ,aristotle consider it necessary to lay down a principle so obvious8 ,simply because among the subtle dialecticians who preceded him the principle had been challenged4 ,the ,platonic dialogue ,euthydemus shows the farcical lengths to which such quibbling was carried4 ,the two brothers vanquish all opponents1 but it is by claiming that the answer ,no does not preclude the answer ,yes4 ,is not the honourable honourable1 and the base base8 asks ,socrates4 ,that is as ,i please1 replies ,dionysodorus4 ,socrates concludes that there is no arguing with such men3 they repudiate the first principles of dialectic4 ,there were1 however1 more respectable practitioners who canvassed on more plausible grounds any form into which ultimate doctrines about contraries and contradictions1 truth and falsehood1 could be put1 and therefore ,aristotle considered it necessary to put forth and defend at elaborate length a statement of a first principle of demonstration4 ,contradictions cannot both be true of the same subject at the same time and in the same sense4 ,this is the original form of the ,law of ,contradiction4 ,the words of the same subject1 at the same time1 and in the same sense1 are carefully chosen to guard against possible quibbles4 ,socrates knows grammar4 ,by ,socrates we must mean the same individual man4 ,and even of the same man the assertion may be true at one time and not at another4 ,there was a time when ,socrates did not know grammar1 though he knows it now4 ,and the assertion may be true in one sense and not in another4 ,it may be true that ,socrates knows grammar1 yet not that he knows everything that is to be known about grammar1 or that he knows as much as ,aristarchus4 ,aristotle acknowledges that this first principle cannot itself be demonstrated1 that is1 deduced from any other4 ,if it is denied1 you can only reduce the denier to an absurdity4 ,and in showing how to proceed in so doing1 he says you must begin by coming to an agreement about the words used1 that they signify the same for one and the other disputant4#c ,no dialectic is possible without this understanding4 ,this first principle of ,dialectic is the original of the ,law of ,identity4 ,while any question as to the truth or falsehood of a question is pending1 from the beginning to the end of any logical process1 the words must continue to be accepted in the same sense4 ,words must have an identical reference to things4 ,incidentally in discussing the ,axiom of ,contradiction 7,greek3 axioma tes antiphaseos71#d ,aristotle lays down what is now known as the ,law of ,excluded ,middle4 ,of two contradictories one or other must be true3 we must either affirm or deny any one thing of any other3 no mean or middle is possible4 ,in their origin1 then1 these so-called ,laws of ,thought were simply the first principles of ,dialectic and ,demonstration4 ,consecutive argument1 coherent ratiocination1 is impossible unless they are taken for granted4 ,if we divorce or abstract them from their original application1 and consider them merely as laws of thinking or of being1 any abstract expression1 or illustration1 or designation of them may easily be pushed into antagonism with other plain truths or first principles equally rudimentary4 ,without entering into the perplexing and voluminous discussion to which these laws have been subjected by logicians within the last hundred years1 a little casuistry is necessary to enable the student to understand within what limits they hold good4 ,socrates is ,socrates4 ,the name ,socrates is a name for something to which you and ,i refer when we use the name4 ,unless we have the same reference1 we cannot hold any argument about the thing1 or make any communication one to another about it4 ,but if we take ,socrates is ,socrates to mean that1 ,an object of thought or thing is identical with itself1 ,an object of thought or thing cannot be other than itself1 and call this a law of thought1 we are met at once by a difficulty4 ,thought1 properly speaking1 does not begin till we pass beyond the identity of an object with itself4 ,thought begins only when we recognise the likeness between one object and others4 ,to keep within the self-identity of the object is to suspend thought4 ,socrates was a native of ,attica1 ,socrates was a wise man1 ,socrates was put to death as a troubler of the commonweal--whenever we begin to think or say anything about ,socrates1 to ascribe any attributes to him1 we pass out of his self-identity into his relations of likeness with other men1 into what he has in common with other men4 ,hegelians express this plain truth with paradoxical point when they say3 ,of any definite existence or thought1 therefore1 it may be said with quite as much truth that it is not1 as that it is1 its own bare self4#e ,or1 ,a thing must other itself in order to be itself4 ,controversialists treat this as a subversion of the laws of ,identity and ,contradiction4 ,but it is only ,hegel's fun--his paradoxical way of putting the plain truth that any object has more in common with other objects than it has peculiar to itself4 ,till we enter into those aspects of agreement with other objects1 we cannot truly be said to think at all4 ,if we say merely that a thing is itself1 we may as well say nothing about it4 ,to lay down this is not to subvert the ,law of ,identity1 but to keep it from being pushed to the extreme of appearing to deny the ,law of ,likeness1 which is the foundation of all the characters1 attributes1 or qualities of things in our thoughts4 ,that self-same objects are like other self-same objects1 is an assumption distinct from the ,law of ,identity1 and any interpretation of it that excludes this assumption is to be repudiated4 ,but does not the law of ,identity as well as the law of the likeness of mutually exclusive identities presuppose that there are objects self-same1 like others1 and different from others8 ,certainly3 this is one of the presuppositions of ,logic4#f ,we assume that the world of which we talk and reason is separated into such objects in our thoughts4 ,we assume that such words as ,socrates represent individual objects with a self-same being or substance2 that such words as wisdom1 humour1 ugliness1 running1 sitting1 here1 there1 represent attributes1 qualities1 characters or predicates of individuals2 that such words as man represent groups or classes of individuals4 ,some logicians in expressing the ,law of ,identity have their eye specially upon the objects signified by general names or abstract names1 man1 education4#g ,a concept is identical with the sum of its characters1 or1 ,classes are identical with the sum of the individuals composing them4 ,the assumptions thus expressed in technical language which will hereafter be explained are undoubtedly assumptions that ,logic makes3 but since they are statements of the internal constitution of some of the identities that words represent1 to call them the ,law of ,identity is to depart confusingly from traditional usage4#h ,that throughout any logical process a word must signify the same object1 is one proposition3 that the object signified by a general name is identical with the sum of the individuals to each of whom it is applicable1 or with the sum of the characters that they bear in common1 is another proposition4 ,logic assumes both3 ,aristotle assumed both3 but it is the first that is historically the original of all expressions of the ,law of ,identity in modern text-books4 ,yet another expression of a ,law of ,identity which is really distinct from and an addition to ,aristotle's original4 ,socrates was an ,athenian1 a philosopher1 an ugly man1 an acute dialectician1 etc4 ,let it be granted that the word ,socrates bears the same signification throughout all these and any number more of predicates1 we may still ask3 ,but what is it that ,socrates signifies8 ,the title ,law of ,identity is sometimes given#i to a theory on this point4 ,socrates is ,socrates4 ,an individual is the identity running through the totality of its attributes4 ,is this not1 it may be asked1 to confuse thought and being1 to resolve ,socrates into a string of words8 ,no3 real existence is one of the admissible predicates of ,socrates3 one of the attributes under which we conceive him4 ,but whether we accept or reject this ,law of ,identity1 it is an addition to ,aristotle's dialectical law of identity2 it is a theory of the metaphysical nature of the identity signified by a ,singular name4 ,and the same may be said of yet another theory of ,identity1 that1 ,an individual is identical with the totality of its predicates1 or 7another way of putting the same theory71 ,an individual is a conflux of generalities4 ,to turn next to the ,laws of ,contradiction and ,excluded ,middle4 ,these also may be subjected to ,casuistry1 making clearer what they assert by showing what they do not deny4 ,they do not deny that things change1 and that successive states of the same thing may pass into one another by imperceptible degrees4 ,a thing may be neither here nor there3 it may be on the passage from here to there3 and1 while it is in motion1 we may say1 with equal truth1 that it is neither here nor there1 or that it is both here and there4 ,youth passes gradually into age1 day into night3 a given man or a given moment may be on the borderland between the two4 ,logic does not deny the existence of indeterminate margins3 it merely lays down that for purposes of clear communication and coherent reasoning the line must be drawn somewhere between b1 and not-b4 ,a difference1 however1 must be recognised between logical negation and the negations of common thought and common speech4 ,the latter are definite to a degree with which the mere ,logic of ,consistency does not concern itself4 ,to realise this is to understand more clearly the limitations of ,formal ,logic4 ,in common speech1 to deny a quality of anything is by implication to attribute to it some other quality of the same kind4 ,let any man tell me that the streets of such and such a town are not paved with wood1 ,i at once conclude that they are paved with some other material4 ,it is the legitimate effect of his negative proposition to convey this impression to my mind4 ,if1 proceeding on this1 ,i go on to ask3 ,then they are paved with granite or asphalt1 or this or that8 and he turns round and says3 ,i did not say they were paved at all1 ,i should be justified in accusing him of a quibble4 ,in ordinary speech1 to deny one kind of pavement is to assert pavement of some kind4 ,similarly1 to deny that ,so-and-so is not in the ,twenty-first ,regiment1 is to imply that he is in another regiment1 that he is in the army in some regiment4 ,to retort upon this inference3 ,he is not in the army at all1 is a quibble3 as much so as it would be to retort3 ,there is no such person in existence4 ,now ,logic does not take account of this implication1 and nothing has contributed more to bring upon it the reproach of quibbling4 ,in ,logic1 to deny a quality is simply to declare a repugnance between it and the subject2 negation is mere sublation1 taking away1 and implies nothing more4 ,not-b is entirely indefinite3 it may cover anything except b4 ,is ,logic then really useless1 or even misleading1 inasmuch as it ignores the definite implication of negatives in ordinary thought and speech8 ,in ignoring this implication1 does ,logic oppose this implication as erroneous8 ,does ,logic shelter the quibbler who trades upon it8 ,by no means3 to jump to this conclusion were a misunderstanding4 ,the fact only is that nothing beyond the logical ,law of ,contradiction needs to be assumed for any of the processes of ,formal ,logic4 ,aristotle required to assume nothing more for his syllogistic formulae1 and ,logic has not yet included in its scope any process that requires any further assumption4 ,if not-b represent everything except b1 everything outside b1 then that ,a is b1 and that ,a is not-b1 cannot both be true1 and one or other of them must be true4 ,whether the scope of ,logic ought to be extended is another question4 ,it seems to me that the scope of ,logic may legitimately be extended so as to take account both of the positive implication of negatives and the negative implication of positives4 ,i therefore deal with this subject in a separate chapter following on the ordinary doctrines of ,immediate ,inference1 where ,i try to explain the simple ,law of ,thought involved4 ,when ,i say that the extension is legitimate1 ,i mean that it may be made without departing from the traditional view of ,logic as a practical science1 conversant with the nature of thought and its expression only in so far as it can provide practical guidance against erroneous interpretations and inferences4 ,the extension that ,i propose is in effect an attempt to bring within the fold of ,practical ,logic some of the results of the dialectic of ,hegel and his followers1 such as ,mr4 ,bradley and ,mr4 ,bosanquet1 ,professor ,caird and ,professor ,wallace4#aj ,the logical processes formulated by ,aristotle are merely stages in the movement of thought towards attaining definite conceptions of reality4 ,to treat their conclusions as positions in which thought may dwell and rest1 is an error1 against which ,logic itself as a practical science may fairly be called upon to guard4 ,it may even be conceded that the ,aristotelian processes are artificial stages1 courses that thought does not take naturally1 but into which it has to be forced for a purpose4 ,to concede this is not to concede that the ,aristotelian logic is useless1 as long as we have reason on our side in holding that thought is benefited and strengthened against certain errors by passing through those artificial stages4 ,footnote #a3 ,the first statement of the ,law of ,identity in the form ,ens est ens is ascribed by ,hamilton 7,lectures1 iii4 #ia7 to ,antonius ,andreas1 a fourteenth century commentator on the ,metaphysics4 ,but ,andreas is merely expounding what ,aristotle sets forth in iii4 #d1 #ajjf a1 b4 ,ens est ens does not mean in ,andreas what ,a is ,a means in ,hamilton4 ,footnote #b3 ,greek3 to gar auto hama huparchein te kai me huparchein adynaton to auto kai kata to auto1 4 4 4 ahute de pason esti bebaiotate ton archon4 iii4 #c1 #ajje;b1 #ai-bc4 ,footnote #c3 ,hamilton credits ,andreas with maintaining1 against ,aristotle1 that the principle of ,identity1 and not the principle of ,contradiction1 is the one absolutely first4 ,which comes first1 is a scholastic question on which ingenuity may be exercised4 ,but in fact ,aristotle put the principle of ,identity first in the above plain sense1 and ,andreas only expounded more formally what ,aristotle had said4 ,footnote #d3 ,greek3 ,metaxu antiphaseos endechetai einai outhen1 all' ananke e phanai e apophanai en kath henos hotioun4 ,metaph4 iii4 #g1 #ajaa;b1 #bc-d4 ,footnote #e3 ,prof4 ,caird's ,hegel1 p4 #ach4 ,footnote #f3 ,see ,venn1 ,empirical ,logic1 #a-h4 ,footnote #g3 ,e4g41 ,hamilton1 lect4 v42 ,veitch's ,institutes of ,logic1 chaps1 xii41 xiii4 ,footnote #h3 ,the confusion probably arises in this way4 ,first1 these laws are formulated as laws of thought that ,logic assumes4 ,second1 a notion arises that these laws are the only postulates of ,logic3 that all logical doctrines can be evolved from them4 ,third1 when it is felt that more than the identical reference of words or the identity of a thing with itself must be assumed in ,logic1 the ,law of ,identity is extended to cover this further assumption4 ,footnote #i3 ,e4g41 ,bosanquet's ,logic1 ii4 #bjg4 ,footnote #aj3 ,bradley1 ,principles of ,logic2 ,bosanquet1 ,logic or ,the ,morphology of ,knowledge2 ,caird1 ,hegel 7in ,blackwood's ,philosophical ,classics72 ,wallace1 ,the ,logic of ,hegel4 ,,book ,i4 ,,the ,,logic ,,of ,,consistency4 ,,syllogism ,,and ,,definition4 ,,part ,i4 ,,the ,,elements ,,of ,,propositions4 ,,chapter ,i4 ,,general ,,names ,,and ,,allied ,,distinctions4 ,to discipline us against the errors we are liable to in receiving knowledge through the medium of words--such is one of the objects of ,logic1 the main object of what may be called the ,logic of ,consistency4 ,strictly speaking1 we may receive knowledge about things through signs or single words1 as a nod1 a wink1 a cry1 a call1 a command4 ,but an assertory sentence1 proposition1 or predication1 is the unit with which ,logic concerns itself--a sentence in which a subject is named and something is said or predicated about it4 ,let a man once understand the errors incident to this regular mode of communication1 and he may safely be left to protect himself against the errors incident to more rudimentary modes4 ,a proposition1 whether long or short1 is a unit1 but it is an analysable unit4 ,and the key to syllogistic analysis is the ,general ,name4 ,every proposition1 every sentence in which we convey knowledge to another1 contains a general name or its equivalent4 ,that is to say1 every proposition may be resolved into a form in which the predicate is a general name4 ,a knowledge of the function of this element of speech is the basis of all logical discipline4 ,therefore1 though we must always remember that the proposition is the real unit of speech1 and the general name only an analytic element1 we take the general name and its allied distinctions in thought and reality first4 ,how propositions are analysed for syllogistic purposes will be shown by-and-by1 but we must first explain various technical terms that logicians have devised to define the features of this cardinal element4 ,the technical terms ,,class1 ,,concept1 ,,notion1 ,,attribute1 ,,extension or ,,denotation1 ,,intension or ,,connotation1 ,,genus1 ,,species1 ,,differentia1 ,,singular ,,name1 ,,collective ,,name1 ,,abstract ,,name1 all centre round it4 ,a general name is a name applicable to a number of different things on the ground of some likeness among them1 as man1 ratepayer1 man of courage1 man who fought at ,waterloo4 ,from the examples it will be seen that a general name logically is not necessarily a single word4 ,any word or combination of words that serves a certain function is technically a general name4 ,the different ways of making in common speech the equivalent of a general name logically are for the grammarian to consider4 ,in the definition of a general name attention is called to two distinct considerations1 the individual objects to each of which the name is applicable1 and the points of resemblance among them1 in virtue of which they have a common name4 ,for those distinctions there are technical terms4 ,,class is the technical term for the objects1 different yet agreeing1 to each of which a general name may be applied4 ,the points of resemblance are called the common ,,attributes of the class4 ,a class may be constituted on one attribute or on several4 ,ratepayer1 woman ratepayer1 unmarried woman ratepayer2 soldier1 ,british soldier1 ,british soldier on foreign service4 ,but every individual to which the general name can be applied must possess the common attribute or attributes4 ,these common attributes are also called the ,,notion of the class1 inasmuch as it is these that the mind notes or should note when the general name is applied4 ,,concept is a synonym perhaps in more common use than notion2 the rationale of this term 7derived from con and capere1 to take or grasp together7 being that it is by means of the points of resemblance that the individuals are grasped or held together by the mind4 ,these common points are the one in the many1 the same amidst the different1 the identity signified by the common name4 ,the name of an attribute as thought of by itself without reference to any individual or class possessing it1 is called an ,,abstract name4 ,by contradistinction1 the name of an individual or a class is ,,concrete4 ,technical terms are wanted also to express the relation of the individuals and the attributes to the general name4 ,the individuals jointly are spoken of as the ,,denotation1 or ,,extension or ,,scope of the name2 the common attributes as its ,,connotation1 ,,intension1 ,,comprehension1 or ,,ground4 ,the whole denotation1 etc41 is the class2 the whole connotation1 etc41 is the concept4#a ,the limits of a class in ,logic are fixed by the common attributes4 ,any individual object that possesses these is a member4 ,the statement of them is the ,,definition4 ,to predicate a general name of any object1 as1 ,this is a cat1 ,this is a very sad affair1 is to refer that object to a class1 which is equivalent to saying that it has certain features of resemblance with other objects1 that it reminds us of them by its likeness to them4 ,thus to say that the predicate of every proposition is a general name1 expressed or implied1 is the same as to say that every predication may be taken as a reference to a class4 ,ordinarily our notion or concept of the common features signified by general names is vague and hazy4 ,the business of ,logic is to make them clear4 ,it is to this end that the individual objects of the class are summoned before the mind4 ,in ordinary thinking there is no definite array or muster of objects3 when we think of dog or cat1 accident1 book1 beggar1 ratepayer1 we do not stop to call before the mind a host of representatives of the class1 nor do we take precise account of their common attributes4 ,the concept of house is what all houses have in common4 ,to make this explicit would be no easy matter1 and yet we are constantly referring objects to the class house4 ,we shall see presently that if we wish to make the connotation or concept clear we must run over the denotation or class1 that is to say1 the objects to which the general name is applied in common usage4 ,try1 for example1 to conceive clearly what is meant by house1 tree1 dog1 walking-stick4 ,you think of individual objects1 so-called1 and of what they have in common4 ,a class may be constituted on one property or on many4 ,there are several points common to all houses1 enclosing walls1 a roof1 a means of exit and entrance4 ,for the full concept of the natural kinds1 men1 dogs1 mice1 etc41 we should have to go to the natural historian4 ,,degrees ,,of ,,generality4 ,one class is said to be of higher generality than another when it includes that other and more4 ,thus animal includes man1 dog1 horse1 etc42 man includes ,aryan1 ,semite1 etc42 ,aryan includes ,hindoo1 ,teuton1 ,celt1 etc4 ,the technical names for higher and lower classes are ,,genus and ,,species4 ,these terms are not fixed as in ,natural ,history to certain grades1 but are purely relative one to another1 and movable up and down a scale of generality4 ,a class may be a species relatively to one class1 which is above it1 and a genus relatively to one below it4 ,thus ,aryan is a species of the genus man1 ,teuton a species of the genus ,aryan4 ,in the graded divisions of ,natural ,history genus and species are fixed names for certain grades4 ,thus3 ,vertebrates form a division2 the next subdivision1 e4g41 ,mammals1 ,birds1 ,reptiles1 etc41 is called a class2 the next1 e4g41 ,rodents1 ,carnivora1 ,ruminants1 an order2 the next1 e4g41 ,rats1 ,squirrels1 ,beavers1 a genus2 the next1 e4g41 ,brown rats1 ,mice1 a species4 ,vertebrates 7division74 ,mammals1 ,birds1 ,reptiles1 etc4 7class74 ,rodents1 ,ruminants1 ,carnivors1 etc4 7order74 ,rats1 ,squirrels1 ,beavers1 etc4 7genus74 ,brown rats1 ,mice1 etc4 7species74 ,if we subdivide a large class into smaller classes1 and1 again1 subdivide these subdivisions1 we come at last to single objects4 ,men ------------ ,europeans1 ,asiatics1 etc4 ------------- ,englishmen1 ,frenchmen1 etc4 --------------------- ,john ,doe1 ,richard ,roe1 etc4 ,a table of higher and lower classes arranged in order has been known from of old as a tree of division or classification4 ,the following is ,porphyry's tree3-- ,being _/ ,corporeal ,incorporeal _/ 7,body7 _/ ,animate ,inanimate _/ 7,living ,being7 _/ ,sensible ,insensible _/ 7,animal7 _/ ,rational ,irrational _/ 7,man7 --------------------------------------- ,socrates1 ,plato1 and other individuals4 ,the single objects are called ,,individuals1 because the division cannot be carried farther4 ,the highest class is technically the ,,summum ,,genus1 or ,genus generalissimum2 the next highest class to any species is the ,,proximum ,,genus2 the lowest group before you descend to individuals is the ,,infima ,,species1 or ,species specialissima4 ,the attribute or attributes whereby a species is distinguished from other species of the same genus1 is called its ,,differentia or ,,differentiae4 ,the various species of houses are differentiated by their several uses1 dwelling-house1 town-house1 ware-house1 public-house4 ,poetry is a species of ,fine ,art1 its differentia being the use of metrical language as its instrument4 ,a lower class1 indicated by the name of its higher class qualified by adjectives or adjective phrases expressing its differential property or properties1 is said to be described ,,per ,,genus ,,et ,,differentiam4 ,examples3 ,black-bird1 note-book1 clever man1 man of ,kent1 eminent ,british painter of marine subjects4 ,by giving a combination of attributes common to him with nobody else1 we may narrow down the application of a name to an individual3 ,the ,commander-in-,chief of the ,british forces at the battle of ,waterloo4 ,other attributes of classes as divided and defined1 have received technical names4 ,an attribute common to all the individuals of a class1 found in that class only1 and following from the essential or defining attributes1 though not included among them1 is called a ,,proprium4 ,an attribute that belongs to some1 but not to all1 or that belongs to all1 but is not a necessary consequence of the essential attributes1 is called an ,,accident4 ,the clearest examples of ,propria are found in mathematical figures4 ,thus1 the defining property of an equilateral triangle is the equality of the sides3 the equality of the angles is a proprium4 ,that the three angles of a triangle are together equal to two right angles is a proprium1 true of all triangles1 and deducible from the essential properties of a triangle4 ,outside ,mathematics1 it is not easy to find propria that satisfy the three conditions of the definition4 ,it is a useful exercise of the wits to try for such4 ,educability--an example of the proprium in mediaeval text-books--is common to men1 and results from man's essential constitution2 but it is not peculiar2 other animals are educable4 ,that man cooks his food is probably a genuine proprium4 ,that horses run wild in ,thibet3 that gold is found in ,california3 that clergymen wear white ties1 are examples of ,accidents4 ,learning is an accident in man1 though educability is a proprium4 ,what is known technically as an ,,inseparable ,,accident1 such as the black colour of the crow or the ,ethiopian1 is not easy to distinguish from the ,proprium4 ,it is distinguished only by the third character1 deducibility from the essence4#b ,accidents that are both common and peculiar are often useful for distinguishing members of a class4 ,distinctive dresses or badges1 such as the gown of a student1 the hood of a ,d4,d41 are accidents1 but mark the class of the individual wearer4 ,so with the colours of flowers4 ,genus1 ,species1 ,differentia1 ,proprium1 and ,accidens have been known since the time of ,porphyry as the ,,five ,,predicables4 ,they are really only terms used in dividing and defining4 ,we shall return to them and endeavour to show that they have no significance except with reference to fixed schemes1 scientific or popular1 of ,division or ,classification4 ,given such a fixed scheme1 very nice questions may be raised as to whether a particular attribute is a defining attribute1 or a proprium1 or an accident1 or an inseparable accident4 ,such questions afford great scope for the exercise of the analytic intellect4 ,we shall deal more particularly with degrees of generality when we come to ,definition4 ,this much has been necessary to explain an unimportant but much discussed point in ,logic1 what is known as the inverse variation of ,connotation and ,denotation4 ,connotation and ,denotation are often said to vary inversely in quantity4 ,the larger the connotation the smaller the denotation1 and vice versa4 ,with certain qualifications the statement is correct enough1 but it is a rough compendious way of expressing the facts and it needs qualification4 ,the main fact to be expressed is that the more general a name is1 the thinner is its meaning4 ,the wider the scope1 the shallower the ground4 ,as you rise in the scale of generality1 your classes are wider but the number of common attributes is less4 ,inversely1 the name of a species has a smaller denotation than the name of its genus1 but a richer connotation4 ,fruit-tree applies to fewer objects than tree1 but the objects denoted have more in common3 so with apple and fruit-tree1 ,ribston ,pippin and apple4 ,again1 as a rule1 if you increase the connotation you contract the area within which the name is applicable4 ,take any group of things having certain attributes in common1 say1 men of ability3 add courage1 beauty1 height of six feet1 chest measurement of #dj inches1 and with each addition fewer individuals are to be found possessing all the common attributes4 ,this is obvious enough1 and yet the expression inverse variation is open to objection4 ,for the denotation may be increased in a sense without affecting the connotation4 ,the birth of an animal may be said to increase the denotation3 every year thousands of new houses are built3 there are swarms of flies in a hot summer and few in a cold4 ,but all the time the connotation of animal1 house1 or fly remains the same3 the word does not change its meaning4 ,it is obviously wrong to say that they vary in inverse proportion4 ,double or treble the number of attributes1 and you do not necessarily reduce the denotation by one-half or one-third4 ,it is1 in short1 the meaning or connotation that is the main thing4 ,this determines the application of a word4 ,as a rule if you increase meaning1 you restrict scope4 ,let your idea1 notion1 or concept of culture be a knowledge of ,mathematics1 ,latin and ,greek3 your men of culture will be more numerous than if you require from each of them these qualifications plus a modern language1 an acquaintance with the ,fine ,arts1 urbanity of manners1 etc4 ,it is just possible to increase the connotation without decreasing the denotation1 to thicken or deepen the concept without diminishing the class4 ,this is possible only when two properties are exactly co-extensive1 as equilaterality and equiangularity in triangles4 ,,singular and ,,proper ,,names4 ,a ,proper or ,singular name is a name used to designate an individual4 ,its function1 as distinguished from that of the general name1 is to be used purely for the purpose of distinctive reference4 ,a man is not called ,tom or ,dick because he is like in certain respects to other ,toms or other ,dicks4 ,the ,toms or the ,dicks do not form a logical class4 ,the names are given purely for purposes of distinction1 to single out an individual subject4 ,the ,arabic equivalent for a ,proper name1 alam1 a mark1 a sign-post1 is a recognition of this4 ,in the expressions a ,napoleon1 a ,hotspur1 a ,harry1 the names are not singular names logically1 but general names logically1 used to signify the possession of certain attributes4 ,a man may be nicknamed on a ground1 but if the name sticks and is often used1 the original meaning is forgotten4 ,if it suggests the individual in any one of his qualities1 any point in which he resembles other individuals1 it is no longer a ,proper or ,singular name logically1 that is1 in logical function4 ,that function is fulfilled when it has called to mind the individual intended4 ,to ask1 as is sometimes done1 whether ,proper names are connotative or denotative1 is merely a confusion of language4 ,the distinction between connotation and denotation1 extension and intension1 applies only to general names4 ,unless a name is general1 it has neither extension nor intension3#c a ,proper or ,singular name is essentially the opposite of a general name and has neither the one nor the other4 ,a nice distinction may be drawn between ,proper and ,singular names1 though they are strict synonyms for the same logical function4 ,it is not essential to the discharge of that function that the name should be strictly appropriated to one object4 ,there are many ,toms and many ,dicks4 ,it is enough that the word indicates the individual without confusion in the particular circumstances4 ,this function may be discharged by words and combinations of words that are not ,proper in the grammatical sense4 ,this man1 the cover of this book1 the ,prime ,minister of ,england1 the seer of ,chelsea1 may be ,singular names as much as ,honolulu or ,lord ,tennyson4 ,in common speech ,singular names are often manufactured ad hoc by taking a general name and narrowing it down by successive qualifications till it applies only to one individual1 as ,the leading subject of the ,sovereign of ,england at the present time4 ,if it so happens that an individual has some attribute or combination peculiar to himself1 he may be suggested by the mention of that attribute or combination3--the inventor of the steam-engine1 the author of ,hudibras4 ,have such names a connotation8 ,the student may exercise his wits on the question4 ,it is a nice one1 an excellent subject of debate4 ,briefly1 if we keep rigid hold of the meaning of connotation1 this ,singular name has none4 ,the combination is a singular name only when it is the subject of a predication or an attribution1 as in the sentences1 ,the position of the leading subject of etc41 is a difficult one1 or ,the leading subject of etc41 wears an eyeglass4 ,in such a sentence as ,so-and-so is the leading subject of etc41 the combined name has a connotation1 but then it is a general and not a singular name4 ,,collective ,,names1 as distinguished from ,general ,names4 ,a collective name is a name for a number of similar units taken as a whole--a name for a totality of similar units1 as army1 regiment1 mob1 mankind1 patrimony1 personal estate4 ,a group or collection designated by a collective name is so far like a class that the individual objects have something in common3 they are not heterogeneous but homogeneous4 ,a mob is a collection of human beings2 a regiment of soldiers2 a library of books4 ,the distinction lies in this1 that whatever is said of a collective name is said about the collection as a whole1 and does not apply to each individual2 whatever is said of a general name applies to each individual4 ,further1 the collective name can be predicated only of the whole group1 as a whole2 the general name is predicable of each1 distributively4 ,mankind has been in existence for thousands of years2 ,the mob passed through the streets4 ,in such expressions as ,an honest man's the noblest work of ,god1 the subject is functionally a collective name4 ,a collective name may be used as a general name when it is extended on the ground of what is common to all such totalities as it designates4 ,an excited mob is dangerous2 ,an army without discipline is useless4 ,the collective name is then connotative of the common characters of the collection4 ,,material ,,or ,,substantial ,,names4 ,the question has been raised whether names of material1 gold1 water1 snow1 coal1 are general or collective singular4 ,in the case of pieces or bits of a material1 it is true that any predicate made concerning the material1 such as ,sugar is sweet1 or ,water quenches thirst1 applies to any and every portion4 ,but the separate portions are not individuals in the whole signified by a material name as individuals are in a class4 ,further1 the name of material cannot be predicated of a portion as a class name can be of an individual4 ,we cannot say1 ,this is a sugar4 ,when we say1 ,this is a piece of sugar1 sugar is a collective name for the whole material4 ,there are probably words on the borderland between general names and collective names4 ,in such expressions as ,this is a coal1 ,the bonnie water o' ,urie1 the material name is used as a general name4 ,the real distinction is between the distributive use and the collective use of a name2 as a matter of grammatical usage1 the same word may be used either way1 but logically in any actual proposition it must be either one or the other4 ,,abstract ,,names are names for the common attributes or concepts on which classes are constituted4 ,a concrete name is a name directly applicable to an individual in all his attributes1 that is1 as he exists in the concrete4 ,it may be written on a ticket and pinned to him4 ,when we have occasion to speak of the point or points in which a number of individuals resemble one another1 we use what is called an abstract name4 ,generous man1 clever man1 timid man1 are concrete names2 generosity1 cleverness1 timidity1 are abstract names4 ,it is disputed whether abstract names are connotative4 ,the question is a confused one3 it is like asking whether the name of a town is municipal4 ,an abstract name is the name of a connotation as a separate object of thought or reference1 conceived or spoken of in abstraction from individual accidents4 ,strictly speaking it is notative rather than connotative3 it cannot be said to have a connotation because it is itself the symbol of what is called the connotation of a general name4#d ,the distinction between abstract names and concrete names is virtually a grammatical distinction1 that is1 a distinction in mode of predication4 ,we may use concrete names or abstract names at our pleasure to express the same meaning4 ,to say that ,john is a timid man is the same thing as saying that ,timidity is one of the properties or characteristics or attributes of ,john4 ,pride and cruelty generally go together2 ,proud men are generally cruel men4 ,general names are predicable of individuals because they possess certain attributes3 to predicate the possession of those attributes is the same thing as to predicate the general name4 ,abstract forms of predication are employed in common speech quite as frequently as concrete1 and are1 as we shall see1 a great source of ambiguity and confusion4 ,footnote #a3 ,it has been somewhat too hastily assumed on the authority of ,mansel 7,note to ,aldrich1 pp4 #af1 #ag7 that ,mill inverted the scholastic tradition in his use of the word ,connotative4 ,mansel puts his statement doubtfully1 and admits that there was some licence in the use of the word ,connotative1 but holds that in ,scholastic ,logic an adjective was said to signify primarily the attribute1 and to connote or signify secondarily 7,greek3 prossemainein7 the subject of inhesion4 ,the truth is that ,mansel's view was a theory of usage not a statement of actual usage1 and he had good reason for putting it doubtfully4 ,as a matter of fact1 the history of the distinction follows the simple type of increasing precision and complexity1 and ,mill was in strict accord with standard tradition4 ,by the ,nominalist commentators on the ,summulae of ,petrus ,hispanus certain names1 adjectives grammatically1 are called ,connotativa as opposed to ,absoluta1 simply because they have a double function4 ,white is connotative as signifying both a subject1 such as ,socrates1 of whom whiteness is an attribute1 and an attribute whiteness3 the names ,socrates and whiteness are ,absolute1 as having but a single signification4 ,occam himself speaks of the subject as the primary signification1 and the attribute as the secondary1 because the answer to ,what is white8 is ,something informed with whiteness1 and the subject is in the nominative case while the attribute is in an oblique case 7,logic1 part ,i4 chap4 x474 ,later on we find that ,tataretus 7,expositio in ,summulas1 ,a4,d4 #aeja71 while mentioning 7,tract4 ,sept4 ,de ,appellationibus7 that it is a matter of dispute among ,doctores whether a connotative name connotat the subject or the attribute1 is perfectly explicit in his own definition1 ,terminus connotativus est qui praeter illud pro quo supponit connotat aliquid adjacere vel non adjacere rei pro qua supponit 7,tract4 ,sept4 ,de ,suppositionibus74 ,and this remained the standard usage as long as the distinction remained in logical text-books4 ,we find it very clearly expressed by ,clichtoveus1 a ,nominalist1 quoted as an authority by ,guthutius in his ,gymnasium ,speculativum1 ,paris1 #afjg 7,de ,terminorum ,cognitione1 pp4 #gh-i74 ,terminus absolutus est1 qui solum illud pro quo in propositione supponit1 significat4 ,connotativus autem1 qui ultra idipsum1 aliud importat4 ,thus man and animal are absolute terms1 which simply stand for 7supponunt pro7 the things they signify4 ,white is a connotative name1 because it stands for 7supponit pro7 a subject in which it is an accident3 and beyond this1 still signifies an accident1 which is in that subject1 and is expressed by an abstract name4 ,only ,clichtoveus drops the verb connotat1 perhaps as a disputable term1 and says simply ultra importat4 ,so in the ,port ,royal ,logic 7#affb71 from which possibly ,mill took the distinction3 ,les noms qui signifient les choses comme modifiees1 marquant premierement et directement la chose1 quoique plus confusement1 et indirectement le mode1 quoique plus distinctement1 sont appeles adjectifs ou connotatifs2 comme rond1 dur1 juste1 prudent 7part i4 chap ii474 ,what ,mill did was not to invert ,scholastic usage but to revive the distinction1 and extend the word connotative to general names on the ground that they also imported the possession of attributes4 ,the word has been as fruitful of meticulous discussion as it was in the ,renaissance of ,logic1 though the ground has changed4 ,the point of ,mill's innovation was1 premising that general names are not absolute but are applied in virtue of a meaning1 to put emphasis on this meaning as the cardinal consideration4 ,what he called the connotation had dropped out of sight as not being required in the ,syllogistic ,forms4 ,this was as it were the point at which he put in his horn to toss the prevalent conception of ,logic as ,syllogistic4 ,the real drift of ,mill's innovation has been obscured by the fact that it was introduced among the preliminaries of ,syllogism1 whereas its real usefulness and significance belongs not to ,syllogism in the strict sense but to ,definition4 ,he added to the confusion by trying to devise forms of ,syllogism based on connotation1 and by discussing the ,axiom of the ,syllogism from this point of view4 ,for syllogistic purposes1 as we shall see1 ,aristotle's forms are perfect1 and his conception of the proposition in extension the only correct conception4 ,whether the centre of gravity in ,consistency ,logic should not be shifted back from ,syllogism to ,definition1 the latter being the true centre of consistency1 is another question4 ,the tendency of ,mill's polemic was to make this change4 ,and possibly the secret of the support it has recently received from ,mr4 ,bradley and ,mr4 ,bosanquet is that they1 following ,hegel1 are moving in the same direction4 ,in effect1 ,mill's doctrine of ,connotation helped to fix a conception of the general name first dimly suggested by ,aristotle when he recognised that names of genera and species signify ,quality1 in showing what sort a thing is4 ,occam carried this a step farther towards clear light by including among ,connotative ,terms such general names as monk1 name of classes that at once suggest a definite attribute4 ,the third step was made by ,mill in extending the term ,connotation to such words as man1 horse1 the ,infimae ,species of the ,schoolmen1 the ,species of modern science4 ,whether connotation was the best term to use for this purpose1 rather than extension1 may be questioned3 but at least it was in the line of tradition through ,occam4 ,footnote #b3 ,the history of the definition of the ,proprium is an example of the tendency of distinctions to become more minute and at the same time more purposeless4 ,aristotle's ,greek3 idion was an attribute1 such as the laugh of the man or the bark of the dog1 common to all of a class and peculiar to the class 7quod convenit omni soli et semper7 yet not comprised in the definition of the class4 ,porphyry recognised three varieties of ,greek3 idia besides this1 four in all1 as follows3--7#a7 an attribute peculiar to a species but not possessed by all1 as knowledge of medicine or geometry2 7#b7 possessed by a whole species but not peculiar to it1 as being a biped in man2 7#c7 peculiar to a species1 and possessed by all at a certain time1 as turning grey in old age2 7#d7 ,aristotle's proprium1 peculiar and possessed by all1 as risibility4 ,the idea of the ,proprium as deducible from or consequent on the essence would seem to have originated in the desire to find something common to all ,poryphyry's four varieties4 ,footnote #c3 ,it is a plausible contention that in the case of the ,singular name the extension is at a minimum and the intension at a maximum1 the extension being one individual1 and the intension the totality of his attributes4 ,but this is an inexact and confused use of words4 ,a name does not extend beyond the individual except when it is used to signify one or more of his prominent qualities1 that is1 is used with the function of a general name4 ,the extension of a ,singular name is zero3 it has no extension4 ,on the other hand1 it suggests1 in its function as a ,singular name1 no properties or qualities2 it suggests only a subject2 i4e41 it has no intension4 ,the ambiguity of the term ,denotation helps the confusion in the case of ,singular names4 ,denote in common speech means to indicate1 to distinguish4 ,but when in ,logic we say that a general name denotes individuals1 we have no thought of indicating or distinguishing3 we mean only that it is applicable to any one1 without respect of individuals1 either in predication or epithetic description4 ,footnote #d3 ,strictly speaking1 as ,i have tried to indicate all along1 the words ,connotation and ,denotation1 or ,extension and ,intension1 apply only to general names4 ,outside general names1 they have no significance4 ,an adjective with its noun is a general name1 of which the adjective gives part of the ,connotation4 ,if we apply the word connotation to signify merely the suggestion of an attribute in whatever grammatical connexion1 then an abstract name is undoubtedly as much connotative as an adjective4 ,the word ,sweetness has the same meaning as ,sweet3 it indicates or signifies1 conveys to the mind of the reader the same attribute3 the only difference is that it does not at the same time indicate a subject in which the attribute is found1 as sweet apple4 ,the meaning is not connoted4 ,,chapter ,,ii4 ,,the ,,syllogistic ,,analysis ,,of ,,propositions ,,into ,,terms4 ,i4--,,the ,,bare ,,analytic ,,forms4 ,the word term is loosely used as a mere synonym for a name3 strictly speaking1 a term 7,greek3 horos1 a boundary7 is one of the parts of a proposition as analysed into ,subject and ,predicate4 ,in ,logic1 a term is a technical word in an analysis made for a special purpose1 that purpose being to test the mutual consistency of propositions4 ,for this purpose1 the propositions of common speech may be viewed as consisting of two ,,terms1 a linkword called the copula 7positive or negative7 expressing a relation between them1 and certain symbols of quantity used to express that relation more precisely4 ,let us indicate the ,subject term by ,s1 and the ,predicate term by ,p4 ,all propositions may be analysed into one or other of four forms3-- ,all ,s is ,p1 ,no ,s is ,p1 ,some ,s is ,p1 ,some ,s is not ,p4 ,all ,s is ,p is called the ,,universal ,,affirmative1 and is indicated by the symbol ,a 7the first vowel of ,affirmo74 ,no ,s is ,p is called the ,,universal ,,negative1 symbol ,e 7the first vowel of ,nego74 ,some ,s is ,p is called the ,,particular ,,affirmative1 symbol ,i 7the second vowel of aff,irmo74 ,some ,s is not ,p is called the ,,particular ,,negative1 symbol ,o 7the second vowel of neg,o74 ,the distinction between ,universal and ,particular is called a distinction in ,,quantity2 between ,affirmative and ,negative1 a distinction in ,,quality4 ,a and ,e1 ,i and ,o1 are of the same quantity1 but of different quality3 ,a and ,i1 ,e and ,o1 same in quality1 different in quantity4 ,in this symbolism1 no provision is made for expressing degrees of particular quantity4 ,some stands for any number short of all3 it may be one1 few1 most1 or all but one4 ,the debates in which ,aristotle's pupils were interested turned mainly on the proof or disproof of general propositions2 if only a proposition could be shown to be not universal1 it did not matter how far or how little short it came4 ,in the ,logic of ,probability1 the degree becomes of importance4 ,distinguish1 in this ,analysis1 to avoid subsequent confusion1 between the ,subject and the ,subject ,term1 the ,predicate and the ,predicate ,term4 ,the ,subject is the ,subject ,term quantified3 in ,a and ,e1#a ,all ,s2 in ,i and ,o1 ,some ,s4 ,the ,predicate is the ,predicate ,term with the ,copula1 positive or negative3 in ,a and ,i1 is ,p2 in ,e and ,o1 is not ,p4 ,it is important also1 in the interest of exactness1 to note that ,s and ,p1 with one exception1 represent general names4 ,they are symbols for classes4 ,p is so always3 ,s also except when the ,subject is an individual object4 ,in the machinery of the ,syllogism1 predications about a ,singular term are treated as ,universal ,affirmatives4 ,socrates is a wise man is of the form ,all ,s is ,p4 ,s and ,p being general names1 the signification of the symbol is is not the same as the is of common speech1 whether the substantive verb or the verb of incomplete predication4 ,in the syllogistic form1 is means is contained in1 is not1 is not contained in4 ,the relations between the terms in the four forms are represented by simple diagrams known as ,euler's circles4 ,illustration3 #a concentric circles of ,p and ,s - ,s in centre ,a #b ,s and ,p in the same circle ,a #c ,s and ,p each in a circle1 overlapping circle4 ,i ,o #d ,s in one circle and ,p in another circle4 ,e #e concentric circles of ,s and ,p - ,p in centre ,i8 ,diagram #e is a purely artificial form1 having no representative in common speech4 ,in the affirmations of common speech1 ,p is always a term of greater extent than ,s4 ,no4 #b represents the special case where ,s and ,p are coextensive1 as in ,all equiangular triangles are equilateral4 ,s and ,p being general names1 they are said to be ,,distributed when the proposition applies to them in their whole extent1 that is1 when the assertion covers every individual in the class4 ,in ,e1 the ,universal ,negative1 both terms are distributed3 ,no ,s is ,p wholly excludes the two classes one from the other1 imports that not one individual of either is in the other4 ,in ,a1 ,s is distributed1 but not ,p4 ,s is wholly in ,p1 but nothing is said about the extent of ,p beyond ,s4 ,in ,o1 ,s is undistributed1 ,p is distributed4 ,a part of ,s is declared to be wholly excluded from ,p4 ,in ,i1 neither ,s nor ,p is distributed4 ,it will be seen that the ,predicate term of a ,negative proposition is always distributed1 of an ,affirmative1 always undistributed4 ,a little indistinctness in the signification of ,p crept into mediaeval text-books1 and has tended to confuse modern disputation about the import of ,predication4 ,unless ,p is a class name1 the ordinary doctrine of distribution is nonsense2 and ,euler's diagrams are meaningless4 ,yet many writers who adopt both follow mediaeval usage in treating ,p as the equivalent of an adjective1 and consequently is as identical with the verb of incomplete predication in common speech4 ,it should be recognised that these syllogistic forms are purely artificial1 invented for a purpose1 namely1 the simplification of syllogising4 ,aristotle indicated the precise usage on which his syllogism is based 7,prior ,analytics1 i4 #a and #d74 ,his form#b for ,all ,s is ,p1 is ,s is wholly in ,p2 for ,no ,s is ,p1 ,s is wholly not in ,p4 ,his copula is not is1 but is in1 and it is a pity that this usage was not kept4 ,all ,s is in ,p would have saved much confusion4 ,but1 doubtless for the sake of simplicity1 the besetting sin of tutorial handbooks1 ,all ,s is ,p crept in instead1 illustrated by such examples as ,all men are mortal4 ,thus the is of the syllogistic form became confused with the is of common speech1 and the syllogistic view of predication as being equivalent to inclusion in1 or exclusion from a class1 was misunderstood4 ,the true ,aristotelian doctrine is not that predication consists in referring subjects to classes1 but only that for certain logical purposes it may be so regarded4 ,the syllogistic forms are artificial forms4 ,they were not originally intended to represent the actual processes of thought expressed in common speech4 ,to argue that when ,i say ,all crows are black1 ,i do not form a class of black things1 and contemplate crows within it as one circle is within another1 is to contradict no intelligent logical doctrine4 ,the root of the confusion lies in quoting sentences from common speech as examples of the logical forms1 forgetting that those forms are purely artificial4 ,omnis homo est mortalis1 ,all men are mortal1 is not an example formally of ,all ,s is ,p4 ,p is a symbol for a substantive word or combination of words1 and mortal is an adjective4 ,strictly speaking1 there is no formal equivalent in common speech1 that is1 in the forms of ordinary use--no strict grammatical formal equivalent--for the syllogistic propositional symbols4 ,we can make an equivalent1 but it is not a form that men would use in ordinary intercourse4 ,all man is in mortal being would be a strict equivalent1 but it is not ,english grammar4 ,instead of disputing confusedly whether ,all ,s is ,p should be interpreted in extension or in comprehension1 it would be better to recognise the original and traditional use of the symbols ,s and ,p as class names1 and employ other symbols for the expression in comprehension or connotation4 ,thus1 let s and p stand for the connotation4 ,then the equivalent for ,all ,s is ,p would be ,all ,s has p1 or p always accompanies s1 or p belongs to all ,s4 ,it may be said that if predication is treated in this way1 ,logic is simplified to the extent of childishness4 ,and indeed1 the manipulation of the bare forms with the help of diagrams and mnemonics is a very humble exercise4 ,the real discipline of ,syllogistic ,logic lies in the reduction of common speech to these forms4 ,this exercise is valuable because it promotes clear ideas about the use of general names in predication1 their ground in thought and reality1 and the liabilities to error that lurk in this fundamental instrument of speech4 ,footnote #a3 ,for perfect symmetry1 the form of ,e should be ,all ,s is not ,p4 ,no ,s is ,p is adopted for ,e to avoid conflict with a form of common speech1 in which ,all ,s is not ,p conveys the meaning of the ,particular ,negative4 ,all advices are not safe does not mean that safeness is denied of all advices1 but that safeness cannot be affirmed of all1 i4e41 ,not all advices are safe1 i4e41 some are not4 ,footnote #b3 ,his most precise form1 ,i should say1 for in ,p is predicated of every ,s he virtually follows common speech4 ,,ii4--,,the ,,practice ,,of ,,syllogistic ,,analysis4 ,the basis of the analysis is the use of general names in predication4 ,to say that in predication a subject is referred to a class1 is only another way of saying that in every categorical sentence the predicate is a general name express or implied3 that it is by means of general names that we convey our thoughts about things to others4 ,milton is a great poet4 ,quoth ,hudibras1 ,i smell a rat4 ,great poet is a general name3 it means certain qualities1 and applies to anybody possessing them4 ,quoth implies a general name1 a name for persons speaking1 connoting or meaning a certain act and applicable to anybody in the performance of it4 ,quoth expresses also past time3 thus it implies another general name1 a name for persons in past time1 connoting a quality which differentiates a species in the genus persons speaking1 and making the predicate term persons speaking in past time4 ,thus the proposition ,quoth ,hudibras1 analysed into the syllogistic form ,s is in ,p1 becomes ,s 7,hudibras7 is in ,p 7persons speaking in past time74 ,the ,predicate term ,p is a class constituted on those properties4 ,smell a rat also implies a general name1 meaning an act or state predicable of many individuals4 ,even if we add the grammatical object of ,quoth to the analysis1 the ,predicate term is still a general name4 ,hudibras is only one of the persons speaking in past time who have spoken of themselves as being in a certain mood of suspicion4#a ,the learner may well ask what is the use of twisting plain speech into these uncouth forms4 ,the use is certainly not obvious4 ,the analysis may be directly useful1 as ,aristotle claimed for it1 when we wish to ascertain exactly whether one proposition contradicts another1 or forms with another or others a valid link in an argument4 ,this is to admit that it is only in perplexing cases that the analysis is of direct use4 ,the indirect use is to familiarise us with what the forms of common speech imply1 and thus strengthen the intellect for interpreting the condensed and elliptical expression in which common speech abounds4 ,there are certain technical names applied to the components of many-worded general names1 ,,categorematic and ,,syncategorematic1 ,,subject and ,,attributive4 ,the distinctions are really grammatical rather than logical1 and of little practical value4 ,a word that can stand by itself as a term is said to be ,categorematic4 ,man1 poet1 or any other common noun4 ,a word that can only form part of a term is ,syncategorematic4 ,under this definition come all adjectives and adverbs4 ,the student's ingenuity may be exercised in applying the distinction to the various parts of speech4 ,a verb may be said to be ,hypercategorematic1 implying1 as it does1 not only a term1 but also a copula4 ,a nice point is whether the ,adjective is categorematic or syncategorematic4 ,the question depends on the definition of term in ,logic4 ,in common speech an adjective may stand by itself as a predicate1 and so might be said to be ,categorematic4 ,this heart is merry4 ,but if a term is a class1 or the name of a class1 it is not ,categorematic in the above definition4 ,it can only help to specify a class when attached to the name of a higher genus4 ,mr4 ,fowler's words ,,subject and ,,attributive express practically the same distinction1 except that ,attributive is of narrower extent than syncategorematic4 ,an ,attributive is a word that connotes an attribute or property1 as hot1 valorous1 and is always grammatically an adjective4 ,the ,,expression ,,of ,,quantity1 that is1 of ,universality or non-universality1 is all-important in syllogistic formulae4 ,in them universality is expressed by ,all or ,none4 ,in ordinary speech universality is expressed in various forms1 concrete and abstract1 plain and figurative1 without the use of all or none4 ,uneasy lies the head that wears a crown4 ,he can't be wrong whose life is in the right4 ,what cat's averse to fish8 ,can the leopard change his spots8 ,the longest road has an end4 ,suspicion ever haunts the guilty mind4 ,irresolution is always a sign of weakness4 ,treason never prospers4 ,a proposition in which the quantity is not expressed is called by ,aristotle ,,indefinite 7,greek3 adioristos74 ,for indefinite#b ,hamilton suggests ,,preindesignate1 undesignated1 that is1 before being received from common speech for the syllogistic mill4 ,a proposition is ,,predesignate when the quantity is definitely indicated4 ,all the above propositions are ,predesignate universals1 and reducible to the form ,all ,s is ,p1 or ,no ,s is ,p4 ,the following propositions are no less definitely particular1 reducible to the form ,i or ,o4 ,in them as in the preceding quantity is formally expressed1 though the forms used are not the artificial syllogistic forms3-- ,afflictions are often salutary4 ,not every advice is a safe one4 ,all that glitters is not gold4 ,rivers generally#c run into the sea4 ,often1 however1 it is really uncertain from the form of common speech whether it is intended to express a universal or a particular4 ,the quantity is not formally expressed4 ,this is especially the case with proverbs and loose floating sayings of a general tendency4 ,for example3-- ,haste makes waste4 ,knowledge is power4 ,light come1 light go4 ,left-handed men are awkward antagonists4 ,veteran soldiers are the steadiest in fight4 ,such sayings are in actual speech for the most part delivered as universals4#d ,it is a useful exercise of the ,socratic kind to decide whether they are really so4 ,this can only be determined by a survey of facts4 ,the best method of conducting such a survey is probably 7#a7 to pick out the concrete subject1 hasty actions1 men possessed of knowledge1 things lightly acquired2 7#b7 to fix the attribute or attributes predicated2 7#c7 to run over the individuals of the subject class and settle whether the attribute is as a matter of fact meant to be predicated of each and every one4 ,this is the operation of ,,induction4 ,if one individual can be found of whom the attribute is not meant to be predicated1 the proposition is not intended as ,universal4 ,mark the difference between settling what is intended and settling what is true4 ,the conditions of truth and the errors incident to the attempt to determine it1 are the business of the ,logic of ,rational ,belief1 commonly entitled ,inductive ,logic4 ,the kind of induction here contemplated has for its aim merely to determine the quantity of a proposition in common acceptation1 which can be done by considering in what cases the proposition would generally be alleged4 ,this corresponds nearly as we shall see to ,aristotelian ,induction1 the acceptance of a universal statement when no instance to the contrary is alleged4 ,it is to be observed that for this operation we do not practically use the syllogistic form ,all ,s is ,p4 ,we do not raise the question ,is ,all ,s1 ,p8 ,that is1 we do not constitute in thought a class ,p3 the class in our minds is ,s1 and what we ask is whether an attribute predicated of this class is truly predicated of every individual of it4 ,suppose we indicate by p the attribute1 knot of attributes1 or concept on which the class ,p is constituted1 then ,all ,s is ,p is equivalent to ,all ,s has p3 and ,has ,all ,s p8 is the form of a question that we have in our minds when we make an inductive survey on the above method4 ,i point this out to emphasise the fact that there is no prerogative in the form ,all ,s is ,p except for syllogistic purposes4 ,this inductive survey may be made a useful ,,collateral ,,discipline4 ,the bare forms of ,syllogistic are a useless item of knowledge unless they are applied to concrete thought4 ,and determining the quantity of a common aphorism or saw1 the limits within which it is meant to hold good1 is a valuable discipline in exactness of understanding4 ,in trying to penetrate to the inner intention of a loose general maxim1 we discover that what it is really intended to assert is a general connexion of attributes1 and a survey of concrete cases leads to a more exact apprehension of those attributes4 ,thus in considering whether ,knowledge is power is meant to be asserted of all knowledge1 we encounter along with such examples as the sailor's knowledge that wetting a rope shortens it1 which enabled some masons to raise a stone to its desired position1 or the knowledge of ,french roads possessed by the ,german invaders1--along with such examples as these we encounter cases where a knowledge of difficulties without a knowledge of the means of overcoming them is paralysing to action4 ,samuel ,daniel says3-- ,where timid knowledge stands considering ,audacious ignorance has done the deed4 ,studying numerous cases where ,knowledge is power is alleged or denied1 we find that what is meant is that a knowledge of the right means of doing anything is power--in short1 that the predicate is not made of all knowledge1 but only of a species of knowledge4 ,take1 again1 ,custom blunts sensibility4 ,putting this in the concrete1 and inquiring what predicate is made about men accustomed to anything 7,s71 we have no difficulty in finding examples where such men are said to become indifferent to it4 ,we find such illustrations as ,lovelace's famous ,paradox3-- ,through foul we follow fair ,for had the world one face ,and earth been bright as air ,we had known neither place4 ,indians smell not their nest ,the ,swiss and ,finn taste best ,the spices of the ,east4 ,so men accustomed to riches are not acutely sensible of their advantages3 dwellers in noisy streets cease to be distracted by the din3 the watchmaker ceases to hear the multitudinous ticking in his shop3 the neighbours of chemical works are not annoyed by the smells like the casual passenger4 ,but we find also that wine-tasters acquire by practice an unusual delicacy of sense2 that the eyes once accustomed to a dim light begin to distinguish objects that were at first indistinguishable2 and so on4 ,what meanings of custom and of sensibility will reconcile these apparently conflicting examples8 ,what are the exact attributes signified by the names8 ,we should probably find that by sensibility is meant emotional sensibility as distinguished from intellectual discrimination1 and that by custom is meant familiarity with impressions whose variations are not attended to1 or subjection to one unvarying impression4 ,to verify the meaning of abstract proverbs in this way is to travel over the road by which the ,greek dialecticians were led to feel the importance of definition4 ,of this more will be said presently4 ,if it is contended that such excursions are beyond the bounds of ,formal ,logic1 the answer is that the exercise is a useful one and that it starts naturally and conveniently from the formulae of ,logic4 ,it is the practice and discipline that historically preceded the ,aristotelian ,logic1 and in the absence of which the ,aristotelian formulae would have a narrowing and cramping effect4 ,,can ,,all ,,propositions ,,be ,,reduced ,,to ,,the ,,syllogistic ,,form8 ,probably3 but this is a purely scientific inquiry1 collateral to ,practical ,logic4 ,the concern of ,practical ,logic is chiefly with forms of proposition that favour inaccuracy or inexactness of thought4 ,when there is no room for ambiguity or other error1 there is no virtue in artificial syllogistic form4 ,the attempt so to reduce any and every proposition may lead1 however1 to the study of what ,mr4 ,bosanquet happily calls the ,morphology of ,judgment1 ,judgment being the technical name for the mental act that accompanies the utterance of a proposition4 ,even in such sentences as ,how hot it is6 or ,it rains1 the rudiment of subject and predicate may be detected4 ,when a man says ,how hot it is1 he conveys the meaning1 though there is no definitely formed subject in his mind1 that the outer world at the moment of his speaking has a certain quality or attribute4 ,so with ,it rains4 ,the study of such examples in their context1 however1 reveals the fact that the same form of ,common speech may cover different subjects and predicates in different connexions4 ,thus in the argument3-- ,whatever is1 is best4 ,it rains6-- the ,subject is ,rain and the ,predicate is now1 is at the present time1 is in the class of present events4 ,footnote #a3 ,remember that when we speak of a general name1 we do not necessarily mean a single word4 ,a general name1 logically viewed1 is simply the name of a genus1 kind1 or class3 and whether this is single-worded or many-worded is1 strictly speaking1 a grammatical question4 ,man1 man-of-ability1 man-of-ability-and-courage1 man-of-ability-and-courage-and-gigantic- stature1 man-who-fought-at-,marathon--these are all general names in their logical function4 ,no matter how the constitutive properties of the class are indicated1 by one word or in combination1 that word or combination is a general name4 ,in actual speech we can seldom indicate by a single word the meaning predicated4 ,footnote #b3 ,the objection taken to the word indefinite1 that the quantity of particular propositions is indefinite1 some meaning any quantity less than all1 is an example of the misplaced and frivolous subtlety that has done so much to disorder the tradition of ,logic4 ,by indefinite is simply meant not definitely expressed as either ,universal or ,particular1 ,total or ,partial4 ,the same objection might be taken to any word used to express the distinction3 the degree of quantity in ,some ,s is not designate any more than it is definite or dioristic4 ,footnote #c3 ,generally4 ,in this word we have an instance of the frequent conflict between the words of common speech and logical terminology4 ,how it arises shall be explained in next chapter4 ,a ,general proposition is a synonym for a ,universal proposition 7if the forms ,a and ,e are so termed73 but generally in common speech means for the most part1 and is represented by the symbol of particular quantity1 ,some4 ,footnote #d3 ,with some logicians it is a mechanical rule in reducing to syllogistic form to treat as ,i or ,o all sentences in which there is no formal expression of quantity4 ,this is to err on the safe side1 but common speakers are not so guarded1 and it is to be presumed rather that they have a universal application in their minds when they do not expressly qualify4 ,,iii4--,,some ,,technical ,,difficulties4 ,the formula for ,,exclusive ,,propositions4 ,none but the brave deserve the fair3 ,no admittance except on business3 ,only ,protestants can sit on the throne of ,england4 ,these propositions exemplify different ways in common speech of naming a subject exclusively1 the predication being made of all outside a certain term4 ,none that are not brave1 etc42 none that are not on business1 etc42 none that are not ,protestants1 etc44 ,no not-,s is ,p4 ,it is only about all outside the given term that the universal assertion is made3 we say nothing universally about the individuals within the term3 we do not say that all ,protestants are eligible1 nor that all persons on business are admitted1 nor that every one of the brave deserves the fair4 ,all that we say is that the possession of the attribute named is an indispensable condition3 a person may possess the attribute1 and yet on other grounds may not be entitled to the predicate4 ,the justification for taking special note of this form in ,logic is that we are apt by inadvertence to make an inclusive inference from it4 ,let it be said that ,none but those who work hard can reasonably expect to pass1 and we are apt to take this as meaning that all who work hard may reasonably expect to pass4 ,but what is denied of every ,not-,s is not necessarily affirmed of every ,s4 ,the expression of ,,tense or ,,time in the ,syllogistic ,forms4 ,seeing that the ,copula in ,s is ,p or ,s is in ,p does not express time1 but only a certain relation between ,s and ,p1 the question arises ,where are we to put time in the analytic formula8 ,wheat is dear2 ,all had fled2 time is expressed in these propositions1 and our formula should render the whole content of what is given4 ,are we to include it in the ,predicate term or in the ,subject term8 ,if it must not be left out altogether1 and we cannot put it with the copula1 we have a choice between the two terms4 ,it is a purely scholastic question4 ,the common technical treatment is to view the tense as part of the predicate4 ,all had fled1 ,all ,s is ,p1 i4e41 the whole subject is included in a class constituted on the attributes of flight at a given time4 ,it may be that the ,predicate is solely a predicate of time4 ,the ,board met yesterday at noon4 ,s is ,p1 i4e41 the meeting of the ,board is one of the events characterised by having happened at a certain time1 agreeing with other events in that respect4 ,but in some cases the time is more properly regarded as part of the subject4 ,e4g41 ,wheat is dear4 ,s does not here stand for wheat collectively1 but for the wheat now in the market1 the wheat of the present time3 it is concerning this that the attribute of dearness is predicated2 it is this that is in the class of dear things4 ,the expression of ,,modality in the ,syllogistic ,forms4 ,propositions in which the predicate is qualified by an expression of necessity1 contingency1 possibility or impossibility i4e41 in ,english by must1 may1 can1 or cannot1 were called in ,mediaeval ,logic ,modal ,propositions4 ,two and two must make four4 ,grubs may become butterflies4 ,z can paint4 ,y cannot fly4 ,there are two recognised ways of reducing such propositions to the form ,s is ,p4 ,one is to distinguish between the ,dictum and the ,mode1 the proposition and the qualification of its certainty1 and to treat the ,dictum as the ,subject and the ,mode as the ,predicate4 ,thus3 ,that two and two make four is necessary2 ,that ,y can fly is impossible4 ,the other way is to treat the ,mode as part of the predicate4 ,the propriety of this is not obvious in the case of ,necessary propositions1 but it is unobjectionable in the case of the other three modes4 ,thus3 ,grubs are things that have the potentiality of becoming butterflies2 ,z has the faculty of painting2 ,y has not the faculty of flying4 ,the chief risk of error is in determining the quantity of the subject about which the ,contingent or ,possible predicate is made4 ,when it is said that ,victories may be gained by accident1 is the predicate made concerning ,all victories or ,some only8 ,here we are apt to confuse the meaning of the contingent assertion with the matter of fact on which in common belief it rests4 ,it is true only that some victories have been gained by accident1 and it is on this ground that we assert in the absence of certain knowledge concerning any victory that it may have been so gained4 ,the latter is the effect of the contingent assertion3 it is made about any victory in the absence of certain knowledge1 that is to say1 formally about all4 ,the history of ,modals in ,logic is a good illustration of intricate confusion arising from disregard of a clear traditional definition4 ,the treatment of them by ,aristotle was simple1 and had direct reference to tricks of disputation practised in his time4 ,he specified four modes1 the four that descended to mediaeval logic1 and he concerned himself chiefly with the import of contradicting these modals4 ,what is the true contradictory of such propositions as1 ,it is possible to be 7,greek3 dynaton einai71 ,it admits of being 7,greek3 endechetai einai71 ,it must be 7,greek3 anankaion einai71 ,it is impossible to be 7,greek3 adynaton einai78 ,what is implied in saying ,no to such propositions put interrogatively8 ,is it possible for ,socrates to fly8 ,no4 ,does this mean that it is not possible for ,socrates to fly1 or that it is possible for ,socrates not to fly8 ,a disputant who had trapped a respondent into admitting that it is possible for ,socrates not to fly1 might have pushed the concession farther in some such way as this3 ,is it possible for ,socrates not to walk8 ,certainly4 ,is it possible for him to walk8 ,yes4 ,when you say that it is possible for a man to do anything do you not believe that it is possible for him to do it8 ,yes4 ,but you have admitted that it is possible for ,socrates not to fly8 ,it was in view of such perplexities as these that ,aristotle set forth the true contradictories of his four ,modals4 ,we may laugh at such quibbles now and wonder that a grave logician should have thought them worth guarding against4 ,but historically this is the origin of the ,modals of ,formal ,logic1 and to divert the names of them to signify other distinctions than those between modes of qualifying the certainty of a statement is to introduce confusion4 ,thus we find ,alexander was a great general1 given as an example of a ,contingent ,modal1 on the ground that though as a matter of fact ,alexander was so he might have been otherwise4 ,it was not necessary that ,alexander should be a great general3 therefore the proposition is contingent4 ,now the distinction between ,necessary truth and ,contingent truth may be important philosophically3 but it is merely confusing to call the character of propositions as one or the other by the name of ,modality4 ,the original ,modality is a mode of expression3 to apply the name to this character is to shift its meaning4 ,a more simple and obviously unwarrantable departure from tradition is to extend the name ,modality to any grammatical qualification of a single verb in common speech4 ,on this understanding ,alexander conquered ,darius is given by ,hamilton as a ,pure proposition1 and ,alexander conquered ,darius honourably as a ,modal4 ,this is a merely grammatical distinction1 a distinction in the mode of composing the predicate term in common speech4 ,in logical tradition ,modality is a mode of qualifying the certainty of an affirmation4 ,the conquest of ,darius by ,alexander was honourable1 or ,alexander in conquering ,darius was an honourable conqueror1 is the syllogistic form of the proposition3 it is simply assertory1 not qualified in any mode4 ,there is a similar misunderstanding in ,mr4 ,shedden's treatment of generally as constituting a ,modal in such sentences1 as ,rivers generally flow into the sea4 ,he argues that as generally is not part either of the ,subject term or of the ,predicate term1 it must belong to the ,copula1 and is therefore a modal qualification of the whole assertion4 ,he overlooked the fact that the word generally is an expression of ,quantity3 it determines the quantity of the ,subject term4 ,finally it is sometimes held 7e4g41 by ,mr4 ,venn7 that the question of ,modality belongs properly to ,scientific or ,inductive ,logic1 and is out of place in ,formal ,logic4 ,this is so far accurate that it is for ,inductive ,logic to expound the conditions of various degrees of certainty4 ,the consideration of ,modality is pertinent to ,formal ,logic only in so far as concerns special perplexities in the expression of it4 ,the treatment of it by ,logicians has been rendered intricate by torturing the old tradition to suit different conceptions of the end and aim of ,logic4 ,,part ,,ii4 ,,definition4 ,,chapter ,i4 ,,imperfect ,,understanding ,,of ,,words ,,and ,,the ,,remedies ,,therefor4--,,dialectic4--,,definition4 ,we cannot inquire far into the meaning of proverbs or traditional sayings without discovering that the common understanding of general and abstract names is loose and uncertain4 ,common speech is a quicksand4 ,consider how we acquire our vocabulary1 how we pick up the words that we use from our neighbours and from books1 and why this is so soon becomes apparent4 ,theoretically we know the full meaning of a name when we know all the attributes that it connotes1 and we are not justified in extending it except to objects that possess all the attributes4 ,this is the logical ideal1 but between the ought to be of ,logic and the is of practical life1 there is a vast difference4 ,how seldom do we conceive words in their full meaning6 ,and who is to instruct us in the full meaning8 ,it is not as in the exact sciences1 where we start with a knowledge of the full meaning4 ,in ,geometry1 for example1 we learn the definitions of the words used1 point1 line1 parallel1 etc41 before we proceed to use them4 ,but in common speech1 we learn words first in their application to individual cases4 ,nobody ever defined good to us1 or fair1 or kind1 or highly educated4 ,we hear the words applied to individual objects3 we utter them in the same connexion3 we extend them to other objects that strike us as like without knowing the precise points of likeness that the convention of common speech includes4 ,the more exact meaning we learn by gradual induction from individual cases4 ,ugly1 beautiful1 good1 bad--we learn the words first as applicable to things and persons3 gradually there arises a more or less definite sense of what the objects so designated have in common4 ,the individual's extension of the name proceeds upon what in the objects has most impressed him when he caught the word3 this may differ in different individuals2 the usage of neighbours corrects individual eccentricities4 ,the child in arms shouts ,da at the passing stranger who reminds him of his father3 for him at first it is a general name applicable to every man3 by degrees he learns that for him it is a singular name4 ,the mode in which words are learnt and extended may be studied most simply in the nursery4 ,a child1 say1 has learnt to say mambro when it sees its nurse4 ,the nurse works a hand-turned sewing machine1 and sings to it as she works4 ,in the street the child sees an organ-grinder singing as he turns his handle3 it calls mambro3 the nurse catches the meaning and the child is overjoyed4 ,the organ-grinder has a monkey3 the child has an india-rubber monkey toy3 it calls this also mambro4 ,the name is extended to a monkey in a picture-book4 ,it has a toy musical box with a handle3 this also becomes mambro1 the word being extended along another line of resemblance4 ,a stroller with a ,french fiddle comes within the denotation of the word3 a towel-rail is also called mambro from some fancied resemblance to the fiddle4 ,a very swarthy hunch-back mambro frightens the child3 this leads to the transference of the word to a terrific coalman with a bag of coals on his back4 ,in a short time the word has become a name for a great variety of objects that have nothing whatever common to all of them1 though each is strikingly like in some point to a predecessor in the series4 ,when the application becomes too heterogeneous1 the word ceases to be of use as a sign and is gradually abandoned1 the most impressive meaning being the last to go4 ,in a child's vocabulary where the word mambro had a run of nearly two years1 its last use was as an adjective signifying ugly or horrible4 ,the history of such a word in a child's language is a type of what goes on in the language of men4 ,in the larger history we see similar extensions under similar motives1 checked and controlled in the same way by surrounding usage4 ,it is obvious that to avoid error and confusion1 the meaning or connotation of names1 the concepts1 should somehow be fixed3 names cannot otherwise have an identical reference in human intercourse4 ,we may call this ideal fixed concept the ,,logical ,,concept3 or we may call it the ,,scientific ,,concept1 inasmuch as one of the main objects of the sciences is to attain such ideals in different departments of study4 ,but in actual speech we have also the ,,personal ,,concept1 which varies more or less with the individual user1 and the ,,popular or ,,vernacular ,,concept1 which1 though roughly fixed1 varies from social sect to social sect and from generation to generation4 ,the variations in ,popular ,concepts may be traced in linguistic history4 ,words change with things and with the aspects of things1 as these change in public interest and importance4 ,as long as the attributes that govern the application of words are simple1 sensible attributes1 little confusion need arise3 the variations are matters of curious research for the philologist1 but are logically insignificant4 ,murray's ,dictionary1 or such books as ,trench's ,english ,past and ,present1 supply endless examples1 as many1 indeed as there are words in the language4 ,clerk has almost as many connotations as our typical mambro3 clerk in holy orders1 church clerk1 town clerk1 clerk of assize1 grocer's clerk4 ,in ,early ,english1 the word meant man in a religious order1 cleric1 clergyman2 ability to read1 write1 and keep accounts being a prominent attribute of the class1 the word was extended on this simple ground till it has ceased altogether to cover its original field except as a formal designation4 ,but no confusion is caused by the variation1 because the property connoted is simple4#a ,so with any common noun3 street1 carriage1 ship1 house1 merchant1 lawyer1 professor4 ,we might be puzzled to give an exact definition of such words1 to say precisely what they connote in common usage2 but the risk of error in the use of them is small4 ,when we come to words of which the logical concept is a complex relation1 an obscure or intangible attribute1 the defects of the popular conception and its tendencies to change and confusion1 are of the greatest practical importance4 ,take such words as ,monarchy1 tyranny1 civil freedom1 freedom of contract1 landlord1 gentleman1 prig1 culture1 education1 temperance1 generosity4 ,not merely should we find it difficult to give an analytic definition of such words3 we might be unable to do so1 and yet flatter ourselves that we had a clear understanding of their meaning4 ,but let two men begin to discuss any proposition in which any such word is involved1 and it will often be found that they take the word in different senses4 ,if the relation expressed is complex1 they have different sides or lines of it in their minds2 if the meaning is an obscure quality1 they are guided in their application of it by different outward signs4 ,monarchy1 in its original meaning1 is applied to a form of government in which the will of one man is supreme1 to make laws or break them1 to appoint or dismiss officers of state and justice1 to determine peace or war1 without control of statute or custom4 ,but supreme power is never thus uncontrolled in reality2 and the word has been extended to cover governments in which the power of the titular head is controlled in many different modes and degrees4 ,the existence of a head1 with the title of ,king or ,emperor1 is the simplest and most salient fact3 and wherever this exists1 the popular concept of a monarchy is realised4 ,the ,president of the ,united ,states has more real power than the ,sovereign of ,great ,britain2 but the one government is called a ,republic and the other a ,monarchy4 ,people discuss the advantages and disadvantages of monarchy without first deciding whether they take the word in its etymological sense of unlimited power1 or its popular sense of titular kingship1 or its logical sense of power definitely limited in certain ways4 ,and often in debate1 monarchy is really a singular term for the government of ,great ,britain4 ,culture1 religious1 generous1 are names for inward states or qualities3 with most individuals some simple outward sign directs the application of the word--it may be manner1 or bearing1 or routine observances1 or even nothing more significant than the cut of the clothes or of the hair4 ,small things undoubtedly are significant1 and we must judge by small things when we have nothing else to go by3 but instead of trying to get definite conceptions for our moral epithets1 and suspending judgment till we know that the use of the epithet is justified1 the trifling superficial sign becomes for us practically the whole meaning of the word4 ,we feel that we must have a judgment of some sort at once3 only simple signs are suited to our impatience4 ,it was with reference to this state of things that ,hegel formulated his paradox that the true abstract thinker is the plain man who laughs at philosophy as what he calls abstract and unpractical4 ,he holds decided opinions for or against this or the other abstraction1 freedom1 tyranny1 revolution1 reform1 socialism1 but what these words mean and within what limits the things signified are desirable or undesirable1 he is in too great a hurry to pause and consider4 ,the disadvantages of this kind of abstract thinking are obvious4 ,the accumulated wisdom of mankind is stored in language4 ,until we have cleared our conceptions1 and penetrated to the full meaning of words1 that wisdom is a sealed book to us4 ,wise maxims are interpreted by us hastily in accordance with our own narrow conceptions4 ,all the vocables of a language may be more or less familiar to us1 and yet we may not have learnt it as an instrument of thought4 ,outside the very limited range of names for what we see and use in the daily routine of life1 food and clothes and the common occupations of men1 words have little meaning for us1 and are the vehicles merely of thin preconceptions and raw prejudices4 ,the remedy for abstract thinking is more thinking1 and in pursuing this two aims may be specified for the sake of clearness1 though they are closely allied1 and progress towards both may often be made by one and the same operation4 7#a7 ,we want to reach a clear and full conception of the meaning of names as used now or at a given time4 ,let us call this the ,verification of the ,meaning4 7#b7 ,we want to fix such conceptions1 and if necessary readjust their boundaries4 ,this is the province of ,definition1 which cannot be effectually performed without ,scientific ,classification or ,division4 ,i4--,,verification ,,of ,,the ,,meaning--,,dialectic4 ,this can only be done by assembling the objects to which the words are applied1 and considering what they have in common4 ,to ascertain the actual connotation we must run over the actual denotation4 ,and since in such an operation two or more minds are better than one1 discussion or dialectic is both more fruitful and more stimulating than solitary reflection or reading4 ,the first to practise this process on a memorable scale1 and with a distinct method and purpose1 was ,socrates4 ,to insist upon the necessity of clear conceptions1 and to assist by his dialectic procedure in forming them1 was his contribution to philosophy4 ,his plan was to take a common name1 profess ignorance of its meaning1 and ask his interlocutor whether he would apply it in such and such an instance1 producing one after another4 ,according to ,xenophon's ,memorabilia he habitually chose the commonest names1 good1 unjust1 fitting1 and so forth1 and tried to set men thinking about them1 and helped them by his questions to form an intelligent conception of the meaning4 ,for example1 what is the meaning of injustice8 ,would you say that the man who cheats or deceives is unjust8 ,suppose a man deceives his enemies1 is there any injustice in that8 ,can the definition be that a man who deceives his friends is unjust8 ,but there are cases where friends are deceived for their own good3 are these cases of injustice8 ,a general may inspirit his soldiers by a falsehood4 ,a man may cajole a weapon out of his friend's hand when he sees him about to commit suicide4 ,a father may deceive his son into taking medicine4 ,would you call these men unjust8 ,by some such process of interrogation we are brought to the definition that a man is unjust who deceives his friends to their hurt4 ,observe that in much of his dialectic the aim of ,socrates was merely to bring out the meaning lying vague and latent1 as it were1 in the common mind4 ,his object was simply what we have called the verification of the meaning4 ,and a dialectic that confines itself to the consideration of what is ordinarily meant as distinct from what ought to be meant may often serve a useful purpose4 ,disputes about words are not always as idle as is sometimes supposed4 ,mr4 ,h4 ,sidgwick truly remarks 7a propos of the terms of ,political ,economy7 that there is often more profit in seeking a definition than in finding it4 ,conceptions are not merely cleared but deepened by the process4 ,mr4 ,sidgwick's remarks are so happy that ,i must take leave to quote them3 they apply not merely to the verification of ordinary meaning but also to the study of special uses by authorities1 and the reasons for those special uses4 ,the truth is--as most readers of ,plato know1 only it is a truth difficult to retain and apply--that what we gain by discussing a definition is often but slightly represented in the superior fitness of the formula that we ultimately adopt2 it consists chiefly in the greater clearness and fulness in which the characteristics of the matter to which the formula refers have been brought before the mind in the process of seeking for it4 ,while we are apparently aiming at definitions of terms1 our attention should be really fixed on distinctions and relations of fact4 ,these latter are what we are concerned to know1 contemplate1 and as far as possible arrange and systematise2 and in subjects where we cannot present them to the mind in ordinary fulness by the exercise of the organs of sense1 there is no way of surveying them so convenient as that of reflecting on our use of common terms4444 ,in comparing different definitions our aim should be far less to decide which we ought to adopt1 than to apprehend and duly consider the grounds on which each has commended itself to reflective minds4 ,we shall generally find that each writer has noted some relation1 some resemblance or difference1 which others have overlooked2 and we shall gain in completeness1 and often in precision1 of view by following him in his observations1 whether or not we follow him in his conclusions4#b ,mr4 ,sidgwick's own discussions of ,wealth1 ,value1 and ,money are models4 ,a clue is often found to the meaning in examining startlingly discrepant statements connected with the same leading word4 ,thus we find some authorities declaring that style cannot be taught or learnt1 while others declare that it can4 ,but on trying to ascertain what they mean by style1 we find that those who say it cannot be taught mean either a certain marked individual character or manner of writing--as in ,buffon's saying1 ,le style c'est l'homme meme--or a certain felicity and dignity of expression1 while those who say style can be taught mean lucid method in the structure of sentences or in the arrangement of a discourse4 ,again in discussions on the rank of poets1 we find different conceptions of what constitutes greatness in poetry lying at the root of the inclusion of this or the other poet among great poets4 ,we find one poet excluded from the first rank of greatness because his poetry was not serious2 another because his poetry was not widely popular2 another because he wrote comparatively little2 another because he wrote only songs or odes and never attempted drama or epic4 ,these various opinions point to different conceptions of what constitutes greatness in poets1 different connotations of great poet4 ,comparing different opinions concerning education we may be led to ask whether it means more than instruction in the details of certain subjects1 whether it does not also import the formation of a disposition to learn or an interest in learning or instruction in a certain method of learning4 ,historically1 dialectic turning on the use of words preceded the attempt to formulate principles of ,definition1 and attempts at precise definition led to ,division and ,classification1 that is to systematic arrangement of the objects to be defined4 ,attempt to define any such word as education1 and you gradually become sensible of the needs in respect of method that forced themselves upon mankind in the history of thought4 ,you soon become aware that you cannot define it by itself alone2 that you are beset by a swarm of more or less synonymous words1 instruction1 discipline1 culture1 training1 and so on2 that these various words represent distinctions and relations among things more or less allied2 and that1 if each must be fixed to a definite meaning1 this must be done with reference to one another and to the whole department of things that they cover4 ,the first memorable attempts at scientific arrangement were ,aristotle's treatises on ,ethics and ,politics1 which had been the subjects of active dialectic for at least a century before4 ,that these the most difficult of all departments to subject to scientific treatment should have been the first chosen was due simply to their preponderating interest3 ,the proper study of mankind is man4 ,the systems of what are known as the ,natural ,sciences are of modern origin3 the first1 that of ,botany1 dates from ,cesalpinus in the sixteenth century4 ,but the principles on which ,aristotle proceeded in dividing and defining1 principles which have gradually themselves been more precisely formulated1 are principles applicable to all systematic arrangements for purposes of orderly study4 ,i give them in the precise formulae which they have gradually assumed in the tradition of ,logic4 ,the principles of ,division are often given in ,formal ,logic1 and the principles of ,classification in ,inductive ,logic1 but there is no valid reason for the separation4 ,the classification of objects in the ,natural ,sciences1 of animals1 plants1 and stones1 with a view to the thorough study of them in form1 structure1 and function1 is more complex than classifications for more limited purposes1 and the tendency is to restrict the word classification to these elaborate systems4 ,but really they are only a series of divisions and subdivisions1 and the same principles apply to each of the subordinate divisions as well as to the division of the whole department of study4 ,,ii4--,,principles ,,of ,,division ,,or ,,classification ,,and ,,definition4 ,confusion in the boundaries of names arises from confused ideas regarding the resemblances and differences of things4 ,as a protective against this confusion1 things must be clearly distinguished in their points of likeness and difference1 and this leads to their arrangement in systems1 that is1 to division and classification4 ,a name is not secure against variation until it has a distinct place in such a system as a symbol for clearly distinguished attributes4 ,nor must we forget1 further1 that systems have their day1 that the best system attainable is only temporary1 and may have to be recast to correspond with changes of things and of man's way of looking at them4 ,the leading principles of ,,division may be stated as follows3-- ,i4 ,every division is made on the ground of differences in some attribute common to all the members of the whole to be divided4 ,this is merely a way of stating what a logical division is4 ,it is a division of a generic whole or genus1 an indefinite number of objects thought of together as possessing some common character or attribute4 ,all have this attribute1 which is technically called the fundamentum divisionis1 or generic attribute4 ,but the whole is divisible into smaller groups 7species71 each of which possesses the common character with a difference 7differentia74 ,thus1 mankind may be divided into ,white men1 ,black men1 ,yellow men1 on ground of the differences in the colour of their skins3 all have skins of some colour3 this is the fundamentum divisionis3 but each subdivision or species has a different colour3 this is the differentia4 ,rectilineal figures are divided into triangles1 quadrangles1 pentagons1 etc41 on the ground of differences in the number of angles4 ,unless there is a fund4 div41 i4e41 unless the differences are differences in a common character1 the division is not a logical division4 ,to divide men into ,europeans1 opticians1 tailors1 blondes1 brunettes1 and dyspeptics is not to make a logical division4 ,this is seen more clearly in connexion with the second condition of a perfect division4 ,,ii4 ,in a perfect division1 the subdivisions or species are mutually exclusive4 ,every object possessing the common character should be in one or other of the groups1 and none should be in more than one4 ,confusion between classes1 or overlapping1 may arise from two causes4 ,it may be due 7#a7 to faulty division1 to want of unity in the fundamentum divisionis2 7#b7 to the indistinct character of the objects to be defined4 7#a7 ,unless the division is based upon a single ground1 unless each species is based upon some mode of the generic character1 confusion is almost certain to arise4 ,suppose the field to be divided1 the objects to be classified1 are three-sided rectilineal plane figures1 each group must be based upon some modification of the three sides4 ,divide them into equilateral1 isosceles1 and scalene according as the three sides are all of equal length1 or two of equal length1 or each of different length1 and you have a perfect division4 ,similarly you can divide them perfectly according to the character of the angles into acute-angled1 right-angled and obtuse-angled4 ,but if you do not keep to a single basis1 as in dividing them into equilateral1 isosceles1 scalene1 and right-angled1 you have a cross-division4 ,the same triangle might be both right-angled and isosceles4 7#b7 ,overlapping1 however1 may be unavoidable in practice owing to the nature of the objects4 ,there may be objects in which the dividing characters are not distinctly marked1 objects that possess the differentiae of more than one group in a greater or less degree4 ,things are not always marked off from one another by hard and fast lines4 ,they shade into one another by imperceptible gradations4 ,a clear separation of them may be impossible4 ,in that case you must allow a certain indeterminate margin between your classes1 and sometimes it may be necessary to put an object into more than one class4 ,to insist that there is no essential difference unless a clear demarcation can be made is a fallacy4 ,a sophistical trick called the ,sorites or ,heap from the classical example of it was based upon this difficulty of drawing sharp lines of definition4 ,assuming that it is possible to say how many stones constitute a heap1 you begin by asking whether three stones form a heap4 ,if your respondent says ,no1 you ask whether four stones form a heap1 then five1 and so on and he is puzzled to say when the addition of a single stone makes that a heap which was not a heap before4 ,or you may begin by asking whether twenty stones form a heap1 then nineteen1 then eighteen1 and so on1 the difficulty being to say when what was a heap ceases to be so4 ,where the objects classified are mixed states or affections1 the products of interacting factors1 or differently interlaced or interfused growths from common roots1 as in the case of virtues1 or emotions1 or literary qualities1 sharp demarcations are impossible4 ,to distinguish between wit and humour1 or humour and pathos1 or pathos and sublimity is difficult because the same composition may partake of more than one character4 ,the specific characters cannot be made rigidly exclusive one of another4 ,even in the natural sciences1 where the individuals are concrete objects of perception1 it may be difficult to decide in which of two opposed groups an object should be included4 ,sydney ,smith has commemorated the perplexities of ,naturalists over the newly discovered animals and plants of ,botany ,bay1 in especial with the ,ornithorynchus1--a quadruped as big as a large cat1 with the eyes1 colour1 and skin of a mole1 and the bill and web-feet of a duck--puzzling ,dr4 ,shaw1 and rendering the latter half of his life miserable1 from his utter inability to determine whether it was a bird or a beast4 ,,iii4 ,the classes in any scheme of division should be of co-ordinate rank4 ,the classes may be mutually exclusive1 and yet the division imperfect1 owing to their not being of equal rank4 ,thus in the ordinary division of the ,parts of ,speech1 parts1 that is1 of a sentence1 ,prepositions and ,conjunctions are not co-ordinate in respect of function1 which is the basis of the division1 with ,nouns1 ,adjectives1 ,verbs1 and ,adverbs4 ,the preposition is a part of a phrase which serves the same function as an adjective1 e4g41 royal army1 army of the king2 it is thus functionally part of a part1 or a particle4 ,so with the conjunction3 it also is a part of a part1 i4e41 part of a clause serving the function of adjective or adverb4 ,,iv4 ,the basis of division 7fundamentum divisionis7 should be an attribute admitting of important differences4 ,the importance of the attribute chosen as basis may vary with the purpose of the division4 ,an attribute that is of no importance in one division1 may be important enough to be the basis of another division4 ,thus in a division of houses according to their architectural attributes1 the number of windows or the rent is of little importance2 but if houses are taxed or rated according to the number of windows or the rent1 these attributes become important enough to be a basis of division for purposes of taxation or rating4 ,they then admit of important differences4 ,that the importance is relative to the purpose of the division should be borne in mind because there is a tendency to regard attributes that are of importance in any familiar or pre-eminent division as if they had an absolute importance4 ,in short1 disregard of this relativity is a fallacy to be guarded against4 ,in the sciences1 the purpose being the attainment and preservation of knowledge1 the objects of study are divided so as to serve that purpose4 ,groups must be formed so as to bring together the objects that have most in common4 ,the question1 ,who are to be placed together8 in any arrangement for purposes of study1 receives the same answer for individuals and for classes that have to be grouped into higher classes1 namely1 ,those that have most in common4 ,this is what ,dr4 ,bain happily calls the golden rule of scientific classification3 ,of the various groupings of resembling things1 preference is given to such as have the greatest number of attributes in common4 ,i slightly modify ,dr4 ,bain's statement3 he says the most numerous and the most important attributes in common4 ,but for scientific purposes number of attributes constitutes importance1 as is well recognised by ,dr4 ,fowler when he says that the test of importance in an attribute proposed as a basis of classification is the number of other attributes of which it is an index or invariable accompaniment4 ,thus in ,zoology the squirrel1 the rat1 and the beaver are classed together as ,rodents1 the difference between their teeth and the teeth of other ,mammalia being the basis of division1 because the difference in teeth is accompanied by differences in many other properties4 ,so the hedge-hog1 the shrew-mouse1 and the mole1 though very unlike in outward appearance and habits1 are classed together as ,insectivora1 the difference in what they feed on being accompanied by a number of other differences4 ,the ,principles of ,,definition4 ,the word definition as used in ,logic shows the usual tendency of words to wander from a strict meaning and become ambiguous4 ,throughout most of its uses it retains this much of a common signification1 the fixing or determining of the boundaries of a class#c by making clear its constituent attributes4 ,now in this making clear two processes may be distinguished1 a material process and a verbal process4 ,we have 7#a7 the clearing up of the common attributes by a careful examination of the objects included in the class3 and we have 7#b7 the statement of these common attributes in language4 ,the rules of definition given by ,dr4 ,bain1 who devotes a separate ,book in his ,logic to the subject of ,definition1 concern the first of these processes3 the rules more commonly given concern mainly the second4 ,one eminent merit in ,dr4 ,bain's treatment is that it recognises the close connexion between ,definition and ,classification4 ,his cardinal rules are reduced to two4 ,i4 ,assemble for comparison representative individuals of the class4 ,,ii4 ,assemble for comparison representative individuals of the contrasted class or classes4 ,seeing that the contrasted classes are contrasted on some basis of division1 this is in effect to recognise that you cannot clearly define any class except in a scheme of classification4 ,you must have a wide genus with its fundamentum divisionis1 and1 within this1 species distinguished by their several differentiae4 ,next1 as to the verbal process1 rules are commonly laid down mostly of a trifling and obvious character4 ,that a definition should state neither more nor less than the common attributes of the class1 or than the attributes signified by the class-name1 is sometimes given as a rule of definition4 ,this is really an explanation of what a definition is1 a definition of a definition4 ,and as far as mere statement goes it is not strictly accurate1 for when the attributes of a genus are known it is not necessary to give all the attributes of the species1 which include the generic attributes as well1 but it is sufficient to give the generic name and the differentia4 ,thus ,poetry may be defined as a ,fine ,art having metrical language as its instrument4 ,this is technically known as definition per genus et differentiam4 ,this mode of statement is a recognition of the connexion between ,definition and ,division4 ,the rule that a definition should not be a synonymous repetition of the name of the class to be defined1 is too obvious to require formal statement4 ,to describe a ,viceroy as a man who exercises viceregal functions1 may have point as an epigram in the case of a faineant viceroy1 but it is not a definition4 ,so with the rule that a definition should not be couched in ambiguous unfamiliar1 or figurative language4 ,to call the camel the ship of the desert is a suggestive and luminous description of a property1 but it is not a definition4 ,so with the noble description of ,faith as the substance of things hoped for1 the evidence of things not seen4 ,but if one wonders why so obvious a rule should be laid down1 the answer is that it has its historical origin in the caprices of two classes of offenders1 mystical philosophers and pompous lexicographers4#d ,that the definition should be simply convertible with the term for the class defined1 so that we may say1 for example1 either3 ,wine is the juice of the grape1 or1 ,the juice of the grape is wine1 is an obvious corollary from the nature of definition1 but should hardly be dignified with the name of a rule4 ,the ,principles of ,,naming4 ,rules have been formulated for the choice of names in scientific definition and classification1 but it may be doubted whether such choice can be reduced to precise rule4 ,it is enough to draw attention to certain considerations obvious enough on reflection4 ,we may take for granted that there should be distinct names for every defining attribute 7a ,terminology7 and for every group or class 7a ,nomenclature74 ,what about the selection of the names8 ,suppose an investigator is struck with likenesses and differences that seem to him important enough to be the basis of a new division1 how should he be guided in his choice of names for the new groups that he proposes8 ,should he coin new names1 or should he take old names and try to fit them with new definitions8 ,the balance of advantages is probably in favour of ,dr4 ,whewell's dictum that in framing scientific terms1 the appropriation of old words is preferable to the invention of new ones4 ,only care must be taken to keep as close as possible to the current meaning of the old word1 and not to run counter to strong associations4 ,this is an obvious precept with a view to avoiding confusion4 ,suppose1 for example1 that in dividing ,governments you take the distribution of political power as your basis of division and come to the conclusion that the most important differences are whether this power is vested in a few or in the majority of the community4 ,you want names to fix this broad division4 ,you decide instead of coining the new word ,pollarchy to express the opposite of ,oligarchy to use the old words ,republic and ,oligarchy4 ,you would find1 as ,sir ,george ,cornewall ,lewis found1 that however carefully you defined the word ,republic1 a division under which the ,british ,government had to be ranked among ,republics would not be generally understood and accepted4 ,using the word in the sense explained above1 ,mr4 ,bagehot maintained that the constitution of ,great ,britain was more ,republican than that of the ,united ,states1 but his meaning was not taken except by a few4 ,the difficulty in choosing between new words and old words to express new meanings is hardly felt in the exact sciences4 ,it is at least at a minimum4 ,the innovator may encounter violent prejudice1 but1 arguing with experts1 he can at least make sure of being understood1 if his new division is based upon real and important differences4 ,but in other subjects the difficulty of transmitting truth or of expressing it in language suited for precise transmission1 is almost greater than the difficulty of arriving at truth4 ,between new names and old names redefined1 the possessor of fresh knowledge1 assuming it to be perfectly verified1 is in a quandary4 ,the objects with which he deals are already named in accordance with loose divisions resting on strong prejudices4 ,the names in current use are absolutely incapable of conveying his meaning4 ,he must redefine them if he is to use them4 ,but in that case he runs the risk of being misunderstood from people being too impatient to master his redefinition4 ,his right to redefine may even be challenged without any reference to the facts to be expressed3 he may simply be accused of circulating false linguistic coin1 of debasing the verbal currency4 ,the other alternative open to him is to coin new words4 ,in that case he runs the risk of not being read at all4 ,his contribution to verified knowledge is passed by as pedantic and unintelligible4 ,there is no simple rule of safety3 between ,scylla and ,charybdis the mariner must steer as best he may4 ,practically the advantage lies with old words redefined1 because thereby discussion is provoked and discussion clears the air4 ,whether it is best to attempt a formal definition or to use words in a private1 peculiar1 or esoteric sense1 and leave this to be gathered by the reader from the general tenor of your utterances1 is a question of policy outside the limits of ,logic4 ,it is for the logician to expound the method of ,definition and the conditions of its application3 how far there are subjects that do not admit of its application profitably must be decided on other grounds4 ,but it is probably true that no man who declines to be bound by a formal definition of his terms is capable of carrying them in a clear unambiguous sense through a heated controversy4 ,footnote #a3 ,except1 perhaps1 in new offices to which the name is extended1 such as ,clerk of ,school ,board4 ,the name1 bearing its most simple and common meaning1 may cause popular misapprehension of the nature of the duties4 ,any uncertainty in meaning may be dangerous in practice3 elections have been affected by the ambiguity of this word4 ,footnote #b3 ,sidgwick's ,political ,economy1 pp4 #eb-c4 ,ed4 #ahhc4 ,footnote #c3 ,some logicians1 however1 speak of defining a thing1 and illustrate this as if by a thing they meant a concrete individual1 the realistic treatment of ,universals lending itself to such expressions4 ,but though the authority of ,aristotle might be claimed for this1 it is better to confine the name in strictness to the main process of defining a class4 ,since1 however1 the method is the same whether it is an individual or a class that we want to make distinct1 there is no harm in the extension of the word definition to both varieties4 ,see ,davidson's ,logic of ,definition1 chap4 ii4 ,footnote #d3 ,see ,davidson's ,logic of ,definition1 chap4 iii4 ,,chapter ,,ii4 ,,the ,,five ,,predicables4--,,verbal ,,and ,,real ,,predication4 ,we give a separate chapter to this topic out of respect for the space that it occupies in the history of ,logic4 ,but except as an exercise in subtle distinction for its own sake1 all that falls to be said about the ,predicables might be given as a simple appendix to the chapter on ,definition4 ,primarily1 the ,five ,predicables or ,heads of ,predicables--,genus1 ,species1 ,differentia1 ,proprium1 and ,accidens--are not predicables at all1 but merely a list or enumeration of terms used in dividing and defining on the basis of attributes4 ,they have no meaning except in connexion with a fixed scheme of division4 ,given such a scheme1 and we can distinguish in it the whole to be divided 7the genus71 the subordinate divisions 7the species71 the attribute or combination of attributes on which each species is constituted 7the differentia71 and other attributes1 which belong to some or all of the individuals but are not reckoned for purposes of division and definition 7,propria and ,accidentia74 ,the list is not itself a logical division3 it is heterogeneous1 not homogeneous2 the two first are names of classes1 the three last of attributes4 ,but corresponding to it we might make a homogeneous division of attributes1 as follows3-- ,attributes ,defining ,non-defining ,generic ,specific ,proprium ,accidens 7,differentia7 ,the origin of the title ,predicables as applied to these five terms is curious1 and may be worth noting as an instance of the difficulty of keeping names precise1 and of the confusion arising from forgetting the purpose of a name4 ,porphyry in his ,greek3 eisagoge or ,introduction explains the five words 7,greek3 phonai7 simply as terms that it is useful for various purposes to know1 expressly mentioning definition and division4 ,but he casually remarks that ,singular names1 ,this man1 ,socrates1 can be predicated only of one individual1 whereas ,genera1 ,species1 ,differentiae1 etc41 are predicables of many4 ,that is to say he describes them as ,predicables simply by contradistinction from ,singular names4 ,a name1 however1 was wanted for the five terms taken all together1 and since they are not a logical division1 but merely a list of terms used in dividing and defining1 there was no apt general designation for them such as would occur spontaneously4 ,thus it became the custom to refer to them as the ,predicables1 a means of reference to them collectively being desiderated1 while the meaning of this descriptive title was forgotten4 ,to call the five divisional elements or ,divisoria ,predicables is to present them as a division of ,predicate ,terms on the basis of their relation to the ,subject ,term3 to suggest that every ,predicate ,term must be either a ,genus or a ,species1 or a ,differentia1 or a ,proprium1 or an ,accidens of the ,subject ,term4 ,they are sometimes criticised as such1 and it is rightly pointed out that the ,predicate is never a species of or with reference to the ,subject4 ,but1 in truth1 the five so-called ,predicables were never meant as a division of predicates in relation to the subject3 it is only the title that makes this misleading suggestion4 ,to complete the confusion it so happens that ,aristotle used three of the ,five terms in what was virtually a division of ,predicates inasmuch as it was a division of ,problems or ,questions4 ,in expounding the methods of ,dialectic in the ,topica he divided ,problems into four classes according to the relation of the ,predicate to the ,subject4 ,the ,predicate must either be simply convertible with the subject or not4 ,if simply convertible1 the two must be coextensive1 and the ,predicate must be either a ,proprium or the ,definition4 ,if not simply convertible1 the ,predicate must either be part of the ,definition or not4 ,if part of the ,definition it must be either a ,generic ,property or a ,differentia 7both of which in this connexion ,aristotle includes under ,genus73 if not part of the ,definition1 it is an ,accident4 ,aristotle thus arrives at a fourfold division of ,problems or ,predicates3--,greek3 genos 7,genus1 including ,differentia1 ,greek3 diaphora72 ,greek3 horos 7,definition72 ,greek3 to idion 7,proprium72 and ,greek3 to symbebekos 7,accidens74 ,the object of it was to provide a basis for his systematic exposition2 each of the four kinds admitted of differences in dialectic method4 ,for us it is a matter of simple curiosity and ingenuity4 ,it serves as a monument of how much ,greek dialectic turned on ,definition1 and it corresponds exactly to the division of attributes into ,defining and ,non-defining given above4 ,it is sometimes said that ,aristotle showed a more scientific mind than ,porphyry in making the ,predicables four instead of five4 ,this is true if ,porphyry's list had been meant as a division of attributes3 but it was not so meant4 ,the distinction between ,,verbal or ,,analytic and ,,real or ,,synthetic ,predication corresponds to the distinction between ,defining and ,non-defining attributes1 and also has no significance except with reference to some scheme of ,division1 scientific and precise or loose and popular4 ,when a proposition predicates of a subject something contained in the full notion1 concept1 or definition of the subject term1 it is called ,verbal1 ,analytic1 or ,explicative3 verbal1 inasmuch as it merely explains the meaning of a name2 explicative for the same reason2 analytic1 inasmuch as it unties the bundle of attributes held together in the concept and pays out one1 or all one by one4 ,when the attributes of the ,predicate are not contained in the concept of the ,subject1 the proposition is called ,real1 ,synthetic1 or ,ampliative1 for parallel reasons4 ,thus3 ,a triangle is a three-sided rectilinear figure is ,verbal or ,analytic2 ,triangles have three angles together equal to two right angles1 or ,triangles are studied in schools1 is ,real or ,synthetic4 ,according to this distinction1 predications of the whole ,definition or of a ,generic attribute or of a ,specific attribute are ,verbal2 predications of ,accident are ,real4 ,a nice point is whether ,propria are ,verbal or ,real4 ,they can hardly be classed with ,verbal1 inasmuch as one may know the full meaning of the name without knowing them3 but it might be argued that they are ,analytic1 inasmuch as they are implicitly contained in the defining attributes as being deducible from them4 ,observe1 however1 that the whole distinction is really valid only in relation to some fixed or accepted scheme of classification or division4 ,otherwise1 what is ,verbal or ,analytic to one man may be ,real or ,synthetic to another4 ,it might even be argued that every proposition is ,analytic to the man who utters it and ,synthetic to the man who receives it4 ,we must make some analysis of a whole of thought before paying it out in words3 and in the process of apprehending the meaning of what we hear or read we must add the other members of the sentence on to the subject4 ,whether or not this is super-subtle1 it clearly holds good that what is ,verbal 7in the sense defined7 to the learned man of science may be ,real to the learner4 ,that the horse has six incisors in each jaw or that the domestic dog has a curly tail1 is a ,verbal ,proposition to the ,natural ,historian1 a mere exposition of defining marks2 but the plain man has a notion of horse or dog into which this defining attribute does not enter1 and to him accordingly the proposition is ,real4 ,but what of propositions that the plain man would at once recognise as ,verbal8 ,charles ,lamb1 for example1 remarks that the statement that a good name shows the estimation in which a man is held in the world is a verbal proposition4 ,where is the fixed scheme of division there8 ,the answer is that by a fixed scheme of division we do not necessarily mean a scheme that is rigidly1 definitely and precisely fixed4 ,to make such schemes is the business of ,science4 ,but the ordinary vocabulary of common intercourse as a matter of fact proceeds upon schemes of division1 though the names used in common speech are not always scientifically accurate1 not always the best that could be devised for the easy acquisition and sure transmission of thorough knowledge4 ,the plain man's vocabulary1 though often twisted aside by such causes as we have specified1 is roughly moulded on the most marked distinguishing attributes of things4 ,this was practically recognised by ,aristotle when he made one of his modes of definition consist in something like what we have called verifying the meaning of a name1 ascertaining the attributes that it signifies in common speech or in the speech of sensible men4 ,this is to ascertain the essence1 ,greek3 ousia1 or ,substantia1 of things1 the most salient attributes that strike the common eye either at once or after the closer inspection that comes of long companionship1 and form the basis of the ordinary vocabulary4 ,properly speaking1 ,mansel says1#a ,all ,definition is an inquiry into ,attributes4 ,our complex notions of ,substances can only be resolved into various ,attributes1 with the addition of an unknown substratum3 a something to which we are compelled to regard these attributes as belonging4 ,man1 for example1 is analysed into ,animality1 ,rationality1 and the something which exhibits these phenomena4 ,pursue the analysis and the result is the same4 ,we have a something corporeal1 animated1 sensible1 rational4 ,an unknown constant must always be added to complete the integration4 ,this unknown constant was what ,locke called the ,real ,essence1 as distinguished from the ,nominal ,essence1 or complex of attributes4 ,it is upon this nominal essence1 upon divisions of things according to attributes1 that common speech rests1 and if it involves many cross-divisions1 this is because the divisions have been made for limited and conflicting purposes4 ,footnote #a3 ,aldrich's ,compendium1 ,appendix1 ,note ,c4 ,the reader may be referred to ,mansel's ,notes ,a and ,c for valuable historical notices of the ,predicables and ,definition4 ,,chapter ,,iii4 ,,aristotle',s ,,categories4 ,in deference to tradition a place must be found in every logical treatise for ,aristotle's ,categories4 ,no writing of the same length has exercised a tithe of its influence on human thought4 ,it governed scholastic thought and expression for many centuries1 being from its shortness and consequent easiness of transcription one of the few books in every educated man's library4 ,it still regulates the subdivisions of ,parts of ,speech in our grammars4 ,its universality of acceptance is shown in the fact that the words category 7,greek3 kategoria7 and predicament1 its ,latin translation1 have passed into common speech4 ,the ,categories have been much criticised and often condemned as a division1 but1 strange to say1 few have inquired what they originally professed to be a division of1 or what was the original author's basis of division4 ,whether the basis is itself important1 is another question3 but to call the division imperfect1 without reference to the author's intention1 is merely confusing1 and serves only to illustrate the fact that the same objects may be differently divided on different principles of division4 ,ramus was right in saying that the ,categories had no logical significance1 inasmuch as they could not be made a basis for departments of logical method2 and ,kant and ,mill in saying that they had no philosophical significance1 inasmuch as they are founded upon no theory of ,knowing and ,being3 but this is to condemn them for not being what they were never intended to be4 ,the sentence in which ,aristotle states the objects to be divided1 and his division of them is so brief and bold that bearing in mind the subsequent history of the ,categories1 one first comes upon it with a certain surprise4 ,he says simply3-- ,of things expressed without syntax 7i4e41 single words71 each signifies either substance1 or quantity1 or quality1 or relation1 or place1 or time1 or disposition 7i4e41 attitude or internal arrangement71 or appurtenance1 or action 7doing71 or suffering 7being done to74#a ,the objects1 then1 that ,aristotle proposed to classify were single words 7the themata simplicia of the ,schoolmen74 ,he explains that by out of syntax 7,greek3 aneu symplokes7 he means without reference to truth or falsehood3 there can be no declaration of truth or falsehood without a sentence1 a combination1 or syntax3 man runs is either true or false1 man by itself1 runs by itself1 is neither4 ,his division1 therefore1 was a division of single words according to their differences of signification1 and without reference to the truth or falsehood of their predication4#b ,signification was thus the basis of division4 ,but according to what differences8 ,the ,categories themselves are so abstract that this question might be discussed on their bare titles interminably4 ,but often when abstract terms are doubtful1 an author's intention may be gathered from his examples4 ,and when ,aristotle's examples are ranged in a table1 certain principles of subdivision leap to the eyes4 ,thus3-- ,substance ,man ,,common ,substance 7,greek3 ousia7 7,greek3 anthropos7 ,,noun 7,substantia7 ---------------------------------------- ---------------------- ,quantity ,five-feet-five 7,greek3 poson7 7,greek3 tripechu7 7,quantitas7 ,quality ,scholarly ,permanent 7,greek3 poion7 7,greek3 grammatikon7 ,,adjective ,attribute 7,qualitas7 ,relation ,bigger 7,greek3 pros ti7 7,greek3 meizon7 7,relatio7 ---------------------------------------- ---------------------- ,place ,in-the-,lyceum 7,greek3 pou7 7,greek3 en ,lykeio7 7,ubi7 ,,adverb ,temporary ,time ,yesterday ,attribute 7,greek3 pote7 7,greek3 chthes7 7,quando7 ---------------------------------------- ---------------------- ,disposition ,reclines 7,greek3 keisthai7 7,greek3 anakeitai7 7,positio7 ,appurtenance ,has-shoes-on 7,greek3 echein7 7,greek3 hypodedetai7 7,habitus7 ,,verb ,action ,cuts ,temporary 7,greek3 poiein7 7,greek3 temnei7 ,attribute 7,actio7 ,passion ,is cut 7,greek3 paschein7 7,greek3 temnetai7 7,passio7 ,in looking at the examples1 our first impression is that ,aristotle has fallen into a confusion4 ,he professes to classify words out of syntax1 yet he gives words with the marks of syntax on them4 ,thus his division is accidentally grammatical1 a division of parts of speech1 parts of a sentence1 into ,nouns1 ,adjectives1 ,adverbs1 and ,verbs4 ,and his subdivisions of these parts are still followed in our grammars4 ,but really it is not the grammatical function that he attends to1 but the signification3 and looking further at the examples1 we see what differences of signification he had in his mind4 ,it is differences relative to a concrete individual1 differences in the words applied to him according as they signify the substance of him or his attributes1 permanent or temporary4 ,take any concrete thing1 ,socrates1 this book1 this table4 ,it must be some kind of a thing1 a man1 a book4 ,it must have some size or quantity1 six feet high1 three inches broad4 ,it must have some quality1 white1 learned1 hard4 ,it must have relations with other things1 half this1 double that1 the son of a father4 ,it must be somewhere1 at some time1 in some attitude1 with some havings1 appendages1 appurtenances1 or belongings1 doing something1 or having something done to it4 ,can you conceive any name 7simple or composite7 applicable to any object of perception1 whose signification does not fall into one or other of these classes8 ,if you cannot1 the categories are justified as an exhaustive division of significations4 ,they are a complete list of the most general resemblances among individual things1 in other words1 of the summa genera1 the genera generalissima of predicates concerning this1 that or the other concrete individual4 ,no individual thing is sui generis3 everything is like other things3 the categories are the most general likenesses4 ,the categories are exhaustive1 but do they fulfil another requisite of a good division--are they mutually exclusive8 ,aristotle himself raised this question1 and some of his answers to difficulties are instructive4 ,particularly his discussion of the distinction between ,second ,substances or ,essences and ,qualities4 ,here he approximates to the modern doctrine of the distinction between ,substance and ,attribute as set forth in our quotation from ,mansel at p4 #aaj4 ,aristotle's ,second ,essences 7,greek3 deuterai ousiai7 are common nouns or general names1 ,species and ,genera1 man1 horse1 animal1 as distinguished from ,singular names1 this man1 this horse1 which he calls ,first ,substances 7,greek3 protai ousiai71 essences par excellence1 to which real existence in the highest sense is attributed4 ,common nouns are put in the ,first ,category because they are predicated in answer to the question1 ,what is this8 ,but he raises the difficulty whether they may not rather be regarded as being in the ,third ,category1 that of ,quality 7,greek3 to poion74 ,when we say1 ,this is a man1 do we not declare what sort of a thing he is8 do we not declare his ,quality8 ,if ,aristotle had gone farther along this line1 he would have arrived at the modern point of view that a man is a man in virtue of his possessing certain attributes1 that general names are applied in virtue of their connotation4 ,this would have been to make the line of distinction between the ,first ,category and the ,third pass between ,first ,essence and ,second1 ranking the ,second ,essences with ,qualities4 ,but ,aristotle did not get out of the difficulty in this way4 ,he solved it by falling back on the differences in common speech4 ,man does not signify the quality simply1 as whiteness does4 ,whiteness signifies nothing but the quality4 ,that is to say1 there is no separate name in common speech for the common attributes of man4 ,his further obscure remark that general names define quality round essence ,greek3 peri ousian1 inasmuch as they signify what sort a certain essence is1 and that genera make this definition more widely than species1 bore fruit in the mediaeval discussions between ,realists and ,nominalists by which the signification of general names was cleared up4 ,another difficulty about the mutual exclusiveness of the ,categories was started by ,aristotle in connexion with the ,fourth ,category1 ,relation 7,greek3 pros ti ,ad aliquid1 ,to something74 ,mill remarks that that could not be a very comprehensive view of the nature of ,relation which would exclude action1 passivity1 and local situation from that ,category1 and many commentators1 from ,simplicius down to ,hamilton1 have remarked that all the last six ,categories might be included under ,relation4 ,this is so far correct that the word ,relation is one of the vaguest and most extensive of words2 but the criticism ignores the strictness with which ,aristotle confined himself in his ,categories to the forms of common speech4 ,it is clear from his examples that in his ,fourth ,category he was thinking only of relation as definitely expressed in common speech4 ,in his meaning1 any word is a relative which is joined with another in a sentence by means of a preposition or a case-inflection4 ,thus disposition is a relative3 it is the disposition of something4 ,this kind of relation is perfect when the related terms reciprocate grammatically2 thus master1 servant1 since we can say either the master of the servant1 or the servant of the master4 ,in mediaeval logic the term ,relata was confined to these perfect cases1 but the ,category had a wider scope with ,aristotle4 ,and he expressly raised the question whether a word might not have as much right to be put in another ,category as in this4 ,indeed1 he went further than his critics in his suggestions of what ,relation might be made to include4 ,thus3 big signifies ,quality2 yet a thing is big with reference to something else1 and is so far a ,relative4 ,knowledge must be knowledge of something1 and is a relative3 why then should we put knowing 7i4e41 learned7 in the ,category of ,quality4 ,hope is a relative1 as being the hope of a man and the hope of something4 ,yet we say1 ,i have hope1 and there hope would be in the category of ,having1 ,appurtenance4 ,for the solution of all such difficulties1 ,aristotle falls back upon the forms of common speech1 and decides the place of words in his categories according to them4 ,this was hardly consistent with his proposal to deal with separate words out of syntax1 if by this was meant anything more than dealing with them without reference to truth or falsehood4 ,he did not and could not succeed in dealing with separate words otherwise than as parts of sentences1 owing their signification to their position as parts of a transient plexus of thought4 ,in so far as words have their being in common speech1 and it is their being in this sense that ,aristotle considers in the ,categories1 it is a transient being4 ,what being they represent besides is1 in the words of ,porphyry1 a very deep affair1 and one that needs other and greater investigation4 ,footnote #a3 ,greek3 ton kata medemian symploken legomenon hekaston etoi ousian semainei1 e poson1 e poion1 e pros ti1 e pou1 e pote1 e keisthai1 e echein1 e poiein1 e paschein4 7,categ4 ii4 #e47 ,footnote #b3 ,to describe the ,categories as a grammatical division1 as ,mansel does in his instructive ,appendix ,c to ,aldrich1 is a little misleading without a qualification4 ,they are non-logical inasmuch as they have no bearing on any logical purpose4 ,but they are grammatical only in so far as they are concerned with words4 ,they are not grammatical in the sense of being concerned with the function of words in predication4 ,the unit of grammar in this sense is the sentence1 a combination of words in syntax2 and it is expressly with words out of syntax that ,aristotle deals1 with single words not in relation to the other parts of a sentence1 but in relation to the things signified4 ,in any strict definition of the provinces of ,grammar and ,logic1 the ,categories are neither grammatical nor logical3 the grammarians have appropriated them for the subdivision of certain parts of the sentence1 but with no more right than the logicians4 ,they really form a treatise by themselves1 which is in the main ontological1 a discussion of substances and attributes as underlying the forms of common speech4 ,in saying this ,i use the word substance in the modern sense3 but it must be remembered that ,aristotle's ,greek3 ousia1 translated substantia1 covered the word as well as the thing signified1 and that his ,categories are primarily classes of words4 ,the union between names and things would seem to have been closer in the ,greek mind than we can now realise4 ,to get at it we must note that every separate word ,greek3 to legomenon is conceived as having a being or thing ,greek3 to on corresponding to it1 so that beings or things ,greek3 ta onta are coextensive with single words3 a being or thing is whatever receives a separate name4 ,this is clear and simple enough1 but perplexity begins when we try to distinguish between this nameable being and concrete being1 which last is ,aristotle's category of ,greek3 ousia1 the being signified by a ,proper or a ,common as distinguished from an ,abstract ,noun4 ,as we shall see1 it is relatively to the highest sense of this last kind of being1 namely1 the being signified by a ,proper name1 that he considers the other kinds of being4 ,,chapter ,,iv4 ,,the ,,controversy ,,about ,,universals4--,,difficulties ,,concerning ,,the ,,relation ,,of ,,general ,,names ,,to ,,thought ,,and ,,to ,,reality4 ,in the opening sentences of his ,isagoge1 before giving his simple explanation of the ,five ,predicables1 ,porphyry mentions certain questions concerning ,genera and ,species1 which he passes over as being too difficult for the beginner4 ,concerning genera and species1 he says1 the question whether they subsist 7i4e41 have real substance71 or whether they lie in the mere thoughts only1 or whether1 granting them to subsist1 they are corporeal or incorporeal1 or whether they subsist apart1 or in sensible things and cohering round them--this ,i shall pass over1 such a question being a very deep affair and one that needs other and greater investigation4 ,this passage1 written about the end of the third century1 ,a4,d41 is a kind of isthmus between ,greek ,philosophy and ,mediaeval3 it summarises questions which had been turned over on every side and most intricately discussed by ,plato and ,aristotle and their successors1 and the bald summary became a starting-point for equally intricate discussions among the ,schoolmen1 among whom every conceivable variety of doctrine found champions4 ,the dispute became known as the dispute about ,universals1 and three ultra-typical forms of doctrine were developed1 known respectively as ,realism1 ,nominalism1 and ,conceptualism4 ,undoubtedly the dispute1 with all its waste of ingenuity1 had a clearing effect1 and we may fairly try now what ,porphyry shrank from1 to gather some simple results for the better understanding of general names and their relations to thoughts and to things4 ,the rival schools had each some aspect of the general name in view1 which their exaggeration served to render more distinct4 ,what does a general name signify8 ,for logical purposes it is sufficient to answer--the points of resemblance as grasped in the mind1 fixed by a name applicable to each of the resembling individuals4 ,this is the signification of the general name logically1 its connotation or concept1 the identical element of objective reference in all uses of a general name4 ,but other questions may be asked that cannot be so simply answered4 ,what is this concept in thought8 ,what is there in our minds corresponding to the general name when we utter it8 ,how is its signification conceived8 ,what is the signification psychologically8 ,we may ask1 further1 ,what is there in nature that the general name signifies8 ,what is its relation to reality8 ,what corresponds to it in the real world8 ,has the unity that it represents among individuals no existence except in the mind8 ,calling this unity1 this one in the many1 the ,universal 7,universale1 ,greek3 to pan71 what is the ,universal ontologically8 ,it was this ontological question that was so hotly and bewilderingly debated among the ,schoolmen4 ,before giving the ultra-typical answers to it1 it may be well to note how this question was mixed up with still other questions of ,theology and ,cosmogony4 ,recognising that there is a unity signified by the general name1 we may go on to inquire into the ground of the unity4 ,why are things essentially like one another8 ,how is the unity maintained8 ,how is it continued8 ,where does the common pattern come from8 ,the question of the nature of the ,universal thus links itself with metaphysical theories of the construction of the world1 or even with the ,darwinian theory of the origin of species4 ,passing by these remoter questions1 we may give the answers of the three extreme schools to the ontological question1 ,what is a ,universal8 ,the answer of the ,ultra-,realists1 broadly put1 was that a ,universal is a substance having an independent existence in nature4 ,of the ,ultra-,nominalists1 that the ,universal is a name and nothing else1 vox et praeterea nihil2 that this name is the only unity among the individuals of a species1 all that they have in common4 ,of the ,ultra-,conceptualists1 that the individuals have more in common than the name1 that they have the name plus the meaning1 vox significatio1 but that the ,universals1 the genera and species1 exist only in the mind4 ,now these extreme doctrines1 as literally interpreted by opponents1 are so easily refuted and so manifestly untenable1 that it may be doubted whether they were ever held by any thinker1 and therefore ,i call them ,ultra-,realism1 ,ultra-,nominalism1 and ,ultra-,conceptualism4 ,they are mere exaggerations or caricatures1 set up by opponents because they can be easily knocked down4 ,to the ,ultra-,realists1 it is sufficient to say that if there existed anywhere a substance having all the common attributes of a species and only these1 having none of the attributes peculiar to any of the individuals of that species1 corresponding to the general name as an individual corresponds to a ,proper or ,singular name1 it would not be the ,universal1 the unity pervading the individuals1 but only another individual4 ,to the ,ultra-,nominalists1 it is sufficient to say that the individuals must have more in common than the name1 because the name is not applied arbitrarily1 but on some ground4 ,the individuals must have in common that on account of which they receive the common name3 to call them by the same name is not to make them of the same species4 ,to the ,ultra-,conceptualists1 it is sufficient to say that when we employ a general name1 as when we say ,socrates is a man1 we do not refer to any passing thought or state of mind1 but to certain attributes independent of what is passing in our minds4 ,we cannot make a thing of this or that species by merely thinking of it as such4 ,the ultra-forms of these doctrines are thus easily shown to be inadequate1 yet each of the three1 ,realism1 ,nominalism1 and ,conceptualism1 represents a phase of the whole truth4 ,thus1 take ,realism4 ,although it is not true that there is anything in reality corresponding to the general name such as there is corresponding to the singular name1 the general name merely signifying attributes of what the singular name signifies1 it does not follow1 as the opponents of ,ultra-,realism hastily assume1 that there is nothing in the real world corresponding to the general name4 ,three senses may be particularised in which ,realism is justified4 7#a7 ,the points of resemblance from which the concept is formed are as real as the individuals themselves4 ,it is true in a sense that it is our thought that gives unity to the individuals of a class1 that gathers the many into one1 and so far the ,conceptualists are right4 ,still we should not gather them into one if they did not resemble one another3 that is the reason why we think of them together3 and the respects in which they resemble one another are as much independent of us and our thinking as the individuals themselves1 as much beyond the power of our thought to change4 ,we must go behind the activity of the mind in unifying to the reason for the unification3 and the ground of unity is found in what really exists4 ,we do not confer the unity3 we do not make all men or all dogs alike3 we find them so4 ,the curly tails in a thousand domestic dogs1 which serve to distinguish them from wolves and foxes1 are as real as the thousand individual domestic dogs4 ,in this sense the ,aristotelian doctrine1 ,universalia in re1 expresses a plain truth4 7#b7 ,the ,platonic doctrine1 formulated by the ,schoolmen as ,universalia ante rem1 has also a plain validity4 ,individuals come and go1 but the type1 the ,universal1 is more abiding4 ,men are born and die3 man remains throughout4 ,the snows of last year have vanished1 but snow is still a reality to be faced4 ,wisdom does not perish with the wise men of any generation4 ,in this plain sense1 at least1 it is true that ,universals exist before ,individuals1 have a greater permanence1 or1 if we like to say so1 a higher1 as it is a more enduring1 reality4 7#c7 ,further1 the idea1 concept1 or universal1 though it cannot be separated from the individual1 and whether or not we ascribe to it the separate suprasensual existence of the archetypal forms of ,plato's poetical fancy1 is a very potent factor in the real world4 ,ideals of conduct1 of manners1 of art1 of policy1 have a traditional life3 they do not pass away with the individuals in whom they have existed1 in whom they are temporarily materialised3 they survive as potent influences from age to age4 ,the idea of ,chaucer's ,man of ,law1 who always seemed busier than he was1 is still with us4 ,mediaeval conceptions of chivalry still govern conduct4 ,the ,universal enters into the ,individual1 takes possession of him1 makes of him its temporary manifestation4 ,nevertheless1 the ,nominalists are right in insisting on the importance of names4 ,what we call the real world is a common object of perception and knowledge to you and me3 we cannot arrive at a knowledge of it without some means of communication with one another3 our means of communication is language4 ,it may be doubted whether even thinking could go far without symbols with the help of which conceptions may be made definite4 ,a concept cannot be explained without reference to a symbol4 ,there is even a sense in which the ,ultra-,nominalist doctrine that the individuals in a class have nothing in common but the name is tenable4 ,denotability by the same name is the only respect in which those individuals are absolutely identical3 in this sense the name alone is common to them1 though it is applied in virtue of their resemblance to one another4 ,finally1 the ,conceptualists are right in insisting on the mind's activity in connexion with general names4 ,genera and species are not mere arbitrary subjective collections3 the union is determined by the characters of the things collected4 ,still it is with the concept in each man's mind that the name is connected3 it is by the activity of thought in recognising likenesses and forming concepts that we are able to master the diversity of our impressions1 to introduce unity into the manifold of sense1 to reduce our various recollections to order and coherence4 ,so much for the ,ontological question4 ,now for the ,,psychological4 ,what is in the mind when we employ a general name8 ,what is the ,universal psychologically8 ,how is it conceived8 ,what breeds confusion in these subtle inquiries is the want of fixed unambiguous names for the things to be distinguished4 ,it is only by means of such names that we can hold on to the distinctions1 and keep from puzzling ourselves4 ,now there are three things to be distinguished in this inquiry1 which we may call the ,concept1 the ,conception1 and the ,conceptual or ,generic ,image4 ,let us call them by these names1 and proceed to explain them4 ,by the ,concept1 ,i understand the meaning of the general name1 what the general name signifies3 by the ,conception1 the mental act or state of him who conceives this meaning4 ,the concept of triangle1 i4e41 what you and ,i mean by the word1 is not my act of mind or your act of mind when we think or speak of a triangle4 ,the ,conception1 which is this act1 is an event or incident in our mental history1 a psychical act or state1 a distinct occurrence1 a particular fact in time as much as the battle of ,waterloo4 ,the concept is the objective reference of the name1 which is the same1 or at least is understood to be the same1 every time we use it4 ,i make a figure on paper with ink or on a blackboard with chalk1 and recognise or conceive it as a triangle3 you also conceive it as such3 we do the same to-morrow3 we did the same yesterday3 each act of conception is a different event1 but the concept is the same throughout4 ,now the psychological question about the ,universal is1 ,what is this conception8 ,we cannot define it positively further than by saying that it consists in realising the meaning of a general name3 the act being unique1 we can only make it intelligible by producing an example of it4 ,but we may define it negatively by distinguishing it from the conceptual image4 ,whenever we conceive anything1 man1 horse1 there is generally present to our minds an image of a man or horse1 with accidents of size1 colour1 position or other categories4 ,but this conceptual image is not the concept1 and the mental act of forming it is not conception4 ,this distinction between mental picturing or imaging and the conception of common attributes is variously expressed4 ,the correlative terms ,intuitive and ,symbolical ,thinking1 ,presentative and ,representative ,knowledge have been employed4#a ,but whatever terms we use1 the distinction itself is vital1 and the want of it leads to confusion4 ,thus the fact that we cannot form a conceptual image composed solely of common attributes has been used to support the argument of ,ultra-,nominalism1 that the individuals classed under a common name have nothing in common but the name4 ,what the word dog signifies1 i4e41 the concept of dog1 is neither big nor little1 neither black nor tan1 neither here nor there1 neither ,newfoundland1 nor ,retriever1 nor ,terrier1 nor ,greyhound1 nor ,pug1 nor ,bulldog4 ,the concept consists only of the attributes common to all dogs apart from any that are peculiar to any variety or any individual4 ,now we cannot form any such conceptual image4 ,our conceptual image is always of some definite size and shape4 ,therefore1 it is argued1 we cannot conceive what a dog means1 and dogs have nothing in common but the name4 ,this1 however1 does not follow4 ,the concept is not the conceptual image1 and forming the image is not conception4 ,we may even1 as in the case of a chiliagon1 or thousand-sided figure1 conceive the meaning without being able to form any definite image4 ,how then1 do we ordinarily proceed in conceiving1 if we cannot picture the common attributes alone and apart from particulars8 ,we attend1 or strive to attend1 only to those aspects of an image which it has in common with the individual things denoted4 ,and if we want to make our conception definite1 we pass in review an indefinite number of the individuals1 case after case4 ,a minor psychological question concerns the nature of the conceptual image4 ,is it a copy of some particular impression1 or a confused blur or blend of many8 ,possibly neither3 possibly it is something like one of ,mr4 ,galton's composite photographs1 photographs produced by exposing the same surface to the impressions of a number of different photographs in succession4 ,if the individuals are nearly alike1 the result is an image that is not an exact copy of any one of the components and yet is perfectly distinct4 ,possibly the image that comes into our mind's eye when we hear such a word as horse or man is of this character1 the result of the impressions of a number of similar things1 but not identical with any one4 ,as1 however1 different persons have different conceptual images of the same concept1 so we may have different conceptual images at different times4 ,it is only the concept that remains the same4 ,but how1 it may be asked1 can the concept remain the same8 ,if the universal or concept psychologically is an intellectual act1 repeated every time we conceive1 what guarantee have we for the permanence of the concept8 ,does this theory not do away with all possibility of defining and fixing concepts8 ,this brings us back to the doctrine already laid down about the truth of ,realism4 ,the theory of the concept is not exhausted when it is viewed only psychologically1 as a psychic act4 ,if we would understand it fully1 we must consider the act in its relations to the real experience of ourselves and others4 ,to fix this act1 we give it a separate name1 calling it the conception3 and then we must go behind the activity of the mind to the objects on which it is exercised4 ,the element of fixity is found in them4 ,and here also the truth of ,nominalism comes in4 ,by means of words we enter into communication with other minds4 ,it is thus that we discover what is real1 and what is merely personal to ourselves4 ,footnote #a3 ,the only objection to these terms is that they have slipped from their moorings in philosophical usage4 ,thus instead of ,leibnitz's use of ,intuitive and ,symbolical1 which corresponds to the above distinction between ,imaging and ,conception1 ,mr4 ,jevons employs the terms to express a distinction among conceptions proper4 ,we can understand what a chiliagon means1 but we cannot form an image of it in our minds1 except in a very confused and imperfect way2 whereas we can form a distinct image of a triangle4 ,mr4 ,jevons would call the conception of the triangle ,intuitive1 of the chiliagon ,symbolical4 ,again1 while ,mansel uses the words ,presentative and ,representative to express our distinction1 a more common usage is to call actual ,perception ,presentative ,knowledge1 and ideation or recollection in idea ,representative4 ,,part ,,iii4 ,,the ,,interpretation ,,of ,,propositions4--,,opposition ,,and ,,immediate ,,inference4 ,,chapter ,i4 ,,theories ,,of ,,predication4--,,theories ,,of ,,judgment4 ,we may now return to the ,syllogistic ,forms1 and the consideration of the compatibility or incompatibility1 implication1 and interdependence of propositions4 ,it was to make this consideration clear and simple that what we have called the ,syllogistic ,form of propositions was devised4 ,when are propositions incompatible8 ,when do they imply one another8 ,when do two imply a third8 ,we have seen in the ,introduction how such questions were forced upon ,aristotle by the disputative habits of his time4 ,it was to facilitate the answer that he analysed propositions into ,subject and ,predicate1 and viewed the ,predicate as a reference to a class3 in other words1 analysed the ,predicate further into a ,copula and a ,class ,term4 ,but before showing how he exhibited the interconnexion of propositions on this plan1 we may turn aside to consider various so-called ,theories of ,predication or of ,judgment4 ,strictly speaking1 they are not altogether relevant to ,logic1 that is to say1 as a practical science3 they are partly logical1 partly psychological theories3 some of them have no bearing whatever on practice1 but are matters of pure scientific curiosity3 but historically they are connected with the logical treatment of propositions as having been developed out of this4 ,the least confusing way of presenting these theories is to state them and examine them both logically and psychologically4 ,the logical question is1 ,has the view any advantage for logical purposes8 ,does it help to prevent error1 to clear up confusion8 ,does it lead to firmer conceptions of the truth8 ,the psychological question is1 ,is this a correct theory of how men actually think when they make propositions8 ,it is a question of what is in the one case1 and of what ought to be for a certain purpose in the other4 ,whether we speak of ,proposition or of ,judgment does not materially affect our answer4 ,a ,judgment is the mental act accompanying a ,proposition1 or that may be expressed in a proposition and cannot be expressed otherwise3 we can give no other intelligible definition or description of a judgment4 ,so a proposition can only be defined as the expression of a judgment3 unless there is a judgment underneath them1 a form of words is not a proposition4 ,let us take1 then1 the different theories in turn4 ,we shall find that they are not really antagonistic1 but only different3 that each is substantially right from its own point of view3 and that they seem to contradict one another only when the point of view is misunderstood4 ,i4 ,that the ,predicate term may be regarded as a class in or from which the ,subject is included or excluded4 ,known as the ,class-,inclusion1 ,class-,reference1 or ,denotative view4 ,this way of analysing propositions is possible1 as we have seen1 because every statement implies a general name1 and the extension or denotation of a general name is a class defined by the common attribute or attributes4 ,it is useful for syllogistic purposes3 certain relations among propositions can be most simply exhibited in this way4 ,but if this is called a ,theory of ,predication or ,judgment1 and taken psychologically as a theory of what is in men's minds whenever they utter a significant ,sentence1 it is manifestly wrong4 ,when discussed as such1 it is very properly rejected4 ,when a man says ,p struck ,q1 he has not necessarily a class of strikers of ,q definitely in his mind4 ,what he has in his mind is the logical equivalent of this1 but it is not this directly4 ,similarly1 ,mr4 ,bradley would be quite justified in speaking of ,two ,terms and a ,copula as a superstition1 if it were meant that these analytic elements are present to the mind of an ordinary speaker4 ,,ii4 ,that every ,proposition may be regarded as affirming or denying an attribute of a subject4 ,known sometimes as the ,connotative or the ,denotative-,connotative view4 ,this also follows from the implicit presence of a general name in every sentence4 ,but it should not be taken as meaning that the man who says3 ,tom came here yesterday1 or ,james generally sits there1 has a clearly analysed ,subject and ,attribute in his mind4 ,otherwise it is as far wrong as the other view4 ,,iii4 ,that every proposition may be regarded as an equation between two terms4 ,known as the ,equational ,view4 ,this is obviously not true for common speech or ordinary thought4 ,but it is a possible way of regarding the analytic components of a proposition1 legitimate enough if it serves any purpose4 ,it is a modification of the ,class-,reference analysis1 obtained by what is known as ,quantification of the ,predicate4 ,in ,all ,s is in ,p1 ,p is undistributed1 and has no symbol of ,quantity4 ,but since the proposition imports that ,all ,s is a part of ,p1 i4e41 ,some ,p1 we may1 if we choose1 prefix the symbol of ,quantity1 and then the proposition may be read ,all ,s ,some ,p4 ,and so with the other forms4 ,is there any advantage in this8 ,yes3 it enables us to subject the formulae to algebraic manipulation4 ,but any logical advantage--any help to thinking8 ,none whatever4 ,the elaborate syllogistic systems of ,boole1 ,de ,morgan1 and ,jevons are not of the slightest use in helping men to reason correctly4 ,the value ascribed to them is merely an illustration of the ,bias of ,happy ,exercise4 ,they are beautifully ingenious1 but they leave every recorded instance of learned ,scholastic trifling miles behind4 ,,iv4 ,that every proposition is the expression of a comparison between concepts4 ,sometimes called the ,conceptualist ,view4 ,to judge1 ,hamilton says1 is to recognise the relation of congruence or confliction in which two concepts1 two individual things1 or a concept and an individual compared together stand to each other4 ,this way of regarding propositions is permissible or not according to our interpretation of the words congruence and confliction1 and the word concept4 ,if by concept we mean a conceived attribute of a thing1 and if by saying that two concepts are congruent or conflicting1 we mean that they may or may not cohere in the same thing1 and by saying that a concept is congruent or conflicting with an individual that it may or may not belong to that individual1 then the theory is a corollary from ,aristotle's analysis4 ,seeing that we must pass through that analysis to reach it1 it is obviously not a theory of ordinary thought1 but of the thought of a logician performing that analysis4 ,the precise point of ,hamilton's theory was that the logician does not concern himself with the question whether two concepts are or are not as a matter of fact found in the same subject1 but only with the question whether they are of such a character that they may be found1 or cannot be found1 in the same subject4 ,in so far as his theory is sound1 it is an abstruse and technical way of saying that we may consider the consistency of propositions without considering whether or not they are true1 and that consistency is the peculiar business of syllogistic logic4 ,v4 ,that the ultimate subject of every judgment is reality4 ,this is the form in which ,mr4 ,bradley and ,mr4 ,bosanquet deny the ,ultra-,conceptualist position4 ,the same view is expressed by ,mill when he says that propositions are concerned with things and not with our ideas of them4 ,the least consideration shows that there is justice in the view thus enounced4 ,take a number of propositions3-- ,the streets are wet4 ,george has blue eyes4 ,the ,earth goes round the ,sun4 ,two and two make four4 ,obviously1 in any of these propositions1 there is a reference beyond the conceptions in the speaker's mind1 viewed merely as incidents in his mental history4 ,they express beliefs about things and the relations among things in rerum natura3 when any one understands them and gives his assent to them1 he never stops to think of the speaker's state of mind1 but of what the words represent4 ,when states of mind are spoken of1 as when we say that our ideas are confused1 or that a man's conception of duty influences his conduct1 those states of mind are viewed as objective facts in the world of realities4 ,even when we speak of things that have in a sense no reality1 as when we say that a centaur is a combination of man and horse1 or that centaurs were fabled to live in the vales of ,thessaly1 it is not the passing state of mind expressed by the speaker as such that we attend to or think of2 we pass at once to the objective reference of the words4 ,psychologically1 then1 the theory is sound3 what is its logical value8 ,it is sometimes put forward as if it were inconsistent with the ,class-reference theory or the theory that judgment consists in a comparison of concepts4 ,historically the origin of its formal statement is its supposed opposition to those theories4 ,but really it is only a misconception of them that it contradicts4 ,it is inconsistent with the ,class-reference view only if by a class we understand an arbitrary subjective collection1 not a collection of things on the ground of common attributes4 ,and it is inconsistent with the ,conceptualist theory only if by a concept we understand not the objective reference of a general name1 but what we have distinguished as a conception or a conceptual image4 ,the theory that the ultimate subject is reality is assumed in both the other theories1 rightly understood4 ,if every proposition is the utterance of a judgment1 and every proposition implies a general name1 and every general name has a meaning or connotation1 and every such meaning is an attribute of things and not a mental state1 it is implied that the ultimate subject of every proposition is reality4 ,but we may consider whether or not propositions are consistent without considering whether or not they are true1 and it is only their mutual consistency that is considered in the syllogistic formulae4 ,thus1 while it is perfectly correct to say that every proposition expresses either truth or falsehood1 or that the characteristic quality of a judgment is to be true or false1 it is none the less correct to say that we may temporarily suspend consideration of truth or falsehood1 and that this is done in what is commonly known as ,formal ,logic4 ,,vi4 ,that every proposition may be regarded as expressing relations between phenomena4 ,bain follows ,mill in treating this as the final import of ,predication4 ,but he indicates more accurately the logical value of this view in speaking of it as important for laying out the divisions of ,inductive ,logic4 ,they differ slightly in their lists of ,universal ,predicates based upon ,import in this sense--,mill's being ,resemblance1 ,coexistence1 ,simple ,sequence1 and ,causal ,sequence1 and ,bain's being ,coexistence1 ,succession1 and ,equality or ,inequality4 ,but both lay stress upon ,coexistence and ,succession1 and we shall find that the distinctions between ,simple ,sequence and ,causal ,sequence1 and between ,repeated and ,occasional ,coexistence1 are all-important in the ,logic of ,investigation4 ,but for syllogistic purposes the distinctions have no relevance4 ,,chapter ,,ii4 ,,the ,,opposition ,,of ,,propositions4--,,the ,,interpretation ,,of ,,no4 ,propositions are technically said to be opposed when1 having the same terms in ,subject and ,predicate1 they differ in ,quantity1 or in ,quality1 or in both4#a ,the practical question from which the technical doctrine has been developed was how to determine the significance of contradiction4 ,what is meant by giving the answer ,no to a proposition put interrogatively8 ,what is the interpretation of ,no8 ,what is the respondent committed to thereby8 ,have all ratepayers a vote8 ,if you answer ,no1 you are bound to admit that some ratepayers have not4 ,o is the ,,contradictory of ,a4 ,if ,a is false1 ,o must be true4 ,so if you deny ,o1 you are bound to admit ,a3 one or other must be true3 either ,some ratepayers have not a vote or ,all have4 ,is it the case that no man can live without sleep8 ,deny this1 and you commit yourself to maintaining that ,some man1 one at least1 can live without sleep4 ,i is the ,contradictory of ,e2 and vice versa4 ,contradictory opposition is distinguished from ,,contrary1 the opposition of one ,universal to another1 of ,a to ,e and ,e to ,a4 ,there is a natural tendency to meet a strong assertion with the very reverse4 ,let it be maintained that women are essentially faithless or that the poor in a lump is bad1 and disputants are apt to meet this extreme with another1 that constancy is to be found only in women or true virtue only among the poor4 ,both extremes1 both ,a and ,e1 may be false3 the truth may lie between3 ,some are1 ,some not4 ,logically1 the denial of ,a or ,e implies only the admission of ,o or ,i4 ,you are not committed to the full contrary4 ,but the implication of the ,contradictory is absolute2 there is no half-way house where the truth may reside4 ,hence the name of ,,excluded ,,middle is applied to the principle that ,of two ,contradictories one or other must be true3 they cannot both be false4 ,while both ,,contraries may be false1 they cannot both be true4 ,it is sometimes said that in the case of ,singular propositions1 the ,contradictory and the ,contrary coincide4 ,a more correct doctrine is that in the case of ,singular propositions1 the distinction is not needed and does not apply4 ,put the question ,is ,socrates wise8 or ,is this paper white8 and the answer ,no admits of only one interpretation1 provided the terms remain the same4 ,socrates may become foolish1 or this paper may hereafter be coloured differently1 but in either case the subject term is not the same about which the question was asked4 ,contrary opposition belongs only to general terms taken universally as subjects4 ,concerning individual subjects an attribute must be either affirmed or denied simply3 there is no middle course4 ,such a proposition as ,socrates is sometimes not wise1 is not a true ,singular proposition1 though it has a ,singular term as grammatical subject4 ,logically1 it is a ,particular proposition1 of which the subject-term is the actions or judgments of ,socrates4#b ,opposition1 in the ordinary sense1 is the opposition of incompatible propositions1 and it was with this only that ,aristotle concerned himself4 ,but from an early period in the history of ,logic1 the word was extended to cover mere differences in ,quantity and ,quality among the four forms ,a ,e ,i ,o1 which differences have been named and exhibited symmetrically in a diagram known as3 ,the ,square of ,opposition4 ,a,contraries,e _/ s ,c e o i n r t o ,s r t ,s u a c u b i b a d a l _/ l t _/ t e _/ d e r _/ i r n a c n s r t s t o n r o i ,c e _/ s _/ ,i,sub-contraries,o ,the four forms being placed at the four corners of the ,square1 and the sides and diagonals representing relations between them thus separated1 a very pretty and symmetrical doctrine is the result4 ,contradictories1 ,a and ,o1 ,e and ,i1 differ both in ,quantity and in ,quality4 ,contraries1 ,a and ,e1 differ in ,quality but not in ,quantity1 and are both ,universal4 ,sub-contraries1 ,i and ,o1 differ in ,quality but not in ,quantity1 and are both ,particular4 ,subalterns1 ,a and ,i1 ,e and ,o1 differ in ,quantity but not in ,quality4 ,again1 in respect of concurrent truth and falsehood there is a certain symmetry4 ,contradictories cannot both be true1 nor can they both be false4 ,contraries may both be false1 but cannot both be true4 ,sub-contraries may both be true1 but cannot both be false4 ,subalterns may both be false and both true4 ,if the ,universal is true1 its subalternate ,particular is true3 but the truth of the ,particular does not similarly imply the truth of its ,subalternating ,universal4 ,this last is another way of saying that the truth of the ,contrary involves the truth of the ,contradictory1 but the truth of the ,contradictory does not imply the truth of the ,contrary4 ,there1 however1 the symmetry ends4 ,the sides and the diagonals of the ,square do not symmetrically represent degrees of incompatibility1 or opposition in the ordinary sense4 ,there is no incompatibility between two ,sub-contraries or a ,subaltern and its ,subalternant4 ,both may be true at the same time4 ,indeed1 as ,aristotle remarked of ,i and ,o1 the truth of the one commonly implies the truth of the other3 to say that some of the crew were drowned1 implies that some were not1 and vice versa4 ,subaltern and ,subalternant also are compatible1 and something more4 ,if a man has admitted ,a or ,e1 he cannot refuse to admit ,i or ,o1 the ,particular of the same ,quality4 ,if ,all poets are irritable1 it cannot be denied that some are so2 if ,none is1 that ,some are not4 ,the admission of the ,contrary includes the admission of the ,contradictory4 ,consideration of ,subalterns1 however1 brings to light a nice ambiguity in ,some4 ,it is only when ,i is regarded as the ,contradictory of ,e1 that it can properly be said to be ,subalternate to ,a4 ,in that case the meaning of ,some is not none1 i4e41 ,some at least4 ,but when ,some is taken as the sign of ,particular quantity simply1 i4e41 as meaning not all1 or some at most1 ,i is not ,subalternate to ,a1 but opposed to it in the sense that the truth of the one is incompatible with the truth of the other4 ,again1 in the diagram ,contrary opposition is represented by a side and ,contradictory by the diagonal2 that is to say1 the stronger form of opposition by the shorter line4 ,the ,contrary is more than a denial3 it is a counter-assertion of the very reverse1 ,greek3 to enantion4 ,are good administrators always good speakers8 ,on the contrary1 they never are4 ,this is a much stronger opposition1 in the ordinary sense1 than a modest contradictory1 which is warranted by the existence of a single exception4 ,if the diagram were to represent incompatibility accurately1 the ,contrary ought to have a longer line than the ,contradictory1 and this it seems to have had in the diagram that ,aristotle had in mind 7,de ,interpret41 c4 #aj74 ,it is only when ,opposition is taken to mean merely difference in ,quantity and ,quality that there can be said to be greater opposition between ,contradictories than between ,contraries4 ,contradictories differ both in ,quantity and in ,quality3 ,contraries1 in ,quality only4 ,there is another sense in which the ,particular ,contradictory may be said to be a stronger opposite than the ,contrary4 ,it is a stronger position to take up argumentatively4 ,it is easier to defend than a ,contrary4 ,but this is because it offers a narrower and more limited opposition4 ,we deal with what is called ,immediate ,inference in the next chapter4 ,pending an exact definition of the process1 it is obvious that two immediate inferences are open under the above doctrines1 7#a7 ,granted the truth of any proposition1 you may immediately infer the falsehood of its ,contradictory4 7#b7 ,granted the truth of any ,contrary1 you may immediately infer the truth of its ,subaltern4#c ,footnote #a3 ,this is the traditional definition of ,opposition from an early period1 though the tradition does not start from ,aristotle4 ,with him opposition 7,greek3 antikeisthai7 meant1 as it still means in ordinary speech1 incompatibility4 ,the technical meaning of ,opposition is based on the diagram 7given afterwards in the text7 known as the ,square of ,opposition1 and probably originated in a confused apprehension of the reason why it received that name4 ,it was called the ,square of ,opposition1 because it was intended to illustrate the doctrine of ,opposition in ,aristotle's sense and the ordinary sense of repugnance or incompatibility4 ,what the ,square brings out is this4 ,if the four forms ,a ,e ,i ,o are arranged symmetrically according as they differ in quantity1 or quality1 or both1 it is seen that these differences do not correspond symmetrically to compatibility and incompatibility3 that propositions may differ in quantity or in quality without being incompatible1 and that they may differ in both 7as ,contradictories7 and be less violently incompatible than when they differ in one only 7as ,contraries74 ,the original purpose of the diagram was to bring this out1 as is done in every exposition of it4 ,hence it was called the ,square of ,opposition4 ,but as a descriptive title this is a misnomer3 it should have been the ,square of ,differences in ,quantity or ,quality4 ,this misnomer has been perpetuated by appropriating ,opposition as a common name for difference in ,quantity or ,quality when the terms are the same and in the same order1 and distinguishing it in this sense from ,repugnance or ,incompatibility 7,tataretus in ,summulas1 ,de ,oppositionibus #aeja1 ,keynes1 ,the ,opposition of ,propositions #ahhg74 ,seeing that there never is occasion to speak of ,opposition in the limited sense except in connexion with the ,square1 there is no real risk of confusion4 ,a common name is certainly wanted in that connexion1 if only to say that ,opposition 7in the limited or diagrammatic sense7 does not mean incompatibility4 ,footnote #b3 ,cp4 ,keynes1 pt4 ii4 ch4 ii4 s4 #eg4 ,aristotle laid down the distinction between ,contrary and ,contradictory to meet another quibble in contradiction1 based on taking the ,universal as a whole and indivisible subject like an ,individual1 of which a given predicate must be either affirmed or denied4 ,footnote #c3 ,i have said that there is little risk of confusion in using the word ,opposition in its technical or limited sense4 ,there is1 however1 a little4 ,when it is said that these ,inferences are based on ,opposition1 or that ,opposition is a mode of ,immediate ,inference1 there is confusion of ideas unless it is pointed out that when this is said1 it is ,opposition in the ordinary sense that is meant4 ,the inferences are really based on the rules of ,contrary and ,contradictory ,opposition2 ,contraries cannot both be true1 and of ,contradictories one or other must be4 ,,chapter ,,iii4 ,,the ,,implication ,,of ,,propositions4--,,immediate ,,formal ,,inference4 --,,education4 ,the meaning of ,inference generally is a subject of dispute1 and to avoid entering upon debatable ground at this stage1 instead of attempting to define ,inference generally1 ,i will confine myself to defining what is called ,formal ,inference1 about which there is comparatively little difference of opinion4 ,,formal ,,inference then is the apprehension of what is implied in a certain datum or admission3 the derivation of one proposition1 called the ,,conclusion1 from one or more given1 admitted1 or assumed propositions1 called the ,,premiss or ,,premisses4 ,when the conclusion is drawn from one proposition1 the inference is said to be ,,immediate2 when more than one proposition is necessary to the conclusion1 the inference is said to be ,,mediate4 ,given the proposition1 ,all poets are irritable1 we can immediately infer that ,nobody that is not irritable is a poet2 and the one admission implies the other4 ,but we cannot infer immediately that all poets make bad husbands4 ,before we can do this we must have a second proposition conceded1 that ,all irritable persons make bad husbands4 ,the inference in the second case is called ,mediate4#a ,the modes and conditions of valid ,mediate ,inference constitute ,syllogism1 which is in effect the reasoning together of separate admissions4 ,with this we shall deal presently4 ,meantime of ,immediate ,inference4 ,to state all the implications of a certain form of proposition1 to make explicit all that it implies1 is the same thing with showing what immediate inferences from it are legitimate4 ,formal inference1 in short1 is the eduction of all that a proposition implies4 ,most of the modes of ,immediate ,inference formulated by logicians are preliminary to the ,syllogistic process1 and have no other practical application4 ,the most important of them technically is the process known as ,conversion1 but others have been judged worthy of attention4 ,,aequipollent ,,or ,,equivalent ,,forms--,,obversion4 ,a,equipollence or ,equivalence 7,greek3 ,isodynamia7 is defined as the perfect agreement in sense of two propositions that differ somehow in expression4#b ,the history of ,a,equipollence in logical treatises illustrates two tendencies4 ,there is a tendency on the one hand to narrow a theme down to definite and manageable forms4 ,but when a useful exercise is discarded from one place it has a tendency to break out in another under another name4 ,a third tendency may also be said to be specially well illustrated--the tendency to change the traditional application of logical terms4 ,in accordance with the above definition of ,a,equipollence or ,equivalence1 which corresponds with ordinary acceptation1 the term would apply to all cases of identical meaning under difference of expression4 ,most examples of the reduction of ordinary speech into syllogistic form would be examples of aequipollence2 all1 in fact1 would be so were it not that ordinary speech loses somewhat in the process1 owing to the indefiniteness of the syllogistic symbol for particular quality1 ,some4 ,and in truth all such transmutations of expression are as much entitled to the dignity of being called ,immediate ,inferences as most of the processes so entitled4 ,dr4 ,bain uses the word with an approach to this width of application in discussing all that is now most commonly called ,immediate ,inference under the title of ,equivalent ,forms4 ,the chief objection to this usage is that the ,converse per accidens is not strictly equivalent4 ,a debater may want for his argument less than the strict equivalent1 and content himself with educing this much from his opponent's admission4 7,whether ,dr4 ,bain is right in treating the ,minor and ,conclusion of a ,hypothetical ,syllogism as being equivalent to the ,major1 is not so much a question of naming47 ,but in the history of the subject1 the traditional usage has been to confine ,a,equipollence to cases of equivalence between positive and negative forms of expression4 ,not all are1 is equivalent to ,some are not3 ,not none is1 to ,some are4 ,in ,pre-,aldrichian text-books1 ,a,equipollence corresponds mainly to what it is now customary to call 7e4g41 ,fowler1 pt4 iii4 c4 ii41 ,keynes1 pt4 ii4 c4 vii47 ,immediate ,inference based on ,opposition4 ,the denial of any proposition involves the admission of its contradictory4 ,thus1 if the negative particle ,not is placed before the sign of ,quantity1 ,all or ,some1 in a proposition1 the resulting proposition is equivalent to the ,contradictory of the original4 ,not all ,s is ,p ,some ,s is not ,p4 ,not any ,s is ,p ,no ,s is ,p4 ,the mediaeval logicians tabulated these equivalents1 and also the forms resulting from placing the negative particle after1 or both before and after1 the sign of ,quantity4 ,under the title of ,a,equipollence1 in fact1 they considered the interpretation of the negative particle generally4 ,if the negative is placed after the universal sign1 it results in the ,contrary3 if both before and after1 in the ,subaltern4 ,the statement of these equivalents is a puzzling exercise which no doubt accounts for the prominence given it by ,aristotle and the ,schoolmen4 ,the latter helped the student with the following ,mnemonic line3 ,prae ,contradic41 post ,contrar41 prae postque ,subaltern4#c ,to ,a,equipollence belonged also the manipulation of the forms known after the ,summulae as ,exponibiles1 notably ,exclusive and ,exceptive propositions1 such as ,none but barristers are eligible1 ,the virtuous alone are happy4 ,the introduction of a negative particle into these already negative forms makes a very trying problem in interpretation4 ,the aequipollence of the ,exponibiles was dropped from text-books long before ,aldrich1 and it is the custom to laugh at them as extreme examples of frivolous scholastic subtlety3 but most modern text-books deal with part of the doctrine of the ,exponibiles in casual exercises4 ,curiously enough1 a form left unnamed by the scholastic logicians because too simple and useless1 has the name ,a,equipollent appropriated to it1 and to it alone1 by ,ueberweg1 and has been adopted under various names into all recent treatises4 ,bain calls it the ,,formal ,,obverse1#d and the title of ,,obversion 7which has the advantage of rhyming with ,,conversion7 has been adopted by ,keynes1 ,miss ,johnson1 and others4 ,fowler 7following ,karslake7 calls it ,,permutation4 ,the title is not a happy one1 having neither rhyme nor reason in its favour1 but it is also extensively used4 ,this immediate inference is a very simple affair to have been honoured with such a choice of terminology4 ,this road is long3 therefore1 it is not short1 is an easy inference3 the second proposition is the ,obverse1 or ,permutation1 or ,a,equipollent1 or 7in ,jevons's title7 the ,immediate ,inference by ,privative ,conception1 of the first4 ,the inference1 such as it is1 depends on the ,law of ,excluded ,middle4 ,either a term ,p1 or its contradictory1 not-,p1 must be true of any given subject1 ,s3 hence to affirm ,p of all or some ,s1 is equivalent to denying not-,p of the same3 and1 similarly1 to deny ,p1 is to affirm not-,p4 ,hence the rule of ,obversion2--,substitute for the predicate term its ,contrapositive1#e and change the ,quality of the proposition4 ,all ,s is ,p ,no ,s is not-,p4 ,no ,s is ,p ,all ,s is not-,p4 ,some ,s is ,p ,some ,s is not not-,p4 ,some ,s is not ,p ,some ,s is not-,p4 ,,conversion4 ,the process takes its name from the interchange of the terms4 ,the ,predicate-term becomes the ,subject-term1 and the ,subject-term the ,predicate-term4 ,when propositions are analysed into relations of inclusion or exclusion between terms1 the assertion of any such relation between one term and another1 implies a ,converse relation between the second term and the first4 ,the statement of this implied assertion is technically known as the ,,converse of the original proposition1 which may be called the ,convertend4 ,three modes of ,conversion are commonly recognised3--7a7 ,,simple ,,conversion2 7b7 ,,conversion per accidens or by limitation2 7c7 ,,conversion ,,by ,,contraposition4 7a7 ,e and ,i can be simply converted1 only the terms being interchanged1 and ,quantity and ,quality remaining the same4 ,if ,s is wholly excluded from ,p1 ,p must be wholly excluded from ,s4 ,if ,some ,s is contained in ,p1 then ,some ,p must be contained in ,s4 7b7 ,a cannot be simply converted4 ,to know that ,all ,s is contained in ,p1 gives you no information about that portion of ,p which is outside ,s4 ,it only enables you to assert that ,some ,p is ,s2 that portion of ,p1 namely1 which coincides with ,s4 ,o cannot be converted either simply or per accidens4 ,some ,s is not ,p does not enable you to make any converse assertion about ,p4 ,all ,p may be ,s1 or ,no ,p may be ,s1 or ,some ,p may be not ,s4 ,all the three following diagrams are compatible with ,some ,s being excluded from ,p4 ,illustration3 ,concentric circles of ,s and ,p - ,p in centre ,s in one circle and ,p in another circle4 ,s and ,p each in a circle1 overlapping circle4 7c7 ,another mode of ,conversion1 known by mediaeval logicians following ,boethius as ,conversio per contra positionem terminorum1 is useful in some syllogistic manipulations4 ,this ,converse is obtained by substituting for the predicate term its ,contrapositive or ,contradictory1 not-,p1 making the consequent change of ,quality1 and simply converting4 ,thus ,all ,s is ,p is converted into the equivalent ,no not-,p is ,s4#f ,some have called it ,conversion by ,negation1 but negation is manifestly too wide and common a word to be thus arbitrarily restricted to the process of substituting for one term its opposite4 ,others 7and this has some mediaeval usage in its favour1 though not the most intelligent7 would call the form ,all not-,p is not-,s 7the ,obverse or ,permutation of ,no not-,p is ,s71 the ,converse by ,contraposition4 ,this is to conform to an imaginary rule that in ,conversion the ,converse must be of the same ,quality with the ,convertend4 ,but the essence of ,conversion is the interchange of ,subject and ,predicate3 the ,quality is not in the definition except by a bungle3 it is an accident4 ,no not-,p is ,s1 and ,some not-,p is ,s are the forms used in ,syllogism1 and therefore specially named4 ,unless a form had a use1 it was left unnamed1 like the ,subalternate forms of ,syllogism3 ,nomen habent nullum3 nec1 si bene colligis1 usum4 ,,table ,,of ,,contrapositive ,,converses4 ,con4 ,con4 ,all ,s is ,p ,no not-,p is ,s ,no ,s is ,p ,some not-,p is ,s ,some ,s is not ,p ,some not-,p is ,s ,some ,s is ,p ,none4 ,when not-,p is substituted for ,p1 ,some ,s is ,p becomes ,some ,s is not not-,p1 and this form is inconvertible4 ,,other ,,forms ,,of ,,immediate ,,inference4 ,i have already spoken of the ,immediate ,inferences based on the rules of ,contradictory and ,contrary ,opposition 7see p4 #ade - ,part ,,iii1 ,ch4 ,,ii74 ,another process was observed by ,thomson1 and named ,immediate ,inference by ,added ,determinants4 ,if it is granted that ,a negro is a fellow-creature1 it follows that ,a negro in suffering is a fellow-creature in suffering4 ,but that this does not follow for every attribute#g is manifest if you take another case3--,a tortoise is an animal3 therefore1 a fast tortoise is a fast animal4 ,the form1 indeed1 holds in cases not worth specifying3 and is a mere handle for quibbling4 ,it could not be erected into a general rule unless it were true that whatever distinguishes a species within a class1 will equally distinguish it in every class in which the first is included4 ,,modal ,,consequence has also been named among the forms of ,immediate ,inference4 ,by this is meant the inference of the lower degrees of certainty from the higher4 ,thus must be is said to imply may be2 and ,none can be to imply ,none is4 ,dr4 ,bain includes also ,material ,obversion1 the analogue of ,formal ,obversion applied to a ,subject4 ,thus ,peace is beneficial to commerce1 implies that ,war is injurious to commerce4 ,dr4 ,bain calls this ,material ,obversion because it cannot be practised safely without reference to the matter of the proposition4 ,we shall recur to the subject in another chapter4 ,footnote #a3 ,i purposely chose disputable propositions to emphasise the fact that ,formal ,logic has no concern with the truth1 but only with the interdependence of its propositions4 ,footnote #b3 ,mark ,duncan1 ,inst4 ,log41 ii4 #e1 #afab4 ,footnote #c3 ,there can be no doubt that in their doctrine of ,a,equipollents1 the ,schoolmen were trying to make plain a real difficulty in interpretation1 the interpretation of the force of negatives4 ,their results would have been more obviously useful if they had seen their way to generalising them4 ,perhaps too they wasted their strength in applying it to the artificial syllogistic forms1 which men do not ordinarily encounter except in the manipulation of syllogisms4 ,their results might have been generalised as follows3-- 7#a7 ,a not placed before the sign of ,quantity contradicts the whole proposition4 ,not ,all ,s is ,p1 not ,no ,s is ,p1 not ,some ,s is ,p1 not ,some ,s is not ,p1 are equivalent respectively to contradictories of the propositions thus negatived4 7#b7 ,a not placed after the sign of ,quantity affects the copula1 and amounts to inverting its ,quality1 thus denying the predicate term of the same quantity of the subject term of which it was originally affirmed1 and vice versa4 ,all ,s is not ,p ,no ,s is ,p4 ,no ,s is not ,p ,all ,s is ,p4 ,some ,s is not ,p ,some ,s is not ,p4 ,some ,s is not not ,p ,some ,s is ,p4 7#c7 ,if a not is placed before as well as after1 the resulting forms are obviously equivalent 7under ,rule #a7 to the assertion of the contradictories of the forms on the right 7in the illustration of ,rule #b74 ,not ,all ,s is not ,p ,no ,s is ,p ,some ,s is ,p4 ,not ,no ,s is not ,p ,all ,s is ,p ,some ,s is not ,p4 ,not ,some ,s is not ,p ,some ,s is not ,p ,all ,s is ,p4 ,not ,some ,s is not not ,p ,some ,s is ,p ,no ,s is ,p4 ,footnote #d3 ,formal to distinguish it from what he called the ,material ,obverse1 about which more presently4 ,footnote #e3 ,the mediaeval word for the opposite of a term1 the word ,contradictory being confined to the propositional form4 ,footnote #f3 ,it is to be regretted that a practice has recently crept in of calling this form1 for shortness1 the ,contrapositive simply4 ,by long-established usage1 dating from ,boethius1 the word ,contrapositive is a technical name for a terminal form1 not-,a1 and it is still wanted for this use4 ,there is no reason why the propositional form should not be called the ,converse by ,contraposition1 or the ,contrapositive ,converse1 in accordance with traditional usage4 ,footnote #g3 ,cf4 ,stock1 part iii4 c4 vii42 ,bain1 ,deduction1 p4 #aji4 ,,chapter ,,iv4 ,,the ,,counter-,,implication ,,of ,,propositions4 ,in discussing the ,axioms of ,dialectic1 ,i indicated that the propositions of common speech have a certain negative implication1 though this does not depend upon any of the so-called ,laws of ,thought1 ,identity1 ,contradiction1 and ,excluded ,middle4 ,since1 however1 the counter-implicate is an important guide in the interpretation of propositions1 it is desirable to recognise it among the modes of ,immediate ,inference4 ,i propose1 then1 first1 to show that people do ordinarily infer at once to a counter-sense2 second1 to explain briefly the ,law of ,thought on which such an inference is justified2 and1 third1 how this law may be applied in the interpretation of propositions1 with a view to making subject and predicate more definite4 ,every affirmation about anything is an implicit negation about something else4 ,every say is a gainsay4 ,that people ordinarily act upon this as a rule of interpretation a little observation is sufficient to show3 and we find also that those who object to having their utterances interpreted by this rule often shelter themselves under the name of ,logic4 ,suppose1 for example1 that a friend remarks1 when the conversation turns on children1 that ,john is a good boy1 the natural inference is that the speaker has in his mind another child who is not a good boy4 ,such an inference would at once be drawn by any actual hearer1 and the speaker would protest in vain that he said nothing about anybody but ,john4 ,suppose there are two candidates for a school appointment1 ,a and ,b1 and that stress is laid upon the fact that ,a is an excellent teacher4 ,a's advocate would at once be understood to mean that ,b was not equally excellent as a teacher4 ,the fairness of such inferences is generally recognised4 ,a reviewer1 for example1 of one of ,mrs4 ,oliphant's historical works1 after pointing out some small errors1 went on to say that to confine himself to censure of small points1 was to acknowledge by implication that there were no important points to find fault with4 ,yet such negative implications are often repudiated as illogical4 ,it would be more accurate to call them extra-logical4 ,they are not condemned by any logical doctrine3 they are simply ignored4 ,they are extra-logical only because they are not legitimated by the ,laws of ,identity1 ,contradiction1 and ,excluded ,middle3 and the reason why ,logic confines itself to those laws is that they are sufficient for ,syllogism and its subsidiary processes4 ,but1 though extra-logical1 to infer a counter-implicate is not unreasonable3 indeed1 if ,definition1 clear vision of things in their exact relations1 is our goal rather than ,syllogism1 a knowledge of the counter-implicate is of the utmost consequence4 ,such an implicate there must always be under an all-pervading ,law of ,thought which has not yet been named1 but which may be called tentatively the law of ,homogeneous ,counter-relativity4 ,the title1 one hopes1 is sufficiently technical-looking3 though cumbrous1 it is descriptive4 ,the law itself is simple1 and may be thus stated and explained4 ,the ,law of ,homogeneous ,counter-relativity4 ,every positive in thought has a contrapositive1 and the positive and contrapositive are of the same kind4 ,the first clause of our law corresponds with ,dr4 ,bain's law of ,discrimination or ,relativity3 it is1 indeed1 an expansion and completion of that law4 ,nothing is known absolutely or in isolation2 the various items of our knowledge are inter-relative2 everything is known by distinction from other things4 ,light is known as the opposite of darkness1 poverty of riches1 freedom of slavery1 in of out2 each shade of colour by contrast to other shades4 ,what ,dr4 ,bain lays stress upon is the element of difference in this inter-relativity4 ,he bases this law of our knowledge on the fundamental law of our sensibility that change of impression is necessary to consciousness4 ,a long continuance of any unvaried impression results in insensibility to it4 ,we have seen instances of this in illustrating the maxim that custom blunts sensibility 7p4 #gd74 ,poets have been beforehand with philosophers in formulating this principle4 ,it is expressed with the greatest precision by ,barbour in his poem of ,the ,bruce1 where he insists that men who have never known slavery do not know what freedom is4 ,thus contrar thingis evermare ,discoverings of t' other are4 ,since1 then1 everything that comes within our consciousness comes as a change or transition from something else1 it results that our knowledge is counter-relative4 ,it is in the clash or conflict of impressions that knowledge emerges3 every item of knowledge has its illuminating foil1 by which it is revealed1 over against which it is defined4 ,every positive in thought has its contrapositive4 ,so much for the element of difference4 ,but this is not the whole of the inter-relativity4 ,the ,hegelians rightly lay stress on the common likeness that connects the opposed items of knowledge4 ,thought is not only distinction2 it is1 at the same time1 relation4#a ,if it marks off one thing from another1 it1 at the same time1 connects one thing with another4 ,nor can either of these functions of thought be separated from the other3 as ,aristotle himself said1 the knowledge of opposites is one4 ,a thing which has nothing to distinguish it is unthinkable1 but equally unthinkable is a thing which is so separated from all other things as to have no community with them4 ,if then the law of contradiction be taken as asserting the self-identity of things or thoughts in a sense that excludes their community--in other words1 if it be not taken as limited by another law which asserts the relativity of the things or thoughts distinguished--it involves a false abstraction4444 ,if1 then1 the world1 as an intelligible world1 is a world of distinction1 differentiation1 individuality1 it is equally true that in it as an intelligible world there are no absolute separations or oppositions1 no antagonisms which cannot be reconciled4#b ,in the penultimate sentence of this quotation ,dr4 ,caird differentiates his theory against a ,logical counter-theory of the ,law of ,identity1 and in the last sentence against an ,ethical counter-theory3 but the point here is that he insists on the relation of likeness among opposites4 ,every impression felt is felt as a change or transition from something else3 but it is a variation of the same impression--the something else1 the contrapositive1 is not entirely different4 ,change itself is felt as the opposite of sameness1 difference of likeness1 and likeness of difference4 ,we do not differentiate our impression against the whole world1 as it were1 but against something nearly akin to it--upon some common ground4 ,the positive and the contrapositive are of the same kind4 ,let us surprise ourselves in the act of thinking and we shall find that our thoughts obey this law4 ,we take note1 say1 of the colour of the book before us3 we differentiate it against some other colour actually before us in our field of vision or imagined in our minds4 ,let us think of the blackboard as black3 the blackness is defined against the whiteness of the figures chalked or chalkable upon it1 or against the colour of the adjacent wall4 ,let us think of a man as a soldier2 the opposite in our minds is not the colour of his hair1 or his height1 or his birthplace1 or his nationality1 but some other profession--soldier1 sailor1 tinker1 tailor4 ,it is always by means of some contrapositive that we make the object of our thoughts definite2 it is not necessarily always the same opposite1 but against whatever opposite it is1 they are always homogeneous4 ,one colour is contradistinguished from another colour1 one shade from another shade3 colour may be contradistinguished from shape1 but it is within the common genus of sensible qualities4 ,a curious confirmation of this law of our thinking has been pointed out by ,mr4 ,carl ,abel4#c ,in ,egyptian hieroglyphics1 the oldest extant language1 we find1 he says1 a large number of symbols with two meanings1 the one the exact opposite of the other4 ,thus the same symbol represents strong and weak2 above--below2 with--without2 for--against4 ,this is what the ,hegelians mean by the reconciliation of antagonisms in higher unities4 ,they do not mean that black is white1 but only that black and white have something in common--they are both colours4 ,i have said that this law of ,homogeneous ,counter-relativity has not been recognised by logicians4 ,this1 however1 is only to say that it has not been explicitly formulated and named1 as not being required for ,syllogism2 a law so all-pervading could not escape recognition1 tacit or express4 ,and accordingly we find that it is practically assumed in ,definition3 it is really the basis of definition per genus et differentiam4 ,when we wish to have a definite conception of anything1 to apprehend what it is1 we place it in some genus and distinguish it from species of the same4 ,in fact our law might be called the ,law of ,specification3 in obeying the logical law of what we ought to do with a view to clear thinking1 we are only doing with exactness and conscious method what we all do and cannot help doing with more or less definiteness in our ordinary thinking4 ,it is thus seen that logicians conform to this law when they are not occupied with the narrow considerations proper to ,syllogism4 ,and another unconscious recognition of it may be found in most logical text-books4 ,theoretically the not-,a of the ,law of ,contradiction--7,a is not not-,a7--is an infinite term4 ,it stands for everything but ,a4 ,this is all that needs to be assumed for ,conversion and ,syllogism4 ,but take the examples given of the ,formal ,obverse or ,permutation1 ,all men are fallible4 ,most authorities would give as the ,formal ,obverse of this1 ,no men are infallible4 ,but1 strictly speaking1 infallible is of more limited and definite signification than not-fallible4 ,not-fallible1 other than fallible1 is brown1 black1 chair1 table1 and every other nameable thing except fallible4 ,thus in ,obversion and ,conversion by ,contraposition1 the homogeneity of the negative term is tacitly assumed2 it is assumed that ,a and not-,a are of the same kind4 ,now to apply this ,law of our ,thought to the interpretation of propositions4 ,whenever a proposition is uttered we are entitled to infer at once 7or immediately7 that the speaker has in his mind some counter-proposition1 in which what is overtly asserted of the ostensible subject is covertly denied of another subject4 ,and we must know what this counter-proposition1 the counter-implicate is1 before we can fully and clearly understand his meaning4 ,but inasmuch as any positive may have more than one contrapositive1 we cannot tell immediately or without some knowledge of the circumstances or context1 what the precise counter-implicate is4 ,the peculiar fallacy incident to this mode of interpretation is1 knowing that there must be some counter-implicate1 to jump rashly or unwarily to the conclusion that it is some definite one4 ,dr4 ,bain applies the term ,material ,obverse to the form1 ,not-,s is not ,p1 as distinguished from the form ,s is not not-,p1 which he calls the ,formal ,obverse1 on the ground that we can infer the ,predicate-contrapositive at once from the form1 whereas we cannot tell the ,subject-contrapositive without an examination of the matter4 ,but in truth we cannot tell either ,predicate-contrapositive or ,subject-contrapositive as it is in the mind of the speaker from the bare utterance4 ,we can only tell that if he has in his mind a proposition definitely analysed into subject and predicate1 he must have contrapositives in his mind of both1 and that they must be homogeneous4 ,let a man say1 ,this book is a quarto4 ,for all that we know he may mean that it is not a folio or that it is not an octavo3 we only know for certain1 under the law of ,homogeneous ,counter-relativity1 that he means some definite other size4 ,under the same law1 we know that he has a homogeneous contrapositive of the subject1 a subject that admits of the same predicate1 some other book in short4 ,what the particular book is we do not know4 ,it would however be a waste of ingenuity to dwell upon the manipulation of formulae founded on this law4 ,the practical concern is to know that for the interpretation of a proposition1 a knowledge of the counter-implicate1 a knowledge of what it is meant to deny1 is essential4 ,the manipulation of formulae1 indeed1 has its own special snare4 ,we are apt to look for the counterparts of them in the grammatical forms of common speech4 ,thus1 it might seem to be a fair application of our law to infer from the sentence1 ,wheat is dear1 that the speaker had in his mind that ,oats or ,sugar or ,shirting or some other commodity is cheap4 ,but this would be a rash conclusion4 ,the speaker may mean this1 but he may also mean that wheat is dear now as compared with some other time3 that is1 the ,positive subject in his mind may be ,wheat as now1 and the ,contrapositive ,wheat as then4 ,so a man may say1 ,all men are mortal1 meaning that the angels never taste death1 angels being the contrapositive of his subject men4 ,or he may mean merely that mortality is a sad thing1 his positive subject being men as they are1 and his contrapositive men as he desires them to be4 ,or his emphasis may be upon the all1 and he may mean only to deny that some one man in his mind 7,mr4 ,gladstone1 for example7 is immortal4 ,it would be misleading1 therefore1 to prescribe propositions as exercises in ,material ,obversion1 if we give that name to the explicit expression of the ,contrapositive ,subject3 it is only from the context that we can tell what this is4 ,the man who wishes to be clearly understood gives us this information1 as when the epigrammatist said3 ,we are all fallible--even the youngest of us4 ,but the chief practical value of the law is as a guide in studying the development of opinions4 ,every doctrine ever put forward has been put forward in opposition to a previous doctrine on the same subject4 ,until we know what the opposed doctrine is1 we cannot be certain of the meaning4 ,we cannot gather it with precision from a mere study of the grammatical or even 7in the narrow sense of the word7 the logical content of the words used4 ,this is because the framers of doctrines have not always been careful to put them in a clear form of subject and predicate1 while their impugners have not moulded their denial exactly on the language of the original4 ,no doubt it would have been more conducive to clearness if they had done so4 ,but they have not1 and we must take them as they are4 ,thus we have seen that the ,hegelian doctrine of ,relativity is directed against certain other doctrines in ,logic and in ,ethics2 that ,ultra-,nominalism is a contradiction of a certain form of ,ultra-,realism2 and that various theories of ,predication each has a backward look at some predecessor4 ,i quote from ,mr4 ,a4,b4 ,walkley a very happy application of this principle of interpretation3-- ,it has always been a matter for speculation why so sagacious an observer as ,diderot should have formulated the wild paradox that the greatest actor is he who feels his part the least4 ,mr4 ,archer's bibliographical research has solved this riddle4 ,diderot's paradox was a protest against a still wilder one4 ,it seems that a previous eighteenth century writer on the stage1 a certain ,saint-,albine1 had advanced the fantastic propositions that none but a magnanimous man can act magnanimity1 that only lovers can do justice to a love scene1 and kindred assertions that read like variations on the familiar ',who drives fat oxen must himself be fat'4 ,diderot saw the absurdity of this2 he saw also the essentially artificial nature of the ,french tragedy and comedy of his own day2 and he hastily took up the position which ,mr4 ,archer has now shown to be untenable4 ,this instance illustrates another principle that has to be borne in mind in the interpretation of doctrines from their historical context of counter-implication4 ,this is the tendency that men have to put doctrines in too universal a form1 and to oppose universal to universal1 that is1 to deny with the flat contrary1 the very reverse1 when the more humble contradictory is all that the truth admits of4 ,if a name is wanted for this tendency1 it might be called the tendency to ,over-,contradiction4 ,between ,all are and ,none are1 the sober truth often is that ,some are and ,some are not1 and the process of evolution has often consisted in the substitution of these sober forms for their more violent predecessors4 ,footnote #a3 ,it is significant of the unsuitableness of the vague unqualified word ,relativity to express a logical distinction that ,dr4 ,bain calls his law the ,law of ,relativity simply1 having regard to the relation of difference1 i4e41 to ,counter-,relativity1 while ,dr4 ,caird applies the name ,relativity simply to the relation of likeness1 i4e41 to ,co-relativity4 ,it is with a view to taking both forms of relation into account that ,i name our law the ,law of ,homogeneous ,counter-relativity4 ,the ,protagorean ,law of ,relativity has regard to yet another relation1 the relation of knowledge to the knowing mind3 these other logical laws are of relations among the various items of knowledge4 ,aristotle's category of ,relation is a fourth kind of relation not to be confused with the others4 ,father--son1 uncle--nephew1 slave--master1 are relata in ,aristotle's sense3 father1 uncle are homogeneous counter-relatives1 varieties of kinship2 so slave1 freeman are counter-relatives in social status4 ,footnote #b3 ,dr4 ,caird's ,hegel1 p4 #acd4 ,footnote #c3 ,see article on ,counter-,sense1 ,contemporary ,review1 ,april1 #ahhd4 ,,part ,,iv4 ,,the ,,interdependence ,,of ,,propositions4--,,mediate ,,inference4 --,,syllogism4 ,,chapter ,i4 ,,the ,,syllogism4 ,we have already defined mediate inference as the derivation of a conclusion from more than one proposition4 ,the type or form of a mediate inference fully expressed consists of three propositions so related that one of them is involved or implied in the other two4 ,distraction is exhausting4 ,modern life is full of distraction 4'4 ,modern life is exhausting4 ,we say nothing of the truth of these propositions4 ,i purposely choose questionable ones4 ,but do they hang together8 ,if you admit the first two1 are you bound in consistency to admit the third8 ,is the truth of the conclusion a necessary consequence of the truth of the premisses8 ,if so1 it is a valid mediate inference from them4 ,when one of the two premisses is more general than the conclusion1 the argument is said to be ,deductive4 ,you lead down from the more general to the less general4 ,the general proposition is called the ,major ,premiss1 or ,grounding ,proposition1 or ,sumption3 the other premiss the ,minor1 or ,applying ,proposition1 or ,subsumption4 ,undue haste makes waste4 ,this is a case of undue hasting4 4'4 ,it is a case of undue wasting4 ,we may1 and constantly do1 apply principles and draw conclusions in this way without making any formal analysis of the propositions4 ,indeed we reason mediately and deductively whenever we make any application of previous knowledge1 although the process is not expressed in propositions at all and is performed so rapidly that we are not conscious of the steps4 ,for example1 ,i enter a room1 see a book1 open it and begin to read4 ,i want to make a note of something3 ,i look round1 see a paper case1 open it1 take a sheet of paper and a pen1 dip the pen in the ink and proceed to write4 ,in the course of all this1 ,i act upon certain inferences which might be drawn out in the form of ,syllogisms4 ,first1 in virtue of previous knowledge ,i recognise what lies before me as a book4 ,the process by which ,i reach the conclusion1 though it passes in a flash1 might be analysed and expressed in propositions4 ,whatever presents certain outward appearances1 contains readable print4 ,this presents such appearances4 4'4,it contains readable print4 ,so with the paper case1 and the pen1 and the ink4 ,i infer from peculiar appearances that what ,i see contains paper1 that the liquid will make a black mark on the white sheet1 and so forth4 ,we are constantly in daily life subsuming particulars under known universals in this way4 ,whatever has certain visible properties1 has certain other properties3 this has the visible ones3 therefore1 it has the others is a form of reasoning constantly latent in our minds4 ,the ,syllogism may be regarded as the explicit expression of this type of deductive reasoning2 that is1 as the analysis and formal expression of this every-day process of applying known universals to particular cases4 ,thus viewed it is simply the analysis of a mental process1 as a psychological fact2 the analysis of the procedure of all men when they reason from signs2 the analysis of the kind of assumptions they make when they apply knowledge to particular cases4 ,the assumptions may be warranted1 or they may not3 but as a matter of fact the individual who makes the confident inference has such assumptions and subsumptions latent in his mind4 ,but practically viewed1 that is logically viewed1 if you regard ,logic as a practical science1 the ,syllogism is a contrivance to assist the correct performance of reasoning together or syllogising in difficult cases4 ,it applies not to mental processes but to results of such expressed in words1 that is1 to propositions4 ,where the ,syllogism comes in as a useful form is when certain propositions are delivered to you ab extra as containing a certain conclusion2 and the connexion is not apparent4 ,these propositions are analysed and thrown into a form in which it is at once apparent whether the alleged connexion exists4 ,this form is the ,syllogism3 it is1 in effect1 an analysis of given arguments4 ,it was as a practical engine or organon that it was invented by ,aristotle1 an organon for the syllogising of admissions in ,dialectic4 ,the germ of the invention was the analysis of propositions into terms4 ,the syllogism was conceived by ,aristotle as a reasoning together of terms4 ,his prime discovery was that whenever two propositions necessarily contain or imply a conclusion1 they have a common term1 that is1 only three terms between them3 that the other two terms which differ in each are the terms of the conclusion2 and that the relation asserted in the conclusion between its two terms is a necessary consequence of their relations with the third term as declared in the premisses4 ,such was ,aristotle's conception of the ,syllogism and such it has remained in ,logic4 ,it is still1 strictly speaking1 a syllogism of terms3 of propositions only secondarily and after they have been analysed4 ,the conclusion is conceived analytically as a relation between two terms4 ,in how many ways may this relation be established through a third term8 ,the various moods and figures of the ,syllogism give the answer to that question4 ,the use of the very abstract word relation makes the problem appear much more difficult than it really is4 ,the great charm of ,aristotle's ,syllogism is its simplicity4 ,the assertion of the conclusion is reduced to its simplest possible kind1 a relation of inclusion or exclusion1 contained or not contained4 ,to show that the one term is or is not contained in the other we have only to find a third which contains the one and is contained or not contained in the other4 ,the practical difficulties1 of course1 consist in the reduction of the conclusions and arguments of common speech to definite terms thus simply related4 ,once they are so reduced1 their independence or the opposite is obvious4 ,therein lies the virtue of the ,syllogism4 ,before proceeding to show in how many ways two terms may be ,syllogised through a third1 we must have technical names for the elements4 ,the third term is called the ,,middle 7,m7 7,greek3 to meson73 the other two the ,extremes 7,greek3 akra74 ,the ,,extremes are the ,subject 7,s7 and the ,predicate 7,p7 of the conclusion4 ,in an affirmative proposition 7the normal form7 ,s is contained in ,p3 hence ,p is called the ,,major#a term 7,greek3 to meixon71 and ,s the ,,minor 7,greek3 to elatton71 being respectively larger and smaller in extension4 ,all difficulty about the names disappears if we remember that in bestowing them we start from the conclusion4 ,that was the problem 7,greek3 problema7 or thesis in dialectic1 the question in dispute4 ,the two ,premisses1 or propositions giving the relations between the two ,extremes and the ,middle1 are named on an equally simple ground4 ,one of them gives the relation between the ,minor ,term1 ,s1 and the ,middle1 ,m4 ,s1 ,all or ,some1 is or is not in ,m4 ,this is called the ,minor ,premiss4 ,the other gives the relation between the ,major ,term and the ,middle4 ,m1 ,all or ,some1 is or is not in ,p4 ,this is called the ,major ,premiss4#b ,footnote #a3 ,aristotle calls the ,major the ,first 7,greek3 to proton7 and the ,minor the last 7,greek3 to eschaton71 probably because that was their order in the conclusion when stated in his most usual form1 ,p is predicated of ,s1 or ,p belongs to ,s4 ,footnote #b3 ,when we speak of the ,minor or the ,major simply1 the reference is to the terms4 ,to avoid a confusion into which beginners are apt to stumble1 and at the same time to emphasise the origin of the names1 the ,premisses might be spoken of at first as the ,minor's ,premiss and the ,major's ,premiss4 ,it was only in the ,middle ,ages when the origin of the ,syllogism had been forgotten1 that the idea arose that the terms were called ,major and ,minor because they occurred in the ,major and the ,minor ,premiss respectively4 ,,chapter ,,ii4 ,,figures ,,and ,,moods ,,of ,,the ,,syllogism4 ,i4--,the ,first ,figure4 ,the forms 7technically called ,,moods1 i4e41 modes7 of the ,first ,figure are founded on the simplest relations with the ,middle that will yield or that necessarily involve the disputed relation between the ,extremes4 ,the simplest type is stated by ,aristotle as follows3 ,when three terms are so related that the last 7the ,minor7 is wholly in the ,middle1 and the ,middle wholly either in or not in the first 7the ,major7 there must be a perfect syllogism of the ,extremes4#a ,when the ,minor is partly in the ,middle1 the ,syllogism holds equally good4 ,thus there are four possible ways in which two terms 7,greek3 oroi1 plane enclosures7 may be connected or disconnected through a third4 ,they are usually represented by circles as being the neatest of figures1 but any enclosing outline answers the purpose1 and the rougher and more irregular it is the more truly will it represent the extension of a word4 ,conclusion ,a4 ,all ,m is in ,p4 ,all ,s is in ,m4 ,all ,s is in ,p4 ,illustration3 concentric circles of ,p1 ,m and ,s - ,s in centre ,conclusion ,e4 ,no ,m is in ,p4 ,all ,s is in ,m4 ,no ,s is in ,p4 ,illustration3 ,concentric circles of ,m and ,s1 ,s in centre and separate circle of ,p ,conclusion ,i4 ,all ,m is in ,p4 ,some ,s is in ,m4 ,some ,s is in ,p4 ,illustration3 ,concentric circles of ,p and ,m1 ,m in centre1 both overlapped by circle of ,s ,conclusion ,o4 ,no ,m is in ,p4 ,some ,s is in ,m4 ,some ,s is not in ,p4 ,illustration3 ,circles of ,m and ,p touching1 each overlapped by circle of ,s ,these four forms constitute what are known as the moods of the ,first ,figure of the ,syllogism4 ,seeing that all propositions may be reduced to one or other of the four forms1 ,a1 ,e1 ,i1 or ,o1 we have in these premisses abstract types of every possible valid argument from general principles4 ,it is all the same whatever be the matter of the proposition4 ,whether the subject of debate is mathematical1 physical1 social or political1 once premisses in these forms are conceded1 the conclusion follows irresistibly1 ex vi formae1 ex necessitate formae4 ,if an argument can be analysed into these forms1 and you admit its propositions1 you are bound in consistency to admit the conclusion--unless you are prepared to deny that if one thing is in another and that other in a third1 the first is in the third1 or if one thing is in another and that other wholly outside a third1 the first is also outside the third4 ,this is called the ,,axiom ,,of ,,syllogism4 ,the most common form of it in ,logic is that known as the ,dictum1 or ,regula de ,omni et ,nullo3 ,whatever is predicated of ,all or ,none of a term1 is predicated of whatever is contained in that term4 ,it has been expressed with many little variations1 and there has been a good deal of discussion as to the best way of expressing it1 the relativity of the word best being often left out of sight4 ,best for what purpose8 ,practically that form is the best which best commands general assent1 and for this purpose there is little to choose between various ways of expressing it4 ,to make it easy and obvious it is perhaps best to have two separate forms1 one for affirmative conclusions and one for negative4 ,thus3 ,whatever is affirmed of all ,m1 is affirmed of whatever is contained in ,m3 and whatever is denied of all ,m1 is denied of whatever is contained in ,m4 ,the only advantage of including the two forms in one expression1 is compendious neatness4 ,a part of a part is a part of the whole1 is a neat form1 it being understood that an individual or a species is part of a genus4 ,what is said of a whole1 is said of every one of its parts1 is really a sufficient statement of the principle3 the whole being the ,middle ,term1 and the ,minor being a part of it1 the ,major is predicable of the ,minor affirmatively or negatively if it is predicable similarly of the ,middle4 ,this ,axiom1 as the name imports1 is indemonstrable4 ,as ,aristotle pointed out in the case of the ,axiom of ,contradiction1 it can be vindicated1 if challenged1 only by reducing the challenger to a practical absurdity4 ,you can no more deny it than you can deny that if a leaf is in a book and the book is in your pocket1 the leaf is in your pocket4 ,if you say that you have a sovereign in your purse and your purse is in your pocket1 and yet that the sovereign is not in your pocket3 will you give me what is in your pocket for the value of the purse8 ,,ii4--,,the ,,minor ,,figures ,,of ,,the ,,syllogism1 ,,and ,,their ,,reduction ,,to ,,the ,,first4 ,the word ,figure 7,greek3 schema7 applies to the form or figure of the premisses1 that is1 the order of the terms in the statement of the premisses1 when the ,major ,premiss is put first1 and the ,minor second4 ,in the ,first ,figure the order is ,m ,p ,s ,m ,but there are three other possible orders or figures1 namely3-- ,fig4 ii4 ,fig4 iii4 ,fig4 iv4 ,,pm ,,mp ,,pm ,,sm ,,ms ,,ms4 ,it results from the doctrines of ,conversion that valid arguments may be stated in these forms1 inasmuch as a proposition in one order of terms may be equivalent to a proposition in another4 ,thus ,no ,m is in ,p is convertible with ,no ,p is in ,m3 consequently the argument ,no ,p is in ,m ,all ,s is in ,m1 in the ,second ,figure is as much valid as when it is stated in the ,first-- ,no ,m is in ,p ,all ,s is in ,m4 ,similarly1 since ,all ,m is in ,s is convertible into ,some ,s is in ,m1 the following arguments are equally valid3-- ,fig4 iii4 ,fig4 i4 ,all ,m is in ,p ,all ,m is in ,p ,all ,m is in ,s ,some ,s is in ,m4 ,using both the above ,converses in place of their ,convertends1 we have-- ,fig4 iv4 ,fig4 i4 ,no ,p is in ,m ,no ,m is in ,p ,all ,m is in ,s ,some ,s is in ,m4 ,it can be demonstrated 7we shall see presently how7 that altogether there are possible four valid forms or moods of the ,second ,figure1 six of the ,third1 and five of the ,fourth4 ,an ingenious ,mnemonic of these various moods and their reduction to the ,first ,figure by the transposition of terms and premisses has come down from the thirteenth century4 ,the first line names the moods of the ,first1 ,normal1 or ,standard ,figure4 ,,barb,ar,a1 ,,cel,ar,ent1 ,,dar,,ii1 ,,fer,,ioque prioris2 ,,ces,ar,e1 ,,cam,estr,es1 ,,fest,in,o1 ,,bar,ok,o1 secundae2 ,tertia ,,dar,apt,i1 ,,dis,am,is1 ,,dat,is,i1 ,,fel,apt,on1 ,,bok,ard,o1 ,,fer,is,oque1 habet2 quarta insuper addit1 ,br,am,ant,,ip1 ,,cam,en,es1 ,,dim,ar,is1 ,,fes,ap,o1 ,fr,es,is,on4 ,the vowels in the names of the ,moods indicate the propositions of the ,syllogism in the four forms1 ,a ,e ,i ,o4 ,to write out any ,mood at length you have only to remember the ,figure1 and transcribe the propositions in the order of ,major ,premiss1 ,minor ,premiss1 and ,conclusion4 ,thus1 the ,second ,figure being ,,pm ,,sm ,,fest,in,o is written-- ,no ,p is in ,m4 ,some ,s is in ,m4 ,some ,s is not in ,p4 ,the ,fourth ,figure being ,,pm ,,ms ,,dim,ar,is is ,some ,p is in ,m4 ,all ,m is in ,s4 ,some ,s is in ,p4 ,the initial letter in a ,minor ,mood indicates that ,mood of the ,first to which it may be reduced4 ,thus ,festino is reduced to ,ferio1 and ,dimaris to ,darii4 ,in the cases of ,baroko and ,bokardo1 ,b indicates that you may employ ,barbara to bring any impugner to confusion1 as shall be afterwards explained4 ,the letters s1 m1 and p are also significant4 ,placed after a vowel1 s indicates that the proposition has to be simply converted4 ,thus1 ,,fest,in,o3-- ,no ,p is in ,m4 ,some ,s is in ,m4 ,some ,s is not in ,p4 ,simply convert the ,major ,premiss1 and you get ,,fer,,io1 of the ,first4 ,no ,m is in ,p4 ,some ,s is in ,m4 ,some ,s is not in ,p4 m 7muta1 or move7 indicates that the premisses have to be transposed4 ,thus1 in ,,cam,estr,es1 you have to transpose the premisses1 as well as simply convert the ,minor ,premiss before reaching the figure of ,,cel,ar,ent4 ,all ,p is in ,m ,no ,m is in ,s ,no ,s is in ,m ,all ,p is in ,m4 ,from this it follows in ,,cel,ar,ent that ,no ,p is in ,s1 and this simply converted yields ,no ,s is in ,p4 ,a simple transposition of the premisses in ,,dim,ar,is of the ,fourth ,some ,p is in ,m ,all ,m is in ,s yields the premisses of ,,dar,,ii ,all ,m is in ,s ,some ,p is in ,m1 but the conclusion ,some ,p is in ,s has to be simply converted4 ,placed after a vowel1 p indicates that the proposition has to be converted per accidens4 ,thus in ,,fel,apt,on of the ,third 7,,mp1 ,,ms7 ,no ,m is in ,p ,all ,m is in ,s ,some ,s is not in ,p you have to substitute for ,all ,m is in ,s its converse by limitation to get the premisses of ,,fer,,io4 ,two of the ,minor ,moods1 ,baroko of the ,second ,figure1 and ,bokardo of the ,third1 cannot be reduced to the ,first ,figure by the ordinary processes of ,conversion and ,transposition4 ,it is for dealing with these intractable moods that ,contraposition is required4 ,thus in ,,bar,ok,o of the ,second 7,,pm1 ,,sm7 ,all ,p is in ,m4 ,some ,s is not in ,m4 ,substitute for the ,major ,premiss its ,converse by ,contraposition1 and for the ,minor its ,formal ,obverse or ,permutation1 and you have ,,fer,,io of the ,first1 with not-,m as the ,middle4 ,no not-,m is in ,p4 ,some ,s is in not-,m1 ,some ,s is not in ,p4 ,the processes might be indicated by the ,mnemonic ,,facs,oc,o1 with c indicating the contraposition of the predicate term or ,formal ,obversion4 ,the reduction of ,,bok,ard,o1 ,some ,m is not in ,p ,all ,m is in ,s ,some ,s is not in ,p1 is somewhat more intricate4 ,it may be indicated by ,,docs,am,osc4 ,you substitute for the ,major ,premiss its ,converse by ,contraposition1 transpose the ,premisses and you have ,,dar,,ii4 ,all ,m is in ,s4 ,some not-,p is in ,m4 ,some not-,p is in ,s4 ,convert now the conclusion by ,contraposition1 and you have ,some ,s is not in ,p4 ,the author of the ,mnemonic apparently did not recognise ,contraposition1 though it was admitted by ,boethius2 and1 it being impossible without this to demonstrate the validity of ,baroko and ,bokardo by showing them to be equivalent with valid moods of the ,first ,figure1 he provided for their demonstration by the special process known as ,reductio ad absurdum4 ,b indicates that ,barbara is the medium4 ,the rationale of the process is this4 ,it is an imaginary opponent that you reduce to an absurdity or self-contradiction4 ,you show that it is impossible with consistency to admit the premisses and at the same time deny the conclusion4 ,for1 let this be done2 let it be admitted as in ,,bar,ok,o that1 ,all ,p is in ,m ,some ,s is not in ,m1 but denied that ,some ,s is not in ,p4 ,the denial of a proposition implies the admission of its ,contradictory4 ,if it is not true that ,some ,s is not in ,p1 it must be true that ,all ,s is in ,p4 ,take this along with the admission that ,all ,p is in ,m1 and you have a syllogism in ,,barb,ar,a1 ,all ,p is in ,m ,all ,s is in ,p1 yielding the conclusion ,all ,s is in ,m4 ,if then the original conclusion is denied1 it follows that ,all ,s is in ,m4 ,but this contradicts the ,minor ,premiss1 which has been admitted to be true4 ,it is thus shown that an opponent cannot admit the premisses and deny the conclusion without contradicting himself4 ,the same process may be applied to ,bokardo4 ,some ,m is not in ,p4 ,all ,m is in ,s4 ,some ,s is not in ,p4 ,deny the conclusion1 and you must admit that ,all ,s is in ,p4 ,syllogised in ,barbara with ,all ,m is in ,s1 this yields the conclusion that ,all ,m is in ,p1 the contradictory of the ,major ,premiss4 ,the beginner may be reminded that the argument ad absurdum is not necessarily confined to ,baroko and ,bokardo4 ,it is applied to them simply because they are not reducible by the ordinary processes to the ,first ,figure4 ,it might be applied with equal effect to other ,moods1 ,,dim,ar,is1 e4g41 of the ,third4 ,some ,m is in ,p4 ,all ,m is in ,s4 ,some ,s is in ,p4 ,let ,some ,s is in ,p be denied1 and ,no ,s is in ,p must be admitted4 ,but if ,no ,s is in ,p and ,all ,m is in ,s1 it follows 7in ,celarent7 that ,no ,m is in ,p1 which an opponent cannot hold consistently with his admission that ,some ,m is in ,p4 ,the beginner sometimes asks3 ,what is the use of reducing the ,minor ,figures to the ,first8 ,the reason is that it is only when the relations between the terms are stated in the ,first ,figure that it is at once apparent whether or not the argument is valid under the ,axiom or ,dictum de ,omni4 ,it is then undeniably evident that if the ,dictum holds the argument holds4 ,and if the ,moods of the ,first ,figure hold1 their equivalents in the other ,figures must hold too4 ,aristotle recognised only two of the ,minor ,figures1 the ,second and ,third1 and thus had in all only fourteen valid moods4 ,the recognition of the ,fourth ,figure is attributed by ,averroes to ,galen4 ,averroes himself rejects it on the ground that no arguments expressed naturally1 that is1 in accordance with common usage1 fall into that form4 ,this is a sufficient reason for not spending time upon it1 if ,logic is conceived as a science that has a bearing upon the actual practice of discussion or discursive thought4 ,and this was probably the reason why ,aristotle passed it over4 ,if however the ,syllogism of ,terms is to be completed as an abstract doctrine1 the ,fourth ,figure must be noticed as one of the forms of premisses that contain the required relation between the extremes4 ,there is a valid syllogism between the extremes when the relations of the three terms are as stated in certain premisses of the ,fourth ,figure4 ,,iii4--,,the ,,sorites4 ,a chain of ,syllogisms is called a ,sorites4 ,thus3-- ,all ,a is in ,b4 ,all ,b is in ,c4 ,all ,c is in ,d4 3 3 3 3 ,all ,x is in ,z4 4'4 ,all ,a is in ,z4 ,a ,minor ,premiss can thus be carried through a series of ,universal ,propositions each serving in turn as a ,major to yield a conclusion which can be syllogised with the next4 ,obviously a ,sorites may contain one particular premiss1 provided it is the first2 and one universal negative premiss1 provided it is the last4 ,a particular or a negative at any other point in the chain is an insuperable bar4 ,footnote #a3 ,greek3 ,hotan oun horoi treis autos echosi pros allelous oste ton eschaton en holo einai to meso1 kai ton meson en holo to kroto e einai e me einai1 ananke ton akron einai syllogismon teleion4 7,anal4 ,prior41 i4 #d47 ,,chapter ,,iii4 ,,the ,,demonstration ,,of ,,the ,,syllogistic ,,moods4--,,the ,,canons ,,of ,,the ,,syllogism4 ,how do we know that the nineteen moods are the only possible forms of valid syllogism8 ,aristotle treated this as being self-evident upon trial and simple inspection of all possible forms in each of his three ,figures4 ,granted the parity between predication and position in or out of a limited enclosure 7term1 ,greek3 horos71 it is a matter of the simplest possible reasoning4 ,you have three such terms or enclosures1 ,s1 ,p and ,m2 and you are given the relative positions of two of them to the third as a clue to their relative positions to one another4 ,is ,s in or out of ,p1 and is it wholly in or wholly out or partly in or partly out8 ,you know how each of them lies toward the third3 when can you tell from this how ,s lies towards ,p8 ,we have seen that when ,m is wholly in or out of ,p1 and ,s wholly or partly in ,m1 ,s is wholly or partly in or out of ,p4 ,try any other given positions in the ,first ,figure1 and you find that you cannot tell from them how ,s lies relatively to ,p4 ,unless the ,major ,premiss is ,universal1 that is1 unless ,m lies wholly in or out of ,p1 you can draw no conclusion1 whatever the ,minor ,premiss may give4 ,given1 e4g41 ,all ,s is in ,m1 it may be that ,all ,s is in ,p1 or that ,no ,s is in ,p1 or that ,some ,s is in ,p1 or that ,some ,s is not in ,p4 ,illustration3 ,circles of ,m and ,p1 overlapping1 with #c instances of a circle of ,s3 #a4 ,s in ,m1 but not in ,p2 #b4 ,s in the overlap of ,m and ,p2 #c4 ,s in ,m1 some ,s in ,p4 ,again1 unless the ,minor ,premiss is affirmative1 no matter what the ,major ,premiss may be1 you can draw no conclusion4 ,for if the ,minor ,premiss is negative1 all that you know is that ,all ,s or ,some ,s lies somewhere outside ,m2 and however ,m may be situated relatively to ,p1 that knowledge cannot help towards knowing how ,s lies relatively to ,p4 ,all ,s may be ,p1 or none of it1 or part of it4 ,given all ,m is in ,p2 the ,all ,s 7or ,some ,s7 which we know to be outside of ,m may lie anywhere in ,p or out of it4 ,illustration3 ,concentric circles of ,p and ,m1 ,m in center1 with #e instances of circle of ,s3 #a4 ,s wholly outside ,p and ,m2 #b4 ,s partly overlapping both ,p and ,m1 and partly outside both2 #c4 ,s overlapping ,p1 but outside ,m2 #d4 ,s wholly within ,p1 but wholly outside ,m2 #e4 ,s touching circle of ,p1 but outside both circles4 ,similarly1 in the ,second ,figure1 trial and simple inspection of all possible conditions shows that there can be no conclusion unless the ,major ,premiss is universal1 and one of the premisses negative4 ,another and more common way of eliminating the invalid forms1 elaborated in the ,middle ,ages1 is to formulate principles applicable irrespective of ,figure1 and to rule out of each ,figure the moods that do not conform to them4 ,these regulative principles are known as ,the ,canons of the ,syllogism4 ,canon ,i4 ,in every syllogism there should be three1 and not more than three1 terms1 and the terms must be used throughout in the same sense4 ,it sometimes happens1 owing to the ambiguity of words1 that there seem to be three terms when there are really four4 ,an instance of this is seen in the sophism3-- ,he who is most hungry eats most4 ,he who eats least is most hungry4 4'4 ,he who eats least eats most4 ,this ,canon1 however1 though it points to a real danger of error in the application of the syllogism to actual propositions1 is superfluous in the consideration of purely formal implication1 it being a primary assumption that terms are univocal1 and remain constant through any process of inference4 ,under this ,canon1 ,mark ,duncan says 7,inst4 ,log41 iv4 #c1 #b71 is comprehended another commonly expressed in this form3 ,there should be nothing in the conclusion that was not in the premisses3 inasmuch as if there were anything in the conclusion that was in neither of the premisses1 there would be four terms in the syllogism4 ,the rule that in every syllogism there must be three1 and only three1 propositions1 sometimes given as a separate ,canon1 is only a corollary from ,canon ,i4 ,canon ,,ii4 ,the ,middle ,term must be distributed once at least in the ,premisses4 ,the ,middle ,term must either be wholly in1 or wholly out of1 one or other of the ,extremes before it can be the means of establishing a connexion between them4 ,if you know only that it is partly in both1 you cannot know from that how they lie relatively to one another3 and similarly if you know only that it is partly outside both4 ,the ,canon of ,distributed ,middle is a sort of counter-relative supplement to the ,dictum de ,omni4 ,whatever is predicable of a whole distributively is predicable of all its several parts4 ,if in neither premiss there is a predication about the whole1 there is no case for the application of the axiom4 ,canon ,,iii4 ,no term should be distributed in the conclusion that was not distributed in the premisses4 ,if an assertion is not made about the whole of a term in the premisses1 it cannot be made about the whole of that term in the conclusion without going beyond what has been given4 ,the breach of this rule in the case of the ,major term is technically known as the ,illicit ,process of the ,major3 in the case of the ,minor term1 ,illicit ,process of the ,minor4 ,great use is made of this canon in cutting off invalid moods4 ,it must be remembered that the ,predicate term is distributed or taken universally in ,o 7,some ,s is not in ,p7 as well as in ,e 7,no ,s is in ,p72 and that ,p is never distributed in affirmative propositions4 ,canon ,,iv4 ,no conclusion can be drawn from two negative premisses4 ,two negative premisses are really tantamount to a declaration that there is no connexion whatever between the ,major and ,minor 7as quantified in the premisses7 and the term common to both premisses2 in short1 that this is not a ,middle term--that the condition of a valid ,syllogism does not exist4 ,there is an apparent exception to this when the real ,middle in an argument is a contrapositive term1 not-,m4 ,thus3-- ,nobody who is not thirsty is suffering from fever4 ,this person is not thirsty4 4'4 ,he is not suffering from fever4 ,but in such cases it is really the absence of a quality or rather the presence of an opposite quality on which we reason2 and the ,minor ,premiss is really ,affirmative of the form ,s is in not-,m4 ,canon ,v4 ,if one premiss is negative1 the conclusion must be negative4 ,if one premiss is negative1 one of the ,extremes must be excluded in whole or in part from the ,middle term4 ,the other must therefore 7under ,canon ,,iv47 declare some coincidence between the ,middle term and the other extreme2 and the conclusion can only affirm exclusion in whole or in part from the area of this coincidence4 ,canon ,,vi4 ,no conclusion can be drawn from two particular premisses4 ,this is evident upon a comparison of terms in all possible positions1 but it can be more easily demonstrated with the help of the preceding canons4 ,the premisses cannot both be particular and yield a conclusion without breaking one or other of those canons4 ,suppose both are affirmative1 ,,ii1 the ,middle is not distributed in either premiss4 ,suppose one affirmative and the other negative1 ,,io1 or ,,oi4 ,then1 whatever the ,figure may be1 that is1 whatever the order of the terms1 only one term can be distributed1 namely1 the predicate of ,o4 ,this 7,canon ,,ii47 must be the ,middle4 ,but in that case there must be ,illicit ,process of the ,major 7,canon ,,iii471 for one of the premisses being negative1 the conclusion is negative 7,canon ,v471 and ,p its predicate is distributed4 ,briefly1 in a negative mood1 both ,major and ,middle must be distributed1 and if both premisses are particular this cannot be4 ,canon ,,vii4 ,if one ,premiss is particular the conclusion is particular4 ,this canon is sometimes combined with what we have given as ,canon ,v41 in a single rule3 ,the conclusion follows the weaker premiss4 ,it can most compendiously be demonstrated with the help of the preceding canons4 ,suppose both premisses affirmative1 then1 if one is particular1 only one term can be distributed in the premisses1 namely1 the subject of the ,universal affirmative premiss4 ,by ,canon ,,ii41 this must be the ,middle1 and the ,minor1 being undistributed in the ,premisses1 cannot be distributed in the conclusion4 ,that is1 the conclusion cannot be ,universal--must be particular4 ,suppose one ,premiss negative1 the other affirmative4 ,one premiss being negative1 the conclusion must be negative1 and ,p must be distributed in the conclusion4 ,before1 then1 the conclusion can be universal1 all three terms1 ,s1 ,m1 and ,p1 must1 by ,canons ,,ii4 and ,,iii41 be distributed in the premisses4 ,but whatever the ,figure of the premisses1 only two terms can be distributed4 ,for if one of the ,premisses be ,o1 the other must be ,a1 and if one of them is ,e1 the other must be ,i4 ,hence the conclusion must be particular1 otherwise there will be illicit process of the ,minor1 or of the ,major1 or of the ,middle4 ,the argument may be more briefly put as follows3 ,in an affirmative mood1 with one premiss particular1 only one term can be distributed in the premisses1 and this cannot be the ,minor without leaving the ,middle undistributed4 ,in a negative mood1 with one premiss particular1 only two terms can be distributed1 and the ,minor cannot be one of them without leaving either the ,middle or the ,major undistributed4 ,armed with these canons1 we can quickly determine1 given any combination of three propositions in one of the ,figures1 whether it is or is not a valid ,syllogism4 ,observe that though these canons hold for all the ,figures1 the ,figure must be known1 in all combinations containing ,a or ,o1 before we can settle a question of validity by ,canons ,,ii4 and ,,iii41 because the distribution of terms in ,a and ,o depends on their order in predication4 ,take ,,aee4 ,in ,fig4 ,i4-- ,all ,m is in ,p ,no ,s is in ,m ,no ,s is in ,p-- the conclusion is invalid as involving an illicit process of the ,major4 ,p is distributed in the conclusion and not in the premisses4 ,in ,fig4 ,,ii4 ,,aee-- ,all ,p is in ,m ,no ,s is in ,m ,no ,s is in ,p-- the conclusion is valid 7,camestres74 ,in ,fig4 ,,iii4 ,,aee-- ,all ,m is in ,p ,no ,m is in ,s ,no ,s is in ,p-- the conclusion is invalid1 there being illicit process of the ,major4 ,in ,fig4 ,,iv4 ,,aee is valid 7,camenes74 ,take ,,eio4 ,a little reflection shows that this combination is valid in all the ,figures if in any1 the distribution of the terms in both cases not being affected by their order in predication4 ,both ,e and ,i are simply convertible4 ,that the combination is valid is quickly seen if we remember that in negative moods both ,major and ,middle must be distributed1 and that this is done by ,e4 ,,eie is invalid1 because you cannot have a universal conclusion with one premiss particular4 ,,aii is valid in ,fig4 ,i4 or ,fig4 ,,iii41 and invalid in ,figs4 ,,ii4 and ,,iv41 because ,m is the subject of ,a in ,i4 and ,,iii4 and predicate in ,,ii4 and ,,iv4 ,,oao is valid only in ,fig4 ,,iii41 because only in that ,figure would this combination of premisses distribute both ,m and ,p4 ,simple exercises of this kind may be multiplied till all possible combinations are exhausted1 and it is seen that only the recognised moods stand the test4 ,if a more systematic way of demonstrating the valid moods is desired1 the simplest method is to deduce from the ,canons special rules for each ,figure4 ,aristotle arrived at these special rules by simple inspection1 but it is easier to deduce them4 ,i4 ,in the ,first ,figure1 the ,major ,premiss must be ,universal1 and the ,minor ,premiss affirmative4 ,to make this evident by the ,canons1 we bear in mind the ,scheme or ,figure-- ,m in ,p ,s in ,m-- and try the alternatives of ,affirmative ,moods and ,negative ,moods4 ,obviously in an affirmative mood the ,middle is undistributed unless the ,major ,premiss is ,universal4 ,in a negative mood1 7#a7 ,if the ,major ,premiss is ,o1 the ,minor must be affirmative1 and ,m is undistributed2 7#b7 if the ,major ,premiss is ,i1 ,m may be distributed by a negative ,minor ,premiss1 but in that case there would be an illicit process of the ,major--,p being distributed in the conclusion 7,canon ,v47 and not in the ,premisses4 ,thus the ,major ,premiss can neither be ,o nor ,i1 and must therefore be either ,a or ,e1 i4e41 must be ,universal4 ,that the ,minor must be affirmative is evident1 for if it were negative1 the conclusion must be negative 7,canon ,v47 and the ,major ,premiss must be affirmative 7,canon ,,iv471 and this would involve illicit process of the ,major1 ,p being distributed in the conclusion and not in the ,premisses4 ,these two special rules leave only four possible valid forms in the ,first ,figure4 ,there are sixteen possible combinations of premisses1 each of the four types of proposition being combinable with itself and with each of the others4 ,,aa ,,ea ,,ia ,,oa ,,ae ,,ee ,,ie ,,oe ,,ai ,,ei ,,ii ,,oi ,,ao ,,eo ,,io ,,oo ,special ,rule ,i4 wipes out the columns on the right with the particular major premisses2 and ,,ae1 ,,ee1 ,,ao1 and ,,eo are rejected by ,special ,rule ,,ii41 leaving ,,barb,ar,a1 ,,cel,ar,ent1 ,,dar,,ii and ,,fer,,io4 ,,ii4 ,in the ,second ,figure1 only ,negative ,moods are possible1 and the ,major ,premiss must be universal4 ,only ,negative moods are possible1 for unless one premiss is negative1 ,m being the predicate term in both-- ,p in ,m ,s in ,m-- is undistributed4 ,only negative moods being possible1 there will be illicit process of the ,major unless the ,major ,premiss is universal1 ,p being its subject term4 ,these special rules reject ,,aa and ,,ai1 and the two columns on the right4 ,to get rid of ,,ee and ,,eo1 we must call in the general ,canon ,,iv42 which leaves us with ,,ea1 ,,ae1 ,,ei1 and ,,ao--,,ces,ar,e1 ,,cam,estr,es1 ,,fest,in,o ,,bar,ok,o4 ,,iii4 ,in the ,third ,figure1 the ,minor ,premiss must be affirmative4 ,otherwise1 the conclusion would be negative1 and the ,major ,premiss affirmative1 and there would be illicit process of the ,major1 ,p being the predicate term in the ,major ,premiss4 ,m in ,p ,m in ,s4 ,this cuts off ,,ae1 ,,ee1 ,,ie1 ,,oe1 ,,ao1 ,,eo1 ,,io1 ,,oo1--the second and fourth rows in the above list4 ,,ii and ,,oi are inadmissible by ,canon ,,vi42 which leaves ,,aa1 ,,ia1 ,,ai1 ,,ea1 ,,oa1 ,,ei--,,dar,apt,i1 ,,dis,am,is1 ,,dat,is,i1 ,,fel,apt,on1 ,,bok,ard,o1 ,,fer,is,o--three affirmative moods and three negative4 ,,iv4 ,the ,fourth ,figure is fenced by three special rules4 7#a7 ,in negative moods1 the ,major ,premiss is universal4 7#b7 ,if the ,minor is negative1 both premisses are universal4 7#c7 ,if the ,major is affirmative1 the ,minor is universal4 7#a7 ,otherwise1 the ,figure being ,p in ,m ,m in ,s1 there would be illicit process of the ,major4 7#b7 ,the ,major must be universal by special rule 7#a71 and if the ,minor were not also universal1 the ,middle would be undisturbed4 7#c7 ,otherwise ,m would be undistributed4 ,rule 7#a7 cuts off the right-hand column1 ,,oa1 ,,oe1 ,,oi1 and ,,oo2 also ,,ie and ,,io4 ,rule 7#b7 cuts off ,,ao1 ,,eo4 ,rule 7#c7 cuts off ,,ai1 ,,ii4 ,,ee goes by general ,canon ,,iv42 and we are left with ,,aa1 ,,ae1 ,,ia1 ,,ea1 ,,ei--,br,am,ant,ip1 ,,cam,en,es1 ,,dim,ar,is1 ,,fes,ap,o1 ,fr,es,is,on4 ,,chapter ,,iv4 ,,the ,,analysis ,,of ,,arguments ,,into ,,syllogistic ,,forms4 ,turning given arguments into syllogistic form is apt to seem as trivial and useless as it is easy and mechanical4 ,in most cases the necessity of the conclusion is as apparent in the plain speech form as in the artificial logical form4 ,the justification of such exercises is that they give familiarity with the instrument1 serving at the same time as simple exercises in ratiocination3 what further uses may be made of the instrument once it is mastered1 we shall consider as we proceed4 ,i4--,,first ,,figure4 ,given the following argument to be put into ,syllogistic form3 ,no war is long popular3 for every war increases taxation2 and the popularity of anything that touches the pocket is short-lived4 ,the simplest method is to begin with the conclusion--,no war is long popular--,no ,s is ,p--then to examine the argument to see whether it yields premisses of the necessary form4 ,keeping the form in mind1 ,celarent of ,fig4 ,i4-- ,no ,m is ,p ,all ,s is ,m ,no ,s is ,p-- we see at once that ,every war increases taxation is of the form ,all ,s is ,m4 ,does the other sentence yield the ,major ,premiss ,no ,m is ,p1 when ,m represents the increasing of taxation1 i4e41 a class bounded by that attribute8 ,we see that the last sentence of the argument is equivalent to saying that ,nothing that increases taxation is long popular2 and this with the ,minor yields the conclusion in ,celarent4 ,nothing that increases taxation is long popular4 ,every war increases taxation4 ,no war is long popular4 ,observe1 now1 what in effect we have done in thus reducing the argument to the ,first ,figure4 ,in effect1 a general principle being alleged as justifying a certain conclusion1 we have put that principle into such a form that it has the same predicate with the conclusion4 ,all that we have then to do in order to inspect the validity of the argument is to see whether the subject of the conclusion is contained in the subject of the general principle4 ,is war one of the things that increase taxation8 ,is it one of that class8 ,if so1 then it cannot long be popular1 long popularity being an attribute that cannot be affirmed of any of that class4 ,reducing to the first figure1 then1 amounts simply to making the predication of the proposition alleged as ground uniform with the conclusion based upon it4 ,the minor premiss or applying proposition amounts to saying that the subject of the conclusion is contained in the subject of the general principle4 ,is the subject of the conclusion contained in the subject of the general principle when the two have identical predicates8 ,if so1 the argument falls at once under the ,dictum de ,omni et ,nullo4 ,two things may be noted concerning an argument thus simplified4 #a4 ,it is not necessary1 in order to bring an argument under the dictum de omni1 to reduce the predicate to the form of an extensive term4 ,in whatever form1 abstract or concrete1 the predication is made of the middle term1 it is applicable in the same form to that which is contained in the middle term4 #b4 ,the quantity of the ,minor ,term does not require special attention1 inasmuch as the argument does not turn upon it4 ,in whatever quantity it is contained in the ,middle1 in that quantity is the predicate of the ,middle predicable of it4 ,these two points being borne in mind1 the attention may be concentrated on the ,middle ,term and its relations with the extremes4 ,that the predicate may be left unanalysed without affecting the simplicity of the argument or in any way obscuring the exhibition of its turning-point1 has an important bearing on the reduction of ,modals4 ,the modality may be treated as part of the predicate without in any way obscuring what it is the design of the syllogism to make clear4 ,we have only to bear in mind that however the predicate may be qualified in the premisses1 the same qualification must be transferred to the conclusion4 ,otherwise we should have the fallacy of ,four ,terms1 quaternio terminorum4 ,to raise the question3 ,what is the proper form for a ,modal of ,possibility1 ,a or ,i8 is to clear up in an important respect our conceptions of the ,universal proposition1 ,victories may be gained by accident4 ,should this be expressed as ,a or ,i8 ,is the predicate applicable to ,all victories or only to ,some8 ,obviously the meaning is that of any victory it may be true that it was gained by accident1 and if we treat the mode as part of the predicate term things that may be gained by accident1 the form of the proposition is ,all ,s is in ,p4 ,but1 it may be asked1 does not the proposition that victories may be gained by accident rest1 as a matter of fact1 on the belief that some victories have been gained in this way8 ,and is not1 therefore1 the proper form of proposition ,some ,s is ,p8 ,this1 however1 is a misunderstanding4 ,what we are concerned with is the formal analysis of propositions as given4 ,and ,some victories have been gained by accident is not the formal analysis of ,victories may be gained by accident4 ,the two propositions do not give the same meaning in different forms3 the meaning as well as the form is different4 ,the one is a statement of a matter of fact3 the other of an inference founded on it4 ,the full significance of the ,modal proper may be stated thus3 ,in view of the fact that some victories have been gained by accident1 we are entitled to say of any victory1 in the absence of certain knowledge1 that it may be one of them4 ,a general proposition1 in short1 is a proposition about a genus1 taken universally4 ,,ii4--,,second ,,figure4 ,for testing arguments from general principles1 the ,first ,figure is the simplest and best form of analysis4 ,but there is one common class of arguments that fall naturally1 as ordinarily expressed1 into the ,second ,figure1 namely1 negative conclusions from the absence of distinctive signs or symptoms1 or necessary conditions4 ,thirst1 for example1 is one of the symptoms of fever3 if a patient is not thirsty1 you can conclude at once that his illness is not fever1 and the argument1 fully expressed1 is in the ,second ,figure4 ,all fever-stricken patients are thirsty4 ,this patient is not thirsty4 4'4 ,he is not fever-stricken4 ,arguments of this type are extremely common4 ,armed with the general principle that ill-doers are ill-dreaders1 we argue from a man's being unsuspicious that he is not guilty4 ,the negative diagnosis of the physician1 as when he argues from the absence of sore throat or the absence of a white speck in the throat that the case before him is not one of scarlatina or diphtheria1 follows this type3 and from its utility in making such arguments explicit1 the ,second ,figure may be called the ,figure of ,negative ,diagnosis4 ,it is to be observed1 however1 that the character of the argument is best disclosed when the ,major ,premiss is expressed by its ,converse by ,contraposition4 ,it is really from the absence of a symptom that the physician concludes2 as1 for example3 ,no patient that has not a sore throat is suffering from scarlatina4 ,and the argument thus expressed is in the ,first ,figure4 ,thus the reduction of ,baroko to the ,first ,figure by contraposition of the ,middle is vindicated as a really useful process4 ,the real ,middle is a contrapositive term1 and the form corresponds more closely to the reasoning when the argument is put in the ,first ,figure4 ,the truth is that if the positive term or sign or necessary condition is prominent as the basis of the argument1 there is considerable risk of fallacy4 ,sore throat being one of the symptoms of scarlatina1 the physician is apt on finding this symptom present to jump to a positive conclusion4 ,this is equivalent technically to drawing a positive conclusion from premisses of the ,second ,figure4 ,all scarlatina patients have sore throat4 ,this patient has sore throat4 ,a positive conclusion is technically known as a ,non-,sequitur 7,doesn't follow74 ,so with arguments from the presence of a necessary condition which is only one of many4 ,given that it is impossible to pass without working at the subject1 or that it is impossible to be a good marksman without having a steady hand1 we are apt to argue that given also the presence of this condition1 a conclusion is implicated4 ,but really the premisses given are only two affirmatives of the ,second ,figure4 ,it is impossible to pass without working at the subject4 ,this1 put into the form ,no not-,m is ,p1 is to say that ,none who have not worked can pass4 ,this is equivalent1 as the converse by contraposition1 with-- ,all capable of passing have worked at the subject4 ,but though ,q has worked at the subject1 it does not follow that he is capable of passing4 ,technically the middle is undistributed4 ,on the other hand1 if he has not worked at the subject1 it follows that he is not capable of passing4 ,we can draw a conclusion at once from the absence of the necessary condition1 though none can be drawn from its presence alone4 ,,third ,,figure4 ,arguments are sometimes advanced in the form of the ,third ,figure4 ,for instance3 ,killing is not always murder3 for tyrannicide is not murder1 and yet it is undoubtedly killing4 ,or again3 ,unpleasant things are sometimes salutary3 for afflictions are sometimes so1 and no affliction can be called pleasant4 ,these arguments1 when analysed into terms1 are1 respectively1 ,felapton and ,disamis4 ,no tyrannicide is murder2 ,all tyrannicide is killing2 ,some killing is not murder4 ,some afflictions are salutary things2 ,all afflictions are unpleasant things2 ,some unpleasant things are salutary things4 ,the syllogistic form cannot in such cases pretend to be a simplification of the argument4 ,the argument would be equally unmistakable if advanced in this form3 ,some ,s is not ,p1 for example1 ,m4 ,some killing is not murder1 e4g41 tyrannicide4 ,some unpleasant things are salutary1 e4g41 some afflictions4 ,there is really no deduction in the third figure1 no leading down from general to particular4 ,the middle term is only an example of the minor4 ,it is the syllogism of ,contradictory ,examples4 ,in actual debate examples are produced to disprove a universal assertion1 affirmative or negative4 ,suppose it is maintained that every wise man has a keen sense of humour4 ,you doubt this3 you produce an instance of the opposite1 say ,milton4 ,the force of your contradictory instance is not increased by exhibiting the argument in syllogistic form3 the point is not made clearer4 ,the ,third ,figure was perhaps of some use in ,yes and ,no ,dialectic4 ,when you had to get everything essential to your conclusion definitely admitted1 it was useful to know that the production of an example to refute a generality involved the admission of two propositions4 ,you must extract from your opponent both that ,milton was a wise man1 and that ,milton had not a keen sense of humour1 before you could drive him from the position that all wise men possess that quality4 ,examples for ,analysis4 ,scarlet flowers have no fragrance3 this flower has no fragrance3 does it follow that this flower is of a scarlet colour8 ,interest in the subject is an indispensable condition of learning easily2 ,z is interested in the subject3 he is bound1 therefore1 to learn easily4 ,it is impossible to be a good shot without having a steady hand3 ,john has a steady hand3 he is capable1 therefore1 of becoming a good shot4 ,some victories have been won by accident2 for example1 ,maiwand4 ,intemperance is more disgraceful than cowardice1 because people have more opportunities of acquiring control of their bodily appetites4 ,some men are not fools1 yet all men are fallible4 ,what follows8 ,some men allow that their memory is not good3 every man believes in his own judgment4 ,what is the conclusion1 and in what ,figure and ,mood may the argument be expressed8 ,an honest man's the noblest work of ,god3 ,z is an honest man3 therefore1 he is--what8 ,examine the logical connexion between the following exclamation and answer3 ,but ,i hear some one exclaiming that wickedness is not easily concealed4 ,to which ,i answer1 ,nothing great is easy4 ,if the attention is actively aroused1 sleep becomes impossible3 hence the sleeplessness of anxiety1 for anxiety is a strained attention upon an impending disaster4 ,to follow truth can never be a subject of regret3 free inquiry does lead a man to regret the days of his childish faith2 therefore it is not following truth4--,j4 ,h4 ,newman4 ,he would not take the crown3 ,therefore 'tis certain he was not ambitious4 ,as he was valiant1 ,i honour him2 as he was ambitious1 ,i slew him4 ,the ,utopians learned the language of the ,greeks with more readiness because they were originally of the same race with them4 ,nothing which is cruel can be expedient1 for cruelty is most revolting to the nature of man4 ,the fifth century saw the foundation of the ,frank dominion in ,gaul1 and the first establishment of the ,german races in ,britain4 ,the former was effected in a single long reign1 by the energy of one great ruling tribe1 which had already modified its traditional usages1 and now1 by the adoption of the language and religion of the conquered1 prepared the way for a permanent amalgamation with them4 ,in the second of the above sentences a general proposition is assumed4 ,show in syllogistic form how the last proposition in the sentence depends upon it4 ,i do not mean to contend that active benevolence may not hinder a man's advancement in the world3 for advancement greatly depends upon a reputation for excellence in some one thing of which the world perceives that it has present need3 and an obvious attention to other things1 though perhaps not incompatible with the excellence itself1 may easily prevent a person from obtaining a reputation for it4 ,pick out the propositions here given as interdependent4 ,examine whether the principle alleged is sufficiently general to necessitate a conclusion4 ,in what form would it be so8 ,,chapter ,v4 ,,enthymemes4 ,there is a certain variety in the use of the word ,enthymeme among logicians4 ,in the narrowest sense1 it is a valid formal syllogism1 with one premiss suppressed4 ,in the widest sense it is simply an argument1 valid or invalid1 formal in expression or informal1 with only one premiss put forward or hinted at1 the other being held in the mind 7,greek3 en thymo74 ,this last is the ,aristotelian sense4 ,it is only among formal logicians of the straitest sect that the narrowest sense prevails4 ,hamilton divides ,enthymemes into three classes according as it is the ,major ,premiss1 the ,minor ,premiss1 or the ,conclusion that is suppressed4 ,thus1 a full syllogism being3-- ,all liars are cowards3 ,caius is a liar3 4'4 ,caius is a coward3-- this may be enthymematically expressed in three ways4 ,i4 ,enthymeme of the ,first ,order 7,major understood74 ,caius is a coward2 for ,caius is a liar4 ,,ii4 ,enthymeme of the ,second ,order 7,minor understood74 ,caius is a coward2 for all liars are cowards4 ,,iii4 ,enthymeme of the ,third ,order 7,conclusion understood74 ,all liars are cowards1 and ,caius is a liar4 ,the ,third ,order is a contribution of ,hamilton's own4 ,it is superfluous1 inasmuch as the conclusion is never suppressed except as a rhetorical figure of speech4 ,hamilton confines the word ,enthymeme to valid arguments1 in pursuance of his view that ,pure ,logic has no concern with invalid arguments4 ,aristotle used ,enthymeme in the wider sense of an elliptically expressed argument4 ,there has been some doubt as to the meaning of his definition1 but that disappears on consideration of his examples4 ,he defines an ,enthymeme 7,prior ,analyt41 ii4 #bg7 as a syllogism from probabilities or signs 7,greek3 syllogismos ex eikoton e semeion74 ,the word syllogism in this connexion is a little puzzling4 ,but it is plain from the examples he gives that he meant here by syllogism not even a correct reasoning1 much less a reasoning in the explicit form of three terms and three propositions4 ,he used syllogism1 in fact1 in the same loose sense in which we use the words reasoning and argument1 applying without distinction of good and bad4 ,the sign1 he says1 is taken in three ways1 in as many ways as there are ,syllogistic ,figures4 7#a7 ,a sign interpreted in the ,first ,figure is conclusive4 ,thus3 ,this person has been drowned1 for he has froth in the trachea4 ,taken in the ,first ,figure with ,all who have froth in the trachea have been drowned as a major premiss1 this argument is valid4 ,the sign is conclusive4 7#b7 ,this patient is fever-stricken1 for he is thirsty4 ,assumed that ,all fever-stricken patients are thirsty1 this is an argument in the ,second ,figure1 but it is not a valid argument4 ,thirst is a sign or symptom of fever1 but not a conclusive sign1 because it is indicative of other ailments also4 ,yet the argument has a certain probability4 7#c7 ,wise men are earnest 7,greek3 spoudaioi71 for ,pittacus is earnest4 ,here the suppressed premiss is that ,pittacus is wise4 ,fully expressed1 the argument is in the ,third ,figure3-- ,pittacus is earnest4 ,pittacus is wise4 4'4 ,wise men are earnest4 ,here again the argument is inconclusive and yet it has a certain probability4 ,the coincidence of wisdom with earnestness in one notable example lends a certain air of probability to the general statement4 ,such are ,aristotle's examples or strict parallels to them4 ,the examples illustrate also what he says in his ,rhetoric as to the advantages of enthymemes4 ,for purposes of persuasion enthymemes are better than explicit syllogisms1 because any inconclusiveness there may be in the argument is more likely to pass undetected4 ,as we shall see1 one main use of the ,syllogism is to force tacit assumptions into light and so make their true connexion or want of connexion apparent4 ,in ,logic enthymemes are recognised only to be shown up3 the elliptical expression is a cover for fallacy1 which it is the business of the logician to strip off4 ,in ,aristotle's examples one of the premisses is expressed4 ,but often the arguments of common speech are even less explicit than this4 ,a general principle is vaguely hinted at3 a subject is referred to a class the attributes of which are assumed to be definitely known4 ,thus3-- ,he was too ambitious to be scrupulous in his choice of means4 ,he was too impulsive not to have made many blunders4 ,each of these sentences contains a conclusion and an enthymematic argument in support of it4 ,the hearer is understood to have in his mind a definite idea of the degree of ambition at which a man ceases to be scrupulous1 or the degree of impulsiveness that is incompatible with accuracy4 ,one form of enthymeme is so common in modern rhetoric as to deserve a distinctive name4 ,it may be called the ,,enthymeme ,,of ,,the ,,abstractly ,,denominated ,,principle4 ,a conclusion is declared to be at variance with the principles of ,political ,economy1 or contrary to the doctrine of ,evolution1 or inconsistent with ,heredity1 or a violation of the sacred principle of ,freedom of ,contract4 ,it is assumed that the hearer is familiar with the principles referred to4 ,as a safeguard against fallacy1 it may be well to make the principle explicit in a proposition uniform with the conclusion4 ,,chapter ,,vi4 ,,the ,,utility ,,of ,,the ,,syllogism4 ,the main use of the ,syllogism is in dealing with incompletely expressed or elliptical arguments from general principals4 ,this may be called ,enthymematic argument1 understanding by ,enthymeme an argument with only one premiss put forward or hinted at1 the other being held in the mind4 ,in order to test whether such reasoning is sound or unsound1 it is of advantage to make the argument explicit in ,syllogistic form4 ,there have been heaps and mazes of discussion about the use of the ,syllogism1 much of it being profitable as a warning against the neglect of ,formal ,logic4 ,again and again it has been demonstrated that the ,syllogism is useless for certain purposes1 and from this it has been concluded that the ,syllogism is of no use at all4 ,the inventor of the ,syllogism had a definite practical purpose1 to get at the simplest1 most convincing1 undeniable and irresistible way of putting admitted or self-evident propositions so that their implication should be apparent4 ,his ambition was to furnish a method for the ,yes and ,no ,dialectician1 and the expounder of science from self-evident principles4 ,a question being put up for discussion1 it was an advantage to analyse it1 and formulate the necessary premisses3 you could then better direct your interrogations or guard your answers4 ,the analysis is similarly useful when you want to construct an argument from self-evident principles4 ,all that the ,syllogism could show was the consistency of the premisses with the conclusion4 ,the conclusion could not go beyond the premisses1 because the questioner could not go beyond the admissions of the respondent4 ,there is indeed an advance1 but not an advance upon the two premisses taken together4 ,there is an advance upon any one of them1 and this advance is made with the help of the other4 ,both must be admitted3 a respondent may admit one without being committed to the conclusion4 ,let him admit both and he cannot without self-contradiction deny the conclusion4 ,that is all4 ,dialectic of the ,yes and ,no kind is no longer practised4 ,does any analogous use for the ,syllogism remain8 ,is there a place for it as a safeguard against error in modern debate8 ,as a matter of fact it is probably more useful now than it was for its original purpose1 inasmuch as modern discussion1 aiming at literary grace and spurning exact formality as smacking of scholasticism and pedantry1 is much more flabby and confused4 ,in the old dialectic play there was generally a clear question proposed4 ,the interrogative form forced this much on the disputants4 ,the modern debater of the unpedantic1 unscholastic school is not so fettered1 and may often be seen galloping wildly about without any game in sight or scent1 his maxim being to-- ,spur boldly on1 and dash through thick and thin1 ,through sense and nonsense1 never out nor in4 ,now the syllogistic analysis may often be of some use in helping us to keep a clear head in the face of a confused argument4 ,there is a brilliant defence of the syllogism as an analysis of arguments in the ,westminster ,review for ,january1 #ahbh4 ,the article was a notice of ,whately's ,logic3 it was written by ,j4 ,s4 ,mill4 ,for some reason it has never been reprinted1 but it puts the utility of the ,syllogism on clearer ground than ,mill afterwards sought for it4 ,can a fallacy in argument be detected at once8 ,is common-sense sufficient8 ,common-sense would require some inspection4 ,how would it proceed8 ,does common-sense inspect the argument in a lump or piecemeal8 ,all at once or step by step8 ,it analyses4 ,how8 ,first1 it separates out the propositions which contribute to the conclusion from those which do not1 the essential from the irrelevant4 ,then it states explicitly all that may have been assumed tacitly4 ,finally1 it enumerates the propositions in order4 ,some such procedure as this would be adopted by common-sense in analysing an argument4 ,but when common-sense has done this1 it has exhibited the argument in a series of syllogisms4 ,such is ,mill's early defence of the ,syllogism4 ,it is weak only in one point1 in failing to represent how common-sense would arrive at the peculiar syllogistic form4 ,it is the peculiar form of logical analysis that is the distinction of the syllogism4 ,when you have disentangled the relevant propositions you have not necessarily put them in this form4 ,the arguments given in text-books to be cast into syllogistic form1 consist only as a rule of relevant propositions1 but they are not yet formal syllogisms4 ,but common-sense had only one other step to make to reach the distinctive form4 ,it had only to ask after analysing the argument1 ,is there any form of statement specially suitable for exhibiting the connexion between a conclusion and the general principle on which it is alleged to depend8 ,ask yourself the question1 and you will soon see that there would be an obvious advantage in making the conclusion and the general principle uniform1 in stating them with the same predicate4 ,but when you do this1 as ,i have already shown 7p4 #aig7 you state the argument in the ,first ,figure of the ,syllogism4 ,it must1 however1 be admitted that it is chiefly for exhibiting1 or forcing into light1 tacit or lurking assumptions that the ,syllogistic form is of use4 ,unless identity of meaning is disguised or distorted by puzzling difference of language1 there is no special illuminative virtue in the ,syllogism4 ,the argument in a ,euclidean demonstration would not be made clearer by being cast into formal ,syllogisms4 ,again1 when the subject matter is simple1 the ,syllogistic form is not really required for protection against error4 ,in such enthymemes as the following for example3-- ,she must be clever3 she is so uncompromisingly ugly4 ,romeo must be in love3 for is he not seventeen8 it is plain to the average intelligence without any knowledge of ,syllogism that the argument takes for granted a general proposition and what the general proposition is4 ,another thing is plain to the average intelligence1 perhaps plainer than to a proficient in the use of the ,syllogism4 ,clearly we cannot infer with certainty that a woman is clever because she is ugly1 unless it is the case that all ugly women are clever4 ,but a ,syllogiser1 seeing that no certain conclusion can be drawn except upon this condition1 is apt to dismiss the argument as altogether worthless4 ,this may be specified as an error incident to the practice of the ,syllogism1 that it inclines us to look for necessarily conclusive premisses1 and to deny all weight to anything short of this4 ,now in ordinary life it is comparatively seldom that such premisses can be found4 ,we are obliged to proceed on maxims that are not of universal scope1 and which lend only a more or less strong colour of probability to cases that can be brought under them4 ,a little learning is a dangerous thing2 ,haste makes waste2 ,slowness of speech is a sign of depth of thought2 ,vivacity is a sign of shallowness3 such are the endoxes or commonplaces of popular knowledge that men bring to bear in daily life4 ,they are not true for all cases1 but some of them are true for most or for a good many1 and they may be applied with a certain probability though they are not rigidly conclusive4 ,the plain man's danger is that he apply them unthinkingly as universals3 the formal logician's danger is that1 seeing them to be inapplicable as universals1 he dismisses them as being void of all argumentative force4 ,it helps to fix the limits of ,formal ,logic to remember that it lies outside its bounds to determine the degree of probability attaching to the application of approximate truths1 such as are the staple of arguments in ordinary affairs4 ,formal ,logic1 we may repeat1 is not concerned with degrees of truth or falsehood1 probability or improbability4 ,it merely shows the interdependency of certain arguments1 the consistency of conclusion with premisses4 ,this1 however1 is a function that might easily be underrated4 ,its value is more indirect than direct4 ,in showing what is required for a certain conclusion1 it puts us on the road to a more exact estimate of the premisses alleged1 a sounder judgment of their worth4 ,well begun is half done3 in undertaking the examination of any argument from authority1 a formal syllogism is a good beginning4 ,,chapter ,,vii4 ,,conditional ,,arguments4--,,hypothetical ,,syllogism1 ,,disjunctive ,,syllogism1 ,,and ,,dilemma4 ,the justification of including these forms of argument in ,logic is simply that they are sometimes used in debate1 and that confusion may arise unless the precise meaning of the premisses employed is understood4 ,aristotle did not include them as now given in his exposition of the ,syllogism1 probably because they have no connexion with the mode of reasoning together to which he appropriated the title4 ,the fallacies connected with them are of such a simple kind that to discuss as a question of method the precise place they should occupy in a logical treatise is a waste of ingenuity4#a ,i4--,,hypothetical ,,syllogisms4 ,if ,a is ,b1 ,c is ,d ,a is ,b ,,modus 4'4,c is ,d ,,ponens4 ,if ,a is ,b1 ,c is ,d ,c is not ,d ,,modus 4'4,a is not ,b ,,tollens4 ,a so-called ,hypothetical ,syllogism is thus seen to be a ,syllogism in which the major premiss is a ,,hypothetical ,,proposition1 that is to say1 a complex proposition in which two propositions are given as so related that the truth of one follows necessarily from the truth of the other4 ,two propositions so related are technically called the ,,antecedent or ,reason1 and the ,,consequent4 ,the meaning and implication of the form1 ,if ,a is ,b1 ,c is ,d1 is expressed in what is known as the ,,law ,,of ,,reason ,,and ,,consequent3-- ,when two propositions are related as ,reason and ,consequent1 the truth of the ,consequent follows from the truth of the ,antecedent1 and the falsehood of the ,antecedent1 from the falsehood of the ,consequent4 ,if ,a is ,b1 ,c is ,d1 implies that ,if ,c is not ,d1 ,a is not ,b4 ,if this subject is educative1 it quickens the wits2 if it does not quicken the wits1 it is not educative4 ,admitted1 then1 that the law of ,reason and ,consequent holds between two propositions--that ,if ,a is ,b1 ,c is ,d3 admitted also the ,antecedent1 the truth of the ,consequent follows4 ,this is the ,,modus ,,ponens or ,positive ,mode1 where you reach a conclusion by obtaining the admission of the ,antecedent4 ,admit the ,antecedent and the truth of the ,consequent follows4 ,with the same ,major ,premiss1 you may also1 under the ,law of ,reason and ,consequent reach a conclusion by obtaining the denial of the ,consequent4 ,this is the ,,modus ,,tollens or ,negative ,mode4 ,deny the ,consequent and one is bound to deny the ,antecedent4 ,but to guard against the fallacy technically known as ,,fallacia ,,consequentis1 we must observe what the relation of ,reason and ,consequent does not imply4 ,the truth of the ,consequent does not involve the truth of the ,antecedent1 and the falsehood of the ,antecedent does not involve the falsehood of the ,consequent4 ,if the harbour is frozen1 the ships cannot come in4 ,if the harbour is not frozen1 it does not follow that the ships can come in3 they may be excluded by other causes4 ,and so1 though they cannot come in1 it does not follow that the harbour is frozen4 ,,questions ,,connected ,,with ,,hypothetical ,,syllogisms4 7#a7 ,are they properly called ,syllogisms8 ,this is purely a question of ,method and ,definition4 ,if we want a separate technical name for forms of argument in which two terms are reasoned together by means of a third1 the ,hypothetical ,syllogism1 not being in such a form1 is not properly so called4 ,the fact is that for the purposes of the ,hypothetical ,argument1 we do not require an analysis into terms at all3 it is superfluous3 we are concerned only with the affirmation or denial of the constituent propositions as wholes4 ,but if we extend the word ,syllogism to cover all arguments in which two propositions necessarily involve a third1 the ,hypothetical ,argument is on this understanding properly enough called a ,syllogism4 7#b7 ,is the inference in the ,hypothetical ,syllogism ,mediate or ,immediate8 ,to answer this question we have to consider whether the ,conclusion can be drawn from either of the two premisses without the help of the other4 ,if it is possible immediately1 it must be educible directly either from the ,major ,premiss or from the ,minor4 7a7 ,some logicians argue as if the ,conclusion were immediately possible from the ,major ,premiss4 ,the ,minor ,premiss and the ,conclusion1 they urge1 are simply equivalent to the ,major ,premiss4 ,but this is a misunderstanding4 ,if ,a is ,b1 ,c is ,d1 is not equivalent to ,a is ,b1 therefore ,c is ,d4 ,if the harbour is frozen1 the ships cannot come in is not to say that the harbour is frozen1 and therefore1 etc4 ,the ,major ,premiss merely affirms the existence of the relation of ,reason and ,consequent between the two propositions4 ,but we cannot thereupon assert the ,conclusion unless the ,minor ,premiss is also conceded2 that is1 the inference of the ,conclusion is ,mediate1 as being from two premisses and not from one alone4 7b7 ,similarly with ,hamilton's contention that the ,conclusion is inferrible immediately from the ,minor ,premiss1 inasmuch as the ,consequent is involved in the ,reason4 ,true1 the ,consequent is involved in the ,reason3 but we cannot infer from ,a is ,b to ,c is ,d1 unless it is conceded that the relation of ,reason and ,consequent holds between them2 that is1 unless the ,major ,premiss is conceded as well as the ,minor4 7#c7 ,can ,hypothetical ,syllogism be reduced to the ,categorical ,form8 ,to oppose ,hypothetical ,syllogisms to ,categorical is misleading1 unless we take note of the precise difference between them4 ,it is only in the form of the ,major ,premiss that they differ3 ,minor ,premiss and ,conclusion are categorical in both4 ,and the meaning of a ,hypothetical ,major ,premiss 7unless it is a mere arbitrary convention between two disputants1 to the effect that the ,consequent will be admitted if the ,antecedent is proved1 or that the ,antecedent will be relinquished if the ,consequent is disproved71 can always be put in the form of a general proposition1 from which1 with the ,minor ,premiss as applying proposition1 a conclusion identical with the original can be drawn in regular ,categorical form4 ,thus3-- ,if the harbour is frozen1 the ships cannot come in4 ,the harbour is frozen4 4'4 ,the ships cannot come in4 ,this is a ,hypothetical ,syllogism1 ,modus ,ponens4 ,express the ,hypothetical ,major in the form of the general proposition which it implies1 and you reach a conclusion 7in ,barbara7 which is only grammatically different from the original4 ,all frozen harbours exclude ships4 ,the harbour is frozen4 4'4 ,it excludes ships4 ,again1 take an example of the ,modus ,tollens-- ,if rain has fallen1 the streets are wet4 ,the streets are not wet4 4'4 ,rain has not fallen4 ,this is reducible1 by formulating the underlying proposition1 to ,camestres or ,baroko of the ,second ,figure4 ,all streets rained upon are wet4 ,the streets are not wet4 4'4 ,they are not streets rained upon4 ,hypothetical ,syllogisms are thus reducible1 by merely grammatical change#b1 or by the statement of self-evident implications1 to the ,categorical form4 ,and1 similarly1 any ,categorical ,syllogism may be reduced to the ,hypothetical form4 ,thus3-- ,all men are mortal4 ,socrates is a man4 4'4 ,socrates is mortal4 ,this argument is not different1 except in the expression of the ,major and the ,conclusion1 from the following3-- ,if ,socrates is a man1 death will overtake him4 ,socrates is a man4 4'4 ,death will overtake him4 ,the advantage of the ,hypothetical form in argument is that it is simpler4 ,it was much used in ,mediaeval ,disputation1 and is still more popular than the ,categorical ,syllogism4 ,perhaps the prominence given to ,hypothetical ,syllogisms as syllogisms in ,post-,renaissance text-books is due to the use of them in the formal disputations of graduands in the ,universities4 ,it was the custom for the ,disputant to expound his argument in this form3-- ,if so and so is the case1 such and such follows4 ,so and so is the case4 4'4 ,such and such follows4 ,to which the ,respondent would reply3 ,accipio antecedentem1 nego consequentiam1 and argue accordingly4 ,petrus ,hispanus does not give the ,hypothetical ,syllogism as a ,syllogism3 he merely explains the true law of ,reason and ,consequent in connexion with the ,fallacia ,consequentis in the section on ,fallacies4 7,summulae4 ,tractatus ,sextus47 ,,ii4--,,disjunctive ,,syllogisms4 ,a ,disjunctive ,syllogism is a syllogism in which the ,major ,premiss is a ,,disjunctive ,,proposition1 i4e41 one in which two propositions are declared to be mutually incompatible4 ,it is of the form ,either ,a is ,b1 or ,c is ,d4#c ,if the disjunction between the alternatives is really complete1 the form implies four hypothetical propositions3-- 7#a7 ,if ,a is ,b1 ,c is not ,d4 7#b7 ,if ,a is not ,b1 ,c is ,d4 7#c7 ,if ,c is ,d1 ,a is not ,b4 7#d7 ,if ,c is not ,d1 ,a is ,b4 ,suppose then that an antagonist has granted you a ,disjunctive ,proposition1 you can1 using this as a ,major ,premiss1 extract from him four different ,conclusions1 if you can get him also to admit the requisite ,minors4 ,the ,mode of two of these is technically called ,,modus ,,ponendo ,,tollens1 the mode that denies the one alternative by granting the other--,a is ,b1 therefore ,c is not ,d2 ,c is ,d1 therefore ,a is not ,b4 ,the other ,mode is also twice open1 the ,,modus ,,tollendo ,,ponens--,a is not ,b1 therefore ,c is ,d2 ,c is not ,d1 therefore ,a is ,b4 ,fallacy is sometimes committed through the ,disjunctive form owing to the fact that in common speech there is a tendency to use it in place of a mere hypothetical1 when there are not really two incompatible alternatives4 ,thus it may be said ,either the witness is perjured1 or the prisoner is guilty1 when the meaning merely is that if the witness is not perjured the prisoner is guilty4 ,but really there is not a valid disjunction and a correct use of the disjunctive form1 unless four hypotheticals are implied1 that is1 unless the concession of either involves the denial of the other1 and the denial of either the concession of the other4 ,now the prisoner may be guilty and yet the witness be perjured2 so that two of the four hypotheticals1 namely-- ,if the witness is perjured1 the prisoner is not guilty1 ,if the prisoner is guilty1 the witness is not perjured-- do not necessarily hold4 ,if1 then1 we would guard against fallacy1 we must always make sure before assenting to a disjunctive proposition that there is really a complete disjunction or mutual incompatibility between the alternatives4 ,,iii4--,,the ,,dilemma4 ,a ,dilemma is a combination of ,hypothetical and ,disjunctive propositions4 ,the word has passed into common speech1 and its ordinary use is a clue to the logical structure4 ,we are said to be in a dilemma when we have only two courses open to us and both of them are attended by unpleasant consequences4 ,in argument we are in this position when we are shut into a choice between two admissions1 and either admission leads to a conclusion which we do not like4 ,the statement of the alternatives as the consequences hypothetically of certain conditions is the major premiss of the dilemma3 once we admit that the relations of ,antecedent and ,consequent are as stated1 we are in a trap1 if trap it is3 we are on the horns of the dilemma1 ready to be tossed from one to the other4 ,for example3-- ,if ,a is ,b1 ,a is ,c1 and if ,a is not ,b1 ,a is ,d4 ,but ,a either is or is not ,b4 ,therefore1 ,a either is ,c or is ,d4 ,if ,a acted of his own motive1 he is a knave2 if ,a did not act of his own motive1 he is a catspaw4 ,but ,a either acted of his own motive or he did not4 ,thereupon ,a is either a knave or a catspaw4 ,this is an example of the ,constructive ,dilemma1 the form of it corresponding to the common use of the word as a choice between equally unpleasant alternatives4 ,the standard example is the dilemma in which the custodians of the ,alexandrian ,library are said to have been put by the ,caliph ,omar in #fdj ,a4,d4 ,if your books are in conformity with the ,koran1 they are superfluous2 if they are at variance with it1 they are pernicious4 ,but they must either be in conformity with the ,koran or at variance with it4 ,therefore they are either superfluous or pernicious4 ,where caution has to be exercised is in accepting the clauses of the ,major4 ,we must make sure that the asserted relations of ,reason and ,consequent really hold4 ,it is there that fallacy is apt to creep in and hide its head4 ,the ,alexandrian ,librarians were rash in accepting the first clause of the conqueror's ,major3 it does not follow that the books are superfluous unless the doctrines of the ,koran are not merely sound but contain all that is worth knowing4 ,the propounder of the dilemma covertly assumes this4 ,it is in the facility that it affords for what is technically known as ,petitio ,principii that the ,dilemma is a useful instrument for the ,sophist4 ,we shall illustrate it further under that head4 ,what is known as the ,destructive ,dilemma is of a somewhat different form4 ,it proceeds upon the denial of the ,consequent as involving the denial of the ,antecedent4 ,in the ,major you obtain the admission that if a certain thing holds1 it must be followed by one or other of two consequences4 ,you then prove by way of ,minor that neither of the alternatives is true4 ,the conclusion is that the antecedent is false4 ,we had an example of this in discussing whether the inference in the ,hypothetical ,syllogism is ,immediate4 ,our argument was in this form3-- ,if the inference is immediate1 it must be drawn either from the ,major alone or from the ,minor alone4 ,but it cannot be drawn from the ,major alone1 neither can it be drawn from the ,minor alone4 ,therefore1 it is not immediate4 ,in this form of ,dilemma1 which is often serviceable for clearness of exposition1 we must as in the other make sure of the truth of the ,major3 we must take care that the alternatives are really the only two open4 ,otherwise the imposing form of the argument is a convenient mask for sophistry4 ,zeno's famous dilemma1 directed to prove that motion is impossible1 covers a petitio principii4 ,if a body moves1 it must move either where it is or where it is not4 ,but a body cannot move where it is3 neither can it move where it is not4 ,conclusion1 it cannot move at all1 i4e41 ,motion is impossible4 ,the conclusion is irresistible if we admit the ,major1 because the ,major covertly assumes the point to be proved4 ,in truth1 if a body moves1 it moves neither where it is nor where it is not1 but from where it is to where it is not4 ,motion consists in change of place3 the ,major assumes that the place is unchanged1 that is1 that there is no motion4 ,footnote #a3 ,for the history of ,hypothetical ,syllogism see ,mansel's ,aldrich1 ,appendix ,i4 ,footnote #b3 ,it may be argued that the change is not merely grammatical1 and that the implication of a general proposition in a hypothetical and vice versa is a strictly logical concern4 ,at any rate such an implication exists1 whether it is the function of the ,grammarian or the ,logician to expound it4 ,footnote #c3 ,some logicians prefer the form ,either ,a is1 or ,b is4 ,but the two alternatives are propositions1 and if ,a is represents a proposition1 the is is not the ,syllogistic copula4 ,if this is understood it does not matter3 the analysis of the alternative propositions is unessential4 ,,chapter ,,viii4 ,,fallacies ,,in ,,deductive ,,argument4--,,petitio ,,principii ,,and ,,ignoratio ,,elenchi4 ,the traditional treatment of ,fallacies in ,logic follows ,aristotle's special treatise ,greek3 ,peri sophistikon elenchon--,concerning ,sophistical ,refutations--,pretended ,disproofs--,argumentative ,tricks4 ,regarding ,logic as in the main a protection against ,fallacies1 ,i have been going on the plan of taking each fallacy in connexion with its special safeguard1 and in accordance with that plan propose to deal here with the two great types of fallacy in deductive argument4 ,both of them were recognised and named by ,aristotle3 but before explaining them it is worth while to indicate ,aristotle's plan as a whole4 ,some of his ,argumentative ,tricks were really peculiar to ,yes-and-,no ,dialectic in its most sportive forms3 but his leading types1 both ,inductive and ,deductive1 are permanent1 and his plan as a whole has historical interest4 ,young readers would miss them from ,logic3 they appeal to the average argumentative boy4 ,he divides ,fallacies broadly into ,verbal ,fallacies 7,greek3 para ten lexin1 in dictione71 and ,non-,verbal ,fallacies 7,greek3 exo tes lexeos1 extra dictionem74 ,the first class are mere ,verbal ,quibbles1 and hardly deserve serious treatment1 still less minute subdivision4 ,the world was young when time was spent upon them4 ,aristotle names six varieties1 but they all turn on ambiguity of word or structure1 and some of them1 being dependent on ,greek syntax1 cannot easily be paralleled in another tongue4 7#a7 ,ambiguity of word 7,greek3 homonymia74 ,as if one were to argue3 ,all cold can be expelled by heat3 ,john's illness is a cold3 therefore it can be expelled by heat4 ,or3 ,some afflictions are cheering1 for afflictions are sometimes light1 and light is always cheering4 ,the serious confusion of ambiguous words is met by ,definition1 as explained at length in pt4 ii4 c i4 7#b7 ,ambiguity of structure 7,greek3 amphibolia74 ,what he was beaten with was what ,i saw him beaten with3 what ,i saw him beaten with was my eye3 therefore1 what he was beaten with was my eye4 ,how do you do8 ,do8 ,do what8 ,i mean1 how do you feel8 ,how do ,i feel8 ,with my fingers1 of course2 but ,i can see very well4 ,no1 no2 ,i mean1 how do you find yourself8 ,then why did you not say so8 ,i never exactly noticed1 but ,i will tell you next time ,i lose myself4 7#c7 ,illicit conjunction 7,greek3 synthesis74 ,socrates is good4 ,socrates is a musician4 ,therefore ,socrates is a good musician4 7#d7 ,illicit disjunction 7,greek3 diairesis74 ,socrates is a good musician4 ,therefore he is a good man4 7#e7 ,ambiguity of pronunciation 7,greek3 prosodia1 fallacia accentus74 ,analogies to words that differ only in accent1 such as ,greek3 ou-with accents psili and persipomeni and ,greek3 ou-with accents psili and oxia1 may be found in differences of pronunciation4 ,hair very thick1 sir1 said a barber to a customer1 whose hair was bushy1 but beginning to turn grey4 ,yes1 ,i daresay4 ,but ,i would rather have it thick than thin4 ,ah1 too thick to-day1 sir4 ,but ,i don't want to dye it4 ,excuse me1 sir1 ,i mean the hair of the hatmosphere1 t-o-d-a-y1 to-day4 ,he said1 saddle me the ass4 ,and they saddled him4 7#f7 ,ambiguity of inflexion 7,greek3 schema tes lexeos1 ,figura dictionis74 ,this is not easy to make intelligible in ,english4 ,the idea is that a termination may be ambiguously interpreted1 a neuter participle1 e4g41 taken for an active4 ,thus3 ,george is ailing4 ,doing what1 did you say8 ,ailing8 ,what is he ailing8 ,ginger-aleing8 ,non-,verbal ,fallacies1 or ,fallacies in thought1 are a more important division4 ,aristotle distinguishes seven4 ,of these1 three are comparatively unimportant and trifling4 ,one of them1 known to the ,schoolmen as ,fallacia ,plurium ,interrogationum1 was peculiar to ,interrogative disputation4 ,it is the trick of putting more than one question as one1 so that a simple ,yes commits the respondent to something implied4 ,have you left off beating your father8 ,if you answer ,yes1 that implies that you have been in the habit of beating him4 ,has the practice of excessive drinking ceased in your part of the country8 ,such questions were unfair when the ,respondent could answer only ,yes or ,no4 ,the modern disputant who demands a plain answer ,yes or ,no1 is sometimes guilty of this trick4 ,two others1 the fallacies known as ,a dicto simpliciter ad dictum secundum quid1 and ,a dicto secundum quid ad dictum simpliciter1 are as common in modern dialectic as they were in ancient4 ,the trick1 conscious or unconscious1 consists in getting assent to a statement with a qualification and proceeding to argue as if it had been conceded without qualification1 and vice versa4 ,for example1 it being admitted that culture is good1 a disputant goes on to argue as if the admission applied to some sort of culture in special1 scientific1 aesthetic1 philosophical or moral4 ,the fallacy was also known as ,fallacia ,accidentis4 ,proving that the ,syllogism is useless for a certain purpose1 and then claiming to have proved that it is useless for any purpose is another example4 ,getting a limited admission and then extending it indefinitely is perhaps the more common of the two forms4 ,it is common enough to deserve a shorter name4 ,the ,fallacia ,consequentis1 or ,non-,sequitur1 which consists specially in ignoring the possibility of a plurality of causes1 has already been partly explained in connexion with the ,hypothetical ,syllogism1 and will be explained further in the ,logic of ,induction4 ,post hoc ergo proper hoc is a purely ,inductive ,fallacy1 and will be explained in connexion with the ,experimental ,methods4 ,there remain the two typical ,deductive ,fallacies1 ,,petitio ,,principii 7,surreptitious ,assumption7 and ,,ignoratio ,,elenchi 7,irrelevant ,argument7 about which we must speak more at length4 ,the phrase of which ,petitio ,principii or ,begging the ,question is a translation--,greek3 to en arche aiteisthai--was applied by ,aristotle to an argumentative trick in debate by ,question and ,answer4 ,the trick consisted in taking for granted a proposition necessary to the refutation without having obtained the admission of it4 ,another expression for the same thing--,greek3 to en arche lambanein--taking the principle for granted--is more descriptive4 ,generally speaking1 ,aristotle says1 ,begging the ,question consists in not demonstrating the theorem4 ,it would be in accordance with this general description to extend the name to all cases of tacitly or covertly1 unwittingly to oneself or to one's opponent1 assuming any premiss necessary to the conclusion4 ,it is the fallacy of ,surreptitious ,assumption1 and all cases of ,enthymematic or ,elliptical argument1 where the unexpressed links in the chain of argument are not fully understood1 are examples of it4 ,by contrast1 the articulate and explicit ,syllogism is an ,expositio ,principii4 ,the only remedy for covert assumptions is to force them into the light4#a ,ignoratio ,elenchi1 ignoring the refutation 7,greek3 tou elenchou agnoia71 is simply arguing beside the point1 distracting the attention by irrelevant considerations4 ,it often succeeds by proving some other conclusion which is not the one in dispute1 but has a superficial resemblance to it1 or is more or less remotely connected with it4 ,it is easier to explain what these fallacies consist in than to illustrate them convincingly4 ,it is chiefly in long arguments that the mischief is done4 ,a ,fallacy1 says ,whately1 which when stated barely in a few sentences would not deceive a child1 may deceive half the world if diluted in a quarto volume4 ,very rarely is a series of propositions put before us in regular form and order1 all bearing on a definite point4 ,a certain conclusion is in dispute1 not very definitely formulated perhaps1 and a mixed host of considerations are tumbled out before us4 ,if we were perfectly clear-headed persons1 capable of protracted concentration of attention1 incapable of bewilderment1 always on the alert1 never in a hurry1 never over-excited1 absolutely without prejudice1 we should keep our attention fixed upon two things while listening to an argument1 the point to be proved1 and the necessary premisses4 ,we should hold the point clearly in our minds1 and watch indefatigably for the corroborating propositions4 ,but none of us being capable of this1 all of us being subject to bewilderment by a rapid whirl of statements1 and all of us biased more or less for or against a conclusion1 the sophist has facilities for doing two things--taking for granted that he has stated the required premisses 7petitio principii71 and proving to perfect demonstration something which is not the point in dispute1 but which we are willing to mistake for it 7ignoratio elenchi74 ,it is chiefly in the heat of argument that either ,petitio or ,ignoratio succeeds4 ,when a fallacy continues to perplex us in cold blood1 it must have in its favour either some deeply-rooted prejudice or some peculiar intricacy in the language used1 or some abstruseness in the matter4 ,if we are not familiar with the matter of the argument1 and have but a vague hold of the words employed1 we are1 of course1 much more easily imposed upon4 ,the famous ,sophisms of antiquity show the fascination exercised over us by proving something1 no matter how irrelevant4 ,if certain steps in an argument are sound1 we seem to be fascinated by them so that we cannot apply our minds to the error1 just as our senses are fascinated by an expert juggler4 ,we have seen how plausibly ,zeno's argument against the possibility of motion hides a ,petitio3 the ,fatalist ,dilemma is another example of the same sort4 ,if it is fated that you die1 you will die whether you call in a doctor or not1 and if it is fated that you will recover1 you will recover whether you call in a doctor or not4 ,but it must be fated either that you die or that you recover4 ,therefore1 you will either die or recover whether you call in a doctor or not4 ,here it is tacitly assumed in the ,major ,premiss that the calling in of a doctor cannot be a link in the fated chain of events4 ,in the statement of both the alternative conditions1 it is assumed that ,fate does not act through doctors1 and the conclusion is merely a repetition of this assumption1 a verbal proposition after an imposing show of argument4 ,if ,fate does not act through doctors1 you will die whether you call in a doctor or not4 ,the fallacy in this case is probably aided by our veneration for the grand abstraction of ,fate and the awful idea of ,death1 which absorbs our attention and takes it away from the artful ,petitio4 ,the ,sophism of ,achilles and the ,tortoise is the most triumphant of examples of ,ignoratio ,elenchi4 ,the point that the ,sophism undertakes to prove is that ,achilles can never overtake a ,tortoise once it has a certain start3 what it really proves1 and proves indisputably1 is that he cannot overtake the ,tortoise within a certain space or time4 ,for simplicity of exposition1 let us assume that the ,tortoise has #ajj yards start and that ,achilles runs ten times as fast4 ,then1 clearly1 ,achilles will not come up with it at the end of #ajj yards1 for while he has run #ajj1 the ,tortoise has run #aj2 nor at the end of #aaj1 for then the ,tortoise has run #a more2 nor at the end of #aaa1 for then the ,tortoise has run #a_/aj more2 nor at the end of #aaa--a_/aj1 for then the ,tortoise has gained #a_/ajj more4 ,so while ,achilles runs this #a_/ajj1 the ,tortoise runs #a_/ajjj2 while he runs the #a_/ajjj1 it runs #a_/ajjjj4 ,thus it would seem that the ,tortoise must always keep ahead3 he can never overtake it4 ,but the conclusion is only a confusion of ideas3 all that is really proved is that ,achilles will not overtake the ,tortoise while running #ajj #aj #a #a_/aj #a_/ajj #a_/ajjj #a_/ajjjj1 etc4 ,that is1 that he will not overtake it till he has completed the sum of this series1 #aaa-a_/i yards4 ,to prove this is an ignoratio elenchi2 what the ,sophist undertakes to prove is that ,achilles will never overtake it1 and he really proves that ,achilles passes it between the #aaath and #aabth yards4 ,the exposure of this sophism is an example also of the value of a technical term4 ,all attempts to expose it without using the term ,ignoratio ,elenchi or something equivalent to it1 succeed only in bewildering the student4 ,it is customary to say that the root of the fallacy lies in assuming that the sum of an infinite series is equal to infinity4 ,this profound error may be implied3 but if any assumption so hard to understand were really required1 the fallacy would have little force with the generality4 ,it has often been argued that the ,syllogism involves a petitio principii1 because the ,major ,premiss contains the ,conclusion1 and would not be true unless the ,conclusion were true4 ,but this is really an ,ignoratio ,elenchi4 ,the fact adduced1 that the ,major ,premiss contains the ,conclusion1 is indisputable2 but this does not prove the ,syllogism guilty of ,petitio4 ,petitio principii is an argumentative trick1 a conscious or unconscious act of deception1 a covert assumption1 and the ,syllogism1 so far from favouring this1 is an expositio principii1 an explicit statement of premisses such that1 if they are true1 the conclusion is true4 ,the ,syllogism merely shows the interdependence of premisses and conclusion2 its only tacit assumption is the ,dictum de ,omni4 ,if1 indeed1 an opponent challenges the truth of the conclusion1 and you adduce premisses necessarily containing it as a refutation1 that is an ignoratio elenchi unless your opponent admits those premisses4 ,if he admits them and denies the conclusion1 you convict him of inconsistency1 but you do not prove the truth of the conclusion4 ,suppose a man to take up the position3 ,i am not mortal1 for ,i have procured the elixir vitae4 ,you do not disprove this by saying1 ,all men are mortal1 and you are a man4 ,in denying that he is mortal1 he denies that all men are mortal4 ,whatever is sufficient evidence that he is not mortal1 is sufficient evidence that all men are not mortal4 ,perhaps it might be said that in arguing1 ,all men are mortal1 and you are a man1 it is not so much ignoratio elenchi as petitio principii that you commit4 ,but be it always remembered that you may commit both fallacies at once4 ,you may both argue beside the point and beg the question in the course of one and the same argument4 ,footnote #a3 ,cp4 ,mr4 ,sidgwick's instructive treatise on ,fallacies1 ,international ,scientific ,series1 p4 #aii4 ,,chapter ,,ix4 ,,formal ,,or ,,aristotelian ,,induction4--,,inductive ,,argument4 ,the distinction commonly drawn between ,deduction and ,induction is that ,deduction is reasoning from general to particular1 and ,induction reasoning from particular to general4 ,but it is really only as modes of argumentation that the two processes can be thus clearly and fixedly opposed4 ,the word ,induction is used in a much wider sense when it is the title of a treatise on the ,methods of ,scientific ,investigation4 ,it is then used to cover all the processes employed in man's search into the system of reality2 and in this search deduction is employed as well as induction in the narrow sense4 ,we may call ,induction in the narrow sense ,formal ,induction or ,inductive ,argument1 or we may simply call it ,aristotelian ,induction inasmuch as it was the steps of ,inductive argument that ,aristotle formulated1 and for which he determined the conditions of validity4 ,let us contrast it with ,deductive argument4 ,in this the questioner's procedure is to procure the admission of a general proposition with a view to forcing the admission of a particular conclusion which is in dispute4 ,in ,inductive argument1 on the other hand1 it is a general proposition that is in dispute1 and the procedure is to obtain the admission of particular cases with a view to forcing the admission of this general proposition4 ,let the question be whether ,all horned animals ruminate4 ,you engage to make an opponent admit this4 ,how do you proceed8 ,you ask him whether he admits it about the various species4 ,does the ox ruminate8 ,the sheep8 ,the goat8 ,and so on4 ,the bringing in of the various particulars is the induction 7,greek3 epagoge74 ,when is this inductive argument complete8 ,when is the opponent bound to admit that all horned animals ruminate8 ,obviously1 when he has admitted it about every one4 ,he must admit that he has admitted it about every one1 in other words1 that the particulars enumerated constitute the whole1 before he can be held bound in consistency to admit it about the whole4 ,the condition of the validity of this argument is ultimately the same with that of ,deductive argument1 the identity for purposes of predication of a generic whole with the sum of its constituent parts4 ,the ,axiom of ,inductive ,argument is1 ,what is predicated of every one of the parts is predicable of the whole4 ,this is the simple converse of the ,axiom of ,deductive argument1 the ,dictum de ,omni1 ,what is predicated of the whole is predicable about every one of the parts4 ,the ,axiom is simply convertible because for purposes of predication generic whole and specific or individual parts taken all together are identical4 ,practically in inductive argument an opponent is worsted when he cannot produce an instance to the contrary4 ,suppose he admits the predicate in question to be true of this1 that and the other1 but denies that this1 that and the other constitute the whole class in question1 he is defeated in common judgement if he cannot instance a member of the class about which the predicate does not hold4 ,hence this mode of induction became technically known as ,inductio per enumerationem simplicem ubi non reperitur instantia contradictoria4 ,when this phrase is applied to a generalisation of fact1 ,nature or ,experience is put figuratively in the position of a ,respondent unable to contradict the inquirer4 ,such in plain language is the whole doctrine of ,inductive ,argument4 ,aristotle's ,inductive ,syllogism is1 in effect1 an expression of this simple doctrine tortuously in terms of the ,deductive ,syllogism4 ,the great master was so enamoured of his prime invention that he desired to impress its form upon everything3 otherwise1 there was no reason for expressing the process of ,induction syllogistically4 ,here is his description of the ,inductive ,syllogism3-- ,induction1 then1 and the ,inductive ,syllogism1 consists in syllogising one extreme with the middle through the other extreme4 ,for example1 if ,b is middle to ,a and ,c1 to prove through ,c that ,a belongs to ,b4#a ,this may be interpreted as follows3 ,suppose a general proposition is in dispute1 and that you wish to make it good by obtaining severally the admission of all the particulars that it sums up4 ,the type of a general proposition in ,syllogistic terminology is the ,major ,premiss1 ,all ,m is ,p4 ,what is the type of the particulars that it sums up8 ,obviously1 the ,conclusion1 ,s is ,p4 ,this particular is contained in the ,major ,premiss1 ,all ,m is ,p2 its truth is accepted as contained in the truth of ,all ,m is ,p4 ,s is one of the parts of the generic whole ,m2 one of the individuals or species contained in the class ,m4 ,if you wish1 then1 to establish ,p of ,all ,m by ,induction1 you must establish ,p of all the parts1 species1 or individuals contained in ,m1 that is1 of all possible ,ss3 you must make good that this1 that and the other ,s is ,p1 and also that this1 that and the other ,s constitute the whole of ,m4 ,you are then entitled to conclude that ,all ,m is ,p3 you have syllogised one ,extreme with the ,middle through the other ,extreme4 ,the formal statement of these premisses and conclusion is the ,inductive ,syllogism4 ,this1 that and the other ,s is ,p1 ,major4 ,this1 that and the other ,s is all ,m1 ,minor4 4'4 ,all ,m is ,p1 ,conclusion4 ,this1 that and the other magnet 7i4e41 magnets individually7 attract iron4 ,this1 that and the other magnet 7i4e41 the individuals separately admitted7 are all magnets4 4'4 ,all magnets attract iron4 ,this1 that and the other ,s being simply convertible with ,all ,m1 you have only to make this conversion and you have a syllogism in ,barbara where this1 that and the other ,s figures as the ,middle ,term4 ,the practical value of this tortuous expression is not obvious4 ,mediaeval logicians shortened it into what was known as the ,inductive ,enthymeme3 ,this1 that and the other1 therefore all1 an obvious conclusion when this1 that and the other constitute all4 ,it is merely an evidence of the great master's intoxication with his grand invention4 ,it is a proof also that ,aristotle really looked at ,induction from the point of view of ,interrogative ,dialectic4 ,his question was1 ,when is a ,respondent bound to admit a general conclusion8 ,and his answer was1 ,when he has admitted a certain number of particulars1 and cannot deny that those particulars constitute the whole whose predicate is in dispute4 ,he was not concerned primarily with the analysis of the steps of an inquirer generalising from ,nature4 ,footnote #a3 ,greek3 epagoge men oun esti kai ho ex epagoges syllogismos to dia tou eterou thateron akron to meso syllogisasthai2 ,oion ei ton ,a ,g meson to ,b1 dia tou ,g deixai to ,a to ,b hyparchon4 7,an4 ,prior41 ii4 #bc47 ,,book ,,ii4 ,,inductive ,,logic1 ,,or ,,the ,,logic ,,of ,,science4 ,,introduction4 ,perhaps the simplest way of disentangling the leading features of the departments of ,logic is to take them in relation to historical circumstances4 ,these features are writ large1 as it were1 in history4 ,if we recognise that all bodies of doctrine have their origin in practical needs1 we may conceive different ages as controlled each by a distinctive spirit1 which issues its mandate to the men of the age1 assigning to them their distinctive work4 ,the mandate issued to the age of ,plato and ,aristotle was ,bring your beliefs into harmony one with another4 ,the ,aristotelian ,logic was framed in response to this order3 its main aim was to devise instruments for making clear the coherence1 the concatenation1 the mutual implication of current beliefs4 ,the mandate of the ,mediaeval ,spirit was ,bring your beliefs into harmony with dogma4 ,the mediaeval logic was contracted from ,aristotle's under this impulse4 ,induction as conceived by him was neglected1 allowed to dwindle1 almost to disappear from ,logic4 ,greater prominence was given to ,deduction4 ,then as ,dogmatic ,authority became aggressive1 and the ,church through its officials claimed to pronounce on matters outside ,theology1 a new spirit was roused1 the mandate of which was1 ,bring your beliefs into harmony with facts4 ,it was under this impulse that a body of methodical doctrine vaguely called ,induction gradually originated4 ,in dealing with the genesis of the ,old ,logic1 we began with ,aristotle4 ,none can dispute his title to be called its founder4 ,but who was the founder of the ,new ,logic8 ,in what circumstances did it originate8 ,the credit of founding ,induction is usually given to ,francis ,bacon1 ,lord ,verulam4 ,that great man claimed it for himself in calling his treatise on the ,interpretation of ,nature the ,novum ,organum4 ,the claim is generally conceded4 ,reid's account of the matter represents the current belief since ,bacon's own time4 ,after man had laboured in the search of truth near two thousand years by the help of ,syllogisms1 ,lord ,bacon proposed the method of ,,induction as a more effectual engine for that purpose4 ,his ,novum ,organum gave a new turn to the thoughts and labours of the inquisitive1 more remarkable and more useful than that which the ,organon of ,aristotle had given before1 and may be considered as a second grand era in the progress of human nature4444 ,most arts have been reduced to rules after they had been brought to a considerable degree of perfection by the natural sagacity of artists2 and the rules have been drawn from the best examples of the art that had been before exhibited2 but the art of philosophical induction was delineated by ,lord ,bacon in a very ample manner before the world had seen any tolerable example of it4#a ,there is a radical misconception here1 which1 for reasons that ,i hope to make plain1 imperatively needs to be cleared up4 ,it obscures the very essence of philosophical induction4 ,there are three ways in which movement in any direction may be helped forward1 ,exhortation1 ,example1 and ,precept4 ,exhortation3 a man may exhort to the practice of an art and thereby give a stimulus4 ,example3 he may practise the art himself1 and show by example how a thing should be done4 ,precept3 he may formulate a clear method1 and so make plain how to do it4 ,let us see what was ,bacon's achievement in each of those three ways4 ,undoubtedly ,bacon's powerful eloquence and high political position contributed much to make the study of ,nature fashionable4 ,he was high in place and great in intellect1 one of the commanding personalities of his time4 ,taking all knowledge for his province1 though study was really but his recreation1 he sketched out a plan of universal conquest with a clearness and confidence that made the mob eager to range themselves under his leadership4 ,he was the magnificent demagogue of science4 ,there had been champions of ,induction before him1 but they had been comparatively obscure and tongue-tied4 ,while1 however1 we admit to the full the great services of this mighty advocate in making an ,inductive method popular1 we should not forget that he had pioneers even in hortatory leadership4 ,his happiest watchword1 the ,interpretation of ,nature1 as distinguished from the ,interpretation of ,authoritative ,books1 was not of his invention4 ,if we read ,whewell's ,history of the ,inductive ,sciences1 we shall find that many before him had aspired to give a new turn to the labors of the inquisitive1 and in particular to substitute inquisition for disquisition4 ,one might compile from ,whewell a long catalogue of eminent men before ,bacon who held that the study of ,nature was the proper work of the inquisitive3 ,leonardo da ,vinci 7#adeb-aeai71 one of the wonders of mankind for versatility1 a miracle of excellence in many things1 painter1 sculptor1 engineer1 architect1 astronomer1 and physicist2 ,copernicus 7#adgc-aedc71 the author of the ,heliocentric theory2 ,telesius 7#aejh-aehh71 a theoretical reformer1 whose ,de ,rerum ,natura 7#aefe7 anticipated not a little of the ,novum ,organum2 ,cesalpinus 7#aebj-afjc71 the ,botanist2 ,gilbert 7#aedj-afjc71 the investigator of ,magnetism4 ,by all these men experiment and observation were advocated as the only way of really increasing knowledge4 ,they all derided mere book-learning4 ,the conception of the world of sense as the original ,,ms4 of which systems of philosophy are but copies1 was a familiar image with them4 ,so also was ,bacon's epigrammatic retort to those who wish to rest on the wisdom of the ancients1 that antiquity is the youth of the world and that we are the true ancients4 ,we are older1 said ,giordano ,bruno1 and have lived longer than our predecessors4 ,this last argument1 indeed1 is much older than the sixteenth century4 ,it was used by the ,doctor ,mirabilis of the thirteenth1 the ,franciscan ,friar1 ,roger ,bacon 7#abad-abib74 ,the later men are1 the more enlightened they are2 and wise men now are ignorant of much the world will some day know4 ,the truth is that if you are in search of a ,father for ,inductive ,philosophy1 the mediaeval friar has better claims than his more illustrious namesake4 ,his enthusiasm for the advancement of learning was not less nobly ambitious and far-reaching1 and he was himself an ardent experimenter and inventor4 ,his ,opus ,majus--an eloquent outline of his projects for a new learning1 addressed in #abfe to ,pope ,clement ,,iv41 through whom he offered to give to the ,church the empire of the world as ,aristotle had given it to ,alexander--was almost incredibly bold1 comprehensive and sagacious4 ,fixing upon ,authority1 ,custom1 ,popular ,opinion1 and the ,pride of ,supposed ,knowledge1 as the four causes of human ignorance1 he urged a direct critical study of the ,scriptures1 and after an acute illustration of the usefulness of ,grammar and ,mathematics 7widely interpreted71 concluded with ,experimental ,science as the great source of human knowledge4 ,i have already quoted 7p4 #ae7 the ,friar's distinction between the two modes of ,knowing1 ,argument and ,experience1 wherein he laid down that it is only experience that makes us feel certain4 ,it were better1 he cried in his impatience1 to burn ,aristotle and make a fresh start than to accept his conclusions without inquiry4 ,experimental ,science1 the sole mistress of ,speculative ,science1 has three great ,prerogatives among other parts of ,knowledge4 ,first1 she tests by experiment the noblest conclusions of all other sciences4 ,next1 she discovers respecting the notions which other sciences deal with1 magnificent truths to which these sciences can by no means attain4 ,her third dignity is that she by her own power and without respect to other sciences investigates the secret of ,nature4 ,so far1 then1 as ,exhortation goes1 ,king ,james's great lawyer and statesman was not in advance of ,pope ,clement's friar4 ,their first principle was the same4 ,it is only by facts that theories can be tested4 ,man must not impose his own preconceptions 7anticipationes mentis7 on nature4 ,man is only the interpreter of nature4 ,both were also at one in holding that the secrets of nature could not be discovered by discussion1 but only by observation and experiment4 ,francis ,bacon1 however1 went beyond all his predecessors in furnishing an elaborate ,method for the interpretation of ,nature4 ,when he protested against the intellect's being left to itself 7intellectus sibi permissus71 he meant more than speculation left unchecked by study of the facts4 ,he meant also that the interpreter must have a method4 ,as man1 he says1 cannot move rocks by the mere strength of his hands without instruments1 so he cannot penetrate to the secrets of ,nature by mere strength of his intellect without instruments4 ,these instruments he undertakes to provide in his ,inductive ,method or ,novum ,organum4 ,and it is important to understand precisely what his methods were1 because it is on the ground of them that he is called the founder of ,inductive ,philosophy1 and because this has created a misapprehension of the methods actually followed by men of science4 ,ingenious1 penetrating1 wide-ranging1 happy in nomenclature1 the ,novum ,organum is a wonderful monument of the author's subtle wit and restless energy2 but1 beyond giving a general impulse to testing speculative fancies by close comparison with facts1 it did nothing for science4 ,his method--with its ,tables of ,preliminary ,muster for the ,intellect 7tabulae comparentiae primae instantiarum ad intellectum1 facts collected and methodically arranged for the intellect to work upon72 its ,elimination upon first inspection of obviously accidental concomitants 7,rejectio sive ,exclusiva naturarum72 its ,provisional ,hypothesis 7,vindemiatio ,prima sive ,interpretatio ,inchoata72 its advance to a true ,induction or final ,interpretation by examination of special instances 7he enumerates twenty-seven1 #c x #c x #c1 ,prerogativas ,instantiarum1 trying to show the special value of each for the inquirer7#b--was beautifully regular and imposing1 but it was only a vain show of a method4 ,it was rendered so chiefly by the end or aim that ,bacon proposed for the inquirer4 ,in this he was not in advance of his age2 on the contrary1 he was probably behind ,roger ,bacon1 and certainly far behind such patient and concentrated thinkers as ,copernicus1 ,gilbert1 and ,galileo--no discredit to the grandeur of his intellect when we remember that science was only his recreation1 the indulgence of his leisure from ,law and ,state4 ,in effect1 his method came to this4 ,collect as many instances as you can of the effect to be investigated1 and the absence of it where you would expect it1 arrange them methodically1 then put aside guesses at the cause which are obviously unsuitable1 then draw up a probably explanation1 then proceed to make this exact by further comparison with instances4 ,it is when we consider what he directed the inquirer to search for that we see why so orderly a method was little likely to be fruitful4 ,he starts from the principle that the ultimate object of all knowledge is use1 practice 7scimus ut operemur74 ,we want to know how ,nature produces things that we may produce them for ourselves1 if we can4 ,the inquirer's first aim1 therefore1 should be to find out how the qualities of bodies are produced1 to discover the formae or formal causes of each quality4 ,an example shows what he meant by this4 ,gold is a crowd or conjugation of various qualities or natures2 it is yellow1 it has a certain weight1 it is malleable or ductile to a certain degree1 it is not volatile 7loses nothing under fire71 it can be melted1 it is soluble4 ,if we knew the forma or formal cause of each of those qualities1 we could make gold1 provided the causes were within our control4 ,the first object1 then1 of the investigator of ,nature is to discover such formae1 in order to be able to effect the transformation of bodies4 ,it may be desirable also to know the latens processus1 any steps not apparent to the senses by which a body grows from its first germs or rudiments1 and the schematismus or ultimate inner constitution of the body4 ,but the discovery of the formae of the constituent qualities 7naturae singulae71 heat1 colour1 density or rarity1 sweetness1 saltness1 and so forth1 is the grand object of the ,interpreter of ,nature2 and it is for this that ,bacon prescribed his method4 ,the ,sylva ,sylvarum1 or ,natural ,history1 a miscellaneous collection of facts and fictions1 observations and traditions1 with guesses at the explanation of them1 affords us a measure of ,bacon's own advancement as an interpreter of ,nature4 ,it was a posthumous work1 and the editor1 his secretary1 tells us that he often said that if he had considered his reputation he would have withheld it from the world1 because it was not digested according to his own method3 yet he persuaded himself that the causes therein assigned were far more certain than those rendered by others1 not for any excellence of his own wit1 but in respect of his continual conversation with ,nature and ,experience1 and mankind might stay upon them till true ,axioms were more fully discovered4 ,when1 however1 we examine the causes assigned1 we find that in practice ,bacon could not carry out his own precepts3 that he did not attempt to creep up to an explanation by slow and patient ascent1 but jumped to the highest generalisations3 and that his explanatory notions were taken not from nature1 but from the ordinary traditions of mediaeval physical science4 ,he deceived himself1 in short1 in thinking that he could throw aside tradition and start afresh from observation4 ,for example4 ,he is struck by the phenomenon of bubbles on water3 ,it seemeth somewhat strange that the air should rise so swiftly1 while it is in the water1 and when it cometh to the top should be stayed by so weak a cover as that of the bubble is4 ,the swift ascent of the air he explains as a motion of percussion1 the water descending and forcing up the air1 and not a motion of levity in the air itself4 ,the cause of the enclosure of the bubble is for that the appetite to resist separation or discontinuance1 which is strong in solids1 is also in liquors1 though fainter and weaker4 ,the same reason is of the roundness of the bubble1 as well for the skin of water as for the air within4 ,for the air likewise avoideth discontinuance1 and therefore casteth itself into a round figure4 ,and for the stop and arrest of the air a little while1 it showeth that the air of itself hath little or no appetite of ascending4#c ,these notions were not taken direct from the facts3 they descended from ,aristotle4 ,he differs from ,aristotle1 however1 in his explanation of the colours of birds' feathers4 ,aristotle giveth the cause vainly that birds are more in the beams of the sun than beasts4 ,but that is manifestly untrue2 for cattle are more in the sun than birds1 that live commonly in the woods or in some covert4 ,the true cause is that the excrementitious moisture of living creatures1 which maketh as well the feathers in birds as the hair in beasts1 passeth in birds through a finer and more delicate strainer than it doth in beasts4 ,for feathers pass through quills1 and hair through skin4 ,it is an instance of percolation or filtering3 other effects of the same cause being the gums of trees1 which are but a fine passage or straining of the juice through the wood and bark1 and ,cornish ,diamonds and ,rock ,rubies1 which are in like manner fine exudations of stone4#d ,these examples of ,bacon's ,inductions are taken from the ,sylva at random4 ,but the example which best of all illustrates his attitude as a scientific investigator is the remark he makes in the ,novum ,organum about the ,copernican theory4 ,elsewhere he says that there is nothing to choose between it and the ,ptolemaic2 and in the ,novum ,organum 7lib4 ii4 #e7 he remarks that no one can hope to terminate the question whether in diurnal motion it is really the earth or the sky that rotates1 unless he shall first have comprehended the nature of spontaneous rotation4 ,that is1 we must first find out the forma or formal cause of spontaneous rotation4 ,this is a veritable instantia crucis1 as fixing ,bacon's place in the mediaeval and not in the new world of scientific speculation4 ,bacon1 in short1 in the practice of induction did not advance an inch beyond ,aristotle4 ,rather he retrograded1 inasmuch as he failed to draw so clear a line between the respective spheres of ,inductive collection of facts and ,explanation4 ,there are two sources of general propositions1 according to ,aristotle1 ,induction and ,nous4 ,by ,induction he meant the generalisation of facts open to sense1 the summation of observed particulars1 the inductio per enumerationem simplicem of the schoolmen4 ,by ,nous he meant the ,reason or ,speculative ,faculty1 as exercised with trained sagacity by experts4 ,thus by ,induction we gather that all horned animals ruminate4 ,the explanation of this is furnished by the ,nous1 and the explanation that commended itself to the trained sagacity of his time was that ,nature having but a limited amount of hard material and having spent this on the horns1 had none left for teeth1 and so provided four stomachs by way of compensation4 ,bacon's guesses at causes are on the same scientific level with this1 only he rather confused matters by speaking of them as if they were inductions from fact1 instead of being merely fancies superinduced upon fact4 ,his theory of interpretation1 it is true1 was so far an advance that he insisted on the necessity of verifying every hypothesis by further appeal to facts1 though in practice he himself exercised no such patience and never realised the conditions of verification4 ,against this1 again1 must be set the fact that by calling his method induction1 and laying so much stress on the collection of facts1 he fostered1 and1 indeed1 fixed in the public mind the erroneous idea that the whole work of science consists in observation4 ,the goal of science1 as ,herschel said1 is ,explanation1 though every explanation must be made to conform to fact1 and explanation is only another term for attaining to higher generalisations1 higher unities4 ,the truth is that ,induction1 if that is the name we use for scientific method1 is not1 as ,reid conceived1 an exception to the usual rule of arts in being the invention of one man4 ,bacon neither invented nor practised it4 ,it was perfected gradually in the practice of men of science4 ,the birthplace of it as a conscious method was in the discussions of the ,royal ,society of ,london1 as the birthplace of the ,aristotelian ,logic was in the discussions of the ,athenian schools4 ,its first great triumph was ,newton's law of ,gravitation4 ,if we are to name it after its first illustrious practitioner1 we must call it the ,newtonian method1 not the ,baconian4 ,newton really stands to the ,scientific ,method of ,explanation as ,aristotle stands to the ,method of ,dialectic and ,deduction4 ,he partly made it explicit in his ,regulae ,philosophandi 7#afhe74 ,locke1 his friend and fellow-member of the ,royal ,society1 who applied the method to the facts of ,mind in his ,essay ,concerning ,human ,understanding 7#afia71 made it still further explicit in the ,fourth ,book of that famous work4 ,it was1 however1 a century and a half later that an attempt was first made to incorporate scientific method with ,logic under the name of ,induction1 and add it as a new wing to the old ,aristotelian building4 ,this was the work of ,john ,stuart ,mill1 whose ,system of ,logic1 ,deductive and ,inductive1 was first published in #ahdc4 ,the genesis of ,mill's ,system of ,logic1 as of other things1 throws light upon its character4 ,and in inquiries into the genesis of anything that man makes we may profitably follow ,aristotle's division of causes4 ,the ,efficient ,cause is the man himself1 but we have also to find out the ,final ,cause1 his object or purpose in making the thing1 the ,material ,cause1 the sources of his material1 and the ,formal ,cause1 the reason why he shaped it as he did4 ,in the case of ,mill's system we have to ask3 ,what first moved him to formulate the methods of scientific investigation8 ,whence did he derive his materials8 ,why did he give his scientific method the form of a supplement to the old ,aristotelian ,logic8 ,we cannot absolutely separate the three inquiries1 but motive1 matter and form each had a traceable influence on the leading features of his ,system4 ,first1 then1 as to his motive4 ,it is a mistake to suppose that ,mill's object was to frame an organon that might assist men of science as ordinarily understood in making discoveries4 ,bacon1 his secretary tells us1 was wont to complain that he should be forced to be a ,workman and a ,labourer in science when he thought he deserved to be an ,architect in this building4 ,and men of science have sometimes rebuked ,mill for his presumption in that1 not being himself an investigator in any department of exact science1 he should volunteer to teach them their business4 ,but ,mill was really guilty of no such presumption4 ,his object1 on the contrary1 was to learn their method with a view to its application to subjects that had not yet undergone scientific treatment4 ,briefly stated1 his purpose was to go to the practical workers in the exact sciences1 ,astronomy1 ,chemistry1 ,heat1 ,light1 ,electricity1 ,molar and ,molecular ,physics2 ascertain1 not so much how they made their discoveries as how they assured themselves and others that their conclusions were sound2 and having ascertained their tests of truth and principles of proof1 to formulate these tests so that they might be applied to propositions outside the range of the exact sciences1 propositions in ,politics1 ,ethics1 ,history1 ,psychology4 ,more particularly he studied how scientific men verify1 and when they accept as proved1 propositions of causation1 explanations of the causes of things4 ,in effect1 his survey of scientific method was designed to lead up to the ,sixth ,book in his ,system1 the ,logic of the ,moral ,sciences4 ,there are multitudes of floating endoxes or current opinions concerning man and his concerns1 assigning causes for the conduct and character of individuals and of communities4 ,mill showed himself quite aware that the same modes of investigation may not be practicable1 and that it may not be possible1 though men are always ready to assign causes with confidence1 to ascertain causes with the same degree of certainty3 but at least the conditions of exact verification should be the same1 and it is necessary to see what they are in order to see how far they can be realised4 ,that such was ,mill's design in the main is apparent on internal evidence1 and it was the internal evidence that first struck me4 ,but there is external evidence as well4 ,we may first adduce some essays on the ,spirit of the ,age1 published in the ,examiner in #ahca1 essays which drew from ,carlyle the exclamation1 ,here is a new ,mystic6 ,these essays have never been republished1 but they contain ,mill's first public expression of the need for a method in social inquiries4 ,he starts from the ,platonic idea that no state can be stable in which the judgment of the wisest in political affairs is not supreme4 ,he foresees danger in the prevalent anarchy of opinion4 ,how is it to be averted8 ,how are men to be brought to accept loyally the judgment of the expert in public affairs8 ,they accept at once and without question the decisions of the specially skilled in the physical sciences4 ,why is this8 ,for one reason1 because there is complete agreement among experts4 ,and why is there this complete agreement8 ,because all accept the same tests of truth1 the same conditions of proof4 ,is it not possible to obtain among political investigators similar unanimity as to their methods of arriving at conclusions1 so as to secure similar respect for their authority8 ,we need not stop to ask whether this was a vain dream1 and whether it must not always be the case that to ensure confidence in a political or moral adviser more is needed than faith in his special knowledge and trained sagacity4 ,our point is that in #ahca ,mill was in search of a method of reasoning in social questions4 ,opportunely soon after1 early in #ahcb1 was published ,herschel's ,discourse on the ,study of ,natural ,philosophy1 the first attempt by an eminent man of science to make the methods of science explicit4 ,mill reviewed this book in the ,examiner1 and there returns more definitely to the quest on which he was bent4 ,the uncertainty1 he says1 that hangs over the very elements of moral and social philosophy proves that the means of arriving at the truth in those sciences are not yet properly understood4 ,and whither can mankind so advantageously turn1 in order to learn the proper means and to form their minds to the proper habits1 as to that branch of knowledge in which by universal acknowledgment the greatest number of truths have been ascertained and the greatest possible degree of certainty arrived at8 ,we learn from ,mill himself that he made an attempt about this time1 while his mind was full of ,herschel's ,discourse1 to connect a scientific method with the body of the ,old ,logic4 ,but he could not make the junction to his satisfaction1 and abandoned the attempt in despair4 ,a little later1 in #ahcg1 upon the appearance of ,whewell's ,history of the ,inductive ,sciences1 he renewed it1 and this time with happier results4 ,whewell's ,philosophy of the ,inductive ,sciences was published in #ahdj1 but by that time ,mill's system was definitely shaped4 ,it was1 then1 to ,herschel and ,whewell1 but especially to the former1 that ,mill owed the raw materials of his ,inductive ,method4 ,but why did he desire to concatenate this with the old ,logic8 ,probably because he considered that this also had its uses for the student of society1 the political thinker4 ,he had inherited a respect for the old ,logic from his father4 ,but it was the point at which he sought to connect the new material with the old1 the point of junction between the two1 that determined the form of his system4 ,we find the explanation of this in the history of the old ,logic4 ,it so happened that ,whately's ,logic was in the ascendant1 and ,whately's treatment of ,induction gives the key to ,mill's4 ,towards the end of the first quarter of this century there was a great revival of the study of ,logic at ,oxford4 ,the study had become mechanical1 ,aldrich's ,compendium1 an intelligent but exceedingly brief abstract of the ,scholastic ,logic1 being the text-book beyond which no tutor cared to go4 ,the man who seems to have given new life to the study was a tutor who subsequently became ,bishop of ,llandaff1 ,edward ,copleston4 ,the first public fruits of the revival begun by him was ,whately's article on ,logic in the ,encyclopaedia ,metropolitana1 published as a separate book in #ahbg4 ,curiously enough1 one of ,whately's most active collaborators in the work was ,john ,henry ,newman1 so that the common room of ,oriel1 which ,mr4 ,froude describes as the centre from which emanated the ,high ,church ,movement1 may also be said to have been the centre from which emanated the movement that culminated in the revolution of ,logic4 ,the publication of ,whately's ,logic made a great stir4 ,it was reviewed by ,mill1 then a young man of twenty-one1 in the ,westminster ,review 7#ahbh71 and by ,hamilton1 then forty-five years of age1 in the ,edinburgh 7#ahcc74 ,there can be no doubt that it awakened ,mill's interest in the subject4 ,a society formed for the discussion of philosophical questions1 and called the ,speculative ,society1 met at ,grote's house in #ahbe1 and for some years following4 ,of this society young ,mill was a member1 and their continuous topic in #ahbg was ,logic1 ,whately's treatise being used as a sort of text-book4 ,it is remarkable that ,mill's review of ,whately1 the outcome of these discussions1 says very little about ,induction4 ,at that stage ,mill's chief concern seems to have been to uphold the usefulness of ,deductive ,logic1 and he even goes so far as to scoff at its eighteenth century detractors and their ambition to supersede it with a system of ,induction4 ,the most striking feature of the article is the brilliant defence of the ,syllogism as an analysis of arguments to which ,i have already referred4 ,he does not deny that an ,inductive ,logic might be useful as a supplement1 but apparently he had not then formed the design of supplying such a supplement4 ,when1 however1 that design seriously entered his mind1 consequent upon the felt need of a method for social investigations1 it was ,whately's conception of ,induction that he fell back upon4 ,historically viewed1 his ,system of ,logic was an attempt to connect the practical conditions of proof set forth in ,herschel's discourse with the theoretic view of ,induction propounded in ,whately's4 ,the tag by which he sought to attach the new material to the old system was the ,inductive ,enthymeme of the ,schoolmen as interpreted by ,whately4 ,whately's interpretation--or misinterpretation--of this ,enthymeme1 and the conception of ,induction underlying it1 since it became ,mill's ruling conception of ,induction1 and virtually the formative principle of his system1 deserves particular attention4 ,this1 that and the other horned animal1 ox1 sheep1 goat1 ruminate2 therefore1 all horned animals ruminate4 ,the traditional view of this ,enthymeme ,i have given in my chapter on ,formal ,induction 7p4 #bch74 ,it is that a ,minor ,premiss is suppressed3 ,this1 that and the other constitute the whole class4 ,this is the form of the ,minor in ,aristotle's ,inductive ,syllogism4 ,but1 ,whately argued1 how do we know that this1 that and the other--the individuals we have examined--constitute the whole class8 ,do we not assume that what belongs to the individuals examined belongs to the whole class8 ,this tacit assumption1 he contended1 is really at the bottom of the ,enthymeme1 and its proper completion is to take this as the ,major ,premiss1 with the enumeration of individuals as the ,minor4 ,thus3-- ,what belongs to the individuals examined belongs to the whole class4 ,the property of the ruminating belongs to the individuals examined1 ox1 sheep1 goat1 etc4 ,therefore1 it belongs to all4 ,in answer to this1 ,hamilton repeated the traditional view1 treating ,whately's view merely as an instance of the prevailing ignorance of the history of ,logic4 ,he pointed out besides that ,whately's ,major was the postulate of a different kind of inference from that contemplated in ,aristotle's ,inductive ,syllogism1 ,material as distinguished from ,formal inference4 ,this is undeniable if we take this syllogism purely as an argumentative syllogism4 ,the all of the conclusion simply covers the individuals enumerated and admitted to be all in the ,minor ,premiss4 ,if a disputant admits the cases produced to be all and can produce none to the contrary1 he is bound to admit the conclusion4 ,now the inference contemplated by ,whately was not inference from an admission to what it implies1 but inference from a series of observations to all of a like kind1 observed and unobserved4 ,it is not worth while discussing what historical justification ,whately had for his view of ,induction4 ,it is at least arguable that the word had come to mean1 if it did not mean with ,aristotle himself1 more than a mere summation of particulars in a general statement4 ,even ,aristotle's respondent in the concession of his ,minor admitted that the individuals enumerated constituted all in the truly general sense1 not merely all observed but all beyond the range of observation4 ,the point1 however1 is insignificant4 ,what really signifies is that while ,hamilton1 after drawing the line between ,formal ,induction and ,material1 fell back and entrenched himself within that line1 ,mill caught up ,whately's conception of ,induction1 pushed forward1 and made it the basis of his ,system of ,logic4 ,in ,mill's definition1 the mere summation of particulars1 ,inductio per enumerationem simplicem ubi non reperitur instantia contradictoria1 is ,induction improperly so called4 ,the only process worthy of the name is ,material ,induction1 inference to the unobserved4 ,here only is there an advance from the known to the unknown1 a veritable inductive hazard4 ,starting then with this conception of inference to the unobserved as the only true inference1 and with an empirical law--a generality extended from observed cases to unobserved--as the type of such inference1 ,mill saw his way to connecting a new ,logic with the old4 ,we must examine this junction carefully1 and the brilliant and plausible arguments by which he supported it2 we shall find that1 biased by this desire to connect the new with the old1 he gave a misleading dialectic setting to his propositions1 and1 in effect1 confused the principles of ,argumentative conclusion on the one hand and of ,scientific ,observation and ,inference on the other4 ,the conception of ,inference which he adopted from ,whately was too narrow on both sides for the uses to which he put it4 ,be it understood that in the central methods both of ,syllogistic and of ,science1 ,mill was substantially in accord with tradition2 it is in his mode of junction1 and the light thereby thrown upon the ends and aims of both1 that he is most open to criticism4 ,as regards the relation between ,deduction and ,induction1 ,mill's chief proposition was the brilliant paradox that all inference is at bottom ,inductive1 that ,deduction is only a partial and accidental stage in a process the whole of which may be called ,induction4 ,an opinion was abroad--fostered by the apparently exclusive devotion of ,logic to ,deduction--that all inference is essentially ,deductive4 ,not so1 answered ,mill1 meeting this extreme with another3 all inference is essentially ,inductive4 ,he arrives at this through the conception that ,induction is a generalisation from observed particulars1 while ,deduction is merely the extension of the generalisation to a new case1 a new particular4 ,the example that he used will make his meaning plain4 ,take a common ,syllogism3-- ,all men are mortal4 ,socrates is a man4 ,socrates is mortal4 ,the proposition1 ,mill says1 that ,socrates is mortal is evidently an inference4 ,it is got at as a conclusion from something else4 ,but do we in reality conclude it from the proposition1 ,all men are mortal8 ,he answers that this cannot be1 because if it is not true that ,socrates is mortal it cannot be true that all men are mortal4 ,it is clear that our belief in the mortality of ,socrates must rest on the same ground as our belief in the mortality of men in general4 ,he goes on to ask whence we derive our knowledge of the general truth1 and answers3 ,of course from observation4 ,now all which man can observe are individual cases4444 ,a general truth is but an aggregate of particular truths4 ,but a general proposition is not merely a compendious form for recording a number of particular facts4444 ,it is also a process of inference4 ,from instances which we have observed we feel warranted in concluding that what we have found true in those instances1 holds in all similar ones1 past1 present1 and future4 ,we then record all that we have observed together with what we infer from our observations1 in one concise expression4 ,a general proposition is thus at once a summary of particular facts and a memorandum of our right to infer from them4 ,and when we make a deduction we are1 as it were1 interpreting this memorandum4 ,but it is upon the particular facts that the inference really rests1 and ,mill contends that we might if we chose infer to the particular conclusion at once without going through the form of a general inference4 ,thus ,mills seeks to make good his point that all inference is essentially ,inductive1 and that it is only for convenience that the word ,induction has been confined to the general induction1 while the word ,deduction is applied to the process of interpreting our memorandum4 ,clear and consecutive as this argument is1 it is fundamentally confusing4 ,it confuses the nature of ,syllogistic conclusion or ,deduction1 and at the same time gives a partial and incomplete account of the ground of ,material inference4 ,the root of the first confusion lies in raising the question of the ground of material inference in connexion with the ,syllogism4 ,as regards the usefulness of the ,syllogism1 this is an ,,ignoratio ,,elenchi4 ,that the ,major and the conclusion rest upon the same ground as matters of belief is indisputable3 but it is irrelevant4 ,in so far as ,socrates is mortal is an inference from facts1 it is not the conclusion of a ,syllogism4 ,this is implicitly and with unconscious inconsistency recognised by ,mill when he represents ,deduction as the interpretation of a memorandum4 ,to represent ,deduction as the interpretation of a memorandum--a very happy way of putting it and quite in accordance with ,roger ,bacon's view--is really inconsistent with regarding ,deduction as an occasional step in the process of ,induction4 ,if ,deduction is the interpretation of a memorandum1 it is no part of the process of inference from facts4 ,the conditions of correct interpretation as laid down in ,syllogism are one thing1 and the methods of correct inference from the facts1 the methods of science that he was in search of1 are another4 ,let us emphasise this view of ,deduction as the interpretation of a memorandum4 ,it corresponds exactly with the view that ,i have taken in discussing the utility of the ,syllogism4 ,suppose we want to know whether a particular conclusion is consistent with our memorandum1 what have we to look to8 ,we have to put our memorandum into such a form that it is at once apparent whether or not it covers our particular case4 ,the ,syllogism aspires to be such a form4 ,that is the end and aim of it4 ,it does not enable us to judge whether the memorandum is a legitimate memorandum or not4 ,it only makes clear that if the memorandum is legitimate1 so is the conclusion4 ,how to make clear and consistent memoranda of our beliefs in words is a sufficiently complete description of the main purpose of ,deductive ,logic4 ,instead1 then1 of trying to present ,deduction and ,induction as parts of the same process1 which he was led to do by his desire to connect the new and the old1 ,mill ought rather1 in consistency as well as in the interests of clear system1 to have drawn a line of separation between the two as having really different ends1 the conditions of correct conclusion from accepted generalities on the one hand1 and the conditions of correct inference from facts on the other4 ,whether the first should be called inference at all is a question of naming that ought to have been considered by itself4 ,we may refuse to call it inference1 but we only confuse ourselves and others if we do not acknowledge that in so doing we are breaking with traditional usage4 ,perhaps the best way in the interests of clearness is to compromise with tradition by calling the one ,formal ,inference and the other ,material ,inference4 ,it is with the latter that the ,physical ,sciences are mainly concerned1 and it was the conditions and methods of its correct performance that ,mill desired to systematise in his ,inductive ,logic4 ,we have next to see how his statement of the grounds of ,material ,inference was affected by his connexion of ,deduction and ,induction4 ,here also we shall find a reason for a clearer separation between the two departments of ,logic4 ,in his antagonism to a supposed doctrine that all reasoning is from general to particular1 ,mill maintained simpliciter that all reasoning is from particulars to particulars4 ,now this is true only secundum quid1 and although in the course of his argument ,mill introduced the necessary qualifications1 the unqualified thesis was confusing4 ,it is perfectly true that we may infer--we can hardly be said to reason--from observed particulars to unobserved4 ,we may even infer1 and infer correctly1 from a single case4 ,the village matron1 called in to prescribe for a neighbour's sick child1 infers that what cured her own child will cure the neighbour's1 and prescribes accordingly4 ,and she may be right4 ,but it is also true that she may be wrong1 and that no fallacy is more common than reasoning from particulars to particulars without the requisite precautions4 ,this is the moral of one of the fables of ,camerarius4 ,two donkeys were travelling in the same caravan1 the one laden with salt1 the other with hay4 ,the one laden with salt stumbled in crossing a stream1 his panniers dipped in the stream1 the salt melted1 and his burden was lightened4 ,when they came to another stream1 the donkey that was laden with hay dipped his panniers in the water1 expecting a similar result4 ,mill's illustrations of correct inference from particulars to particulars were really irrelevant4 ,what we are concerned with in considering the grounds of ,inference1 is the condition of correct inference1 and no inference to an unobserved case is sound unless it is of a like kind with the observed case or cases on which it is founded1 that is to say1 unless we are entitled to make a general proposition4 ,we need not go through the form of making a general proposition1 but if a general proposition for all particulars of a certain description is not legitimate1 no more is the particular inference4 ,mill1 of course1 did not deny this1 he was only betrayed by the turn of his polemic into an unqualified form of statement that seemed to ignore it4 ,but this was not the worst defect of ,mill's attempt at a junction of old and new through ,whately's conception of ,induction4 ,a more serious defect was due to the insufficiency of this conception to represent all the modes of scientific inference4 ,when a certain attribute has been found in a certain connexion in this1 that1 and the other1 to the extent of all observed instances1 we infer that it will be found in all1 that the connexion that has obtained within the range of our actual experience has obtained beyond that range and will obtain in the future4 ,call this an observed uniformity of nature3 we hold ourselves justified in expecting that the observed uniformities of nature will continue4 ,such an observed uniformity--that ,all animals have a nervous system1 that ,all animals die1 that ,quinine cures ague--is also called an ,empirical ,law4 ,but while we are justified in extending an empirical law beyond the limits within which it has been observed to hold good1 it is a mistake to suppose that the main work of science is the collection of empirical laws1 and that the only scientific inference is the inference from the observed prevalence of an empirical law to its continuance4 ,with science the collection of empirical laws is only a preliminary3 the goal of science1 in ,herschel's phrase1 is explanation4 ,in giving such prominence to empirical laws in his theory1 ,mill confined ,induction to a narrower scope than science ascribes to it4 ,science aims at reaching the causes of things3 it tries to penetrate behind observed uniformities to the explanation of them4 ,in fact1 as long as a science consists only of observed uniformities1 as long as it is in the empirical stage1 it is a science only by courtesy4 ,astronomy was in this stage before the discovery of the ,law of ,gravitation4 ,medicine is merely empirical as long as its practice rests upon such generalisations as that ,quinine cures ague1 without knowing why4 ,it is true that this explanation may consist only in the discovery of a higher or deeper uniformity1 a more recondite law of connexion3 the point is that these deeper laws are not always open to observation1 and that the method of reaching them is not merely observing and recording4 ,in the body of his ,inductive ,logic1 ,mill gave a sufficient account of the ,method of ,explanation as practised in scientific inquiry4 ,it was only his mode of approaching the subject that was confusing1 and made it appear as if the proper work of science were merely extending observed generalities1 as when we conclude that all men will die because all men have died1 or that all horned animals ruminate because all hitherto observed have had this attribute4 ,a minor source of confusion incident to the same controversy was his refusing the title of ,induction proper to a mere summary of particulars4 ,he seemed thereby to cast a slight upon the mere summation of particulars4 ,and yet1 according to his theory1 it was those particulars that were the basis of the ,induction properly so called4 ,that all men will die is an inference from the observation summed up in the proposition that all men have died4 ,if we refuse the name of ,induction to the general proposition of fact1 what are we to call it8 ,the truth is that the reason why the word ,induction is applied indifferently to the general proposition of fact and the general proposition applicable to all time is that1 once we are sure of the facts1 the transition to the inference is so simple an affair that it has not been found necessary in practice to distinguish them by different names4 ,our criticism of ,mill would itself mislead if it were taken to mean that the methods of science which he formulated are not the methods of science or that his system of those methods is substantially incomplete4 ,his ,inductive ,logic as a system of scientific method was a great achievement in organisation1 a veritable ,novum ,organum of knowledge4 ,what kept him substantially right was that the methods which he systematised were taken from the practice of men of science4 ,our criticism amounts only to this1 that in correlating the new system with the old he went upon a wrong track4 ,for more than two centuries ,deduction had been opposed to ,induction1 the ars disserendi to the ars inveniendi4 ,in trying to reconcile them and bring them under one roof1 ,mill drew the bonds too tight4 ,in stating the terms of the union between the two partners1 he did not separate their spheres of work with sufficient distinctness4 ,mill's theory of ,deduction and ,induction and the voluminous criticism to which in its turn it has been subjected have undoubtedly been of great service in clearing up the foundations of reasoning4 ,but the moral of it is that if we are to make the methods of ,science a part of ,logic1 and to name this department ,induction1 it is better to discard altogether the questions of ,general and ,particular which are pertinent to ,syllogism1 and to recognise the new department simply as being concerned with a different kind of inference1 inference from facts to what lies beyond them1 inference from the observed to the unobserved4 ,that this is the general aim and proper work of ,science is evident from its history4 ,get at the secrets of ,nature by the study of ,nature1 penetrate to what is unknown and unexperienced by help of what is known and has been experienced1 was the cry of the early reformers of ,science4 ,thus only1 in ,roger ,bacon's phrase1 could certainty--assured1 well grounded1 rational belief--be reached4 ,this doctrine1 like every other1 can be understood only by what it was intended to deny4 ,the way of reaching certainty that ,roger ,bacon repudiated was argument1 discussion1 dialectic4 ,this concludes a question but does not make us feel certain1 or acquiesce in the contemplation of truth that is not also found in ,experience4 ,argument is not necessarily useless2 the proposition combated is only that by it alone--by discussion that does not go beyond accepted theories or conceptions--rational belief about the unknown cannot be reached4 ,the proposition affirmed is that to this end the conclusions of argument must be tested by experience4 ,observation of facts then is a cardinal part of the method of ,science4 ,the facts on which our inferences are based1 by which our conclusions are tested1 must be accurate4 ,but in thus laying emphasis on the necessity of accurate observation1 we must beware of rushing to the opposite extreme1 and supposing that observation alone is enough4 ,observation1 the accurate use of the senses 7by which we must understand inner as well as outer sense71 is not the whole work of ,science4 ,we may stare at facts every minute of our waking day without being a whit the wiser unless we exert our intellects to build upon them or under them4 ,to make our examination fruitful1 we must have conceptions1 theories1 speculations1 to bring to the test4 ,the comparison of these with the facts is the inductive verification of them4 ,science has to exercise its ingenuity both in making hypotheses and in contriving occasions for testing them by observation4 ,these contrived occasions are its artificial experiments1 which have come to be called experiments simply by contrast with conclusive observations for which ,nature herself furnishes the occasion4 ,the observations of ,science are not passive observations4 ,the word experiment simply means trial1 and every experiment1 natural or artificial1 is the trial of a hypothesis4 ,in the language of ,leonardo da ,vinci1 ,theory is the general1 ,experiments are the soldiers4 ,observation and ,inference go hand in hand in the work of ,science1 but with a view to a methodical exposition of its methods1 we may divide them broadly into ,methods of ,observation and ,methods of ,inference4 ,there are errors specially incident to ,observation1 and errors specially incident to ,inference4 ,how to observe correctly and how to make correct inferences from our observations are the two objects of our study in ,inductive ,logic3 we study the examples of ,science because they have been successful in accomplishing those objects4 ,that all inference to the unobserved is founded on facts1 on the data of experience1 need not be postulated4 ,it is enough to say that ,inductive ,logic is concerned with inference in so far as it is founded on the data of experience4 ,but inasmuch as all the data of experience are not of equal value as bases of inference1 it is well to begin with an analysis of them1 if we wish to take a comprehensive survey of the various modes of inference and the conditions of their validity4 ,footnote #a3 ,hamilton's ,reid1 p4 #gab4 ,footnote #b3 ,the ,novum ,organum was never completed4 ,of the nine heads of special aids to the intellect in the final interpretation he completed only the first1 the list of ,prerogative ,instances4 ,footnote #c3 ,sylva ,sylvarum1 ,century ,i1 #bd4 ,footnote #d3 ,sylva ,sylvarum1 ,century ,i1 #e4 ,,chapter ,i4 ,,the ,,data ,,of ,,experience ,,as ,,grounds ,,of ,,inference ,,or ,,rational ,,belief4 ,if we examine any of the facts or particulars on which an inference to the unobserved is founded1 we shall find that they are not isolated individuals or attributes1 separate objects of perception or thought1 but relations among things and their qualities1 constituents1 or ingredients4 ,take the particular from which ,mill's village matron inferred1 the fact on which she based her expectation of a cure for her neighbour's child4 ,it is a relation between things4 ,we have the first child's ailment1 the administration of the drug1 and the recovery1 a series of events in sequence4 ,this observed sequence is the fact from which she is said to infer1 the datum of experience4 ,she expects this sequence to be repeated in the case of her neighbour's child4 ,similarly we shall find that1 in all cases where we infer1 the facts are complex1 are not mere isolated things1 but relations among things--using the word thing in its widest sense--relations which we expect to find repeated1 or believe to have occurred before1 or to be occurring now beyond the range of our observation4 ,these relations1 which we may call coincidences or conjunctions1 are the data of experience from which we start in our beliefs or inferences about the unexperienced4 ,the problem of ,inductive ,logic being to determine when or on what conditions such beliefs are rational1 we may begin by distinguishing the data of coincidence or conjunction accordingly4 ,there are certain coincidences that we expect to find repeated beyond the occasions on which we have observed them1 and others that we do not expect to find repeated4 ,if it is a sound basis of inference that we are in search of1 it is evidently to these first1 the coincidences that we are assured of finding again1 that we must direct our study4 ,let us see whether they can be specified4 7#a7 ,if there is no causal connexion between ,a and ,b1 using these as symbols for the members of a coincidence--the objects that are presented together--we do not expect the coincidence to be repeated4 ,if ,a and ,b are connected as cause and effect1 we expect the effect to recur in company with the cause4 ,we expect that when the cause reappears in similar circumstances1 the effect also will reappear4 ,you are hit1 e4g41 by a snowball1 and the blow is followed by a feeling of pain4 ,the sun1 we shall say1 was shining at the moment of the impact of the snowball on your body4 ,the sunshine preceded your feeling of pain as well as the blow4 ,but you do not expect the pain to recur next time that the sun shines4 ,you do expect it to recur next time you are hit by a snowball4 ,the taking of food and a certain feeling of strength are causally connected4 ,if we go without food1 we are not surprised when faintness or weariness supervenes4 ,suppose that when our village matron administered her remedy to her own child1 a dog stood by the bedside and barked4 ,the barking in that case would precede the cure4 ,now1 if the matron were what we should call a superstitious person1 and believed that this concomitant had a certain efficacy1 that the dog's barking and the cure were causally connected1 she would take the dog with her when she went to cure her neighbour's child4 ,otherwise she would not4 ,she would say that the barking was an accidental1 casual1 fortuitous coincidence1 and would build no expectation upon it4 ,these illustrations may serve to remind us of the familiar fact that the causal nexus is at least one of the things that we depend on in our inferences to the unobserved4 ,to a simple sequence we attach no importance1 but a causal sequence or consequence that has been observed is a mainstay of inference4 ,whether the causal sequence holds or not as a matter of fact1 we depend upon it if we believe in it as a matter of fact4 ,but unless it does hold as a matter of fact1 it is valueless as a guide to the unknown1 and our belief is irrational4 ,clearly1 therefore1 if rational belief is what we aim at1 it is of importance that we should make sure of cause and effect as matter of fact in the sequence of events4 ,one large department of ,inductive ,logic1 the so-called ,experimental ,methods1 is designed to help us in thus making sure1 i4e41 in ascertaining causal sequence as a matter of fact4 ,it is assumed that by careful observation of the circumstances1 we can distinguish between mere simple sequence and causal sequence or consequence1 and methods are recommended of observing with the proper precautions against error4 ,observe that these methods1 though called ,inductive1 are not concerned with arriving at general propositions4 ,the principle we go upon is simply this1 that if it can be ascertained as matter of fact that a certain thing is related to another as cause and effect1 we may count upon the same relation as holding in unobserved ,nature1 on the general ground that like causes produce like effects in like circumstances4 ,observe1 also1 that ,i deliberately speak of the causal relation as a relation among phenomena4 ,whether this use of the words cause and effect is philosophically justifiable1 is a question that will be raised and partly discussed later on4 ,here ,i simply follow the common usage1 in accordance with which objects of perception1 e4g41 the administration of a drug and the recovery of a patient1 are spoken of as cause and effect4 ,such observable sequences are causal sequences in the ordinary sense1 and it is part of the work of ,science to observe them4 ,i do not deny that the true cause1 of the cause that science aims ultimately at discovering1 is to be found in the latent constitution or composition of the things concerned4 ,only that1 as we shall see more precisely1 is a cause of another description4 ,meantime1 let us take the word to cover what it undoubtedly covers in ordinary speech1 the perceptible antecedent of a perceptible consequent4 ,strictly speaking1 as we shall find1 ,science has only one method of directly observing when events are in causal sequence4 ,but there are various indirect methods1 which shall be described in some sort of order4 ,for the practical purposes of life1 a single ascertained causal sequence is of little value as a basis of inference1 because we can infer only to its repetition in identical circumstances4 ,suppose our village matron had been able to ascertain as a matter of fact--a feat as we shall find not to be achieved by direct observation--that the drug did cure her child1 this knowledge by itself would have been practically valueless1 because the only legitimate inference would have been that an exactly similar dose would have the same effect in exactly similar circumstances4 ,but1 as we shall find1 though practically valueless1 a single ascertained causal sequence is of supreme value in testing scientific speculations as to the underlying causes4 7#b7 ,we have next to see whether there are any other rational expectations based on observed facts4 ,we may lay down as a principle the following3-- ,if a conjunction or coincidence has constantly been repeated within our experience1 we expect it to recur and believe that it has recurred outside our experience4 ,how far such expectations are rational1 and with what degrees of confidence they should be entertained1 are the questions for the ,logic of ,inference1 but we may first note that we do as a matter of habit found expectations on repeated coincidence1 and indeed guide our daily life in this way4 ,if we meet a man repeatedly in the street at a certain hour1 we go out expecting to meet him3 it is a shock to our expectations1 a surprise1 when we do not4 ,if we are walking along a road and find poles set up at regular intervals1 we continue our walk expecting to find a pole coincident with the end of each interval4 ,what ,mill calls the uniformities of ,nature1 the uniformities expressed in general propositions1 are from the point of view of the observer1 examples of repeated coincidence4 ,birth1 growth1 decay1 death1 are not isolated or variable coincidences with organised being3 all are born1 all grow1 all decay1 and all die4 ,these uniformities constitute the order of ,nature3 the coincidences observed are not occasional1 occurring once in a way or only now and then2 they turn up again and again4 ,trees are among the uniformities on the varied face of ,nature3 certain relations between the soil and the plant1 between trunk1 branches1 and leaves are common to them4 ,for us who observe1 each particular tree that comes under our observation is a repetition of the coincidence4 ,and so with animals3 in each we find certain tissues1 certain organs1 conjoined on an invariable plan4 ,technically these uniformities have been divided into uniformities of ,sequence and uniformities of ,coexistence4 ,thus the repeated alternation of day and night is a uniformity of ,sequence3 the invariable conjunction of inertia with weight is a uniformity of ,coexistence4 ,but the distinction is really immaterial to ,logic4 ,what ,logic is concerned with is the observation of the facts and the validity of any inference based on them3 and in these respects it makes no difference whether the uniformity that we observe and found upon is one of ,sequence or of ,coexistence4 ,it was exclusively to such inferences1 inferences from observed facts of repeated coincidence1 that ,mill confined himself in his theory of ,induction1 though not in his exposition of the methods4 ,these are the inferences for which we must postulate what he calls the ,uniformity of ,nature4 ,every induction1 he says1 following ,whately1 may be thrown into the form of a ,syllogism1 in which the principle of the ,uniformity of ,nature is the ,major ,premiss1 standing to the inference in the relation in which the ,major ,premiss of a ,syllogism stands to the conclusion4 ,if we express this abstractly denominated principle in propositional form1 and take it in connexion with ,mill's other saying that the course of ,nature is not a uniformity but uniformities1 we shall find1 ,i think1 that this postulated ,major ,premiss amounts to an assumption that the observed ,uniformities of ,nature continue4 ,mill's ,inductive ,syllogism thus made explicit would be something like this3-- ,all the observed uniformities of ,nature continue4 ,that all men have died is an observed uniformity4 ,therefore1 it continues2 i4e41 all men will die and did die before the beginning of record4 ,there is no doubt that this is a perfectly sound postulate4 ,like all ultimate postulates it is indemonstrable2 ,mill's derivation of it from ,experience did not amount to a demonstration4 ,it is simply an assumption on which we act4 ,if any man cares to deny it1 there is no argument that we can turn against him4 ,we can only convict him of practical inconsistency1 by showing that he acts upon this assumption himself every minute of his waking day4 ,if we do not believe in the continuance of observed uniformities1 why do we turn our eyes to the window expecting to find it in its accustomed order of place8 ,why do we not look for it in another wall8 ,why do we dip our pens in ink1 and expect the application of them to white paper to be followed by a black mark8 ,the principle is sound1 but is it our only postulate in inference to the unobserved1 and does the continuance of empirical laws represent all that ,science assumes in its inferences8 ,mill was not satisfied about this question4 ,he pointed out a difficulty which a mere belief in empirical continuity does not solve4 ,why do we believe more confidently in some uniformities than in others8 ,why would a reported breach of one be regarded with more incredulity than that of another8 ,suppose a traveller to return from a strange country and report that he had met men with heads growing beneath their shoulders1 why would this be pronounced more incredible than a report that he had seen a grey crow8 ,all crows hitherto observed have been black1 and in all men hitherto observed the heads have been above the shoulders3 if the mere continuity of observed uniformities is all that we go upon in our inferences1 a breach of the one uniformity should be just as improbable as a breach of the other1 neither more nor less4 ,mill admitted the difficulty1 and remarked that whoever could solve it would have solved the problem of ,induction4 ,now it seems to me that this particular difficulty may be solved1 and yet leave another behind4 ,it may be solved within the limits of the principle of emperical--meaning by that observational--continuity4 ,the uniform blackness of the crow is an exception within a wider uniformity3 the colour of animals is generally variable4 ,hence we are not so much surprised at the reported appearance of a grey crow3 it is in accordance with the more general law4 ,on the other hand1 the uniform position of the head relative to other parts of the body is a uniformity as wide as the animal kingdom3 it is a coincidence repeated as often as animals have been repeated1 and merely on the principle that uniformities continue1 it has an absolutely uncontradicted series in its favour4 ,but is this principle really all that we assume8 ,do we not also assume that behind the observed fact uniformity1 there is a cause for it1 a cause that does not appear on the surface of the observation1 but must be sought outside of its range8 ,and do not the various degrees of confidence with which we expect a repetition of the coincidence1 depend upon the extent of our knowledge of the producing causes and the mode of their operation8 ,at bottom our belief in the continuance of the observed uniformities rests on a belief in the continuance of the producing causes1 and till we know what these are our belief has an inferior warrant3 there is less reason for our confidence4 ,to go back to the illustrations with which we started4 ,if we have met a man every day for months at a certain place at a certain hour1 it is reasonable to expect to meet him there to-morrow1 even if our knowledge does not go beyond the observed facts of repeated coincidence4 ,but if we know also what brings him there1 and that this cause continues1 we have a stronger reason for our expectation4 ,and so with the case of poles at regular intervals on a road4 ,if we know why they are placed there1 and the range of the purpose1 we expect their recurrence more confidently within the limits of that purpose4 ,this further knowledge is a warrant for stronger confidence1 because if we know the producing causes1 we are in a better position for knowing whether anything is likely to defeat the coincidence4 ,a uniformity is said to be explained when its cause is known1 and an inference from an explained uniformity is always more certain than an inference from a uniformity that is merely empirical in the sense of being simply observed4 ,now1 the special work of ,science is to explain1 in the sense of discovering the causes at work beneath what lies open to observation4 ,in so doing it follows a certain method1 and obeys certain conditions of satisfactory explanation4 ,its explanations are inferences from facts1 inasmuch as it is conformity with observed facts1 with outward signs of underlying causal nexus1 that is the justification of them4 ,but they are not inferences from facts in the sense above described as empirical inference4 ,in its explanations also ,science postulates a principle that may be called the ,uniformity of ,nature4 ,but this principle is not merely that observed uniformities continue4 ,it may be expressed rather as an assumption that the underlying causes are uniform in their operation1 that as they have acted beneath the recorded experiences of mankind1 so they have acted before and will continue to act4 ,the foregoing considerations indicate a plan for a roughly systematic arrangement of the methods of ,induction4 ,seeing that all inference from the data of experience presupposes causal connexion among the data from which we infer1 all efforts at establishing sound bases of inference1 or rational ground for expectation fall1 broadly speaking1 under two heads3 7#a7 ,methods of ascertaining causal connexion among phenomena as a matter of fact1 that is1 ,methods of ,observation2 and 7#b7 ,methods of ascertaining what the causal connexion is1 that is1 ,methods of ,explanation4 ,these constitute the body of ,inductive ,logic4 ,but there is a preliminary and a pendant4 ,without raising the question of causal connexion1 we are liable to certain errors in ascertaining in what sequence and with what circumstances events really occurred4 ,these tendencies to error deserve to be pointed out by way of warning1 and this ,i shall attempt in a separate chapter on observation of facts of simple sequence4 ,this is preliminary to the special methods of observing causal sequence4 ,then1 by way of pendant1 ,i shall consider two modes of empirical inference from data in which the causal connexion has not been ascertained or explained--,inference from approximate generalisations to particular cases1 and ,inference from ,analogy4 ,most of these methods in one form or another were included by ,mill in his system of ,inductive ,logic1 and the great merit of his work was that he did include them1 though at some sacrifice of consistency with his introductory theory4 ,with regard to the kind of empirical inference which that theory1 following the lead of ,whately1 took as the type of all inference1 ,logic has really little to say4 ,it was this probably that was in ,mill's mind when he said that there is no ,logic of ,observation1 ignoring the fact that the ,experimental ,methods are really methods of observation1 as well as the ,methods of ,eliminating ,chance by calculation of ,probability4 ,there is no method of observing uniformities except simply observing them4 ,nor indeed is there any method of inferring from them3 we can only point out that in every particular inference from them we assume or postulate their continuance generally4 ,as regards their observation1 we may point out further that a special fallacy is incident to it1 the fallacy of ignoring exceptions4 ,if we are prepossessed or prejudiced in favour of a uniformity1 we are apt to observe only the favourable instances1 and to be blind to cases where the supposed invariable coincidence does not occur4 ,thus1 as ,bacon remarked among his ,idola1 we are apt to remember when our dreams come true1 and to forget when they do not4 ,suppose we take up the notion that a new moon on a ,saturday is invariably followed by twenty days of unsettled weather1 one or two or a few cases in which this notably holds good are apt to be borne in mind1 while cases where the weather is neither conspicuously good nor bad are apt to be overlooked4 ,but when a warning has been given against this besetting fallacy1 ,logic has nothing further to say about empirical uniformities1 except that we may infer from them with some degree of reasonable probability1 and that if we want ground for a more certain inference we should try to explain them4 ,,chapter ,,ii4 ,,ascertainment ,,of ,,simple ,,facts ,,in ,,their ,,order4--,,personal ,,observation4 --,,hearsay ,,evidence--,,method ,,of ,,testing ,,traditional ,,evidence4 ,all beliefs as to simple matter of fact must rest ultimately on observation4 ,but1 of course1 we believe many things to have happened that we have never seen4 ,as ,chaucer says3-- ,but ,god forbede but men shoulde 'lieve ,wel more thing than men han seen with eye4 ,man shall not weenen everything a lie ,but if himself it seeth or else doth4 ,for the great bulk of matters of fact that we believe we are necessarily dependent on the observations of others4 ,and if we are to apply scientific method to the ascertainment of this1 we must know what errors we are liable to in our recollections of what we have ourselves witnessed1 and what errors are apt to arise in the tradition of what purports to be the evidence of eye-witnesses4 ,i4--,,personal ,,observation4 ,it is hard to convince anybody that he cannot trust implicitly to his memory of what he has himself seen4 ,we are ready enough to believe that others may be deceived3 but not our own senses4 ,seeing is believing4 ,it is well1 however1 that we should realise that all observation is fallible1 even our own4 ,three great besetting fallacies or tendencies to error may be specified3-- #a4 ,liability to have the attention fastened on special incidents1 and so diverted from other parts of the occurrence4 #b4 ,liability to confuse and transpose the sequence of events4 #c4 ,liability to substitute inference for fact4 ,it is upon the first of these weaknesses in man as an observing machine that jugglers chiefly depend on working their marvels4 ,sleight of hand counts for much1 but diverting the spectator's eyes for a good deal more4 ,that is why they have music played and patter incessantly as they operate4 ,their patter is not purposeless3 it is calculated to turn our eyes away from the movements of their nimble hands4 ,it must be borne in mind that in any field of vision there are many objects1 and that in any rapid succession of incidents much more passes before the eyes than the memory can retain in its exact order4 ,it is of course in moments of excitement and hurry1 when our observation is distracted1 that we are most subject to fallacious illusions of memory4 ,unconsciously we make a coherent picture of what we have seen1 and very often it happens that the sequence of events is not what actually passed1 but what we were prejudiced in favour of seeing4 ,hence the unlikelihood of finding exact agreement among the witnesses of any exciting occurrence1 a quarrel1 a railway accident1 a collision at sea1 the incidents of a battle4 ,it commonly happens1 says ,mr4 ,kinglake1#a that incidents occurring in a battle are told by the most truthful bystanders with differences more or less wide4 ,in the attack on the ,great ,redoubt in the ,battle of the ,alma1 a young officer1 ,anstruther1 rushed forward and planted the colours of the ,royal ,welsh--but where8 ,some distinctly remembered seeing him dig the butt-end of the flagstaff into the parapet3 others as distinctly remembered seeing him fall several paces before he reached it4 ,similarly with the incidents of the death of the ,prince ,imperial near the ,italezi ,hills in the ,zulu ,war4 ,he was out as a volunteer with a reconnoitring party4 ,they had off-saddled at a kraal and were resting1 when a band of ,zulus crept up through the long grass1 and suddenly opened fire and made a rush forward4 ,our scouts at once took horse1 as a reconnoitring party was bound to do1 and scampered off1 but the ,prince was overtaken and killed4 ,at the ,court-,martial which ensued1 the five troopers gave the most conflicting accounts of particulars which an unskilled investigator would think could not possibly have been mistaken by eye-witnesses of the same event4 ,one said that the ,prince had given the order to mount before the ,zulus fired3 another that he gave the order directly after3 a third was positive that he never gave the order at all1 but that it was given after the surprise by the officer in command4 ,one said that he saw the ,prince vault into the saddle as he gave the order3 another that his horse bolted as he laid hold of the saddle1 and that he ran alongside trying to get up4 ,the evidence before any ,court of ,inquiry into an exciting occurrence is almost certain to reveal similar discrepancies4 ,but what we find it hard to realise is that we ourselves can possibly be mistaken in what we have a distinct and positive recollection of having seen4 ,it once happened to myself in a ,london street to see a drunken woman thrown under a cab by her husband4 ,two cabs were running along1 a four-wheeler and a hansom3 the woman staggered almost under the first1 and was thrown under the second4 ,as it happened the case never got beyond the police station to which the parties were conveyed after fierce opposition from some neighbours1 who sympathised entirely with the man4 ,the woman herself1 when her wounds were dressed1 acknowledged the justice of her punishment1 and refused to charge her husband4 ,i was all the more willing to acquiesce in this because ,i found that while ,i had the most distinct impression of having seen the four-wheeler run over the woman's body1 and should have been obliged to swear accordingly1 there could be no doubt that it was really the hansom that had done so4 ,this was not only the evidence of the neighbours1 which ,i suspected at the time of being a trick1 but of the cabdriver1 who had stopped at the moment to abide the results of the accident4 ,i afterwards had the curiosity to ask an eminent police magistrate1 ,sir ,john ,bridge1 whether this illusion of memory on my part--which ,i can only account for by supposing that my eyes had been fixed on the sufferer and that ,i had unconsciously referred her injuries to the heavier vehicle--would have entirely discredited my testimony in his ,court4 ,his answer was that it would not2 that he was constantly meeting with such errors1 and that if he found a number of witnesses of the same occurrence exactly agreed in every particular1 he would suspect that they had talked the matter over and agreed upon what they were to say4 ,this was the opinion of an experienced judge1 a skilled critic of the defects of personal observation4 ,an ,old ,bailey counsel for the defence1 who is equally acquainted with the weakness of human memory1 takes advantage of the fact that it is not generally understood by a ,jury1 and makes the fallacious assumption that glaring discrepancies are irreconcilable with the good faith of the witnesses who differ4#b ,,ii4--,,tradition4--,,hearsay ,,evidence4 ,next in value to personal observation1 we must place the report1 oral or written1 of an eye-witness4 ,this is the best evidence we can get if we have not witnessed an occurrence ourselves4 ,yet ,courts of ,law1 which in consideration of the defects of personal observation require more than one witness to establish the truth1 exclude hearsay evidence altogether in certain cases1 and not without reason4 ,in hearing a report we are in the position of observers of a series of significant sounds1 and we are subject to all the fallacies of observation already mentioned4 ,in an aggravated degree1 for words are harder to observe than visible things4 ,our attention is apt to be more listless than in presence of the actual events4 ,our minds dwell upon parts of the narrative to the neglect of other parts1 and in the coherent story or description that we retain in our memories1 sequences are apt to be altered and missing links supplied in accordance with what we were predisposed to hear4 ,thus hearsay evidence is subject to all the imperfections of the original observer1 in addition to the still more insidious imperfections of the second observer4 ,how quickly in the course of a few such transmissions hearsay loses all evidentiary value is simply illustrated by the game known as ,russian ,scandal4 ,one of a company1 ,a1 writes down a short tale or sketch1 and reads it to ,b4 ,b repeats it to ,c1 ,c to ,d1 and so on4 ,when it has thus gone the round of the company1 the last hearer writes down his version1 and it is compared with the original4 ,with every willingness to play fair1 the changes are generally considerable and significant4 ,sometimes it is possible to compare an oral tradition with a contemporary written record4 ,in one of ,mr4 ,hayward's ,essays--,the ,pearls and ,mock ,pearls of ,history--there are some examples of this disenchanting process4 ,there is1 for instance1 a pretty story of an exchange of courtesies between the leaders of the ,french and ,english ,guards at the battle of ,fontenoy4 ,the tradition runs that ,lord ,charles ,hay stepped in front of his men and invited the ,french ,guards to fire1 to which ,m4 d',auteroche with no less chivalry responded3 ,monsieur1 we never fire first2 you fire4 ,what really passed we learn from a letter from ,lord ,charles ,hay to his mother1 which happens to have been preserved4 ,i advanced before our regiment1 and drank to the ,frenchmen1 and told them we were the ,english ,guards1 and hoped they would stand till we came1 and not swim the ,scheldt as they did the ,maine at ,dettingen4 ,tradition has changed this lively piece of buffoonery into an act of stately and romantic courtesy4 ,the change was probably made quite unconsciously by some tenth or hundredth transmitter1 who remembered only part of the story1 and dressed the remainder to suit his own fancy4 ,the question has been raised1 ,for how long can oral tradition be trusted8 ,newton was of opinion that it might be trusted for eighty years after the event4 ,others have named forty years4 ,but if this means that we may believe a story that we find in circulation forty years after the alleged events1 it is wildly extravagant4 ,it does injustice to the ,mythopoeic ,faculty of man4 ,the period of time that suffices for the creation of a full-blown myth1 must be measured by hours rather than by years4 ,i will give an instance from my own observation1 if that has not been entirely discredited by my previous confessions4 ,the bazaars of the ,east are generally supposed to be the peculiar home of myth1 hotbeds in which myths grow with the most amazing speed1 but the locality of my myth is ,aberdeen4 ,in the summer of #ahhg our town set up in one of its steeples a very fine carillon of ,belgian bells4 ,there was much public excitement over the event3 the descriptions of enthusiastic promoters had prepared us to hear silvery music floating all over the town and filling the whole air4 ,on the day fixed for the inauguration1 four hours after the time announced for the first ceremonial peal1 not having heard the bells1 ,i was in a shop and asked if anything had happened to put off the ceremony4 ,yes1 ,i was told2 there had been an accident2 they had not been properly hung1 and when the wife of the ,lord ,provost had taken hold of a string to give the first pull1 the whole machinery had come down4 ,as a matter of fact all that had happened was that the sound of the bells was faint1 barely audible a hundred yards from the belfry1 and not at all like what had been expected4 ,there were hundreds of people in the streets1 and the myth had originated somehow among those who had not heard what they went out to hear4 ,the shop where it was repeated circumstantially to me was in the main street1 not more than a quarter of a mile from where the carillon had been played in the hearing of a large but disappointed crowd4 ,i could not help reflecting that if ,i had been a mediaeval chronicler1 ,i should have gone home and recorded the story1 which continued to circulate for some days in spite of the newspapers3 and two hundred years hence no historian would have ventured to challenge the truth of the contemporary evidence4 ,,iii4--,,method ,,of ,,testing ,,traditional ,,evidence4 ,it is obvious that the tests applied to descriptive testimony in ,courts of ,law cannot be applied to the assertions of ,history4 ,it is a supreme canon of historical evidence that only the statements of contemporaries can be admitted3 but most even of their statements must rest on hearsay1 and even when the historian professes to have been an eye-witness1 the range of his observation is necessarily limited1 and he cannot be put into the witness-box and cross-examined4 ,is there then no way of ascertaining historical fact8 ,must we reject history as altogether unworthy of credit8 ,the rational conclusion only is that very few facts can be established by descriptive testimony such as would satisfy a ,court of ,law4 ,those who look for such ascertainment are on a wrong track1 and are doomed to disappointment4 ,it is told of ,sir ,walter ,raleigh that when he was writing his ,history of the ,world1 he heard from his prison in the ,tower a quarrel outside1 tried to find out the rights and the wrongs and the course of it1 and failing to satisfy himself after careful inquiry1 asked in despair how he could pretend to write the history of the world when he could not find out the truth about what occurred under his own windows4 ,but this was really to set up an impossible standard of historical evidence4 ,the method of testing historical evidence follows rather the lines of the ,newtonian method of ,explanation1 which we shall afterwards describe4 ,we must treat any historical record as being itself in the first place a fact to be explained4 ,the statement at least is extant3 our first question is1 ,what is the most rational way of accounting for it8 ,can it be accounted for most probably by supposing the event stated to have really occurred with all the circumstances alleged8 ,or is it a more probable hypothesis that it was the result of an illusion of memory on the part of the original observer1 if it professes to be the record of an eye-witness1 or on the part of some intermediate transmitter1 if it is the record of a tradition8 ,to qualify ourselves to answer the latter kind of question with reasonable probability we must acquaint ourselves with the various tendencies to error in personal observation and in tradition1 and examine how far any of them are likely to have operated in the given case4 ,we must study the operation of these tendencies within our experience1 and apply the knowledge thus gained4 ,we must learn from actual observation of facts what the ,mythopoeic ,faculty is capable of in the way of creation and transmutation1 and what feats are beyond its powers1 and then determine with as near a probability as we can how far it has been active in the particular case before us4 ,footnote #a3 ,the ,invasion of the ,crimea1 iii4 #abd ,footnote #b3 ,the truth is1 that we see much less than is commonly supposed4 ,not every impression is attended to that is made on the retina1 and unless we do attend we cannot1 properly speaking1 be said to see4 ,walking across to college one day1 ,i was startled by seeing on the face of a clock in my way that it was ten minutes to twelve1 whereas ,i generally passed that spot about twenty minutes to twelve4 ,i hurried on1 fearing to be late1 and on my arrival found myself in very good time4 ,on my way back1 passing the clock again1 ,i looked up to see how much it was fast4 ,it marked ten minutes to eight4 ,it had stopped at that time4 ,when ,i passed before ,i had really seen only the minute hand4 ,the whole dial must have been on my retina1 but ,i had looked at or attended to only what ,i was in doubt about1 taking the hour for granted4 ,i am bound to add that my business friends hint that it is only absorbed students that are capable of such mistakes1 and that alert men of business are more circumspect4 ,that can only be because they are more alive to the danger of error4 ,,chapter ,,iii4 ,,ascertainment ,,of ,,facts ,,of ,,causation4 ,i4--,,post ,,hoc ,,ergo ,,propter ,,hoc4 ,one of the chief contributions of the ,old ,logic to ,inductive ,method was a name for a whole important class of misobservations4 ,the fallacy entitled ,post ,hoc ergo ,propter ,hoc--,after1 therefore1 ,because of--consisted in alleging mere sequence as a proof of consequence or causal sequence4 ,the sophist appeals to experience1 to observed facts3 the sequence which he alleges has been observed4 ,but the appeal is fallacious3 the observation on which he relies amounts only to this1 that the one event has followed upon the other4 ,this much must be observable in all cases of causal sequence1 but it is not enough for proof4 ,post hoc ergo propter hoc may be taken as a generic name for imperfect proof of causation from observed facts of succession4 ,the standard example of the fallacy is the old ,kentish peasant's argument that ,tenterden ,steeple was the cause of ,goodwin ,sands4 ,sir ,thomas ,more 7as ,latimer tells the story in one of his ,sermons to ridicule incautious inference7 had been sent down into ,kent as a commissioner to inquire into the cause of the silting up of ,sandwich ,haven4 ,among those who came to his court was the oldest inhabitant1 and thinking that he from his great age must at least have seen more than anybody else1 ,more asked him what he had to say as to the cause of the sands4 ,forsooth1 sir1 was the greybeard's answer1 ,i am an old man3 ,i think that ,tenterden ,steeple is the cause of ,goodwin ,sands4 ,for ,i am an old man1 and ,i may remember the building of ,tenterden ,steeple1 and ,i may remember when there was no steeple at all there4 ,and before that ,tenterden ,steeple was in building1 there was no manner of speaking of any flats or sands that stopped the haven2 and1 therefore1 ,i think that ,tenterden ,steeple is the cause of the destroying and decaying of ,sandwich ,haven4 ,this must be taken as ,latimer meant it to be1 as a ridiculous example of a purely imbecile argument from observation1 but the appeal to experience may have more show of reason and yet be equally fallacious4 ,the believers in ,kenelm ,digby's ,ointment of ,honour appealed to experience in support of its efficacy4 ,the treatment was to apply the ointment1 not to the wound1 but to the sword that had inflicted it1 to dress this carefully at regular intervals1 and1 meantime1 having bound up the wound1 to leave it alone for seven days4 ,it was observed that many cures followed upon this treatment4 ,but those who inferred that the cure was due to the bandaging of the sword1 failed to observe that there was another circumstance that might have been instrumental1 namely1 the exclusion of the air and the leaving of the wound undisturbed while the natural healing processes went on4 ,and it was found upon further observation that binding up the wound alone answered the purpose equally well whether the sword was dressed or not4 ,in cases where post hoc is mistaken for propter hoc1 simple sequence for causal sequence1 there is commonly some bias of prejudice or custom which fixes observation on some one antecedent and diverts attention from other circumstances and from what may be observed to follow in other cases4 ,in the minds of ,digby and his followers there was probably a veneration for the sword as the weapon of honour1 and a superstitious belief in some secret sympathy between the sword and its owner4 ,so when the practice of poisoning was common1 and suspicion was flurried by panic fear1 observation was often at fault4 ,pope ,clement ,,viii4 was said to have been killed by the fumes of a poisoned candle which was placed in his bedroom4 ,undoubtedly candles were there1 but those who attributed the ,pope's death to them took no notice of the fact that a brazier of burning charcoal was at the same time in the apartment with no sufficient outlet for its fumes4 ,prince ,eugene is said to have received a poisoned letter1 which he suspected and immediately threw from him4 ,to ascertain whether his suspicions were well founded the letter was administered to a dog1 which1 to make assurance doubly sure1 was fortified by an antidote4 ,the dog died1 but no inquiry seems to have been made into the character of the antidote4 ,hotspur's retort to ,glendower showed a sound sense of the true value to be attached to mere priority4 ,glendower4 ,at my nativity ,the front of heaven was full of fiery shapes1 ,of burning cressets3 and at my birth ,the frame and huge foundation of the earth ,shaked like a coward4 ,hotspur4 ,why so it would have done at the same season1 if your mother's cat had but kittened1 though yourself had never been born4 #a ,hen4 ,,iv41 #c1 #a1 #ac4 ,we all admit at once that the retort was just4 ,what principle of sound conclusion was involved in it8 ,it is the business of ,inductive ,logic to make such principles explicit4 ,taking ,post ,hoc ergo ,propter ,hoc as a generic name for fallacious arguments of causation based on observed facts1 for the fallacious proof of causation from experience1 the question for ,logic is1 ,what more than mere sequence is required to prove consequence8 ,when do observations of ,post ,hoc warrant the conclusion ,propter ,hoc8 ,,ii4--,,meaning ,,of ,,cause4--,,methods ,,of ,,observation--,,mill',s ,,experimental ,,methods4 ,the methods formulated by ,mill under the name of ,experimental ,methods are methods actually practised by men of science with satisfactory results1 and are perfectly sound in principle4 ,they were1 indeed1 in substance1 taken by him from the practice of the scientific laboratory and study as generalised by ,herschel4 ,in effect what ,mill did was to restate them and fit them into a system4 ,but the controversies into which he was tempted in so doing have somewhat obscured their exact function in scientific inquiry4 ,hostile critics1 finding that they did not serve the ends that he seemed to claim for them1 have jumped to the conclusion that they are altogether illusory and serve no purpose at all4 ,first1 we must dismiss the notion1 encouraged by ,mill's general theory of ,inference1 that the ,experimental ,methods have anything special to do with the observation and inferential extension of uniformities such as that death is common to all organised beings4 ,one of the ,methods1 as we shall see1 that named by ,mill the ,method of ,agreement1 does incidentally and collaterally establish empirical laws in the course of its observations1 and this probably accounts for the prominence given to it in ,mill's system4 ,but this is not its end and aim1 and the leading ,method1 that named by him the ,method of ,difference1 establishes as fact only a particular case of causal coincidence4 ,it is with the proof of theories of causation that the ,experimental ,methods are concerned3 they are methods of observing with a view to such proof4#a ,the next point to be made clear is that the facts of causation with which the ,methods are concerned are observable facts1 relations among phenomena1 but that the causal relations or conditions of which they are the proof are not phenomena1 in the meaning of being manifest to the senses1 but rather noumena1 inasmuch as they are reached by reasoning from what is manifest4 ,take1 for example1 what is known as the quaquaversus principle in ,hydrostatics1 that pressure upon a liquid is propagated equally in all directions4 ,we cannot observe this extension of pressure among the liquid particles directly4 ,it cannot be traced among the particles by any of our senses4 ,but we can assume that it is so1 consider what ought to be visible if it is so1 and then observe whether the visible facts are in accordance with the hypothesis4 ,a box can be made1 filled with water1 and so fitted with pistons on top and bottom and on each of its four sides that they will indicate the amount of pressure on them from within4 ,let pressure then be applied through a hole in the top1 and the pistons show that it has been communicated to them equally4 ,the application of the pressure and the yielding of the pistons are observable facts1 facts in causal sequence3 what happens among the particles of the liquid is not observed but reasonably conjectured1 is not phenomenal but noumenal4 ,this distinction1 necessary to an understanding of the scope of the ,methods1 was somewhat obscured by ,mill in his preliminary discussion of the meaning of cause4 ,very rightly1 though somewhat inconsistently with his first theory of ,induction1 he insists that the notion of ,cause being the root of the whole theory of ,induction1 it is indispensable that this idea should at the very outset of our inquiry be1 with the utmost practicable degree of precision1 fixed and determined4 ,but in this determination1 not content with simply recognising that it is with phenomena that the ,experimental ,methods primarily deal1 it being indeed only phenomena that can be the subjects of experimental management and observation1 he starts by declaring that science has not to do with any causes except such as are phenomenal--when ,i speak of the cause of any phenomenon1 ,i do not mean a cause which is not itself a phenomenon--and goes on to define as the only correct meaning of cause the sum total of conditions1 including among them conditions which are not phenomenal1 in the sense of being directly open to observation4 ,when ,mill protested that he had regard only to phenomenal causes1 he spoke as the partisan of a philosophical tradition4 ,it would have been well if he had acted upon his own remark that the proper understanding of the scientific method of investigating cause is independent of metaphysical analysis of what cause means4 ,curiously enough1 this remark is the preface to an analysis of cause which has but slight relevance to science1 and is really the continuation of a dispute begun by ,hume4 ,this is the key to his use of the word phenomenon3 it must be interpreted with reference to this3 when he spoke of causes as phenomenal1 he opposed the word to occult in some supposed metaphysical sense4#b ,and this irrelevant discussion1 into the vortex of which he allowed himself to be carried1 obscured the fact1 elsewhere fully recognised by ,mill himself1 that science does attempt to get beyond phenomena at ultimate laws which are not themselves phenomena though they bind phenomena together4 ,the colligation of the facts1 to use ,whewell's phrase1 is not a phenomenon1 but a noumenon4 ,the truth is that a very simple analysis of cause is sufficient for the purposes of scientific inquiry4 ,it is enough to make sure that causal sequence or consequence shall not be confounded with simple sequence4 ,causal sequence is simple sequence and something more1 that something more being expressed by calling it causal4 ,what we call a cause is not merely antecedent or prior in time to what we call its effect3 it is so related to the effect that if it or an equivalent event had not happened the effect would not have happened4 ,anything in the absence of which a phenomenon would not have come to pass as it did come to pass is a cause in the ordinary sense4 ,we may describe it as an indispensable antecedent1 with this reservation 7which will be more fully understood afterwards71 that if we speak of a general effect1 such as death1 the antecedents must be taken with corresponding generality4 ,it is misleading to suggest1 as ,mill does1 by defining cause as the sum total of conditions--a definition given to back up his conception of cause as phenomenal--that science uses the word cause in a different meaning from that of ordinary speech4 ,it is quite true that the cause1 philosophically speaking1 is the sum total of the conditions1 positive and negative1 taken together3 the whole of the contingencies of every description1 which being realised1 the consequent invariably follows4 ,but this does not imply any discrepancy between the scientific or philosophical meaning and the ordinary meaning4 ,it is only another way of saying that the business of science or philosophy is to furnish a complete explanation of an event1 an account of all its indispensable antecedents4 ,the plain man would not refuse the name of cause to anything that science or philosophy could prove to be an indispensable antecedent1 but his interest in explanation is more limited4 ,it is confined to what he wants to know for the purpose he has in hand4 ,nor could the man of science consistently refuse the name of cause to what the plain man applies it to1 if it really was something in consequence of which the event took place4 ,only his interest in explanation is different4 ,the indispensable antecedents that he wants to know may not be the same4 ,science or philosophy applies itself to the satisfaction of a wider curiosity3 it wants to know all the causes1 the whole why1 the sum total of conditions4 ,to that end the various departments of science interest themselves in various species of conditions4 ,but all understand the word cause in the ordinary sense4 ,we must not conclude from accidental differences in explanation or statement of cause1 dependent on the purpose in view1 that the word ,cause is used in different senses4 ,in answering a question as to the cause of anything1 we limit ourselves to what we suppose our interrogator to be ignorant of and desirous of knowing4 ,if asked why the bells are ringing1 we mention a royal marriage1 or a victory1 or a church meeting1 or a factory dinner hour1 or whatever the occasion may be4 ,we do not consider it necessary to mention that the bells are struck by a clapper4 ,our hearer understands this without our mentioning it4 ,nor do we consider it necessary to mention the acoustic condition1 that the vibration of the bells is communicated to our ears through the air1 or the physiological condition1 that the vibrations in the drums of our ears are conveyed by a certain mechanism of bone and tissue to the nerves4 ,our hearer may not care to know this1 though quite prepared to admit that these conditions are indispensable antecedents4 ,similarly1 a physiographer1 in stating the cause of the periodical inundation of the ,nile1 would consider it enough to mention the melting of snow on the mountains in the interior of ,africa1 without saying anything of such conditions as the laws of gravity or the laws of liquefaction by heat1 though he knows that these conditions are also indispensable4 ,death is explained by the doctor when referred to a gunshot wound1 or a poison1 or a virulent disease4 ,the ,pathologist may inquire further1 and the ,moral ,philosopher further still4 ,but all inquiries into indispensable conditions are inquiries into cause4 ,and all alike have to be on their guard against mistaking simple sequence for consequence4 ,to speak of the sum total of conditions1 as the ,cause in a distinctively scientific sense1 is misleading in another direction4 ,it rather encourages the idea that science investigates conditions in the lump1 merely observing the visible relations between sets of antecedents and their consequents4 ,now this is the very thing that science must avoid in order to make progress4 ,it analyses the antecedent situation1 tries to separate the various coefficients1 and finds out what they are capable of singly4 ,it must recognise that some of the antecedents of which it is in search are not open to observation4 ,it is these1 indeed1 for the most part that constitute the special subject-matter of the sciences in ,molar as well as in ,molecular ,physics4 ,for practical every-day purposes1 it is chiefly the visible succession of phenomena that concerns us1 and we are interested in the latent conditions only in as far as they provide safer ground for inference regarding such visible succession4 ,but to reach the latent conditions is the main work of science4 ,it is1 however1 only through observation of what is open to the senses that science can reach the underlying conditions1 and1 therefore1 to understand its methods we must consider generally what is open to observation in causal succession4 ,what can be observed when phenomena follow one another as cause and effect1 that is1 when the one happens in consequence of the happening of the other8 ,in ,hume's theory1 which ,mill formally adopted with a modification1#c there is nothing observable but the constancy or invariability of the connexion4 ,when we say that ,fire burns1 there is nothing to be observed except that a certain sensation invariably follows upon close proximity to fire4 ,but this holds good only if our observation is arbitrarily limited to the facts enounced in the expression4 ,if this theory were sound1 science would be confined to the observation of empirical laws4 ,but that there is something wrong with it becomes apparent when we reflect that it has been ascertained beyond doubt that in many observed changes1 and presumably in all1 there is a transference of energy from one form to another4 ,the paralogism really lies in the assumption from which ,hume deduced his theory1 namely1 that every idea is a copy of some impression4 ,as a matter of fact1 we have ideas that are not copies of any one impression1 but a binding together1 colligation1 or intellection of several impressions4 ,psychological analysis shows us that even when we say that things exist with certain qualities1 we are expressing not single impressions or mental phenomena1 but supposed causes and conditions of such1 noumena in short1 which connect our recollections of many separate impressions and expectations of more4 ,the ,experimental ,methods proceed on the assumption that there is other outward and visible evidence of causal connexion than invariability of sequence4 ,in the leading ,method it is assumed that when events may be observed to follow one another in a certain way1 they are in causal sequence4 ,if we can make sure that an antecedent change is the only change that has occurred in an antecedent situation1 we have proof positive that any immediately subsequent change in the situation is a consequent1 that the successive changes are in causal sequence4 ,thus when ,pascal's barometer was carried to the top of ,puy le ,dome1 and the mercury in it fell1 the experimenters argued that the fall of the mercury was causally connected with the change of elevation1 all the other circumstances remaining the same4 ,this is the foundation of the so-called ,method of ,difference4 ,to determine that the latent condition was a difference in the weight of the atmosphere1 needed other observations1 calculations and inferences2 but if it could be shown that the elevation was the only antecedent changed in a single instance1 causal connexion was established between this and the phenomenon of the fall of the barometer4 ,it is obvious that in coming to this conclusion we assume what cannot be demonstrated but must simply be taken as a working principle to be confirmed by its accordance with experience1 that nothing comes into being without some change in the antecedent circumstances4 ,this is the assumption known as the ,law of ,causation--ex nihilo nihil fit4 ,again1 certain observable facts are taken as evidence that there is no causal connexion4 ,on the assumption that any antecedent in whose absence a phenomenon takes place is not causally connected with it1 we set aside or eliminate various antecedents as fortuitous or non-causal4 ,this negative principle1 as we shall see1 is the foundation of what ,mill called the ,method of ,agreement4 ,be it remarked1 once for all1 that before coming to a conclusion on the ,positive ,method or ,method of ,difference1 we may often have to make many observations on the ,negative ,method4 ,thus ,pascal's experimenters1 before concluding that the change of altitude was the only influential change1 tried the barometer in exposed positions and in sheltered1 when the wind blew and when it was calm1 in rain and in fog1 in order to prove that these circumstances were indifferent4 ,we must expound and illustrate the methods separately1 but every method known to science may have in practice to be employed in arriving at a single conclusion4 ,footnote #a3 ,this is implied1 as ,i have already remarked1 in the word ,experimental4 ,an experiment is a proof or trial3 of what8 ,of a theory1 a conjecture4 ,footnote #b3 ,if we remember1 as becomes apparent on exact psychological analysis1 that things and their qualities are as much noumena and not1 strictly speaking1 phenomena as the attraction of gravity or the quaquaversus principle in liquid pressure1 the prejudice against occultism is mitigated4 ,footnote #c3 ,the modification was that causation is not only invariable but also unconditional sequence4 ,this addition of unconditionality as part of the meaning of cause1 after defining cause as the sum total of the conditions1 is very much like arguing in a circle4 ,after all1 the only point recognised in the theory as observable is the invariability of the sequence4 ,but this is less important than the fact that in his canons of the ,experimental ,methods ,mill recognised that more is observable4 ,,chapter ,,iv4 ,,methods ,,of ,,observation4--,,single ,,difference4 ,i4--,,the ,,principle ,,of ,,single ,,difference4--,,mill',s ,,canon4 ,on what principle do we decide1 in watching a succession of phenomena1 that they are connected as cause and effect1 that one happened in consequence of the happening of another8 ,it may be worded as follows3-- ,when the addition of an agent is followed by the appearance or its subtraction by the disappearance of a certain effect1 no other influential circumstance having been added or subtracted at the same time or in the meantime1 and no change having occurred among the original circumstances1 that agent is a cause of the effect4 ,on this principle we would justify our belief in the causal properties of common things--that fire burns1 that food appeases hunger1 that water quenches thirst1 that a spark ignites gunpowder1 that taking off a tight shoe relieves a pinched foot4 ,we have observed the effect following when there was no other change in the antecedent circumstances1 when the circumstance to which we refer it was simply added to or subtracted from the prior situation4 ,suppose we doubt whether a given agent is or is not capable of producing a certain effect in certain circumstances1 how do we put it to the proof8 ,we add it singly or subtract it singly1 taking care that everything else remains as before1 and watch the result4 ,if we wish to know whether a spoonful of sugar can sweeten a cup of tea1 we taste the tea without the sugar1 then add the sugar1 and taste again4 ,the isolated introduction of the agent is the proof1 the experiment4 ,if we wish to know whether a pain in the foot is due to a tight lacing1 we relax the lacing and make no other change3 if the pain then disappears1 we refer it to the lacing as the cause4 ,the proof is the disappearance of the pain on the subtraction of the single antecedent4 ,the principle on which we decide that there is causal connexion is the same whether we make the experimental changes ourselves or merely watch them as they occur--the only course open to us with the great forces of nature which are beyond the power of human manipulation4 ,in any case we have proof of causation when we can make sure that there was only one difference in the antecedent circumstances corresponding to the difference of result4 ,mill's statement of this principle1 which he calls the ,canon of the ,method of ,difference1 is somewhat more abstract1 but the proof relied upon is substantially the same4 ,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 former1 the circumstance in which alone the two instances differ is the effect1 or#a the cause1 or an indispensable part of the cause1 of the phenomenon4 ,mill's statement has the merit of exactness1 but besides being too abstract to be easy of application1 the canon is apt to mislead in one respect4 ,the wording of it suggests that the two instances required must be two separate sets of circumstances1 such as may be put side by side and compared1 one exhibiting the phenomenon and the other not4 ,now in practice it is commonly one set of circumstances that we observe with a special circumstance introduced or withdrawn3 the two instances1 the data of observation1 are furnished by the scene before and the scene after the experimental interference4 ,in the case1 for example1 of a man shot in the head and falling dead1 death being the phenomenon in question1 the instance where it does not occur is the man's condition before he received the wound1 and the instance where it does occur is his condition after1 the single circumstance of difference being the wound1 a difference produced by the addition or introduction of a new circumstance4 ,again1 take the common coin and feather experiment1 contrived to show that the resistance of the air is the cause of the feather's falling to the ground more slowly than the coin4 ,the phenomenon under investigation is the retardation of the feather4 ,when the two are dropped simultaneously in the receiver of an air-pump1 the air being left in1 the feather flutters to the ground after the coin4 ,this is the instance where the phenomenon occurs4 ,then the air is pumped out of the receiver1 and the coin and the feather being dropped at the same instant reach the ground together4 ,this is the instance where the phenomenon does not occur4 ,the single circumstances of difference is the presence of air in the former instance1 a difference produced by the subtraction of a circumstance4 ,mill's ,canon is framed so as to suit equally whether the significant difference is produced by addition to or subtraction from an existing sum of circumstances4 ,but that is misleading in so far as it suggests that the two instances must be separate sets of circumstances1 is shown by the fact that it misled himself when he spoke of the application of the method in social investigations1 such as the effect of ,protection on national wealth4 ,in order1 he says1 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 ,we must have two nations alike in all natural advantages and disadvantages2 resembling each other in every quality physical and moral2 habits1 usages1 laws1 and institutions1 and differing only in the circumstance that the one has a prohibitory tariff and the other has not4 ,it being impossible ever to find two such instances1 he concluded that the ,method of ,difference could not be applied in social inquiries4 ,but really it is not necessary in order to have two instances that we should have two different nations3 the same nation before and after a new law or institution fulfils that requirement4 ,the real difficulty1 as we shall see1 is to satisfy the paramount condition that the two instances shall differ in a single circumstance4 ,every new enactment would be an experiment after the ,method of ,difference1 if all circumstances but it remained the same till its results appeared4 ,it is because this seldom or never occurs that decisive observation is difficult or impossible1 and the simple method of difference has to be supplemented by other means4 ,to introduce or remove a circumstance singly is the typical application of the principle2 but it may be employed also to compare the effects of different agents1 each added alone to exactly similar circumstances4 ,a simple example is seen in ,mr4 ,jamieson's agricultural experiments to determine the effects of different manures1 such as coprolite and superphosphate1 on the growth of crops4 ,care is taken to have all the antecedent circumstances as exactly alike as possible1 except as regards the agency whose effects are to be observed4 ,a field is chosen of uniform soil and even exposure and divided into plots3 it is equally drained so as to have the same degree of moisture throughout2 the seed is carefully selected for the whole sowing4 ,between the sowing and the maturing of the crop all parts of the field are open to the same weather4 ,each plot may thus be regarded as practically composing the same set of conditions1 and any difference in the product may with reasonable probability be ascribed to the single difference in the antecedents1 the manures which it is desired to compare4 ,,ii4--,,application ,,of ,,the ,,principle4 ,the principle of referring a phenomenon to the only immediately preceding change in antecedent circumstances that could possibly have affected it1 is so simple and so often employed by everybody every day1 that at first we do not see how there can be any difficulty about it or any possibility of error4 ,and once we understand how many difficulties there are in reaching exact knowledge even on this simple principle1 and what care has to be taken1 we are apt to overrate its value1 and to imagine that it carries us further than it really does4 ,the scientific expert must know how to apply this principle1 and a single application of it with the proper precautions may take him days or weeks1 and yet all that can be made good by it may carry but a little way towards the knowledge of which he is in search4 ,when the circumstances are simple and the effect follows at once1 as when hot water scalds1 or a blow with a stick breaks a pane of glass1 there can be no doubt of the causal connexion so far1 though plenty of room for further inquiry into the why4 ,but the mere succession of phenomena may be obscure4 ,we may introduce more than one agent without knowing it1 and if some time elapses between the experimental interference and the appearance of the effect1 other agents may come in without our knowledge4 ,we must know exactly what it is that we introduce and all the circumstances into which we introduce it4 ,we are apt to ignore the presence of antecedents that are really influential in the result4 ,a man heated by work in the harvest field hastily swallows a glass of water1 and drops down dead4 ,there is no doubt that the drinking of the water was a causal antecedent1 but the influential circumstance may not have been the quantity or the quality of the liquid but its temperature1 and this was introduced into the situation as well as a certain amount of the liquid components4 ,in making tea we put in so much tea and so much boiling water4 ,but the temperature of the pot is also an influential circumstance in the resulting infusion4 ,so in chemical experiments1 where one might expect the result to depend only upon the proportions of the ingredients1 it is found that the quantity is also influential1 the degree of heat evolved entering as a factor into the result4 ,before we can apply the principle of single difference1 we must make sure that there is really only a single difference between the instances that we bring into comparison4 ,the air-pump was invented shortly before the foundation of the ,royal ,society1 and its members made many experiments with this new means of isolating an agent and thus discovering its potentialities4 ,for example1 live animals were put into the receiver1 and the air exhausted1 with the result that they quickly died4 ,the absence of the air being the sole difference1 it was thus proved to be indispensable to life4 ,but air is a composite agent1 and when means were contrived of separating its components1 the effects of oxygen alone and of carbonic acid alone were experimentally determined4 ,a good example of the difficulty of excluding agencies other than those we are observing1 of making sure that none such intrude1 is found in the experiments that have been made in connexion with spontaneous generation4 ,the question to be decided is whether life ever comes into existence without the antecedent presence of living germs4 ,and the method of determining this is to exclude all germs rigorously from a compound of inorganic matter1 and observe whether life ever appears4 ,if we could make sure in any one case that no germs were antecedently present1 we should have proved that in that case at least life was spontaneously generated4 ,the difficulty here arises from the subtlety of the agent under observation4 ,the notion that maggots are spontaneously generated in putrid meat1 was comparatively easy to explode4 ,it was found that when flies were excluded by fine wire-gauze1 the maggots did not appear4 ,but in the case of microscopic organisms proof is not so easy4 ,the germs are invisible1 and it is difficult to make certain of their exclusion4 ,a ,french experimenter1 ,pouchet1 thought he had obtained indubitable cases of spontaneous generation4 ,he took infusions of vegetable matter1 boiled them to a pitch sufficient to destroy all germs of life1 and hermetically sealed up the liquid in glass flasks4 ,after an interval1 micro-organisms appeared4 ,doubts as to the conclusion that they had been spontaneously generated turned upon two questions3 whether all germs in the liquid had been destroyed by the preliminary boiling1 and whether germs could have found access in the course of the interval before life appeared4 ,at a certain stage in ,pouchet's process he had occasion to dip the mouths of the flasks in mercury4 ,it occurred to ,pasteur in repeating the experiments that germs might have found their way in from the atmospheric dust on the surface of this mercury4 ,that this was so was rendered probable by his finding that when he carefully cleansed the surface of the mercury no life appeared afterwards in his flasks4 ,the application of the principle in human affairs is rendered uncertain by the immense complication of the phenomena1 the difficulty of experiment1 and the special liability of our judgments to prejudice4 ,that men and communities of men are influenced by circumstances is not to be denied1 and the influence of circumstances1 if it is to be traced at all1 must be traced through observed facts4 ,observation of the succession of phenomena must be part at least of any method of tracing cause and effect4 ,we must watch what follows upon the addition of new agencies to a previously existing sum4 ,but we can seldom or never get a decisive observation from one pair of instances1 a clear case of difference of result preceded by a single difference in the antecedents4 ,the simple ,method of ,experimental ,addition or ,subtraction is practically inapplicable4 ,we can do nothing with a man analogous to putting him into a hermetically sealed retort4 ,any man or any community that is the subject of our observations must be under manifold influences4 ,each of them probably works some fraction of the total change observable1 but how are they to be disentangled8 ,consider1 for example1 how impossible it would be to prove in an individual case1 on the strict principle of ,single ,difference1 that ,evil communications corrupt good manners4 ,moral deterioration may be observed following upon the introduction of an evil companion1 but how can we make sure that no other degrading influence has operated1 and that no original depravity has developed itself in the interval8 ,yet such propositions of moral causation can be proved from experience with reasonable probability4 ,only it must be by more extended observations than the strict ,method of ,difference takes into account4 ,the method is to observe repeated coincidences between evil companionship and moral deterioration1 and to account for this in accordance with still wider observations of the interaction of human personalities4 ,for equally obvious reasons the simple ,method of ,difference is inapplicable to tracing cause and effect in communities4 ,every new law or repeal of an old law is the introduction of a new agency1 but the effects of it are intermixed with the effects of other agencies that operate at the same time4 ,thus ,professor ,cairnes remarks1 concerning the introduction of a high ,protective ,tariff into the ,united ,states in #ahfa1 that before its results could appear in the trade and manufacture of the ,states1 there occurred 7#a7 ,the great ,civil ,war1 attended with enormous destruction of capital2 7#b7 ,consequent upon this the creation of a huge national debt1 and a great increase of taxation2 7#c7 ,the issue of an inconvertible paper currency1 deranging prices and wages2 7#d7 ,the discovery of great mineral resources and oil-springs2 7#e7 ,a great extension of railway enterprise4 ,obviously in such circumstances other methods than the ,method of ,difference must be brought into play before there can be any satisfactory reasoning on the facts observed4 ,still what investigators aim at is the isolation of the results of single agencies4 ,footnote #a3 ,prof4 ,bain1 who adopts ,mill's ,canon1 silently drops the words within brackets4 ,they seem to be an inadvertence4 ,the circumstance1 in all the examples that ,mill gives1 is an antecedent circumstance4 ,herschel's statement1 of which ,mill's is an adaptation1 runs as follows3 ,if we can either find produced by nature1 or produce designedly for ourselves1 two instances which agree exactly in all but one particular and differ in that one1 its influence in producing the phenomenon1 if it have any1 must thereby be rendered apparent4 ,,chapter ,v4 ,,methods ,,of ,,observation4--,,elimination4--,,single ,,agreement4 ,i4--,,the ,,principle ,,of ,,elimination4 ,the essence of what ,mill calls the ,method of ,agreement is really the elimination#a of accidental1 casual1 or fortuitous antecedents4 ,it is a method employed when we are given an effect and set to work to discover the cause4 ,it is from the effect that we start and work back4 ,we make a preliminary analysis of the antecedents2 call the roll1 as it were1 of all circumstances present before the effect appeared4 ,then we proceed to examine other instances of the same effect1 and other instances of the occurrence of the various antecedents1 and bring to bear the principle that any antecedent in the absence of which the effect has appeared or on the presence of which it has not appeared may be set aside as fortuitous1 as being not an indispensable antecedent4 ,this is really the guiding principle of the method as a method of observation4 ,let the inquiry1 for example1 be into the cause of ,endemic ,goitre4 ,instances of the disease have been collected from the medical observations of all countries over many years4 ,why is it endemic in some localities and not in others8 ,we proceed on the assumption that the cause1 whatever it is1 must be some circumstance common to all localities where it is endemic4 ,if any such circumstance is obvious at once1 we may conclude on the mere principle of repeated coincidence that there is causal connexion between it and the disease1 and continue our inquiry into the nature of the connexion4 ,but if no such circumstance is obvious1 then in the course of our search for it we eliminate1 as fortuitous1 conditions that are present in some cases but absent in others4 ,one of the earliest theories was that endemic goitre was connected with the altitude and configuration of the ground1 some notorious centres of it being deeply cleft mountain valleys1 with little air and wind and damp marshy soil4 ,but wider observation found it in many valleys neither narrower nor deeper than others that were exempt1 and also in wide exposed valleys such as the ,aar4 ,was it due to the geological formation8 ,this also had to be abandoned1 for the disease is often incident within very narrow limits1 occurring in some villages and sparing others though the geological formation is absolutely the same4 ,was it due to the character of the drinking-water8 ,especially to the presence of lime or magnesia8 ,this theory was held strongly1 and certain springs characterised as goitre-springs4 ,but the springs in some goitre centres show not a trace of magnesia4 ,the comparative immunity of coast regions suggested that it might be owing to a deficiency of iodine in the drinking-water and the air1 and many instances were adduced in favour of this4 ,but further inquiries made out the presence of iodine in considerable quantities1 in the air1 the water1 and the vegetation of districts where goitre was widely prevalent2 while in ,cuba it is said that not a trace of iodine is discoverable either in the air or the water1 and yet it is quite free from goitre4 ,after a huge multiplication of instances1 resulting in the elimination of every local condition that had been suggested as a possible cause1 ,hirsch came to the conclusion that the true cause must be a morbid poison1 and that endemic goitre has to be reckoned among the infectious diseases4#b ,on this negative principle1 that if a circumstance comes and goes without bringing the phenomenon in its train1 the phenomenon is causally independent of it1 common-sense is always at work disconnecting events that are occasionally coincident in time4 ,a bird sings at our window1 for example1 and the clock ticks on the mantelpiece4 ,but the clock does not begin to tick when the bird begins to sing1 nor cease to tick when the bird flies away4 ,accordingly1 if the clock should stop at any time1 and we wished to inquire into the cause1 and anybody were to suggest that the stoppage of the clock was caused by the stoppage of a bird's song outside1 we should dismiss the suggestion at once4 ,we should eliminate this circumstance from our inquiry1 on the ground that from other observations we knew it to be a casual or fortuitous concomitant4 ,hotspur's retort to ,glendover 7p4 #big7 was based on this principle4 ,when poetic sentiment or superstition rejects a verdict of common-sense or science1 it is because it imagines a causal connexion to exist that is not open to observation1 as in the case of the grandfather's clock which stopped short never to go again when the old man died4 ,,ii4--,,the ,,principle ,,of ,,single ,,agreement4 ,the procedure in ,mill's ,method of ,agreement consists in thus eliminating fortuitous antecedents or concomitants till only one remains4 ,we see the nature of the proof relied upon when we ask1 ,how far must elimination be carried in order to attain proof of causal connexion8 ,the answer is that we must go on till we have eliminated all but one4 ,we must multiply instances of the phenomenon1 till we have settled of each of the antecedents except one that it is not the cause4 ,we must have taken account of all the antecedents1 and we must have found in our observations that all but one have been only occasionally present4 ,when all the antecedents of an effect except one can be absent without the disappearance of the effect1 that one is causally connected with the effect1 due precautions being taken that no other circumstances have been present besides those taken account of4 ,mill's ,canon of the ,method of ,agreement is substantially identical with this3-- ,when two or more instances of the phenomenon under investigation have only one circumstance in common1 the circumstance in which alone all the instances agree is the cause 7or effect7 of the given phenomenon4 ,herschel's statement1 on which this canon is founded1 runs as follows3 ,any circumstance in which all the facts without exception agree1 may be the cause in question1 or if not1 at least a collateral effect of the same cause3 if there be but one such point of agreement1 the possibility becomes a certainty4 ,all the instances examined must agree in one circumstance--hence the title ,method of ,agreement4 ,but it is not in the agreement merely that the proof consists1 but the agreement in one circumstance combined with difference in all the other circumstances1 when we are certain that every circumstance has come within our observation4 ,it is the singleness of the agreement that constitutes the proof just as it is the singleness of the difference in the ,method of ,difference4#c ,it has been said that ,mill's ,method of ,agreement amounts after all only to an uncontradicted ,inductio per enumerationem simplicem1 which he himself stigmatised as ,induction improperly so called4 ,but this is not strictly correct4 ,it is a misunderstanding probably caused by calling the method that of agreement simply1 instead of calling it the ,method of ,single ,agreement1 so as to lay stress upon the process of elimination by which the singleness is established4 ,it is true that in the course of our observations we do perform an induction by simple enumeration4 ,in eliminating1 we at the same time generalise4 ,that is to say1 in multiplying instances for the elimination of non-causes1 we necessarily at the same time multiply instances where the true causal antecedent1 if there is only one possible1 is present4 ,an antecedent containing the true cause must always be there when the phenomenon appears1 and thus we may establish by our eliminating observations a uniformity of connexion between two facts4 ,take1 for example1 ,roger ,bacon's inquiry into the cause of the colours of the rainbow4 ,his first notion seems to have been to connect the phenomenon with the substance crystal1 probably from his thinking of the crystal firmament then supposed to encircle the universe4 ,he found the rainbow colours produced by the passage of light through hexagonal crystals4 ,but on extending his observations1 he found that the passage of light through other transparent mediums was also attended by the phenomenon4 ,he found it in dewdrops1 in the spray of waterfalls1 in drops shaken from the oar in rowing4 ,he thus eliminated the substance crystal1 and at the same time established the empirical law that the passage of light through transparent mediums of a globular or prismatic shape was a causal antecedent of the rainbow colours4#d ,ascertainment of invariable antecedents may thus proceed side by side with that of variable antecedents1 the use of the elimination being simply to narrow the scope of the inquiry4 ,but the proof set forth in ,mill's ,canon does not depend merely on one antecedent or concomitant being invariably present1 but also on the assumption that all the influential circumstances have been within our observation4 ,then only can we be sure that the instances have only one circumstance in common4 ,the truth is that owing to the difficulty of fulfilling this condition1 proof of causation in accordance with ,mill's ,canon is practically all but impossible4 ,it is not attained in any of the examples commonly given4 ,the want of conclusiveness is disguised by the fact that both elimination and positive observation of mere agreement or uniform concomitance are useful and suggestive in the search for causes1 though they do not amount to complete proof such as the ,canon describes4 ,thus in the inquiry into the cause of goitre1 the elimination serves some purpose though the result is purely negative4 ,when the inquirer is satisfied that goitre is not originated by any directly observable local conditions1 altitude1 temperature1 climate1 soil1 water1 social circumstances1 habits of exertion1 his search is profitably limited4 ,and mere frequency1 much more constancy of concomitance1 raises a presumption of causal connexion1 and looking out for it is valuable as a mode of reconnoitring4 ,the first thing that an inquirer naturally asks when confronted by numerous instances of a phenomenon is1 ,what have they in common8 ,and if he finds that they have some one circumstance invariably or even frequently present1 although he cannot prove that they have no other circumstance in common as the ,cannon of ,single ,agreement requires1 the presumption of causal connexion is strong enough to furnish good ground for further inquiry4 ,if an inquirer finds an illness with marked symptoms in a number of different households1 and finds also that all the households get their milk supply from the same source1 this is not conclusive proof of causation1 but it is a sufficient presumption to warrant him in examining whether there is any virulent ingredient in the milk4 ,thus varying the circumstances so as to bring out a common antecedent1 though it does not end in exact proof1 may indicate causal connexion though it does not prove what the nature of the connexion is4 ,roger ,bacon's observations indicated that the production of rainbow colours was connected with the passage of light through a transparent globe or prism4 ,it was reserved for ,newton to prove by other methods that white light was composed of rays1 and that those rays were differently refracted in passing through the transparent medium4 ,we have another example of how far mere agreement1 revealed by varying the circumstances1 carries us towards discovery of the cause1 in ,wells's investigation of the cause of dew4 ,comparing the numerous instances of dew appearing without visible fall of moisture1 ,wells found that they all agreed in the comparative coldness of the surface dewed4 ,this was all the agreement that he established by observation2 he did not carry observation to the point of determining that there was absolutely no other common circumstance3 when he had simply discovered dewed surfaces1 he tried next to show by reasoning from other knows facts how the coldness of the surface affected the aqueous vapour of the neighbouring air4 ,he did not establish his ,theory of ,dew by the ,method of ,agreement3 but the observation of an agreement or common feature in a number of instances was a stage in the process by which he reached his theory4 ,,iii4--,,mill',s ,,joint ,,method ,,of ,,agreement ,,and ,,difference4 ,after examining a variety of instances in which an effect appears1 and finding that they all agree in the antecedent presence of some one circumstance1 we may proceed to examine instances otherwise similar 7in pari materia1 as ,prof4 ,fowler puts it7 where the effect does not appear4 ,if these all agree in the absence of the circumstance that is uniformly present with the effect1 we have corroborative evidence that there is causal connexion between this circumstance and the effect4 ,the principle of this method seems to have been suggested to ,mill by ,wells's investigations into ,dew4 ,wells exposed a number of polished surfaces of various substances1 and compared those in which there was a copious deposit of dew with those in which there was little or none4 ,if he could have got two surfaces1 one dewed and the other not1 identical in every concomitant but one1 he would have attained complete proof on the principle of ,single ,difference4 ,but this being impracticable1 he followed a course which approximated to the method of eliminating every circumstance but one from instances of dew1 and every circumstance but one in the instances of no-dew4 ,mill sums up as follows the results of his experiments3 ,it 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 seem therefore to have detected the characteristic difference between the substances on which the dew is produced1 and those on which it is not produced4 ,and thus have been realised the requisitions of what we have termed the ,indirect ,method of ,difference1 or the ,joint ,method of ,agreement and ,difference4 ,the ,canon of this ,method is accordingly stated by ,mill as follows3-- ,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 circumstance2 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 ,in practice1 however1 this theoretical standard of proof is never attained4 ,what investigators really proceed upon is the presumption afforded1 to use ,prof4 ,bain's terms1 by ,agreement in ,presence combined with ,agreement in ,absence4 ,when it is found that all substances which have a strong smell agree in being readily oxidisable1 and that the marsh gas or carbonetted hydrogen which has no smell is not oxidisable at common temperatures1 the presumption that oxidation is one of the causal circumstances in smell is strengthened1 even though we have not succeeded in eliminating every circumstance but this one from either the positive or the negative instances4 ,so in the following examples given by ,prof4 ,fowler there is not really a compliance with the theoretical requirements of ,mill's ,method3 there is only an increased presumption from the double agreement4 ,the ,joint ,method of ,agreement and ,difference 7or the ,indirect ,method of ,difference1 or1 as ,i should prefer to call it1 the ,double ,method of ,agreement7 is being continually employed by us in the ordinary affairs of life4 ,if when ,i take a particular kind of food1 ,i find that ,i invariably suffer from some particular form of illness1 whereas1 when ,i leave it off1 ,i cease to suffer1 ,i entertain a double assurance that the food is the cause of my illness4 ,i have observed that a certain plant is invariably plentiful on a particular soil2 if1 with a wide experience1 ,i fail to find it growing on any other soil1 ,i feel confirmed in my belief that there is in this particular soil some chemical constituent1 or some peculiar combination of chemical constituents1 which is highly favourable1 if not essential1 to the growth of the plant4 ,footnote #a3 ,elimination1 or setting aside as being of no concern1 must not be confounded with the exclusion of agents practised in applying the ,method of ,difference4 ,we use the word in its ordinary sense of putting outside the sphere of an argument4 ,by a curious slip1 ,professor ,bain follows ,mill in applying the word sometimes to the process of singling out or disentangling a causal circumstance4 ,this is an inadvertent departure from the ordinary usage1 according to which elimination means discarding from consideration as being non-essential4 ,footnote #b3 ,hirsch's ,geographical and ,historical ,pathology1 ,creighton's translation1 vol4 ii4 pp4 #aba-bjb4 ,footnote #c3 ,the bare titles ,difference and ,agreement1 though they have the advantage of simplicity1 are apt to puzzle beginners inasmuch as in the ,method of ,difference the agreement among the instances is at a maximum1 and the difference at a minimum1 and vice versa in the ,method of ,agreement4 ,in both ,methods it is really the isolation of the connexion between antecedent and sequent that constitutes the proof4 ,footnote #d3 ,that rainbows in the sky are produced by the passage of light through minute drops in the clouds was an inference from this observed uniformity4 ,,chapter ,,vi4 ,,methods ,,of ,,observation4--,,minor ,,methods4 ,i4--,,concomitant ,,variations4 ,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 ,this simple principle is constantly applied by us in connecting and disconnecting phenomena4 ,if we hear a sound which waxes and wanes with the rise and fall of the wind1 we at once connect the two phenomena4 ,we may not know what the causal connexion is1 but if they uniformly vary together1 there is at once a presumption that the one is causally dependent on the other1 or that both are effects of the same cause4 ,this principle was employed by ,wells in his researches into ,dew4 ,some bodies are worse conductors of heat than others1 and rough surfaces radiate heat more rapidly than smooth4 ,wells made observations on conductors and radiators of various degrees1 and found that the amount of dew deposited was greater or less according as the objects conducted heat slowly or radiated heat rapidly4 ,he thus established what ,herschel called a scale of intensity between the conducting and radiating properties of the bodies bedewed1 and the amount of the dew deposit4 ,the explanation was that in bad conductors the surface cools more quickly than in good conductors because heat is more slowly supplied from within4 ,similarly in rough surfaces there is a more rapid cooling because heat is given off more quickly4 ,but whatever the explanation might be1 the mere concomitant variation of the dew deposit with these properties showed that there was some causal connexion between them4 ,it must be remembered that the mere fact of concomitant variation is only an index that some causal connexion exists4 ,the nature of the connexion must be ascertained by other means1 and may remain a problem1 one of the uses of such observed facts being indeed to suggest problems1 for inquiry4 ,thus a remarkable concomitance has been observed between spots on the sun1 displays of ,aurora ,borealis1 and magnetic storms4 ,the probability is that they are causally connected1 but science has not yet discovered how4 ,similarly in the various sciences properties are arranged in scales of intensity1 and any correspondence between two scales becomes a subject for investigation on the assumption that it points to a causal connexion4 ,we shall see afterwards how in social investigations concomitant variations in averages furnish material for reasoning4 ,when two variants can be precisely measured1 the ratio of the variation may be ascertained by the ,method of ,single ,difference4 ,we may change an antecedent in degree1 and watch the corresponding change in the effect1 taking care that no other agent influences the effect in the meantime4 ,often when we cannot remove an agent altogether1 we may remove it in a measurable amount1 and observe the result4 ,we cannot remove friction altogether1 but the more it is diminished1 the further will a body travel under the impulse of the same force4 ,until a concomitant variation has been fully explained1 it is merely an empirical law1 and any inference that it extends at the same rate beyond the limits of observation must be made with due caution4 ,parallel variation1 says ,professor ,bain1 is sometimes interrupted by critical points1 as in the expansion of bodies by heat1 which suffers a reverse near the point of cooling4 ,again1 the energy of a solution does not always follow the strength2 very dilute solutions occasionally exercise a specific power not possessed in any degree by stronger4 ,so1 in the animal body1 food and stimulants operate proportionally up to a certain point1 at which their further operation is checked by the peculiarities in the structure of the living organs4444 ,we cannot always reason from a few steps in a series to the whole series1 partly because of the occurrence of critical points1 and partly from the development at the extremes of new and unsuspected powers4 ,sir ,john ,herschel remarks that until very recently 'the formulae empirically deduced for the elasticity of steam1 those for the resistance of fluids1 and on other similar subjects1 have almost invariably failed to support the theoretical structures that have been erected upon them'4#a ,,ii4--,,single ,,residue4 ,subduct from any phenomenon such part as previous induction has shown to be the effect of certain antecedents1 and the residue of the phenomenon is the effect of the remaining antecedents4 ,complicated phenomena1 in which several causes concurring1 opposing1 or quite independent of each other1 operate at once1 so as to produce a compound effect1 may be simplified by subducting the effect of all the known causes1 as well as the nature of the case permits1 either by deductive reasoning or by appeal to experience1 and thus leaving as it were a residual phenomenon to be explained4 ,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#b ,it is obvious that this is not a primary method of observation1 but a method that may be employed with great effect to guide observation when a considerable advance has been made in accurate knowledge of agents and their mode of operation4 ,the greatest triumph of the method1 the discovery of the planet ,neptune1 was won some years after the above passage from ,herschel's ,discourse was written4 ,certain perturbations were observed in the movements of the planet ,uranus3 that is to say1 its orbit was found not to correspond exactly with what it should be when calculated according to the known influences of the bodies then known to astronomers4 ,these perturbations were a residual phenomenon4 ,it was supposed that they might be due to the action of an unknown planet1 and two astronomers1 ,adams and ,le ,verrier1 simultaneously calculated the position of a body such as would account for the observed deviations4 ,when telescopes were directed to the spot thus indicated1 the planet ,neptune was discovered4 ,this was in ,september1 #ahdf3 before its actual discovery1 ,sir ,john ,herschel exulted in the prospect of it in language that strikingly expresses the power of the method4 ,we see it1 he said1 as ,columbus saw ,america from the shores of ,spain4 ,its movements have been felt1 trembling along the far-reaching line of our analysis1 with a certainty hardly inferior to that of ocular demonstration4#c ,many of the new elements in ,chemistry have been discovered in this way4 ,for example1 when distinctive spectrums had been observed for all known substances1 then on the assumption that every substance has a distinctive spectrum1 the appearance of lines not referable to any known substance indicated the existence of hitherto undiscovered substances and directed search for them4 ,thus ,bunsen in #ahfj discovered two new alkaline metals1 ,caesium and ,rubidium4 ,he was examining alkalies left from the evaporation of a large quantity of mineral water from ,durkheim4 ,on applying the spectroscope to the flame which this particular salt or mixture of salts gave off1 he found that some bright lines were visible which he had never observed before1 and which he knew were not produced either by potash or soda4 ,he then set to work to analyse the mixture1 and ultimately succeeded in separating two new alkaline substances4 ,when he had succeeded in getting them separate1 it was of course by the ,method of ,difference that he ascertained them to be capable of producing the lines that had excited his curiosity4 ,footnote #a3 ,bain's ,logic1 vol4 ii4 p4 #fd4 ,footnote #b3 ,herschel's ,discourse1 ,sec4 #aeh4 ,footnote #c3 ,de ,morgan's ,budget of ,paradoxes1 p4 #bcg4 ,,chapter ,,vii4 ,,the ,,method ,,of ,,explanation4 ,given perplexity as to the cause of any phenomenon1 what is our natural first step8 ,we may describe it as searching for a clue3 we look carefully at the circumstances with a view to finding some means of assimilating what perplexes us to what is already within our knowledge4 ,our next step is to make a guess1 or conjecture1 or1 in scientific language1 a hypothesis4 ,we exercise our ,reason or ,nous1 or ,imagination1 or whatever we choose to call the faculty1 and try to conceive some cause that strikes us as sufficient to account for the phenomenon4 ,if it is not at once manifest that this cause has really operated1 our third step is to consider what appearances ought to present themselves if it did operate4 ,we then return to the facts in question1 and observe whether those appearances do present themselves4 ,if they do1 and if there is no other way of accounting for the effect in all its circumstances1 we conclude that our guess is correct1 that our hypothesis is proved1 that we have reached a satisfactory explanation4 ,these four steps or stages may be distinguished in most protracted inquiries into cause4 ,they correspond to the four stages of what ,mr4 ,jevons calls the ,inductive ,method par excellence1 ,preliminary ,observation1 ,hypothesis1 ,deduction and ,verification4 ,seeing that the word ,induction is already an overloaded drudge1 perhaps it would be better to call these four stages the ,method of ,explanation4 ,the word ,induction1 if we keep near its original and most established meaning1 would apply strictly only to the fourth stage1 the ,verification1 the bringing in of the facts to confirm our hypothesis4 ,we might call the method the ,newtonian method1 for all four stages are marked in the prolonged process by which he made good his theory of ,gravitation4 ,to give the name of ,inductive ,method simply to all the four stages of an orderly procedure from doubt to a sufficient explanation is to encourage a widespread misapprehension4 ,there could be no greater error than to suppose that only the senses are used in scientific investigation4 ,there is no error that men of science are so apt to resent in the mouths of the non-scientific4 ,yet they have partly brought it on themselves by their loose use of the word ,induction1 which they follow ,bacon in wresting from the traditional meaning of ,induction1 using it to cover both ,induction or the bringing in of facts--an affair mainly of ,observation--and ,reasoning1 the exercise of ,nous1 the process of constructing satisfactory hypotheses4 ,in reaction against the popular misconception which ,bacon encouraged1 it is fashionable now to speak of the use of ,imagination in ,science4 ,this is well enough polemically4 ,imagination as commonly understood is akin to the constructive faculty in ,science1 and it is legitimate warfare to employ the familiar word of high repute to force general recognition of the truth4 ,but in common usage ,imagination is appropriated to creative genius in the ,fine ,arts1 and to speak of ,imagination in ,science is to suggest that ,science deals in fictions1 and has discarded ,newton's declaration ,hypotheses non fingo4 ,in a fight for popular respect1 men of science may be right to claim for themselves ,imagination2 but in the interests of clear understanding1 the logician must deplore that they should defend themselves from a charge due to their abuse of one word by making an equally unwarrantable and confusing extension of another4 ,call it what we will1 the faculty of likely guessing1 of making probable hypotheses1 of conceiving in all its circumstances the past situation or the latent and supramicroscopical situation out of which a phenomenon has emerged1 is one of the most important of the scientific man's special gifts4 ,it is by virtue of it that the greatest advancements of knowledge have been achieved1 the cardinal discoveries in ,molar and ,molecular ,physics1 ,biology1 ,geology1 and all departments of ,science4 ,we must not push the idea of stages in explanatory method too far3 the right explanation may be reached in a flash4 ,the idea of stages is really useful mainly in trying to make clear the various difficulties in investigation1 and the fact that different men of genius may show different powers in overcoming them4 ,the right hypothesis may occur in a moment1 as if by simple intuition1 but it may be tedious to prove1 and the gifts that tell in proof1 such as ,newton's immense mathematical power in calculating what a hypothesis implies1 ,darwin's patience in verifying1 ,faraday's ingenuity in devising experiments1 are all great gifts1 and may be serviceable at different stages4 ,but without originality and fertility in probable hypothesis1 nothing can be done4 ,the dispute between ,mill and ,whewell as to the place and value of hypotheses in science was in the main a dispute about words4 ,mill did not really undervalue hypothesis1 and he gave a most luminous and accurate account of the conditions of proof4 ,but here and there he incautiously spoke of the hypothetical method 7by which he meant what we have called the method of ,explanation7 as if it were a defective kind of proof1 a method resorted to by science when the experimental methods could not be applied4 ,whether his language fairly bore this construction is not worth arguing1 but this was manifestly the construction that ,whewell had in his mind when he retorted1 as if in defence of hypotheses1 that the inductive process consists in framing successive hypotheses1 the comparison of these with the ascertained facts of nature1 and the introduction into them of such modifications as the comparison may render necessary4 ,this is a very fair description of the whole method of explanation4 ,there is nothing really inconsistent with it in ,mill's account of his hypothetical method2 only he erred himself or was the cause of error in others in suggesting1 intentionally or unintentionally1 that the ,experimental ,methods were different methods of proof4 ,the hypothetical method1 as he described it1 consisting of ,induction1 ,ratiocination1 and ,verification1 really comprehends the principles of all modes of observation1 whether naturally or artificially experimental4 ,we see this at once when we ask how the previous knowledge is got in accordance with which hypotheses are framed4 ,the answer must be1 by ,observation4 ,however profound the calculations1 it must be from observed laws1 or supposed analogues of them1 that we start4 ,and it is always by ,observation that the results of these calculations are verified4 ,both ,mill and ,whewell1 however1 confined themselves too exclusively to the great hypotheses of the ,sciences1 such as ,gravitation and the ,undulatory ,theory of ,light4 ,in the consideration of scientific method1 it is a mistake to confine our attention to these great questions1 which from the multitude of facts embraced can only be verified by prolonged and intricate inquiry4 ,attempts at the explanation of the smallest phenomena proceed on the same plan1 and the verification of conjectures about them is subject to the same conditions1 and the methods of investigation and the conditions of verification can be studied most simply in the smaller cases4 ,further1 ,i venture to think it a mistake to confine ourselves to scientific inquiry in the narrow sense1 meaning thereby inquiry conducted within the pale of the exact sciences4 ,for not merely the exact sciences but all men in the ordinary affairs of life must follow the same methods or at least observe the same principles and conditions1 in any satisfactory attempt to explain4 ,tares appear among the wheat4 ,good seed was sown3 whence1 then1 come the tares8 ,an enemy has done this4 ,if an enemy has actually been observed sowing the tares1 his agency can be proved by descriptive testimony4 ,but if he has not been seen in the act1 we must resort to what is known in ,courts of ,law as circumstantial evidence4 ,this is the hypothetical method of science4 ,that the tares are the work of an enemy is a hypothesis3 we examine all the circumstances of the case in order to prove1 by inference from our knowledge of similar cases1 that thus1 and thus only1 can those circumstances be accounted for4 ,similarly1 when a question is raised as to the authorship of an anonymous book4 ,we first search for a clue by carefully noting the diction1 the structure of the sentences1 the character and sources of the illustration1 the special tracks of thought4 ,we proceed upon the knowledge that every author has characteristic turns of phrase and imagery and favourite veins of thought1 and we look out for such internal evidence of authorship in the work before us4 ,special knowledge and acumen may enable us to detect the authorship at once from the general resemblance to known work4 ,but if we would have clear proof1 we must show that the resemblance extends to all the details of phrase1 structure and imagery3 we must show that our hypothesis of the authorship of ,,xyz explains all the circumstances4 ,and even this is not sufficient1 as many erroneous guesses from internal evidence may convince us4 ,we must establish further that there is no other reasonable way of accounting for the matter and manner of the book2 for example1 that it is not the work of an imitator4 ,an imitator may reproduce all the superficial peculiarities of an author with such fidelity that the imitation can hardly be distinguished from the original3 thus few can distinguish between ,fenton's work and ,pope's in the translation of the ,odyssey4 ,we must take such known facts into account in deciding a hypothesis of authorship4 ,such hypotheses can seldom be decided on internal evidence alone3 other circumstantial evidence--other circumstances that ought to be discoverable if the hypothesis is correct--must be searched for4 ,the operation of causes that are manifest only in their effects must be proved by the same method as the operation of past causes that have left only their effects behind them4 ,whether light is caused by a projection of particles from a luminous body or by an agitation communicated through an intervening medium cannot be directly observed4 ,the only proof open is to calculate what should occur on either hypothesis1 and observe whether this does occur4 ,in such a case there is room for the utmost calculating power and experimental ingenuity4 ,the mere making of the general hypothesis or guess is simple enough1 both modes of transmitting influence1 the projection of moving matter and the travelling of an undulation or wave movement1 being familiar facts4 ,but it is not so easy to calculate exactly how a given impulse would travel1 and what phenomena of ray and shadow1 of reflection1 refraction and diffraction ought to be visible in its progress4 ,still1 no matter how intricate the calculation1 its correspondence with what can be observed is the only legitimate proof of the hypothesis4 ,,ii4--,,obstacles ,,to ,,explanation4--,,plurality ,,of ,,causes ,,and ,,intermixture ,,of ,,effects4 ,there are two main ways in which explanation may be baffled4 ,there may exist more than one cause singly capable of producing the effect in question1 and we may have no means of determining which of the equally sufficient causes has actually been at work4 ,for all that appears the tares in our wheat may be the effect of accident or of malicious design3 an anonymous book may be the work of an original author or of an imitator4 ,again1 an effect may be the joint result of several co-operating causes1 and it may be impossible to determine their several potencies4 ,the bitter article in the ,quarterly may have helped to kill ,john ,keats1 but it co-operated with an enfeebled constitution and a naturally over-sensitive temperament1 and we cannot assign its exact weight to each of these coefficients4 ,death may be the result of a combination of causes2 organic disease co-operating with exposure1 over-fatigue co-operating with the enfeeblement of the system by disease4 ,the technical names for these difficulties1 ,plurality of ,causes and ,intermixture of ,effects1 are apt to confuse without some clearing up4 ,in both kinds of difficulty more causes than one are involved3 but in the one kind of case there is a plurality of possible or equally probable causes1 and we are at a loss to decide which3 in the other kind of case there is a plurality of co-operating causes2 the effect is the result or product of several causes working conjointly1 and we are unable to assign to each its due share4 ,it is with a view to overcoming these difficulties that ,science endeavours to isolate agencies and ascertain what each is capable of singly4 ,mill and ,bain treat ,plurality of ,causes and ,intermixture of ,effects in connexion with the ,experimental ,methods4 ,it is better1 perhaps1 to regard them simply as obstacles to explanation1 and the ,experimental ,methods as methods of overcoming those obstacles4 ,the whole purpose of the ,experimental ,methods is to isolate agencies and effects3 unless they can be isolated1 the ,methods are inapplicable4 ,in situations where the effects observable may be referred with equal probability to more than one cause1 you cannot eliminate so as to obtain a single agreement4 ,the ,method of ,agreement is frustrated4 ,and an investigator can get no light from mixed effects1 unless he knows enough of the causes at work to be able to apply the ,method of ,residues4 ,if he does not1 he must simply look out for or devise instances where the agencies are at work separately1 and apply the principle of ,single ,difference4 ,great1 however1 as the difficulties are1 the theory of ,plurality and ,intermixture baldly stated makes them appear greater than they are in practice4 ,there is a consideration that mitigates the complication1 and renders the task of unravelling it not altogether hopeless4 ,this is that different causes have distinctive ways of operating1 and leave behind them marks of their presence by which their agency in a given case may be recognised4 ,an explosion1 for example1 occurs4 ,there are several explosive agencies1 capable of causing as much destruction as meets the eye at the first glance4 ,the agent in the case before us may be gunpowder or it may be dynamite4 ,but the two agents are not so alike in their mode of operation as to produce results identical in every circumstance4 ,the expert inquirer knows by previous observation that when gunpowder acts the objects in the neighbourhood are blackened2 and that an explosion of dynamite tears and shatters in a way peculiar to itself4 ,he is thus able to interpret the traces1 to make and prove a hypothesis4 ,a man's body is found dead in water4 ,it may be a question whether death came by drowning or by previous violence4 ,he may have been suffocated and afterwards thrown into the water4 ,but the circumstances will tell the true story4 ,death by drowning has distinctive symptoms4 ,if drowning was the cause1 water will be found in the stomach and froth in the trachea4 ,thus1 though there may be a plurality of possible causes1 the causation in the given case may be brought home to one by distinctive accompaniments1 and it is the business of the scientific inquirer to study these4 ,what is known as the ripple-mark in sandstone surfaces may be produced in various ways4 ,the most familiar way is by the action of the tides on the sand of the sea-shore1 and the interpreter who knows this way only would ascribe the marks at once to this agency4 ,but ripple-marks are produced also by the winds on drifting sands1 by currents of water where no tidal influence is felt1 and in fact by any body of water in a state of oscillation4 ,is it1 then1 impossible to decide between these alternative possibilities of causation8 ,no3 wind-ripples and current-ripples and tidal-ripples have each their own special character and accompanying conditions1 and the hypothesis of one rather than another may be made good by means of these4 ,in rock-formations1 ,mr4 ,page says1#a there are many things which at first sight seem similar1 and yet on more minute examination1 differences are detected and conditions discovered which render it impossible that these appearances can have arisen from the same causation4 ,the truth is that generally when we speak of plurality of causes1 of alternative possibilities of causation1 we are not thinking of the effect in its individual entirety1 but only of some general or abstract aspect of it4 ,when we say1 e4g41 that death may be produced by a great many different causes1 poison1 gunshot wounds1 disease of this or that organ1 we are thinking of death in the abstract1 not of the particular case under consideration1 which as an individual case1 has characters so distinctive that only one combination of causes is possible4 ,the effort of science is to become less and less abstract in this sense1 by observing agencies or combinations of agencies apart and studying the special characters of their effects4 ,that knowledge is then applied1 on the assumption that where those characters are present1 the agent or combination of agencies has been at work4 ,given an effect to be explained1 it is brought home to one out of several possible alternatives by circumstantial evidence4 ,bacon's phrase1 ,instantia ,crucis1#b or ,finger-post ,instance1 might be conveniently appropriated as a technical name for a circumstance that is decisive between rival hypotheses4 ,this was1 in effect1 proposed by ,sir ,john ,herschel1#c who drew attention to the importance of these crucial instances1 and gave the following example3 ,a curious example is given by ,m4 ,fresnel1 as decisive1 in his mind1 of the question between the two great opinions on the nature of light1 which1 since the time of ,newton and ,huyghens1 have divided philosophers4 ,when two very clean glasses are laid one on the other1 if they be not perfectly flat1 but one or both in an almost imperceptible degree convex or prominent1 beautiful and vivid colours will be seen between them2 and if these be viewed through a red glass1 their appearance will be that of alternate dark and bright stripes4444 ,now1 the coloured stripes thus produced are explicable on both theories1 and are appealed to by both as strong confirmatory facts2 but there is a difference in one circumstance according as one or the other theory is employed to explain them4 ,in the case of the ,huyghenian doctrine1 the intervals between the bright stripes ought to appear absolutely black2 in the other1 half bright1 when viewed in a particular manner through a prism4 ,this curious case of difference was tried as soon as the opposing consequences of the two theories were noted by ,m4 ,fresnel1 and the result is stated by him to be decisive in favour of that theory which makes light to consist in the vibrations of an elastic medium4 ,,iii4--,,the ,,proof ,,of ,a ,,hypothesis4 ,the completest proof of a hypothesis is when that which has been hypothetically assumed to exist as a means of accounting for certain phenomena is afterwards actually observed to exist or is proved by descriptive testimony to have existed4 ,our argument1 for example1 from internal evidence that ,mill in writing his ,logic aimed at furnishing a method for social investigations is confirmed by a letter to ,miss ,caroline ,fox1 in which he distinctly avowed that object4 ,the most striking example of this crowning verification in ,science is the discovery of the planet ,neptune1 in which case an agent hypothetically assumed was actually brought under the telescope as calculated4 ,examples almost equally striking have occurred in the history of the ,evolution doctrine4 ,hypothetical ancestors with certain peculiarities of structure have been assumed as links between living species1 and in some cases their fossils have actually been found in the geological register4 ,such triumphs of verification are necessarily rare4 ,for the most part the hypothetical method is applied to cases where proof by actual observation is impossible1 such as prehistoric conditions of the earth or of life upon the earth1 or conditions in the ultimate constitution of matter that are beyond the reach of the strongest microscope4 ,indeed1 some would confine the word hypothesis to cases of this kind4 ,this1 in fact1 was done by ,mill3 hypothesis1 as he defined it1 was a conjecture not completely proved1 but with a large amount of evidence in its favour4 ,but seeing that the procedure of investigation is the same1 namely1 conjecture1 calculation and comparison of facts with the calculated results1 whether the agency assumed can be brought to the test of direct observation or not1 it seems better not to restrict the word hypothesis to incompletely proved conjectures1 but to apply it simply to a conjecture made at a certain stage in whatever way it may afterwards be verified4 ,in the absence of direct verification1 the proof of a hypothesis is exclusive sufficiency to explain the circumstances4 ,the hypothesis must account for all the circumstances1 and there must be no other way of accounting for them4 ,another requirement was mentioned by ,newton in a phrase about the exact meaning of which there has been some contention4 ,the first of his ,regulae ,philosophandi laid down that the cause assumed must be a vera causa4 ,we are not1 the ,rule runs1 to admit other causes of natural things than such as both are true1 and suffice for explaining their phenomena4#d ,it has been argued that the requirement of verity is superfluous2 that it is really included in the requirement of sufficiency2 that if a cause is sufficient to explain the phenomena it must ipso facto be the true cause4 ,this may be technically arguable1 given a sufficient latitude to the word sufficiency3 nevertheless1 it is convenient to distinguish between mere sufficiency to explain the phenomena in question1 and the proof otherwise that the cause assigned really exists in rerum natura1 or that it operated in the given case4 ,the frequency with which the expression vera causa has been used since ,newton's time shows that a need is felt for it1 though it may be hard to define verity precisely as something apart from sufficiency4 ,if we examine the common usage of the expression we shall probably find that what is meant by insisting on a vera causa is that we must have some evidence for the cause assigned outside the phenomena in question4 ,in seeking for verification of a hypothesis we must extend our range beyond the limited facts that have engaged our curiosity and that demand explanation4 ,there can be little doubt that ,newton himself aimed his rule at the ,cartesian hypothesis of ,vortices4 ,this was an attempt to explain the solar system on the hypothesis that cosmic space is filled with a fluid in which the planets are carried round as chips of wood in a whirlpool1 or leaves or dust in a whirlwind4 ,now this is so far a vera causa that the action of fluid vortices is a familiar one3 we have only to stir a cup of tea with a bit of stalk in it to get an instance4 ,the agency supposed is sufficient also to account for the revolution of a planet round the sun1 given sufficient strength in the fluid to buoy up the planet4 ,but if there were such a fluid in space there would be other phenomena3 and in the absence of these other phenomena the hypothesis must be dismissed as imaginary4 ,the fact that comets pass into and out of spaces where the vortices must be assumed to be in action without exhibiting any perturbation is an instantia crucis against the hypothesis4 ,if by the requirement of a vera causa were meant that the cause assigned must be one directly open to observation1 this would undoubtedly be too narrow a limit4 ,it would exclude such causes as the ether which is assumed to fill interstellar space as a medium for the propagation of light4 ,the only evidence for such a medium and its various properties is sufficiency to explain the phenomena4 ,like suppositions as to the ultimate constitution of bodies1 it is of the nature of what ,professor ,bain calls a ,representative ,fiction3 the only condition is that it must explain all the phenomena1 and that there must be no other way of explaining all4 ,when it is proved that light travels with a finite velocity1 we are confined to two alternative ways of conceiving its transmission1 a projection of matter from the luminous body and the transference of vibrations through an intervening medium4 ,either hypothesis would explain many of the facts3 our choice must rest with that which best explains all4 ,but supposing that all the phenomena of light were explained by attributing certain properties to this intervening medium1 it would probably be held that the hypothesis of an ether had not been fully verified till other phenomena than those of light had been shown to be incapable of explanation on any other hypothesis4 ,if the properties ascribed to it to explain the phenomena of light sufficed at the same time to explain otherwise inexplicable phenomena connected with ,heat1 ,electricity1 or ,gravity1 the evidence of its reality would be greatly strengthened4 ,not only must the circumstances in hand be explained1 but other circumstances must be found to be such as we should expect if the cause assigned really operated4 ,take1 for example1 the case of ,erratic blocks or boulders1 huge fragments of rock found at a distance from their parent strata4 ,the lowlands of ,england1 ,scotland1 and ,ireland1 and the great central plain of ,northern ,europe contain many such fragments4 ,their composition shows indubitably that they once formed part of hills to the northward of their present site4 ,they must somehow have been detached and transported to where we now find them4 ,how8 ,one old explanation is that they were carried by witches1 or that they were themselves witches accidentally dropped and turned into stone4 ,any such explanation by supernatural means can neither be proved nor disproved4 ,some logicians would exclude such hypotheses altogether on the ground that they cannot be rendered either more or less probable by subsequent examination4#e ,the proper scientific limit1 however1 is not to the making of hypotheses1 but to the proof of them4 ,the more hypotheses the merrier3 only if such an agency as witchcraft is suggested1 we should expect to find other evidence of its existence in other phenomena that could not otherwise be explained4 ,again1 it has been suggested that the erratic boulders may have been transported by water4 ,water is so far a vera causa that currents are known to be capable of washing huge blocks to a great distance4 ,but blocks transported in this way have the edges worn off by the friction of their passage3 and1 besides1 currents strong enough to dislodge and force along for miles blocks as big as cottages must have left other marks of their presence4 ,the explanation now received is that glaciers and icebergs were the means of transport4 ,but this explanation was not accepted till multitudes of circumstances were examined all tending to show that glaciers had once been present in the regions where the erratic blocks are found4 ,the minute habits of glaciers have been studied where they still exist3 how they slowly move down carrying fragments of rock2 how icebergs break off when they reach water1 float off with their load1 and drop it when they melt2 how they grind and smooth the surfaces of rocks over which they pass or that are frozen into them3 how they undercut and mark the faces of precipices past which they move2 how moraines are formed at the melting ends of them1 and so forth4 ,when a district exhibits all the circumstances that are now observed to attend the action of glaciers the proof of the hypothesis that glaciers were once there is complete4 ,footnote #a3 ,page's ,philosophy of ,geology1 p4 #ch4 ,footnote #b3 ,crux in this phrase means a cross erected at the parting of ways1 with arms to tell whither each way leads4 ,footnote #c3 ,discourse1 ,sec4 #bah4 ,footnote #d3 ,causas rerum naturalium non plures admitti debere quam quae et veriae sint et carum phenomenis explicandis sufficiant4 ,footnote #e3 ,see ,prof4 ,fowler on the ,conditions of ,hypotheses1 ,inductive ,logic1 pp4 #ajj-aae4 ,,chapter ,,viii4 ,,supplementary ,,methods ,,of ,,investigation4 ,i4--,,the ,,maintenance ,,of ,,averages4--,,supplement ,,to ,,the ,,method ,,of ,,difference4 ,a certain amount of law obtains among events that are usually spoken of as matters of chance or accident in the individual case4 ,every kind of accident recurs with a certain uniformity4 ,if we take a succession of periods1 and divide the total number of any kind of event by the number of periods1 we get what is called the average for that period3 and it is observed that such averages are maintained from period to period4 ,over a series of years there is a fixed proportion between good harvests and bad1 between wet days and dry3 every year nearly the same number of suicides takes place1 the same number of crimes1 of accidents to life and limb1 even of suicides1 crimes1 or injuries by particular means3 every year in a town nearly the same number of children stray from their parents and are restored by the police3 every year nearly the same number of persons post letters without putting an address on them4 ,this maintenance of averages is simple matter of observation1 a datum of experience1 an empirical law4 ,once an average for any kind of event has been noted1 we may count upon its continuance as we count upon the continuance of any other kind of observed uniformity4 ,insurance companies proceed upon such empirical laws of average in length of life and immunity from injurious accidents by sea or land3 their prosperity is a practical proof of the correctness and completeness of the observed facts and the soundness of their inference to the continuance of the average4 ,the constancy of averages is thus a guide in practice4 ,but in reasoning upon them in investigations of cause1 we make a further assumption than continued uniformity4 ,we assume that the maintenance of the average is due to the permanence of the producing causes4 ,we regard the average as the result of the operation of a limited sum of forces and conditions1 incalculable as regards their particular incidence1 but always pressing into action1 and thus likely to operate a certain number of times within a limited period4 ,assuming the correctness of this explanation1 it would follow that any change in the average is due to some change in the producing conditions2 and this derivative law is applied as a help in the observation and explanation of social facts4 ,statistics are collected and classified3 averages are struck3 and changes in the average are referred to changes in the concomitant conditions4 ,with the help of this law1 we may make a near approach to the precision of the ,method of ,difference4 ,a multitude of unknown or unmeasured agents may be at work on a situation1 but we may accept the average as the result of their joint operation4 ,if then a new agency is introduced or one of the known agents is changed in degree1 and this is at once followed by a change in the average1 we may with fair probability refer the change in the result to the change in the antecedents4 ,the difficulty is to find a situation where only one antecedent has been changed before the appearance of the effect4 ,this difficulty may be diminished in practice by eliminating changes that we have reason to know could not have affected the circumstances in question4 ,suppose1 for example1 our question is whether the ,education ,act of #ahgb had an influence in the decrease of juvenile crime4 ,such a decrease took place post hoc2 was it propter hoc8 ,we may at once eliminate or put out of account the abolition of ,purchase in the ,army or the extension of the ,franchise as not having possibly exercised any influence on juvenile crime4 ,but with all such eliminations1 there may still remain other possible influences1 such as an improvement in the organisation of the ,police1 or an expansion or contraction in employment4 ,can you tell me in the face of chronology1 a leading statesman once asked1 that the ,crimes ,act of #ahhg did not diminish disorder in ,ireland8 ,but chronological sequence alone is not a proof of causation as long as there are other contemporaneous changes of condition that may also have been influential4 ,the great source of fallacy is our proneness to eliminate or isolate in accordance with our prejudices4 ,this has led to the gibe that anything can be proved by statistics4 ,undoubtedly statistics may be made to prove anything if you have a sufficiently low standard of proof and ignore the facts that make against your conclusion4 ,but averages and variations in them are instructive enough if handled with due caution4 ,the remedy for rash conclusions from statistics is not no statistics1 but more of them and a sound knowledge of the conditions of reasonable proof4 ,,ii4--,,the ,,presumption ,,from ,,extra-,,casual ,,coincidence4 ,we have seen that repeated coincidence raises a presumption of causal connexion between the coinciding events4 ,if we find two events going repeatedly together1 either abreast or in sequence1 we infer that the two are somehow connected in the way of causation1 that there is a reason for the coincidence in the manner of their production4 ,it may not be that the one produces the other1 or even that their causes are in any way connected3 but at least1 if they are independent one of the other1 both are tied down to happen at the same place and time1--the coincidence of both with time and place is somehow fixed4 ,but though this is true in the main1 it is not true without qualification4 ,we expect a certain amount of repeated coincidence without supposing causal connexion4 ,if certain events are repeated very often within our experience1 if they have great positive frequency1 we may observe them happening together more than once without concluding that the coincidence is more than fortuitous4 ,for example1 if we live in a neighbourhood possessed of many black cats1 and sally forth to our daily business in the morning1 a misfortune in the course of the day might more than once follow upon our meeting a black cat as we went out without raising in our minds any presumption that the one event was the result of the other4 ,certain planets are above the horizon at certain periods of the year and below the horizon at certain other periods4 ,all through the year men and women are born who afterwards achieve distinction in various walks of life1 in love1 in war1 in business1 at the bar1 in the pulpit4 ,we perceive a certain number of coincidences between the ascendancy of certain planets and the birth of distinguished individuals without suspecting that planetary influence was concerned in their superiority4 ,marriages take place on all days of the year3 the sun shines on a good many days at the ordinary time for such ceremonies2 some marriages are happy1 some unhappy2 but though in the case of many happy marriages the sun has shone upon the bride1 we regard the coincidence as merely accidental4 ,men often dream of calamities and often suffer calamities in real life3 we should expect the coincidence of a dream of calamity followed by a reality to occur more than once as a result of chance4 ,there are thousands of men of different nationalities in business in ,london1 and many fortunes are made3 we should expect more than one man of any nationality represented there to make a fortune without arguing any connexion between his nationality and his success4 ,we allow1 then1 for a certain amount of repeated coincidence without presuming causal connexion3 can any rule be laid down for determining the exact amount8 ,prof4 ,bain has formulated the following rule3 ,consider the positive frequency of the phenomena themselves1 how great frequency of coincidence must follow from that1 supposing there is neither connexion nor repugnance4 ,if there be greater frequency1 there is connexion2 if less1 repugnance4 ,i do not know that we can go further definite in precept4 ,the number of casual coincidences bears a certain proportion to the positive frequency of the coinciding phenomena3 that proportion is to be determined by common-sense in each case4 ,it may be possible1 however1 to bring out more clearly the principle on which common-sense proceeds in deciding what chance will and will not account for1 although our exposition amounts only to making more clear what it is that we mean by chance as distinguished from assignable reason4 ,i would suggest that in deciding what chance will not account for1 we make regressive application of a principle which may be called the principle of ,equal and ,unequal ,alternatives1 and which may be worded as follows3-- ,of a given number of possible alternatives1 all equally possible1 one of which is bound to occur at a given time1 we expect each to have its turn an equal number of times in the long run4 ,if several of the alternatives are of the same kind1 we expect an alternative of that kind to recur with a frequency proportioned to their greater number4 ,if any of the alternatives has an advantage1 it will recur with a frequency proportioned to the strength of that advantage4 ,situations in which alternatives are absolutely equal are rare in nature1 but they are artificially created for games of chance1 as in tossing a coin1 throwing dice1 drawing lots1 shuffling and dealing a pack of cards4 ,the essence of all games of chance is to construct a number of equal alternatives1 making them as nearly equal as possible1 and to make no prearrangement which of the number shall come off4 ,we then say that this is determined by chance4 ,if we ask why we believe that when we go on bringing off one alternative at a time1 each will have its turn1 part of the answer undoubtedly is that given by ,de ,morgan1 namely1 that we know no reason why one should be chosen rather than another4 ,this1 however1 is probably not the whole reason for our belief4 ,the rational belief in the matter is that it is only in the long run or on the average that each of the equal alternatives will have its turn1 and this is probably founded on the experience of actual trial4 ,the mere equality of the alternatives1 supposing them to be perfectly equal1 would justify us as much in expecting that each would have its turn in a single revolution of the series1 in one complete cycle of the alternatives4 ,this1 indeed1 may be described as the natural and primitive expectation which is corrected by experience4 ,put six balls in a wicker bottle1 shake them up1 and roll one out3 return this one1 and repeat the operation3 at the end of six draws we might expect each ball to have had its turn of being drawn if we went merely on the abstract equality of the alternatives4 ,but experience shows us that in six successive draws the same ball may come out twice or even three or four times1 although when thousands of drawings are made each comes out nearly an equal number of times4 ,so in tossing a coin1 heads may turn up ten or twelve times in succession1 though in thousands of tosses heads and tails are nearly equal4 ,runs of luck are thus within the rational doctrine of chances3 it is only in the long run that luck is equalised supposing that the events are pure matter of chance1 that is1 supposing the fundamental alternatives to be equal4 ,if three out of six balls are of the same colour1 we expect a ball of that colour to come out three times as often as any other colour on the average of a long succession of tries4 ,this illustrates the second clause of our principle4 ,the third is illustrated by a loaded coin or die4 ,by making regressive application of the principle thus ascertained by experience1 we often obtain a clue to special causal connexion4 ,we are at least enabled to isolate a problem for investigation4 ,if we find one of a number of alternatives recurring more frequently than the others1 we are entitled to presume that they are not equally possible1 that there is some inequality in their conditions4 ,the inequality may simply lie in the greater possible frequency of one of the coinciding events1 as when there are three black balls in a bottle of six4 ,we must therefore discount the positive frequency before looking for any other cause4 ,suppose1 for example1 we find that the ascendancy of ,jupiter coincides more frequently with the birth of men afterwards distinguished in business than with the birth of men otherwise distinguished1 say in war1 or at the bar1 or in scholarship4 ,we are not at liberty to conclude planetary influence till we have compared the positive frequency of the different modes of distinction4 ,the explanation of the more frequently repeated coincidence may simply be that more men altogether are successful in business than in war or law or scholarship4 ,if so1 we say that chance accounts for the coincidence1 that is to say1 that the coincidence is casual as far as planetary influence is concerned4 ,so in epidemics of fever1 if we find on taking a long average that more cases occur in some streets of a town than in others1 we are not warranted in concluding that the cause lies in the sanitary conditions of those streets or in any special liability to infection without first taking into account the number of families in the different streets4 ,if one street showed on the average ten times as many cases as another1 the coincidence might still be judged casual if there were ten times as many families in it4 ,apart from the fallacy of overlooking the positive frequency1 certain other fallacies or liabilities to error in applying this doctrine of chances may be specified4 #a4 ,we are apt1 under the influence of prepossession or prejudice1 to remember certain coincidences better than others1 and so to imagine extra-casual coincidence where none exists4 ,this bias works in confirming all kinds of established beliefs1 superstitious and other1 beliefs in dreams1 omens1 retributions1 telepathic communications1 and so forth4 ,many people believe that nobody who thwarts them ever comes to good1 and can produce numerous instances from experience in support of this belief4 #b4 ,we are apt1 after proving that there is a residuum beyond what chance will account for on due allowance made for positive frequency1 to take for granted that we have proved some particular cause for this residuum4 ,now we have not really explained the residuum by the application of the principle of chances3 we have only isolated a problem for explanation4 ,there may be more than chance will account for3 yet the cause may not be the cause that we assign off-hand4 ,take1 for example1 the coincidence that has been remarked between race and different forms of ,christianity in ,europe4 ,if the distribution of religious systems were entirely independent of race1 it might be said that you would expect one system to coincide equally often with different races in proportion to the positive number of their communities4 ,but the ,greek system is found almost solely among ,slavonic peoples1 the ,roman among ,celtic1 and the ,protestant among ,teutonic4 ,the coincidence is greater than chance will account for4 ,is the explanation then to be found in some special adaptability of the religious system to the character of the people8 ,this may be the right explanation1 but we have not proved it by merely discounting chance4 ,to prove this we must show that there was no other cause at work1 that character was the only operative condition in the choice of system1 that political combinations1 for example1 had nothing to do with it4 ,the presumption from extra-casual coincidence is only that there is a special cause3 in determining what that is we must conform to the ordinary conditions of explanation4 ,so coincidence between membership of the ,government and a classical education may be greater than chance would account for1 and yet the circumstance of having been taught ,latin and ,greek at school may have had no special influence in qualifying the members for their duties4 ,the proportion of classically educated in the ,government may be greater than the proportion of them in the ,house of ,commons1 and yet their eminence may be in no way due to their education4 ,men of a certain social position have an advantage in the competition for office1 and all those men have been taught ,latin and ,greek as a matter of course4 ,technically speaking1 the coinciding phenomena may be independent effects of the same cause4 #c4 ,where the alternative possibilities are very numerous1 we are apt not to make due allowance for the number1 sometimes overrating it1 sometimes underrating it4 ,the fallacy of underrating the number is often seen in games of chance1 where the object is to create a vast number of alternatives1 all equally possible1 equally open to the player1 without his being able to affect the advent of one more than another4 ,in whist1 for example1 there are some six billions of possible hands4 ,yet it is a common impression that1 one night with another1 in the course of a year1 a player will have dealt to him about an equal number of good and bad hands4 ,this is a fallacy4 ,a very much longer time is required to exhaust the possible combinations4 ,suppose a player to have #bjjj hands in the course of a year3 this is only one set1 one combination1 out of thousands of millions of such sets possible4 ,among those millions of sets1 if there is nothing but chance in the matter1 there ought to be all proportions of good and bad1 some sets all good1 some all bad1 as well as some equally divided between good and bad4#a ,sometimes1 however1 the number of possible alternatives is overrated4 ,thus1 visitors to ,london often remark that they never go there without meeting somebody from their own locality1 and they are surprised at this as if they had the same chance of meeting their fellow-visitors and any other of the four millions of the metropolis4 ,but really the possible alternatives of rencounter are far less numerous4 ,the places frequented by visitors to ,london are filled by much more limited numbers3 the possible rencounters are to be counted by thousands rather than by millions4 ,footnote #a3 ,see ,de ,morgan's ,essay on ,probabilities1 c4 vi41 ,on ,common ,notions of ,probability4 ,,chapter ,,ix4 ,,probable ,,inference ,,to ,,particulars--,,the ,,measurement ,,of ,,probability4 ,undoubtedly there are degrees of probability4 ,not only do we expect some events with more confidence than others3 we may do so1 and our confidence may be misplaced3 but we have reason to expect some with more confidence than others4 ,there are different degrees of rational expectation4 ,can those degrees be measured numerically8 ,the question has come into ,logic from the mathematicians4 ,the calculation of ,probabilities is a branch of ,mathematics4 ,we have seen how it may be applied to guide investigation by eliminating what is due to chance1 and it has been vaguely conceived by logicians that what is called the calculus of probabilities might be found useful also in determining by exact numerical measurement the probability of single events4 ,dr4 ,venn1 who has written a separate treatise on the ,logic of ,chance1 mentions accurate quantitative apportionment of our belief as one of the goals which ,logic should strive to attain4 ,the following passage will show his drift4#a ,a man in good health would doubtless like to know whether he will be alive this time next year4 ,the fact will be settled one way or the other in due time1 if he can afford to wait1 but if he wants a present decision1 ,statistics and the ,theory of ,probability can alone give him any information4 ,he learns that the odds are1 say five to one that he will survive1 and this is an answer to his question as far as any answer can be given4 ,statisticians are gradually accumulating a vast mass of data of this general character4 ,what they may be said to aim at is to place us in the position of being able to say1 in any given time or place1 what are the odds for or against any at present indeterminable fact which belongs to a class admitting of statistical treatment4 ,again1 outside the regions of statistics proper--which deal1 broadly speaking1 with events which can be numbered or measured1 and which occur with some frequency--there is still a large field as to which some better approach to a reasoned intensity of belief can be acquired4 ,what will be the issue of a coming war8 ,which party will win in the next election8 ,will a patient in the crisis of a given disease recover or not8 ,that statistics are lying here in the background1 and are thus indirectly efficient in producing and graduating our belief1 ,i fully hold2 but there is such a large intermediate process of estimating1 and such scope for the exercise of a practised judgment1 that no direct appeal to statistics in the common sense can directly help us4 ,in sketching out therefore the claims of an ,ideal condition of knowledge1 we ought clearly to include a due apportionment of belief to every event of such a class as this4 ,it is an obvious defect that one man should regard as almost certain what another man regards as almost impossible4 ,short1 therefore1 of certain prevision of the future1 we want complete agreement as to the degree of probability of every future event3 and for that matter of every past event as well4 ,technically speaking1 if we extend the name ,modality 7see p4 #gh7 to any qualification of the certainty of a statement of belief1 what ,dr4 ,venn here desiderates1 as he has himself suggested1 is a more exact measurement of the ,modality of propositions4 ,we speak of things as being certain1 possible1 impossible1 probable1 extremely probable1 faintly probable1 and so forth3 taking certainty as the highest degree of probability#b shading gradually down to the zero of the impossible1 can we obtain an exact numerical measure for the gradations of assurance8 ,to examine the principles of all the cases in which chances for and against an occurrence have been calculated from real or hypothetical data1 would be to trespass into the province of ,mathematics1 but a few simple cases will serve to show what it is that the calculus attempts to measure1 and what is the practical value of the measurement as applied to the probability of a single event4 ,suppose there are #ajj balls in a box1 #cj white and #gj black1 all being alike except in respect of colour1 we say that the chances of drawing a black ball as against a white are as #g to #c1 and the probability of drawing black is measured by the fraction #g_/aj4 ,in believing this we proceed on the principle already explained 7p4 #cef7 of ,proportional ,chances4 ,we do not know for certain whether black or white will emerge1 but knowing the antecedent situation we expect black rather than white with a degree of assurance corresponding to the proportions of the two in the box4 ,it is our degree of rational assurance that we measure by this fraction1 and the rationality of it depends on the objective condition of the facts1 and is the same for all men1 however much their actual degree of confidence may vary with individual temperament4 ,that black will be drawn seven times out of every ten on an average if we go on drawing to infinity1 is as certain as any empirical law3 it is the probability of a single draw that we measure by the fraction #g_/aj4 ,when we build expectations of single events on statistics of observed proportions of events of that kind1 it is ultimately on the same principle that rational expectation rests4 ,that the proportion will obtain on the average we regard as certain3 the ratio of favourable cases to the whole number of possible alternatives is the measure of rational expectation or probability in regard to a particular occurrence4 ,if every year five per cent4 of the children of a town stray from their guardians1 the probability of this or that child's going astray is #a_/bj4 ,the ratio is a correct measure only on the assumption that the average is maintained from year to year4 ,without going into the combination of probabilities1 we are now in a position to see the practical value of such a calculus as applied to particular cases4 ,there has been some misunderstanding among logicians on the point4 ,mr4 ,jevons rebuked ,mill for speaking disrespectfully of the calculus1 eulogised it as one of the noblest creations of the human intellect1 and quoted ,butler's saying that ,probability is the guide of life4 ,but when ,butler uttered this famous saying he was probably not thinking of the mathematical calculus of probabilities as applied to particular cases1 and it was this special application to which ,mill attached comparatively little value4 ,the truth is that we seldom calculate or have any occasion to calculate individual chances except as a matter of curiosity4 ,it is true that insurance offices calculate probabilities1 but it is not the probability of this or that man dying at a particular age4 ,the precise shade of probability for the individual1 in so far as this depends on vital statistics1 is a matter of indifference to the company as long as the average is maintained4 ,our expectations about any individual life cannot be measured by a calculation of the chances because a variety of other elements affect those expectations4 ,we form beliefs about individual cases1 but we try to get surer grounds for them than the chances as calculable from statistical data4 ,suppose a person were to institute a home for lost dogs1 he would doubtless try to ascertain how many dogs were likely to go astray1 and in so doing would be guided by statistics4 ,but in judging of the probability of the straying of a particular dog1 he would pay little heed to statistics as determining the chances1 but would proceed upon empirical knowledge of the character of the dog and his master4 ,even in betting on the field against a particular horse1 the bookmaker does not calculate from numerical data such as the number of horses entered or the number of times the favourite has been beaten3 he tries to get at the pedigree and previous performances of the various horses in the running4 ,we proceed by calculation of chances only when we cannot do better4 ,footnote #a3 ,empirical ,logic1 p4 #eef4 ,footnote #b3 ,mr4 ,jevons held that all inference is merely probable and that no inference is certain4 ,but this is a purposeless repudiation of common meaning1 which he cannot himself consistently adhere to4 ,we find him saying that if a penny is tossed into the air it will certainly come down on one side or the other1 on which side being a matter of probability4 ,in common speech probability is applied to a degree of belief short of certainty1 but to say that certainty is the highest degree of probability does no violence to the common meaning4 ,,chapter ,x4 ,,inference ,,from ,,analogy4 ,the word ,analogy was appropriated by ,mill1 in accordance with the usage of the eighteenth century1 to designate a ground of inference distinct from that on which we proceed in extending a law1 empirical or scientific1 to a new case4 ,but it is used in various other senses1 more or less similar1 and in order to make clear the exact logical sense1 it is well to specify some of these4 ,the original word ,greek3 analogia1 as employed by ,aristotle1 corresponds to the word ,proportion in ,arithmetic3 it signified an equality of ratios1 ,greek3 isotes logon3 two compared with four is analogous to four compared with eight4 ,there is something of the same meaning in the technical use of the word in ,physiology1 where it is used to signify similarity of function as distinguished from similarity of structure1 which is called homology3 thus the tail of a whale is analogous to the tail of a fish1 inasmuch as it is similarly used for motion1 but it is homologous with the hind legs of a quadruped2 a man's arms are homologous with a horse's fore legs1 but they are not analogous inasmuch as they are not used for progression4 ,apart from these technical employments1 the word is loosely used in common speech for any kind of resemblance4 ,thus ,de ,quincey speaks of the analogical power in memory1 meaning thereby the power of recalling things by their inherent likeness as distinguished from their casual connexions or their order in a series4 ,but even in common speech1 there is a trace of the original meaning3 generally when we speak of analogy we have in our minds more than one pair of things1 and what we call the analogy is some resemblance between the different pairs4 ,this is probably what ,whately had in view when he defined analogy as resemblance of relations4 ,in a strict logical sense1 however1 as defined by ,mill1 sanctioned by the previous usage of ,butler and ,kant1 analogy means more than a resemblance of relations4 ,it means a preponderating resemblance between two things such as to warrant us in inferring that the resemblance extends further4 ,this is a species of argument distinct from the extension of an empirical law4 ,in the extension of an empirical law1 the ground of inference is a coincidence frequently repeated within our experience1 and the inference is that it has occurred or will occur beyond that experience3 in the argument from analogy1 the ground of inference is the resemblance between two individual objects or kinds of objects in a certain number of points1 and the inference is that they resemble one another in some other point1 known to belong to the one1 but not known to belong to the other4 ,two things go together in many cases1 therefore in all1 including this one1 is the argument in extending a generalisation3 ,two things agree in many respects1 therefore in this other1 is the argument from analogy4 ,the example given by ,reid in his ,intellectual ,powers has become the standard illustration of the peculiar argument from analogy4 ,we may observe a very great similitude between this earth which we inhabit1 and the other planets1 ,saturn1 ,jupiter1 ,mars1 ,venus and ,mercury4 ,they all revolve round the sun1 as the earth does1 although at different distances and in different periods4 ,they borrow all their light from the sun1 as the earth does4 ,several of them are known to revolve round their axis like the earth1 and by that means have like succession of day and night4 ,some of them have moons1 that serve to give them light in the absence of the sun1 as our moon does to us4 ,they are all1 in their motions1 subject to the same law of gravitation as the earth is4 ,from all this similitude it is not unreasonable to think that these planets may1 like our earth1 be the habitation of various orders of living creatures4 ,there is some probability in this conclusion from analogy4#a ,the argument from analogy is sometimes said to range through all degrees of probability from certainty to zero4 ,but this is true only if we take the word analogy in its loosest sense for any kind of resemblance4 ,if we do this1 we may call any kind of argument an argument from analogy1 for all inferences turn upon resemblance4 ,i believe that if ,i throw my pen in the air it will come down again1 because it is like other ponderable bodies4 ,but if we use the word in its limited logical sense1 the degree of probability is much nearer zero than certainty4 ,this is apparent from the conditions that logicians have formulated of a strict argument from analogy4 #a4 ,the resemblance must be preponderating4 ,in estimating the value of an argument from analogy1 we must reckon the points of difference as counting against the conclusion1 and also the points in regard to which we do not know whether the two objects agree or differ4 ,the numerical measure of value is the ratio of the points of resemblance to the points of difference plus the unknown points4 ,thus1 in the argument that the planets are inhabited because they resemble the earth in some respects and the earth is inhabited1 the force of the analogy is weakened by the fact that we know very little about the surface of the planets4 #b4 ,in a numerical estimate all circumstances that hang together as effects of one cause must be reckoned as one4 ,otherwise1 we might make a fallaciously imposing array of points of resemblance4 ,thus in ,reid's enumeration of the agreements between the earth and the planets1 their revolution round the sun and their obedience to the law of gravitation should count as one point of resemblance4 ,if two objects agree in a1 b1 c1 d1 e1 but b follows from a1 and d and e from c1 the five points count only as two4 #c4 ,if the object to which we infer is known to possess some property incompatible with the property inferred1 the general resemblance counts for nothing4 ,the moon has no atmosphere1 and we know that air is an indispensable condition of life4 ,hence1 however much the moon may resemble the earth1 we are debarred from concluding that there are living creatures on the moon such as we know to exist on the earth4 ,we know also that life such as it is on the earth is possible only within certain limits of temperature1 and that ,mercury is too hot for life1 and ,saturn too cold1 no matter how great the resemblance to the earth in other respects4 #d4 ,if the property inferred is known or presumed to be a concomitant of one or more of the points of resemblance1 any argument from analogy is superfluous4 ,this is1 in effect1 to say that we have no occasion to argue from general resemblance when we have reason to believe that a property follows from something that an object is known to possess4 ,if we knew that any one of the planets possessed all the conditions1 positive and negative1 of life1 we should not require to reckon up all the respects in which it resembles the earth in order to create a presumption that it is inhabited4 ,we should be able to draw the conclusion on other grounds than those of analogy4 ,newton's famous inference that the diamond is combustible is sometimes quoted as an argument from analogy4 ,but1 technically speaking1 it was rather1 as ,professor ,bain has pointed out1 of the nature of an extended generalisation4 ,comparing bodies in respect of their densities and refracting powers1 he observed that combustible bodies refract more than others of the same density2 and observing the exceptionally high refracting power of the diamond1 he inferred from this that it was combustible1 an inference afterwards confirmed by experiment4 ,the concurrence of high refracting power with inflammability was an empirical law2 and ,newton1 perceiving the law1 extended it to the adjacent case of the diamond4 ,the remark is made by ,brewster that had ,newton known the refractive powers of the minerals greenockite and octohedrite1 he would have extended the inference to them1 and would have been mistaken4#b ,from these conditions it will be seen that we cannot conclude with any high degree of probability from analogy alone4 ,this is not to deny1 as ,mr4 ,jevons seems to suppose1 that analogies1 in the sense of general resemblances1 are often useful in directing investigation4 ,when we find two things very much alike1 and ascertain that one of them possesses a certain property1 the presumption that the other has the same is strong enough to make it worth while trying whether as a matter of fact it has4 ,it is said that a general resemblance of the hills near ,ballarat in ,australia to the ,californian hills where gold had been found suggested the idea of digging for gold at ,ballarat4 ,this was a lucky issue to an argument from analogy1 but doubtless many have dug for gold on similar general resemblances without finding that the resemblance extended to that particular4 ,similarly1 many of the extensions of the ,pharmacopeia have proceeded upon general resemblances1 the fact that one drug resembles another in certain properties being a sufficient reason for trying whether the resemblance goes further4 ,the lucky guesses of what is known as natural sagacity are often analogical4 ,a man of wide experience in any subject-matter such as the weather1 or the conduct of men in war1 in business1 or in politics1 may conclude to the case in hand from some previous case that bears a general resemblance to it1 and very often his conclusions may be perfectly sound though he has not made a numerical estimate of the data4 ,the chief source of fallacy in analogical argument is ignoring the number of points of difference4 ,it often happens that an amount of resemblance only sufficient for a rhetorical simile is made to do duty as a solid argument4 ,thus the resemblance between a living body and the body politic is sometimes used to support inferences from successful therapeutic treatment to ,state policy4 ,the advocates of annual ,parliaments in the time of the ,commonwealth based their case on the serpent's habit of annually casting its skin4 ,wisest of beasts the serpent see1 ,just emblem of eternity1 ,and of a ,state's duration2 ,each year an annual skin he takes1 ,and with fresh life and vigour wakes ,at every renovation4 ,britain6 that serpent imitate4 ,thy ,commons ,house1 that skin of ,state1 ,by annual choice restore2 ,so choosing thou shall live secure1 ,and freedom to thy sons inure1 ,till ,time shall be no more4 ,carlyle's saying that a ship could never be taken round ,cape ,horn if the crew were consulted every time the captain proposed to alter the course1 if taken seriously as an analogical argument against ,representative ,government1 is open to the objection that the differences between a ship and a ,state are too great for any argument from one to the other to be of value4 ,it was such fallacious analogies as these that ,heine had in view in his humorous prayer1 ,heaven defend us from the ,evil ,one and from metaphors4 ,footnote #a3 ,hamilton's ,reid1 p4 #bcf4 ,footnote #b3 ,bain's ,logic1 ii4 #ade4 ,,printed ,,at ,,the ,,edinburgh ,,press1 #i ,,and #ab ,,young ,,street 99 99 99 99 99 ,transcriber's ,note3 page #aac3 'aneo symplokes' corrected to 'aneu symplokes'