,,logic ,,deductive ,,and ,,inductive ,first ,edition1 ,june #ahih4 7,grant ,richards47 ,second ,edition1 ,november #aija4 7,grant ,richards47 ,third ,edition1 ,january #aijf4 7,a4 ,moring ,ltd47 ,reprinted1 ,january #aijh4 7,a4 ,moring ,ltd47 ,reprinted1 ,may #aiji4 7,a4 ,moring ,ltd47 ,reprinted1 ,july #aiaj4 7,a4 ,moring ,ltd47 ,reprinted1 ,september #aiaa4 7,a4 ,moring ,ltd47 ,reprinted1 ,november #aiab4 7,a4 ,moring ,ltd47 ,reprinted1 ,april #aiac4 7,a4 ,moring ,ltd47 ,reprinted1 ,may #aibj4 7,simpkin47 ,,logic ,,deductive ,,and ,,inductive ,,by ,,carveth ,,read1 ,m4,a4 ,,author ,,of ,,the ,,metaphysics ,,of ,,nature ,,natural ,,and ,,social ,,morals ,,etc4 ,,fourth ,,edition ,,enlarged1 ,,and ,,partly ,,rewritten ,,simpkin1 ,,marshall1 ,,hamilton1 ,,kent ,,co4 ,,ltd41 #d ,,stationers' ,,hall ,,court4 ,,london1 ,e4,c4#d ,,preface ,in this edition of my ,logic1 the text has been revised throughout1 several passages have been rewritten1 and some sections added4 ,the chief alterations and additions occur in cc4 i41 v41 ix41 xiii41 xvi41 xvii41 xx4 ,the work may be considered1 on the whole1 as attached to the school of ,mill2 to whose ,system of ,logic1 and to ,bain's ,logic1 it is deeply indebted4 ,amongst the works of living writers1 the ,empirical ,logic of ,dr4 ,venn and the ,formal ,logic of ,dr4 ,keynes have given me most assistance4 ,to some others acknowledgments have been made as occasion arose4 ,for the further study of contemporary opinion1 accessible in ,english1 one may turn to such works as ,mr4 ,bradley's ,principles of ,logic1 ,dr4 ,bosanquet's ,logic2 or the ,morphology of ,knowledge1 ,prof4 ,hobhouse's ,theory of ,knowledge1 ,jevon's ,principles of ,science1 and ,sigwart's ,logic4 ,ueberweg's ,logic1 and ,history of ,logical ,doctrine is invaluable for the history of our subject4 ,the attitude toward ,logic of the ,pragmatists or ,humanists may best be studied in ,dr4 ,schiller's ,formal ,logic1 and in ,mr4 ,alfred ,sidgwick's ,process of ,argument and recent ,elementary ,logic4 ,the second part of this last work1 on the ,risks of ,reasoning1 gives an admirably succinct account of their position4 ,i agree with the ,humanists that1 in all argument1 the important thing to attend to is the meaning1 and that the most serious difficulties of reasoning occur in dealing with the matter reasoned about2 but ,i find that a pure science of relation has a necessary place in the system of knowledge1 and that the formul known as laws of contradiction1 syllogism and causation are useful guides in the framing and testing of arguments and experiments concerning matters of fact4 ,incisive criticism of traditionary doctrines1 with some remarkable reconstructions1 may be read in ,dr4 ,mercier's ,new ,logic4 ,in preparing successive editions of this book1 ,i have profited by the comments of my friends3 ,mr4 ,thomas ,whittaker1 ,prof4 ,claude ,thompson1 ,dr4 ,armitage ,smith1 ,mr4 ,alfred ,sidgwick1 ,dr4 ,schiller1 ,prof4 ,spearman1 and ,prof4 ,sully1 have made important suggestions2 and ,i might have profited more by them1 if the frame of my book1 or my principles1 had been more elastic4 ,as to the present edition1 useful criticisms have been received from ,mr4 ,s4,c4 ,dutt1 of ,cotton ,college1 ,assam1 and from ,prof4 ,m4,a4 ,roy1 of ,midnapore2 and1 especially1 ,i must heartily thank my colleague1 ,dr4 ,wolf1 for communications that have left their impress upon nearly every chapter4 ,,carveth ,,read4 ,,london1 ,august1 #aiad ,,contents ,,page ,,preface v ,,chapter ,i ,,introductory #a4 ,definition of ,logic #a #b4 ,general character of proof #b #c4 ,division of the subject #e #d4 ,uses of ,logic #f #e4 ,relation of ,logic to other sciences #h to ,mathematics 7p4 #h72 to concrete ,sciences 7p4 #aj72 to ,metaphysics 7p4 #aj72 to regulative sciences 7p4 #aa7 #f4 ,schools of ,logicians #aa ,relation to ,psychology 7p4 #ac7 ,,chapter ,,ii ,,general ,,analysis ,,of ,,propositions #a4 ,propositions and ,sentences #af #b4 ,subject1 ,predicate and ,copula #ag #c4 ,compound ,propositions #ag #d4 ,import of ,propositions #ai #e4 ,form and ,matter #bb #f4 ,formal and ,material ,logic #bc #g4 ,symbols used in ,logic #bd ,,chapter ,,iii ,,of ,,terms ,,and ,,their ,,denotation #a4 ,some ,account of ,language necessary #bg #b4 ,logic1 ,grammar and ,rhetoric #bh #c4 ,words are ,categorematic or ,syncategorematic #bi #d4 ,terms ,concrete or ,abstract #cj #e4 ,concrete ,terms1 ,singular1 ,general or ,collective #cc ,,chapter ,,iv ,,the ,,connotation ,,of ,,terms #a4 ,connotation of ,general ,names #cg #b4 ,question of ,proper ,names #ch other ,singular ,names 7p4 #dj7 #c4 ,question of ,abstract ,terms #dj #d4 ,univocal and ,equivocal ,terms #da ,connotation determined by the suppositio 7p4 #dc7 #e4 ,absolute and ,relative ,terms #dc #f4 ,relation of ,denotation to ,connotation #df #g4 ,contradictory ,terms #dg #h4 ,positive and ,negative ,terms #ej ,infinites2 ,privitives2 ,contraries 7pp4 #ej-ea7 ,,chapter ,v ,,classification ,,of ,,propositions #a4 ,as to ,quantity #ec ,quantity of the ,predicate 7p4 #ef7 #b4 ,as to ,quality #eg ,infinite ,propositions 7p4 #eg7 #c4 ,a4 ,i4 ,e4 ,o4 #eh #d4 ,as to ,relation #ei ,change of ,relation 7p4 #fj72 ,interpretation of 'either1 or' 7p4 #fc72 ,function of the hypothetical form 7p4 #fd7 #e4 ,as to ,modality #ff #f4 ,verbal and ,real ,propositions #fg ,,chapter ,,vi ,,conditions ,,of ,,immediate ,,inference #a4 ,meaning of ,inference #fi #b4 ,immediate and ,mediate ,inference #gj #c4 ,the ,laws of ,thought #gb #d4 ,identity #gc #e4 ,contradiction and ,excluded ,middle #gd #f4 ,the ,scope of ,formal ,inference #gf ,,chapter ,,vii ,,immediate ,,inferences #a4 ,plan of the ,chapter #gi #b4 ,subalternation #gi #c4 ,connotative ,subalternation #hj #d4 ,conversion #hb ,reciprocality 7p4 #hd7 #e4 ,obversion #he #f4 ,contrary ,opposition #hg #g4 ,contradictory ,opposition #hg #h4 ,sub-contrary ,opposition #hh #i4 ,the ,square of ,opposition #hi #aj4 ,secondary modes of ,immediate ,inference #ij #aa4 ,immediate ,inferences from ,conditionals #ic ,,chapter ,,viii ,,order ,,of ,,terms1 ,,euler',s ,,diagrams1 ,,logical ,,equations1 ,,existential ,,import ,,of ,,propositions #a4 ,order of ,terms in a proposition #ie #b4 ,euler's ,diagrams #ig #c4 ,propositions considered as ,equations #aja #d4 ,existential ,import of ,propositions #ajd ,,chapter ,,ix ,,formal ,,conditions ,,of ,,mediate ,,inference #a4 ,nature of ,mediate ,inference and ,syllogism #ajg #b4 ,general ,canons of the ,syllogism #ajh ,definitions of ,categorical ,syllogism2 ,middle ,term2 ,minor ,term2 ,major ,term2 ,minor and ,major ,premise 7p4 #aji7 ,illicit ,process 7p4 #aaj72 ,distribution of the ,middle 7p4 #aaj72 ,negative ,premises 7p4 #aab72 ,particular ,premises 7p4 #aac7 #c4 ,dictum de omni et nullo #aae #d4 ,syllogism in relation to the ,laws of ,thought #aaf #e4 ,other ,kinds of ,mediate ,inference #aah ,,chapter ,x ,,categorical ,,syllogisms #a4 ,illustrations of the ,syllogism #aba #b4 ,of ,figures #abb #c4 ,of ,moods #abc #d4 ,how valid ,moods are determined #abd #e4 ,special ,canons of the ,four ,figures #abf #f4 ,ostensive ,reduction and the ,mnemonic ,verses #abg #g4 ,another version of the ,mnemonic ,verses #acb #h4 ,indirect ,reduction #acb #i4 ,uses of the several ,figures #acd #aj4 ,scientific ,value of ,reduction #ace #aa4 ,euler's ,diagrams for the ,syllogism #acf ,,chapter ,,xi ,,abbreviated ,,and ,,compound ,,arguments #a4 ,popular ,arguments ,informal #ach #b4 ,the ,enthymeme #aci #c4 ,monosyllogism1 ,polysyllogism1 ,prosyllogism1 ,episyllogism #ada #d4 ,the ,epicheirema #adb #e4 ,the ,sorites #adb #f4 ,the ,antinomy #ade ,,chapter ,,xii ,,conditional ,,syllogisms #a4 ,the ,hypothetical ,syllogism #adg #b4 ,the ,disjunctive ,syllogism #aeb #c4 ,the ,dilemma #aed ,,chapter ,,xiii ,,transition ,,to ,,induction #a4 ,formal ,consistency and ,material ,truth #aei #b4 ,real ,general ,propositions assert more than has been directly observed #afj #c4 ,hence1 formally1 a ,syllogism's ,premises seem to beg the ,conclusion #afb #d4 ,materially1 a ,syllogism turns upon the resemblance of the ,minor to the ,middle ,term2 and thus extends the ,major ,premise to new cases #afc #e4 ,restatement of the ,dictum for material reasoning #afe #f4 ,uses of the ,syllogism #afg #g4 ,analysis of the ,uniformity of ,nature1 considered as the formal ground of all reasoning #afi #h4 ,grounds of our belief in ,uniformity #agc ,,chapter ,,xiv ,,causation #a4 ,the most important aspect of ,uniformity in relation to ,induction is ,causation #agd #b4 ,definition of ,cause explained3 five marks of ,causation #age #c4 ,how strictly the conception of ,cause can be applied depends upon the subject under investigation #ahc #d4 ,scientific conception of ,effect4 ,plurality of ,causes #ahe #e4 ,some condition1 but not the whole cause1 may long precede the ,effect2 and some co-effect1 but not the whole effect1 may long survive the ,cause #ahg #f4 ,mechanical ,causes and the homogeneous ,intermixture of ,effects2 ,chemical ,causes and the heteropathic ,intermixture of ,effects #ahh #g4 ,tendency1 ,resultant1 ,counteraction1 ,elimination1 ,resolution1 ,analysis1 ,reciprocity #ahi ,,chapter ,,xv ,,inductive ,,method #a4 ,outline of ,inductive investigation #aib #b4 ,induction defined #aif #c4 ,perfect ,induction #aif #d4 ,imperfect ,induction methodical or immethodical #aig #e4 ,observation and ,experiment1 the material ground of ,induction1 compared #aih #f4 ,the principle of ,causation is the formal ground of ,induction #bja #g4 ,the ,inductive ,canons are derived from the principle of ,causation1 the more readily to detect it in facts observed #bjb ,,chapter ,,xvi ,,the ,,canons ,,of ,,direct ,,induction #a4 ,the ,canon of ,agreement #bjf ,negative ,instances 7p4 #bjh72 ,plurality of ,causes 7p4 #bjh7 ,agreement may show connection without direct ,causation 7p4 #bji7 #b4 ,the ,canon of ,agreement in ,presence and in ,absence #bab ,it tends to disprove a ,plurality of ,causes 7p4 #bac7 #c4 ,the ,canon of ,difference #baf ,may be applied to observations 7p4 #bba7 #d4 ,the ,canon of ,variations #bbb ,how related to ,agreement and ,difference 7p4 #bbb72 ,the ,graphic ,method 7p4 #bbg72 ,critical points 7p4 #bcj72 ,progressive effects 7p4 #bca72 ,gradations 7p4 #bca7 #e4 ,the ,canon of ,residues #bcb ,,chapter ,,xvii ,,combination ,,of ,,induction ,,with ,,deduction #a4 ,deductive character of ,formal ,induction #bcf #b4 ,further complication of ,deduction with ,induction #bch #c4 ,the ,direct ,deductive 7or ,physical7 ,method #bdj #d4 ,opportunities of ,error in the ,physical ,method #bdc #e4 ,the ,inverse ,deductive 7or ,historical7 ,method #bdf #f4 ,precautions in using the ,historical ,method #bea #g4 ,the ,comparative ,method #bee #h4 ,historical ,evidence #bfa ,,chapter ,,xviii ,,hypotheses #a4 ,hypothesis defined and distinguished from ,theory #bff #b4 ,an ,hypothesis must be verifiable #bfh #c4 ,proof of ,hypotheses #bgj 7#a7 ,must an hypothetical agent be directly observable8 7p4 #bgj72 ,vera causa 7p4 #bga7 7#b7 ,an ,hypothesis must be adequate to its pretensions 7p4 #bgb72 ,exceptio probat regulam 7p4 #bgd7 7#c7 ,every competing ,hypothesis must be excluded 7p4 #bge72 ,crucial instance 7p4 #bgg7 7#d7 ,hypotheses must agree with the laws of ,nature 7p4 #bgi7 #d4 ,hypotheses necessary in scientific investigation #bhj #e4 ,the ,method of ,abstractions #bhc ,method of ,limits 7p4 #bhd72 ,in what sense all knowledge is hypothetical 7p4 #bhf7 ,,chapter ,,xix ,,laws ,,classified2 ,,explanation2 ,,co-,,existence2 ,,analogy #a4 ,axioms2 ,primary ,laws2 ,secondary ,laws1 ,derivative or ,empirical2 ,facts #bhh #b4 ,secondary ,laws either ,invariable or ,approximate ,generalisations #bib #c4 ,secondary ,laws trustworthy only in ',adjacent ,cases' #bic #d4 ,secondary ,laws of ,succession or of ,co-existence #bie ,natural ,kinds 7p4 #bif72 ,co-existence of concrete things to be deduced from ,causation 7p4 #big7 #e4 ,explanation consists in tracing resemblance1 especially of ,causation #bii #f4 ,three modes of ,explanation #cjb ,analysis 7p4 #cjb72 ,concatenation 7p4 #cjb72 ,subsumption 7p4 #cjc7 #g4 ,limits of ,explanation #cje #h4 ,analogy #cjg ,,chapter ,,xx ,,probability #a4 ,meaning of ,chance and ,probability #caj #b4 ,probability as a fraction or proportion #cab #c4 ,probability depends upon experience and statistics #cac #d4 ,it is a kind of ,induction1 and pre-supposes ,causation #cae #e4 ,of ,averages and the ,law of ,error #cah #f4 ,interpretation of probabilities #cbd ,personal ,equation 7p4 #cbe72 meaning of ',expectation' 7p4 #cbe7 #g4 ,rules of the combination of ,probabilities #cbe ,detection of a hidden ,cause 7p4 #cbf72 oral tradition 7p4 #cbg72 circumstantial and analogical evidence 7p4 #cbh7 ,,chapter ,,xxi ,,division ,,and ,,classification #a4 ,classification1 scientific1 special and popular #ccj #b4 ,uses of classification #ccb #c4 ,classification1 ,deductive and ,inductive #ccd #d4 ,division1 or ,deductive ,classification3 its ,rules #cce #e4 ,rules for testing a ,division #ccg #f4 ,inductive ,classification #cci #g4 ,difficulty of ,natural ,classification #cda #h4 ,darwin's influence on the theory of ,classification #cdb #i4 ,classification of ,inorganic ,bodies also dependent on ,causation #cdf ,,chapter ,,xxii ,,nomenclature1 ,,definition1 ,,predicables #a4 ,precise thinking needs precise language #cdh #b4 ,nomenclature and ,terminology #cdi #c4 ,definition #ceb #d4 ,rules for testing a ,definition #ceb #e4 ,every ,definition is relative to a ,classification #cec #f4 ,difficulties of ,definition #cef ,proposals to substitute the ,type 7p4 #cef7 #g4 ,the ,limits of ,definition #ceg #h4 ,the five ,predicables #ceh ,porphyry's ,tree 7p4 #cfa7 #i4 ,realism and ,nominalism #cfd #aj4 ,the ,predicaments #cff ,,chapter ,,xxiii ,,definition ,,of ,,common ,,terms #a4 ,the rigour of scientific method must be qualified #cfi #b4 ,still1 ,language comprises the ,nomenclature of an imperfect ,classification1 to which every ,definition is relative2 #cgj #c4 and an imperfect ,terminology #cgd #d4 ,maxims and precautions of ,definition #cge #e4 ,words of common language in scientific use #cgh #f4 ,how ,definitions affect the cogency of arguments #chj ,,chapter ,,xxiv ,,fallacies #a4 ,fallacy defined and divided #che #b4 ,formal ,fallacies of ,deduction #che #c4 ,formal ,fallacies of ,induction #chh #d4 ,material ,fallacies classified #cid #e4 ,fallacies of ,observation #cid #f4 ,begging the ,question #cif #g4 ,surreptitious ,conclusion #cih #h4 ,ambiguity #djj #i4 ,fallacies1 a natural rank growth of the ,human mind1 not easy to classify1 or exterminate #djc ,,questions #dje ,,logic ,,chapter ,i ,,introductory #a4 ,logic is the science that explains what conditions must be fulfilled in order that a proposition may be proved1 if it admits of proof4 ,not1 indeed1 every such proposition2 for as to those that declare the equality or inequality of numbers or other magnitudes1 to explain the conditions of their proof belongs to ,mathematics3 they are said to be quantitative4 ,but as to all other propositions1 called qualitative1 like most of those that we meet with in conversation1 in literature1 in politics1 and even in sciences so far as they are not treated mathematically 7say1 ,botany and ,psychology72 propositions that merely tell us that something happens 7as that salt dissolves in water71 or that something has a certain property 7as that ice is cold73 as to these1 it belongs to ,logic to show how we may judge whether they are true1 or false1 or doubtful4 ,when propositions are expressed with the universality and definiteness that belong to scientific statements1 they are called laws2 and laws1 so far as they are not laws of quantity1 are tested by the principles of ,logic1 if they at all admit of proof4 ,but it is plain that the process of proving cannot go on for ever2 something must be taken for granted2 and this is usually considered to be the case 7#a7 with particular facts that can only be perceived and observed1 and 7#b7 with those highest laws that are called 'axioms' or 'first principles1' of which we can only say that we know of no exceptions to them1 that we cannot help believing them1 and that they are indispensable to science and to consistent thought4 ,logic1 then1 may be briefly defined as the science of proof with respect to qualitative laws and propositions1 except those that are axiomatic4 #b4 ,proof may be of different degrees or stages of completeness4 ,absolute proof would require that a proposition should be shown to agree with all experience and with the systematic explanation of experience1 to be a necessary part of an all-embracing and self-consistent philosophy or theory of the universe2 but as no one hitherto has been able to frame such a philosophy1 we must at present put up with something less than absolute proof4 ,logic1 assuming certain principles to be true of experience1 or at least to be conditions of consistent discourse1 distinguishes the kinds of propositions that can be shown to agree with these principles1 and explains by what means the agreement can best be exhibited4 ,such principles are those of ,contradiction 7chap4 vi471 the ,syllogism 7chap4 ix471 ,causation 7chap4 xiv471 and ,probabilities 7chap4 xx474 ,to bring a proposition or an argument under them1 or to show that it agrees with them1 is logical proof4 ,the extent to which proof is requisite1 again1 depends upon the present purpose3 if our aim be general truth for its own sake1 a systematic investigation is necessary2 but if our object be merely to remove some occasional doubt that has occurred to ourselves or to others1 it may be enough to appeal to any evidence that is admitted or not questioned4 ,thus1 if a man doubts that some acids are compounds of oxygen1 but grants that some compounds of oxygen are acids1 he may agree to the former proposition when you point out that it has the same meaning as the latter1 differing from it only in the order of the words4 ,this is called proof by immediate inference4 ,again1 suppose that a man holds in his hand a piece of yellow metal1 which he asserts to be copper1 and that we doubt this1 perhaps suggesting that it is really gold4 ,then he may propose to dip it in vinegar2 whilst we agree that1 if it then turns green1 it is copper and not gold4 ,on trying this experiment the metal does turn green2 so that we may put his argument in this way3-- ,whatever yellow metal turns green in vinegar is copper2 ,this yellow metal turns green in vinegar2 ,therefore1 this yellow metal is copper4 ,such an argument is called proof by mediate inference2 because one cannot see directly that the yellow metal is copper2 but it is admitted that any yellow metal is copper that turns green in vinegar1 and we are shown that this yellow metal has that property4 ,now1 however1 it may occur to us1 that the liquid in which the metal was dipped was not vinegar1 or not pure vinegar1 and that the greenness was due to the impurity4 ,our friend must thereupon show by some means that the vinegar was pure2 and then his argument will be that1 since nothing but the vinegar came in contact with the metal1 the greenness was due to the vinegar2 or1 in other words1 that contact with that vinegar was the cause of the metal turning green4 ,still1 on second thoughts1 we may suspect that we had formerly conceded too much2 we may reflect that1 although it had often been shown that copper turned green in vinegar1 whilst gold did not1 yet the same might not always happen4 ,may it not be1 we might ask1 that just at this moment1 and perhaps always for the future gold turns1 and will turn green in vinegar1 whilst copper does not and never will again8 ,he will probably reply that this is to doubt the uniformity of causation3 he may hope that we are not serious3 he may point out to us that in every action of our life we take such uniformity for granted4 ,but he will be obliged to admit that1 whatever he may say to induce us to assent to the principle of ,nature's uniformity1 his arguments will not amount to logical proof1 because every argument in some way assumes that principle4 ,he has come1 in fact1 to the limits of ,logic4 ,just as ,euclid does not try to prove that 'two magnitudes equal to the same third are equal to one another1' so the ,logician 7as such7 does not attempt to prove the uniformity of causation and the other principles of his science4 ,even when our purpose is to ascertain some general truth1 the results of systematic inquiry may have various degrees of certainty4 ,if ,logic were confined to strict demonstration1 it would cover a narrow field4 ,the greater part of our conclusions can only be more or less probable4 ,it may1 indeed1 be maintained1 not unreasonably1 that no judgments concerning matters of fact can be more than probable4 ,some say that all scientific results should be considered as giving the average of cases1 from which deviations are to be expected4 ,many matters can only be treated statistically and by the methods of ,probability4 ,our ordinary beliefs are adopted without any methodical examination4 ,but it is the aim1 and it is characteristic1 of a rational mind to distinguish degrees of certainty1 and to hold each judgment with the degree of confidence that it deserves1 considering the evidence for and against it4 ,it takes a long time1 and much self-discipline1 to make some progress toward rationality2 for there are many causes of belief that are not good grounds for it--have no value as evidence4 ,evidence consists of 7#a7 observation2 7#b7 reasoning checked by observation and by logical principles2 7#c7 memory--often inaccurate2 7#d7 testimony--often untrustworthy1 but indispensable1 since all we learn from books or from other men is taken on testimony2 7#e7 the agreement of all our results4 ,on the other hand1 belief is caused by many influences that are not evidence at all3 such are 7#a7 desire1 which makes us believe in whatever serves our purpose2 fear and suspicion1 which 7paradoxically7 make us believe in whatever seems dangerous2 7#b7 habit1 which resists whatever disturbs our prejudices2 7#c7 vanity1 which delights to think oneself always right and consistent and disowns fallibility2 7#d7 imitativeness1 suggestibility1 fashion1 which carry us along with the crowd4 ,all these1 and nobler things1 such as love and fidelity1 fix our attention upon whatever seems to support our prejudices1 and prevent our attending to any facts or arguments that threaten to overthrow them4 #c4 ,two departments of ,logic are usually recognised1 ,deduction and ,induction2 that is1 to describe them briefly1 proof from principles1 and proof from facts4 ,classification is sometimes made a third department2 sometimes its topics are distributed amongst those of the former two4 ,in the present work the order adopted is1 ,deduction in chaps4 ii4 to xiii42 ,induction in chaps4 xiii4 to xx42 and1 lastly1 ,classification4 ,but such divisions do not represent fundamentally distinct and opposed aspects of the science4 ,for although1 in discussing any question with an opponent who makes admissions1 it may be possible to combat his views with merely deductive arguments based upon his admissions2 yet in any question of general truth1 ,induction and ,deduction are mutually dependent and imply one another4 ,this may be seen in one of the above examples4 ,it was argued that a certain metal must be copper1 because every metal is copper that turns green when dipped in vinegar4 ,so far the proof appealed to a general proposition1 and was deductive4 ,but when we ask how the general proposition is known to be true1 experiments or facts must be alleged2 and this is inductive evidence4 ,deduction then depends on ,induction4 ,but if we ask1 again1 how any number of past experiments can prove a general proposition1 which must be good for the future as well as for the past1 the uniformity of causation is invoked2 that is1 appeal is made to a principle1 and that again is deductive proof4 ,induction then depends upon ,deduction4 ,we may put it in this way3 ,deduction depends on ,induction1 if general propositions are only known to us through the facts3 ,induction depends on ,deduction1 because one fact can never prove another1 except so far as what is true of the one is true of the other and of any other of the same kind2 and because1 to exhibit this resemblance of the facts1 it must be stated in a general proposition4 #d4 ,the use of ,logic is often disputed3 those who have not studied it1 often feel confident of their ability to do without it2 those who have studied it1 are sometimes disgusted with what they consider to be its superficial analysis of the grounds of evidence1 or needless technicality in the discussion of details4 ,as to those who1 not having studied ,logic1 yet despise it1 there will be time enough to discuss its utility with them1 when they know something about it2 and as for those who1 having studied it1 turn away in disgust1 whether they are justified every man must judge for himself1 when he has attained to equal proficiency in the subject4 ,meanwhile1 the following considerations may be offered in its favour3 ,logic states1 and partly explains and applies1 certain abstract principles which all other sciences take for granted2 namely1 the axioms above mentioned--the principles of ,contradiction1 of the ,syllogism and of ,causation4 ,by exercising the student in the apprehension of these truths1 and in the application of them to particular propositions1 it educates the power of abstract thought4 ,every science is a model of method1 a discipline in close and consecutive thinking2 and this merit ,logic ought to possess in a high degree4 ,for ages ,logic has served as an introduction to ,philosophy that is1 to ,metaphysics and speculative ,ethics4 ,it is of old and honourable descent3 a man studies ,logic in very good company4 ,it is the warp upon which nearly the whole web of ancient1 medival and modern ,philosophy is woven4 ,the history of thought is hardly intelligible without it4 ,as the science of proof1 ,logic gives an account of the general nature of evidence deductive and inductive1 as applied in the physical and social sciences and in the affairs of life4 ,the general nature of such evidence3 it would be absurd of the logician to pretend to instruct the chemist1 economist and merchant1 as to the special character of the evidence requisite in their several spheres of judgment4 ,still1 by investigating the general conditions of proof1 he sets every man upon his guard against the insufficiency of evidence4 ,one application of the science of proof deserves special mention3 namely1 to that department of ,rhetoric which has been the most developed1 relating to persuasion by means of oratory1 leader-writing1 or pamphleteering4 ,it is usually said that ,logic is useful to convince the judgment1 not to persuade the will3 but one way of persuading the will is to convince the judgment that a certain course is advantageous2 and although this is not always the readiest way1 it is the most honourable1 and leads to the most enduring results4 ,logic is the backbone of ,rhetoric4 ,it has been disputed whether ,logic is a science or an art2 and1 in fact1 it may be considered in both ways4 ,as a statement of general truths1 of their relations to one another1 and especially to the first principles1 it is a science2 but it is an art when1 regarding truth as an end desired1 it points out some of the means of attaining it--namely1 to proceed by a regular method1 to test every judgment by the principles of ,logic1 and to distrust whatever cannot be made consistent with them4 ,logic does not1 in the first place1 teach us to reason4 ,we learn to reason as we learn to walk and talk1 by the natural growth of our powers with some assistance from friends and neighbours4 ,the way to develop one's power of reasoning is1 first1 to set oneself problems and try to solve them4 ,secondly1 since the solving of a problem depends upon one's ability to call to mind parallel cases1 one must learn as many facts as possible1 and keep on learning all one's life2 for nobody ever knew enough4 ,thirdly one must check all results by the principles of ,logic4 ,it is because of this checking1 verifying1 corrective function of ,logic that it is sometimes called a ,regulative or ,normative ,science4 ,it cannot give any one originality or fertility of invention2 but it enables us to check our inferences1 revise our conclusions1 and chasten the vagaries of ambitious speculation4 ,it quickens our sense of bad reasoning both in others and in ourselves4 ,a man who reasons deliberately1 manages it better after studying ,logic than he could before1 if he is sincere about it and has common sense4 #e4 ,the relation of ,logic to other sciences3 7a7 ,logic is regarded by ,spencer as co-ordinate with ,mathematics1 both being ,abstract ,sciences--that is1 sciences of the relations in which things stand to one another1 whatever the particular things may be that are so related2 and this view seems to be1 on the whole1 just--subject1 however1 to qualifications that will appear presently4 ,mathematics treats of the relations of all sorts of things considered as quantities1 namely1 as equal to1 or greater or less than1 one another4 ,things may be quantitatively equal or unequal in degree1 as in comparing the temperature of bodies2 or in duration2 or in spatial magnitude1 as with lines1 superficies1 solids2 or in number4 ,and it is assumed that the equality or inequality of things that cannot be directly compared1 may be proved indirectly on the assumption that 'things equal to the same thing are equal1' etc4 ,logic also treats of the relations of all sorts of things1 but not as to their quantity4 ,it considers 7i7 that one thing may be like or unlike another in certain attributes1 as that iron is in many ways like tin or lead1 and in many ways unlike carbon or sulphur3 7ii7 that attributes co-exist or coinhere 7or do not7 in the same subject1 as metallic lustre1 hardness1 a certain atomic weight and a certain specific gravity coinhere in iron3 and 7iii7 that one event follows another 7or is the effect of it71 as that the placing of iron in water causes it to rust4 ,the relations of likeness and of coinherence are the ground of ,classification2 for it is by resemblance of coinhering attributes that things form classes3 coinherence is the ground of judgments concerning ,substance and ,attribute1 as that iron is metallic2 and the relation of succession1 in the mode of ,causation1 is the chief subject of the department of ,induction4 ,it is usual to group together these relations of attributes and of order in time1 and call them qualitative1 in order to contrast them with the quantitative relations which belong to ,mathematics4 ,and it is assumed that qualitative relations of things1 when they cannot be directly perceived1 may be proved indirectly by assuming the axiom of the ,syllogism 7chap4 ix47 and the law of ,causation 7chap4 xiv474 ,so far1 then1 ,logic and ,mathematics appear to be co-ordinate and distinct sciences4 ,but we shall see hereafter that the satisfactory treatment of that special order of events in time which constitutes ,causation1 requires a combination of ,logic with ,mathematics2 and so does the treatment of ,probability4 ,and1 again1 ,logic may be said to be1 in a certain sense1 'prior to' or 'above' ,mathematics as usually treated4 ,for the ,mathematics assume that one magnitude must be either equal or unequal to another1 and that it cannot be both equal and unequal to it1 and thus take for granted the principles of ,contradiction and ,excluded ,middle2 but the statement and elucidation of these ,principles are left to ,logic 7chap4 vi474 ,the ,mathematics also classify and define magnitudes1 as 7in ,geometry7 triangles1 squares1 cubes1 spheres2 but the principles of classification and definition remain for ,logic to discuss4 7b7 ,as to the concrete ,sciences1 such as ,astronomy1 ,chemistry1 ,zoology1 ,sociology--,logic 7as well as ,mathematics7 is implied in them all2 for all the propositions of which they consist involve causation1 co-existence1 and class-likeness4 ,logic is therefore said to be prior to them or above them3 meaning by 'prior' not that it should be studied earlier1 for that is not a good plan2 meaning by 'above' not in dignity1 for distinctions of dignity amongst liberal studies are absurd4 ,but it is a philosophical idiom to call the abstract 'prior to1' or 'higher than1' the concrete 7see ,porphyry's ,tree1 chap4 xxii4 #h72 and ,logic is more abstract than ,astronomy or ,sociology4 ,philosophy may thank that idiom for many a foolish notion4 7c7 ,but1 as we have seen1 ,logic does not investigate the truth1 trustworthiness1 or validity of its own principles2 nor does ,mathematics3 this task belongs to ,metaphysics1 or ,epistemology1 the criticism of knowledge and beliefs4 ,logic assumes1 for example1 that things are what to a careful scrutiny they seem to be2 that animals1 trees1 mountains1 planets1 are bodies with various attributes1 existing in space and changing in time2 and that certain principles1 such as ,contradiction and ,causation1 are true of things and events4 ,but ,metaphysicians have raised many plausible objections to these assumptions4 ,it has been urged that natural objects do not really exist on their own account1 but only in dependence on some mind that contemplates them1 and that even space and time are only our way of perceiving things2 or1 again1 that although things do really exist on their own account1 it is in an entirely different way from that in which we know them4 ,as to the principle of ,contradiction--that if an object has an attribute1 it cannot at the same time and in the same way be without it 7e4g41 if an animal is conscious1 it is false that it is not conscious7--it has been contended that the speciousness of this principle is only due to the obtuseness of our minds1 or even to the poverty of language1 which cannot make the fine distinctions that exist in ,nature4 ,and as to ,causation1 it is sometimes doubted whether events always have physical causes2 and it is often suggested that1 granting they have physical causes1 yet these are such as we can neither perceive nor conceive2 belonging not to the order of ,nature as we know it1 but to the secret inwardness and reality of ,nature1 to the wells and reservoirs of power1 not to the spray of the fountain that glitters in our eyes--'occult causes1' in short4 ,now these doubts and surmises are metaphysical spectres which it remains for ,metaphysics to lay4 ,logic has no direct concern with them 7although1 of course1 metaphysical discussion is expected to be logical71 but keeps the plain path of plain beliefs1 level with the comprehension of plain men4 ,metaphysics1 as examining the grounds of ,logic itself1 is sometimes regarded as 'the higher ,logic'2 and1 certainly1 the study of ,metaphysics is necessary to every one who would comprehend the nature and functions of ,logic1 or the place of his own mind and of ,reason in the world4 7d7 ,the relation of ,logic to ,psychology will be discussed in the next section4 7e7 ,as a ,regulative ,science1 pointing out the conditions of true inference 7within its own sphere71 ,logic is co-ordinate with 7i7 ,ethics1 considered as assigning the conditions of right conduct1 and with 7ii7 sthetics1 considered as determining the principles of criticism and good taste4 #f4 ,three principal schools of ,logicians are commonly recognised3 ,nominalist1 ,conceptualist1 and ,materialist1 who differ as to what it is that ,logic really treats of3 the ,nominalists say1 'of language'2 the ,conceptualists1 'of thought'2 the ,materialists1 'of relations of fact4' ,to illustrate these positions let us take authors who1 if some of them are now neglected1 have the merit of stating their contrasted views with a distinctness that later refinements tend to obscure4 7a7 ,whately1 a well-known ,nominalist1 regarded ,logic as the ,science and ,art of ,reasoning1 but at the same time as entirely conversant about language2 that is to say1 it is the business of ,logic to discover those modes of statement which shall ensure the cogency of an argument1 no matter what may be the subject under discussion4 ,thus1 ,all fish are cold-blooded1 some cold-blooded things are fish3 this is a sound inference by the mere manner of expression2 and equally sound is the inference1 ,all fish are warm-blooded1 some warm-blooded things are fish4 ,the latter proposition may be false1 but it follows2 and 7according to this doctrine7 ,logic is only concerned with the consistent use of words3 the truth or falsity of the proposition itself is a question for ,zoology4 ,the short-coming of extreme ,nominalism lies in speaking of language as if its meaning were unimportant4 ,but ,whately did not intend this3 he was a man of great penetration and common-sense4 7b7 ,hamilton1 our best-known ,conceptualist1 defined ,logic as the science of the formal laws of thought1 and of thought as thought1 that is1 without regard to the matter thought about4 ,just as ,whately regarded ,logic as concerned merely with cogent forms of statement1 so ,hamilton treated it as concerned merely with the necessary relations of thought4 ,this doctrine is called ,conceptualism1 because the simplest element of thought is the ,concept2 that is1 an abstract idea1 such as is signified by the word man1 planet1 colour1 virtue2 not a representative or generic image1 but the thought of all attributes common to any class of things4 ,men1 planets1 colours1 virtuous actions or characters1 have1 severally1 something in common on account of which they bear these general names2 and the thought of what they have in common1 as the ground of these names1 is a ,concept4 ,to affirm or deny one concept of another1 as ,some men are virtuous1 or ,no man is perfectly virtuous1 is to form a ,judgment1 corresponding to the ,proposition of which the other schools of ,logic discourse4 ,conceptualism1 then1 investigates the conditions of consistent judgment4 ,to distinguish ,logic from ,psychology is most important in connection with ,conceptualism4 ,concepts and ,judgments being mental acts1 or products of mental activity1 it is often thought that ,logic must be a department of ,psychology4 ,it is recognised of course1 that ,psychology deals with much more than ,logic does1 with sensation1 pleasure and pain1 emotion1 volition2 but in the region of the intellect1 especially in its most deliberate and elaborate processes1 namely1 conception1 judgment1 and reasoning1 ,logic and ,psychology seem to occupy common ground4 ,in fact1 however1 the two sciences have little in common except a few general terms1 and even these they employ in different senses4 ,it is usual to point out that ,psychology tries to explain the subjective processes of conception1 judgment and reasoning1 and to give their natural history2 but that ,logic is wholly concerned with the results of such processes1 with concepts1 judgments and reasonings1 and merely with the validity of the results1 that is1 with their truth or consistency2 whilst ,psychology has nothing to do with their validity1 but only with their causes4 ,besides1 the logical judgment 7in ,formal ,logic at least7 is quite a different thing from the psychological3 the latter involves feeling and belief1 whereas the former is merely a given relation of concepts4 ,s is ,p3 that is a model logical judgment2 there can be no question of believing it2 but it is logically valid if ,m is ,p and ,s is ,m4 ,when1 again1 in ,logic1 one deals with belief1 it depends upon evidence2 whereas1 in ,psychology belief is shown to depend upon causes which may have evidentiary value or may not2 for ,psychology explains quite impartially the growth of scientific insight and the growth of prejudice4 7c7 ,mill1 ,bain1 and ,venn are the chief ,materialist logicians2 and to guard against the error of confounding ,materialism in ,logic with the ontological doctrine that nothing exists but ,matter1 it may suffice to remember that in ,metaphysics all these philosophers are ,idealists4 ,materialism in ,logic consists in regarding propositions as affirming or denying relations 7cf4 #e7 between matters-of-fact in the widest sense2 not only physical facts1 but ideas1 social and moral relations2 it consists1 in short1 in attending to the meaning of propositions4 ,it treats the first principles of ,contradiction and ,causation as true of things so far as they are known to us1 and not merely as conditions or tendencies of thought2 and it takes these principles as conditions of right thinking1 because they seem to hold good of ,nature and human life4 ,to these differences of opinion it will be necessary to recur in the next chapter 7 #d72 but here ,i may observe that it is easy to exaggerate their importance in ,logic4 ,there is really little at issue between schools of logicians as such1 and as far as their doctrines run parallel2 it is on the metaphysical grounds of their study1 or as to its scope and comprehension1 that they find a battle-field4 ,the present work generally proceeds upon the third1 or ,materialist doctrine4 ,if ,deduction and ,induction are regarded as mutually dependent parts of one science1 uniting the discipline of consistent discourse with the method of investigating laws of physical phenomena1 the ,materialist doctrine1 that the principles of ,logic are founded on fact1 seems to be the most natural way of thinking4 ,but if the unity of ,deduction and ,induction is not disputed by the other schools1 the ,materialist may regard them as allies exhibiting in their own way the same body of truths4 ,the ,nominalist may certainly claim that his doctrine is indispensable3 consistently cogent forms of statement are necessary both to the ,conceptualist and to the ,materialist2 neither the relations of thought nor those of fact can be arrested or presented without the aid of language or some equivalent system of signs4 ,the ,conceptualist may urge that the ,nominalist's forms of statement and argument exist for the sake of their meaning1 namely1 judgments and reasonings2 and that the ,materialist's laws of ,nature are only judgments founded upon our conceptions of ,nature2 that the truth of observations and experiments depends upon our powers of perception2 that perception is inseparable from understanding1 and that a system of ,induction may be constructed upon the axiom of ,causation1 regarded as a principle of ,reason1 just as well as by considering it as a law of ,nature1 and upon much the same lines4 ,the ,materialist1 admitting all this1 may say that a judgment is only the proximate meaning of a proposition1 and that the ultimate meaning1 the meaning of the judgment itself1 is always some matter-of-fact2 that the other schools have not hitherto been eager to recognise the unity of ,deduction and ,induction or to investigate the conditions of trustworthy experiments and observations within the limits of human understanding2 that thought is itself a sort of fact1 as complex in its structure1 as profound in its relations1 as subtle in its changes as any other fact1 and therefore at least as hard to know2 that to turn away from the full reality of thought in perception1 and to confine ,logic to artificially limited concepts1 is to abandon the effort to push method to the utmost and to get as near truth as possible2 and that as to ,causation being a principle of ,reason rather than of ,nature1 the distinction escapes his apprehension1 since ,nature seems to be that to which our private minds turn upon questions of ,causation for correction and instruction2 so that if he does not call ,nature the ,universal ,reason1 it is because he loves severity of style4 ,,chapter ,,ii ,,general ,,analysis ,,of ,,propositions #a4 ,since ,logic discusses the proof or disproof1 or 7briefly7 the testing of propositions1 we must begin by explaining their nature4 ,a proposition1 then1 may first be described in the language of grammar as a sentence indicative2 and it is usually expressed in the present tense4 ,it is true that other kinds of sentences1 optative1 imperative1 interrogative1 exclamatory1 if they express or imply an assertion1 are not beyond the view of ,logic2 but before treating such sentences1 ,logic1 for greater precision1 reduces them to their equivalent sentences indicative4 ,thus1 ,i wish it were summer may be understood to mean1 ,the coming of summer is an object of my desire4 ,thou shalt not kill may be interpreted as ,murderers are in danger of the judgment4 ,interrogatories1 when used in argument1 if their form is affirmative1 have negative force1 and affirmative force if their form is negative4 ,thus1 ,do hypocrites love virtue8 anticipates the answer1 ,no4 ,are not traitors the vilest of mankind8 anticipates the answer1 ,yes4 ,so that the logical form of these sentences is1 ,hypocrites are not lovers of virtue2 ,traitors are the vilest of mankind4 ,impersonal propositions1 such as ,it rains1 are easily rendered into logical forms of equivalent meaning1 thus3 ,rain is falling2 or 7if that be tautology71 ,the clouds are raining4 ,exclamations may seem capricious1 but are often part of the argument4 ,shade of ,chatham6 usually means ,chatham1 being aware of our present foreign policy1 is much disgusted4 ,it is in fact1 an appeal to authority1 without the inconvenience of stating what exactly it is that the authority declares4 #b4 ,but even sentences indicative may not be expressed in the way most convenient to logicians4 ,salt dissolves in water is a plain enough statement2 but the logician prefers to have it thus3 ,salt is soluble in water4 ,for he says that a proposition is analysable into three elements3 7#a7 a ,subject 7as ,salt7 about which something is asserted or denied2 7#b7 a ,predicate 7as soluble in water7 which is asserted or denied of the ,subject1 and 7#c7 the ,copula 7is or are1 or is not or are not71 the sign of relation between the ,subject and ,predicate4 ,the ,subject and ,predicate are called the ,terms of the proposition3 and the ,copula may be called the sign of predication1 using the verb 'to predicate' indefinitely for either 'to affirm' or 'to deny4' ,thus ,s is ,p means that the term ,p is given as related in some way to the term ,s4 ,we may1 therefore1 further define a ,proposition as 'a sentence in which one term is predicated of another4' ,in such a proposition as ,salt dissolves1 the copula 7is7 is contained in the predicate1 and1 besides the subject1 only one element is exhibited3 it is therefore said to be secundi adjacentis4 ,when all three parts are exhibited1 as in ,salt is soluble1 the proposition is said to be tertii adjacentis4 ,for the ordinary purposes of ,logic1 in predicating attributes of a thing or class of things1 the copula is1 or is not1 sufficiently represents the relation of subject and predicate2 but when it is desirable to realise fully the nature of the relation involved1 it may be better to use a more explicit form4 ,instead of saying ,salt--is--soluble1 we may say ,solubility--coinheres with--the nature of salt1 or ,the putting of salt in water--is a cause of--its dissolving3 thus expanding the copula into a full expression of the relation we have in view1 whether coinherence or causation4 #c4 ,the sentences of ordinary discourse are1 indeed1 for the most part1 longer and more complicated than the logical form of propositions2 it is in order to prove them1 or to use them in the proof of other propositions1 that they are in ,logic reduced as nearly as possible to such simple but explicit expressions as the above 7tertii adjacentis74 ,a ,compound ,proposition1 reducible to two or more simple ones1 is said to be exponible4 ,the modes of compounding sentences are explained in every grammar-book4 ,one of the commonest forms is the copulative1 such as ,salt is both savoury and wholesome1 equivalent to two simple propositions3 ,salt is savoury2 ,salt is wholesome4 ,pure water is neither sapid nor odorous1 equivalent to ,water is not sapid2 ,water is not odorous4 ,or1 again1 ,tobacco is injurious1 but not when used in moderation1 equivalent to ,much tobacco is injurious2 a little is not4 ,another form of ,exponible is the ,exceptive1 as ,kladderadatsch is published daily1 except on week-days1 equivalent to ,kladderadatsch is published on ,sunday2 it is not published any other day4 ,still another ,exponible is the ,exclusive1 as ,only men use fire1 equivalent to ,men are users of fire2 ,no other animals are4 ,exceptive and exclusive sentences are1 however1 equivalent forms2 for we may say1 ,kladderadatsch is published only on ,sunday2 and ,no animals use fire1 except men4 ,there are other compound sentences that are not exponible1 since1 though they contain two or more verbal clauses1 the construction shows that these are inseparable4 ,thus1 ,if cats are scarce1 mice are plentiful1 contains two verbal clauses2 but if cats are scarce is conditional1 not indicative2 and mice are plentiful is subject to the condition that cats are scarce4 ,hence the whole sentence is called a ,conditional ,proposition4 ,for the various forms of ,conditional ,propositions see chap4 v4 #d4 ,but1 in fact1 to find the logical force of recognised grammatical forms is the least of a logician's difficulties in bringing the discourses of men to a plain issue4 ,metaphors1 epigrams1 innuendoes and other figures of speech present far greater obstacles to a lucid reduction whether for approval or refutation4 ,no rules can be given for finding everybody's meaning4 ,the poets have their own way of expressing themselves2 sophists1 too1 have their own way4 ,and the point often lies in what is unexpressed4 ,thus1 barbarous nations make1 the civilised write history1 means that civilised nations do not make history1 which none is so brazen as openly to assert4 ,or1 again1 ,alcibiades is dead1 but ,x is still with us2 the whole meaning of this 'exponible' is that ,x would be the lesser loss to society4 ,even an epithet or a suffix may imply a proposition3 ,this personage may mean ,x is a pretentious nobody4 ,how shall we interpret such illusive predications except by cultivating our literary perceptions1 by reading the most significant authors until we are at home with them8 ,but1 no doubt1 to disentangle the compound propositions1 and to expand the abbreviations of literature and conversation1 is a useful logical exercise4 ,and if it seem a laborious task thus to reduce to its logical elements a long argument in a speech or treatise1 it should be observed that1 as a rule1 in a long discourse only a few sentences are of principal importance to the reasoning1 the rest being explanatory or illustrative digression1 and that a close scrutiny of these cardinal sentences will frequently dispense us from giving much attention to the rest4 #d4 ,but now1 returning to the definition of a ,proposition given in #b1 that it is 'a sentence in which one term is predicated of another1' we must consider what is the import of such predication4 ,for the definition1 as it stands1 seems to be purely ,nominalist4 ,is a proposition nothing more than a certain synthesis of words2 or1 is it meant to correspond with something further1 a synthesis of ideas1 or a relation of facts8 ,conceptualist logicians1 who speak of judgments instead of propositions1 of course define the judgment in their own language4 ,according to ,hamilton1 it is a recognition of the relation of congruence or confliction in which two concepts stand to each other4 ,to lighten the sentence1 ,i have omitted one or two qualifications 7,hamilton's ,lectures on ,logic1 xiii474 ,thus1 he goes on if we compare the thoughts water1 iron1 and rusting1 we find them congruent1 and connect them into a single thought1 thus3 water rusts iron--in that case we form a judgment4 ,when a judgment is expressed in words1 he says1 it is called a proposition4 ,but has a proposition no meaning beyond the judgment it expresses8 ,mill1 who defines it as a portion of discourse in which a predicate is affirmed or denied of a subject 7,logic1 ,book #a41 chap4 iv4 #a471 proceeds to inquire into the import of propositions 7,book #a41 chap4 v471 and finds three classes of them3 7a7 those in which one proper name is predicated of another2 and of these ,hobbes's ,nominalist definition is adequate1 namely1 that a proposition asserts or denies that the predicate is a name for the same thing as the subject1 as ,tully is ,cicero4 7b7 ,propositions in which the predicate means a part 7or the whole7 of what the subject means1 as ,horses are animals1 ,man is a rational animal4 ,these are ,verbal ,propositions 7see below3 chap4 v4 #f71 and their import consists in affirming or denying a coincidence between the meanings of names1 as ,the meaning of 'animal' is part of the meaning of 'horse4' ,they are partial or complete definitions4 ,but 7c7 there are also ,real ,propositions1 whose predicates do not mean the same as their subjects1 and whose import consists in affirming or denying one of five different kinds of matter of fact3 7#a7 ,that the subject exists1 or does not2 as if we say ,the bison exists1 ,the great auk is extinct4 7#b7 ,co-existence1 as ,man is mortal2 that is1 the being subject to death coinheres with the qualities on account of which we call certain objects men4 7#c7 ,succession1 as ,night follows day4 7#d7 ,causation 7a particular kind of ,succession71 as ,water rusts iron4 7#e7 ,resemblance1 as ,the colour of this geranium is like that of a soldier's coat1 or ,a ,b4 ,on comparing this list of real predications with the list of logical relations given above 7chap4 i4 #e 7a771 it will be seen that the two differ only in this1 that ,i have there omitted simple ,existence4 ,nothing simply exists1 unrelated either in ,nature or in knowledge4 ,such a proposition as ,the bison exists may1 no doubt1 be used in ,logic 7subject to interpretation7 for the sake of custom or for the sake of brevity2 but it means that some specimens are still to be found in ,n4 ,america1 or in ,zoological gardens4 ,controversy as to the ,import of ,propositions really turns upon a difference of opinion as to the scope of ,logic and the foundations of knowledge4 ,mill was dissatisfied with the congruity of concepts as the basis of a judgment4 ,clearly1 mere congruity does not justify belief4 ,in the proposition ,water rusts iron1 the concepts water1 rust and iron may be congruous1 but does any one assert their connection on that ground8 ,in the proposition ,murderers are haunted by the ghosts of their victims1 the concepts victim1 murderer1 ghost have a high degree of congruity2 yet1 unfortunately1 ,i cannot believe it3 there seems to be no such cheap defence of innocence4 ,now1 ,mill held that ,logic is concerned with the grounds of belief1 and that the scope of ,logic includes ,induction as well as ,deduction2 whereas1 according to ,hamilton1 ,induction is only ,modified ,logic1 a mere appendix to the theory of the forms of thought as thought4 ,indeed1 ,mill endeavoured in his ,logic to probe the grounds of belief deeper than usual1 and introduced a good deal of ,metaphysics--either too much or not enough--concerning the ground of axioms4 ,but1 at any rate1 his great point was that belief1 and therefore 7for the most part7 the ,real ,proposition1 is concerned not merely with the relations of words1 or even of ideas1 but with matters of fact2 that is1 both propositions and judgments point to something further1 to the relations of things which we can examine1 not merely by thinking about them 7comparing them in thought71 but by observing them with the united powers of thought and perception4 ,this is what convinces us that water rusts iron3 and the difficulty of doing this is what prevents our feeling sure that murderers are haunted by the ghosts of their victims4 ,hence1 although ,mill's definition of a proposition1 given above1 is adequate for propositions in general2 yet that kind of proposition 7the ,real7 with regard to which ,logic 7in ,mill's view7 investigates the conditions of proof1 may be more explicitly and pertinently defined as 'a predication concerning the relation of matters of fact4' #e4 ,this leads to a very important distinction to which we shall often have to refer in subsequent pages--namely1 the distinction between the ,form and the ,matter of a proposition or of an argument4 ,the distinction between ,form and ,matter1 as it is ordinarily employed1 is easily understood4 ,an apple growing in the orchard and a waxen apple on the table may have the same shape or form1 but they consist of different materials2 two real apples may have the same shape1 but contain distinct ounces of apple-stuff1 so that after one is eaten the other remains to be eaten4 ,similarly1 tables may have the same shape1 though one be made of marble1 another of oak1 another of iron4 ,the form is common to several things1 the matter is peculiar to each4 ,metaphysicians have carried the distinction further3 apples1 they say1 may have not only the same outward shape1 but the same inward constitution1 which1 therefore1 may be called the ,form of apple-stuff itself--namely1 a certain pulpiness1 juiciness1 sweetness1 etc42 qualities common to all dessert apples3 yet their ,matter is different1 one being here1 another there--differing in place or time1 if in nothing else4 ,the definition of a species is the form of every specimen of it4 ,to apply this distinction to the things of ,logic3 it is easy to see how two propositions may have the same ,form but different ,matter3 not using ',form' in the sense of 'shape1' but for that which is common to many things1 in contrast with that which is peculiar to each4 ,thus1 ,all male lions are tawny and ,all water is liquid at #ej ,fahrenheit1 are two propositions that have the same form1 though their matter is entirely different4 ,they both predicate something of the whole of their subjects1 though their subjects are different1 and so are the things predicated of them4 ,again1 ,all male lions have tufted tails and ,all male lions have manes1 are two propositions having the same form and1 in their subjects1 the same matter1 but different matter in their predicates4 ,if1 however1 we take two such propositions as these3 ,all male lions have manes and ,some male lions have manes1 here the matter is the same in both1 but the form is different--in the first1 predication is made concerning every male lion2 in the second of only some male lions2 the first is universal1 the second is particular4 ,or1 again1 if we take ,some tigers are man-eaters and ,some tigers are not man-eaters1 here too the matter is the same1 but the form is different2 for the first proposition is affirmative1 whilst the second is negative4 #f4 ,now1 according to ,hamilton and ,whately1 pure ,logic has to do only with the ,form of propositions and arguments4 ,as to their ,matter1 whether they are really true in fact1 that is a question1 they said1 not for ,logic1 but for experience1 or for the special sciences4 ,but ,mill desired so to extend logical method as to test the material truth of propositions3 he thought that he could expound a method by which experience itself and the conclusions of the special sciences may be examined4 ,to this method it may be objected1 that the claim to determine ,material ,truth takes for granted that the order of ,nature will remain unchanged1 that 7for example7 water not only at present is a liquid at #ej ,fahrenheit1 but will always be so2 whereas 7although we have no reason to expect such a thing7 the order of ,nature may alter--it is at least supposable--and in that event water may freeze at such a temperature4 ,any matter of fact1 again1 must depend on observation1 either directly1 or by inference--as when something is asserted about atoms or ether4 ,but observation and material inference are subject to the limitations of our faculties2 and however we may aid observation by microscopes and micrometers1 it is still observation2 and however we may correct our observations by repetition1 comparison and refined mathematical methods of making allowances1 the correction of error is only an approximation to accuracy4 ,outside of ,formal ,reasoning1 suspense of judgment is your only attitude4 ,but such objections imply that nothing short of absolute truth has any value2 that all our discussions and investigations in science or social affairs are without logical criteria2 that ,logic must be confined to symbols1 and considered entirely as mental gymnastics4 ,in this book prominence will be given to the character of ,logic as a formal science1 and it will also be shown that ,induction itself may be treated formally2 but it will be assumed that logical forms are valuable as representing the actual relations of natural and social phenomena4 #g4 ,symbols are often used in ,logic instead of concrete terms1 not only in ,symbolic ,logic where the science is treated algebraically 7as by ,dr4 ,venn in his ,symbolic ,logic71 but in ordinary manuals2 so that it may be well to explain the use of them before going further4 ,it is a common and convenient practice to illustrate logical doctrines by examples3 to show what is meant by a ,proposition we may give salt is soluble1 or water rusts iron3 the copulative exponible is exemplified by salt is savoury and wholesome2 and so on4 ,but this procedure has some disadvantages3 it is often cumbrous2 and it may distract the reader's attention from the point to be explained by exciting his interest in the special fact of the illustration4 ,clearly1 too1 so far as ,logic is formal1 no particular matter of fact can adequately illustrate any of its doctrines4 ,accordingly1 writers on ,logic employ letters of the alphabet instead of concrete terms1 7say7 ,x instead of salt or instead of iron1 and 7say7 ,y instead of soluble or instead of rusted by water2 and then a proposition may be represented by ,x is ,y4 ,it is still more usual to represent a proposition by ,s is 7or is not7 ,p1 ,s being the initial of ,subject and ,p of ,predicate2 though this has the drawback that if we argue--,s is ,p1 therefore ,p is ,s1 the symbols in the latter proposition no longer have the same significance1 since the former subject is now the predicate4 ,again1 negative terms frequently occur in ,logic1 such as not-water1 or not-iron1 and then if water or iron be expressed by ,x1 the corresponding negative may be expressed by x2 or1 generally1 if a capital letter stand for a positive term1 the corresponding small letter represents the negative4 ,the same device may be adopted to express contradictory terms3 either of them being ,x1 the other is x 7see chap4 iv41 #g-h72 or the contradictory terms may be expressed by x and x1 y and y4 ,and as terms are often compounded1 it may be convenient to express them by a combination of letters3 instead of illustrating such a case by boiling water or water that is boiling1 we may write ,,xy2 or since positive and negative terms may be compounded1 instead of illustrating this by water that is not boiling1 we may write ,xy4 ,the convenience of this is obvious2 but it is more than convenient2 for1 if one of the uses of ,logic be to discipline the power of abstract thought1 this can be done far more effectually by symbolic than by concrete examples2 and if such discipline were the only use of ,logic it might be best to discard concrete illustrations altogether1 at least in advanced text-books1 though no doubt the practice would be too severe for elementary manuals4 ,on the other hand1 to show the practical applicability of ,logic to the arguments and proofs of actual life1 or even of the concrete sciences1 merely symbolic illustration may be not only useless but even misleading4 ,when we speak of politics1 or poetry1 or species1 or the weather1 the terms that must be used can rarely have the distinctness and isolation of ,x and ,y2 so that the perfunctory use of symbolic illustration makes argument and proof appear to be much simpler and easier matters than they really are4 ,our belief in any proposition never rests on the proposition itself1 nor merely upon one or two others1 but upon the immense background of our general knowledge and beliefs1 full of circumstances and analogies1 in relation to which alone any given proposition is intelligible4 ,indeed1 for this reason1 it is impossible to illustrate ,logic sufficiently3 the reader who is in earnest about the cogency of arguments and the limitation of proofs1 and is scrupulous as to the degrees of assent that they require1 must constantly look for illustrations in his own knowledge and experience and rely at last upon his own sagacity4 ,,chapter ,,iii ,,of ,,terms ,,and ,,their ,,denotation #a4 ,in treating of ,deductive ,logic it is usual to recognise three divisions of the subject3 first1 the doctrine of ,terms1 words1 or other signs used as subjects or predicates2 secondly1 the doctrine of ,propositions1 analysed into terms related2 and1 thirdly1 the doctrine of the ,syllogism in which propositions appear as the grounds of a conclusion4 ,the terms employed are either letters of the alphabet1 or the words of common language1 or the technicalities of science2 and since the words of common language are most in use1 it is necessary to give some account of common language as subserving the purposes of ,logic4 ,it has been urged that we cannot think or reason at all without words1 or some substitute for them1 such as the signs of algebra2 but this is an exaggeration4 ,minds greatly differ1 and some think by the aid of definite and comprehensive picturings1 especially in dealing with problems concerning objects in space1 as in playing chess blindfold1 inventing a machine1 planning a tour on an imagined map4 ,most people draw many simple inferences by means of perceptions1 or of mental imagery4 ,on the other hand1 some men think a good deal without any continuum of words and without any imagery1 or with none that seems relevant to the purpose4 ,still the more elaborate sort of thinking1 the grouping and concatenation of inferences1 which we call reasoning1 cannot be carried far without language or some equivalent system of signs4 ,it is not merely that we need language to express our reasonings and communicate them to others3 in solitary thought we often depend on words--'talk to ourselves1' in fact2 though the words or sentences that then pass through our minds are not always fully formed or articulated4 ,in ,logic1 moreover1 we have carefully to examine the grounds 7at least the proximate grounds7 of our conclusions2 and plainly this cannot be done unless the conclusions in question are explicitly stated and recorded4 ,conceptualists say that ,logic deals not with the process of thinking 7which belongs to ,psychology7 but with its results2 not with conceiving but with concepts2 not with judging but with judgments4 ,is the concept self-consistent or adequate8 ,logic asks2 is the judgment capable of proof8 ,now1 it is only by recording our thoughts in language that it becomes possible to distinguish between the process and the result of thought4 ,without language1 the act and the product of thinking would be identical and equally evanescent4 ,but by carrying on the process in language and remembering or otherwise recording it1 we obtain a result which may be examined according to the principles of ,logic4 #b4 ,as ,logic1 then1 must give some account of language1 it seems desirable to explain how its treatment of language differs from that of ,grammar and from that of ,rhetoric4 ,grammar is the study of the words of some language1 their classification and derivation1 and of the rules of combining them1 according to the usage at any time recognised and followed by those who are considered correct writers or speakers4 ,composition may be faultless in its grammar1 though dull and absurd4 ,rhetoric is the study of language with a view to obtaining some special effect in the communication of ideas or feelings1 such as picturesqueness in description1 vivacity in narration1 lucidity in exposition1 vehemence in persuasion1 or literary charm4 ,some of these ends are often gained in spite of faulty syntax or faulty logic2 but since the few whom bad grammar saddens or incoherent arguments divert are not carried away1 as they else might be1 by an unsophisticated orator1 ,grammar and ,logic are necessary to the perfection of ,rhetoric4 ,not that ,rhetoric is in bondage to those other sciences2 for foreign idioms and such figures as the ellipsis1 the anacoluthon1 the oxymoron1 the hyperbole1 and violent inversions have their place in the magnificent style2 but authors unacquainted with ,grammar and ,logic are not likely to place such figures well and wisely4 ,indeed1 common idioms1 though both grammatically and rhetorically justifiable1 both correct and effective1 often seem illogical4 ',to fall asleep1' for example1 is a perfect ,english phrase2 yet if we examine severally the words it consists of1 it may seem strange that their combination should mean anything at all4 ,but ,logic only studies language so far as necessary in order to state1 understand1 and check the evidence and reasonings that are usually embodied in language4 ,and as long as meanings are clear1 good ,logic is compatible with false concords and inelegance of style4 #c4 ,terms are either ,simple or ,composite3 that is to say1 they may consist either of a single word1 as ',chaucer1' 'civilisation'2 or of more than one1 as 'the father of ,english poetry1' or 'modern civilised nations4' ,logicians classify words according to their uses in forming propositions2 or1 rather1 they classify the uses of words as terms1 not the words themselves2 for the same word may fall into different classes of terms according to the way in which it is used4 7,cf4 ,mr4 ,alfred ,sidgwick's ,distinction and the ,criticism of ,beliefs1 chap4 xiv47 ,thus words are classified as ,categorematic or ,syncategorematic4 ,a word is ,categorematic if used singly as a term without the support of other words3 it is ,syncategorematic when joined with other words in order to constitute the subject or predicate of a proposition4 ,if we say ,venus is a planet whose orbit is inside the ,earth's1 the subject1 ',venus1' is a word used categorematically as a simple term2 the predicate is a composite term whose constituent words 7whether substantive1 relative1 verb1 or preposition7 are used syncategorematically4 ,prepositions1 conjunctions1 articles1 adverbs1 relative pronouns1 in their ordinary use1 can only enter into terms along with other words having a substantive1 adjectival or participial force2 but when they are themselves the things spoken of and are used substantively 7suppositio materialis71 they are categorematic4 ,in the proposition1 ',of' was used more indefinitely three hundred years ago than it is now1 'of' is categorematic4 ,on the other hand1 all substantives may be used categorematically2 and the same self-sufficiency is usually recognised in adjectives and participles4 ,some1 however1 hold that the categorematic use of adjectives and participles is due to an ellipsis which the logician should fill up2 that instead of ,gold is heavy1 he should say ,gold is a heavy metal2 instead of ,the sun is shining1 ,the sun is a body shining4 ,but in these cases the words 'metal' and 'body' are unmistakable tautology1 since 'metal' is implied in gold and 'body' in sun4 ,but1 as we have seen1 any of these kinds of word1 substantive1 adjective1 or participle1 may occur syncategorematically in connection with others to form a composite term4 #d4 ,most terms 7the exceptions and doubtful cases will be discussed hereafter7 have two functions1 a denotative and a connotative4 ,a term's denotative function is1 to be the name or sign of something or some multitude of things1 which are said to be called or denoted by the term4 ,its connotative function is1 to suggest certain qualities and characteristics of the things denoted1 so that it cannot be used literally as the name of any other things2 which qualities and characteristics are said to be implied or connoted by the term4 ,thus 'sheep' is the name of certain animals1 and its connotation prevents its being used of any others4 ,that which a term directly indicates1 then1 is its ,denotation2 that sense or customary use of it which limits the ,denotation is its ,connotation 7ch4 iv474 ,hamilton and others use ',extension' in the sense of ,denotation1 and ',intension' or ',comprehension' in the sense of ,connotation4 ,now1 terms may be classified1 first according to what they stand for or denote2 that is1 according to their ,denotation4 ,in this respect1 the use of a term is said to be either ,concrete or ,abstract4 ,a term is ,concrete when it denotes a 'thing'2 that is1 any person1 object1 fact1 event1 feeling or imagination1 considered as capable of having 7or consisting of7 qualities and a determinate existence4 ,thus 'cricket ball' denotes any object having a certain size1 weight1 shape1 colour1 etc4 7which are its qualities71 and being at any given time in some place and related to other objects--in the bowler's hands1 on the grass1 in a shop window4 ,any 'feeling of heat' has a certain intensity1 is pleasurable or painful1 occurs at a certain time1 and affects some part or the whole of some animal4 ,an imagination1 indeed 7say1 of a fairy71 cannot be said in the same sense to have locality2 but it depends on the thinking of some man who has locality1 and is definitely related to his other thoughts and feelings4 ,a term is ,abstract1 on the other hand1 when it denotes a quality 7or qualities71 considered by itself and without determinate existence in time1 place1 or relation to other things4 ',size1' 'shape1' 'weight1' 'colour1' 'intensity1' 'pleasurableness1' are terms used to denote such qualities1 and are then abstract in their denotation4 ',weight' is not something with a determinate existence at a given time2 it exists not merely in some particular place1 but wherever there is a heavy thing2 and1 as to relation1 at the same moment it combines in iron with solidity and in mercury with liquidity4 ,in fact1 a quality is a point of agreement in a multitude of different things2 all heavy things agree in weight1 all round things in roundness1 all red things in redness2 and an abstract term denotes such a point 7or points7 of agreement among the things denoted by concrete terms4 ,abstract terms result from the analysis of concrete things into their qualities2 and conversely a concrete term may be viewed as denoting the synthesis of qualities into an individual thing4 ,when several things agree in more than one quality1 there may be an abstract term denoting the union of qualities in which they agree1 and omitting their peculiarities2 as 'human nature' denotes the common qualities of men1 'civilisation' the common conditions of civilised peoples4 ,every general name1 if used as a concrete term1 has1 or may have1 a corresponding abstract term4 ,sometimes the concrete term is modified to form the abstract1 as 'greedy--greediness'2 sometimes a word is adapted from another language1 as 'man--humanity'2 sometimes a composite term is used1 as 'mercury--the nature of mercury1' etc4 ,the same concrete may have several abstract correlatives1 as 'man--manhood1 humanity1 human nature'2 'heavy--weight1 gravity1 ponderosity'2 but in such cases the abstract terms are not used quite synonymously2 that is1 they imply different ways of considering the concrete4 ,whether a word is used as a concrete or abstract term is in most instances plain from the word itself1 the use of most words being pretty regular one way or the other2 but sometimes we must judge by the context4 ',weight' may be used in the abstract for 'gravity1' or in the concrete for a measure2 but in the latter sense it is syncategorematic 7in the singular71 needing at least the article 'a 7or the7 weight4' ',government' may mean 'supreme political authority1' and is then abstract2 or1 the men who happen to be ministers1 and is then concrete2 but in this case1 too1 the article is usually prefixed4 ',the life' of any man may mean his vitality 7abstract71 as in ,thus following life in creatures we dissect2 or1 the series of events through which he passes 7concrete71 as in 'the life of ,nelson as narrated by ,southey4' ,it has been made a question whether the denotation of an abstract term may itself be the subject of qualities4 ,apparently 'weight' may be greater or less1 'government' good or bad1 'vitality' intense or dull4 ,but if every subject is modified by a quality1 a quality is also modified by making it the subject of another2 and1 if so1 it seems then to become a new quality4 ,the compound terms 'great weight1' 'bad government1' 'dull vitality1' have not the same denotation as the simple terms 'weight1 'government1' 'vitality'3 they imply1 and may be said to connote1 more special concrete experience1 such as the effort felt in lifting a trunk1 disgust at the conduct of officials1 sluggish movements of an animal when irritated4 ,it is to such concrete experiences that we have always to refer in order fully to realise the meaning of abstract terms1 and therefore1 of course1 to understand any qualification of them4 #e4 ,concrete terms may be subdivided according to the number of things they denote and the way in which they denote them4 ,a term may denote one thing or many3 if one1 it is called ,singular2 if many1 it may do so distributively1 and then it is ,general2 or1 as taken all together1 and then it is ,collective3 one1 then2 any one of many2 many in one4 ,among ,singular ,terms1 each denoting a single thing1 the most obvious are ,proper ,names1 such as ,gibraltar or ,george ,washington1 which are merely marks of individual things or persons1 and may form no part of the common language of a country4 ,they are thus distinguished from other ,singular ,terms1 which consist of common words so combined as to restrict their denotation to some individual1 such as1 'the strongest man on earth4' ,proper ,terms are often said to be arbitrary signs1 because their use does not depend upon any reason that may be given for them4 ,gibraltar had a meaning among the ,moors when originally conferred2 but no one now knows what it was1 unless he happens to have learned it2 yet the name serves its purpose as well as if it were ,rooke's ,nest4 ,every ,newton or ,newport year by year grows old1 but to alter the name would cause only confusion4 ,if such names were given by mere caprice it would make no difference2 and they could not be more cumbrous1 ugly1 or absurd than many of those that are given 'for reasons4' ,the remaining kinds of ,singular ,terms are drawn from the common resources of the language4 ,thus the pronouns 'he1' 'she1' 'it1' are singular terms1 whose present denotation is determined by the occasion and context of discourse3 so with demonstrative phrases--'the man1' 'that horse4' ,descriptive names may be more complex1 as 'the wisest man of ,gotham1' which is limited to some individual by the superlative suffix2 or 'the ,german ,emperor1' which is limited by the definite article--the general term ',german ,emperor' being thereby restricted either to the reigning monarch or to the one we happen to be discussing4 ,instead of the definite1 the indefinite article may be used to make general terms singular1 as 'a ,german ,emperor was crowned at ,versailles' 7individua vaga74 ,abstract ,terms are ostensively singular3 'whiteness' 7e4g47 is one quality4 ,but their full meaning is general3 'whiteness' stands for all white things1 so far as white4 ,abstract terms1 in fact1 are only formally singular4 ,general ,terms are words1 or combinations of words1 used to denote any one of many things that resemble one another in certain respects4 ',george ,,iii4' is a ,singular ,term denoting one man2 but ',king' is a ,general ,term denoting him and all other men of the same rank2 whilst the compound 'crowned head' is still more general1 denoting kings and also emperors4 ,it is the nature of a general term1 then1 to be used in the same sense of whatever it denotes2 and its most characteristic form is the ,class-name1 whether of objects1 such as 'king1' 'sheep1' 'ghost'2 or of events1 such as 'accession1' 'purchase1' 'manifestation4' ,things and events are known by their qualities and relations2 and every such aspect1 being a point of resemblance to some other things1 becomes a ground of generalisation1 and therefore a ground for the need and use of general terms4 ,hence general terms are far the most important sort of terms in ,logic1 since in them general propositions are expressed and1 moreover 7with rare exceptions71 all predicates are general4 ,for1 besides these typical class-names1 attributive words are general terms1 such as 'royal1' 'ruling1' 'woolly1' 'bleating1' 'impalpable1' 'vanishing4' ,infinitives may also be used as general terms1 as ',to err is human'2 but for logical purposes they may have to be translated into equivalent substantive forms1 as ,foolish actions are characteristic of mankind4 ,abstract terms1 too1 are 7as ,i observed7 equivalent to general terms2 'folly' is abstract for 'foolish actions4' ',honesty is the best policy' means people who are honest may hope to find their account in being so2 that is1 in the effects of their honest actions1 provided they are wise in other ways1 and no misfortunes attend them4 ,the abstract form is often much the more succinct and forcible1 but for logical treatment it needs to be interpreted in the general form4 ,by antonomasia proper names may become general terms1 as if we say ',a ,johnson' would not have written such a book--i4e41 any man of his genius for elaborate eloquence4 ,a ,collective ,term denotes a multitude of similar things considered as forming one whole1 as 'regiment1' 'flock1' 'nation'3 not distributively1 that is1 not the similar things severally2 to denote them we must say 'soldiers of the regiment1' 'sheep of the flock1' and so on4 ,if in a multitude of things there is no resemblance1 except the fact of being considered as parts of one whole1 as 'the world1' or 'the town of ,nottingham' 7meaning its streets and houses1 open spaces1 people1 and civic organisation71 the term denoting them as a whole is ,singular2 but 'the world' or 'town of ,nottingham1' meaning the inhabitants only1 is ,collective4 ,in their strictly collective use1 all such expressions are equivalent to singular terms2 but many of them may also be used as general terms1 as when we speak of 'so many regiments of the line1' or discuss the 'plurality of worlds'2 and in this general use they denote any of a multitude of things of the same kind--regiments1 or habitable worlds4 ,names of substances1 such as 'gold1' 'air1' 'water1' may be employed as singular1 collective1 or general terms2 though1 perhaps1 as singular terms only figuratively1 as when we say ,gold is king4 ,if we say with ,thales1 ',water is the source of all things1' 'water' seems to be used collectively4 ,but substantive names are frequently used as general terms4 ,for example1 ,gold is heavy means 'in comparison with other things1' such as water4 ,and1 plainly1 it does not mean that the aggregate of gold is heavier than the aggregate of water1 but only that its specific gravity is greater2 that is1 bulk for bulk1 any piece of gold is heavier than water4 ,finally1 any class-name may be used collectively if we wish to assert something of the things denoted by it1 not distributively but altogether1 as that ,sheep are more numerous than wolves4 ,,chapter ,,iv ,,the ,,connotation ,,of ,,terms #a4 ,terms are next to be classified according to their ,connotation--that is1 according to what they imply as characteristic of the things denoted4 ,we have seen that general names are used to denote many things in the same sense1 because the things denoted resemble one another in certain ways3 it is this resemblance in certain points that leads us to class the things together and call them by the same name2 and therefore the points of resemblance constitute the sense or meaning of the name1 or its ,connotation1 and limit its applicability to such things as have these characteristic qualities4 ',sheep' for example1 is used in the same sense1 to denote any of a multitude of animals that resemble one another3 their size1 shape1 woolly coats1 cloven hoofs1 innocent ways and edibility are well known4 ,when we apply to anything the term 'sheep1' we imply that it has these qualities3 'sheep1' denoting the animal1 connotes its possessing these characteristics2 and1 of course1 it cannot1 without a figure of speech or a blunder1 be used to denote anything that does not possess all these qualities4 ,it is by a figure of speech that the term 'sheep' is applied to some men2 and to apply it to goats would be a blunder4 ,most people are very imperfectly aware of the connotation of the words they use1 and are guided in using them merely by the custom of the language4 ,a man who employs a word quite correctly may be sadly posed by a request to explain or define it4 ,moreover1 so far as we are aware of the connotation of terms1 the number and the kind of attributes we think of1 in any given case1 vary with the depth of our interest1 and with the nature of our interest in the things denoted4 ',sheep' has one meaning to a touring townsman1 a much fuller one to a farmer1 and yet a different one to a zoologist4 ,but this does not prevent them agreeing in the use of the word1 as long as the qualities they severally include in its meaning are not incompatible4 ,all general names1 and therefore not only class-names1 like 'sheep1' but all attributives1 have some connotation4 ',woolly' denotes anything that bears wool1 and connotes the fact of bearing wool2 'innocent' denotes anything that habitually and by its disposition does no harm 7or has not been guilty of a particular offence71 and connotes a harmless character 7or freedom from particular guilt72 'edible' denotes whatever can be eaten with good results1 and connotes its suitability for mastication1 deglutition1 digestion1 and assimilation4 #b4 ,but whether all terms must connote as well as denote something1 has been much debated4 ,proper names1 according to what seems the better opinion1 are1 in their ordinary use1 not connotative4 ,to say that they have no meaning may seem violent3 if any one is called ,john ,doe1 this name1 no doubt1 means a great deal to his friends and neighbours1 reminding them of his stature and physiognomy1 his air and gait1 his wit and wisdom1 some queer stories1 and an indefinite number of other things4 ,but all this significance is local or accidental2 it only exists for those who know the individual or have heard him described3 whereas a general name gives information about any thing or person it denotes to everybody who understands the language1 without any particular knowledge of the individual4 ,we must distinguish1 in fact1 between the peculiar associations of the proper name and the commonly recognised meaning of the general name4 ,this is why proper names are not in the dictionary4 ,such a name as ,london1 to be sure1 or ,napoleon ,buonaparte1 has a significance not merely local2 still1 it is accidental4 ,these names are borne by other places and persons than those that have rendered them famous4 ,there are ,londons in various latitudes1 and1 no doubt1 many ,napoleon ,buonapartes in ,louisiana2 and each name has in its several denotations an altogether different suggestiveness4 ,for its suggestiveness is in each application determined by the peculiarities of the place or person denoted2 it is not given to the different places 7or to the different persons7 because they have certain characteristics in common4 ,however1 the scientific grounds of the doctrine that proper names are non-connotative1 are these3 ,the peculiarities that distinguish an individual person or thing are admitted to be infinite1 and anything less than a complete enumeration of these peculiarities may fail to distinguish and identify the individual4 ,for1 short of a complete enumeration of them1 the description may be satisfied by two or more individuals2 and in that case the term denoting them1 if limited by such a description1 is not a proper but a general name1 since it is applicable to two or more in the same sense4 ,the existence of other individuals to whom it applies may be highly improbable2 but1 if it be logically possible1 that is enough4 ,on the other hand1 the enumeration of infinite peculiarities is certainly impossible4 ,therefore proper names have no assignable connotation4 ,the only escape from this reasoning lies in falling back upon time and place1 the principles of individuation1 as constituting the connotation of proper names4 ,two things cannot be at the same time in the same place3 hence 'the man who was at a certain spot on the bridge of ,lodi at a certain instant in a certain year' suffices to identify ,napoleon ,buonaparte for that instant4 ,supposing no one else to have borne the name1 then1 is this its connotation8 ,no one has ever thought so4 ,and1 at any rate1 time and place are only extrinsic determinations 7suitable indeed to events like the battle of ,lodi1 or to places themselves like ,london72 whereas the connotation of a general term1 such as 'sheep1' consists of intrinsic qualities4 ,hence1 then1 the scholastic doctrine 'that individuals have no essence' 7see chap4 xxii4 #i71 and ,hamilton's dictum 'that every concept is inadequate sic to the individual1' are justified4 ,general names1 when used as proper names1 lose their connotation1 as ,euxine or ,newfoundland4 ,singular terms1 other than ,proper1 have connotation2 either in themselves1 like the singular pronouns 'he1' 'she1' 'it1' which are general in their applicability1 though singular in application2 or1 derivatively1 from the general names that combine to form them1 as in 'the first ,emperor of the ,french' or the ',capital of the ,british ,empire4' #c4 ,whether ,abstract ,terms have any connotation is another disputed question4 ,we have seen that they denote a quality or qualities of something1 and that is precisely what general terms connote3 'honesty' denotes a quality of some men2 'honest' connotes the same quality1 whilst denoting the men who have it4 ,the denotation of abstract terms thus seems to exhaust their force or meaning4 ,it has been proposed1 however1 to regard them as connoting the qualities they directly stand for1 and not denoting anything2 but surely this is too violent4 ,to denote something is the same as to be the name of something 7whether real or unreal71 which every term must be4 ,it is a better proposal to regard their denotation and connotation as coinciding2 though open to the objection that 'connote' means 'to mark along with' something else1 and this plan leaves nothing else4 ,mill thought that abstract terms are connotative when1 besides denoting a quality1 they suggest a quality of that quality 7as 'fault' implies 'hurtfulness'72 but against this it may be urged that one quality cannot bear another1 since every qualification of a quality constitutes a distinct quality in the total 7'milk-whiteness' is distinct from 'whiteness1' cf4 chap4 iii4 #d74 ,after all1 if it is the most consistent plan1 why not say that abstract1 like proper1 terms have no connotation8 ,but if abstract terms must be made to connote something1 should it not be those things1 indefinitely suggested1 to which the qualities belong8 ,thus 'whiteness' may be considered to connote either snow or vapour1 or any white thing1 apart from one or other of which the quality has no existence2 whose existence therefore it implies4 ,by this course the denotation and connotation of abstract and of general names would be exactly reversed4 ,whilst the denotation of a general name is limited by the qualities connoted1 the connotation of an abstract name includes all the things in which its denotation is realised4 ,but the whole difficulty may be avoided by making it a rule to translate1 for logical purposes1 all abstract into the corresponding general terms4 #d4 ,if we ask how the connotation of a term is to be known1 the answer depends upon how it is used4 ,if used scientifically1 its connotation is determined by1 and is the same as1 its definition2 and the definition is determined by examining the things to be denoted1 as we shall see in chap4 xxii4 ,if the same word is used as a term in different sciences1 as 'property' in ,law and in ,logic1 it will be differently defined by them1 and will have1 in each use1 a correspondingly different connotation4 ,but terms used in popular discourse should1 as far as possible1 have their connotations determined by classical usage1 i4e41 by the sense in which they are used by writers and speakers who are acknowledged masters of the language1 such as ,dryden and ,burke4 ,in this case the classical connotation determines the definition2 so that to define terms thus used is nothing else than to analyse their accepted meanings4 ,it must not1 however1 be supposed that in popular use the connotation of any word is invariable4 ,logicians have attempted to classify terms into ,univocal 7having only one meaning7 and quivocal 7or ambiguous72 and no doubt some words 7like 'civil1' 'natural1' 'proud1' 'liberal1' 'humorous'7 are more manifestly liable to ambiguous use than some others4 ,but in truth all general terms are popularly and classically used in somewhat different senses4 ,figurative or tropical language chiefly consists in the transfer of words to new senses1 as by metaphor or metonymy4 ,in the course of years1 too1 words change their meanings2 and before the time of ,dryden our whole vocabulary was much more fluid and adaptable than it has since become4 ,such authors as ,bacon1 ,milton1 and ,sir ,thomas ,browne often used words derived from the ,latin in some sense they originally had in ,latin1 though in ,english they had acquired another meaning4 ,spenser and ,shakespeare1 besides this practice1 sometimes use words in a way that can only be justified by their choosing to have it so2 whilst their contemporaries1 ,beaumont and ,fletcher1 write the perfect modern language1 as ,dryden observed4 ,lapse of time1 however1 is not the chief cause of variation in the sense of words4 ,the matters which terms are used to denote are often so complicated or so refined in the assemblage1 interfusion1 or gradation of their qualities1 that terms do not exist in sufficient abundance and discriminativeness to denote the things and1 at the same time1 to convey by connotation a determinate sense of their agreements and differences4 ,in discussing politics1 religion1 ethics1 sthetics1 this imperfection of language is continually felt2 and the only escape from it1 short of coining new words1 is to use such words as we have1 now in one sense1 now in another somewhat different1 and to trust to the context1 or to the resources of the literary art1 in order to convey the true meaning4 ,against this evil the having been born since ,dryden is no protection4 ,it behoves us1 then1 to remember that terms are not classifiable into ,univocal and quivocal1 but that all terms are susceptible of being used quivocally1 and that honesty and lucidity require us to try1 as well as we can1 to use each term univocally in the same context4 ,the context of any proposition always proceeds upon some assumption or understanding as to the scope of the discussion1 which controls the interpretation of every statement and of every word4 ,this was called by ,de ,morgan the universe of discourse3 an older name for it1 revived by ,dr4 ,venn1 and surely a better one1 is suppositio4 ,if we are talking of children1 and 'play' is mentioned1 the suppositio limits the suggestiveness of the word in one way2 whilst if ,monaco is the subject of conversation1 the same word 'play1' under the influence of a different suppositio1 excites altogether different ideas4 ,hence to ignore the suppositio is a great source of fallacies of equivocation4 ',man' is generally defined as a kind of animal2 but 'animal' is often used as opposed to and excluding man4 ',liberal' has one meaning under the suppositio of politics1 another with regard to culture1 and still another as to the disposal of one's private means4 ,clearly1 therefore1 the connotation of general terms is relative to the suppositio1 or universe of discourse4 #e4 ,relative and ,absolute ,terms4--,some words go in couples or groups3 like 'up-down1' 'former-latter1' 'father-mother-children1' 'hunter-prey1' 'cause-effect1' etc4 ,these are called ,relative ,terms1 and their nature1 as explained by ,mill1 is that the connotations of the members of such a pair or group are derived from the same set of facts 7the fundamentum relationis74 ,there cannot be an 'up' without a 'down1' a 'father' without a 'mother' and 'child'2 there cannot be a 'hunter' without something hunted1 nor 'prey' without a pursuer4 ,what makes a man a 'hunter' is his activities in pursuit2 and what turns a chamois into 'prey' is its interest in these activities4 ,the meaning of both terms1 therefore1 is derived from the same set of facts2 neither term can be explained without explaining the other1 because the relation between them is connoted by both2 and neither can with propriety be used without reference to the other1 or to some equivalent1 as 'game' for 'prey4' ,in contrast with such ,relative ,terms1 others have been called ,absolute or ,non-relative4 ,whilst 'hunter' and 'prey' are relative1 'man' and 'chamois' have been considered absolute1 as we may use them without thinking of any special connection between their meanings4 ,however1 if we believe in the unity of ,nature and in the relativity of knowledge 7that is1 that all knowledge depends upon comparison1 or a perception of the resemblances and differences of things71 it follows that nothing can be completely understood except through its agreements or contrasts with everything else1 and that all terms derive their connotation from the same set of facts1 namely1 from general experience4 ,thus both man and chamois are animals2 this fact is an important part of the meaning of both terms1 and to that extent they are relative terms4 ',five yards' and 'five minutes' are very different notions1 yet they are profoundly related2 for their very difference helps to make both notions distinct2 and their intimate connection is shown in this1 that five yards are traversed in a certain time1 and that five minutes are measured by the motion of an index over some fraction of a yard upon the dial4 ,the distinction1 then1 between relative and non-relative terms must rest1 not upon a fundamental difference between them 7since1 in fact1 all words are relative71 but upon the way in which words are used4 ,we have seen that some words1 such as 'up-down1' 'cause-effect1' can only be used relatively2 and these may1 for distinction1 be called ,correlatives4 ,but other words1 whose meanings are only partially interdependent1 may often be used without attending to their relativity1 and may then be considered as ,absolute4 ,we cannot say 'the hunter returned empty handed1' without implying that 'the prey escaped'2 but we may say 'the man went supperless to bed1' without implying that 'the chamois rejoiced upon the mountain4' ,such words as 'man' and 'chamois' may1 then1 in their use1 be1 as to one another1 non-relative4 ,to illustrate further the relativity of terms1 we may mention some of the chief classes of them4 ,numerical order3 #ast1 #bnd1 #crd1 etc42 #ast implies #bnd1 and #bnd #ast2 and #crd implies #ast and #bnd1 but these do not imply #crd2 and so on4 ,order in ,time or ,place3 before-after2 early-punctual-late2 right-middle-left2 ,north-,south1 etc4 ,as to ,extent1 ,volume1 and ,degree3 greater-equal-less2 large-medium-small2 whole and part4 ,genus and ,species are a peculiar case of whole and part 7cf4 chaps4 xxi4-ii4-iii474 ,sometimes a term connotes all the attributes that another does1 and more besides1 which1 as distinguishing it1 are called differential4 ,thus 'man' connotes all that 'animal' does1 and also 7as differenti7 the erect gait1 articulate speech1 and other attributes4 ,in such a case as this1 where there are well-marked classes1 the term whose connotation is included in the others' is called a ,genus of that ,species4 ,we have a ,genus1 triangle2 and a ,species1 isosceles1 marked off from all other triangles by the differential quality of having two equal sides3 again--,genus1 book2 ,species1 quarto2 ,difference1 having each sheet folded into four leaves4 ,there are other cases where these expressions 'genus' and 'species' cannot be so applied without a departure from usage1 as1 e4g41 if we call snow a species of the genus 'white1' for 'white' is not a recognised class4 ,the connotation of white 7i4e41 whiteness7 is1 however1 part of the connotation of snow1 just as the qualities of 'animal' are amongst those of 'man'2 and for logical purposes it is desirable to use 'genus and species' to express that relativity of terms which consists in the connotation of one being part of the connotation of the other4 ,two or more terms whose connotations severally include that of another term1 whilst at the same time exceeding it1 are 7in relation to that other term7 called ,co-ordinate4 ,thus in relation to 'white1' snow and silver are co-ordinate2 in relation to colour1 yellow and red and blue are co-ordinate4 ,and when all the terms thus related stand for recognised natural classes1 the co-ordinate terms are called co-ordinate species2 thus man and chamois are 7in ,logic7 co-ordinate species of the genus animal4 #f4 ,from such examples of terms whose connotations are related as whole and part1 it is easy to see the general truth of the doctrine that as connotation decreases1 denotation increases3 for 'animal1' with less connotation than man or chamois1 denotes many more objects2 'white1' with less connotation than snow or silver1 denotes many more things1 ,it is not1 however1 certain that this doctrine is always true in the concrete3 since there may be a term connoting two or more qualities1 all of which qualities are peculiar to all the things it denotes2 and1 if so1 by subtracting one of the qualities from its connotation1 we should not increase its denotation4 ,if 'man1' for example1 has among mammals the two peculiar attributes of erect gait and articulate speech1 then1 by omitting 'articulate speech' from the connotation of man1 we could not apply the name to any more of the existing mammalia than we can at present4 ,still we might have been able to do so2 there might have been an erect inarticulate ape1 and perhaps there once was one2 and1 if so1 to omit 'articulate' from the connotation of man would make the term 'man' denote that animal 7supposing that there was no other difference to exclude it74 ,hence1 potentially1 an increase of the connotation of any term implies a decrease of its denotation4 ,and1 on the other hand1 we can only increase the denotation of a term1 or apply it to more objects1 by decreasing its connotation2 for1 if the new things denoted by the term had already possessed its whole connotation1 they must already have been denoted by it4 ,however1 we may increase the known denotation without decreasing the connotation1 if we can discover the full connotation in things not formerly supposed to have it1 as when dolphins were discovered to be mammals2 or if we can impose the requisite qualities upon new individuals1 as when by annexing some millions of ,africans we extend the denotation of ',british subject' without altering its connotation4 ,many of the things noticed in this chapter1 especially in this section and the preceding1 will be discussed at greater length in the chapters on ,classification and ,definition4 #g4 ,contradictory ,relative ,terms4--,every term has1 or may have1 another corresponding with it in such a way that1 whatever differential qualities 7 #e7 it connotes1 this other connotes merely their absence2 so that one or the other is always formally predicable of any ,subject1 but both these terms are never predicable of the same ,subject in the same relation3 such pairs of terms are called ,contradictories4 ,whatever ,subject we take1 it is either visible or invisible1 but not both2 either human or non-human1 but not both4 ,this at least is true formally1 though in practice we should think ourselves trifled with if any one told us that ',a mountain is either human or non-human1 but not both4' ,it is symbolic terms1 such as ,x and x1 that are properly said to be contradictories in relation to any subject whatever1 ,s or ,m4 ,for1 as we have seen1 the ordinary use of terms is limited by some suppositio1 and this is true of ,contradictories4 ',human' and 'non-human' may refer to zoological classification1 or to the scope of physical1 mental1 or moral powers--as if we ask whether to flourish a dumbbell of a ton weight1 or to know the future by intuition1 or impeccability1 be human or non-human4 ,similarly1 'visible' and 'invisible' refer either to the power of emitting or reflecting light1 so that the words have no hold upon a sound or a scent1 or else to power of vision and such qualifications as 'with the naked eye' or 'with a microscope4' ,again1 the above definition of ,contradictories tells us that they cannot be predicated of the same ,subject in the same relation2 that is1 at the same time or place1 or under the same conditions4 ,the lamp is visible to me now1 but will be invisible if ,i turn it out2 one side of it is now visible1 but the other is not3 therefore without this restriction1 in the same relation1 few or no terms would be contradictory4 ,if a man is called wise1 it may mean 'on the whole' or 'in a certain action'2 and clearly a man may for once be wise 7or act wisely7 who1 on the whole1 is not-wise4 ,so that here again1 by this ambiguity1 terms that seem contradictory are predicable of the same subject1 but not in the same relation4 ,in order to avoid the ambiguity1 however1 we have only to construct the term so as to express the relation1 as 'wise on the whole'2 and this immediately generates the contradictory 'not-wise on the whole4' ,similarly1 at one age a man may have black hair1 at another not-black hair2 but the difficulty is practically removable by stating the age referred to4 ,still1 this case easily leads us to a real difficulty in the use of contradictory terms1 a difficulty arising from the continuous change or 'flux' of natural phenomena4 ,if things are continually changing1 it may be urged that contradictory terms are always applicable to the same subject1 at least as fast as we can utter them3 for if we have just said that a man's hair is black1 since 7like everything else7 his hair is changing1 it must now be not-black1 though 7to be sure7 it may still seem black4 ,the difficulty1 such as it is1 lies in this1 that the human mind and its instrument language are not equal to the subtlety of ,nature4 ,all things flow1 but the terms of human discourse assume a certain fixity of things2 everything at every moment changes1 but for the most part we can neither perceive this change nor express it in ordinary language4 ,this paradox1 however1 may1 ,i suppose1 be easily over-stated4 ,the change that continually agitates ,nature consists in the movements of masses or molecules1 and such movements of things are compatible with a considerable persistence of their qualities4 ,not only are the molecular changes always going on in a piece of gold compatible with its remaining yellow1 but its persistent yellowness depends on the continuance of some of those changes4 ,similarly1 a man's hair may remain black for some years2 though1 no doubt1 at a certain age its colour may begin to be problematical1 and the applicability to it of 'black' or 'not-black' may become a matter of genuine anxiety4 ,whilst being on our guard1 then1 against fallacies of contradiction arising from the imperfect correspondence of fact with thought and language1 we shall often have to put up with it4 ,candour and humility having been satisfied by the above acknowledgment of the subtlety of ,nature1 we may henceforward proceed upon the postulate--that it is possible to use contradictory terms such as cannot both be predicated of the same subject in the same relation1 though one of them may be2 that1 for example1 it may be truly said of a man for some years that his hair is black2 and1 if so1 that during those years to call it not-black is false or extremely misleading4 ,the most opposed terms of the literary vocabulary1 however1 such as 'wise-foolish1' 'old-young1' 'sweet-bitter1' are rarely true contradictories3 wise and foolish1 indeed1 cannot be predicated of the same man in the same relation2 but there are many middling men1 of whom neither can be predicated on the whole4 ,for the comparison of quantities1 again1 we have three correlative terms1 'greater--equal--less1' and none of these is the contradictory of either of the others4 ,in fact1 the contradictory of any term is one that denotes the sum of its co-ordinates 7 #f72 and to obtain a contradictory1 the surest way is to coin one by prefixing to the given term the particle 'not' or 7sometimes7 'non'3 as 'wise1 not-wise1' 'human1 non-human1' 'greater1 not-greater4' ,the separate word 'not' is surer to constitute a contradictory than the usual prefixes of negation1 'un-' or 'in-1' or even 'non'2 since compounds of these are generally warped by common use from a purely negative meaning4 ,thus1 ',nonconformist' does not denote everybody who fails to conform4 ',unwise' is not equivalent to 'not-wise1' but means 'rather foolish'2 a very foolish action is not-wise1 but can only be called unwise by meiosis or irony4 ,still1 negatives formed by 'in' or 'un' or 'non' are sometimes really contradictory of their positives2 as 'visible1 invisible1' 'equal1 unequal4' #h4 ,the distinction between ,positive and ,negative terms is not of much value in ,logic1 what importance would else attach to it being absorbed by the more definite distinction of contradictories4 ,for contradictories are positive and negative in essence and1 when least ambiguously stated1 also in form4 ,and1 on the other hand1 as we have seen1 when positive and negative terms are not contradictory1 they are misleading4 ,as with 'wise-unwise1' so with many others1 such as 'happy-unhappy'2 which are not contradictories2 since a man may be neither happy nor unhappy1 but indifferent1 or 7again7 so miserable that he can only be called unhappy by a figure of speech4 ,in fact1 in the common vocabulary a formal negative often has a limited positive sense2 and this is the case with unhappy1 signifying the state of feeling in the milder shades of ,purgatory4 ,when a ,negative term is fully contradictory of its ,positive it is said to be ,infinite2 because it denotes an unascertained multitude of things1 a multitude only limited by the positive term and the suppositio2 thus 'not-wise' denotes all except the wise1 within the suppositio of 'intelligent beings4' ,formally 7disregarding any suppositio71 such a negative term stands for all possible terms except its positive3 x denotes everything but ,x2 and 'not-wise' may be taken to include stones1 triangles and hippogriffs4 ,and even in this sense1 a negative term has some positive meaning1 though a very indefinite one1 not a specific positive force like 'unwise' or 'unhappy'3 it denotes any and everything that has not the attributes connoted by the corresponding positive term4 ,privative ,terms connote the absence of a quality that normally belongs to the kind of thing denoted1 as 'blind' or 'deaf4' ,we may predicate 'blind' or 'deaf' of a man1 dog or cow that happens not to be able to see or hear1 because the powers of seeing and hearing generally belong to those species2 but of a stone or idol these terms can only be used figuratively4 ,indeed1 since the contradictory of a privative carries with it the privative limitation1 a stone is strictly 'not-blind'3 that is1 it is 'not-something-that-normally-having-sigh t-wants-it4' ,contrary ,terms are those that 7within a certain genus or suppositio7 severally connote differential qualities that are1 in fact1 mutually incompatible in the same relation to the same thing1 and therefore cannot be predicated of the same subject in the same relation2 and1 so far1 they resemble ,contradictory ,terms3 but they differ from contradictory terms in this1 that the differential quality connoted by each of them is definitely positive2 no ,contrary ,term is infinite1 but is limited to part of the suppositio excluded by the others2 so that1 possibly1 neither of two ,contraries is truly predicable of a given subject4 ,thus 'blue' and 'red' are ,contraries1 for they cannot both be predicated of the same thing in the same relation2 but are not ,contradictories1 since1 in a given case1 neither may be predicable3 if a flower is blue in a certain part1 it cannot in the same part be red2 but it may be neither blue nor red1 but yellow2 though it is certainly either blue or not-blue4 ,all co-ordinate terms are formal ,contraries2 but if1 in fact1 a series of co-ordinates comprises only two 7as male-female71 they are empirical ,contradictories2 since each includes all that area of the suppositio which the other excludes4 ,the extremes of a series of co-ordinate terms are ,opposites2 as1 in a list of colours1 white and black1 the most strongly contrasted1 are said to be opposites1 or as among moods of feeling1 rapture and misery are opposites4 ,but this distinction is of slight logical importance4 ,imperfect ,positive and ,negative couples1 like 'happy and unhappy1' which 7as we have seen7 are not contradictories1 are often called ,opposites4 ,the members of any series of ,contraries are all included by any one of them and its contradictory1 as all colours come under 'red' and 'not-red1' all moods of feeling under 'happy' and 'not-happy4' ,,chapter ,v ,,the ,,classification ,,of ,,propositions #a4 ,logicians classify ,propositions according to ,quantity1 ,quality1 ,relation and ,modality4 ,as to ,quantity1 propositions are either ,universal or ,particular2 that is to say1 the predicate is affirmed or denied either of the whole subject or of a part of it--of ,all or of ,some ,s4 ,all ,s is ,p 7that is1 ,p is predicated of all ,s74 ,some ,s is ,p 7that is1 ,p is predicated of some ,s74 ,an ,universal ,proposition may have for its subject a singular term1 a collective1 a general term distributed1 or an abstract term4 7#a7 ,a proposition having a singular term for its subject1 as ,the ,queen has gone to ,france1 is called a ,singular ,proposition2 and some ,logicians regard this as a third species of proposition with respect to quantity1 distinct from the ,universal and ,particular2 but that is needless4 7#b7 ,a collective term may be the subject1 as ,the ,black ,watch is ordered to ,india4 ,in this case1 as well as in singular propositions1 a predication is made concerning the whole subject as a whole4 7#c7 ,the subject may be a general term taken in its full denotation1 as ,all apes are sagacious2 and in this case a ,predication is made concerning the whole subject distributively2 that is1 of each and everything the subject stands for4 7#d7 ,propositions whose subjects are abstract terms1 though they may seem to be formally ,singular1 are really as to their meaning distributive ,universals2 since whatever is true of a quality is true of whatever thing has that quality so far as that quality is concerned4 ,truth will prevail means that ,all true propositions are accepted at last 7by sheer force of being true1 in spite of interests1 prejudices1 ignorance and indifference74 ,to bear this in mind may make one cautious in the use of abstract terms4 ,in the above paragraphs a distinction is implied between ,singular and ,distributive ,universals2 but1 technically1 every term1 whether subject or predicate1 when taken in its full denotation 7or universally71 is said to be 'distributed1' although this word1 in its ordinary sense1 would be directly applicable only to general terms4 ,in the above examples1 then1 ',queen1' ',black ,watch1' 'apes1' and 'truth' are all distributed terms4 ,indeed1 a simple definition of the ,universal ,proposition is 'one whose subject is distributed4' ,a ,particular ,proposition is one that has a general term for its subject1 whilst its predicate is not affirmed or denied of everything the subject denotes2 in other words1 it is one whose subject is not distributed3 as ,some lions inhabit ,africa4 ,in ordinary discourse it is not always explicitly stated whether predication is universal or particular2 it would be very natural to say ,lions inhabit ,africa1 leaving it1 as far as the words go1 uncertain whether we mean all or some lions4 ,propositions whose quantity is thus left indefinite are technically called 'preindesignate1' their quantity not being stated or designated by any introductory expression2 whilst propositions whose quantity is expressed1 as ,all foundling-hospitals have a high death-rate1 or ,some wine is made from grapes1 are said to be 'predesignate4' ,now1 the rule is that preindesignate propositions are1 for logical purposes1 to be treated as particular2 since it is an obvious precaution of the science of proof1 in any practical application1 not to go beyond the evidence4 ,still1 the rule may be relaxed if the universal quantity of a preindesignate proposition is well known or admitted1 as in ,planets shine with reflected light--understood of the planets of our solar system at the present time4 ,again1 such a proposition as ,man is the paragon of animals is not a preindesignate1 but an abstract proposition2 the subject being elliptical for ,man according to his proper nature2 and the translation of it into a predesignate proposition is not ,all men are paragons2 nor can ,some men be sufficient1 since an abstract can only be adequately rendered by a distributed term2 but we must say1 ,all men who approach the ideal4 ,universal real propositions1 true without qualification1 are very scarce2 and we often substitute for them general propositions1 saying perhaps--generally1 though not universally1 ,s is ,p4 ,such general propositions are1 in strictness1 particular2 and the logical rules concerning universals cannot be applied to them without careful scrutiny of the facts4 ,the marks or predesignations of ,quantity commonly used in ,logic are3 for ,universals1 ,all1 ,any1 ,every1 ,whatever 7in the negative ,no or ,no one1 see next 72 for ,particulars1 ,some4 ,now ,some1 technically used1 does not mean ,some only1 but ,some at least 7it may be one1 or more1 or all74 ,if it meant ',some only1' every particular proposition would be an exclusive exponible 7chap4 ii4 #c72 since ,only some men are wise implies that ,some men are not wise4 ,besides1 it may often happen in an investigation that all the instances we have observed come under a certain rule1 though we do not yet feel justified in regarding the rule as universal2 and this situation is exactly met by the expression ,some 7it may be all74 ,the words ,many1 ,most1 ,few are generally interpreted to mean ,some2 but as ,most signifies that exceptions are known1 and ,few that the exceptions are the more numerous1 propositions thus predesignate are in fact exponibles1 mounting to ,some are and ,some are not4 ,if to work with both forms be too cumbrous1 so that we must choose one1 apparently ,few are should be treated as ,some are not4 ,the scientific course to adopt with propositions predesignate by ,most or ,few1 is to collect statistics and determine the percentage2 thus1 ,few men are wise--say #b per cent4 ,the ,quantity of a proposition1 then1 is usually determined entirely by the quantity of the subject1 whether all or some4 ,still1 the quantity of the predicate is often an important consideration2 and though in ordinary usage the predicate is seldom predesignate1 ,logicians agree that in every ,negative ,proposition 7see #b7 the predicate is 'distributed1' that is to say1 is denied altogether of the subject1 and that this is involved in the form of denial4 ,to say ,some men are not brave1 is to declare that the quality for which men may be called brave is not found in any of the ,some men referred to3 and to say ,no men are proof against flattery1 cuts off the being 'proof against flattery' entirely from the list of human attributes4 ,on the other hand1 every ,affirmative ,proposition is regarded as having an undistributed predicate2 that is to say1 its predicate is not affirmed exclusively of the subject4 ,some men are wise does not mean that 'wise' cannot be predicated of any other beings2 it is equivalent to ,some men are wise 7whoever else may be74 ,and ,all elephants are sagacious does not limit sagacity to elephants3 regarding 'sagacious' as possibly denoting many animals of many species that exhibit the quality1 this proposition is equivalent to ',all elephants are some sagacious animals4' ,the affirmative predication of a quality does not imply exclusive possession of it as denial implies its complete absence2 and1 therefore1 to regard the predicate of an affirmative proposition as distributed would be to go beyond the evidence and to take for granted what had never been alleged4 ,some ,logicians1 seeing that the quantity of predicates1 though not distinctly expressed1 is recognised1 and holding that it is the part of ,logic to make explicit in language whatever is implicit in thought1 have proposed to exhibit the quantity of predicates by predesignation1 thus3 ',some men are some wise 7beings7'2 'some men are not any brave 7beings7'2 etc4 ,this is called the ,quantification of the ,predicate1 and leads to some modifications of ,deductive ,logic which will be referred to hereafter4 7,see #c2 chap4 vii4 #d1 and chap4 viii4 #c47 #b4 ,as to ,quality1 ,propositions are either ,affirmative or ,negative4 ,an ,affirmative ,proposition is1 formally1 one whose copula is affirmative 7or1 has no negative sign71 as ,s--is--,p1 ,all men--are--partial to themselves4 ,a ,negative ,proposition is one whose copula is negative 7or1 has a negative sign71 as ,s--is not--,p1 ,some men--are not--proof against flattery4 ,when1 indeed1 a ,negative ,proposition is of ,universal ,quantity1 it is stated thus3 ,no ,s is ,p1 ,no men are proof against flattery2 but1 in this case1 the detachment of the negative sign from the copula and its association with the subject is merely an accident of our idiom2 the proposition is the same as ,all men--are not--proof against flattery4 ,it must be distinguished1 therefore1 from such an expression as ,not every man is proof against flattery2 for here the negative sign really restricts the subject2 so that the meaning is--,some men at most 7it may be none7 are proof against flattery2 and thus the proposition is ,particular1 and is rendered--,some men--are not--proof against flattery4 ,when the negative sign is associated with the predicate1 so as to make this an ,infinite ,term 7chap4 iv4 #h71 the proposition is called an ,infinite ,proposition1 as ,s is not-,p 7or p71 ,all men are--incapable of resisting flattery1 or are--not-proof against flattery4 ,infinite propositions1 when the copula is affirmative1 are formally1 themselves affirmative1 although their force is chiefly negative2 for1 as the last example shows1 the difference between an infinite and a negative proposition may depend upon a hyphen4 ,it has been proposed1 indeed1 with a view to superficial simplification1 to turn all ,negatives into ,infinites1 and thus render all propositions ,affirmative in ,quality4 ,but although every proposition both affirms and denies something according to the aspect in which you regard it 7as ,snow is white denies that it is any other colour1 and ,snow is not blue affirms that it is some other colour71 yet there is a great difference between the definite affirmation of a genuine affirmative and the vague affirmation of a negative or infinite2 so that materially an affirmative infinite is the same as a negative4 ,generally ,mill's remark is true1 that affirmation and denial stand for distinctions of fact that cannot be got rid of by manipulation of words4 ,whether granite sinks in water1 or not2 whether the rook lives a hundred years1 or not2 whether a man has a hundred dollars in his pocket1 or not2 whether human bones have ever been found in ,pliocene strata1 or not2 such alternatives require distinct forms of expression4 ,at the same time1 it may be granted that many facts admit of being stated with nearly equal propriety in either ,quality1 as ,no man is proof against flattery1 or ,all men are open to flattery4 ,but whatever advantage there is in occasionally changing the ,quality of a proposition may be gained by the process of ,obversion 7chap4 vii4 #e72 whilst to use only one ,quality would impair the elasticity of logical expression4 ,it is a postulate of ,logic that the negative sign may be transferred from the copula to the predicate1 or from the predicate to the copula1 without altering the sense of a proposition2 and this is justified by the experience that not to have an attribute and to be without it are the same thing4 #c4 ,a4 ,i4 ,e4 ,o4--,combining the two kinds of ,quantity1 ,universal and ,particular1 with the two kinds of ,quality1 ,affirmative and ,negative1 we get four simple types of proposition1 which it is usual to symbolise by the letters ,a4 ,i4 ,e4 ,o41 thus3 ,a4 ,universal ,affirmative -- ,all ,s is ,p4 ,i4 ,particular ,affirmative -- ,some ,s is ,p4 ,e4 ,universal ,negative -- ,no ,s is ,p4 ,o4 ,particular ,negative -- ,some ,s is not ,p4 ,as an aid to the remembering of these symbols we may observe that ,a4 and ,i4 are the first two vowels in affirmo and that ,e4 and ,o4 are the vowels in nego4 ,it must be acknowledged that these four kinds of proposition recognised by ,formal ,logic constitute a very meagre selection from the list of propositions actually used in judgment and reasoning4 ,those ,logicians who explicitly quantify the predicate obtain1 in all1 eight forms of proposition according to ,quantity and ,quality3 ,u4 ,toto-total ,affirmative -- ,all ,x is all ,y4 ,a4 ,toto-partial ,affirmative -- ,all ,x is some ,y4 ,y4 ,parti-total ,affirmative -- ,some ,x is all ,y4 ,i4 ,parti-partial ,affirmative -- ,some ,x is some ,y4 ,e4 ,toto-total ,negative -- ,no ,x is any ,y4 4 ,toto-partial ,negative -- ,no ,x is some ,y4 ,o4 ,parti-total ,negative -- ,some ,x is not any ,y4 4 ,parti-partial ,negative -- ,some ,x is not some ,y4 ,here ,a4 ,i4 ,e4 ,o4 correspond with those similarly symbolised in the usual list1 merely designating in the predicates the quantity which was formerly treated as implicit4 #d4 ,as to ,relation1 propositions are either ,categorical or ,conditional4 ,a ,categorical ,proposition is one in which the predicate is directly affirmed or denied of the subject without any limitation of time1 place1 or circumstance1 extraneous to the subject1 as ,all men in ,england are secure of justice2 in which proposition1 though there is a limitation of place 7'in ,england'71 it is included in the subject4 ,of this kind are nearly all the examples that have yet been given1 according to the form ,s is ,p4 ,a ,conditional ,proposition is so called because the predication is made under some limitation or condition not included in the subject1 as ,if a man live in ,england1 he is secure of justice4 ,here the limitation 'living in ,england' is put into a conditional sentence extraneous to the subject1 'he1' representing any man4 ,conditional propositions1 again1 are of two kinds--,hypothetical and ,disjunctive4 ,hypothetical propositions are those that are limited by an explicit conditional sentence1 as above1 or thus3 ,if ,joe ,smith was a prophet1 his followers have been unjustly persecuted4 ,or in symbols thus3 ,if ,a is1 ,b is2 ,if ,a is ,b1 ,a is ,c2 ,if ,a is ,b1 ,c is ,d4 ,disjunctive propositions are those in which the condition under which predication is made is not explicit but only implied under the disguise of an alternative proposition1 as ,joe ,smith was either a prophet or an impostor4 ,here there is no direct predication concerning ,joe ,smith1 but only a predication of one of the alternatives conditionally on the other being denied1 as1 ,if ,joe ,smith was not a prophet he was an impostor2 or1 ,if he was not an impostor1 he was a prophet4 ,symbolically1 ,disjunctives may be represented thus3 ,a is either ,b or ,c1 ,either ,a is ,b or ,c is ,d4 ,formally1 every ,conditional may be expressed as a ,categorical4 ,for our last example shows how a ,disjunctive may be reduced to two ,hypotheticals 7of which one is redundant1 being the contrapositive of the other2 see chap4 vii4 #aj74 ,and a ,hypothetical is reducible to a ,categorical thus3 ,if the sky is clear1 the night is cold may be read--,the case of the sky being clear is a case of the night being cold2 and this1 though a clumsy plan1 is sometimes convenient4 ,it would be better to say ,the sky being clear is a sign of the night being cold1 or a condition of it4 ,for1 as ,mill says1 the essence of a ,hypothetical is to state that one clause of it 7the indicative7 may be inferred from the other 7the conditional74 ,similarly1 we might write3 ,proof of ,joe ,smith's not being a prophet is a proof of his being an impostor4 ,this turning of ,conditionals into ,categoricals is called a ,change of ,relation2 and the process may be reversed3 ,all the wise are virtuous may be written1 ,if any man is wise he is virtuous2 or1 again1 ,either a man is not-wise or he is virtuous4 ,but the categorical form is usually the simplest4 ,if1 then1 as substitutes for the corresponding conditionals1 categoricals are formally adequate1 though sometimes inelegant1 it may be urged that ,logic has nothing to do with elegance2 or that1 at any rate1 the chief elegance of science is economy1 and that therefore1 for scientific purposes1 whatever we may write further about conditionals must be an ugly excrescence4 ,the scientific purpose of ,logic is to assign the conditions of proof4 ,can we1 then1 in the conditional form prove anything that cannot be proved in the categorical8 ,or does a conditional require to be itself proved by any method not applicable to the ,categorical8 ,if not1 why go on with the discussion of ,conditionals8 ,for all laws of ,nature1 however stated1 are essentially categorical4 ',if a straight line falls on another straight line1 the adjacent angles are together equal to two right angles'2 ',if a body is unsupported1 it falls'2 ',if population increases1 rents tend to rise'3 here 'if' means 'whenever' or 'all cases in which'2 for to raise a doubt whether a straight line is ever conceived to fall upon another1 whether bodies are ever unsupported1 or population ever increases1 is a superfluity of scepticism2 and plainly the hypothetical form has nothing to do with the proof of such propositions1 nor with inference from them4 ,still1 the disjunctive form is necessary in setting out the relation of contradictory terms1 and in stating a ,division 7chap4 xxi471 whether formal 7as ,a is ,b or not-,b7 or material 7as ,cats are white1 or black1 or tortoiseshell1 or tabby74 ,and in some cases the hypothetical form is useful4 ,one of these occurs where it is important to draw attention to the condition1 as something doubtful or especially requiring examination4 ,if there is a resisting medium in space1 the earth will fall into the sun2 ,if the ,corn ,laws are to be re-enacted1 we had better sell railways and buy land3 here the hypothetical form draws attention to the questions whether there is a resisting medium in space1 whether the ,corn ,laws are likely to be re-enacted2 but as to methods of inference and proof1 the hypothetical form has nothing to do with them4 ,the propositions predicate causation3 ,a resisting medium in space is a condition of the earth's falling into the sun2 ,a ,corn ,law is a condition of the rise of rents1 and of the fall of railway profits4 ,a second case in which the hypothetical is a specially appropriate form of statement occurs where a proposition relates to a particular matter and to future time1 as ,if there be a storm to-morrow1 we shall miss our picnic4 ,such cases are of very slight logical interest4 ,it is as exercises in formal thinking that hypotheticals are of most value2 inasmuch as many people find them more difficult than categoricals to manipulate4 ,in discussing ,conditional ,propositions1 the conditional sentence of a ,hypothetical1 or the first alternative of a ,disjunctive1 is called the ,antecedent2 the indicative sentence of a ,hypothetical1 or the second alternative of a ,disjunctive1 is called the ,consequent4 ,hypotheticals1 like ,categoricals1 have been classed according to ,quantity and ,quality4 ,premising that the quantity of a ,hypothetical depends on the quantity of its ,antecedent 7which determines its limitation71 whilst its quality depends on the quality of its consequent 7which makes the predication71 we may exhibit four forms3 ,a4 ,if ,a is ,b1 ,c is ,d2 ,i4 ,sometimes when ,a is ,b1 ,c is ,d2 ,e4 ,if ,a is ,b1 ,c is not ,d2 ,o4 ,sometimes when ,a is ,b1 ,c is not ,d4 ,but ,i4 and ,o4 are rarely used4 ,as for ,disjunctives1 it is easy to distinguish the two quantities thus3 ,a4 ,either ,a is ,b1 or ,c is ,d2 ,i4 ,sometimes either ,a is ,b or ,c is ,d4 ,but ,i4 is rarely used4 ,the distinction of quality1 however1 cannot be made3 there are no true negative forms2 for if we write-- ,neither is ,a ,b1 nor ,c ,d1 there is here no alternative predication1 but only an ,exponible equivalent to ,no ,a is ,b1 and ,no ,c is ,d4 ,and if we write-- ,either ,a is not ,b1 or ,c is not ,d1 this is affirmative as to the alternation1 and is for all methods of treatment equivalent to ,a4 ,logicians are divided in opinion as to the interpretation of the conjunction 'either1 or'2 some holding that it means 'not both1' others that it means 'it may be both4' ,grammatical usage1 upon which the question is sometimes argued1 does not seem to be established in favour of either view4 ,if we say ,a man so precise in his walk and conversation is either a saint or a consummate hypocrite2 or1 again1 ,one who is happy in a solitary life is either more or less than man2 we cannot in such cases mean that the subject may be both4 ,on the other hand1 if it be said that the author of ',a ,tale of a ,tub' is either a misanthrope or a dyspeptic1 the alternatives are not incompatible4 ,or1 again1 given that ,x4 is a lunatic1 or a lover1 or a poet1 the three predicates have much congruity4 ,it has been urged that in ,logic1 language should be made as exact and definite as possible1 and that this requires the exclusive interpretation 'not both4' ,but it seems a better argument1 that ,logic 7#a7 should be able to express all meanings1 and 7#b71 as the science of evidence1 must not assume more than is given2 to be on the safe side1 it must in doubtful cases assume the least1 just as it generally assumes a preindesignate term to be of particular quantity2 and1 therefore 'either1 or' means 'one1 or the other1 or both4' ,however1 when both the alternative propositions have the same subject1 as ,either ,a is ,b1 or ,a is ,c1 if the two predicates are contrary or contradictory terms 7as 'saint' and 'hypocrite1' or 'saint' and 'not-saint'71 they cannot in their nature be predicable in the same way of the same subject2 and1 therefore1 in such a case 'either1 or' means one or the other1 but not both in the same relation4 ,hence it seems necessary to admit that the conjunction 'either1 or' may sometimes require one interpretation1 sometimes the other2 and the rule is that it implies the further possibility 'or both1' except when both alternatives have the same subject whilst the predicates are contrary or contradictory terms4 ,if1 then1 the disjunctive ,a is either ,b or ,c 7,b and ,c being contraries7 implies that both alternatives cannot be true1 it can only be adequately rendered in hypotheticals by the two forms--7#a7 ,if ,a is ,b1 it is not ,c1 and 7#b7;,if ,a is not ,b1 it is ,c4 ,but if the disjunctive ,a is either ,b or ,c 7,b and ,c not being contraries7 implies that both may be true1 it will be adequately translated into a hypothetical by the single form1 ,if ,a is not ,b1 it is ,c4 ,we cannot translate it into--,if ,a is ,b1 it is not ,c1 for1 by our supposition1 if ',a is ,b' is true1 it does not follow that ',a is ,c' must be false4 ,logicians are also divided in opinion as to the function of the hypothetical form4 ,some think it expresses doubt2 for the consequent depends on the antecedent1 and the antecedent1 introduced by 'if1' may or may not be realised1 as in ,if the sky is clear1 the night is cold3 whether the sky is1 or is not1 clear being supposed to be uncertain4 ,and we have seen that some hypothetical propositions seem designed to draw attention to such uncertainty1 as--,if there is a resisting medium in space1 etc4 ,but other ,logicians lay stress upon the connection of the clauses as the important matter3 the statement is1 they say1 that the consequent may be inferred from the antecedent4 ,some even declare that it is given as a necessary inference2 and on this ground ,sigwart rejects particular hypotheticals1 such as ,sometimes when ,a is ,b1 ,c is ,d2 for if it happens only sometimes the connexion cannot be necessary4 ,indeed1 it cannot even be probably inferred without further grounds4 ,but this is also true whenever the antecedent and consequent are concerned with different matter4 ,for example1 ,if the soul is simple1 it is indestructible4 ,how do you know that8 ,because ,every simple substance is indestructible4 ,without this further ground there can be no inference4 ,the fact is that conditional forms often cover assertions that are not true complex propositions but a sort of euthymemes 7chap4 xi4 #b71 arguments abbreviated and rhetorically disguised4 ,thus3 ,if patience is a virtue there are painful virtues--an example from ,dr4 ,keynes4 ,expanding this we have-- ,patience is painful2 ,patience is a virtue3 ,some virtue is painful4 ,and then we see the equivocation of the inference2 for though patience be painful to learn1 it is not painful as a virtue to the patient man4 ,the hypothetical1 ',if ,plato was not mistaken poets are dangerous citizens1' may be considered as an argument against the laureateship1 and may be expanded 7informally7 thus3 ',all ,plato's opinions deserve respect2 one of them was that poets are bad citizens2 therefore it behoves us to be chary of encouraging poetry4' ,or take this disjunctive1 ',either ,bacon wrote the works ascribed to ,shakespeare1 or there were two men of the highest genius in the same age and country4' ,this means that it is not likely there should be two such men1 that we are sure of ,bacon1 and therefore ought to give him all the glory4 ,now1 if it is the part of ,logic 'to make explicit in language all that is implicit in thought1' or to put arguments into the form in which they can best be examined1 such propositions as the above ought to be analysed in the way suggested1 and confirmed or refuted according to their real intention4 ,we may conclude that no single function can be assigned to all hypothetical propositions3 each must be treated according to its own meaning in its own context4 #e4 ,as to ,modality1 propositions are divided into ,pure and ,modal4 ,a ,modal proposition is one in which the predicate is affirmed or denied1 not simply but cum modo1 with a qualification4 ,and some ,logicians have considered any adverb occurring in the predicate1 or any sign of past or future tense1 enough to constitute a modal3 as ',petroleum is dangerously inflammable'2 ',english will be the universal language4' ,but far the most important kind of modality1 and the only one we need consider1 is that which is signified by some qualification of the predicate as to the degree of certainty with which it is affirmed or denied4 ,thus1 ',the bite of the cobra is probably mortal1' is called a ,contingent or ,problematic ,modal3 ',water is certainly composed of oxygen and hydrogen' is an ,assertory or ,certain ,modal3 ',two straight lines cannot enclose a space' is a ,necessary or ,apodeictic ,modal 7the opposite being inconceivable74 ,propositions not thus qualified are called ,pure4 ,modal propositions have had a long and eventful history1 but they have not been found tractable by the resources of ordinary ,logic1 and are now generally neglected by the authors of text-books4 ,no doubt such propositions are the commonest in ordinary discourse1 and in some rough way we combine them and draw inferences from them4 ,it is understood that a combination of assertory or of apodeictic premises may warrant an assertory or an apodeictic conclusion2 but that if we combine either of these with a problematic premise our conclusion becomes problematic2 whilst the combination of two problematic premises gives a conclusion less certain than either4 ,but if we ask ',how much less certain8' there is no answer4 ,that the modality of a conclusion follows the less certain of the premises combined1 is inadequate for scientific guidance2 so that1 as ,deductive ,logic can get no farther than this1 it has abandoned the discussion of ,modals4 ,to endeavour to determine the degree of certainty attaching to a problematic judgment is not1 however1 beyond the reach of ,induction1 by analysing circumstantial evidence1 or by collecting statistics with regard to it4 ,thus1 instead of ',the cobra's bite is probably fatal1' we might find that it is fatal #hj times in #ajj4 ,then1 if we know that of those who go to ,india #c in #ajjj are bitten1 we can calculate what the chances are that any one going to ,india will die of a cobra's bite 7chap4 xx474 #f4 ,verbal and ,real ,propositions4--,another important division of propositions turns upon the relation of the predicate to the subject in respect of their connotations4 ,we saw1 when discussing ,relative ,terms1 that the connotation of one term often implies that of another2 sometimes reciprocally1 like 'master' and 'slave'2 or by inclusion1 like species and genus2 or by exclusion1 like contraries and contradictories4 ,when terms so related appear as subject and predicate of the same proposition1 the result is often tautology--e4g41 ,the master has authority over his slave2 ,a horse is an animal2 ,red is not blue2 ,british is not foreign4 ,whoever knows the meaning of 'master1' 'horse1' 'red1' ',british1' learns nothing from these propositions4 ,hence they are called ,verbal propositions1 as only expounding the sense of words1 or as if they were propositions only by satisfying the forms of language1 not by fulfilling the function of propositions in conveying a knowledge of facts4 ,they are also called ',analytic' and ',explicative1' when they separate and disengage the elements of the connotation of the subject4 ,doubtless1 such propositions may be useful to one who does not know the language2 and ,definitions1 which are verbal propositions whose predicates analyse the whole connotations of their subjects1 are indispensable instruments of science 7see chap4 xxii474 ,of course1 hypothetical propositions may also be verbal1 as ,if the soul be material it is extended2 for 'extension' is connoted by 'matter'2 and1 therefore1 the corresponding disjunctive is verbal--,either the soul is not material1 or it is extended4 ,but a true divisional disjunctive can never be verbal 7chap4 xxi4 #d1 rule #a74 ,on the other hand1 when there is no such direct relation between subject and predicate that their connotations imply one another1 but the predicate connotes something that cannot be learnt from the connotation of the subject1 there is no longer tautology1 but an enlargement of meaning--e4g41 ,masters are degraded by their slaves2 ,the horse is the noblest animal2 ,red is the favourite colour of the ,british army2 ,if the soul is simple1 it is indestructible4 ,such propositions are called ,real1 ,synthetic1 or ,ampliative1 because they are propositions for which a mere understanding of their subjects would be no substitute1 since the predicate adds a meaning of its own concerning matter of fact4 ,to any one who understands the language1 a verbal proposition can never be an inference or conclusion from evidence2 nor can a verbal proposition ever furnish grounds for an inference1 except as to the meaning of words4 ,the subject of real and verbal propositions will inevitably recur in the chapters on ,definition2 but tautologies are such common blemishes in composition1 and such frequent pitfalls in argument1 that attention cannot be drawn to them too early or too often4 ,,chapter ,,vi ,,conditions ,,of ,,immediate ,,inference #a4 ,the word ,inference is used in two different senses1 which are often confused but should be carefully distinguished4 ,in the first sense1 it means a process of thought or reasoning by which the mind passes from facts or statements presented1 to some opinion or expectation4 ,the data may be very vague and slight1 prompting no more than a guess or surmise2 as when we look up at the sky and form some expectation about the weather1 or from the trick of a man's face entertain some prejudice as to his character4 ,or the data may be important and strongly significant1 like the footprint that frightened ,crusoe into thinking of cannibals1 or as when news of war makes the city expect that ,consols will fall4 ,these are examples of the act of inferring1 or of inference as a process2 and with inference in this sense ,logic has nothing to do2 it belongs to ,psychology to explain how it is that our minds pass from one perception or thought to another thought1 and how we come to conjecture1 conclude and believe 7cf4 chap4 i4 #f74 ,in the second sense1 'inference' means not this process of guessing or opining1 but the result of it2 the surmise1 opinion1 or belief when formed2 in a word1 the conclusion3 and it is in this sense that ,inference is treated of in ,logic4 ,the subject-matter of ,logic is an inference1 judgment or conclusion concerning facts1 embodied in a proposition1 which is to be examined in relation to the evidence that may be adduced for it1 in order to determine whether1 or how far1 the evidence amounts to proof4 ,logic is the science of ,reasoning in the sense in which 'reasoning' means giving reasons1 for it shows what sort of reasons are good4 ,whilst ,psychology explains how the mind goes forward from data to conclusions1 ,logic takes a conclusion and goes back to the data1 inquiring whether those data1 together with any other evidence 7facts or principles7 that can be collected1 are of a nature to warrant the conclusion4 ,if we think that the night will be stormy1 that ,john ,doe is of an amiable disposition1 that water expands in freezing1 or that one means to national prosperity is popular education1 and wish to know whether we have evidence sufficient to justify us in holding these opinions1 ,logic can tell us what form the evidence should assume in order to be conclusive4 ,what form the evidence should assume3 ,logic cannot tell us what kinds of fact are proper evidence in any of these cases2 that is a question for the man of special experience in life1 or in science1 or in business4 ,but whatever facts constitute the evidence1 they must1 in order to prove the point1 admit of being stated in conformity with certain principles or conditions2 and of these principles or conditions ,logic is the science4 ,it deals1 then1 not with the subjective process of inferring1 but with the objective grounds that justify or discredit the inference4 #b4 ,inferences1 in the ,logical sense1 are divided into two great classes1 the ,immediate and the ,mediate1 according to the character of the evidence offered in proof of them4 ,strictly1 to speak of inferences1 in the sense of conclusions1 as immediate or mediate1 is an abuse of language1 derived from times before the distinction between inference as process and inference as result was generally felt4 ,no doubt we ought rather to speak of ,immediate and ,mediate ,evidence2 but it is of little use to attempt to alter the traditional expressions of the science4 ,an ,immediate ,inference1 then1 is one that depends for its proof upon only one other proposition1 which has the same1 or more extensive1 terms 7or matter74 ,thus that one means to national prosperity is popular education is an immediate inference1 if the evidence for it is no more than the admission that popular education is a means to national prosperity3 ,similarly1 it is an immediate inference that ,some authors are vain1 if it be granted that ,all authors are vain4 ,an ,immediate ,inference may seem to be little else than a verbal transformation2 some ,logicians dispute its claims to be called an inference at all1 on the ground that it is identical with the pretended evidence4 ,if we attend to the meaning1 say they1 an immediate inference does not really express any new judgment2 the fact expressed by it is either the same as its evidence1 or is even less significant4 ,if from ,no men are gods we prove that ,no gods are men1 this is nugatory2 if we prove from it that ,some men are not gods1 this is to emasculate the sense1 to waste valuable information1 to lose the commanding sweep of our universal proposition4 ,still1 in ,logic1 it is often found that an immediate inference expresses our knowledge in a more convenient form than that of the evidentiary proposition1 as will appear in the chapter on ,syllogisms and elsewhere4 ,and by transforming an universal into a particular proposition1 as ,no men are gods1 therefore1 ,some men are not gods1--we get a statement which1 though weaker1 is far more easily proved2 since a single instance suffices4 ,moreover1 by drawing all possible immediate inferences from a given proposition1 we see it in all its aspects1 and learn all that is implied in it4 ,a ,mediate ,inference1 on the other hand1 depends for its evidence upon a plurality of other propositions 7two or more7 which are connected together on logical principles4 ,if we argue-- ,no men are gods2 ,alexander the ,great is a man2 ,alexander the ,great is not a god3 this is a ,mediate ,inference4 ,the evidence consists of two propositions connected by the term 'man1' which is common to both 7a ,middle ,term71 mediating between 'gods' and ',alexander4' ,mediate ,inferences comprise ,syllogisms with their developments1 and ,inductions2 and to discuss them further at present would be to anticipate future chapters4 ,we must now deal with the principles or conditions on which ,immediate ,inferences are valid3 commonly called the ,laws of ,thought4 #c4 ,the ,laws of ,thought are conditions of the logical statement and criticism of all sorts of evidence2 but as to ,immediate ,inference1 they may be regarded as the only conditions it need satisfy4 ,they are often expressed thus3 7#a7 ,the principle of ,identity--',whatever is1 is'2 7#b7 ,the principle of ,contradiction--',it is impossible for the same thing to be and not be'2 7#c7 ,the principle of ,excluded ,middle--',anything must either be or not be4' ,these principles are manifestly not 'laws' of thought in the sense in which 'law' is used in ,psychology2 they do not profess to describe the actual mental processes that take place in judgment or reasoning1 as the 'laws of association of ideas' account for memory and recollection4 ,they are not natural laws of thought2 but1 in relation to thought1 can only be regarded as laws when stated as precepts1 the observance of which 7consciously or not7 is necessary to clear and consistent thinking3 e4g41 ,never assume that the same thing can both be and not be4 ,however1 treating ,logic as the science of thought only as embodied in propositions1 in respect of which evidence is to be adduced1 or which are to be used as evidence of other propositions1 the above laws or principles must be restated as the conditions of consistent argument in such terms as to be directly applicable to propositions4 ,it was shown in the chapter on the connotation of terms1 that terms are assumed by ,logicians to be capable of definite meaning1 and of being used univocally in the same context2 if1 or in so far as1 this is not the case1 we cannot understand one another's reasons nor even pursue in solitary meditation any coherent train of argument4 ,we saw1 too1 that the meanings of terms were related to one another3 some being full correlatives2 others partially inclusive one of another1 as species of genus2 others mutually incompatible1 as contraries2 or alternatively predicable1 as contradictories4 ,we now assume that propositions are capable of definite meaning according to the meaning of their component terms and of the relation between them2 that the meaning1 the fact asserted or denied1 is what we are really concerned to prove or disprove2 that a mere change in the words that constitute our terms1 or of construction1 does not affect the truth of a proposition as long as the meaning is not altered1 or 7rather7 as long as no fresh meaning is introduced2 and that if the meaning of any proposition is true1 any other proposition that denies it is false4 ,this postulate is plainly necessary to consistency of statement and discourse2 and consistency is necessary1 if our thought or speech is to correspond with the unity and coherence of ,nature and experience2 and the ,laws of ,thought or ,conditions of ,immediate ,inference are an analysis of this postulate4 #d4 ,the principle of ,identity is usually written symbolically thus3 ,a is ,a2 not-,a is not-,a4 ,it assumes that there is something that may be represented by a term2 and it requires that1 in any discussion1 every relevant term1 once used in a definite sense1 shall keep that meaning throughout4 ,socrates in his father's workshop1 at the battle of ,delium1 and in prison1 is assumed to be the same man denotable by the same name2 and similarly1 'elephant1' or 'justice1' or 'fairy1' in the same context1 is to be understood of the same thing under the same suppositio4 ,but1 further1 it is assumed that of a given term another term may be predicated again and again in the same sense under the same conditions2 that is1 we may speak of the identity of meaning in a proposition as well as in a term4 ,to symbolise this we ought to alter the usual formula for ,identity and write it thus3 ,if ,b is ,a1 ,b is ,a2 if ,b is not-,a1 ,b is not-,a4 ,if ,socrates is wise1 he is wise2 if fairies frequent the moonlight1 they do2 if ,justice is not of this world1 it is not4 ,whatever affirmation or denial we make concerning any subject1 we are bound to adhere to it for the purposes of the current argument or investigation4 ,of course1 if our assertion turns out to be false1 we must not adhere to it2 but then we must repudiate all that we formerly deduced from it4 ,again1 whatever is true or false in one form of words is true or false in any other3 this is undeniable1 for the important thing is identity of meaning2 but in ,formal ,logic it is not very convenient4 ,if ,socrates is wise1 is it an identity to say ',therefore the master of ,plato is wise'2 or1 further that he 'takes enlightened views of life'8 ,if ,every man is fallible1 is it an identical proposition that ,every man is liable to error8 ,it seems pedantic to demand a separate proposition that ,fallible is liable to error4 ,but1 on the other hand1 the insidious substitution of one term for another speciously identical1 is a chief occasion of fallacy4 ,how if we go on to argue3 therefore1 ,every man is apt to blunder1 prone to confusion of thought1 inured to self-contradiction8 ,practically1 the substitution of identities must be left to candour and good-sense2 and may they increase among us4 ,formal ,logic is1 no doubt1 safest with symbols2 should1 perhaps1 content itself with ,a and ,b2 or1 at least1 hardly venture beyond ,y and ,z4 #e4 ,the principle of ,contradiction is usually written symbolically1 thus3 ,a is not not-,a4 ,but1 since this formula seems to be adapted to a single term1 whereas we want one that is applicable to propositions1 it may be better to write it thus3 ,b is not both ,a and not-,a4 ,that is to say3 if any term may be affirmed of a subject1 the contradictory term may1 in the same relation1 be denied of it4 ,a leaf that is green on one side of it may be not-green on the other2 but it is not both green and not-green on the same surface1 at the same time1 and in the same light4 ,if a stick is straight1 it is false that it is at the same time not-straight3 having granted that two angles are equal1 we must deny that they are unequal4 ,but is it necessarily false that the stick is 'crooked'2 must we deny that either angle is 'greater or less' than the other8 ,how far is it permissible to substitute any other term for the formal contradictory8 ,clearly1 the principle of ,contradiction takes for granted the principle of ,identity1 and is subject to the same difficulties in its practical application4 ,as a matter of fact and common sense1 if we affirm any term of a ,subject1 we are bound to deny of that ,subject1 in the same relation1 not only the contradictory but all synonyms for this1 and also all contraries and opposites2 which1 of course1 are included in the contradictory4 ,but who shall determine what these are8 ,without an authoritative ,logical ,dictionary to refer to1 where all contradictories1 synonyms1 and contraries may be found on record1 ,formal ,logic will hardly sanction the free play of common sense4 ,the principle of ,excluded ,middle may be written3 ,b is either ,a or not-,a2 that is1 if any term be denied of a subject1 the contradictory term may1 in the same relation1 be affirmed4 ,of course1 we may deny that a leaf is green on one side without being bound to affirm that it is not-green on the other4 ,but in the same relation a leaf is either green or not-green2 at the same time1 a stick is either bent or not-bent4 ,if we deny that ,a is greater than ,b1 we must affirm that it is not-greater than ,b4 ,whilst1 then1 the principle of ,contradiction 7that 'of contradictory predicates1 one being affirmed1 the other is denied '7 might seem to leave open a third or middle course1 the denying of both contradictories1 the principle of ,excluded ,middle derives its name from the excluding of this middle course1 by declaring that the one or the other must be affirmed4 ,hence the principle of ,excluded ,middle does not hold good of mere contrary terms4 ,if we deny that a leaf is green1 we are not bound to affirm it to be yellow2 for it may be red2 and then we may deny both contraries1 yellow and green4 ,in fact1 two contraries do not between them cover the whole predicable area1 but contradictories do3 the form of their expression is such that 7within the suppositio7 each includes all that the other excludes2 so that the subject 7if brought within the suppositio7 must fall under the one or the other4 ,it may seem absurd to say that ,mont ,blanc is either wise or not-wise2 but how comes any mind so ill-organised as to introduce ,mont ,blanc into this strange company8 ,being there1 however1 the principle is inexorable3 ,mont ,blanc is not-wise4 ,in fact1 the principles of ,contradiction and ,excluded ,middle are inseparable2 they are implicit in all distinct experience1 and may be regarded as indicating the two aspects of ,negation4 ,the principle of ,contradiction says3 ,b is not both ,a and not-,a1 as if not-,a might be nothing at all2 this is abstract negation4 ,but the principle of ,excluded ,middle says3 ,granting that ,b is not ,a1 it is still something--namely1 not-,a2 thus bringing us back to the concrete experience of a continuum in which the absence of one thing implies the presence of something else4 ,symbolically3 to deny that ,b is ,a is to affirm that ,b is not ,a1 and this only differs by a hyphen from ,b is not-,a4 ,these principles1 which were necessarily to some extent anticipated in chap4 iv4 #g1 the next chapter will further illustrate4 #f4 ,but first we must draw attention to a maxim 7also already mentioned71 which is strictly applicable to ,immediate ,inferences1 though 7as we shall see7 in other kinds of proof it may be only a formal condition3 this is the general caution not to go beyond the evidence4 ,an immediate inference ought to contain nothing that is not contained 7or formally implied7 in the proposition by which it is proved4 ,with respect to quantity in denotation1 this caution is embodied in the rule 'not to distribute any term that is not given distributed4' ,thus1 if there is a predication concerning ',some ,s1' or ',some men1' as in the forms ,i4 and ,o41 we cannot infer anything concerning ',all ,s4' or ',all men'2 and1 as we have seen1 if a term is given us preindesignate1 we are generally to take it as of particular quantity4 ,similarly1 in the case of affirmative propositions1 we saw that this rule requires us to assume that their predicates are undistributed4 ,as to the grounds of this maxim1 not to go beyond the evidence1 not to distribute a term that is given as undistributed1 it is one of the things so plain that to try to justify is only to obscure them4 ,still1 we must here state explicitly what ,formal ,logic assumes to be contained or implied in the evidence afforded by any proposition1 such as ',all ,s is ,p4' ,if we remember that in chap4 iv4 #g1 it was assumed that every term may have a contradictory2 and if we bear in mind the principles of ,contradiction and ,excluded ,middle1 it will appear that such a proposition as ',all ,s is ,p' tells us something not only about the relations of ',s' and ',p1' but also of their relations to 'not-,s' and 'not-,p'2 as1 for example1 that ',s is not not-,p1' and that 'not-,p is not-,s4' ,it will be shown in the next chapter how ,logicians have developed these implications in series of ,immediate ,inferences4 ,if it be asked whether it is true that every term1 itself significant1 has a significant contradictory1 and not merely a formal contradictory1 generated by force of the word 'not1' it is difficult to give any better answer than was indicated in #c-e1 without venturing further into ,metaphysics4 ,i shall merely say1 therefore1 that1 granting that some such term as ',universe' or ',being' may have no significant contradictory1 if it stand for 'whatever can be perceived or thought of'2 yet every term that stands for less than ',universe' or ',being' has1 of course1 a contradictory which denotes the rest of the universe4 ,and since every argument or train of thought is carried on within a special 'universe of discourse1' or under a certain suppositio1 we may say that within the given suppositio every term has a contradictory1 and that every predication concerning a term implies some predication concerning its contradictory4 ,but the name of the suppositio itself has no contradictory1 except with reference to a wider and inclusive suppositio4 ,the difficulty of actual reasoning1 not with symbols1 but about matters of fact1 does not arise from the principles of ,logic1 but sometimes from the obscurity or complexity of the facts1 sometimes from the ambiguity or clumsiness of language1 sometimes from the deficiency of our own minds in penetration1 tenacity and lucidity4 ,one must do one's best to study the facts1 and not be too easily discouraged4 ,,chapter ,,vii ,,immediate ,,inferences #a4 ,under the general title of ,immediate ,inference ,logicians discuss three subjects1 namely1 ,opposition1 ,conversion1 and ,obversion2 to which some writers add other forms1 such as ,whole and ,part in ,connotation1 ,contraposition1 ,inversion1 etc4 ,of ,opposition1 again1 all recognise four modes3 ,subalternation1 ,contradiction1 ,contrariety and ,sub-contrariety4 ,the only peculiarities of the exposition upon which we are now entering are1 that it follows the lead of the three ,laws of ,thought1 taking first those modes of ,immediate ,inference in which ,identity is most important1 then those which plainly involve ,contradiction and ,excluded ,middle2 and that this method results in separating the modes of ,opposition1 connecting ,subalternation with ,conversion1 and the other modes with ,obversion4 ,to make up for this departure from usage1 the four modes of ,opposition will be brought together again in #i4 #b4 ,subalternation4--,opposition being the relation of propositions that have the same matter and differ only in form 7as ,a41 ,e41 ,i41 ,o471 propositions of the forms ,a4 and ,i4 are said to be ,subalterns in relation to one another1 and so are ,e4 and ,o42 the universal of each quality being distinguished as 'subalternans1' and the particular as 'subalternate4' ,it follows from the principle of ,identity that1 the matter of the propositions being the same1 if ,a4 is true ,i4 is true1 and that if ,e4 is true ,o4 is true2 for ,a4 and ,e4 predicate something of ,all ,s or ,all men2 and since ,i4 and ,o4 make the same predication of ,some ,s or ,some men1 the sense of these particular propositions has already been predicated in ,a4 or ,e4 ,if ,all ,s is ,p1 ,some ,s is ,p2 if ,no ,s is ,p1 ,some ,s is not ,p2 or1 if ,all men are fond of laughing1 ,some men are2 if ,no men are exempt from ridicule1 ,some men are not4 ,similarly1 if ,i4 is false ,a4 is false2 if ,o4 is false ,e4 is false4 ,if we deny any predication about ,some ,s1 we must deny it of ,all ,s2 since in denying it of ,some1 we have denied it of at least part of ,all2 and whatever is false in one form of words is false in any other4 ,on the other hand1 if ,i4 is true1 we do not know that ,a4 is2 nor if ,o4 is true1 that ,e4 is2 for to infer from ,some to ,all would be going beyond the evidence4 ,we shall see in discussing ,induction that the great problem of that part of ,logic is1 to determine the conditions under which we may in reality transcend this rule and infer from ,some to ,all2 though even there it will appear that1 formally1 the rule is observed4 ,for the present it is enough that ,i4 is an immediate inference from ,a41 and ,o4 from ,e42 but that ,a4 is not an immediate inference from ,i41 nor ,e4 from ,o4 #c4 ,connotative ,subalternation4--,we have seen 7chap4 iv4 #f7 that if the connotation of one term is only part of another's its denotation is greater and includes that other's4 ,hence genus and species stand in subaltern relation1 and whatever is true of the genus is true of the species3 ,if ,all animal life is dependent on vegetation1 ,all human life is dependent on vegetation4 ,on the other hand1 whatever is not true of the species or narrower term1 cannot be true of the whole genus3 ,if it is false that ',all human life is happy1' it is false that ',all animal life is happy4' ,similar inferences may be drawn from the subaltern relation of predicates2 affirming the species we affirm the genus4 ,to take ,mill's example1 if ,socrates is a man1 ,socrates is a living creature4 ,on the other hand1 denying the genus we deny the species3 if ,socrates is not vicious1 ,socrates is not drunken4 ,such cases as these are recognised by ,mill and ,bain as immediate inferences under the principle of ,identity4 ,but some ,logicians might treat them as imperfect syllogisms1 requiring another premise to legitimate the conclusion1 thus3 ,all animal life is dependent on vegetation2 ,all human life is animal life2 ,all human life is dependent on vegetation4 ,or again3 ,all men are living creatures2 ,socrates is a man2 ,socrates is a living creature4 ,the decision of this issue turns upon the question 7cf4 chap4 vi4 #c7 how far a ,logician is entitled to assume that the terms he uses are understood1 and that the identities involved in their meanings will be recognised4 ,and to this question1 for the sake of consistency1 one of two answers is required2 failing which1 there remains the rule of thumb4 ,first1 it may be held that no terms are understood except those that are defined in expounding the science1 such as 'genus' and 'species1' 'connotation' and 'denotation4' ,but very few ,logicians observe this limitation2 few would hesitate to substitute 'not wise' for 'foolish4' ,yet by what right8 ,malvolio being foolish1 to prove that he is not-wise1 we may construct the following syllogism3 ,foolish is not-wise2 ,malvolio is foolish2 ,malvolio is not-wise4 ,is this necessary8 ,why not8 ,secondly1 it may be held that all terms may be assumed as understood unless a definition is challenged4 ,this principle will justify the substitution of 'not-wise' for 'foolish'2 but it will also legitimate the above cases 7concerning 'human life' and ',socrates'7 as immediate inferences1 with innumerable others that might be based upon the doctrine of relative terms3 for example1 ,the hunter missed his aim3 therefore1 ,the prey escaped4 ,and from this principle it will further follow that all apparent syllogisms1 having one premise a verbal proposition1 are immediate inferences 7cf4 chap4 ix4 #d74 ,closely connected with such cases as the above are those mentioned by ,archbishop ,thomson as ,immediate ,inferences by added ,determinants 7,laws of ,thought1 #hg74 ,he takes the case3 ',a negro is a fellow-creature3 therefore1 ,a negro in suffering is a fellow-creature in suffering4' ,this rests upon the principle that to increase the connotations of two terms by the same attribute or determinant does not affect the relationship of their denotations1 since it must equally diminish 7if at all7 the denotations of both classes1 by excluding the same individuals1 if any want the given attribute4 ,but this principle is true only when the added attribute is not merely the same verbally1 but has the same significance in qualifying both terms4 ,we cannot argue ,a mouse is an animal2 therefore1 ,a large mouse is a large animal2 for 'large' is an attribute relative to the normal magnitude of the thing described4 #d4 ,conversion is ,immediate ,inference by transposing the terms of a given proposition without altering its quality4 ,if the quantity is also unaltered1 the inference is called ',simple ,conversion'2 but if the quantity is changed from universal to particular1 it is called ',conversion by limitation' or 'per accidens4' ,the given proposition is called the 'convertend'2 that which is derived from it1 the 'converse4' ,departing from the usual order of exposition1 ,i have taken up ,conversion next to ,subalternation1 because it is generally thought to rest upon the principle of ,identity1 and because it seems to be a good method to exhaust the forms that come only under ,identity before going on to those that involve ,contradiction and ,excluded ,middle4 ,some1 indeed1 dispute the claims of ,conversion to illustrate the principle of ,identity2 and if the sufficient statement of that principle be ',a is ,a1' it may be a question how ,conversion or any other mode of inference can be referred to it4 ,but if we state it as above 7chap4 vi4 #c71 that whatever is true in one form of words is true in any other1 there is no difficulty in applying it to ,conversion4 ,thus1 to take the simple conversion of ,i41 ,some ,s is ,p2 ,some ,p is ,s4 ,some poets are business-like2 ,some business-like men are poets4 ,here the convertend and the converse say the same thing1 and this is true if that is4 ,we have1 then1 two cases of simple conversion3 of ,i4 7as above7 and of ,e4 ,for ,e43 ,no ,s is ,p2 ,no ,p is ,s4 ,no ruminants are carnivores2 ,no carnivores are ruminants4 ,in converting ,i41 the predicate 7,p7 when taken as the new subject1 being preindesignate1 is treated as particular2 and in converting ,e41 the predicate 7,p71 when taken as the new subject1 is treated as universal1 according to the rule in chap4 v4 #a4 ,a4 is the one case of conversion by limitation3 ,all ,s is ,p2 ,some ,p is ,s4 ,all cats are grey in the dark2 ,some things grey in the dark are cats4 ,the predicate is treated as particular1 when taking it for the new subject1 according to the rule not to go beyond the evidence4 ,to infer that ,all things grey in the dark are cats would be palpably absurd2 yet no error of reasoning is commoner than the simple conversion of ,a4 ,the validity of conversion by limitation may be shown thus3 if1 ,all ,s is ,p1 then1 by subalternation1 ,some ,s is ,p1 and therefore1 by simple conversion1 ,some ,p is ,s4 ,o4 cannot be truly converted4 ,if we take the proposition3 ,some ,s is not ,p1 to convert this into ,no ,p is ,s1 or ,some ,p is not ,s1 would break the rule in chap4 vi4 #f2 since ,s1 undistributed in the convertend1 would be distributed in the converse4 ,if we are told that ,some men are not cooks1 we cannot infer that ,some cooks are not men4 ,this would be to assume that ',some men' are identical with ',all men4' ,by quantifying the predicate1 indeed1 we may convert ,o4 simply1 thus3 ,some men are not cooks ,no cooks are some men4 ,and the same plan has some advantage in converting ,a42 for by the usual method per accidens1 the converse of ,a4 being ,i41 if we convert this again it is still ,i41 and therefore means less than our original convertend4 ,thus3 ,all ,s is ,p ,some ,p is ,s ,some ,s is ,p4 ,such knowledge1 as that ,all ,s 7the whole of it7 is ,p1 is too precious a thing to be squandered in pure ,logic2 and it may be preserved by quantifying the predicate2 for if we convert ,a4 to ,y41 thus-- ,all ,s is ,p ,some ,p is all ,s-- we may reconvert ,y4 to ,a4 without any loss of meaning4 ,it is the chief use of quantifying the predicate that1 thereby1 every proposition is capable of simple conversion4 ,the conversion of propositions in which the relation of terms is inadequately expressed 7see chap4 ii41 #b7 by the ordinary copula 7is or is not7 needs a special rule4 ,to argue thus-- ,a is followed by ,b ,something followed by ,b is ,a-- would be clumsy formalism4 ,we usually say1 and we ought to say-- ,a is followed by ,b ,b follows ,a 7or is preceded by ,a74 ,now1 any relation between two terms may be viewed from either side--,a3 ,b or ,b3 ,a4 ,it is in both cases the same fact2 but1 with the altered point of view1 it may present a different character4 ,for example1 in the ,immediate ,inference--,a ,b ,b ,a--a diminishing turns into an increasing ratio1 whilst the fact predicated remains the same4 ,given1 then1 a relation between two terms as viewed from one to the other1 the same relation viewed from the other to the one may be called the ,reciprocal4 ,in the cases of ,equality1 ,co-existence and ,simultaneity1 the given relation and its reciprocal are not only the same fact1 but they also have the same character3 in the cases of ,greater and ,less and ,sequence1 the character alters4 ,we may1 then1 state the following rule for the conversion of propositions in which the whole relation explicitly stated is taken as the copula3 ,transpose the terms1 and for the given relation substitute its reciprocal4 ,thus-- ,a is the cause of ,b ,b is the effect of ,a4 ,the rule assumes that the reciprocal of a given relation is definitely known2 and so far as this is true it may be extended to more concrete relations-- ,a is a genus of ,b ,b is a species of ,a ,a is the father of ,b ,b is a child of ,a4 ,but not every relational expression has only one definite reciprocal4 ,if we are told that ,a is the brother of ,b1 we can only infer that ,b is either the brother or the sister of ,a4 ,a list of all reciprocal relations is a desideratum of ,logic4 #e4 ,obversion 7otherwise called ,permutation or quipollence7 is ,immediate ,inference by changing the quality of the given proposition and substituting for its predicate the contradictory term4 ,the given proposition is called the 'obvertend1' and the inference from it the 'obverse4' ,thus the obvertend being--,some philosophers are consistent reasoners1 the obverse will be--,some philosophers are not inconsistent reasoners4 ,the legitimacy of this mode of reasoning follows1 in the case of affirmative propositions1 from the principle of ,contradiction1 that if any term be affirmed of a subject1 the contradictory term may be denied 7chap4 vi4 #c74 ,to obvert affirmative propositions1 then1 the rule is--,insert the negative sign1 and for the predicate substitute its contradictory term4 ,a4 ,all ,s is ,p ,no ,s is not-,p ,all men are fallible ,no men are infallible4 ,i4 ,some ,s is ,p some ,s is not-,p ,some philosophers are consistent ,some philosophers are not inconsistent4 ,in agreement with this mode of inference1 we have the rule of modern ,english grammar1 that 'two negatives make an affirmative4' ,again1 by the principle of ,excluded ,middle1 if any term be denied of a subject1 its contradictory may be affirmed3 to obvert negative propositions1 then1 the rule is--,remove the negative sign1 and for the predicate substitute its contradictory term4 ,e4 ,no ,s is ,p ,all ,s is not-,p ,no matter is destructible ,all matter is indestructible4 ,o4 ,some ,s is not ,p ,some ,s is not-,p ,some ideals are not attainable ,some ideals are unattainable4 ,thus1 by obversion1 each of the four propositions retains its quantity but changes its quality3 ,a4 to ,e41 ,i4 to ,o41 ,e4 to ,a41 ,o4 to ,i4 ,and all the obverses are infinite propositions1 the affirmative infinites having the sense of negatives1 and the negative infinites having the sense of affirmatives4 ,again1 having obtained the obverse of a given proposition1 it may be desirable to recover the obvertend2 or it may at any time be requisite to change a given infinite proposition into the corresponding direct affirmative or negative2 and in such cases the process is still obversion4 ,thus1 if ,no ,s is not-,p be given us to recover the obvertend or to find the corresponding affirmative2 the proposition being formally negative1 we apply the rule for obverting negatives3 ',remove the negative sign1 and for the predicate substitute its contradictory4' ,this yields the affirmative ,all ,s is ,p4 ,similarly1 to obtain the obvertend of ,all ,s is not-,p1 apply the rule for obverting ,affirmatives2 and this yields ,no ,s is ,p4 #f4 ,contrariety4--,we have seen in chap4 iv4 #h1 that contrary terms are such that no two of them are predicable in the same way of the same subject1 whilst perhaps neither may be predicable of it4 ,similarly1 ,contrary ,propositions may be defined as those of which no two are ever both true together1 whilst perhaps neither may be true2 or1 in other words1 both may be false4 ,this is the relation between ,a4 and ,e4 when concerned with the same matter3 as ,a4--,all men are wise2 ,e4--,no men are wise4 ,such propositions cannot both be true2 but they may both be false1 for some men may be wise and some not4 ,they cannot both be true2 for1 by the principle of ,contradiction1 if wise may be affirmed of ,all men1 not-wise must be denied2 but ,all men are not-wise is the obverse of ,no men are wise1 which therefore may also be denied4 ,at the same time we cannot apply to ,a4 and ,e4 the principle of ,excluded ,middle1 so as to show that one of them must be true of the same matter4 ,for if we deny that ,all men are wise1 we do not necessarily deny the attribute 'wise' of each and every man3 to say that ,not all are wise may mean no more than that ,some are not4 ,this gives a proposition in the form of ,o42 which1 as we have seen1 does not imply its subalternans1 ,e4 ,if1 however1 two ,singular ,propositions1 having the same matter1 but differing in quality1 are to be treated as universals1 and therefore as ,a4 and ,e41 they are1 nevertheless1 contradictory and not merely contrary2 for one of them must be false and the other true4 #g4 ,contradiction is a relation between two propositions analogous to that between contradictory terms 7one of which being affirmed of a subject the other is denied7--such1 namely1 that one of them is false and the other true4 ,this is the case with the forms ,a4 and ,o41 and ,e4 and ,i41 in the same matter4 ,if it be true that ,all men are wise1 it is false that ,some men are not wise 7equivalent by obversion to ,some men are not-wise72 or else1 since the ',some men' are included in the ',all men1' we should be predicating of the same men that they are both 'wise' and 'not-wise'2 which would violate the principle of ,contradiction4 ,similarly1 ,no men are wise1 being by obversion equivalent to ,all men are not-wise1 is incompatible with ,some men are wise1 by the same principle of ,contradiction4 ,but1 again1 if it be false that ,all men are wise1 it is always true that ,some are not wise2 for though in denying that 'wise' is a predicate of ',all men' we do not deny it of each and every man1 yet we deny it of ',some men4' ,of ',some men1' therefore1 by the principle of ,excluded ,middle1 'not-wise' is to be affirmed2 and ,some men are not-wise1 is by obversion equivalent to ,some men are not wise4 ,similarly1 if it be false that ,no men are wise1 which by obversion is equivalent to ,all men are not-wise1 then it is true at least that ,some men are wise4 ,by extending and enforcing the doctrine of relative terms1 certain other inferences are implied in the contrary and contradictory relations of propositions4 ,we have seen in chap4 iv4 that the contradictory of a given term includes all its contraries3 'not-blue1' for example1 includes red and yellow4 ,hence1 since ,the sky is blue becomes by obversion1 ,the sky is not not-blue1 we may also infer ,the sky is not red1 etc4 ,from the truth1 then1 of any proposition predicating a given term1 we may infer the falsity of all propositions predicating the contrary terms in the same relation4 ,but1 on the other hand1 from the falsity of a proposition predicating a given term1 we cannot infer the truth of the predication of any particular contrary term4 ,if it be false that ,the sky is red1 we cannot formally infer1 that ,the sky is blue 7cf4 chap4 iv4 #h74 #h4 ,sub-contrariety is the relation of two propositions1 concerning the same matter that may both be true but are never both false4 ,this is the case with ,i4 and ,o4 ,if it be true that ,some men are wise1 it may also be true that ,some 7other7 men are not wise4 ,this follows from the maxim in chap4 vi4 #f1 not to go beyond the evidence4 ,for if it be true that ,some men are wise1 it may indeed be true that ,all are 7this being the subalternans73 and if ,all are1 it is 7by contradiction7 false that ,some are not2 but as we are only told that ,some men are1 it is illicit to infer the falsity of ,some are not1 which could only be justified by evidence concerning ,all men4 ,but if it be false that ,some men are wise1 it is true that ,some men are not wise2 for1 by contradiction1 if ,some men are wise is false1 ,no men are wise is true2 and1 therefore1 by subalternation1 ,some men are not wise is true4 #i4 ,the ,square of ,opposition4--,by their relations of ,subalternation1 ,contrariety1 ,contradiction1 and ,sub-contrariety1 the forms ,a4 ,i4 ,e4 ,o4 7having the same matter7 are said to stand in ,opposition3 and ,logicians represent these relations by a square having ,a4 ,i4 ,e4 ,o4 at its corners3 ,a4 ,contraries ,e4 ,s ,co s ,s u nt e u b ra i b a di r a l ct o l t ct o t e di r e r ra i r n nt e n s ,co s s ,i4 ,sub-contraries ,o4 ,as an aid to the memory1 this diagram is useful2 but as an attempt to represent the logical relations of propositions1 it is misleading4 ,for1 standing at corners of the same square1 ,a4 and ,e41 ,a4 and ,i41 ,e4 and ,o41 and ,i4 and ,o41 seem to be couples bearing the same relation to one another2 whereas we have seen that their relations are entirely different4 ,the following traditional summary of their relations in respect of truth and falsity is much more to the purpose3 7#a7 ,if ,a4 is true1 ,i4 is true1 ,e4 is false1 ,o4 is false4 7#b7 ,if ,a4 is false1 ,i4 is unknown1 ,e4 is unknown1 ,o4 is true4 7#c7 ,if ,i4 is true1 ,a4 is unknown1 ,e4 is false1 ,o4 is unknown4 7#d7 ,if ,i4 is false1 ,a4 is false1 ,e4 is true1 ,o4 is true4 7#e7 ,if ,e4 is true1 ,a4 is false1 ,i4 is false1 ,o4 is true4 7#f7 ,if ,e4 is false1 ,a4 is unknown1 ,i4 is true1 ,o4 is unknown4 7#g7 ,if ,o4 is true1 ,a4 is false1 ,i4 is unknown1 ,e4 is unknown4 7#h7 ,if ,o4 is false1 ,a4 is true1 ,i4 is true1 ,e4 is false4 ,where1 however1 as in cases #b1 #c1 #f1 #g1 alleging either the falsity of universals or the truth of particulars1 it follows that two of the three ,opposites are unknown1 we may conclude further that one of them must be true and the other false1 because the two unknown are always ,contradictories4 #aj4 ,secondary modes of ,immediate ,inference are obtained by applying the process of ,conversion or ,obversion to the results already obtained by the other process4 ,the best known secondary form of ,immediate ,inference is the ,contrapositive1 and this is the converse of the obverse of a given proposition4 ,thus3 ,,datum4 ,,obverse4 ,,contrapositive4 ,a4 ,all ,s is ,p ,no ,s is not-,p ,no not-,p is ,s ,i4 ,some ,s is ,p ,some ,s is not not-,p 7none7 ,e4 ,no ,s is ,p ,all ,s is not-,p ,some not-,p is ,s ,o4 ,some ,s is not ,p ,some ,s is not-,p ,some not-,p is ,s ,there is no contrapositive of ,i41 because the obverse of ,i4 is in the form of ,o41 and we have seen that ,o4 cannot be converted4 ,o41 however1 has a contrapositive 7,some not-,p is ,s72 and this is sometimes given instead of the converse1 and called the 'converse by negation4' ,contraposition needs no justification by the ,laws of ,thought1 as it is nothing but a compounding of conversion with obversion1 both of which processes have already been justified4 ,i give a table opposite of the other ways of compounding these primary modes of ,immediate ,inference4 ,a ,i ,e ,o ---------------------------------------- ---------------------------------------- #a ,all ,a is ,b ,some ,a is ,b ,no ,a is ,b ,some ,a is not ,b ---------------------------------------- ---------------------------------------- ,obverse #b ,no ,a is b ,some ,a is not b ,all ,a is b ,some ,a is b ---------------------------------------- ---------------------------------------- ,converse #c ,some ,b is ,a ,some ,b is ,a ,no ,b is ,a ---------------------------------------- ---------------------------------------- ,obverse of #d ,some ,b is not a ,some ,b is not a ,all ,b is a ,converse ---------------------------------------- ---------------------------------------- ,contra- positive #e ,no b is ,a ,some b is ,a ,some b is ,a ---------------------------------------- ---------------------------------------- ,obverse of #f ,all b is a ,some b is not a ,some b is not a ,contrapos ---------------------------------------- ---------------------------------------- ,converse of ,obverse #g ,some a is ,b of ,converse ---------------------------------------- ---------------------------------------- ,obverse of ,converse of #h ,some a is not b ,obverse of ,converse ---------------------------------------- ---------------------------------------- ,converse of ,obverse #i ,some a is b of ,contrapos ---------------------------------------- ---------------------------------------- ,obverse of ,converse of #aj ,some a is not ,b ,obverse of ,contrapos ---------------------------------------- ---------------------------------------- ,in this table a and b stand for not-,a and not-,b and had better be read thus3 for ,no ,a is b1 ,no ,a is not-,b2 for ,all b is a 7col4 #f71 ,all not-,b is not-,a2 and so on4 ,it may not1 at first1 be obvious why the process of alternately obverting and converting any proposition should ever come to an end2 though it will1 no doubt1 be considered a very fortunate circumstance that it always does end4 ,on examining the results1 it will be found that the cause of its ending is the inconvertibility of ,o4 ,for ,e41 when obverted1 becomes ,a42 every ,a1 when converted1 degenerates into ,i42 every ,i41 when obverted1 becomes ,o42 ,o cannot be converted1 and to obvert it again is merely to restore the former proposition3 so that the whole process moves on to inevitable dissolution4 ,i4 and ,o4 are exhausted by three transformations1 whilst ,a4 and ,e4 will each endure seven4 ,except ,obversion1 ,conversion and ,contraposition1 it has not been usual to bestow special names on these processes or their results4 ,but the form in columns #g and #aj 7,some a is ,b--,some a is not ,b71 where the original predicate is affirmed or denied of the contradictory of the original subject1 has been thought by ,dr4 ,keynes to deserve a distinctive title1 and he has called it the ',inverse4' ,whilst the ,inverse is one form1 however1 ,inversion is not one process1 but is obtained by different processes from ,e4 and ,a4 respectively4 ,in this it differs from ,obversion1 ,conversion1 and ,contraposition1 each of which stands for one process4 ,the ,inverse form has been objected to on the ground that the inference ,all ,a is ,b ,some not-,a is not ,b1 distributes ,b 7as predicate of a negative proposition71 though it was given as undistributed 7as predicate of an affirmative proposition74 ,but ,dr4 ,keynes defends it on the ground that 7#a7 it is obtained by obversions and conversions which are all legitimate and 7#b7 that although ,all ,a is ,b does not distribute ,b in relation to ,a1 it does distribute ,b in relation to some not-,a 7namely1 in relation to whatever not-,a is not-,b74 ,this is one reason why1 in stating the rule in chap4 vi4 #f1 ,i have written3 an immediate inference ought to contain nothing that is not contained1 or formally implied1 in the proposition from which it is inferred2 and have maintained that every term formally implies its contradictory within the suppositio4 #aa4 ,immediate ,inferences from ,conditionals are those which consist--7#a7 in changing a ,disjunctive into a ,hypothetical1 or a ,hypothetical into a ,disjunctive1 or either into a ,categorical2 and 7#b7 in the relations of ,opposition and the equivalences of ,obversion1 ,conversion1 and secondary or compound processes1 which we have already examined in respect of ,categoricals4 ,as no new principles are involved1 it may suffice to exhibit some of the results4 ,we have already seen 7chap4 v4 #d7 how ,disjunctives may be read as ,hypotheticals and ,hypotheticals as ,categoricals4 ,and1 as to ,opposition1 if we recognise four forms of ,hypothetical ,a4 ,i4 ,e4 ,o41 these plainly stand to one another in a ,square of ,opposition1 just as ,categoricals do4 ,thus ,a4 and ,e4 7,if ,a is ,b1 ,c is ,d1 and ,if ,a is ,b1 ,c is not ,d7 are contraries1 but not contradictories2 since both may be false 7,c may sometimes be ,d1 and sometimes not71 though they cannot both be true4 ,and if they are both false1 their subalternates are both true1 being respectively the contradictories of the universals of opposite quality1 namely1 ,i4 of ,e41 and ,o4 of ,a4 ,but in the case of ,disjunctives1 we cannot set out a satisfactory ,square of ,opposition2 because1 as we saw 7chap4 v4 #d71 the forms required for ,e4 and ,o4 are not true ,disjunctives1 but ,exponibles4 ,the ,obverse1 ,converse1 and ,contrapositive1 of ,hypotheticals 7admitting the distinction of quality7 may be exhibited thus3 ,,datum4 ,,obverse4 ,a4 ,if ,a is ,b1 ,c is ,d ,if ,a is ,b1 ,c is not d ,i4 ,sometimes when ,a is ,b1 ,c is ,d ,sometimes when ,a is ,b1 ,c is not d ,e4 ,if ,a is ,b1 ,c is not ,d ,if ,a is ,b1 ,c is d ,o4 ,sometimes when ,a is ,b1 ,c is not ,d ,sometimes when ,a is ,b1 ,c is d ,,converse4 ,,contrapositive4 ,sometimes when ,c is ,d1 ,a is ,b ,if ,c is d1 ,a is not ,b ,sometimes when ,c is ,d1 ,a is ,b 7none7 ,if ,c is ,d1 ,a is not ,b ,sometimes when ,c is d1 ,a is ,b 7none7 ,sometimes when ,c is d1 ,a is ,b ,as to ,disjunctives1 the attempt to put them through these different forms immediately destroys their disjunctive character4 ,still1 given any proposition in the form ,a is either ,b or ,c1 we can state the propositions that give the sense of obversion1 conversion1 etc41 thus3 ,,datum4--,a is either ,b or ,c2 ,,obverse4--,a is not both b and c2 ,,converse4--,something1 either ,b or ,c1 is ,a2 ,,contrapositive4--,nothing that is both b and c is ,a4 ,for a ,disjunctive in ,i41 of course1 there is no ,contrapositive4 ,given a ,disjunctive in the form ,either ,a is ,b or ,c is ,d1 we may write for its ,obverse--,in no case is ,a b1 and ,c at the same time d4 ,but no ,converse or ,contrapositive of such a ,disjunctive can be obtained1 except by first casting it into the hypothetical or categorical form4 ,the reader who wishes to pursue this subject further1 will find it elaborately treated in ,dr4 ,keynes' ,formal ,logic1 ,part ,,ii42 to which work the above chapter is indebted4 ,,chapter ,,viii ,,order ,,of ,,terms1 ,,euler',s ,,diagrams1 ,,logical ,,equations1 ,,existential ,,import ,,of ,,propositions #a4 ,of the terms of a proposition which is the ,subject and which the ,predicate8 ,in most of the exemplary propositions cited by ,logicians it will be found that the subject is a substantive and the predicate an adjective1 as in ,men are mortal4 ,this is the relation of ,substance and ,attribute which we saw 7chap4 i4 #e7 to be the central type of relations of coinherence2 and on this model other predications may be formed in which the subject is not a substance1 but is treated as if it were1 and could therefore be the ground of attributes2 as ,fame is treacherous1 ,the weather is changeable4 ,but1 in literature1 sentences in which the adjective comes first are not uncommon1 as ,loud was the applause1 ,dark is the fate of man1 ,blessed are the peacemakers1 and so on4 ,here1 then1 'loud1' 'dark' and 'blessed' occupy the place of the logical subject4 ,are they really the subject1 or must we alter the order of such sentences into ,the applause was loud1 etc48 ,if we do1 and then proceed to convert1 we get ,loud was the applause1 or 7more scrupulously7 ,some loud noise was the applause4 ,the last form1 it is true1 gives the subject a substantive word1 but 'applause' has become the predicate2 and if the substantive 'noise' was not implied in the first form1 ,loud is the applause1 by what right is it now inserted8 ,the recognition of ,conversion1 in fact1 requires us to admit that1 formally1 in a logical proposition1 the term preceding the copula is subject and the one following is predicate4 ,and1 of course1 materially considered1 the mere order of terms in a proposition can make no difference in the method of proving it1 nor in the inferences that can be drawn from it4 ,still1 if the question is1 how we may best cast a literary sentence into logical form1 good grounds for a definite answer may perhaps be found4 ,we must not try to stand upon the naturalness of expression1 for ,dark is the fate of man is quite as natural as ,man is mortal4 ,when the purpose is not merely to state a fact1 but also to express our feelings about it1 to place the grammatical predicate first may be perfectly natural and most effective4 ,but the grounds of a logical order of statement must be found in its adaptation to the purposes of proof and inference4 ,now general propositions are those from which most inferences can be drawn1 which1 therefore1 it is most important to establish1 if true2 and they are also the easiest to disprove1 if false2 since a single negative instance suffices to establish the contradictory4 ,it follows that1 in re-casting a literary or colloquial sentence for logical purposes1 we should try to obtain a form in which the subject is distributed--is either a singular term or a general term predesignate as ',all' or ',no4' ,seeing1 then1 that most adjectives connote a single attribute1 whilst most substantives connote more than one attribute2 and that therefore the denotation of adjectives is usually wider than that of substantives2 in any proposition1 one term of which is an adjective and the other a substantive1 if either can be distributed in relation to the other1 it is nearly sure to be the substantive2 so that to take the substantive term for subject is our best chance of obtaining an universal proposition4 ,these considerations seem to justify the practice of ,logicians in selecting their examples4 ,for similar reasons1 if both terms of a proposition are substantive1 the one with the lesser denotation is 7at least in affirmative propositions7 the more suitable subject1 as ,cats are carnivores4 ,and if one term is abstract1 that is the more suitable subject2 for1 as we have seen1 an abstract term may be interpreted by a corresponding concrete one distributed1 as ,kindness is infectious2 that is1 ,all kind actions suggest imitation4 ,if1 however1 a controvertist has no other object in view than to refute some general proposition laid down by an opponent1 a particular proposition is all that he need disentangle from any statement that serves his purpose4 #b4 ,toward understanding clearly the relations of the terms of a proposition1 it is often found useful to employ diagrams2 and the diagrams most in use are the circles of ,euler4 ,these circles represent the denotation of the terms4 ,suppose the proposition to be ,all hollow-horned animals ruminate3 then1 if we could collect all ruminants upon a prairie1 and enclose them with a circular palisade2 and segregate from amongst them all the hollow-horned beasts1 and enclose them with another ring-fence inside the other2 one way of interpreting the proposition 7namely1 in denotation7 would be figured to us thus3 ,illustration3 ,,fig4 #a4 ,an ,universal ,affirmative may also state a relation between two terms whose denotation is co-extensive4 ,a definition always does this1 as ,man is a rational animal2 and this1 of course1 we cannot represent by two distinct circles1 but at best by one with a thick circumference1 to suggest that two coincide1 thus3 ,illustration3 ,,fig4 #b4 ,the ,particular ,affirmative ,proposition may be represented in several ways4 ,in the first place1 bearing in mind that ',some' means 'some at least1 it may be all1' an ,i4 proposition may be represented by ,figs4 #a and #b2 for it is true that ,some horned animals ruminate1 and that ,some men are rational4 ,secondly1 there is the case in which the ',some things' of which a predication is made are1 in fact1 not all2 whilst the predicate1 though not given as distributed1 yet might be so given if we wished to state the whole truth2 as if we say ,some men are ,chinese4 ,this case is also represented by ,fig4 #a1 the outside circle representing ',men1' and the inside one ',chinese4' ,thirdly1 the predicate may appertain to some only of the subject1 but to a great many other things1 as in ,some horned beasts are domestic2 for it is true that some are not1 and that certain other kinds of animals are1 domestic4 ,this case1 therefore1 must be illustrated by overlapping circles1 thus3 ,illustration3 ,,fig4 #c4 ,the ,universal ,negative is sufficiently represented by a single ,fig4 7#d73 two circles mutually exclusive1 thus3 ,illustration3 ,,fig4 #d4 ,that is1 ,no horned beasts are carnivorous4 ,lastly1 the ,particular ,negative may be represented by any of the ,figs4 #a1 #c1 and #d2 for it is true that ,some ruminants are not hollow-horned1 that ,some horned animals are not domestic1 and that ,some horned beasts are not carnivorous4 ,besides their use in illustrating the denotative force of propositions1 these circles may be employed to verify the results of ,obversion1 ,conversion1 and the secondary modes of ,immediate ,inference4 ,thus the ,obverse of ,a4 is clear enough on glancing at ,figs4 #a and #b2 for if we agree that whatever term's denotation is represented by a given circle1 the denotation of the contradictory term shall be represented by the space outside that circle2 then if it is true that ,all hollow horned animals are ruminants1 it is at the same time true that ,no hollow-horned animals are not-ruminants2 since none of the hollow-horned are found outside the palisade that encloses the ruminants4 ,the ,obverse of ,i41 ,e4 or ,o4 may be verified in a similar manner4 ,as to the ,converse1 a ,definition is of course susceptible of ,simple ,conversion1 and this is shown by ,fig4 #b3 ',men are rational animals' and ',rational animals are men4' ,but any other ,a4 proposition is presumably convertible only by limitation1 and this is shown by ,fig4 #a2 where ,all hollow-horned animals are ruminants1 but we can only say that ,some ruminants are hollow-horned4 ,that ,i4 may be simply converted may be seen in ,fig4 #c1 which represents the least that an ,i4 proposition can mean2 and that ,e4 may be simply converted is manifest in ,fig4 #d4 ,as for ,o41 we know that it cannot be converted1 and this is made plain enough by glancing at ,fig4 #a2 for that represents the ,o41 ,some ruminants are not hollow-horned1 but also shows this to be compatible with ,all hollow-horned animals are ruminants 7,a474 ,now in conversion there is 7by definition7 no change of quality4 ,the ,converse1 then1 of ,some ruminants are not hollow-horned must be a negative proposition1 having 'hollow-horned' for its subject1 either in ,e4 or ,o42 but these would be respectively the contrary and contradictory of ,all hollow-horned animals are ruminants2 and1 therefore1 if this be true1 they must both be false4 ,but 7referring still to ,fig4 #a7 the legitimacy of contrapositing ,o4 is equally clear2 for if ,some ruminants are not hollow-horned1 ,some animals that are not hollow-horned are ruminants1 namely1 all the animals between the two ring-fences4 ,similar inferences may be illustrated from ,figs4 #c and #d4 ,and the ,contraposition of ,a4 may be verified by ,figs4 #a and #b1 and the ,contraposition of ,e4 by ,fig4 #d4 ,lastly1 the ,inverse of ,a4 is plain from ,fig4 #a--,some things that are not hollow-horned are not ruminants1 namely1 things that lie outside the outer circle and are neither 'ruminants' nor 'hollow-horned4' ,and the ,inverse of ,e may be studied in ,fig4 #d--,some things that are not-horned beasts are carnivorous4 ,notwithstanding the facility and clearness of the demonstrations thus obtained1 it may be said that a diagrammatic method1 representing denotations1 is not properly logical4 ,fundamentally1 the relation asserted 7or denied7 to exist between the terms of a proposition1 is a relation between the terms as determined by their attributes or connotation2 whether we take ,mill's view1 that a proposition asserts that the connotation of the subject is a mark of the connotation of the predicate2 or ,dr4 ,venn's view1 that things denoted by the subject 7as having its connotation7 have 7or have not7 the attribute connoted by the predicate2 or1 the ,conceptualist view1 that a judgment is a relation of concepts 7that is1 of connotations74 ,with a few exceptions artificially framed 7such as 'kings now reigning in ,europe'71 the denotation of a term is never directly and exhaustively known1 but consists merely in 'all things that have the connotation4' ,if the value of logical training depends very much upon our habituating ourselves to construe propositions1 and to realise the force of inferences from them1 according to the connotation of their terms1 we shall do well not to turn too hastily to the circles1 but rather to regard them as means of verifying in denotation the conclusions that we have already learnt to recognise as necessary in connotation4 #c4 ,the equational treatment of propositions is closely connected with the diagrammatic4 ,hamilton thought it a great merit of his plan of quantifying the predicate1 that thereby every proposition is reduced to its true form--an equation4 ,according to this doctrine1 the proposition ,all ,x is all ,y 7,u47 equates ,x and ,y2 the proposition ,all ,x is some ,y 7,a47 equates ,x with some part of ,y2 and similarly with the other affirmatives 7,y4 and ,i474 ,and so far it is easy to follow his meaning3 the ,xs are identical with some or all the ,ys4 ,but1 coming to the negatives1 the equational interpretation is certainly less obvious4 ,the proposition ,no ,x is ,y 7,e47 cannot be said in any sense to equate ,x and ,y2 though1 if we obvert it into ,all ,x is some not-,y1 we have 7in the same sense1 of course1 as in the above affirmative forms7 ,x equated with part at least of 'not-,y4' ,but what is that sense8 ,clearly not the same as that in which mathematical terms are equated1 namely1 in respect of some mode of quantity4 ,for if we may say ,some ,x is some ,y1 these ,xs that are also ,ys are not merely the same in number1 or mass1 or figure2 they are the same in every respect1 both quantitative and qualitative1 have the same positions in time and place1 are in fact identical4 ,the proposition #bbd means that any two things added to any other two are1 in respect of number1 equal to any three things added to one other thing2 and this is true of all things that can be counted1 however much they may differ in other ways4 ,but ,all ,x is all ,y means that ,xs and ,ys are the same things1 although they have different names when viewed in different aspects or relations4 ,thus all equilateral triangles are equiangular triangles2 but in one case they are named from the equality of their angles1 and in the other from the equality of their sides4 ,similarly1 ',british subjects' and 'subjects of ,king ,george ,v' are the same people1 named in one case from the person of the ,crown1 and in the other from the ,imperial ,government4 ,these logical equations1 then1 are in truth identities of denotation2 and they are fully illustrated by the relations of circles described in the previous section4 ,when we are told that logical propositions are to be considered as equations1 we naturally expect to be shown some interesting developments of method in analogy with the equations of ,mathematics2 but from ,hamilton's innovations no such thing results4 ,this cannot be said1 however1 of the equations of ,symbolic ,logic2 which are the starting-point of very remarkable processes of ratiocination4 ,as the subject of ,symbolic ,logic1 as a whole1 lies beyond the compass of this work1 it will be enough to give ,dr4 ,venn's equations corresponding with the four propositional forms of common ,logic4 ,according to this system1 universal propositions are to be regarded as not necessarily implying the existence of their terms2 and therefore1 instead of giving them a positive form1 they are translated into symbols that express what they deny4 ,for example1 the proposition ,all devils are ugly need not imply that any such things as 'devils' really exist2 but it certainly does imply that ,devils that are not ugly do not exist4 ,similarly1 the proposition ,no angels are ugly implies that ,angels that are ugly do not exist4 ,therefore1 writing x for 'devils1' y for 'ugly1' and y for 'not-ugly1' we may express ,a41 the universal affirmative1 thus3 ,a4 xy #j4 ,that is1 x that is not y is nothing2 or1 ,devils that are not-ugly do not exist4 ,and1 similarly1 writing x for 'angels' and y for 'ugly1' we may express ,e41 the universal negative1 thus3 ,e4 xy #j4 ,that is1 x that is y is nothing2 or1 ,angels that are ugly do not exist4 ,on the other hand1 particular propositions are regarded as implying the existence of their terms1 and the corresponding equations are so framed as to express existence4 ,with this end in view1 the symbol v is adopted to represent 'something1' or indeterminate reality1 or more than nothing4 ,then1 taking any particular affirmative1 such as ,some metaphysicians are obscure1 and writing x for 'metaphysicians1' and y for 'obscure1' we may express it thus3 ,i4 xy v4 ,that is1 x that is y is something2 or1 ,metaphysicians that are obscure do occur in experience 7however few they may be1 or whether they all be obscure74 ,and1 similarly1 taking any particular negative1 such as ,some giants are not cruel1 and writing x for 'giants' and y for 'not-cruel1' we may express it thus3 ,o4 xy v4 ,that is1 x that is not y is something2 or1 giants that are not-cruel do occur--in romances1 if nowhere else4 ,clearly1 these equations are1 like ,hamilton's1 concerned with denotation4 ,a4 and ,e4 affirm that the compound terms xy and xy have no denotation2 and ,i4 and ,o4 declare that xy and xy have denotation1 or stand for something4 ,here1 however1 the resemblance to ,hamilton's system ceases2 for the ,symbolic ,logic1 by operating upon more than two terms simultaneously1 by adopting the algebraic signs of operations1 1-1 1 7with a special signification71 and manipulating the symbols by quasi-algebraic processes1 obtains results which the common ,logic reaches 7if at all7 with much greater difficulty4 ,if1 indeed1 the value of logical systems were to be judged of by the results obtainable1 formal deductive ,logic would probably be superseded4 ,and1 as a mental discipline1 there is much to be said in favour of the symbolic method4 ,but1 as an introduction to philosophy1 the common ,logic must hold its ground4 7,venn3 ,symbolic ,logic1 c4 #g47 #d4 ,does ,formal ,logic involve any general assumption as to the real existence of the terms of propositions8 ,in the first place1 ,logic treats primarily of the relations implied in propositions4 ,this follows from its being the science of proof for all sorts of 7qualitative7 propositions2 since all sorts of propositions have nothing in common except the relations they express4 ,but1 secondly1 relations without terms of some sort are not to be thought of2 and1 hence1 even the most formal illustrations of logical doctrines comprise such terms as ,s and ,p1 ,x and ,y1 or x and y1 in a symbolic or representative character4 ,terms1 therefore1 of some sort are assumed to exist 7together with their negatives or contradictories7 for the purposes of logical manipulation4 ,thirdly1 however1 that ,formal ,logic cannot as such directly involve the existence of any particular concrete terms1 such as 'man' or 'mountain1' used by way of illustration1 is implied in the word 'formal1' that is1 'confined to what is common or abstract'2 since the only thing common to all terms is to be related in some way to other terms4 ,the actual existence of any concrete thing can only be known by experience1 as with 'man' or 'mountain'2 or by methodically justifiable inference from experience1 as with 'atom' or 'ether4' ,if 'man' or 'mountain1' or ',cuzco' be used to illustrate logical forms1 they bring with them an existential import derived from experience2 but this is the import of language1 not of the logical forms4 ',centaur' and ',el ,dorado' signify to us the non-existent2 but they serve as well as 'man' and ',london' to illustrate ,formal ,logic4 ,nevertheless1 fourthly1 the existence or non-existence of particular terms may come to be implied3 namely1 wherever the very fact of existence1 or of some condition of existence1 is an hypothesis or datum4 ,thus1 given the proposition ,all ,s is ,p1 to be ,p is made a condition of the existence of ,s3 whence it follows that an ,s that is not ,p does not exist 7xy #j74 ,on the further hypothesis that ,s exists1 it follows that ,p exists4 ,on the hypothesis that ,s does not exist1 the existence of ,p is problematic2 but1 then1 if ,p does exist we cannot convert the proposition2 since ,some ,p is ,s 7,p existing7 would involve the existence of ,s2 which is contrary to the hypothesis4 ,assuming that ,universals do not1 whilst ,particulars do1 imply the existence of their subjects1 we cannot infer the subalternate 7,i4 or ,o47 from the subalternans 7,a4 or ,e471 for that is to ground the actual on the problematic2 and for the same reason we cannot convert ,a4 per accidens4 ,assuming1 again1 a certain suppositio or universe1 to which in a given discussion every argument shall refer1 then1 any propositions whose terms lie outside that suppositio are irrelevant1 and for the purposes of that discussion are sometimes called false2 though it seems better to call them irrelevant or meaningless1 seeing that to call them false implies that they might in the same case be true4 ,thus propositions which1 according to the doctrine of ,opposition1 appear to be ,contradictories1 may then cease to be so2 for of ,contradictories one is true and the other false2 but1 in the case supposed1 both are meaningless4 ,if the subject of discussion be ,zoology1 all propositions about centaurs or unicorns are absurd2 and such specious ,contradictories as ,no centaurs play the lyre--,some centaurs do play the lyre2 or ,all unicorns fight with lions--,some unicorns do not fight with lions1 are both meaningless1 because in ,zoology there are no centaurs nor unicorns2 and1 therefore1 in this reference1 the propositions are not really contradictory4 ,but if the subject of discussion or suppositio be ,mythology or ,heraldry1 such propositions as the above are to the purpose1 and form legitimate pairs of ,contradictories4 ,in ,formal ,logic1 in short1 we may make at discretion any assumption whatever as to the existence1 or as to any condition of the existence of any particular term or terms2 and then certain implications and conclusions follow in consistency with that hypothesis or datum4 ,still1 our conclusions will themselves be only hypothetical1 depending on the truth of the datum2 and1 of course1 until this is empirically ascertained1 we are as far as ever from empirical reality4 7,venn3 ,symbolic ,logic1 c4 #f2 ,keynes3 ,formal ,logic1 ,part ,,ii4 c4 #g3 cf4 ,wolf3 ,studies in ,logic47 ,,chapter ,,ix ,,formal ,,conditions ,,of ,,mediate ,,inference #a4 ,a ,mediate ,inference is a proposition that depends for proof upon two or more other propositions1 so connected together by one or more terms 7which the evidentiary propositions1 or each pair of them1 have in common7 as to justify a certain conclusion1 namely1 the proposition in question4 ,the type or 7more properly7 the unit of all such modes of proof1 when of a strictly logical kind1 is the ,syllogism1 to which we shall see that all other modes are reducible4 ,it may be exhibited symbolically thus3 ,m is ,p2 ,s is ,m3 ,s is ,p4 ,syllogisms may be classified1 as to quantity1 into ,universal or ,particular1 according to the quantity of the conclusion2 as to quality1 into ,affirmative or ,negative1 according to the quality of the conclusion2 and1 as to relation1 into ,categorical1 ,hypothetical and ,disjunctive1 according as all their propositions are categorical1 or one 7at least7 of their evidentiary propositions is a hypothetical or a disjunctive4 ,to begin with ,categorical ,syllogisms1 of which the following is an example3 ,all authors are vain2 ,cicero is an author3 ,cicero is vain4 ,here we may suppose that there are no direct means of knowing that ,cicero is vain2 but we happen to know that all authors are vain and that he is an author2 and these two propositions1 put together1 unmistakably imply that he is vain4 ,in other words1 we do not at first know any relation between ',cicero' and 'vanity'2 but we know that these two terms are severally related to a third term1 'author1' hence called a ,middle ,term2 and thus we perceive1 by mediate evidence1 that they are related to one another4 ,this sort of proof bears an obvious resemblance 7though the relations involved are not the same7 to the mathematical proof of equality between two quantities1 that cannot be directly compared1 by showing the equality of each of them to some third quantity3 ,a ,b ,c ,a ,c4 ,here ,b is a middle term4 ,we have to inquire1 then1 what conditions must be satisfied in order that a ,syllogism may be formally conclusive or valid4 ,a specious ,syllogism that is not really valid is called a ,parasyllogism4 #b4 ,general ,canons of the ,syllogism4 7#a7 ,a ,syllogism contains three1 and no more1 distinct propositions4 7#b7 ,a ,syllogism contains three1 and no more1 distinct univocal terms4 ,these two ,canons imply one another4 ,three propositions with less than three terms can only be connected in some of the modes of ,immediate ,inference4 ,three propositions with more than three terms do not show that connection of two terms by means of a third1 which is requisite for proving a ,mediate ,inference4 ,if we write-- ,all authors are vain2 ,cicero is a statesman-- there are four terms and no middle term1 and therefore there is no proof4 ,or if we write-- ,all authors are vain2 ,cicero is an author3 ,cicero is a statesman-- here the term 'statesman' occurs without any voucher2 it appears in the inference but not in the evidence1 and therefore violates the maxim of all formal proof1 'not to go beyond the evidence4' ,it is true that if any one argued-- ,all authors are vain2 ,cicero wrote on philosophy3 ,cicero is vain-- this could not be called a bad argument or a material fallacy2 but it would be a needless departure from the form of expression in which the connection between the evidence and the inference is most easily seen4 ,still1 a mere adherence to the same form of words in the expression of terms is not enough3 we must also attend to their meaning4 ,for if the same word be used ambiguously 7as 'author' now for 'father' and anon for 'man of letters'71 it becomes as to its meaning two terms2 so that we have four in all4 ,then1 if the ambiguous term be the ,middle1 no connection is shown between the other two2 if either of the others be ambiguous1 something seems to be inferred which has never been really given in evidence4 ,the above two ,canons are1 indeed1 involved in the definition of a categorical syllogism1 which may be thus stated3 ,a ,categorical ,syllogism is a form of proof or reasoning 7way of giving reasons7 in which one categorical proposition is established by comparing two others that contain together only three terms1 or that have one and only one term in common4 ,the proposition established1 derived1 or inferred1 is called the ,conclusion3 the evidentiary propositions by which it is proved are called the ,premises4 ,the term common to the premises1 by means of which the other terms are compared1 is called the ,middle ,term2 the subject of the conclusion is called the ,minor ,term2 the predicate of the conclusion1 the ,major ,term4 ,the premise in which the minor term occurs is called the ,minor ,premise2 that in which the major term occurs is called the ,major ,premise4 ,and a ,syllogism is usually written thus3 ,major ,premise--,all authors 7,middle7 are vain 7,major72 ,minor ,premise--,cicero 7,minor7 is an author 7,middle73 ,conclusion-- ,cicero 7,minor7 is vain 7,major74 ,here we have three propositions with three terms1 each term occurring twice4 ,the minor and major terms are so called1 because1 when the conclusion is an universal affirmative 7which only occurs in ,barbara2 see chap4 x4 #f71 its subject and predicate are respectively the less and the greater in extent or denotation2 and the premises are called after the peculiar terms they contain3 the expressions 'major premise' and 'minor premise' have nothing to do with the order in which the premises are presented2 though it is usual to place the major premise first4 7#c7 ,no term must be distributed in the conclusion unless it is distributed in the premises4 ,it is usual to give this as one of the ,general ,canons of the ,syllogism2 but we have seen 7chap4 vi4 #f7 that it is of wider application4 ,indeed1 'not to go beyond the evidence' belongs to the definition of formal proof4 ,a breech of this rule in a syllogism is the fallacy of ,illicit ,process of the ,minor1 or of the ,major1 according to which term has been unwarrantably distributed4 ,the following parasyllogism illicitly distributes both terms of the conclusion3 ,all poets are pathetic2 ,some orators are not poets3 ,no orators are pathetic4 7#d7 ,the ,middle ,term must be distributed at least once in the premises 7in order to prove a conclusion in the given terms74 ,for the use of mediate evidence is to show the relation of terms that cannot be directly compared2 this is only possible if the middle term furnishes the ground of comparison2 and this 7in ,logic7 requires that the whole denotation of the middle should be either included or excluded by one of the other terms2 since if we only know that the other terms are related to some of the middle1 their respective relations may not be with the same part of it4 ,it is true that in what has been called the numerically definite syllogism1 an inference may be drawn1 though our canon seems to be violated4 ,thus3 #fj sheep in #ajj are horned2 #fj sheep in #ajj are blackfaced3 at least #bj blackfaced sheep in #ajj are horned4 ,but such an argument1 though it may be correct ,arithmetic1 is not ,logic at all2 and when such numerical evidence is obtainable the comparatively indefinite arguments of ,logic are needless4 ,another apparent exception is the following3 ,most men are #e feet high2 ,most men are semi-rational3 ,some semi-rational things are #e feet high4 ,here the ,middle ,term 7men7 is distributed in neither premise1 yet the indisputable conclusion is a logical proposition4 ,the premises1 however1 are really arithmetical2 for 'most' means 'more than half1' or more than #ej per cent4 ,still1 another apparent exception is entirely logical4 ,suppose we are given1 the premises--,all ,p is ,m1 and ,all ,s is ,m--the middle term is undistributed4 ,but take the obverse of the contrapositive of both premises3 ,all m is p2 ,all m is s3 ,some s is p4 ,here we have a conclusion legitimately obtained2 but it is not in the terms originally given4 ,for ,mediate ,inference depending on truly logical premises1 then1 it is necessary that one premise should distribute the middle term2 and the reason of this may be illustrated even by the above supposed numerical exceptions4 ,for in them the premises are such that1 though neither of the two premises by itself distributes the ,middle1 yet they always overlap upon it4 ,if each premise dealt with exactly half the ,middle1 thus barely distributing it between them1 there would be no logical proposition inferrible4 ,we require that the middle term1 as used in one premise1 should necessarily overlap the same term as used in the other1 so as to furnish common ground for comparing the other terms4 ,hence ,i have defined the middle term as 'that term common to both premises by means of which the other terms are compared4' 7#e7 ,one at least of the premises must be affirmative2 or1 from two negative premises nothing can be inferred 7in the given terms74 ,the fourth ,canon required that the middle term should be given distributed1 or in its whole extent1 at least once1 in order to afford sure ground of comparison for the others4 ,but that such comparison may be effected1 something more is requisite2 the relation of the other terms to the ,middle must be of a certain character4 ,one at least of them must be1 as to its extent or denotation1 partially or wholly identified with the ,middle2 so that to that extent it may be known to bear to the other term1 whatever relation we are told that so much of the ,middle bears to that other term4 ,now1 identity of denotation can only be predicated in an affirmative proposition3 one premise1 then1 must be affirmative4 ,if both premises are negative1 we only know that both the other terms are partly or wholly excluded from the ,middle1 or are not identical with it in denotation3 where they lie1 then1 in relation to one another we have no means of knowing4 ,similarly1 in the mediate comparison of quantities1 if we are told that ,a and ,c are both of them unequal to ,b1 we can infer nothing as to the relation of ,c to ,a4 ,hence the premises-- ,no electors are sober2 ,no electors are independent-- however suggestive1 do not formally justify us in inferring any connection between sobriety and independence4 ,formally to draw a conclusion1 we must have affirmative grounds1 such as in this case we may obtain by obverting both premises3 ,all electors are not-sober2 ,all electors are not-independent3 ,some who are not-independent are not-sober4 ,but this conclusion is not in the given terms4 7#f7 7a7 ,if one premise be negative1 the conclusion must be negative3 and 7b7 to prove a negative conclusion1 one premise must be negative4 7a7 ,for we have seen that one premise must be affirmative1 and that thus one term must be partly 7at least7 identified with the ,middle4 ,if1 then1 the other premise1 being negative1 predicates the exclusion of the remaining term from the ,middle1 this remaining term must be excluded from the first term1 so far as we know the first to be identical with the ,middle3 and this exclusion will be expressed by a negative conclusion4 ,the analogy of the mediate comparison of quantities may here again be noticed3 if ,a is equal to ,b1 and ,b is unequal to ,c1 ,a is unequal to ,c4 7b7 ,if both premises be affirmative1 the relations to the ,middle of both the other terms are more or less inclusive1 and therefore furnish no ground for an exclusive inference4 ,this also follows from the function of the middle term4 ,for the more convenient application of these canons to the testing of syllogisms1 it is usual to derive from them three ,corollaries3 7i7 ,two particular premises yield no conclusion4 ,for if both premises be affirmative1 all their terms are undistributed1 the subjects by predesignation1 the predicates by position2 and therefore the middle term must be undistributed1 and there can be no conclusion4 ,if one premise be negative1 its predicate is distributed by position3 the other terms remaining undistributed4 ,but1 by ,canon #f1 the conclusion 7if any be possible7 must be negative2 and therefore its predicate1 the major term1 will be distributed4 ,in the premises1 therefore1 both the middle and the major terms should be distributed1 which is impossible3 e4g41 ,some ,m is not ,p2 ,some ,s is ,m3 ,some ,s is not ,p4 ,here1 indeed1 the major term is legitimately distributed 7though the negative premise might have been the minor72 but ,m1 the middle term1 is distributed in neither premise1 and therefore there can be no conclusion4 ,still1 an exception may be made by admitting a bi-designate conclusion3 ,some ,p is ,m2 ,some ,s is not ,m3 ,some ,s is not some ,p4 7ii7 ,if one premise be particular1 so is the conclusion4 ,for1 again1 if both premises be affirmative1 they only distribute one term1 the subject of the universal premise1 and this must be the middle term4 ,the minor term1 therefore1 is undistributed1 and the conclusion must be particular4 ,if one premise be negative1 the two premises together can distribute only two terms1 the subject of the universal and the predicate of the negative 7which may be the same premise74 ,one of these terms must be the middle2 the other 7since the conclusion is negative7 must be the major4 ,the minor term1 therefore1 is undistributed1 and the conclusion must be particular4 7iii7 ,from a particular major and a negative minor premise nothing can be inferred4 ,for the minor premise being negative1 the major premise must be affirmative 7#eth ,canon72 and therefore1 being particular1 distributes the major term neither in its subject nor in its predicate4 ,but since the conclusion must be negative 7#fth ,canon71 a distributed major term is demanded1 e4g41 ,some ,m is ,p2 ,no ,s is ,m3 ------ ,here the minor and the middle terms are both distributed1 but not the major 7,p72 and1 therefore1 a negative conclusion is impossible4 #c4 ,first ,principle or ,axiom of the ,syllogism4--,hitherto in this chapter we have been analysing the conditions of valid mediate inference4 ,we have seen that a single step of such inference1 a ,syllogism1 contains1 when fully expressed in language1 three propositions and three terms1 and that these terms must stand to one another in the relations required by the fourth1 fifth1 and sixth ,canons4 ,we now come to a principle which conveniently sums up these conditions2 it is called the ,dictum de omni et nullo1 and may be stated thus3 ,whatever is predicated 7affirmatively or negatively7 of a term distributed1 ,with which term another term can be 7partly or wholly7 identified1 ,may be predicated in like manner 7affirmatively or negatively7 of the latter term 7or part of it74 ,thus stated 7nearly as by ,whately in the introduction to his ,logic7 the ,dictum follows line by line the course of a ,syllogism in the ,first ,figure 7see chap4 ,x4 #b74 ,to return to our former example3 ,all authors are vain is the same as--,vanity is predicated of all authors2 ,cicero is an author is the same as--,cicero is identified as an author2 therefore ,cicero is vain1 or--,vanity may be predicated of ,cicero4 ,the ,dictum then requires3 7#a7 three propositions2 7#b7 three terms2 7#c7 that the middle term be distributed2 7#d7 that one premise be affirmative1 since only by an affirmative proposition can one term be identified with another2 7#e7 that if one premise be negative the conclusion shall be so too1 since whatever is predicated of the middle term is predicated in like manner of the minor4 ,thus far1 then1 the ,dictum is wholly analytic or verbal1 expressing no more than is implied in the definitions of ',syllogism' and ',middle ,term'2 since 7as we have seen7 all the ,general ,canons 7except the third1 which is a still more general condition of formal proof7 are derivable from those definitions4 ,however1 the ,dictum makes a further statement of a synthetic or real character1 namely1 that when these conditions are fulfilled an inference is justified2 that then the major and minor terms are brought into comparison through the middle1 and that the major term may be predicated affirmatively or negatively of all or part of the minor4 ,it is this real assertion that justifies us in calling the ,dictum an ,axiom4 #d4 ,whether the ,laws of ,thought may not fully explain the ,syllogism without the need of any synthetic principle has1 however1 been made a question4 ,take such a syllogism as the following3 ,all domestic animals are useful2 ,all pugs are domestic animals3 ,all pugs are useful4 ,here 7an ingenious man might urge71 having once identified pugs with domestic animals1 that they are useful follows from the ,law of ,identity4 ,if we attend to the meaning1 and remember that what is true in one form of words is true in any other form1 then1 all domestic animals being useful1 of course pugs are4 ,it is merely a case of subalternation3 we may put it in this way3 ,all domestic animals are useful3 ,some domestic animals 7e4g41 pugs7 are useful4 ,the derivation of negative syllogisms from the ,law of ,contradiction 7he might add7 may be shown in a similar manner4 ,but the force of this ingenious argument depends on the participial clause--'having once identified pugs with domestic animals4' ,if this is a distinct step of the reasoning1 the above syllogism cannot be reduced to one step1 cannot be exhibited as mere subalternation1 nor be brought directly under the law of ,identity4 ,if 'pug1' 'domestic1' and 'useful' are distinct terms2 and if 'pug' and 'useful' are only known to be connected because of their relations to 'domestic'3 this is something more than the ,laws of ,thought provide for3 it is not ,immediate ,inference1 but ,mediate2 and to justify it1 scientific method requires that its conditions be generalised4 ,the ,dictum1 then1 as we have seen1 does generalise these conditions1 and declares that when such conditions are satisfied a ,mediate ,inference is valid4 ,but1 after all 7to go back a little71 consider again that proposition ,all pugs are domestic animals3 is it a distinct step of the reasoning2 that is to say1 is it a ,real ,proposition8 ,if1 indeed1 'domestic' is no part of the definition of 'pug1' the proposition is real1 and is a distinct part of the argument4 ,but take such a case as this3 ,all dogs are useful2 ,all pugs are dogs4 ,here we clearly have1 in the minor premise1 only a verbal proposition2 to be a dog is certainly part of the definition of 'pug4' ,but1 if so1 the inference ',all pugs are useful' involves no real mediation1 and the argument is no more than this3 ,all dogs are useful2 ,some dogs 7e4g41 pugs7 are useful4 ,similarly1 if the major premise be verbal1 thus3 ,all men are rational2 ,socrates is a man-- to conclude that ',socrates is rational' is no ,mediate ,inference2 for so much was implied in the minor premise1 ',socrates is a man1' and the major premise adds nothing to this4 ,hence we may conclude 7as anticipated in chap4 vii4 #c7 that 'any apparent syllogism1 having one premise a verbal proposition1 is really an ,immediate ,inference'2 but that1 if both premises are real propositions1 the ,inference is ,mediate1 and demands for its explanation something more than the ,laws of ,thought4 ,the fact is that to prove the minor to be a case of the middle term may be an exceedingly difficult operation 7chap4 xiii4 #g74 ,the difficulty is disguised by ordinary examples1 used for the sake of convenience4 #e4 ,other kinds of ,mediate ,inference exist1 yielding valid conclusions1 without being truly syllogistic4 ,such are mathematical inferences of ,equality1 as-- ,a ,b ,c ,a ,c4 ,here1 according to the usual logical analysis1 there are strictly four terms--7#a7 ,a1 7#b7 equal to ,b1 7#c7 ,b1 7#d7 equal to ,c4 ,similarly with the argument a fortiori1 ,a ,b ,c 7much more7 ,a ,c4 ,this also is said to contain four terms3 7#a7 ,a1 7#b7 greater than ,b1 7#c7 ,b1 7#d7 greater than ,c4 ,such inferences are nevertheless intuitively sound1 may be verified by trial 7within the limits of sense-perception71 and are generalised in appropriate axioms of their own1 corresponding to the ,dictum of the syllogism2 as ',things equal to the same thing are equal to one another1' etc4 ,now1 surely1 this is an erroneous application of the usual logical analysis of propositions4 ,both ,logic and ,mathematics treat of the relations of terms2 but whilst ,mathematics employs the sign for only one kind of relation1 and for that relation exclusive of the terms2 ,logic employs the same signs 7is or is not7 for all relations1 recognising only a difference of quality in predication1 and treating every other difference of relation as belonging to one of the terms related4 ,thus ,logicians read ,a--is--equal to ,b3 as if equal to ,b could possibly be a term co-relative with ,a4 ,whence it follows that the argument ,a ,b ,c ,a ,c contains four terms2 though everybody sees that there are only three4 ,in fact 7as observed in chap4 ii4 #b7 the sign of logical relation 7is or is not71 whilst usually adequate for class-reasoning 7coinherence7 and sometimes extensible to causation 7because a cause implies a class of events71 should never be stretched to include other relations in such a way as to sacrifice intelligence to formalism4 ,and1 besides mathematical or quantitative relations1 there are others 7usually considered qualitative because indefinite7 which cannot be justly expressed by the logical copula4 ,we ought to read propositions expressing time-relations 7and inferences drawn accordingly7 thus3 ,b--is before--,c2 ,a--is before--,b3 ,a--is before--,c4 ,and in like manner ,a--is simultaneous with--,b2 etc4 ,such arguments 7as well as the mathematical7 are intuitively sound and verifiable1 and might be generalised in axioms if it were worth while3 but it is not1 because no method could be founded on such axioms4 ,the customary use of relative terms justifies some ,mediate ,inferences1 as1 ,the father of a father is a grand-father4 ,some cases1 however1 that at first seem obvious1 are really delusive unless further data be supplied4 ,thus ,a co-exists with ,b1 ,b with ,c2 ,a with ,c--is not sound unless ,b is an instantaneous event2 for where ,b is perdurable1 ,a may co-exist with it at one time and ,c at another4 ,again3 ,a is to the left of ,b1 ,b of ,c2 ,a of ,c4 ,this may pass2 but it is not a parallel argument that if ,a is north of ,b and ,b west of ,c1 then ,a is north-west of ,c3 for suppose that ,a is a mile to the north of ,b1 and ,b a yard to the west of ,c1 then ,a is practically north of ,c2 at least1 its westward position cannot be expressed in terms of the mariner's compass4 ,in such a case we require to know not only the directions but the distances of ,a and ,c from ,b2 and then the exact direction of ,a from ,c is an affair of mathematical calculation4 ,qualitative reasoning concerning position is only applicable to things in one dimension of space1 or in time considered as having one dimension4 ,under these conditions we may frame the following generalisation concerning all ,mediate ,inferences3 ,two terms definitely related to a third1 and one of them positively1 are related to one another as the other term is related to the third 7that is1 positively or negatively72 provided that the relations given are of the same kind 7that is1 of ,time1 or ,coinherence1 or ,likeness1 or ,equality74 ,thus1 to illustrate by relations of ,time-- ,b is simultaneous with ,c2 ,a is not simultaneous with ,b3 ,a is not simultaneous with ,c4 ,here the relations are of the same kind but of different logical quality1 and 7as in the syllogism7 a negative copula in the premises leads to a negative conclusion4 ,an examination in detail of particular cases would show that the above generalisation concerning all ,mediate ,inferences is subject to too many qualifications to be called an ,axiom2 it stands to the real ,axioms 7the ,dictum1 etc47 as the notion of the ,uniformity of ,nature does to the definite principles of natural order 7cf4 chap4 xiii4 #i74 ,,chapter ,x ,,categorical ,,syllogisms #a4 ,the type of logical1 deductive1 mediate1 categorical ,inference is a ,syllogism directly conformable with the ,dictum3 as-- ,all carnivores 7,m7 are excitable 7,p72 ,cats 7,s7 are carnivores 7,m73 ,cats 7,s7 are excitable 7,p74 ,in this example ,p is predicated of ,m1 a term distributed2 in which term1 ,m1 ,s is given as included2 so that ,p may be predicated of ,s4 ,many arguments1 however1 are of a type superficially different from the above3 as-- ,no wise man 7,p7 fears death 7,m72 ,balbus 7,s7 fears death 7,m73 ,balbus 7,s7 is not a wise man 7,p74 ,in this example1 instead of ,p being predicated of ,m1 ,m is predicated of ,p1 and yet ,s is given as included not in ,p1 but in ,m4 ,the divergence of such a syllogism from the ,dictum may1 however1 be easily shown to be superficial by writing1 instead of ,no wise man fears death1 the simple1 converse1 ,no man who fears death is wise4 ,again3 ,some dogs 7,m7 are friendly to man 7,p72 ,all dogs 7,m7 are carnivores 7,s73 ,some carnivores 7,s7 are friendly to man 7,p74 ,here ,p is predicated of ,m undistributed2 and instead of ,s being included in ,m1 ,m is included in ,s3 so that the divergence from the type of syllogism to which the ,dictum directly applies is still greater than in the former case4 ,but if we transpose the premises1 taking first ,all dogs 7,m7 are carnivores 7,p71 then ,p is predicated of ,m distributed2 and1 simply converting the other premise1 we get-- ,some things friendly to man 7,s7 are dogs 7,m73 whence it follows that-- ,some things friendly to man 7,s7 are carnivores 7,p72 and this is the simple converse of the original conclusion4 ,once more3 ,no pigs 7,p7 are philosophers 7,m72 ,some philosophers 7,m7 are hedonists 7,s73 ,some hedonists 7,s7 are not pigs 7,p74 ,in this case1 instead of ,p being predicated of ,m distributed1 ,m is predicated of ,p distributed2 and instead of ,s 7or part of it7 being included in ,m1 we are told that some ,m is included in ,s4 ,still there is no real difficulty4 ,simply convert both the premises1 and we have3 ,no philosophers 7,m7 are pigs 7,p72 ,some hedonists 7,s7 are philosophers 7,m74 ,whence the same conclusion follows2 and the whole syllogism plainly conforms directly to the ,dictum4 ,such departures as these from the normal syllogistic form are said to constitute differences of ,figure 7see #b72 and the processes by which they are shown to be unessential differences are called ,reduction 7see #f74 #b4 ,figure is determined by the position of the ,middle ,term in the premises2 of which position there are four possible variations4 ,the middle term may be subject of the major premise1 and predicate of the minor1 as in the first example above2 and this position1 being directly conformable to the requirements of the ,dictum1 is called the ,first ,figure4 ,or the middle term may be predicate of both premises1 as in the second of the above examples2 and this is called the ,second ,figure4 ,or the middle term may be subject of both premises1 as in the third of the above examples2 and this is called the ,third ,figure4 ,or1 finally1 the middle term may be predicate of the major premise1 and subject of the minor1 as in the fourth example given above2 and this is the ,fourth ,figure4 ,it may facilitate the recollection of this most important point if we schematise the figures thus3 ,i4 ,,ii4 ,,iii4 ,,iv4 ,m---,p ,p---,m ,m---,p ,p---,m _/ _/ _/ ,s---,m ,s---,m ,m---,s ,m---,s ,the horizontal lines represent the premises1 and at the angles formed with them by the slanting or by the perpendicular lines the middle term occurs4 ,the schema of ,figure ,,iv4 resembles ,z1 the last letter of the alphabet3 this helps one to remember it in contrast with ,figure ,i41 which is thereby also remembered4 ,figures ,,ii4 and ,,iii4 seem to stand back to back4 #c4 ,the ,moods of each ,figure are the modifications of it which arise from different combinations of propositions according to quantity and quality4 ,in ,figure ,i41 for example1 four ,moods are recognised3 ,a4,a4,a41 ,e4,a4,e41 ,a4,i4,i41 ,e4,i4,o4 ,a4 ,all ,m is ,p2 ,a4 ,all ,s is ,m3 ,a4 ,all ,s is ,p4 ,e4 ,no ,m is ,p2 ,a4 ,all ,s is ,m3 ,e4 ,no ,s is ,p4 ,a4 ,all ,m is ,p2 ,i4 ,some ,s is ,m3 ,i4 ,some ,s is ,p4 ,e4 ,no ,m is ,p2 ,i4 ,some ,s is ,m3 ,o4 ,some ,s is not ,p4 ,now1 remembering that there are four ,figures1 and four kinds of propositions 7,a4 ,i4 ,e4 ,o471 each of which propositions may be major premise1 minor premise1 or conclusion of a syllogism1 it appears that in each ,figure there may be #fd ,moods1 and therefore #bef in all4 ,on examining these #bef ,moods1 however1 we find that only #bd of them are valid 7i4e41 of such a character that the conclusion strictly follows from the premises71 whilst #e of these #bd are needless1 because their conclusions are 'weaker' or less extensive than the premises warrant2 that is to say1 they are particular when they might be universal4 ,thus1 in ,figure ,i41 besides the above #d ,moods1 ,a4,a4,i4 and ,e4,a4,o4 are valid in the sense of being conclusive2 but they are superfluous1 because included in ,a4,a4,a4 and ,e4,a4,e4 ,omitting1 then1 these #e needless ,moods1 which are called ',subalterns' because their conclusions are subaltern 7chap4 vii4 #b7 to those of other ,moods1 there remain #ai ,moods that are valid and generally recognised4 #d4 ,how these #ai ,moods are determined must be our next inquiry4 ,there are several ways more or less ingenious and interesting2 but all depend on the application1 directly or indirectly1 of the ,six ,canons1 which were shown in the last chapter to be the conditions of ,mediate ,inference4 7#a7 ,one way is to begin by finding what ,moods of ,figure ,i4 conform to the ,dictum4 ,now1 the ,dictum requires that1 in the major premise1 ,p be predicated of a term distributed1 from which it follows that no ,mood can be valid whose major premise is particular1 as in ,i4,a4,i4 or ,o4,a4,o4 ,again1 the ,dictum requires that the minor premise be affirmative 7with which term another is identified72 so that no ,mood can be valid whose minor premise is negative1 as in ,a4,e4,e4 or ,a4,o4,o4 ,by such considerations we find that in ,figure ,i41 out of #fd ,moods possible1 only six are valid1 namely1 those above-mentioned in #c1 including the two subalterns4 ,the second step of this method is to test the ,moods of the ,second1 ,third1 and ,fourth ,figures1 by trying whether they can be reduced to one or other of the four ,moods of the ,first 7as briefly illustrated in #a1 and to be further explained in #f74 7#b7 ,another way is to take the above six ,general or ,common ,canons1 and to deduce from them ,special ,canons for testing each ,figure3 an interesting method1 which1 on account of its length1 will be treated of separately in the next section4 7#c7 ,direct application of the ,common ,canons is1 perhaps1 the simplest plan4 ,first write out the #fd ,moods that are possible without regard to ,figure1 and then cross out those which violate any of the ,canons or ,corollaries1 thus3 ,,aaa1 ,a,a,e 7#fth ,can4 b74 ,,aai4 ,a,a,o 7#fth ,can4 b74 ,a,e,a 7#fth ,can4 a7 ,,aee1 ,a,e,i 7#fth ,can4 a7 ,,aeo1 ,a,i,a 7,cor4 ii47 ,a,i,e 7#fth ,can4 b7 ,,aii1 ,a,i,o 7#fth ,can4 b7 ,a,o,a 7#fth ,can4 a7 ,a,o,e 7,cor4 ii47 ,a,o,i 7#fth ,can4 a7 ,,aoo4 ,whoever has the patience to go through the remaining #dh ,moods will discover that of the whole #fd only #aa are valid1 namely3 ,a4,a4,a41 ,a4,a4,i41 ,a4,e4,e41 ,a4,e4,o41 ,a4,i4,i41 ,a4,o4,o41 ,e4,a4,e41 ,e4,a4,o41 ,e4,i4,o41 ,i4,a4,i41 ,o4,a4,o4 ,these #aa ,moods have next to be examined in each ,figure1 and if valid in every ,figure there will still be #dd moods in all4 ,we find1 however1 that in the ,first ,figure1 ,a4,e4,e41 ,a4,e4,o41 ,a4,o4,o4 involve illicit process of the major term 7#crd ,can472 ,i4,a4,i41 ,o4,a4,o4 involve undistributed ,middle 7#dth ,can472 and ,a4,a4,i41 ,e4,a4,o4 are subalterns4 ,in the ,second ,figure all the affirmative ,moods1 ,a4,a4,a41 ,a4,a4,i41 ,a4,i4,i41 ,i4,a4,i41 involve undistributed ,middle2 ,o4,a4,o4 gives illicit process of the major term2 and ,a4,e4,o41 ,e4,a4,o4 are subalterns4 ,in the ,third ,figure1 ,a4,a4,a41 ,e4,a4,e41 involve illicit process of the minor term 7#crd ,can472 ,a4,e4,e41 ,a4,e4,o41 ,a4,o4,o41 illicit process of the major term4 ,in the ,fourth ,figure1 ,a4,a4,a4 and ,e4,a4,e4 involve illicit process of the minor term2 ,a4,i4,i41 ,a4,o4,o41 undistributed ,middle2 ,o4,a4,o4 involves illicit process of the major term2 and ,a4,e4,o4 is subaltern4 ,those moods of each ,figure which1 when tried by these tests1 are not rejected1 are valid1 namely3 ,fig4 ,i4--,a4,a4,a41 ,e4,a4,e41 ,a4,i4,i41 ,e4,i4,o4 7,a4,a4,i41 ,e4,a4,o41 ,subaltern72 ,fig4 ,,ii4--,e4,a4,e41 ,a4,e4,e41 ,e4,i4,o41 ,a4,o4,o4 7,e4,a4,o41 ,a4,e4,o41 ,subaltern72 ,fig4 ,,iii4--,a4,a4,i41 ,i4,a4,i41 ,a4,i4,i41 ,e4,a4,o41 ,o4,a4,o41 ,e4,i4,o42 ,fig4 ,,iv4--,a4,a4,i41 ,a4,e4,e41 ,i4,a4,i41 ,e4,a4,o41 ,e4,i4,o4 7,a4,e4,o41 ,subaltern74 ,thus1 including subaltern ,moods1 there are six valid in each ,figure4 ,in ,fig4 ,,iii4 alone there is no subaltern ,mood1 because in that ,figure there can be no universal conclusion4 #e4 ,special ,canons of the several ,figures1 deduced from the ,common ,canons1 enable us to arrive at the same result by a somewhat different course4 ,they are not1 perhaps1 necessary to the ,science1 but afford a very useful means of enabling one to thoroughly appreciate the character of formal syllogistic reasoning4 ,accordingly1 the proof of each rule will be indicated1 and its elaboration left to the reader4 ,there is no difficulty1 if one bears in mind that ,figure is determined by the position of the middle term4 ,fig4 ,i41 ,rule 7a73 ,the minor premise must be affirmative4 ,for1 if not1 in negative ,moods there will be illicit process of the major term4 ,applying this rule to the eleven possible ,moods given in #d1 as remaining after application of the ,common ,canons1 it eliminates ,a4,e4,e41 ,a4,e4,o41 ,a4,o4,o4 7b7 ,the major premise must be universal4 ,for1 if not1 the minor premise being affirmative1 the middle term will be undistributed4 ,this rule eliminates ,i4,a4,i41 ,o4,a4,o42 leaving six ,moods1 including two subalterns4 ,fig4 ,,ii4 7a7 ,one premise must be negative4 ,for else neither premise will distribute the middle term4 ,this rule eliminates ,a4,a4,a41 ,a4,a4,i41 ,a4,i4,i41 ,i4,a4,i4 7b7 ,the major premise must be universal4 ,for else1 the conclusion being negative1 there will be illicit process of the major term4 ,this eliminates ,i4,a4,i41 ,o4,a4,o42 leaving six ,moods1 including two subalterns4 ,fig4 ,,iii4 7a7 ,the minor premise must be affirmative4 ,for else1 in negative moods there will be illicit process of the major term4 ,this rule eliminates ,a4,e4,e41 ,a4,e4,o41 ,a4,o4,o4 7b7 ,the conclusion must be particular4 ,for1 if not1 the minor premise being affirmative1 there will be illicit process of the minor term4 ,this eliminates ,a4,a4,a41 ,a4,e4,e41 ,e4,a4,e42 leaving six ,moods4 ,fig4 ,,iv4 7a7 ,when the major premise is affirmative1 the minor must be universal4 ,for else the middle term is undistributed4 ,this eliminates ,a4,i4,i41 ,a4,o4,o4 7b7 ,when the minor premise is affirmative the conclusion must be particular4 ,otherwise there will be illicit process of the minor term4 ,this eliminates ,a4,a4,a41 ,e4,a4,e4 7c7 ,when either premise is negative1 the major must be universal4 ,for else1 the conclusion being negative1 there will be illicit process of the major term4 ,this eliminates ,o4,a4,o42 leaving six ,moods1 including one subaltern4 #f4 ,reduction is either--7#a7 ,ostensive or 7#b7 ,indirect4 ,ostensive ,reduction consists in showing that an argument given in one ,mood can also be stated in another2 the process is especially used to show that the ,moods of the second1 third1 and fourth ,figures are equivalent to one or another ,mood of the first ,figure4 ,it thus proves the validity of the former ,moods by showing that they also essentially conform to the ,dictum1 and that all ,categorical ,syllogisms are only superficial varieties of one type of proof4 ,to facilitate ,reduction1 the recognised ,moods have all had names given them2 which names1 again1 have been strung together into mnemonic verses of great force and pregnancy3 ,barbara1 ,celarent1 ,darii1 ,ferioque prioris3 ,cesare1 ,camestres1 ,festino1 ,baroco1 secund3 ,tertia1 ,darapti1 ,disamis1 ,datisi1 ,felapton1 ,bocardo1 ,ferison1 habet3 ,quarta insuper addit ,bramantip1 ,camenes1 ,dimaris1 ,fesapo1 ,fresison4 ,in the above verses the names of the ,moods of ,fig4 ,i4 begin with the first four consonants ,b1 ,c1 ,d1 ,f1 in alphabetical order2 and the names of all other ,moods likewise begin with these letters1 thus signifying 7except in ,baroco and ,bocardo7 the mood of ,fig4 ,i41 to which each is equivalent1 and to which it is to be reduced3 as ,bramantip to ,barbara1 ,camestres to ,celarent1 and so forth4 ,the vowels ,a1 ,e1 ,i1 ,o1 occurring in the several names1 give the quantity and quality of major premise1 minor premise1 and conclusion in the usual order4 ,the consonants s and p1 occurring after a vowel1 show that the proposition which the vowel stands for is to be converted either 7s7 simply or 7p7 per accidens2 except where s or p occurs after the third vowel of a name1 the conclusion3 then it refers not to the conclusion of the given ,mood 7say ,disamis71 but to the conclusion of that ,mood of the first ,figure to which the given ,mood is reduced 7,darii74 ,m 7mutare1 metathesis7 means 'transpose the premises' 7as of ,camestres74 ,c means 'substitute the contradictory of the conclusion for the foregoing premise1' a process of the ,indirect ,reduction to be presently explained 7see ,baroco1 #h74 ,the other consonants1 r1 n1 t 7with b and d1 when not initial71 occurring here and there1 have no mnemonic significance4 ,what now is the problem of ,reduction8 ,the difference of ,figures depends upon the position of the ,middle ,term4 ,to reduce a ,mood of any other ,figure to the form of the ,first1 then1 we must so manipulate its premises that the ,middle ,term shall be subject of the major premise and predicate of the minor premise4 ,now in ,fig4 ,,ii4 the ,middle ,term is predicate of both premises2 so that the minor premise may need no alteration1 and to convert the major premise may suffice4 ,this is the case with ,cesare1 which reduces to ,celarent by simply converting the major premise2 and with ,festino1 which by the same process becomes ,ferio4 ,in ,camestres1 however1 the minor premise is negative2 and1 as this is impossible in ,fig4 ,i41 the premises must be transposed1 and the new major premise must be simply converted3 then1 since the transposition of the premises will have transposed the terms of the conclusion 7according to the usual reading of syllogisms71 the new conclusion must be simply converted in order to prove the validity of the original conclusion4 ,the process may be thus represented 7s4c4 meaning 'simply convert'7 ,camestres4 ,celarent4 ,all ,p is ,m2 ---- _/--- ,no ,m is ,s2 c_/ _/ s_/ _/ ,no ,s is ,m3 ----_/ --- ,all ,p is ,m3 s4c4 ,no ,s is ,p4 ----------- ,no ,p is ,s4 ,the ,ostensive ,reduction of ,baroco also needs special explanation2 for as it used to be reduced indirectly1 its name gives no indication of the ostensive process4 ,to reduce it ostensively let us call it ,faksnoko1 where k means 'obvert the foregoing premise4' ,by thus obverting 7k7 and simply converting 7s7 7in sum1 contrapositing7 the major premise1 and obverting the minor premise1 we get a syllogism in ,ferio1 thus3 ,baroco or ,faksnoko4 ,ferio4 contrap ,all ,p is ,m2 ----------------------- ,no m 7not-,m7 is ,p2 obv ,some ,s is not ,m3 ----------------------- ,some ,s is m 7not-,m73 ,some ,s is not ,p4 ,some ,s is not ,p4 ,in ,fig4 ,,iii4 the middle term is subject of both premises2 so that1 to reduce its ,moods to the ,first ,figure1 it may be enough to convert the minor premise4 ,this is the case with ,darapti1 ,datisi1 ,felapton1 and ,ferison4 ,but1 with ,disamis1 since the major premise must in the ,first ,figure be universal1 we must transpose the premises1 and then simply convert the new minor premise2 and1 lastly1 since the major and minor terms have now changed places1 we must simply convert the new conclusion in order to verify the old one4 ,thus3 ,disamis4 ,darii4 ,some ,m is ,p2 ---- _/--- ,all ,m is ,s2 s4_/ _/ _/c4 _/ ,all ,m is ,s3 ----_/ --- ,some ,p is ,m3 s4c4 ,some ,s is ,p4 ------------- ,some ,p is ,s4 ,bocardo1 like ,baroco1 indicates by its name the indirect process4 ,to reduce it ostensively let its name be ,doksamrosk1 and proceed thus3 ,bocardo or ,doksamrosk4 ,darii4 ,some ,m is not ,p2 ---------- _/--------- ,all ,m is ,s2 _/ _/ _/ contrap _/ ,all ,m is ,s3 ----------_/ --------- ,some p 7not-,p7 is ,m3 convert obvert ,some ,s is not ,p4 ------------------------- ,some p 7not-,p7 is ,s4 ,in ,fig4 ,,iv4 the position of the middle term is1 in both premises1 the reverse of what it is in the ,first ,figure2 we may therefore reduce its ,moods either by transposing the premises1 as with ,bramantip1 ,camenes1 and ,dimaris2 or by converting both premises1 the course pursued with ,fesapo and ,fresison4 ,it may suffice to illustrate by the case of ,bramantip3 ,bramantip4 ,barbara4 ,all ,p is ,m2 ---------- _/------ ,all ,m is ,s2 _/ _/ ,all ,m is ,s3 ----------_/ ------ ,all ,p is ,m3 convert per acc4 ,some ,s is ,p4 ----------------------- ,all ,p is ,s4 ,this case shows that a final significant consonant 7s1 p1 or sk7 in the name of any ,mood refers to the conclusion of the new syllogism in the ,first ,figure2 since p in ,bramantip cannot refer to that ,mood's own conclusion in ,i42 which1 being already particular1 cannot be converted per accidens4 ,finally1 in ,fig4 ,i41 ,darii and ,ferio differ respectively from ,barbara and ,celarent only in this1 that their minor premises1 and consequently their conclusions1 are subaltern to the corresponding propositions of the universal ,moods2 a difference which seems insufficient to give them rank as distinct forms of demonstration4 ,and as for ,barbara and ,celarent1 they are easily reducible to one another by obverting their major premises and the new conclusions1 thus3 ,barbara4 ,celarent4 obv4 ,all ,m is ,p2 ----------------------- ,no ,m is p 7not-,p72 ,all ,s is ,m3 ----------------------- ,all ,s is ,m3 obv4 ,all ,s is ,p4 ------------------- ,no ,s is p 7not-,p74 ,there is1 then1 only one fundamental syllogism4 #g4 ,a new version of the mnemonic lines was suggested in ,mind ,no4 #bg1 with the object of 7#a7 freeing them from all meaningless letters1 7#b7 showing by the name of each ,mood the ,figure to which it belongs1 7#c7 giving names to indicate the ostensive reduction of ,baroco and ,bocardo4 ,to obtain the first two objects1 l is used as the mark of ,fig4 ,i41 n of ,fig ,,ii41 r of ,fig4 ,,iii41 t of ,fig4 ,,iv4 ,the verses 7to be scanned discreetly7 are as follows3 ,balala1 ,celalel1 ,dalii1 ,felioque prioris3 ,faksnoko ,cesane1 ,camenes1 ,fesinon1 secund3 ,banoco1 ,tertia1 ,darapri1 ,drisamis1 ,darisi1 ,ferapro1 ,doksamrosk 1 ,ferisor habet3 ,quarta insuper addit4 ,bocaro ,bamatip1 ,cametes1 ,dimatis1 ,fesapto1 ,fesistot4 ,de ,morgan praised the old verses as more full of meaning than any others that ever were made2 and in defence of the above alteration it may be said that they now deserve that praise still more4 #h4 ,indirect reduction is the process of proving a ,mood to be valid by showing that the supposition of its invalidity involves a contradiction4 ,take ,baroco1 and 7since the doubt as to its validity is concerned not with the truth of the premises1 but with their relation to the conclusion7 assume the premises to be true4 ,then1 if the conclusion be false1 its contradictory is true4 ,the conclusion being in ,o41 its contradictory will be in ,a4 ,substituting this ,a4 for the minor premise of ,baroco1 we have the premises of a syllogism in ,barbara1 which will be found to give a conclusion in ,a41 contradictory of the original minor premise2 thus3 ,baroco4 ,barbara4 ,all ,p is ,m2 ----------------- ,all ,p is ,m2 ,some ,s is not ,m3 ----- _/----- ,all ,s is ,p3 _/ contradictory _/ _/ contradictory _/ ,some ,s is not ,p ------_/ ------ ,all ,s is ,m4 ,but the original minor premise1 ,some ,s is not ,m1 is true by hypothesis2 and therefore the conclusion of ,barbara1 ,all ,s is ,m1 is false4 ,this falsity cannot1 however1 be due to the form of ,barbara1 which we know to be valid2 nor to the major premise1 which1 being taken from ,baroco1 is true by hypothesis3 it must1 therefore1 lie in the minor premise of ,barbara1 ,all ,s is ,p2 and since this is contradictory of the conclusion of ,baroco ,some ,s is not ,p1 that conclusion was true4 ,similarly1 with ,bocardo1 the ,indirect ,reduction proceeds by substituting for the major premise the contradictory of the conclusion2 thus again obtaining the premises of a syllogism in ,barbara1 whose conclusion is contradictory of the original major premise4 ,hence the initial ,b in ,baroco and ,bocardo3 it points to a syllogism in ,barbara as the means of ,indirect ,reduction 7,reductio ad impossibile74 ,any other ,mood may be reduced indirectly3 as1 for example1 ,dimaris4 ,if this is supposed to be invalid and the conclusion false1 substitute the contradictory of the conclusion for the major premise1 thus obtaining the premises of ,celarent3 ,dimaris4 ,celarent4 contradictory ,some ,p is ,m2 --------- -------- ,no ,s is ,p2 _/ _/ ,all ,m is ,s3 -----------_/--------- ,all ,m is ,s3 _/ contradictory_/ ,some ,s is ,p4 ----------- -------- ,no ,m is ,p simply converted ,no ,p is ,m ,the conclusion of ,celarent1 simply converted1 contradicts the original major premise of ,dimaris1 and is therefore false4 ,therefore the major premise of ,celarent is false1 and the conclusion of ,dimaris is true4 ,we might1 of course1 construct mnemonic names for the ,indirect ,reduction of all the ,moods3 the name of ,dimaris would then be ,cicari4 #i4 ,the need or use of any ,figure but the ,first has been much discussed by ,logicians4 ,since1 in actual debate1 arguments are rarely stated in syllogistic form1 and1 therefore1 if reduced to that form for closer scrutiny1 generally have to be treated with some freedom2 why not always throw them at once into the ,first ,figure8 ,that ,figure has manifest advantages3 it agrees directly with the ,dictum2 it gives conclusions in all four propositional forms1 and therefore serves every purpose of full affirmation or denial1 of showing agreement or difference 7total or partial71 of establishing the contradictories of universal statements2 and it is the only ,figure in which the subject and predicate of the conclusion occupy the same positions in the premises1 so that the course of argument has in its mere expression an easy and natural flow4 ,still1 the ,second ,figure also has a very natural air in some kinds of negative arguments4 ,the parallelism of the two premises1 with the middle term as predicate in both1 brings out very forcibly the necessary difference between the major and minor terms that is involved in their opposite relations to the middle term4 ,p is not1 whilst ,s is1 ,m1 says ,cesare3 that drives home the conviction that ,s is not ,p4 ,similarly in ,camestres3 ,deer do1 oxen do not1 shed their horns4 ,what is the conclusion8 ,the ,third ,figure1 again1 furnishes in ,darapti and ,felapton1 the most natural forms of stating arguments in which the middle term is singular3 ,socrates was truthful2 ,socrates was a ,greek3 ,some ,greek was truthful4 ,reducing this to ,fig ,i41 we should get for the minor premise1 ,some ,greek was ,socrates3 which is certainly inelegant4 ,still1 it might be urged that1 in relation to proof1 elegance is an extraneous consideration4 ,and as for the other advantage claimed for ,fig4 ,,iii4--that1 as it yields only particular conclusions1 it is useful in establishing contradictories against universals--for that purpose none of its ,moods can be better than ,darii or ,ferio4 ,as for ,fig4 ,,iv41 no particular advantage has been claimed for it4 ,it is of comparatively late recognition 7sometimes called the ',galenian1' after ,galen1 its supposed discoverer72 and its scientific claim to exist at all is disputed4 ,it is said to be a mere inversion of ,fig4 ,i42 which is not true in any sense in which ,figs4 ,,ii4 and ,,iii4 may not be condemned as partial inversions of ,fig4 ,i41 and as having therefore still less claim to recognition4 ,it is also said to invert the order of thought2 as if thought had only one order1 or as if the order of thought had anything to do with ,formal ,logic4 ,surely1 if distinction of ,figure be recognised at all1 the ,fourth ,figure is scientifically necessary1 because it is inevitably generated by an analysis of the possible positions of the middle term4 #aj4 ,is ,reduction necessary1 however2 or have not all the ,figures equal and independent validity8 ,in one sense not only every ,figure but each ,mood has independent validity3 for any one capable of abstract thinking sees its validity by direct inspection2 and this is true not only of the abstract ,moods1 but very frequently of particular concrete arguments4 ,but science aims at unifying knowledge2 and after reducing all possible arguments that form categorical syllogisms to the nineteen ,moods1 it is another step in the same direction to reduce these ,moods to one form4 ,this is the very nature of science3 and1 accordingly1 the efforts of some ,logicians to expound separate principles of each ,figure seem to be supererogatory4 ,grant that they succeed2 and what can the next step be1 but either to reduce these principles to the ,dictum1 or the ,dictum and the rest to one of these principles8 ,unless this can be done there is no science of ,formal ,logic4 ,if it is done1 what is gained by reducing the principles of the other ,figures to the ,dictum1 instead of the ,moods of the other ,figures to those of the first ,figure8 ,it may1 perhaps1 be said that to show 7#a7 that the ,moods of the second1 third1 and fourth ,figures flow from their own principles 7though1 in fact1 these principles are laboriously adapted to the ,moods72 and 7#b7 that these principles may be derived from the ,dictum1 is the more uncompromisingly gradual and regular method3 but is not ,formal ,logic already sufficiently encumbered with formalities8 #aa4 ,euler's diagrams are used to illustrate the syllogism1 though not very satisfactorily1 thus3 ,barbara-- ,illustration3 ,,fig4 #e4 ,celarent-- ,illustration3 ,,fig4 #f4 ,darii-- ,illustration3 ,,fig4 #g4 ,remembering that ',some' means ',it may be all1' it is plain that any one of these diagrams in ,fig4 #g1 or the one given above for ,barbara1 may represent the denotative relations of ,p1 ,m and ,s in ,darii2 though no doubt the diagram we generally think of as representing ,darii is ,no4 #a in ,fig4 #g4 ,remembering that ,a may be ,u1 and that1 therefore1 wherever ,a occurs there may be only one circle for ,s and ,p1 these syllogisms may be represented by only two circles1 and ,barbara by only one4 ,ferio-- ,illustration3 ,,fig4 #h4 ,here1 again1 probably1 we generally think of ,no4 #a as the diagram representing ,ferio2 but #b1 or #c1 or that given above for ,celarent1 is compatible with the premises4 ,if instead of dealing with ,m1 ,p1 and ,s1 a concrete example be taken of ,darii or ,ferio1 a knowledge of the facts of the case will show what diagram is suitable to it4 ,but1 then1 surely it must be possible to do without the diagram4 ,these diagrams1 of course1 can be used to illustrate ,moods of the other ,figures4 ,,chapter ,,xi ,,abbreviated ,,and ,,compound ,,arguments #a4 ,in ordinary discussion1 whether oral or written1 it is but rarely that the forms of ,logic are closely adhered to4 ,we often leave wide gaps in the structure of our arguments1 trusting the intelligence of those addressed to bridge them over2 or we invert the regular order of propositions1 beginning with the conclusion1 and mentioning the premises1 perhaps1 a good while after1 confident that the sagacity of our audience will make all smooth4 ,sometimes a full style1 like ,macaulay's1 may1 by means of amplification and illustration1 spread the elements of a single syllogism over several pages--a pennyworth of logic steeped in so much eloquence4 ,these practices give a great advantage to sophists2 who would find it very inconvenient to state explicitly in ,mood and ,figure the pretentious antilogies which they foist upon the public2 and1 indeed1 such licences of composition often prevent honest men from detecting errors into which they themselves have unwittingly fallen1 and which1 with the best intentions1 they strive to communicate to others3 but we put up with these drawbacks to avoid the inelegance and the tedium of a long discourse in accurate syllogisms4 ,many departures from the strictly logical statement of reasonings consist in the use of vague or figurative language1 or in the substitution for one another of expressions supposed to be equivalent1 though1 in fact1 dangerously discrepant4 ,against such occasions of error the logician can provide no safeguard1 except the advice to be careful and discriminating in what you say or hear4 ,but as to any derangement of the elements of an argument1 or the omission of them1 ,logic effectually aids the task of restoration2 for it has shown what the elements are that enter into the explicit statement of most ratiocinations1 namely1 the four forms of propositions and what that connected order of propositions is which most easily and surely exposes the validity or invalidity of reasoning1 namely1 the premises and conclusion of the ,syllogism4 ,logic has even gone so far as to name certain abbreviated forms of proof1 which may be regarded as general types of those that actually occur in debate1 in leading articles1 pamphlets and other persuasive or polemic writings--namely1 the ,enthymeme1 ,epicheirema and ,sorites4 #b4 ,the ,enthymeme1 according to ,aristotle1 is the ,syllogism of probable reasoning about practical affairs and matters of opinion1 in contrast with the ,syllogism of theoretical demonstration upon necessary grounds4 ,but1 as now commonly treated1 it is an argument with one of its elements omitted2 a ,categorical ,syllogism1 having one or other of its premises1 or else its conclusion1 suppressed4 ,if the major premise be suppressed1 it is called an ,enthymeme of the ,first ,order2 if the minor premise be wanting1 it is said to be of the ,second ,order2 if the conclusion be left to be understood1 there is an ,enthymeme of the ,third ,order4 ,let the following be a complete ,syllogism3 ,all free nations are enterprising2 ,the ,dutch are a free nation3 ,the ,dutch are enterprising4 ,reduced to ,enthymemes1 this argument may be put thus3 ,in the ,first ,order3 ,the ,dutch are a free nation3 ,the ,dutch are enterprising4 ,in the ,second ,order-- ,all free nations are enterprising2 ,the ,dutch are enterprising4 ,in the ,third ,order-- ,all free nations are enterprising2 ,and the ,dutch are a free nation4 ,it is certainly very common to meet with arguments whose statement may be represented by one or other of these three forms2 indeed1 the ,enthymeme is the natural substitute for a full syllogism in oratory3 whence the transition from ,aristotle's to the modern meaning of the term4 ,the most unschooled of men readily apprehend its force2 and a student of ,logic can easily supply the proposition that may be wanted in any case to complete a syllogism1 and thereby test the argument's formal validity4 ,in any ,enthymeme of the ,third ,order1 especially1 to supply the conclusion cannot present any difficulty at all2 and hence it is a favourite vehicle of innuendo1 as in ,hamilton's example3 ,every liar is a coward2 ,and ,caius is a liar4 ,the frankness of this statement and its reticence1 together1 make it a biting sarcasm upon ,caius4 ,the process of finding the missing premise in an ,enthymeme of either the ,first or the ,second ,order1 so as to constitute a syllogism1 is sometimes called ,reduction2 and for this a simple rule may be given3 ,take that term of the given premise which does not occur in the conclusion 7and which must therefore be the ,middle71 and combine it with that term of the conclusion which does not occur in the given premise2 the proposition thus formed is the premise which was requisite to complete the ,syllogism4 ,if the premise thus constituted contain the predicate of the conclusion1 the ,enthymeme was of the ,first ,order2 if it contain the subject of the conclusion1 the ,enthymeme was of the ,second ,order4 ,that a statement in the form of a ,hypothetical ,proposition may really be an ,enthymeme 7as observed in chap4 v4 #d7 can easily be shown by recasting one of the above ,enthymemes thus3 ,if all free nations are enterprising1 the ,dutch are enterprising4 ,such statements should be treated according to their true nature4 ,to reduce the argument of any ordinary discourse to logical form1 the first care should be to make it clear to oneself what exactly the conclusion is1 and to state it adequately but as succinctly as possible4 ,then look for the evidence4 ,this may be of an inductive character1 consisting of instances1 examples1 analogies2 and1 if so1 of course its cogency must be evaluated by the principles of ,induction1 which we shall presently investigate4 ,but if the evidence be deductive1 it will probably consist of an ,enthymeme1 or of several ,enthymemes one depending on another4 ,each ,enthymeme may be isolated and expanded into a syllogism4 ,and we may then inquire3 7#a7 whether the syllogisms are formally correct according to ,barbara 7or whatever the appropriate ,mood72 7#b7 whether the premises1 or the ultimate premises1 are true in fact4 #c4 ,a ,monosyllogism is a syllogism considered as standing alone or without relation to other arguments4 ,but1 of course1 a disputant may be asking to prove the premises of any syllogism2 in which case other syllogisms may be advanced for that purpose4 ,when the conclusion of one syllogism is used to prove another1 we have a chain-argument which1 stated at full length1 is a ,polysyllogism4 ,in any ,polysyllogism1 again1 a syllogism whose conclusion is used as the premise of another1 is called in relation to that other a ,prosyllogism2 whilst a syllogism one of whose premises is the conclusion of another syllogism1 is in relation to that other an ,episyllogism4 ,two modes of abbreviating a ,polysyllogism1 are usually discussed1 the ,epicheirema and the ,sorites4 #d4 ,an ,epicheirema is a syllogism for one or both of whose premises a reason is added2 as-- ,all men are mortal1 for they are animals2 ,socrates is a man1 for rational bipeds are men3 ,socrates is mortal4 ,the ,epicheirema is called ,single or ,double1 says ,hamilton1 according as an adscititious proposition attaches to one or both of the premises4 ,the above example is of the double kind4 ,the ,single ,epicheirema is said to be of the ,first ,order1 if the adscititious proposition attach to the major premise2 if to the minor1 of the ,second ,order4 7,hamilton's ,logic3 ,lecture xix47 ,an ,epicheirema1 then1 is an abbreviated chain of reasoning1 or ,polysyllogism1 comprising an ,episyllogism with one or two enthymematic ,prosyllogisms4 ,the major premise in the above case1 ,all men are mortal1 for they are animals1 is an ,enthymeme of the ,first ,order1 suppressing its own major premise1 and may be restored thus3 ,all animals are mortal2 ,all men are animals3 ,all men are mortal4 ,the minor premise1 ,socrates is a man1 for rational bipeds are men1 is an ,enthymeme of the ,second ,order1 suppressing its own minor premise1 and may be restored thus3 ,all rational bipeds are men2 ,socrates is a rational biped3 ,socrates is a man4 #e4 ,the ,sorites is a ,polysyllogism in which the ,conclusions1 and even some of the ,premises1 are suppressed until the arguments end4 ,if the chain of arguments were freed of its enthymematic character1 the suppressed conclusions would appear as premises of ,episyllogisms4 ,two varieties of ,sorites are recognised1 the ,aristotelian 7so called1 though not treated of by ,aristotle71 and the ,goclenian 7named after its discoverer1 ,goclenius of ,marburg1 who flourished about #afjj ,a4,d474 ,in order to compare these two forms of argument1 it will be convenient to place side by side ,hamilton's classical examples of them4 ,aristotelian4 ,goclenian4 ,bucephalus is a horse2 ,an animal is a substance2 ,a horse is a quadruped2 ,a quadruped is an animal2 ,a quadruped is an animal2 ,a horse is a quadruped2 ,an animal is a substance3 ,bucephalus is a horse3 ,bucephalus is a substance4 ,bucephalus is a substance4 ,the reader wonders what is the difference between these two forms4 ,in the ,aristotelian ,sorites the minor term occurs in the first premise1 and the major term in the last2 whilst in the ,goclenian the major term occurs in the first premise1 and the minor in the last4 ,but since the character of premises is fixed by their terms1 not by the order in which they are written1 there cannot be a better example of a distinction without a difference4 ,at a first glance1 indeed1 there may seem to be a more important point involved2 the premises of the ,aristotelian ,sorites seem to proceed in the order of ,fig4 ,,iv4 ,but if that were really so the conclusion would be1 ,some ,substance is ,bucephalus4 ,that1 on the contrary1 every one writes the conclusion1 ,bucephalus is a substance1 proves that the logical order of the premises is in ,fig4 ,i4 ,logically1 therefore1 there is absolutely no difference between these two forms1 and pure reason requires either that the ,aristotelian ,sorites disappear from the text-books1 or that it be regarded as in ,fig4 ,,iv41 and its conclusion converted4 ,it is the shining merit of ,goclenius to have restored the premises of the ,sorites to the usual order of ,fig4 ,i43 whereby he has raised to himself a monument more durable than brass1 and secured indeed the very cheapest immortality4 ,the common ,sorites1 then1 being in ,fig4 ,i41 its rules follow from those of ,fig4 ,i3 7#a7 ,only one premise can be particular2 and1 if any1 only that in which the minor term occurs4 ,for1 just as in ,fig ,i41 a particular premise anywhere else involves undistributed ,middle4 7#b7 ,only one premise can be negative2 and1 if any1 only that in which the major term occurs4 ,for if there were two negative premises1 at the point where the second entered the chain of argument there must be a syllogism with two negative premises1 which is contrary to ,rule #e2 whilst if one premise be negative it must be that which contains the major term1 for the same reason as in ,fig4 ,i41 namely1 that the conclusion will be negative1 and that therefore only a negative major premise can prevent illicit process of the major term4 ,if we expand a ,sorites into its constituent syllogisms1 the conclusions successively suppressed will reappear as major premises2 thus3 7#a7 ,an animal is a substance2 ,a quadruped is an animal3 ,a quadruped is a substance4 7#b7 ,a quadruped is a substance2 ,a horse is a quadruped3 ,a horse is a substance4 7#c7 ,a horse is a substance3 ,bucephalus is a horse3 ,bucephalus is a substance4 ,this suffices to show that the ,protosyllogism of a ,goclenian ,sorites is an ,enthymeme of the ,third ,order2 after which the argument is a chain of ,enthymemes of the ,first ,order1 or of the ,first and ,third combined1 since the conclusions as well as the major premises are omitted1 except in the last one4 ,lest it should be thought that the ,sorites is only good for arguments so frivolous as the above1 ,i subjoin an example collected from various parts of ,mill's ,political ,economy3-- ,the cost of labour depends on the efficiency of labour2 ,the rate of profits depends on the cost of labour2 ,the investment of capital depends on the rate of profits2 ,wages depend on the investment of capital3 ,wages depend on the efficiency of labour4 ,had it occurred to ,mill to construct this ,sorites1 he would have modified his doctrine of the wages-fund1 and would have spared many critics the malignant joy of refuting him4 #f4 ,the ,antinomy is a combination of arguments by which contradictory attributes are proved to be predicable of the same subject4 ,in symbols1 thus3 ,all ,m is ,p2 ,all ,n is p2 ,all ,s is ,m3 ,all ,s is ,n3 ,all ,s is ,p4 ,all ,s is p4 ,now1 by the principle of ,contradiction1 ,s cannot be ,p and p 7not-,p73 therefore1 if both of the above syllogisms are sound1 ,s1 as the subject of contradictory attributes1 is logically an impossible thing4 ,the contradictory conclusions are called1 respectively1 ,thesis and ,antithesis4 ,to come to particulars1 we may argue3 7#a7 that a constitution which is at once a monarchy1 an aristocracy and a democracy1 must comprise the best elements of all three forms2 and must1 therefore1 be the best of all forms of government3 the ,british ,constitution is1 therefore1 the best of all4 ,but 7#b7 such a constitution must also comprise the worst elements of monarchy1 aristocracy and democracy2 and1 therefore1 must be the worst of all forms4 ,are we1 then1 driven to conclude that the ,british ,constitution1 thus proved to be both the best and worst1 does not really exist at all1 being logically impossible8 ,the proofs seem equally cogent2 but perhaps neither the best nor the worst elements of the simpler constitutions need be present in our own in sufficient force to make it either good or bad4 ,again3 7#a7 ,every being who is responsible for his actions is free2 ,man is responsible for his actions3 ,man is free4 7#b7 ,every being whose actions enter into the course of nature is not free2 ,man is such a being3 ,man is not free4 ,does it1 then1 follow that ',man1' as the subject of contradictory attributes1 is a nonentity8 ,this doctrine1 or something like it1 has been seriously entertained2 but if to any reader it seem extravagant 7as it certainly does to me71 he will no doubt find an error in the above arguments4 ,perhaps the major term is ambiguous4 ,for other examples it is enough to refer to the ,critique of ,pure ,reason1 where ,kant sets out the ,antinomies of ,rational ,cosmology4 ,but even if we do not agree with ,kant that the human understanding1 in attempting to deal with certain subjects beyond its reach1 inevitably falls into such contradictory reasonings2 yet it can hardly be doubted that we not unfrequently hold opinions which1 if logically developed1 result in ,antinomies4 ,and1 accordingly1 the ,antinomy1 if it cannot be imputed to ,reason herself1 may be a very fair1 and a very wholesome argumentum ad hominem4 ,it was the favourite weapon of the ,pyrrhonists against the dogmatic philosophies that flourished after the death of ,aristotle4 ,,chapter ,,xii ,,conditional ,,syllogisms #a4 ,conditional ,syllogisms may be generally described as those that contain conditional propositions4 ,they are usually divided into two classes1 ,hypothetical and ,disjunctive4 ,a ,hypothetical ,syllogism is one that consists of a ,hypothetical ,major ,premise1 a ,categorical ,minor ,premise1 and a ,categorical ,conclusion4 ,two ,moods are usually recognised the ,modus ponens1 in which the antecedent of the hypothetical major premise is affirmed2 and the ,modus tollens sic1 in which its consequent is denied4 7#a7 ,modus ponens1 or ,constructive4 ,if ,a is ,b1 ,c is ,d2 ,a is ,b3 ,c is ,d4 ,if ,aristotle's reasoning is conclusive1 ,plato's theory of ,ideas is erroneous2 ,aristotle's reasoning is conclusive3 ,plato's theory of ,ideas is erroneous4 ,rule of the ,modus ponens3 ,the antecedent of the major premise being affirmed in the minor premise1 the consequent is also affirmed in the conclusion4 7#b7 ,modus tollens1 or ,destructive4 ,if ,a is ,b1 ,c is ,d2 ,c is not ,d3 ,a is not ,b4 ,if ,pythagoras is to be trusted1 ,justice is a number2 ,justice is not a number3 ,pythagoras is not to be trusted4 ,rule of the ,modus tollens3 ,the consequent of the major premise being denied in the minor premise1 the antecedent is denied in the conclusion4 ,by using negative major premises two other forms are obtainable3 then1 either by affirming the antecedent or by denying the consequent1 we draw a negative conclusion4 ,thus 7,modus ponens73 7,modus tollens73 ,if ,a is ,b1 ,c is not ,d2 ,if ,a is ,b1 ,c is not ,d2 ,a is ,b3 ,c is ,d3 ,c is not ,d4 ,a is not ,b4 ,further1 since the antecedent of the major premise1 taken by itself1 may be negative1 it seems possible to obtain four more forms1 two in each ,mood1 from the following major premises3 7#a7 ,if ,a is not ,b1 ,c is ,d2 7#b7 ,if ,a is not ,b1 ,c is not ,d4 ,but since the quality of a ,hypothetical ,proposition is determined by the quality of its consequent1 not at all by the quality of its antecedent1 we cannot get from these two major premises any really new ,moods1 that is to say1 ,moods exhibiting any formal difference from the four previously expounded4 ,it is obvious that1 given the hypothetical major premise-- ,if ,a is ,b1 ,c is ,d-- we cannot1 by denying the antecedent1 infer a denial of the consequent4 ,that ,a is ,b1 is a mark of ,c being ,d2 but we are not told that it is the sole and indispensable condition of it4 ,if men read good books1 they acquire knowledge2 but they may acquire knowledge by other means1 as by observation4 ,for the same reason1 we cannot by affirming the consequent infer the affirmation of the antecedent3 ,caius may have acquired knowledge2 but we cannot thence conclude that he has read good books4 ,to see this in another light1 let us recall chap4 v4 #d1 where it was shown that a hypothetical proposition may be translated into a categorical one2 whence it follows that a ,hypothetical ,syllogism may be translated into a ,categorical ,syllogism4 ,treating the above examples thus1 we find that the ,modus ponens 7with affirmative major premise7 takes the form of ,barbara1 and the ,modus tollens the form of ,camestres3 ,modus ponens4 ,barbara4 ,if ,a is ,b1 ,c is ,d2 ,the case of ,a being ,b is a case of ,c being ,d2 ,a is ,b3 ,this is a case of ,a being ,b3 ,c is ,d4 ,this is a case of ,c being ,d4 ,now if1 instead of this1 we affirm the consequent1 to form the new minor premise1 ,this is a case of ,c being ,d1 there will be a ,syllogism in the ,second ,figure with two affirmative premises1 and therefore the fallacy of undistributed ,middle4 ,again3 ,modus tollens4 ,camestres4 ,if ,a is ,b1 ,c is ,d2 ,the case of ,a being ,b is a case of ,c being ,d3 ,c is not ,d3 ,this is not a case of ,c being ,d3 ,a is not ,b4 ,this is not a case of ,a being ,b4 ,but if1 instead of this1 we deny the antecedent1 to form the new minor premise1 ,this is not a case of ,a being ,b1 there arises a syllogism in the ,first ,figure with a negative minor premise1 and therefore the fallacy of illicit process of the major term4 ,by thus reducing the ,hypothetical ,syllogism to the ,categorical form1 what is lost in elegance is gained in intelligibility4 ,for1 first1 we may justify ourselves in speaking of the hypothetical premise as the major1 and of the categorical premise as the minor2 since in the categorical form they contain respectively the major and minor terms4 ,and1 secondly1 we may justify ourselves in treating the ,hypothetical ,syllogism as a kind of ,mediate ,inference1 in spite of the fact that it does not exhibit two terms compared by means of a third2 since in the ,categorical form such terms distinctly appear3 a new term 7',this'7 emerges in the position of the minor2 the place of the ,middle is filled by the antecedent of the major premise in the ,modus ponens1 and by the consequent in the ,modus tollens4 ,the mediate element of the inference in a ,hypothetical ,syllogism consists in asserting1 or denying1 the fulfilment of a given condition2 just as in a ,categorical syllogism to identify the minor term with the ,middle is a condition of the major term's being predicated of it4 ,in the hypothetical proposition-- ,if ,a is ,b1 ,c is ,d-- the ,antecedent1 ,a is ,b1 is the conditio sufficiens1 or mark1 of the ,consequent1 ,c is ,d2 and therefore the ,consequent1 ,c is ,d1 is a conditio sine qua non of the antecedent1 ,a is ,b2 and it is by means of affirming the former condition1 or else denying the latter1 that a conclusion is rendered possible4 ,indeed1 we need not say that the element of mediation consists in affirming1 or denying1 the fulfilment of a given condition3 it is enough to say 'in affirming4' ,for thus to explain the ,modus tollens1 reduce it to the ,modus ponens 7contrapositing the major premise and obverting the minor73 ,celarent4 ,if ,a is ,b1 ,c is ,d3 ,the case of ,c being not-,d is ,if ,c is not-,d1 ,a is not ,b2 not a case of ,a being ,b2 ,c is not-,d3 ,this is a case of ,c being ,a is not ,b4 not-,d3 ,this is not a case of ,a being ,b4 ,the above four forms commonly treated of as ,hypothetical ,syllogisms1 are called by ,ueberweg and ,dr4 ,keynes ',hypothetico-,categorical4' ,ueberweg restricts the name ',hypothetical' simply 7and ,dr4 ,keynes the name ',conditional'7 to such ,syllogisms as the following1 having two ,hypothetical ,premises3 ,if ,c is ,d1 ,e is ,f2 ,if ,a is ,b1 ,c is ,d3 ,if ,a is ,b1 ,e is ,f4 ,if we recognise particular hypothetical propositions 7see chap4 v4 #d71 it is obvious that such ,syllogisms may be constructed in all the ,moods and ,figures of the ,categorical ,syllogism2 and of course they may be translated into ,categoricals4 ,we often reason in this hypothetical way4 ,for example3 ,if the margin of cultivation be extended1 rents will rise2 ,if prices of produce rise1 the margin of cultivation will be extended3 ,if prices of produce rise1 rents will rise4 ,but the function of the ,hypothetical ,syllogism 7commonly so called71 as also of the ,disjunctive ,syllogism 7to be discussed in the next section7 is to get rid of the conditional element of the premises1 to pass from suspense to certainty1 and obtain a decisive categorical conclusion2 whereas these ,syllogisms with two hypothetical premises leave us still with a hypothetical conclusion4 ,this circumstance seems to ally them more closely with ,categorical ,syllogisms than with those that are discussed in the present chapter4 ,that they are ,categoricals in disguise may be seen by considering that the above syllogism is not materially significant1 unless in each proposition the word ',if' is equivalent to ',whenever4' ,accordingly1 the name ',hypothetical ,syllogism1' is here employed in the older usage4 #b4 ,a ,disjunctive ,syllogism consists of a ,disjunctive ,major ,premise1 a ,categorical ,minor ,premise1 and a ,categorical ,conclusion4 ,how many ,moods are to be recognised in this kind of argument depends on whether the alternatives of the ,disjunctive ,premise are regarded as mutually exclusive or possibly coincident4 ,in saying ',either ,a is ,b1 or ,c is ,d1' do we mean 'either1 but not both1' or 'either1 it may be both'8 7,see chap4 v4 #d47 ,when the alternatives of the ,disjunctive are not exclusive1 we have only the ,modus tollendo ponens4 ,either ,a is ,b1 or ,c is ,d2 ,a is not ,b 7or ,c is not ,d73 ,c is ,d 7or ,a is ,b74 ,either wages fall1 or the weaker hands are dismissed2 ,wages do not fall3 ,the weaker hands are dismissed4 ,but we cannot argue-- ,wages fall3 ,the weaker hands are not dismissed2 since in 'hard times' both events may happen together4 ,rule of the ,modus tollendo ponens3 ,if one alternative be denied1 the other is affirmed4 ,when1 however1 the alternatives of the ,disjunctive are mutually exclusive1 we have also the ,modus ponendo tollens4 ,either ,a is ,b1 or ,c is ,d2 ,a is ,b 7or ,c is ,d73 ,c is not ,d 7or ,a is not ,b74 ,either the ,tories or the ,whigs win the election2 ,the ,tories win3 ,the ,whigs do not win4 ,we may also1 of course1 argue as above in the ,modus tollendo ponens-- ,the ,tories do not win3 ,the ,whigs do4 ,but in this example1 to make the ,modus tollendo ponens materially valid1 it must be impossible that the election should result in a tie4 ,the danger of the ,disjunctive ,proposition is that the alternatives may not1 between them1 exhaust the possible cases4 ,only contradictory alternatives are sure to cover the whole ground4 ,rule of the ,modus ponendo tollens3 ,if one alternative be affirmed1 the other is denied4 ,since a disjunctive proposition may be turned into a hypothetical proposition 7chap4 v4 #d17 a ,disjunctive ,syllogism may be turned into a ,hypothetical ,syllogism3 ,modus tollendo ponens4 ,modus ponens4 ,either ,a is ,b1 or ,c is ,d2 ,if ,a is not ,b1 ,c is ,d2 ,a is not ,b3 ,a is not ,b3 ,c is ,d4 ,c is ,d4 ,similarly the ,modus ponendo tollens is equivalent to that kind of ,modus ponens which may be formed with a negative major premise2 for if the alternatives of a disjunctive proposition be exclusive1 the corresponding hypothetical be affirmative or negative3 ,modus ponendo tollens4 ,modus ponens4 ,either ,a is ,b1 or ,c is ,d2 ,if ,a is ,b1 ,c is not ,d2 ,a is ,b3 ,a is ,b3 ,c is not ,d4 ,c is not ,d4 ,hence1 finally1 a ,disjunctive ,syllogism being equivalent to a ,hypothetical1 and a ,hypothetical to a ,categorical2 a ,disjunctive ,syllogism is equivalent and reducible to a ,categorical4 ,it is a form of ,mediate ,inference in the same sense as the ,hypothetical ,syllogism is2 that is to say1 the conclusion depends upon an affirmation1 or denial1 of the fulfilment of a condition implied in the disjunctive major premise4 #c4 ,the ,dilemma is perhaps the most popularly interesting of all forms of proof4 ,it is a favourite weapon of orators and wits2 and impaled upon the horns of a dilemma is a painful situation in which every one delights to see his adversary4 ,it seems to have been described by ,rhetoricians before finding its way into works on ,logic2 and ,logicians1 to judge from their diverse ways of defining it1 have found some difficulty in making up their minds as to its exact character4 ,there is a famous ,dilemma employed by ,demosthenes1 from which the general nature of the argument may be gathered3 ,if schines joined in the public rejoicings1 he is inconsistent2 if he did not1 he is unpatriotic2 ,but either he joined1 or he did not join3 ,therefore he is either inconsistent or unpatriotic4 ,that is1 reduced to symbols3 ,if ,a is ,b1 ,c is ,d2 and if ,e is ,f1 ,g is ,h3 ,but either ,a is ,b1 or ,e is ,f2 ,either ,c is ,d or ,g is ,h 7,complex ,constructive74 ,this is a compound ,conditional ,syllogism1 which may be analysed as follows3 ,either ,a is ,b or ,e is ,f4 ,suppose that ,e is not ,f3 ,suppose that ,a is not ,b3 ,then ,a is ,b4 ,then ,e is ,f4 ,but if ,a is ,b1 ,c is ,d2 ,but if ,e is ,f1 ,g is ,h2 7,a is ,b73 7,e is ,f73 ,c is ,d4 ,g is ,h4 ,either ,c is ,d or ,g is ,h4 ,a ,dilemma1 then1 is a compound ,conditional ,syllogism1 having for its ,major ,premise two ,hypothetical ,propositions1 and for its ,minor ,premise a ,disjunctive ,proposition1 whose alternative terms either affirm the ,antecedents or deny the ,consequents of the two ,hypothetical ,propositions forming the ,major ,premise4 ,the hypothetical propositions in the major premise1 may have all four terms distinct 7as in the above example72 and then the conclusion is a disjunctive proposition1 and the ,dilemma is said to be ,complex4 ,or the two hypothetical propositions may have a common antecedent or a common consequent2 and then the conclusion is a categorical proposition1 and the ,dilemma is said to be ,simple4 ,again1 the alternatives of the disjunctive minor premise may be affirmative or negative3 if affirmative1 the ,dilemma is called ,constructive2 and if negative1 ,destructive4 ,using1 then1 only affirmative hypothetical propositions in the major premise1 there are four ,moods3 #a4 ,the ,simple ,constructive-- ,if ,a is ,b1 ,c is ,d2 and if ,e is ,f1 ,c is ,d3 ,but either ,a is ,b1 or ,e is ,f3 ,c is ,d4 ,if the ,tories win the election1 the ,government will avoid innovation2 and if the ,whigs win1 the ,house of ,lords will prevent them innovating3 ,but either the ,tories or the ,whigs will win3 ,there will be no innovation4 #b4 ,the ,complex ,constructive-- ,if ,a is ,b1 ,c is ,d2 and if ,e is ,f1 ,g is ,h3 ,but either ,a is ,b1 or ,e is ,f3 ,either ,c is ,d or ,g is ,h4 ,if appearance is all that exists1 reality is a delusion2 and if there is a substance beyond consciousness1 knowledge of reality is impossible3 ,but either appearance is all1 or there is a substance beyond consciousness3 ,either reality is a delusion1 or a knowledge of it is impossible4 #c4 ,simple ,destructive-- ,if ,a is ,b1 ,c is ,d2 and if ,a is ,b1 ,e is ,f3 ,but either ,c is not ,d1 or ,e is not ,f3 ,a is not ,b4 ,if table-rappers are to be trusted1 the departed are spirits2 and they also exert mechanical energy3 ,but either the departed are not spirits1 or they do not exert mechanical energy3 ,table-rappers are not to be trusted4 #d4 ,complex ,destructive-- ,if ,a is ,b1 ,c is ,d2 and if ,e is ,f1 ,g is ,h3 ,but either ,c is not ,d1 or ,g is not ,h3 ,either ,a is not ,b1 or ,e is not ,f4 ,if poetic justice is observed1 virtue is rewarded2 and if the mirror is held up to ,nature1 the villain triumphs3 ,but either virtue is not rewarded1 or the villain does not triumph3 ,either poetic justice is not observed1 or the mirror is not held up to ,nature4 ,such are the four ,moods of the ,dilemma that emerge if we only use affirmative hypotheticals for the major premise2 but1 certainly1 it is often quite as natural to employ two negative hypotheticals 7indeed1 one might be affirmative and the other negative2 but waive that72 and then four more moods emerge1 all having negative conclusions4 ,it is needless to intimidate the reader by drawing up these four moods in battle array3 they always admit of reduction to the foregoing moods by obverting the hypotheticals4 ,still1 by the same process we may greatly decrease the number of moods of the ,categorical ,syllogism2 and just as some ,syllogisms are most simply expressed in ,celarent or ,cesare1 so some ,dilemmas are most simply stated with negative major premises--e4g41 ,the example of a ,simple ,constructive ,dilemma above given would run more naturally thus3 ,if the ,tories win1 the ,government will not innovate2 and if the ,whigs1 the ,lords will not let them3 and similarly ,demosthenes' ,dilemma--,if schines joined1 he is not consistent2 and if he did not1 he is not patriotic4 ,moreover1 the propriety of recognising ,dilemmas with negative major premises1 follows from the above analysis of the ,dilemma into a combination of ,conditional ,syllogisms1 even if 7as in #a of this chapter7 we take account of only four ,moods of the ,hypothetical ,syllogism4 ,in the rhetorical use of the ,dilemma1 it may be observed that the disjunction in the minor premise ought to be obvious1 or 7at any rate7 easily acceptable to the audience4 ,thus1 ,either the ,tories or the ,whigs will win2 ,either schines joined in the rejoicings1 or he did not2 such propositions are not likely to be disputed4 ,but if the orator must stop to prove his minor premise1 the smacking effect of this figure 7if the expression be allowed7 will be lost4 ,hence the minor premises of other examples given above are only fit for a select audience4 ,that ,either ghosts are not spirits1 or they do not exert mechanical energy1 supposes a knowledge of the principle1 generally taught by physical philosophers1 that only matter is the vehicle of energy2 and that ,either appearance is all1 or there is substance beyond consciousness1 is a doctrine which only metaphysical philosophers could be expected to understand1 and upon which they could not be expected to agree4 ,however1 the chief danger is that a plausible disjunction may not be really such as to exclude any middle ground3 ,either the ,tories or the ,whigs win1 is bad1 if a tie be possible2 though in the above argument this is negligible1 seeing that a tie cannot directly cause innovations4 ,either schines joined in the rejoicings1 or he did not1 does not allow for a decent conformity with the public movement where resistance would be vain2 yet such conformity as need not be inconsistent with subsequent condemnation of the proceedings1 nor incompatible with patriotic reserve founded on a belief that the rejoicings are premature and ominous4 ,another rhetorical consideration is1 that the alternatives of the disjunctive conclusion of a ,complex ,dilemma should both point the same way1 should be equally distasteful or paradoxical4 ',either inconsistent or unpatriotic'3 horrid words to a politician6 ',either no reality or no possible knowledge of it'3 very disappointing to an anxious inquirer6 ,thus the disjunctive conclusion is as bad for an opponent as the categorical one in a ,simple ,dilemma4 ,logicians further speak of the ,trilemma1 with three ,hypotheticals and a corresponding triple ,disjunction2 and of a ,polylemma1 with any further number of perplexities4 ,but anyone who has a taste for logical forms may have it amply gratified in numerous text-books4 ,,chapter ,,xiii ,,transition ,,to ,,induction #a4 ,having now discussed ,terms1 ,propositions1 ,immediate and ,mediate ,inferences1 and investigated the conditions of formal truth or consistency1 we have next to consider the conditions of material truth3 whether 7or how far7 it is possible to arrive at propositions that accurately represent the course of nature or of human life4 ,hitherto we have dealt with no sort of proof that gives any such assurance4 ,a valid syllogism guarantees the truth of its conclusion1 provided the premises be true3 but what of the premises8 ,the relation between the premises of a valid syllogism and its conclusion is the same as the relation between the antecedent and consequent of a hypothetical proposition4 ,if ,a is ,b1 ,c is ,d3 grant that ,a is ,b1 and it follows that ,c is ,d2 and1 similarly1 grant the premises of a syllogism1 and the conclusion follows4 ,again1 grant that ,c is not ,d1 and it follows that ,a is not ,b2 and1 similarly1 if the conclusion of a valid syllogism be false1 it follows that one1 or other1 or both of the premises must be false4 ,but1 once more1 grant that ,c is ,d1 and it does not follow that ,a is ,b2 so neither1 if the conclusion of a syllogism be true1 does it follow that the premises are4 ,for example3-- ,sociology is an exact science2 ,mathematics is a branch of ,sociology3 ,mathematics is an exact science4 ,here the conclusion is true although the premises are absurd4 ,or again3-- ,mathematics is an exact science2 ,sociology is a branch of ,mathematics3 ,sociology is an exact science4 ,here the major premise is true1 but the minor is false1 and the conclusion is false4 ,in both cases1 however1 whether the conclusion be true or false1 it equally follows from the premises1 if there is any cogency in ,barbara4 ,the explanation of this is1 that ,barbara has only formal cogency2 and that whether the conclusion of that1 or any other valid mood1 shall be true according to fact and experience1 depends upon how the form is filled up4 ,how to establish the premises1 then1 is a most important problem2 and it still remains to be solved4 #b4 ,we may begin by recalling the distinction between the denotation and connotation of a general term3 the denotation comprising the things or events which the term is a name for2 the connotation comprising the common qualities on account of which these things are called by the same name4 ,obviously1 there are very few general terms whose denotation is exhaustively known2 since the denotation of a general term comprises all the things that have its connotation1 or that ever have had1 or that ever will have it1 whether they exist here1 or in ,australia1 or in the ,moon1 or in the utmost stars4 ,no one has examined all men1 all mammoths1 all crystals1 all falling bodies1 all cases of fever1 all revolutions1 all stars--nor even all planets1 since from time to time new ones are discerned4 ,we have names for animals that existed long before there were men to observe them1 and of which we know only a few bones1 the remains of multitudinous species2 and for others that may continue to exist when men have disappeared from the earth4 ,if1 indeed1 we definitely limit the time1 or place1 or quantity of matter to be explored1 we may sometimes learn1 within the given limits1 all that there is to know3 as all the bones of a particular animal1 or the list of ,english monarchs hitherto1 or the names of all the members of the ,house of ,commons at the present time4 ,such cases1 however1 do not invalidate the above logical truth that few general terms are exhaustively known in their denotation2 for the very fact of assigning limits of time and place impairs the generality of a term4 ,the bones of a certain animal may be all examined1 but not the bones of all animals1 nor even of one species4 ,the ,english monarchs that have reigned hitherto may be known1 but there may be many still to reign4 ,the general terms1 then1 with which ,logic is chiefly concerned1 the names of ,causes and ,kinds1 such as gravitation1 diseases1 social events1 minerals1 plants and animals1 stand for some facts that are1 or have been1 known1 and for a great many other similar ones that have not been1 and never will be1 known4 ,the use of a general term depends not upon our direct knowledge of everything comprised in its denotation1 but upon our readiness to apply it to anything that has its connotation1 whether we have seen the thing or not1 and even though we never can perceive it2 as when a man talks freely of the ichthyosaurus1 or of the central heat of planets1 or of atoms and ether4 ,hence ,universal ,propositions1 which consist of general terms1 deceive us1 if we suppose that their predicates are directly known to be related to all the facts denoted by their subjects4 ,in exceptional cases1 in which the denotation of a subject is intentionally limited1 such exhaustive direct knowledge may be possible2 as that all the bones of a certain animal consist of phosphate of lime1 or that every member of the present ,parliament wears a silk hat4 ,but what predication is possible concerning the hats of all members of ,parliament from the beginning8 ,ordinarily1 then1 whilst the relation of predicate to subject has been observed in some cases1 in much the greater number of cases our belief about it depends upon something besides observation1 or may be said 7in a certain sense7 to be taken on trust4 ',all rabbits are herbivorous'3 why do we believe that8 ,we may have seen a few wild rabbits feeding3 or have kept tame ones1 and tried experiments with their diet2 or have read of their habits in a book of ,natural ,history2 or have studied the anatomy and physiology of the digestive system in many sorts of animals3 but with whatever care we add testimony and scientific method to our own observation1 it still remains true that the rabbits observed by ourselves and others are few in comparison with those that live1 have lived and will live4 ,similarly of any other universal proposition2 that it 'goes beyond the evidence' of direct observation plainly follows from the fact that the general terms1 of which such propositions consist1 are never exhaustively known in their denotation4 ,what right have we then to state ,universal ,propositions8 ,that is the problem of ,inductive ,logic4 #c4 ,universal ,propositions1 of course1 cannot always be proved by syllogisms2 because to prove a universal proposition by a syllogism1 its premises must be universal propositions2 and1 then1 these must be proved by others4 ,this process may sometimes go a little way1 thus3 ,all men are mortal1 because ,all animals are2 and ,all animals are mortal1 because ,all composite bodies are subject to dissolution4 ,were there no limit to such sorites1 proof would always involve a regressus ad infinitum1 for which life is too short2 but1 in fact1 prosyllogisms soon fail us4 ,clearly1 the form of the ,syllogism must itself be misleading if the universal proposition is so3 if we think that premises prove the conclusion because they themselves have been established by detailed observation1 we are mistaken4 ,the consideration of any example will show this4 ,suppose any one to argue3 ,all ruminants are herbivorous2 ,camels are ruminants3 ,camels are herbivorous4 ,have we1 then1 examined all ruminants8 ,if so1 we must have examined all camels1 and cannot need a syllogism to prove their herbivorous nature3 instead of the major premise proving the conclusion1 the proof of the conclusion must then be part of the proof of the major premise4 ,but if we have not examined all ruminants1 having omitted most giraffes1 most deer1 most oxen1 etc41 how do we know that the unexamined 7say1 some camels7 are not exceptional8 ,camels are vicious enough to be carnivorous2 and indeed it is said that ,bactrian camels will eat flesh rather than starve1 though of course their habit is herbivorous4 ,or1 again1 it is sometimes urged that-- ,all empires decay3 ,britain will decay4 ,this is manifestly a prediction3 at present ,britain flourishes1 and shows no signs of decay4 ,yet a knowledge of its decay seems necessary1 to justify any one in asserting the given premise4 ,if it is a question whether ,britain will decay1 to attempt 7while several empires still flourish7 to settle the matter by asserting that all empires decay1 seems to be 'a begging of the question4' ,but although this latter case is a manifest prediction1 it does not really differ from the former one2 for the proof that camels are herbivorous has no limits in time4 ,if valid1 it shows not only that they are1 but also that they will be1 herbivorous4 ,hence1 to resort to a dilemma1 it may be urged3 ,if all the facts of the major premise of any syllogism have been examined1 the syllogism is needless2 and if some of them have not been examined1 it is a petitio principii4 ,but either all have been examined1 or some have not4 ,therefore2 the syllogism is either useless or fallacious4 #d4 ,a way of escape from this dilemma is provided by distinguishing between the formal and material aspects of the syllogism considered as a means of proof4 ,it begs the question formally1 but not materially2 that is to say1 if it be a question whether camels are herbivorous1 and to decide it we are told that 'all ruminants are1' laying stress upon the 'all1' as if all had been examined1 though in fact camels have not been1 then the question as to camels is begged4 ,the form of a universal proposition is then offered as evidence1 when in fact the evidence has not been universally ascertained4 ,but if in urging that 'all ruminants are herbivorous' no more is meant than that so many other ruminants of different species are known to be herbivorous1 and that the ruminant stomach is so well adapted to a coarse vegetable diet1 that the same habit may be expected in other ruminants1 such as camels1 the argument then rests upon material evidence without unfairly implying the case in question4 ,now the nature of the material evidence is plainly this1 that the resemblance of camels to deer1 oxen1 etc41 in chewing the cud1 justifies us in believing that they have a further resemblance in feeding on herbs2 in other words1 we assume that resemblance is a ground of inference4 ,another way of putting this difficulty which we have just been discussing1 with regard to syllogistic evidence1 is to urge that by the ,laws of ,syllogism a conclusion must never go beyond the premises1 and that therefore no progress in knowledge can ever be established1 except by direct observation4 ,now1 taking the syllogism formally1 this is true3 if the conclusion go beyond the premises1 there must be either four terms1 or illicit process of the major or minor term4 ,but1 taking it materially1 the conclusion may cover facts which were not in view when the major premise was laid down2 facts of which we predicate something not as the result of direct observation1 but because they resemble in a certain way those facts which had been shown to carry the predicate when the major premise was formed4 ',what sort of resemblance is a sufficient ground of inference8' is1 therefore1 the important question alike in material ,deduction and in ,induction2 and in endeavouring to answer it we shall find that the surest ground of inference is resemblance of causation4 ,for example1 it is due to causation that ruminants are herbivorous4 ,their instincts make them crop the herb1 and their stomachs enable them easily to digest it2 and in these characters camels are like the other ruminants4 #e4 ,in ch4 ix1 #c1 the ,dictum de omni et nullo was stated3 ',whatever may be predicated of a term distributed may be predicated of anything that can be identified with that term4' ,nothing was there said 7as nothing was needed7 of the relations that might be implied in the predication4 ,but now that it comes to the ultimate validity of predication1 we must be clear as to what these relations are2 and it will also be convenient to speak no longer of terms1 as in ,formal ,logic1 but of the things denoted4 ,what relations1 then1 can be determined between concrete facts or phenomena 7physical or mental7 with the greatest certainty of general truth2 and what axioms are there that sanction mediate inferences concerning those relations8 ,in his ,logic 7,b4 ,,ii4 c4 #b1 #c7 ,mill gives as the axiom of syllogistic reasoning1 instead of the ,dictum3 ,a thing which co-exists with another thing1 which other co-exists with a third thing1 also co-exists with that third thing4 ,thus the peculiar properties of ,socrates co-exist with the attributes of man1 which co-exist with mortality3 therefore1 ,socrates is mortal4 ,but1 again1 he says that the ground of the syllogism is ,induction2 that man is mortal is an induction4 ,and1 further1 the ground of ,induction is causation2 the law of causation is the ultimate major premise of every sound induction4 ,now causation is the principle of the succession of phenomena3 how1 then1 can the syllogism rest on an axiom concerning co-existence8 ,on reflection1 too1 it must appear that ',man is mortal' predicates causation3 the human constitution issues in death4 ,the explanation of this inconsistency may perhaps be found in the history of ,mill's work4 ,books ,i4 and ,,ii4 were written in #ahca2 but being unable at that time to explain ,induction1 he did not write ,book ,,iii4 until #ahcg-h4 ,then1 no doubt1 he revised the earlier ,books1 but not enough to bring his theory of the syllogism into complete agreement with the theory of ,induction2 so that the axiom of co-existence was allowed to stand4 ,mill also introduced the doctrine of ,natural ,kinds as a ground of ,induction supplementary1 at least provisionally1 to causation2 and to reasoning about ,kinds1 or ,substance and ,attribute1 his axiom of co-existence is really adapted4 ,kinds are groups of things that agree amongst themselves and differ from all others in a multitude of qualities3 these qualities co-exist1 or co-inhere1 with a high degree of constancy2 so that where some are found others may be inferred4 ,their co-inherence is not to be considered an ultimate fact2 for1 since everything which occurs is determined by laws of causation and collocations of the original causes1 it follows that the co-existences observable amongst effects cannot themselves be the subject of any similar set of laws distinct from laws of causation 7,b4 ,,iii4 c4 #e1 #i74 ,according to the theory of evolution 7worked out since ,mill wrote71 ,kinds--that is1 species of plants1 animals and minerals--with their qualities are all due to causation4 ,still1 as we can rarely1 or never1 trace the causes with any fullness or precision1 a great deal of our reasoning1 as1 e4g41 about men and camels1 does in fact trust to the relative permanence of natural ,kinds as defined by co-inhering attributes4 ,to see this more clearly1 we should consider that causation and natural ,kinds are not at present separable2 propositions about causation in concrete phenomena 7as distinct from abstract 'forces'7 always involve the assumption of ,kinds4 ,for example--',water rusts iron1' or the oxygen of water combines with iron immersed in it to form rust3 this statement of causation assumes that water1 oxygen1 iron1 and iron-rust are known ,kinds4 ,on the other hand1 the constitution of every concrete thing1 and manifestly of every organised body1 is always undergoing change1 that is1 causation1 upon which fact its properties depend4 ,how1 then1 can we frame principles of mediate reasoning1 about such things8 ,so far as we consider them as ,kinds1 it is enough to say3 ,whatever can be identified as a specimen of a known substance or ,kind has the properties of that ,kind4 ,so far as we consider them as in the relation of causation1 we may say3 ,whatever relation of events can be identified with the relation of cause and effect is constant4 ,and these principles may be generalised thus3 ,whatever is constantly related to a phenomenon 7cause or ,kind71 determined by certain characters1 is related in the same way to any phenomenon1 that has the same characters4 ,taking this as axiom of the syllogism materially treated1 we see that herbivorousness1 being constantly related to ruminants1 is constantly related to camels2 mortality to man and1 therefore1 to ,socrates2 rusting to the immersion of iron in water generally and1 therefore1 to this piece of iron4 ,nota not1 nota rei ipsius is another statement of the same principle2 still another is ,mill's axiom1 ,whatever has a mark has what it is a mark of4 ,a mark is anything 7,a7 that is never found without something else 7,b7--a phenomenon constantly related to another phenomenon--so that wherever ,a is found1 ,b may be expected3 human nature is a mark of mortality4 #f4 ,the ,syllogism has sometimes been discarded by those who have only seen that1 as formally stated1 it is either useless or fallacious3 but those who also perceive its material grounds retain and defend it4 ,in fact1 great advantages are gained by stating an argument as a formal syllogism4 ,for1 in the first place1 we can then examine separately the three conditions on which the validity of the argument depends3 7#a7 ,are the ,premises so connected that1 if they are true1 the ,conclusion follows8 ,this depends upon the formal principles of chap4 x4 7#b7 ,is the ,minor ,premise true8 ,this question can only arise when the minor premise is a real proposition2 and then it may be very difficult to answer4 ,water rusts iron2 but is the metal we are now dealing with a fair specimen of iron8 ,few people1 comparatively1 know how to determine whether diamonds1 or even gold or silver coins1 are genuine4 ,that ,camels are ruminants is now a verbal proposition to a ,zoologist1 but not to the rest of us2 and to the ,zoologist the ascertaining of the relation in which camels stand to such ruminants as oxen and deer1 was not a matter of analysing words but of dissecting specimens4 ,what a long controversy as to whether the human race constitutes a ,family of the ,primates6 ,that 'the ,british ,empire is an empire' affords no matter for doubt or inquiry2 but how difficult to judge whether the ,british ,empire resembles ,assyria1 ,egypt1 ,rome1 ,spain in those characters and circumstances that caused their downfall6 7#c7 ,is the ,major ,premise true8 ,are all ruminants herbivorous8 ,if there be any exceptions to the rule1 camels are likely enough to be among the exceptions4 ,and here the need of ,inductive ,logic is most conspicuous3 how can we prove our premises when they are universal propositions8 ,universal propositions1 however1 are also involved in proving the minor premise3 to prove a thing to be iron1 we must know the constant reactions of iron4 ,a second advantage of the syllogism is1 that it makes us fully aware of what an inference implies4 ,an inference must have some grounds1 or else it is a mere prejudice2 but whatever the grounds1 if sufficient in a particular case1 they must be sufficient for all similar cases1 they must admit of being generalised2 and to generalise the grounds of the inference1 is nothing else than to state the major premise4 ,if the evidence is sufficient to justify the argument that camels are herbivorous because they are ruminants1 it must also justify the major premise1 ,all ruminants are herbivorous2 for else the inference cannot really depend merely upon the fact of ruminating4 ,to state our evidence syllogistically1 then1 must be possible1 if the evidence is mediate and of a logical kind2 and to state it in this formal way1 as depending on the truth of a general principle 7the major premise71 increases our sense of responsibility for the inference that is thus seen to imply so much2 and if any negative instances lie within our knowledge1 we are the more likely to remember them4 ,the use of syllogisms therefore tends to strengthen our reasonings4 ,a third advantage is1 that to formulate an accurate generalisation may be useful to others3 it is indeed part of the systematic procedure of science4 ,the memoranda of our major premises1 or reasons for believing anything1 may be referred to by others1 and either confirmed or refuted4 ,when such a memorandum is used for further inferences1 these inferences are said1 in the language of ,formal ,logic1 to be drawn from it1 as if the conclusion were contained in our knowledge of the major premise2 but1 considering the limited extent of the material evidence1 it is better to say that the inference is drawn according to the memorandum or major premise1 since the grounds of the major premise and of the conclusion are in fact the same 7,mill3 ,logic1 ,b4 ,,ii4 c4 #c74 ,inductive proofs may be stated in ,syllogisms1 and inductive inferences are drawn according to the ,law of ,causation4 #g4 ,to assume that resemblance is a ground of inference1 and that substance and attribute1 or cause and effect1 are phenomena constantly related1 implies belief in the ,uniformity of ,nature4 ,the ,uniformity of ,nature cannot be defined1 and is therefore liable to be misunderstood4 ,in many ways ,nature seems not to be uniform3 there is great variety in the sizes1 shapes1 colours and all other properties of things3 bodies falling in the open air--pebbles1 slates1 feathers--descend in different lines and at different rates2 the wind and weather are proverbially uncertain2 the course of trade or of politics1 is full of surprises4 ,yet common maxims1 even when absurd1 testify to a popular belief that the relations of things are constant3 the doctrine of ,st4 ,swithin and the rhyme beginning ',evening red and morning grey1' show that the weather is held to be not wholly unpredictable2 as to human affairs1 it is said that 'a green ,yule makes a fat churchyard1' that 'trade follows the flag1' and that 'history repeats itself'2 and ,superstition knows that witches cannot enter a stable-door if a horse-shoe is nailed over it1 and that the devil cannot cross a threshold inscribed with a perfect pentagram4 ,but the surest proof of a belief in the uniformity of nature is given by the conduct of men and animals2 by that adherence to habit1 custom and tradition1 to which in quiet times they chiefly owe their safety1 but which would daily disappoint and destroy them1 if it were not generally true that things may be found where they have been left and that in similar circumstances there are similar events4 ,now this general belief1 seldom distinctly conceived1 for the most part quite unconscious 7as a principle71 merely implied in what men do1 is also the foundation of all the ,sciences2 which are entirely occupied in seeking the ,laws 7that is1 the ,uniformities7 of ,nature4 ,as the uniformity of nature cannot be defined1 it cannot be proved2 the most convincing evidence in its favour is the steady progress made by ,science whilst trusting in it4 ,nevertheless1 what is important is not the comprehensive but indeterminate notion of ,uniformity so much as a number of ,first ,principles1 which may be distinguished in it as follows3 7#a7 ,the ,principles of ,contradiction and ,excluded ,middle 7ch4 vi4 #c7 declare that in a given relation to a given phenomenon any two or more other phenomena are incompatible 7,b is not ,a and a72 whilst the given phenomenon either stands related to another phenomenon or not 7,b is either ,a or a74 ,it is not only a matter of ,logic but of fact that1 if a leaf is green1 it is not under the same conditions red or blue1 and that if it is not green it is some other colour4 7#b7 ,certain ,axioms of ,mediate ,evidence3 as1 in ,mathematics1 'that magnitudes equal to the same magnitude are equal to one another'2 and1 in ,logic1 the ,dictum or its material equivalent4 7#c7 ,that all ,times and all ,spaces are commensurable2 although in certain relations of space 7as 7 the unit of measurement must be infinitely small4--,if ,time really trotted with one man and galloped with another1 as it seems to2 if space really swelled in places1 as ,de ,quincey dreamed that it did2 life could not be regulated1 experience could not be compared and science would be impossible4 ,the ,mathematical ,axioms would then never be applicable to space or time1 or to the objects or processes that fill them4 7#d7 ,the ,persistence of ,matter and ,energy3 the physical principle that1 in all changes of the universe1 the quantities of ,matter and ,energy 7actual and potential1 so-called7 remain the same4--,for example1 as to matter1 although dew is found on the grass at morning without any apparent cause1 and although a candle seems to burn away to a scrap of blackened wick1 yet every one knows that the dew has been condensed from vapour in the air1 and that the candle has only turned into gas and smoke4 ,as to energy1 although a stone thrown up to the housetop and resting there has lost actual energy1 it has gained such a position that the slightest touch may bring it to the earth again in the same time as it took to travel upwards2 so on the house-top it is said to have potential energy4 ,when a boiler works an engine1 every time the piston is thrust forward 7mechanical energy71 an equivalent in heat 7molecular energy7 is lost4 ,but for the elucidation of these principles1 readers must refer to treatises of ,chemistry and ,physics4 7#e7 ,causation1 a special form of the foregoing principles of the persistence of matter and energy1 we shall discuss in the next chapter4 ,it is not to be conceived of as anything occult or noumenal1 but merely as a special mode of the uniformity of ,nature or experience4 7#f7 ,certain ,uniformities of ,co-existence2 but for want of a general principle of ,co-existence1 corresponding to ,causation 7the principle of ,succession71 we can only classify these uniformities as follows3 7a7 ,the ,geometrical2 as that1 in a four-sided figure1 if the opposite angles are equal1 the opposite sides are equal and parallel4--,countless similar uniformities of co-existence are disclosed by ,geometry4 ,the co-existent facts do not cause one another1 nor are they jointly caused by something else2 they are mutually involved3 such is the nature of space4 7b7 ,universal co-inherences among the properties of concrete things4--,the chief example is the co-inherence of gravity with inertia in all material bodies4 ,there is1 ,i believe1 no other entirely satisfactory case2 but some good approximations to such uniformity are known to physical science4 7c7 ,co-existence due to ,causation2 such as the positions of objects in space at any time4--,the houses of a town are where they are1 because they were put there2 and they remain in their place as long as no other causes arise strong enough to remove or destroy them4 ,similarly1 the relative positions of rocks in geological strata1 and of trees in a forest1 are due to causes4 7d7 ,the co-inherence of properties in ,natural ,kinds2 which we call the constitution1 defining characters1 or specific nature of such things4--,oxygen1 platinum1 sulphur and the other elements2 water1 common salt1 alcohol and other compounds2 the various species of plants and animals3 all these are known to us as different groups of co-inherent properties4 ,it may be conjectured that these groupings of properties are also due to causation1 and sometimes the causes can be traced3 but very often the causes are still unknown2 and1 until resolved into their causes1 they must be taken as necessary data in the investigation of nature4 ,laws of the co-inherence of the properties of ,kinds do not1 like laws of causation1 admit of methodical proof upon their own principles1 but only by constancy in experience and statistical probability 7c4 xix1 #d74 7e7 ,there are also a few cases in which properties co-exist in an unaccountable way1 without being co-extensive with any one species1 genus1 or order3 as most metals are whitish1 and scarlet flowers are wanting in fragrance4 7,on this #g1 see ,venn's ,empirical ,logic1 c4 #d47 #h4 ,inasmuch as ,axioms of ,uniformity are ultimate truths1 they cannot be deduced2 and inasmuch as they are universal1 no proof by experience can ever be adequate4 ,the grounds of our belief in them seem to be these3 7#a7 ,every inference takes for granted an order of ,nature corresponding with it2 and every attempt to explain the origin of anything assumes that it is the transformation of something else3 so that uniformity of order and conservation of matter and energy are necessary presuppositions of reasoning4 7#b7 ,on the rise of philosophic reflection1 these tacit presuppositions are first taken as dogmas1 and later as postulates of scientific generalisation1 and of the architectonic unification of science4 ,here they are indispensable4 7#c7 ,the presuppositions or postulates are1 in some measure1 verifiable in practical life and in scientific demonstration1 and the better verifiable as our methods become more exact4 7#d7 ,there is a cause of this belief that cannot be said to contain any evidence for it1 namely1 the desire to find in ,nature a foundation for confidence in our own power to foresee and to control events4 ,,chapter ,,xiv ,,causation #a4 ,for the theory of ,induction1 the specially important aspect of the ,uniformity of ,nature is ,causation4 ,for 7#a7 the ,principles of ,contradiction and ,excluded ,middle are implied in all logical operations1 and need no further explication4 7#b7 ,that one thing is a mark of another or constantly related to it1 must be established by ,induction2 and the surest of all marks is a ,cause4 ,so that the application of the axiom of the ,syllogism in particular cases requires1 when most valid1 a previous appeal to ,causation4 7#c7 ,the uniformity of ,space and of ,time is involved in ,causation1 so far as we conceive ,causation as essentially matter in motion--for motion is only known as a traversing of space in time2 and so far as forces vary in any way according to the distance between bodies2 so that if space and time were not uniform1 causation would be irregular4 ,not that time and space are agents1 but they are conditions of every agent's operation4 7#d7 ,the persistence of ,matter and ,energy1 being nothing else than ,causation in the general movement of the world1 is applied under the name of that principle in explaining any particular limited phenomenon1 such as a soap-bubble1 or a thunderstorm1 or the tide4 7#e7 ,as to co-existences1 the ,geometrical do not belong to ,logic3 those involved in the existence of plants1 animals1 and inorganic bodies1 must1 as far as possible1 be traced to causes2 and so1 of course1 must the relative positions of objects in space at any time3 and what ,co-existences remain do not admit of methodical inductive treatment2 they will be briefly discussed in chap4 xix4 ,causation1 then1 is that mode or aspect of the ,uniformity of ,nature which especially concerns us in ,induction2 and we must make it as definite as possible4 ,it is nothing occult1 but merely a convenient name for phenomena in a particular relation to other phenomena1 called their effect4 ,similarly1 if the word 'force' is sometimes used for convenience in analysing causation1 it means nothing more than something in time and space1 itself moving1 or tending to move1 or hindering or accelerating other things4 ,if any one does not find these words convenient for the purpose1 he can use others4 #b4 ,a ,cause1 according to ,mill1 is the invariable unconditional antecedent of a given phenomenon4 ,to enlarge upon this3 7#a7 ,a ,cause is relative to a given phenomenon1 called the ,effect4 ,logic has no method for investigating the cause of the universe as a whole1 but only of a part or epoch of it3 we select from the infinite continuum of ,nature any portion that is neither too large nor too small for a trained mind to comprehend4 ,the magnitude of the phenomenon may be a matter of convenience4 ,if the cause of disease in general be too wide a problem1 can fevers be dealt with2 or1 if that be too much1 is typhus within the reach of inquiry8 ,in short1 how much can we deal with accurately8 7#b7 ,the given phenomenon is always an event2 that is to say1 not a new thing 7nothing is wholly new71 but a change in something1 or in the relative position of things4 ,we may ask the cause of the phases of the moon1 of the freezing of water1 of the kindling of a match1 of a deposit of chalk1 of the differentiation of species4 ,to inquire the cause of ,france being a republic1 or ,russia an autocracy1 implies that these countries were once otherwise governed1 or had no government3 to inquire the cause of the earth being shaped like an orange1 implies that the matter of the earth had once another shape4 7#c7 ,the ,cause is antecedent to the ,effect1 which accordingly is often called its consequent4 ,this is often misunderstood and sometimes disputed4 ,it has been said that the meaning of 'cause' implies an 'effect1' so that until an effect occurs there can be no cause4 ,but this is a blunder2 for whilst the word 'cause' implies 'effect1' it also implies the relative futurity of the effect2 and effect implies the relative priority of the cause4 ,the connotation of the words1 therefore1 agrees well enough with ,mill's doctrine4 ,in fact1 the danger is that any pair of contrasted words may suggest too strongly that the phenomena denoted are separate in ,nature2 whereas every natural process is continuous4 ,if water1 dripping from the roof wears away a stone1 it fell on the roof as rain2 the rain came from a condensing cloud2 the cloud was driven by the wind from the sea1 whence it exhaled2 and so on4 ,there is no known beginning to this1 and no break in it4 ,we may take any one of these changes1 call it an effect1 and ask for its cause2 or call it a cause1 and ask for its effect4 ,there is not in ,nature one set of things called causes and another called effects2 but every change is both cause 7or a condition7 of the future and effect of the past2 and whether we consider an event as the one or the other1 depends upon the direction of our curiosity or interest4 ,still1 taking the event as effect1 its cause is the antecedent process2 or1 taking it as a cause1 its effect is the consequent process4 ,this follows from the conception of causation as essentially motion2 for that motion takes time is 7from the way our perceptive powers grow7 an ultimate intuition4 ,but1 for the same reason1 there is no interval of time between cause and effect2 since all the time is filled up with motion4 ,nor must it be supposed that the whole cause is antecedent to the effect as a whole3 for we often take the phenomenon on such a scale that minutes1 days1 years1 ages1 may elapse before we consider the cause as exhausted 7e4g41 an earthquake1 a battle1 an expansion of credit1 natural selection operating on a given variety72 and all that time the effect has been accumulating4 ,but we may further consider such a cause as made up of moments or minute factors1 and the effect as made up of corresponding moments2 and then the cause1 taken in its moments1 is antecedent throughout to the effect1 taken in its corresponding moments4 7#d7 ,the ,cause is the invariable antecedent of the effect2 that is to say1 whenever a given cause occurs it always has the same effect3 in this1 in fact1 consists the ,uniformity of ,causation4 ,accordingly1 not every antecedent of an event is its ,cause3 to assume that it is so1 is the familiar fallacy of arguing 'post hoc ergo propter hoc4' ,every event has an infinite number of antecedents that have no ascertainable connection with it3 if a picture falls from the wall in this room1 there may have occurred1 just previously1 an earthquake in ,new ,zealand1 an explosion in a ,japanese arsenal1 a religious riot in ,india1 a political assassination in ,russia and a vote of censure in the ,house of ,commons1 besides millions of other less noticeable events1 between none of which and the falling of the picture can any direct causation be detected2 though1 no doubt1 they are all necessary occurrences in the general world-process1 and remotely connected4 ,the cause1 however1 was that a door slammed violently in the room above and shook the wall1 and that the picture was heavy and the cord old and rotten4 ,even if two events invariably occur one after the other1 as day follows night1 or as the report follows the flash of a gun1 they may not be cause and effect1 though it is highly probable that they are closely connected by causation2 and in each of these two examples the events are co-effects of a common cause1 and may be regarded as elements of its total effect4 ,still1 whilst it is not true that every antecedent1 or that every invariable antecedent1 of an event is its cause1 the cause is conceived of as some change in certain conditions1 or some state and process of things1 such that should it exactly recur the same event would invariably follow4 ,if we consider the antecedent state and process of things very widely or very minutely1 it never does exactly recur2 nor does the consequent4 ,but the purpose of induction is to get as near the truth as possible within the limits set by our faculties of observation and calculation4 ,complex causal instances that are most unlikely to recur as a whole1 may be analysed into the laws of their constituent conditions4 7#e7 ,the ,cause is the ,unconditional ,antecedent4 ,a cause is never simple1 but may be analysed into several conditions2 and ',condition' means any necessary factor of a ,cause3 any thing or agent that exerts1 absorbs1 transforms1 or deflects energy2 or any relation of time or space in which agents stand to one another4 ,a positive condition is one that cannot be omitted without frustrating the effect2 a negative condition is one that cannot be introduced without frustrating the effect4 ,in the falling of the picture1 e4g41 the positive conditions were the picture 7as being heavy71 the slamming of the door1 and the weakness of the cord3 a negative condition was that the picture should have no support but the cord4 ,when ,mill1 then1 defines the ,cause of any event as its unconditional antecedent1 he means that it is that group of conditions 7state and process of things7 which1 without any further condition1 is followed by the event in question3 it is the least antecedent that suffices1 positive conditions being present and negative absent4 ,whatever item of the antecedent can be left out1 then1 without affecting the event1 is no part of the cause4 ,earthquakes have happened in ,new ,zealand and votes of censure in the ,house of ,commons without a picture's falling in this room3 they were not unconditional antecedents2 something else was needed to bring down a picture4 ,unconditionality also distinguishes a true cause from an invariable antecedent that is only a co-effect3 for when day follows night something else happens2 the ,earth rotates upon her axis3 a flash of gunpowder is not an unconditional antecedent of a report2 the powder must be ignited in a closed chamber4 ,by common experience1 and more precisely by experiment1 it is found possible to select from among the antecedents of an event a certain number upon which1 so far as can be perceived1 it is dependent1 and to neglect the rest3 to purge the cause of all irrelevant antecedents is the great art of inductive method4 ,remote or minute conditions may indeed modify the event in ways so refined as to escape our notice4 ,subject to the limitations of our human faculties1 however1 we are able in many cases to secure an unconditional antecedent upon which a certain event invariably follows4 ,everybody takes this for granted3 if the gas will not burn1 or a gun will not go off1 we wonder 'what can be wrong with it1' that is1 what positive condition is wanting1 or what negative one is present4 ,no one now supposes that gunnery depends upon those remotest of all causes1 the stars1 or upon the sun being in ,sagittarius rather than in ,aquarius1 or that one shoots straightest with a silver bullet1 or after saying the alphabet backwards4 7#f7 ,that the ,cause of any event is an ,immediate ,antecedent follows from its being an unconditional one4 ,for if there are three events1 ,a ,b ,c1 causally connected1 it is plain that ,a is not the unconditional antecedent of ,c1 but requires the further condition of first giving rise to ,b4 ,but that is not all2 for the ,b that gives rise to ,c is never merely the effect of ,a2 it involves something further4 ,take such a simple case as the motion of the earth round the sun 7neglecting all other conditions1 the other planets1 etc472 and let the earth's motion at three successive moments be ,a ,b ,c3 ,a is not the whole cause of ,b in velocity and direction2 we must add relation to the sun1 say x4 ,but then1 again1 the cause of ,c will not be merely ,bx1 for the relation to the sun will have altered2 so that we must represent it as ,bx'4 ,the series1 therefore1 is ,ax ,bx' ,c4 ,what is called a remote cause is1 therefore1 doubly conditional2 first1 because it supposes an intervening cause2 and secondly1 because it only in part determines the conditions that constitute this intervening cause4 ,the immediacy of a cause being implied in its unconditionalness1 is an important clue to it2 but as far as the detection of causes depends upon sense-perception1 our powers 7however aided by instruments7 are unequal to the subtlety of ,nature4 ,between the event and what seems to us the immediate antecedent many things 7molecular or etherial changes7 may happen in ,chemistry or ,physics4 ,the progress of science would be impossible were not observation supplemented by hypothesis and calculation4 ,and where phenomena are treated upon a large scale1 as in the biological and social sciences1 immediacy1 as a mark of causation1 must be liberally interpreted4 ,so far1 then1 as to the qualitative character of ,causation4 7#g7 ,but to complete our account of it1 we must briefly consider its quantitative character4 ,as to the ,matter contained1 and as to the ,energy embodied1 ,cause and ,effect are conceived to be equal4 ,as to matter1 indeed1 they may be more properly called identical2 since the effect is nothing but the cause redistributed4 ,when oxygen combines with hydrogen to form water1 or with mercury to form red precipitate1 the weight of the compound is exactly equal to the weight of the elements combined in it2 when a shell explodes and knocks down a wall1 the materials of the shell and wall are scattered about4 ,as to energy1 we see that in the heavenly bodies1 which meet with no sensible impediment1 it remains the same from age to age3 with things 'below the moon' we have to allow for the more or less rapid conversion of the visible motion of a mass into other forms of energy1 such as sound and heat4 ,but the right understanding of this point involves physical considerations of some difficulty1 as to which the reader must refer to appropriate books1 such as ,balfour ,stewart's on ,the ,conservation of ,energy4 ,the comprehension of the quantitative aspect of causation is greatly aided by ,bain's analysis of any cause into a ',moving or an ,inciting ,power' and a ',collocation' of circumstances4 ,when a demagogue by making a speech stirs up a mob to a riot1 the speech is the moving or inciting power2 the mob already in a state of smouldering passion1 and a street convenient to be wrecked1 are the collocation4 ,when a small quantity of strychnine kills a man1 the strychnine is the inciting power2 the nature of his nervo-muscular system1 apt to be thrown into spasms by that drug1 and all the organs of his body dependent on that system1 are the collocation4 ,now any one who thinks only of the speech1 or the drug1 in these cases1 may express astonishment at the disproportion of cause and effect3 ,what great events from trivial causes spring6 ,but1 remembering that the whole cause of the riot included the excited mob1 every one sees that its muscular power is enough to wreck a street2 and remembering that breathing depends upon the normal action of the intercostal muscles1 it is plain that if this action is stopped by strychnine1 a man must die4 ,again1 a slight rise of temperature may be a sufficient inciting power to occasion extensive chemical changes in a collocation of elements otherwise stable2 a spark is enough to explode a powder magazine4 ,hence1 when sufficient energy to account for any effect cannot be found in the inciting power1 or manifestly active condition1 we must look for it in the collocation which is often supposed to be passive4 ,and that reminds us of another common misapprehension1 namely1 that in ,nature some things are passive and others active3 the distinction between 'agent' and 'patient4' ,this is a merely relative distinction3 in ,nature all things are active4 ,to the eye some things seem at rest and others in motion2 but we know that nothing is really at rest1 that everything palpitates with molecular change1 and whirls with the planet through space4 ,everything that is acted upon reacts according to its own nature3 the quietest-looking object 7say1 a moss-covered stone71 if we try to push or lift it1 pushes or pulls us back1 assuring us that 'action and reaction are equal and opposite4' ',inertia' does not mean want of vigour1 but may be metaphorically described as the inexpugnable resolve of everything to have its own way4 ,the equality of cause and effect defines and interprets the unconditionality of causation4 ,the cause1 we have seen1 is that group of conditions which1 without any further condition1 is followed by a given event4 ,but how is such a group to be conceived8 ,unquantified1 it admits only of a general description3 quantified1 it must mean a group of conditions equal to the effect in mass and energy1 the essence of the physical world4 ,apparently1 a necessary conception of the human mind3 for if a cause seem greater than its effect1 we ask what has become of the surplus matter and energy2 or if an effect seem greater than its cause1 we ask whence the surplus matter and energy has arisen4 ,so convinced of this truth is every experimenter1 that if his results present any deviation from it1 he always assumes that it is he who has made some mistake or oversight1 never that there is indeterminism or discontinuity in ,nature4 ,the transformation of matter and energy1 then1 is the essence of causation3 because it is continuous1 causation is immediate2 and because in the same circumstances the transformation always follows the same course1 a cause has invariably the same effect4 ,if a fire be lit morning after morning in the same grate1 with coal1 wood1 and paper of the same quality and similarly arranged1 there will be each day the same flaming of paper1 crackling of wood and glowing of coal1 followed in about the same time by the same reduction of the whole mass partly to ashes and partly to gases and smoke that have gone up the chimney4 ,the flaming1 crackling and glowing are1 physically1 modes of energy2 and the change of materials into gas and ashes is a chemical and physical redistribution3 and1 if some one be present1 he will be aware of all this2 and then1 besides the physical changes1 there will be sensations of light1 sound and heat2 and these again will be always the same in the same circumstances4 ,the ,cause of any event1 then1 when exactly ascertainable1 has five marks3 it is 7quantitatively7 equal to the effect1 and 7qualitatively7 the immediate1 unconditional1 invariable antecedent of the effect4 #c4 ,this scientific conception of causation has been developed and rendered definite by the investigations of those physical sciences that can avail themselves of exact experiments and mathematical calculation2 and it is there1 in ,chemistry and ,physics1 that it is most at home4 ,the conception can indeed be carried into the ,biological and ,social ,sciences1 even in its quantitative form1 by making the proper allowances4 ,for the limbs of animals are levers1 and act upon mechanical principles2 and digestion and the aeration of the blood by breathing are partly chemical processes4 ,there is a quantitative relation between the food a man eats and the amount of work he can do4 ,the numbers of any species of plant or animal depend upon the food supply4 ,the value of a country's imports is equal to the value of its exports and of the services it renders to foreigners4 ,but1 generally1 the less experiment and exact calculation are practicable in any branch of inquiry1 the less rigorously can the conception of causation be applied there1 the more will its application depend upon the qualitative marks1 and the more need there will be to use it judiciously4 ,in every inquiry the greatest possible precision must be aimed at2 but it is unreasonable to expect in any case more precise proof than the subject admits of in the existing state of culture4 ,wherever mental action is involved1 there is a special difficulty in applying the physical notion of causation4 ,for if a ,cause be conceived of as matter in motion1 a thought1 or feeling1 or volition can be neither cause nor effect4 ,and since mental action is involved in all social affairs1 and in the life of all men and animals1 it may seem impossible to interpret social or vital changes according to laws of causation4 ,still1 animals and men are moving bodies2 and it is recognised that their thoughts and feelings are so connected with their movements and with the movements of other things acting upon them1 that we can judge of one case by another2 although the connection is by no means well understood1 and the best words 7such as all can agree to use7 have not yet been found to express even what we know about it4 ,hence1 a regular connection being granted1 ,i have not hesitated1 to use biological and social events and the laws of them1 to illustrate causation and induction2 because1 though less exact than chemical or mechanical examples1 they are to most people more familiar and interesting4 ,in practical affairs1 it is felt that everything depends upon causation2 how to play the fiddle1 or sail a yacht1 or get one's living1 or defeat the enemy4 ,the price of pig-iron six months hence1 the prospects of the harvest1 the issue in a ,coroner's ,court1 ,home ,rule and ,socialism1 are all questions of causation4 ,but1 in such cases1 the conception of a cause is rarely applied in its full scientific acceptation1 as the unconditional antecedent1 or 'all the conditions' 7neither more nor less7 upon which the event depends4 ,this is not because men of affairs are bad logicians1 or incapable of scientific comprehension2 for very often the reverse is conspicuously true2 but because practical affairs call for promptitude and a decisive seizing upon what is predominantly important4 ,how learn to play the fiddle8 ,go to a good teacher4 7,then1 beginning young enough1 with natural aptitude and great diligence1 all may be well47 ,how defeat the enemy8 ,be two to one at the critical juncture4 7,then1 if the men are brave1 disciplined1 well armed and well fed1 there is a good chance of victory47 ,will the price of iron improve8 ,yes3 for the market is oversold3 7that is1 many have sold iron who have none to deliver1 and must at some time buy it back2 and that will put up the price--if the stock is not too great1 if the demand does not fall off1 and if those who have bought what they cannot pay for are not in the meanwhile obliged to sell47 ,these prompt and decisive judgments 7with the parenthetic considerations unexpressed7 as to what is the ,cause1 or predominantly important condition1 of any event1 are not as good as a scientific estimate of all the conditions1 when this can be obtained2 but1 when time is short1 the insight of trained sagacity may be much better than an imperfect theoretical treatment of such problems4 #d4 ,to regard the ,effect of certain antecedents in a narrow selective way1 is another common mistake4 ,in the full scientific conception of an ,effect it is the sum of the unconditional consequences of a given state and process of things3 the consequences immediately flowing from that situation without further conditions4 ,always to take account of all the consequences of any cause would no doubt be impracticable2 still the practical1 as well as the scientific interest1 often requires that we should enlarge our views of them2 and there is no commoner error in private effort or in legislation than to aim at some obvious good1 whilst overlooking other consequences of our action1 the evil of which may far outweigh that good4 ,an important consequence of eating is to satisfy hunger1 and this is the ordinary motive to eat2 but it is a poor account of the physiological consequences4 ,an important consequence of firing a gun is the propulsion of the bullet or shell2 but there are many other consequences in the whole effect1 and one of them is the heating of the barrel1 which1 accumulating with rapid firing1 may at last put the gun out of action4 ,the tides have consequences to shipping and in the wear and tear of the coast that draw every one's attention2 but we are told that they also retard the rotation of the earth1 and at last may cause it to present always the same face to the sun1 and1 therefore1 to be uninhabitable4 ,such concurrent consequences of any cause may be called its ,co-effects3 the ,effect being the sum of them4 ,the neglect to take account of the whole effect 7that is1 of all the co-effects7 in any case of causation is perhaps the reason why many philosophers have maintained the doctrine of a ,plurality of ,causes3 meaning not that more than one condition is operative in the antecedent of every event 7which is true71 but that the same event may be due at different times to different antecedents1 that in fact there may be vicarious causes4 ,if1 however1 we take any effect as a whole1 this does not seem to be true4 ,a fire may certainly be lit in many ways3 with a match or a flint and steel1 or by rubbing sticks together1 or by a flash of lightning3 have we not here a plurality of causes8 ,not if we take account of the whole effect2 for then we shall find it modified in each case according to the difference of the cause4 ,in one case there will be a burnt match1 in another a warm flint1 in the last a changed state of electrical tension4 ,and similar differences are found in cases of death under different conditions1 as stabbing1 hanging1 cholera2 or of shipwreck from explosion1 scuttling1 tempest4 ,hence a ,coroner's ,court expects to find1 by examining a corpse1 the precise cause of death4 ,in short1 if we knew the facts minutely enough1 it would be found that there is only one ,cause 7sum of conditions7 for each ,effect 7sum of co-effects71 and that the order of events is as uniform backwards as forwards4 ,still1 as we are far from knowing events minutely1 it is necessary in practical affairs1 and even in the more complex and unmanageable scientific investigations1 especially those that deal with human life1 to acknowledge a possible plurality of causes for any effect4 ,indeed1 forgetfulness of this leads to many rash generalisations2 as that 'revolutions always begin in hunger'2 or that 'myths are a disease of language4' ,then there is great waste of ingenuity in reconciling such propositions with the recalcitrant facts4 ,a scientific method recognises that there may be other causes of effects thus vaguely conceived1 and then proceeds to distinguish in each class of effects the peculiarities due to different causes4 #e4 ,the understanding of the complex nature of ,causes and ,effects helps us to overcome some other difficulties that perplex the use of these words4 ,we have seen that the true cause is an immediate antecedent2 but if the cause is confounded with one of its constituent conditions1 it may seem to have long preceded the event which is regarded as its effect4 ,thus1 if one man's death is ascribed to another's desire of revenge1 this desire may have been entertained for years before the assassination occurred3 similarly1 if a shipwreck is ascribed to a sunken reef1 the rock was waiting for ages before the ship sailed that way4 ,but1 of course1 neither the desire of revenge nor the sunken rock was 'the sum of the conditions' on which the one or the other event depended3 as soon as this is complete the effect appears4 ,we have also seen the true effect of any state and process of things is the immediate consequence2 but if the effect be confounded with one of its constituent factors1 it may seem to long outlive the cessation of the cause4 ,thus1 in nearly every process of human industry and art1 one factor of the effect--a road1 a house1 a tool1 a picture--may1 and generally does1 remain long after the work has ceased3 but such a result is not the whole effect of the operations that produce it4 ,the other factors may be1 and some always are1 evanescent4 ,in most of such works some heat is produced by hammering or friction1 and the labourers are fatigued2 but these consequences soon pass off4 ,hence the effect as a whole only momentarily survives the cause4 ,consider a pendulum which1 having been once set agoing1 swings to and fro in an arc1 under the joint control of the shaft1 gravitation and its own inertia3 at every moment its speed and direction change2 and each change may be considered as an effect1 of which the antecedent change was one condition4 ,in such a case as this1 which1 though a very simple1 is a perfectly fair example of all causation1 the duration of either cause or effect is quite insensible3 so that1 as ,dr4 ,venn says1 an ,effect1 rigorously conceived1 is only the initial tendency of its ,cause4 #f4 ,mill contrasted two forms under which causation appears to us3 that is to say1 the conditions constituting a cause may be modified1 or 'intermixed' in the effect1 in two ways1 which are typified respectively by ,mechanical and ,chemical action4 ,in mechanical causation1 which is found in ,astronomy and all branches of ,physics1 the effects are all reducible to modes of energy1 and are therefore commensurable with their causes4 ,they are either directly commensurable1 as in the cases treated of in the consideration of the mechanical powers2 or1 if different forms of energy enter into cause and effect1 such as mechanical energy1 electrical energy1 heat1 these different forms are severally reducible to units1 between which equivalents have been established4 ,hence ,mill calls this the homogeneous intermixture of effects1 because the antecedents and consequents are fundamentally of the same kind4 ,in chemical causation1 on the other hand1 cause and effect 7at least1 as they present themselves to us7 differ in almost every way3 in the act of combination the properties of elements 7except weight7 disappear1 and are superseded by others in the compound4 ,if1 for example1 mercury 7a heavy1 silvery liquid7 be heated in contact with oxygen 7a colourless gas71 oxide of mercury is formed 7red precipitate1 which is a powder74 ,this compound presents very different phenomena from those of its elements2 and hence ,mill called this class of cases the heteropathic intermixture of effects4 ,still1 in chemical action1 the effect is not 7in ,nature7 heterogeneous with the cause3 for the weight of a compound is equal to the sum of the weights of the elements that are merged in it2 and an equivalence has been ascertained between the energy of chemical combination and the heat1 light1 etc41 produced in the act of combination4 ,the heteropathic intermixture of effects is also found in organic processes 7which1 indeed1 are partly chemical73 as when a man eats bread and milk1 and by digestion and assimilation converts them into nerve1 muscle and bone4 ,such phenomena may make us wonder that people should ever have believed that 'effects resemble their causes1' or that 'like produces like4' ,a dim recognition of the equivalence of cause and effect in respect of matter and motion may have aided the belief2 and the resemblance of offspring to parents may have helped3 but it is probably a residuum of magical rites2 in which to whistle may be regarded as a means of raising the wind1 because the wind whistles2 and rain-wizards may make a victim shed tears that the clouds also may weep4 #g4 ,another consideration arises out of the complex character of causes and effects4 ,when a cause consists of two or more conditions or forces1 we may consider what effect any one of them would have if it operated alone1 that is to say1 its ,tendency4 ,this is best illustrated by the ,parallelogram of ,forces3 if two forces acting upon a point1 but not in the same direction1 be represented by straight lines drawn in the direction of the forces1 and in length proportional to their magnitudes1 these lines1 meeting in an angle1 represent severally the tendencies of the forces2 whilst if the parallelogram be completed on these lines1 the diagonal drawn from the point in which they meet represents their ,resultant or effect4 ,again1 considering the tendency of any force if it operated alone1 we may say that1 when combined with another force 7not in the same direction7 in any resultant1 its tendency is counteracted3 either partially1 when the direction of the resultant is different2 or wholly when1 the other force being equal and opposite1 the resultant is equilibrium4 ,if the two forces be in the same direction1 they are merely added together4 ,counteraction is only one mode of combination2 in no case is any force destroyed4 ,sometimes the separate tendencies of combined forces can only be theoretically distinguished3 as when the motion of a projectile is analysed into a tendency to travel in the straight line of its discharge1 and a tendency to fall straight to the ground4 ,but sometimes a tendency can be isolated3 as when1--after dropping a feather in some place sheltered from the wind1 and watching it drift to and fro1 as the air1 offering unequal resistances to its uneven surface1 counteracts its weight with varying success1 until it slowly settles upon the ground1--we take it up and drop it again in a vacuum1 when it falls like lead4 ,here we have the tendency of a certain cause 7namely1 the relation between the feather and the earth7 free from counteraction3 and this is called the ,elimination of the counteracting circumstances4 ,in this case indeed there is physical elimination2 whereas1 in the case of a projectile1 when we say that its actual motion is resolvable 7neglecting the resistance of the air7 into two tendencies1 one in the line of discharge1 the other earthwards1 there is only theoretical elimination of either tendency1 considered as counteracting the other2 and this is more specifically called the ,resolution or ,analysis of the total effect into its component conditions4 ,now1 ,elimination and ,resolution may be said to be the essential process of ,induction in the widest sense of the term1 as including the combination of ,induction with ,deduction4 ,the several conditions constituting any cause1 then1 by aiding or counteracting one another's tendencies1 jointly determine the total effect4 ,hence1 viewed in relation one to another1 they may be said to stand in ,reciprocity or mutual influence4 ,this relation at any moment is itself one of co-existence1 though it is conceived with reference to a possible effect4 ,as ,kant says1 all substances1 as perceived in space at the same time1 are in reciprocal activity4 ,and what is true of the world of things at any moment 7as connected1 say1 by gravity71 is true of any selected group of circumstances which we regard as the particular cause of any event to come4 ,the use of the concept of reciprocity1 then1 lies in the analysis of a cause3 we must not think of reciprocity as obtaining in the succession of cause and effect1 as if the effect could turn back upon its cause2 for as the effect arises its cause disappears1 and is irrecoverable by ,nature or ,magic4 ,there are many cases of rhythmic change and of moving equilibria1 in which one movement or process produces another1 and this produces something closely resembling the former1 and so on in long series2 as with the swing of a pendulum or the orbit of a planet3 but these are series of cause and effect1 not of reciprocity4 ,,chapter ,,xv ,,inductive ,,method #a4 ,it is necessary to describe briefly the process of investigating laws of causation1 not with the notion of teaching any one the ,art of ,discovery1 which each man pursues for himself according to his natural gifts and his experience in the methods of his own science1 but merely to cast some light upon the contents of the next few chapters4 ,logic is here treated as a process of proof2 proof supposes that some general proposition or hypothesis has been suggested as requiring proof2 and the search for such propositions may spring from scientific curiosity or from practical interests4 ,we may1 as ,bain observes 7,logic3 ,b4 iii4 ch4 #e71 desire to detect a process of causation either 7#a7 amidst circumstances that have no influence upon the process but only obscure it2 as when1 being pleased with a certain scent in a garden1 we wish to know from what flower it rises2 or1 being attracted by the sound of some instrument in an orchestra1 we desire to know which it is3 or 7#b7 amidst circumstances that alter the effect from what it would have been by the sole operation of some cause2 as when the air deflects a falling feather2 or in some more complex case1 such as a rise or fall of prices that may extend over many years4 ,to begin with1 we must form definite ideas as to what the phenomenon is that we are about to investigate2 and in a case of any complexity this is best done by writing a detailed description of it3 e4g41 to investigate the cause of a recent fall of prices1 we must describe exactly the course of the phenomenon1 dating the period over which it extends1 recording the successive fluctuations of prices1 with their maxima and minima1 and noting the classes of goods or securities that were more or less affected1 etc4 ,then the first step of elimination 7as ,bain further observes7 is to analyse the situation mentally1 in the light of analogies suggested by our experience or previous knowledge4 ,dew1 for example1 is moisture formed upon the surface of bodies from no apparent source4 ,but two possible sources are easily suggested by common experience3 is it deposited from the air1 like the moisture upon a mirror when we breathe upon it2 or does it exude from the bodies themselves1 like gum or turpentine8 ,or1 again1 as to a fall of prices1 a little experience in business1 or knowledge of ,economics1 readily suggests two possible explanations3 either cheaper production in making goods or carrying them2 or a scarcity of that in which the purchasing power of the chief commercial nations is directly expressed1 namely1 gold4 ,having thus analysed the situation and considered the possibility of one1 two1 three1 or more possible causes1 we fix upon one of them for further investigation2 that is to say1 we frame an hypothesis that this is the cause4 ,when an effect is given to find its cause1 an inquirer nearly always begins his investigations by thus framing an hypothesis as to the cause4 ,the next step is to try to verify this ,hypothesis4 ,this we may sometimes do by varying the circumstances of the phenomenon1 according to the ,canons of direct ,inductive ,proof to be discussed in the next chapter2 that is to say1 by observing or experimenting in such a way as to get rid of or eliminate the obscuring or disturbing conditions4 ,thus1 to find out which flower in a garden gives a certain scent1 it is usually enough to rely on observation1 going up to the likely flowers one after the other and smelling them3 at close quarters1 the greater relative intensity of the scent is sufficiently decisive4 ,or we may resort to a sort of experiment1 plucking a likely flower1 as to which we frame the hypothesis 7this is the cause71 and carrying it to some place where the air is free from conflicting odours4 ,should observation or experiment disprove our first hypothesis we try a second2 and so on until we succeed1 or exhaust the known possibilities4 ,but if the phenomenon is so complex and extensive as a continuous fall of prices1 direct observation or experiment is a useless or impossible method2 and we must then resort to ,deduction2 that is1 to indirect ,induction4 ,if1 for example1 we take the hypothesis that the fall is due to a scarcity of gold1 we must show that there is a scarcity2 what effect such a scarcity may be expected to have upon prices from the acknowledged laws of prices1 and from the analogy of other cases of an expanded or restricted currency2 that this expectation agrees with the statistics of recent commerce3 and finally1 that the alternative hypothesis that the fall is due to cheaper production is not true2 either because there has not been a sufficient cheapening of general production2 or because1 if there has been1 the results to be rationally expected from it are not such as to agree with the statistics of recent commerce4 7,ch4 xviii47 ,but now suppose that1 a phenomenon having been suggested for explanation1 we are unable at the time to think of any cause--to frame any hypothesis about it2 we must then wait for the phenomenon to occur again1 and1 once more observing its course and accompaniments and trying to recall its antecedents1 do our best to conceive an hypothesis1 and proceed as before4 ,thus1 in the first great epidemic of influenza1 some doctors traced it to a deluge in ,china1 others to a volcanic eruption near ,java2 some thought it a mild form of ,asiatic plague1 and others caught a specific microbe4 ,as the disease often recurred1 there were fresh opportunities of framing hypotheses2 and the microbe was identified4 ,again1 the investigation may take a different form3 given a supposed ,cause to find its ,effect2 e4g41 a new chemical element1 to find what compounds it forms with other elements2 or1 the spots on the sun--have they any influence upon our weather8 ,here1 if the given cause be under control1 as a new element may be1 it is possible to try experiments with it according to the ,canons of ,inductive ,proof4 ,the inquirer may form some hypothesis or expectation as to the effects1 to guide his observation of them1 but will be careful not to hold his expectation so confidently as to falsify his observation of what actually happens4 ,but if the cause be1 like the sun-spots1 not under control1 the inquirer will watch on all sides what events follow their appearance and development2 he must watch for consequences of the new cause he is studying in many different circumstances1 that his observations may satisfy the canons of proof4 ,but he will also resort for guidance to deduction2 arguing from the nature of the cause1 if anything is known of its nature1 what consequences may be expected1 and comparing the results of this deduction with any consequent which he suspects to be connected with the cause4 ,and if the results of deduction and observation agree1 he will still consider whether the facts observed may not be due to some other cause4 ,a cause1 however1 may be under control and yet be too dangerous to experiment with2 such as the effects of a poison--though1 if too dangerous to experiment with upon man1 it may be tried upon animals2 or such as a proposed change of the constitution by legislation2 or even some minor ,act of ,parliament1 for altering the ,poor ,law1 or regulating the hours of labour4 ,here the first step must be deductive4 ,we must ask what consequences are to be expected from the nature of the change 7comparing it with similar changes71 and from the laws of the special circumstances in which it is to operate8 ,and sometimes we may partially verify our deduction by trying experiments upon a small scale or in a mild form4 ,there are conflicting deductions as to the probable effect of giving ,home ,rule to ,ireland2 and experiments have been made in more or less similar cases1 as in the ,colonies and in some foreign countries4 ,as to the proposal to make eight hours the legal limit of a day's labour in all trades1 we have all tried to forecast the consequences of this2 and by way of verification we might begin with nine hours2 or we might induce some other country to try the experiment first4 ,still1 no verification by experiments on a small scale1 or in a mild form1 or in somewhat similar yet different circumstances1 can be considered logically conclusive4 ,what proofs are conclusive we shall see in the following chapters4 #b4 ,to begin with the conditions of direct ,induction4--,an ,induction is an universal real proposition1 based on observation1 in reliance on the uniformity of ,nature3 when well ascertained1 it is called a ,law4 ,thus1 that all life depends on the presence of oxygen is 7#a7 an universal proposition2 7#b7 a real one1 since the 'presence of oxygen' is not connoted by 'life'2 7#c7 it is based on observation2 7#d7 it relies on the uniformity of ,nature1 since all cases of life have not been examined4 ,such a proposition is here called 'an induction1' when it is inductively proved2 that is1 proved by facts1 not merely deduced from more general premises 7except the premise of ,nature's uniformity73 and by the 'process of induction' is meant the method of inductive proof4 ,the phrase 'process of induction' is often used in another sense1 namely for the inference or judgment by which such propositions are arrived at4 ,but it is better to call this 'the process of hypothesis1' and to regard it as a preliminary to the process of induction 7that is1 proof71 as furnishing the hypothesis which1 if it can stand the proper tests1 becomes an induction or law4 #c4 ,inductive proofs are usually classed as ,perfect and ,imperfect4 ,they are said to be perfect when all the instances within the scope of the given proposition have been severally examined1 and the proposition has been found true in each case4 ,but we have seen 7chap4 xiii4 #b7 that the instances included in universal propositions concerning ,causes and ,kinds cannot be exhaustively examined3 we do not know all planets1 all heat1 all liquids1 all life1 etc42 and we never can1 since a man's life is never long enough4 ,it is only where the conditions of time1 place1 etc41 are arbitrarily limited that examination can be exhaustive4 ,perfect induction might show 7say7 that every member of the present ,house of ,commons has two ,christian names4 ,such an argument is sometimes exhibited as a ,syllogism in ,darapti with a ,minor premise in ,u41 which legitimates a ,conclusion in ,a41 thus3 ,a4,b4 to ,z have two ,christian names2 ,a4,b4 to ,z are all the present ,m4,p4's3 ,all the present ,m4,p4's have two ,christian names4 ,but in such an investigation there is no need of logical method to find the major premise2 it is mere counting3 and to carry out the syllogism is a hollow formality4 ,accordingly1 our definition of ,induction excludes the kind unfortunately called ,perfect1 by including in the notion of ,induction a reliance on the uniformity of ,nature2 for this would be superfluous if every instance in question had been severally examined4 ,imperfect ,induction1 then1 is what we have to deal with3 the method of showing the credibility of an universal real proposition by an examination of some of the instances it includes1 generally a small fraction of them4 #d4 ,imperfect ,induction is either ,methodical or ,immethodical4 ,now1 ,method is procedure upon a principle2 and if the method is to be precise and conclusive1 the principle must be clear and definite4 ,there is a ,geometrical ,method1 because the axioms of ,geometry are clear and definite1 and by their means1 with the aid of definitions1 laws are deduced of the equality of lines and angles and other relations of position and magnitude in space4 ,the process of proof is purely ,deductive 7the axioms and definitions being granted74 ,diagrams are used not as facts for observation1 but merely to fix our attention in following the general argument2 so that it matters little how badly they are drawn1 as long as their divergence from the conditions of the proposition to be proved is not distracting4 ,even the appeal to superposition to prove the equality of magnitudes 7as in ,euclid ,i4 #d71 is not an appeal to observation1 but to our judgment of what is implied in the foregoing conditions4 ,hence no inference is required from the special case to all similar ones2 for they are all proved at once4 ,there is also1 as we have seen1 a method of ,deductive ,logic resting on the ,principles of ,consistency and the ,dictum de omni et nullo4 ,and we shall find that there is a method of ,inductive ,logic1 resting on the principle of ,causation4 ,but there are a good many general propositions1 more or less trustworthy within a certain range of conditions1 which cannot be methodically proved for want of a precise principle by which they may be tested2 and they1 therefore1 depend upon ,immethodical ,induction1 that is1 upon the examination of as many instances as can be found1 relying for the rest upon the undefinable principle of the ,uniformity of ,nature1 since we are not able to connect them with any of its definite modes enumerated in chap4 xiii4 #g4 ,to this subject we shall return in chap4 xix41 after treating of ,methodical ,induction1 or the means of determining that a relation of events is of the nature of cause and effect1 because the relation can be shown to have the marks of causation1 or some of them4 #e4 ,observations and ,experiments are the material grounds of ,induction4 ,an experiment is an observation made under prepared1 and therefore known1 conditions2 and1 when obtainable1 it is much to be preferred4 ,simple observation shows that the burning of the fire depends1 for one thing1 on the supply of air2 but it cannot show us that it depends on oxygen4 ,to prove this we must make experiments as by obtaining pure oxygen and pure nitrogen 7which1 mixed in the proportion of one to four1 form the air7 in separate vessels1 and then plunging a burning taper into the oxygen--when it will blaze fiercely2 and again plunging it into the nitrogen--when it will be extinguished4 ,this shows that the greater part of the air does nothing to keep the fire alight1 except by diminishing its intensity and so making it last longer4 ,experiments are more perfect the more carefully they are prepared1 and the more completely the conditions are known under which the given phenomenon is to be observed4 ,therefore1 they become possible only when some knowledge has already been gained by observation2 for else the preparation which they require could not be made4 ,observation1 then1 was the first material ground of ,induction1 and in some sciences it remains the chief ground4 ,the heavenly bodies1 the winds and tides1 the strata of the earth1 and the movements of history1 are beyond our power to experiment with4 ,experiments upon the living body or mind are indeed resorted to when practicable1 even in the case of man1 as now in all departments of ,psychology2 but1 if of a grave nature1 they are usually thought unjustifiable4 ,and in political affairs experiments are hindered by the reflection1 that those whose interests are affected must bear the consequences and may resent them4 ,hence1 it is in physical and chemical inquiries and in the physiology of plants and animals 7under certain conditions7 that direct experiment is most constantly practised4 ,where direct experiment is possible1 however1 it has many advantages over unaided observation4 ,if one experiment does not enable us to observe the phenomenon satisfactorily1 we may try again and again2 whereas the mere observer1 who wishes to study the bright spots on ,mars1 or a commercial crisis1 must wait for a favourable opportunity4 ,again1 in making experiments we can vary the conditions of the phenomenon1 so as to observe its different behaviour in each case2 whereas he who depends solely on observation must trust the bounty of nature to supply him with a suitable diversity of instances4 ,it is a particular advantage of experiment that a phenomenon may sometimes be 'isolated1' that is1 removed from the influence of all agents except that whose operation we desire to observe1 or except those whose operation is already known3 whereas a simple observer1 who has no control over the conditions of the subject he studies1 can never be quite sure that its movements or changes are not due to causes that have never been conspicuous enough to draw his attention4 ,finally1 experiment enables us to observe coolly and circumspectly and to be precise as to what happens1 the time of its occurrence1 the order of successive events1 their duration1 intensity and extent4 ,but whether we proceed by observation or experiment1 the utmost attainable exactness of measurements and calculation is requisite2 and these presuppose some ,unit1 in multiples or divisions of which the result may be expressed4 ,this unit cannot be an abstract number as in ,arithmetic1 but must be one something--an hour1 or a yard1 or a pound--according to the nature of the phenomenon to be measured4 ,but what is an hour1 or a yard or a pound8 ,there must in each case be some constant ,standard of reference to give assurance that the unit may always have the same value4 ,the ,english pound is defined by a certain lump of platinum preserved at ,westminster4 ,the unit may be identical with the standard or some division or multiple of it2 and1 in measuring the same kind of phenomena1 different units may be used for different purposes as long as each bears a constant relation to the standard4 ,thus1 taking the rotation of the earth as the standard of ,time1 the convenient unit for long periods is a year 7which is a multiple72 for shorter periods1 a day 7which is identical72 for shorter still1 an hour 7which is a division71 or a second1 or a thousandth of a second4 7,see ,jevons' ,principles of ,science1 ch4 #ad47 #f4 ,the principle of ,causation is the formal ground of ,induction2 and the ,inductive ,canons derived from it are means of testing the formal sufficiency of observations to justify the statement of a ,law4 ,if we can observe the process of cause and effect in nature we may generalise our observation into a law1 because that process is invariable4 ,first1 then1 can we observe the course of cause and effect8 ,our power to do so is limited by the refinement of our senses aided by instruments1 such as lenses1 thermometers1 balances1 etc4 ,if the causal process is essentially molecular change1 as in the maintenance of combustion by oxygen1 we cannot directly observe it2 if the process is partly cerebral or mental1 as in social movements which depend on feeling and opinion1 it can but remotely be inferred2 even if the process is a collision of moving masses 7billiard-balls71 we cannot really observe what happens1 the elastic yielding1 and recoil and the internal changes that result2 though no doubt photography will throw some light upon this1 as it has done upon the galloping of horses and the impact of projectiles4 ,direct observation is limited to the effect which any change in a phenomenon 7or its index7 produces upon our senses2 and what we believe to be the causal process is a matter of inference and calculation4 ,the meagre and abstract outlines of ,inductive ,logic are apt to foster the notion1 that the evidence on which ,science rests is simple2 but it is amazingly intricate and cumulative4 ,secondly1 so far as we can observe the process of nature1 how shall we judge whether a true causal instance1 a relation of cause and effect1 is before us8 ,by looking for the five marks of ,causation4 ,thus1 in the experiment above described1 showing that oxygen supports combustion1 we find--7#a7 that the taper which only glowed before being plunged into the oxygen1 bursts into flame when there--,sequence2 7#b7 that this begins to happen at once without perceptible interval--,immediacy2 7#c7 that no other agent or disturbing circumstance was present 7the preparation of the experiment having excluded any such thing7--,unconditionalness2 7#d7 the experiment may be repeated as often as we like with the same result--,invariableness4 ,invariableness1 indeed1 ,i do not regard as formally necessary to be shown1 supposing the other marks to be clear2 for it can only be proved within our experience2 and the very object of ,induction is to find grounds of belief beyond actual experience4 ,however1 for material assurance1 to guard against his own liability to error1 the inquirer will of course repeat his experiments4 ,the above four are the qualitative marks of ,causation3 the fifth and quantitative mark is the ,equality of ,cause and ,effect2 and this1 in the above example1 the ,chemist determines by showing that1 instead of the oxygen and wax that have disappeared during combustion1 an equivalent weight of carbon dioxide1 water1 etc41 has been formed4 ,here1 then1 we have all the marks of causation2 but in the ordinary judgments of life1 in history1 politics1 criticism1 business1 we must not expect such clear and direct proofs2 in subsequent chapters it will appear how different kinds of evidence are combined in different departments of investigation4 #g4 ,the ,inductive ,canons1 to be explained in the next chapter1 describe the character of observations and experiments that justify us in drawing conclusions about causation2 and1 as we have mentioned1 they are derived from the principle of ,causation itself4 ,according to that principle1 cause and effect are invariably1 immediately and unconditionally antecedent and consequent1 and are equal as to the matter and energy embodied4 ,invariability can only be observed1 in any of the methods of induction1 by collecting more and more instances1 or repeating experiments4 ,of course it can never be exhaustively observed4 ,immediacy1 too1 in direct ,induction1 is a matter for observation the most exact that is possible4 ,succession1 or the relation itself of antecedent and consequent1 must either be directly observed 7or some index of it72 or else ascertained by showing that energy gained by one phenomenon has been lost by another1 for this implies succession4 ,but to determine the unconditionality of causation1 or the indispensability of some condition1 is the great object of the methods1 and for that purpose the meaning of unconditionality may be further explicated by the following rules for the determination of a ,cause4 ,a4 ,,qualitative ,,determination ,i4--,for ,positive ,instances4 ,to prove a supposed ,cause3 7a7 ,any agent whose introduction among certain conditions 7without further change7 is followed by a given phenomenon2 or1 7b7 whose removal is followed by the cessation 7or modification7 of that phenomenon1 is 7so far7 the cause or an indispensable condition of it4 ,to find the ,effect3 7c7 ,any event that follows a given phenomenon1 when there is no further change2 or1 7d7 that does not occur when the conditions of a former occurrence are exactly the same1 except for the absence of that phenomenon1 is the effect of it 7or is dependent on it74 ,,ii4--,for ,negative ,instances4 ,to exclude a supposed ,cause3 7a7 ,any agent that can be introduced among certain conditions without being followed by a given phenomenon 7or that is found without that phenomenon72 or 7b7 that can be removed when that phenomenon is present without impairing it 7or that is absent when that phenomenon is present71 is not the cause1 or does not complete the cause1 of that phenomenon in those circumstances4 ,to exclude a supposed ,effect3 7c7 ,any event that occurs without the introduction 7or presence7 of a given phenomenon2 or 7d7 that does not occur when that phenomenon is introduced 7or is present71 is not the effect of that phenomenon4 99 99 99 99 99 ,subject to the conditions thus stated1 the rules may be briefly put as follows3 ,i4 7a7 ,that which 7without further change7 is followed by a given event is its cause4 ,,ii4 7a7 ,that which is not so followed is not the cause4 ,i4 7b7 ,that which cannot be left out without impairing a phenomenon is a condition of it4 ,,ii4 7b7 ,that which can be left out is not a condition of it4 ,b4 ,,quantitative ,,determination ,the ,equality of ,cause and ,effect may be further explained by these rules3 ,,iii4 7a7 ,when a cause 7or effect7 increases or decreases1 so does its effect 7or cause74 ,,iii4 7b7 ,if two phenomena1 having the other marks of cause and effect1 seem unequal1 the less contains an unexplored factor4 ,,iii4 7c7 ,if an antecedent and consequent do not increase or decrease correspondingly1 they are not cause and effect1 so far as they vary4 ,it will next be shown that these propositions are variously combined in ,mill's five ,canons of ,induction3 ,agreement1 the ,joint ,method1 ,difference1 ,variations1 ,residues4 ,the first three are sometimes called ,qualitative ,methods1 and the two last ,quantitative2 and although this grouping is not quite accurate1 seeing that ,difference is often used quantitatively1 yet it draws attention to an important distinction between a mere description of conditions and determination by exact measurement4 ,to avoid certain misunderstandings1 some slight alterations have been made in the wording of the ,canons4 ,it may seem questionable whether the ,canons add anything to the above propositions3 ,i think they do4 ,they are not discussed in the ensuing chapter merely out of reverence for ,mill1 or regard for a nascent tradition2 but because1 as describing the character of observations and experiments that justify us in drawing conclusions about causation1 they are guides to the analysis of observations and to the preparation of experiments4 ,to many eminent investigators the ,canons 7as such7 have been unknown2 but they prepared their work effectively so far only as they had definite ideas to the same purport4 ,a definite conception of the conditions of proof is the necessary antecedent of whatever preparations may be made for proving anything4 ,,chapter ,,xvi ,,the ,,canons ,,of ,,direct ,,induction #a4 ,let me begin by borrowing an example from ,bain 7,logic3 ,b4 ,,iii4 c4 #f74 ,the ,north-,east wind is generally detested in this country3 as long as it blows few people feel at their best4 ,occasional well-known causes of a wind being injurious are violence1 excessive heat or cold1 excessive dryness or moisture1 electrical condition1 the being laden with dust or exhalations4 ,let the hypothesis be that the last is the cause of the ,north-,east wind's unwholesome quality2 since we know it is a ground current setting from the pole toward the equator and bent westward by the rotation of the earth2 so that1 reaching us over thousands of miles of land1 it may well be fraught with dust1 effluvia1 and microbes4 ,now1 examining many cases of ,north-,east wind1 we find that this is the only circumstance in which all the instances agree3 for it is sometimes cold1 sometimes hot2 generally dry1 but sometimes wet2 sometimes light1 sometimes violent1 and of all electrical conditions4 ,each of the other circumstances1 then1 can be omitted without the ,n4,e4 wind ceasing to be noxious2 but one circumstance is never absent1 namely1 that it is a ground current4 ,that circumstance1 therefore1 is probably the cause of its injuriousness4 ,this case illustrates3-- 7,i7 ,,the ,,canon ,,of ,,agreement4 ,if two or more instances of a phenomenon under investigation have only one other circumstance 7antecedent or consequent7 in common1 that circumstance is probably the cause 7or an indispensable condition7 or the effect of the phenomenon1 or is connected with it by causation4 ,this rule of proof 7so far as it is used to establish direct causation7 depends1 first1 upon observation of an invariable connection between the given phenomenon and one other circumstance2 and1 secondly1 upon ,i4 7a7 and ,,ii4 7b7 among the propositions obtained from the unconditionality of causation at the close of the last chapter4 ,to prove that ,a is causally related to p1 suppose two instances of the occurrence of ,a1 an antecedent1 and p1 a consequent1 with concomitant facts or events--and let us represent them thus3 ,antecedents3 ,a ,b ,c ,a ,d ,e ,consequents3 p q r p s t2 and suppose further that1 in this case1 the immediate succession of events can be observed4 ,then ,a is probably the cause1 or an indispensable condition1 of p4 ,for1 as far as our instances go1 ,a is the invariable antecedent of p2 and p is the invariable consequent of ,a4 ,but the two instances of ,a or p agree in no other circumstance4 ,therefore ,a is 7or completes7 the unconditional antecedent of p4 ,for ,b and ,c are not indispensable conditions of p1 being absent in the second instance 7,rule ,,ii4 7b772 nor are ,d and ,e1 being absent in the first instance4 ,moreover1 q and r are not effects of ,a1 being absent in the second instance 7,rule ,,ii4 7d772 nor are s and t1 being absent in the first instance4 ,it should be observed that the cogency of the proof depends entirely upon its tending to show the unconditionality of the sequence ,a-p1 or the indispensability of ,a as a condition of p4 ,that p follows ,a1 even immediately1 is nothing by itself3 if a man sits down to study and1 on the instant1 a hand-organ begins under his window1 he must not infer malice in the musician3 thousands of things follow one another every moment without traceable connection2 and this we call 'accidental4' ,even invariable sequence is not enough to prove direct causation2 for1 in our experience does not night invariable follow day8 ,the proof requires that the instances be such as to show not merely what events are in invariable sequence1 but also what are not4 ,from among the occasional antecedents of p 7or consequents of ,a7 we have to eliminate the accidental ones4 ,and this is done by finding or making 'negative instances' in respect of each of them4 ,thus the instance ,a ,d ,e p s t is a negative instance of ,b and ,c considered as supposable causes of p 7and of q and r as supposable effects of ,a72 for it shows that they are absent when p 7or ,a7 is present4 ,to insist upon the cogency of 'negative instances' was ,bacon's great contribution to ,inductive ,logic4 ,if we neglect them1 and merely collect examples of the sequence ,a-p1 this is 'simple enumeration'2 and although simple enumeration1 when the instances of agreement are numerous enough1 may give rise to a strong belief in the connection of phenomena1 yet it can never be a methodical or logical proof of causation1 since it does not indicate the unconditionalness of the sequence4 ,for simple enumeration of the sequence ,a-p leaves open the possibility that1 besides ,a1 there is always some other antecedent of p1 say ,x2 and then ,x may be the cause of p4 ,to disprove it1 we must find1 or make1 a negative instance of ,x--where p occurs1 but ,x is absent4 ,so far as we recognise the possibility of a plurality of causes1 this method of ,agreement cannot be quite satisfactory4 ,for then1 in such instances as the above1 although ,d is absent in the first1 and ,b in the second1 it does not follow that they are not the causes of p2 for they may be alternative causes3 ,b may have produced p in the first instance1 and ,d in the second2 ,a being in both cases an accidental circumstance in relation to p4 ,to remedy this shortcoming by the method of ,agreement itself1 the only course is to find more instances of p4 ,we may never find a negative instance of ,a2 and1 if not1 the probability that ,a is the cause of p increases with the number of instances4 ,but if there be no antecedent that we cannot sometimes exclude1 yet the collection of instances will probably give at last all the causes of p2 and by finding the proportion of instances in which ,a1 ,b1 or ,x precedes p1 we may estimate the probability of any one of them being the cause of p in any given case of its occurrence4 ,but this is not enough4 ,since there cannot really be vicarious causes1 we must define the effect 7p7 more strictly1 and examine the cases to find whether there may not be varieties of p1 with each of which one of the apparent causes is correlated3 ,a with p#a ,b with p#aa1 ,x with p#aaa4 ,or1 again1 it may be that none of the recognised antecedents is effective3 as we here depend solely on observation1 the true conditions may be so recondite and disguised by other phenomena as to have escaped our scrutiny4 ,this may happen even when we suppose that the chief condition has been isolated3 the drinking of foul water was long believed to cause dysentery1 because it was a frequent antecedent2 whilst observation had overlooked the bacillus1 which was the indispensable condition4 ,again1 though we have assumed that1 in the instances supposed above1 immediate sequence is observable1 yet in many cases it may not be so1 if we rely only on the canon of ,agreement2 if instances cannot be obtained by experiment1 and we have to depend on observation4 ,the phenomena may then be so mixed together that ,a and p seem to be merely concomitant2 so that1 though connection of some sort may be rendered highly probable1 we may not be able to say which is cause and which is effect4 ,we must then try 7as ,bain says7 to trace the expenditure of energy3 if p gains when ,a loses1 the course of events if from ,a to p4 ,moreover1 where succession cannot be traced1 the method of ,agreement may point to a connection between two or more facts 7perhaps as co-effects of a remote cause7 where direct causation seems to be out of the question3 e4g41 that ,negroes1 though of different tribes1 different localities1 customs1 etc41 are prognathous1 woolly-haired and dolichocephalic4 ,the ,method of ,agreement1 then1 cannot by itself prove causation4 ,its chief use 7as ,mill says7 is to suggest hypotheses as to the cause2 which must then be used 7if possible7 experimentally to try if it produces the given effect4 ,a bacillus1 for example1 being always found with a certain disease1 is probably the chief condition of it3 give it to a guinea-pig1 and observe whether the disease appears in that animal4 ,men often use arguments which1 if they knew it1 might be shown to conform more or less to this canon2 for they collect many instances to show that two events are connected2 but usually neglect to bring out the negative side of the proof2 so that their arguments only amount to simple enumeration4 ,thus ,ascham in his ,toxophilus1 insisting on the national importance of archery1 argues that victory has always depended on superiority in shooting2 and1 to prove it1 he shows how the ,parthians checked the ,romans1 ,sesostris conquered a great part of the known world1 ,tiberius overcame ,arminius1 the ,turks established their empire1 and the ,english defeated the ,french 7with many like examples7--all by superior archery4 ,but having cited these cases to his purpose1 he is content2 whereas he might have greatly strengthened his proof by showing how one or the other instance excludes other possible causes of success4 ,thus3 the cause was not discipline1 for the ,romans were better disciplined than the ,parthians2 nor yet the boasted superiority of a northern habitat1 for ,sesostris issued from the south2 nor better manhood1 for here the ,germans probably had the advantage of the ,romans2 nor superior civilisation1 for the ,turks were less civilised than most of those they conquered2 nor numbers1 nor even a good cause1 for the ,french were more numerous than the ,english1 and were shamefully attacked by ,henry ,v4 on their own soil4 ,many an argument from simple enumeration may thus be turned into an induction of greater plausibility according to the ,canon of ,agreement4 ,still1 in the above case1 the effect 7victory7 is so vaguely conceived1 that a plurality of causes must be allowed for3 although1 e4g41 discipline did not enable the ,romans to conquer the ,parthians1 it may have been their chief advantage over the ,germans2 and it was certainly important to the ,english under ,henry ,v4 in their war with the ,french4 ,here is another argument1 somewhat similar to the above1 put forward by ,h4 ,spencer with a full consciousness of its logical character4 ,states that make war their chief object1 he says1 assume a certain type of organisation1 involving the growth of the warrior class and the treatment of labourers as existing solely to sustain the warriors2 the complete subordination of individuals to the will of the despotic soldier-king1 their property1 liberty and life being at the service of the ,state2 the regimentation of society not only for military but also for civil purposes2 the suppression of all private associations1 etc4 ,this is the case in ,dahomey and in ,russia1 and it was so at ,sparta1 in ,egypt1 and in the empire of the ,yncas4 ,but the similarity of organisation in these ,states cannot have been due to race1 for they are all of different races2 nor to size1 for some are small1 some large2 nor to climate or other circumstances of habitat1 for here again they differ widely3 the one thing they have in common is the military purpose2 and this1 therefore1 must be the cause of their similar organisation4 7,political ,institutions47 ,by this method1 then1 to prove that one thing is causally connected with another1 say ,a with p1 we show1 first1 that in all instances of p1 ,a is present2 and1 secondly1 that any other supposable cause of p may be absent without disturbing p4 ,we next come to a method the use of which greatly strengthens the foregoing1 by showing that where p is absent ,a is also absent1 and 7if possible7 that ,a is the only supposable cause that is always absent along with p4 #b4 ,,the ,,canon ,,of ,,the ,,joint ,,method ,,of ,,agreement ,,in ,,presence ,,and ,,in ,,absence4 ,if 7#a7 two or more instances in which a phenomenon occurs have only one other circumstance 7antecedent or consequent7 in common1 while 7#b7 two or more instances in which it does not occur 7though in important points they resemble the former set of instances7 have nothing else in common save the absence of that circumstance--the circumstance in which alone the two sets of instances differ throughout 7being present in the first set and absent in the second7 is probably the effect1 or the cause1 or an indispensable condition of the phenomenon4 ,the first clause of this ,canon is the same as that of the method of ,agreement1 and its significance depends upon the same propositions concerning causation4 ,the second clause1 relating to instances in which the phenomenon is absent1 depends for its probative force upon ,prop4 ,,ii4 7a71 and ,i4 7b73 its function is to exclude certain circumstances 7whose nature or manner of occurrence gives them some claim to consideration7 from the list of possible causes 7or effects7 of the phenomenon investigated4 ,it might have been better to state this second clause separately as the ,canon of the ,method of ,exclusions4 ,to prove that ,a is causally related to p1 let the two sets of instances be represented as follows3 ,instances of ,presence4 ,instances of ,absence4 ,a ,b ,c ,c ,h ,f p q r r x v ,a ,d ,e ,b ,d ,k p s t q y s ,a ,f ,g ,e ,g ,m p u v t f u ,then ,a is probably the cause or a condition of p1 or p is dependent upon ,a3 first1 by the ,canon of ,agreement in ,presence1 as represented by the first set of instances2 and1 secondly1 by ,agreement in ,absence in the second set of instances4 ,for there we see that ,c1 ,h1 ,f1 ,b1 ,d1 ,k1 ,e1 ,g1 ,m occur without the phenomenon p1 and therefore 7by ,prop4 ,,ii4 7a77 are not its cause1 or not the whole cause1 unless they have been counteracted 7which is a point for further investigation74 ,we also see that r1 v1 q1 s1 t1 u occur without ,a1 and therefore are not the effects of ,a4 ,and1 further1 if the negative instances represent all possible cases1 we see that 7according to ,prop4 ,i4 7b77 ,a is the cause of p1 because it cannot be omitted without the cessation of p4 ,the inference that ,a and p are cause and effect1 suggested by their being present throughout the first set of instances1 is therefore strengthened by their being both absent throughout the second set4 ,so far as this ,double ,method1 like the ,single ,method of ,agreement1 relies on observation1 sequence may not be perceptible in the instances observed1 and then1 direct causation cannot be proved by it1 but only the probability of causal connection2 and1 again1 the real cause1 though present1 may be so obscure as to evade observation4 ,it has1 however1 one peculiar advantage1 namely1 that if the second list of instances 7in which the phenomenon and its supposed antecedent are both absent7 can be made exhaustive1 it precludes any hypothesis of a plurality of causes2 since all possible antecedents will have been included in this list without producing the phenomenon4 ,thus1 in the above symbolic example1 taking the first set of instances1 the supposition is left open that ,b1 ,c1 ,d1 ,e1 ,f1 ,g may1 at one time or another1 have been a condition of p2 but1 in the second list1 these antecedents all occur1 here or there1 without producing p1 and therefore 7unless counteracted somehow7 cannot be a condition of p4 ,a1 then1 stands out as the one thing that is present whenever p is present1 and absent whenever p is absent4 ,stated in this abstract way1 the ,double ,method may seem very elaborate and difficult2 yet1 in fact1 its use may be very simple4 ,tyndall1 to prove that dispersed light in the air is due to motes1 showed by a number of cases 7#a7 that any gas containing motes is luminous2 7#b7 that air in which the motes had been destroyed by heat1 and any gas so prepared as to exclude motes1 are not luminous4 ,all the instances are of gases1 and the result is3 motes--luminosity2 no motes--no luminosity4 ,darwin1 to show that cross-fertilisation is favourable to flowers1 placed a net about #ajj flower-heads1 and left #ajj others of the same varieties exposed to the bees3 the former bore no seed1 the latter nearly #c1jjj4 ,we must assume that1 in ,darwin's judgment1 the net did not screen the flowers from light and heat sufficiently to affect the result4 ,there are instructive applications of this ,double ,method in ,wallace's ,darwinism4 ,in chap4 viii41 on ,colour in ,animals1 he observes1 that the usefulness of their coloration to animals is shown by the fact that1 as a rule1 colour and marking are constant in each species of wild animal1 while1 in almost every domesticated animal1 there arises great variability4 ,we see this in our horses and cattle1 our dogs and cats1 our pigeons and poultry4 ,now the essential difference between the conditions of life of domesticated and wild animals is1 that the former are protected by man1 while the latter have to protect themselves4 ,wild animals protect themselves by acquiring qualities adapted to their mode of life2 and coloration is a very important one1 its chief1 though not its only use1 being concealment4 ,hence a useful coloration having been established in any species1 individuals that occasionally may vary from it1 will generally1 perish2 whilst1 among domestic animals1 variation of colour or marking is subject to no check except the taste of owners4 ,we have1 then1 two lists of instances2 first1 innumerable species of wild animals in which the coloration is constant and which depend upon their own qualities for existence2 secondly1 several species of domestic animals in which the coloration is not constant1 and which do not depend upon their own qualities for existence4 ,in the former list two circumstances are present together 7under all sorts of conditions72 in the latter they are absent together4 ,the argument may be further strengthened by adding a third list1 parallel to the first1 comprising domestic animals in which coloration is approximately constant1 but where 7as we know7 it is made a condition of existence by owners1 who only breed from those specimens that come up to a certain standard of coloration4 ,wallace goes on to discuss the colouring of arctic animals4 ,in the arctic regions1 he says1 some animals are wholly white all the year round1 such as the polar bear1 the ,american polar hare1 the snowy owl and the ,greenland falcon3 these live amidst almost perpetual snow4 ,others1 that live where the snow melts in summer1 only turn white in winter1 such as the arctic hare1 the arctic fox1 the ermine and the ptarmigan4 ,in all these cases the white colouring is useful1 concealing the herbivores from their enemies1 and also the carnivores in approaching their prey2 this usefulness1 therefore1 is a condition of the white colouring4 ,two other explanations have1 however1 been suggested3 first1 that the prevalent white of the arctic regions directly colours the animals1 either by some photographic or chemical action on the skin1 or by a reflex action through vision 7as in the chameleon72 secondly1 that a white skin checks radiation and keeps the animals warm4 ,but there are some exceptions to the rule of white colouring in arctic animals which refute these hypotheses1 and confirm the author's4 ,the sable remains brown throughout the winter2 but it frequents trees1 with whose bark its colour assimilates4 ,the musk-sheep is brown and conspicuous2 but it is gregarious1 and its safety depends upon its ability to recognise its kind and keep with the herd4 ,the raven is always black2 but it fears no enemy and feeds on carrion1 and therefore does not need concealment for either defence or attack4 ,the colour of the sable1 then1 though not white1 serves for concealment2 the colour of the musk-sheep serves a purpose more important than concealment2 the raven needs no concealment4 ,there are thus two sets of instances3--in one set the animals are white 7a7 all the year1 7b7 in winter2 and white conceals them 7a7 all the year1 7b7 in winter2 in the other set1 the animals are not white1 and to them either whiteness would not give concealment1 or concealment would not be advantageous4 ,and this second list refutes the rival hypotheses3 for the sable1 the musk-sheep and the raven are as much exposed to the glare of the snow1 and to the cold1 as the other animals are4 #c4 ,,the ,,canon ,,of ,,difference4 ,if an instance in which a phenomenon occurs1 and an instance in which it does not occur1 have every other circumstance in common save one1 that one 7whether consequent or antecedent7 occurring only in the former2 the circumstance in which alone the two instances differ is the effect1 or the cause1 or an indispensable condition of the phenomenon4 ,this follows from ,props4 ,i 7a7 and 7b71 in chapter xv4 #g4 ,to prove that ,a is a condition of p1 let two instances1 such as the ,canon requires1 be represented thus3 ,a ,b ,c ,b ,c p q r q r ,then ,a is the cause or a condition of p4 ,for1 in the first instance1 ,a being introduced 7without further change71 p arises 7,prop4 ,i4 7a772 and1 in the second instance1 ,a having been removed 7without other change71 p disappears 7,prop4 ,i4 7b774 ,similarly we may prove1 by the same instances1 that p is the effect of ,a4 ,the order of the phenomena and the immediacy of their connection is a matter for observation1 aided by whatever instruments and methods of inspection and measurement may be available4 ,as to the invariability of the connection1 it may of course be tested by collecting more instances or making more experiments2 but it has been maintained1 that a single perfect experiment according to this method is sufficient to prove causation1 and therefore implies invariability 7since causation is uniform71 though no other instances should ever be obtainable2 because it establishes once for all the unconditionality of the connection ,a ,b ,c p q r4 ,now1 formally this is true2 but in any actual investigation how shall we decide what is a satisfactory or perfect experiment8 ,such an experiment requires that in the negative instance ,b ,c q r1 ,,bc shall be the least assemblage of conditions necessary to co-operate with ,a in producing p2 and that it is so cannot be ascertained without either general prior knowledge of the nature of the case or special experiments for the purpose4 ,so that invariability will not really be inferred from a single experiment2 besides that every prudent inquirer repeats his experiments1 if only to guard against his own liability to error4 ,the supposed plurality of causes does not affect the method of ,difference4 ,in the above symbolic case1 ,a is clearly one cause 7or condition7 of p1 whatever other causes may be possible2 whereas with the ,single ,method of ,agreement1 it remained doubtful 7admitting a plurality of causes7 whether ,a1 in spite of being always present with p1 was ever a cause or condition of it4 ,this method of ,difference without our being distinctly aware of it1 is oftener than any other the basis of ordinary judgments4 ,that the sun gives light and heat1 that food nourishes and fire burns1 that a stone breaks a window or kills a bird1 that the turning of a tap permits or checks the flow of water or of gas1 and thousands of other propositions are known to be true by rough but often emphatic applications of this method in common experience4 ,the method of ,difference may be applied either 7#a7 by observation1 on finding two instances 7distinct assemblages of conditions7 differing only in one phenomenon together with its antecedent or consequent2 or 7#b7 by experiment1 and then1 either 7a7 by preparing two instances that may be compared side by side1 or 7b7 by taking certain conditions1 and then introducing 7or subtracting7 some agent1 supposed to be the cause1 to see what happens3 in the latter case the two instances are the same assemblage of conditions considered before and1 again1 after1 the introduction of the agent4 ,as an example of 7a7 there is an experiment to show that radium gives off heat3 take two glass tubes1 in one put some chloride of radium1 in both thermometers1 and close them with cotton-wool4 ,soon the thermometer in the tube along with radium reads #ed ,f4 higher than the other one4 ,the tube without the radium1 whose temperature remains unaltered1 is called the control experiment4 ,most experiments are of the type 7b72 and since the ,canon1 which describes two co-existing instances1 does not readily apply to this type1 an alternative version may be offered3 ,any agent whose introduction into known circumstances 7without further change7 is immediately followed by a definite phenomenon is a condition of the occurrence of that phenomenon4 ,the words into known circumstances are necessary to emphasise what is required by this ,method1 namely1 that the two instances differ in only one thing2 for this cannot be ascertained unless all the other conditions are known2 and this further implies that they have been prepared4 ,it is1 therefore1 not true 7as ,sigwart asserts7 that this method determines only one condition of a phenomenon1 and that it is then necessary to inquire into the other conditions4 ,if they were not known they must be investigated2 but then the experiment would not have been made upon this method4 ,practically1 experiments have to be made in all degrees of imperfection1 and the less perfect they are1 that is1 the less the circumstances are known beforehand1 the more remains to be done4 ,a common imperfection is delay1 or the occurrence of a latent period between the introduction of an agent and the manifestation of its effects2 it cannot then be the unconditional cause2 though it may be an indispensable remote condition of whatever change occurs4 ,if1 feeling out of sorts1 you take a drug and some time afterwards feel better1 it is not clear on this ground alone that the drug was the cause of recovery1 for other curative processes may have been active meanwhile--food1 or sleep1 or exercise4 ,any book of ,physics or of ,chemistry will furnish scores of examples of the method of ,difference3 such as ,galileo's experiment to show that air has weight1 by first weighing a vessel filled with ordinary air1 and then filling it with condensed air and weighing it again2 when the increased weight can only be due to the greater quantity of air contained4 ,the melting-point of solids is determined by heating them until they do melt 7as silver at #ajjj ,c41 gold at #abej1 platinum at #bjjj72 for the only difference between bodies at the time of melting and just before is the addition of so much heat4 ,similarly with the boiling point of liquids4 ,that the transmission of sound depends upon the continuity of an elastic ponderable medium1 is proved by letting a clock strike in a vacuum 7under a glass from which the air has been withdrawn by an air pump71 and standing upon a non-elastic pedestal3 when the clock be seen to strike1 but makes only such a faint sound as may be due to the imperfections of the vacuum and the pedestal4 ,the experiments by which the chemical analysis or synthesis of various forms of matter is demonstrated are simple or compound applications of this method of ,difference1 together with the quantitative mark of causation 7that cause and effect are equal72 since the bodies resulting from an analysis are equal in weight to the body analysed1 and the body resulting from a synthesis is equal in weight to the bodies synthesised4 ,that an electric current resolves water into oxygen and hydrogen may be proved by inserting the poles of a galvanic battery in a vessel of water2 when this one change is followed by another1 the rise of bubbles from each pole and the very gradual decrease of the water4 ,if the bubbles are caught in receivers placed over them1 it can be shown that the joint weight of the two bodies of gas thus formed is equal to the weight of the water that has disappeared2 and that the gases are respectively oxygen and hydrogen may then be shown by proving that they have the properties of those gases according to further experiments by the method of ,difference2 as 7e4g47 that one of them is oxygen because it supports combustion1 etc4 ,when water was first decomposed by the electric current1 there appeared not only oxygen and hydrogen1 but also an acid and an alkali4 ,these products were afterwards traced to impurities of the water and of the operator's hands4 ,mill observes that in any experiment the effect1 or part of it1 may be due1 not to the supposed agent1 but to the means employed in introducing it4 ,we should know not only the other conditions of an experiment1 but that the agent or change introduced is nothing else than what it is supposed to be4 ,in the more complex sciences the method of ,difference is less easily applicable1 because of the greater difficulty of being sure that only one circumstance at a time has altered2 still1 it is frequently used4 ,thus1 if by dividing a certain nerve certain muscles are paralysed1 it is shown that normally that nerve controls those muscles4 ,that the sense of smell in flies and cockroaches is connected with the antennae has been shown by cutting them off3 whereupon the insects can no longer find carrion4 ,in his work on ,earthworms1 ,darwin shows that1 though sensitive to mechanical tremors1 they are deaf 7or1 at least1 not sensitive to sonorous vibrations transmitted through the air71 by the following experiment4 ,he placed a pot containing a worm that had come to the surface1 as usual at night1 upon a table1 whilst close by a piano was violently played2 but the worm took no notice of the noise4 ,he then placed the pot upon the piano1 whilst it was being played1 when the worm1 probably feeling mechanical vibrations1 hastily slid back into its burrow4 ,when1 instead of altering one circumstance in an instance 7which we have done our best not otherwise to disturb7 and then watching what follows1 we try to find two ready-made instances of a phenomenon1 which only differ in one other circumstance1 it is1 of course1 still more difficult to be sure that there is only one other circumstance in which they differ4 ,it may be worth while1 however1 to look for such instances4 ,thus1 that the temperature of ocean currents influences the climate of the shores they wash1 seems to be shown by the fact that the average temperature of ,newfoundland is lower than that of the ,norwegian coast some #ae farther north4 ,both regions have great continents at their back2 and as the mountains of ,norway are higher and capped with perennial snow1 we might expect a colder climate there3 but the shore of ,norway is visited by the ,gulf ,stream1 whilst the shore of ,newfoundland is traversed by a cold current from ,greenland4 ,again1 when in #ahda the railway from ,rouen to ,paris was being built1 gangs of ,english and gangs of ,french workmen were employed upon it1 and the ,english got through about one-third more work per man than the ,french4 ,it was suspected that this difference was due to one other difference1 namely1 that the ,english fed better1 preferring beef to thin soup4 ,now1 logically1 it might have been objected that the evidence was unsatisfactory1 seeing that the men differed in other things besides diet--in 'race' 7say71 which explains so much and so easily4 ,but the ,frenchmen1 having been induced to try the same diet as the ,english1 were1 in a few days1 able to do as much work3 so that the two instances were better than they looked4 ,it often happens that evidence1 though logically questionable1 is good when used by experts1 whose familiarity with the subject makes it good4 #d4 ,,the ,,canon ,,of ,,concomitant ,,variations4 ,whatever phenomenon varies in any manner whenever another phenomenon 7consequent or antecedent7 varies in some particular manner no other change having concurred is either the cause or effect of that phenomenon or is connected with it through some fact of causation4 ,this is not an entirely fresh method1 but may be regarded as a special case either of ,agreement or of ,difference1 to prove the cause or effect1 not of a phenomenon as a whole1 but of some increment of it 7positive or negative74 ,there are certain forces1 such as gravitation1 heat1 friction1 that can never be eliminated altogether1 and therefore can only be studied in their degrees4 ,to such phenomena the method of ,difference cannot be applied1 because there are no negative instances4 ,but we may obtain negative instances of a given quantity of such a phenomenon 7say1 heat71 and may apply the method of ,difference to that quantity4 ,thus1 if the heat of a body increases #aj degrees1 from #fj to #gj1 the former temperature of #fj was a negative instance in respect of those #aj degrees2 and if only one other circumstance 7say1 friction7 has altered at the same time1 that circumstance 7if an antecedent7 is the cause4 ,accordingly1 if in the above ,canon we insert1 after 'particular manner1' no other change having concurred1 it is a statement of the method of ,difference as applicable to the increment of a phenomenon1 instead of to the phenomenon as a whole2 and we may then omit the last clause--or is connected1 etc44 ,for these words are inserted to provide for the case of co-effects of a common cause 7such as the flash and report of a gun72 but if no other change 7such as the discharge of a gun7 has concurred with the variations of two phenomena1 there cannot have been a common cause1 and they are therefore cause and effect4 ,if1 on the other hand1 we omit the clause no other change having concurred1 the ,canon is a statement of the method of ,agreement as applicable to the increment of a phenomenon instead of to the phenomenon as a whole2 and it is then subject to the imperfections of that method3 that is to say1 it leaves open the possibilities1 that an inquirer may overlook a plurality of causes2 or may mistake a connection of two phenomena1 which 7like the flash and report of a gun7 are co-effects of a common cause1 for a direct relation of cause and effect4 ,it may occur to the reader that we ought also to distinguish ,qualitative and ,quantitative ,variations as two orders of phenomena to which the present method is applicable4 ,but1 in fact1 ,qualitative ,variations may be adequately dealt with by the foregoing methods of ,agreement1 ,double ,agreement1 and ,difference2 because a change of quality or property entirely gets rid of the former phase of that quality1 or substitutes one for another2 as when the ptarmigan changes from brown to white in winter1 or as when a stag grows and sheds its antlers with the course of the seasons4 ,the peculiar use of the method of ,variations1 however1 is to formulate the conditions of proof in respect of those causes or effects which cannot be entirely got rid of1 but can be obtained only in greater or less amount2 and such phenomena are or course1 quantitative4 ,even when there are two parallel series of phenomena the one quantitative and the other qualitative--like the rate of air-vibration and the pitch of sound1 or the rate of ether-vibration and the colour-series of the spectrum--the method of ,variations is not applicable4 ,for 7#a7 two such series cannot be said to vary together1 since the qualitative variations are heterogeneous3 #eab3 #egf is a definite ratio2 but the corresponding notes1 ,c1 ,d1 in the treble clef1 present only a difference4 ,hence 7#b7 the correspondence of each note with each number is a distinct fact4 ,each octave even is a distinct fact2 there is a difference between ,c #fd and ,c #abh that could never have been anticipated without the appropriate experience4 ,there is1 therefore1 no such law of these parallel series as there is for temperature and change of volume 7say7 in mercury4 ,similar remarks apply to the physical and sensitive light-series4 ,we may illustrate the two cases of the method thus 7putting a dash against any letter1 ,a' or p'1 to signify an increase or decrease of the phenomenon the letter stands for73 ,agreement in ,variations 7other changes being admissible7-- ,a ,b ,c ,a' ,d ,e ,a'' ,f ,g p q r p' s t p'' u v ,here the accompanying phenomena 7,b ,c q r1 ,d ,e s t1 ,f ,g u v7 change from time to time1 and the one thing in which the instances agree throughout is that any increase of ,a 7,a' or ,a''7 is followed or accompanied by an increase of p 7p' or p''73 whence it is argued that ,a is the cause of p1 according to ,prop4 ,,iii4 7a7 7ch4 xv4 #g74 ,still1 it is supposable that1 in the second instance1 ,d or ,e may be the cause of the increment of p2 and that1 in the third instance1 ,f or ,g may be its cause3 though the probability of such vicarious causation decreases rapidly with the increase of instances in which ,a and p vary together4 ,and1 since an actual investigation of this type must rely on observation1 it is further possible that some undiscovered cause1 ,x1 is the real determinant of both ,a and p and of their concomitant variations4 ,professor ,ferri1 in his ,criminal ,sociology1 observes3 ,i have shown that in ,france there is a manifest correspondence of increase and decrease between the number of homicides1 assaults and malicious wounding1 and the more or less abundant vintage1 especially in the years of extraordinary variations1 whether of failure of the vintage 7#ahec-e1 #ahei1 #ahfg1 #ahgc1 #ahgh-hj71 attended by a remarkable diminution of crime 7assaults and wounding71 or of abundant vintages 7#ahej1 #ahef-h1 #ahfb-c1 #ahfe1 #ahfh1 #ahgd-e71 attended by an increase of crime 7p4 #aag1 ,eng4 trans474 ,and earlier he had remarked that such crimes also in their oscillations from month to month display a characteristic increase during the vintage periods1 from ,june to ,december1 notwithstanding the constant diminution of other offences 7p4 #gg74 ,this is necessarily an appeal to the canon of ,concomitant ,variations1 because ,france is never without her annual vintage1 nor yet without her annual statistics of crime4 ,still1 it is an argument whose cogency is only that of ,agreement1 showing that probably the abuse of the vintage is a cause of crimes of violence1 but leaving open the supposition1 that some other circumstance or circumstances1 arising or varying from year to year1 may determine the increase or decrease of crime2 or that there is some unconsidered agent which affects both the vintage and crimes of violence4 ,french sunshine1 it might be urged1 whilst it matures the generous grape1 also excites a morbid fermentation in the human mind4 ,difference in ,variations may be symbolically represented thus 7no other change having concurred73 ,a ,b ,a' ,b ,a'' ,b p q1 p' q1 p'' q4 ,here the accompanying phenomena are always the same ,b_/q2 and the only point in which the successive instances differ is in the increments of ,a 7,a'1 ,a''7 followed by corresponding increments of p 7p'1 p''73 hence the increment of ,a is the cause of the increment of p4 ,for examples of the application of this method1 the reader should refer to some work of exact science4 ,he will find in ,deschanel's ,natural ,philosophy1 c4 #cb1 an account of some experiments by which the connection between heat and mechanical work has been established4 ,it is there shown that whenever work is performed by the agency of heat as in driving an engine1 an amount of heat disappears equivalent to the work performed2 and whenever mechanical work is spent in generating heat as in rubbing two sticks together1 the heat generated is equivalent to the work thus spent4 ,and an experiment of ,joule's is described1 which consisted in fixing a rod with paddles in a vessel of water1 and making it revolve and agitate the water by means of a string wound round the rod1 passed over a pulley and attached to a weight that was allowed to fall4 ,the descent of the weight was measured by a graduated rule1 and the rise of the water's temperature by a thermometer4 ,it was found that the heat communicated to the water by the agitation amounted to one pound-degree ,fahrenheit for every #ggb foot-pounds of work expended by the falling weight4 ,as no other material change seems to take place during such an experiment1 it shows that the progressive expenditure of mechanical energy is the cause of the progressive heating of the water4 ,the thermometer itself illustrates this method4 ,it has been found that the application of heat to mercury expands it according to a law2 and hence the volume of the mercury1 measured by a graduated index1 is used to indicate the temperature of the air1 water1 animal body1 etc41 in which the thermometer is immersed1 or with which it is brought into contact4 ,in such cases1 if no other change has taken place1 the heat of the air1 water1 or body is the cause of the rise of the mercury in its tube4 ,if some other substance 7say spirit7 be substituted for mercury in constructing a thermometer1 it serves the same purpose1 provided the index be graduated according to the law of the expansion of that substance by heat1 as experimentally determined4 ,instances of phenomena that do not vary together indicate the exclusion of a supposed cause 7by ,prop4 ,,iii 7c774 ,the stature of the human race has been supposed to depend on temperature2 but there is no correspondence4 ,the not varying together1 however1 must not be confused with varying inversely1 which when regular indicates a true concomitance4 ,it is often a matter of convenience whether we regard concomitant phenomena as varying directly or inversely4 ,it is usual to say--'the greater the friction the less the speed'2 but it is really more intelligible to say--'the greater the friction the more rapidly molar is converted into molecular motion4' ,the ,graphic ,method exhibits ,concomitant ,variations to the eye1 and is extensively used in physical and statistical inquiries4 ,along a horizontal line 7the abscissa7 is measured one of the conditions 7or agents7 with which the inquiry is concerned1 called the ,variable2 and along perpendiculars 7ordinates7 is measured some phenomenon to be compared with it1 called the ,variant4 ,thus1 the expansion of a liquid by heat may be represented by measuring degrees of temperature along the horizontal1 and the expansion of a column of the liquids in units of length along the perpendicular4 ,illustration3 ,,fig4 #i4 ,in the next diagram 7,fig4 #aj71 reduced from one given by ,mr4 ,c4,h4 ,denyer in an article on the ,price of ,tea 7,economic ,journal1 ,no4 #i71 the condition measured horizontally is ,time2 and1 vertically1 three variants are measured simultaneously1 so that their relations to one another from time to time may be seen at a glance4 ,from this it is evident that1 as the duty on tea falls1 the price of tea falls1 whilst the consumption of tea rises2 and1 in spite of some irregularity of correspondence in the courses of the three phenomena1 their general causal connection can hardly be mistaken4 ,however1 the causal connection may also be inferred by general reasoning2 the statistical ,induction can be confirmed by a ,deduction2 thus illustrating the combined method of proof to be discussed in the next chapter4 ,without such confirmation the proof by ,concomitant ,variations would not be complete2 because1 from the complexity of the circumstances1 social statistics can only yield evidence according to the method of ,agreement in ,variations4 ,for1 besides the agents that are measured1 there may always be some other important influence at work4 ,during the last fifty years1 for example1 crime has decreased whilst education has increased3 true1 but at the same time wages have risen and many other things have happened4 ,illustration3 ,,fig4 #aj4 ,it will be noticed that in the diagram the three lines1 especially those of ,price and ,consumption 7which may be considered natural resultants1 in contrast with the arbitrary fixation of a ,tax71 do not depart widely from regular curves2 and accordingly1 assuming the causes at work to vary continuously during the intervals between points of measurement1 curves may be substituted4 ,in fact1 a curve often represents the course of a phenomenon more truthfully than can be done by a line that zigzags along the exact measurements2 because it is less influenced by temporary and extraordinary causes that may obscure the operation of those that are being investigated4 ,on the other hand1 the abrupt deviations of a punctilious zigzag may have their own logical value1 as will appear in the next section4 ,in working with the ,method of ,variations one must allow for the occurrence in a series of 'critical points1' at which sudden and sometimes heterogeneous changes may take place4 ,every substance exists at different temperatures in three states1 gaseous1 liquid1 solid2 and when the change takes place1 from one state to another1 the series of variations is broken4 ,water1 e4g41 follows the general law that cooling is accompanied by decrease of volume between #bab and #ci ,f43 but above #bab1 undergoes a sudden expansion in becoming a gas2 and below #ci begins to expand1 until at #cb the expansion is considerable on its becoming solid4 ,this illustrates a common experience that concomitant variations are most regular in the 'median range1' and are apt to become irregular at the extremities of the series1 where new conditions begin to operate4 ,the ,canon of ,variations1 again1 deals not with sudden irruptions of a cause1 force or agent1 but with some increase or decrease of an agent already present1 and a corresponding increase or decrease of some other phenomenon--say an increase of tax and a rise of price4 ,but there are cases in which the energy of a cause is not immediately discharged and dissipated4 ,whilst a tax of #f;d4 per lb4 on tea raises the price per lb4 by about #f;d41 however long it lasts1 the continuous application of friction to a body may gradually raise its temperature to the point of combustion2 because heat is received faster than it is radiated1 and therefore accumulates4 ,such cases are treated by ,mill under the title of 'progressive effects' 7,logic3 ,b4 ,,iii41 c4 #ae73 he gives as an example of it the acceleration of falling bodies4 ,the storage of effects is a fact of the utmost importance in all departments of nature1 and is especially interesting in ,biology and ,sociology1 where it is met with as heredity1 experience1 tradition4 ,evolution of species of plants and animals would 7so far as we know7 be impossible1 if the changes 7however caused7 that adapt some individuals better than others to the conditions of life were not inherited by1 and accumulated in1 their posterity4 ,the eyes in the peacock's tail are supposed to have reached their present perfection gradually1 through various stages that may be illustrated by the ocelli in the wings of the ,argus pheasant and other genera of ,phasianid4 ,similarly the progress of societies would be impossible without tradition1 whereby the improvements made in any generation may be passed on to the next1 and the experience of mankind may be gradually accumulated in various forms of culture4 ,the earliest remains of culture are flint implements and weapons2 in which we can trace the effect of tradition in the lives of our remote forefathers1 as they slowly through thousands of years learnt to improve the chipping of flints1 until the first rudely shaped lumps gave place to works of unmistakable design1 and these to the beautiful weapons contemporary with the ,bronze ,age4 ,the ,method of ,gradations1 the arranging of any phenomena to be studied in series1 according to the degree in which some character is exhibited1 is1 perhaps1 the most definite device in the ,art of ,discovery4 7,bain3 ,induction1 c4 #f1 and ,app4 ,,ii47 ,if the causes are unknown it is likely to suggest hypotheses3 and if the causes are partly known1 variation in the character of the series is likely to indicate a corresponding variation of the conditions4 #e4 ,,the ,,canon ,,of ,,residues4 ,subduct from any phenomenon such part as previous inductions have shown to be the effect of certain antecedents1 and the residue of the phenomenon is the effect of the remaining antecedents4 ,the phenomenon is here assumed to be an effect3 a similar ,canon may be framed for residuary causes4 ,this also is not a fresh method1 but a special case of the method of ,difference4 ,for if we suppose the phenomenon to be p q r1 and the antecedent to be ,a ,b ,c1 and that we already know ,b and ,c to have 7either severally or together7 the consequents q r1 in which their efficacy is exhausted2 we may regard ,b ,c q r as an instance of the absence of p obtained deductively from the whole phenomenon ,a ,b ,c p q r by our knowledge of the laws of ,b and ,c2 so that ,a ,b ,c p q r is an instance of the presence of p1 differing otherwise from ,b ,c q r in nothing except that ,a is also present4 ,by the ,canon of ,difference1 therefore ,a is the cause of p4 ,or1 again1 when phenomena thus treated are strictly quantitative1 the method may be based on ,prop4 ,,iii4 7b71 ch4 xv4 #g4 ,of course1 if ,a can be obtained apart from ,b ,c and directly experimented with so as to produce p1 so much the better2 and this may often be done2 but the special value of the method of ,residues appears1 when some complex phenomenon has been for the most part accounted for by known causes1 whilst there remains some excess1 or shortcoming1 or deviation from the result which those causes alone would lead us to expect1 and this residuary fact has to be explained in relation to the whole4 ,here the negative instance is constituted by deduction1 showing what would happen but for the interference of some unknown cause which is to be investigated2 and this prominence of the deductive process has led some writers to class the method as deductive4 ,but we have seen that all the ,canons involve deduction2 and1 considering how much in every experiment is assumed as already known 7what circumstances are 'material1' and when conditions may be called 'the same'71 the wonder is that no one has insisted upon regarding every method as concerned with residues4 ,in fact1 as scientific explanation progresses1 the phenomena that may be considered as residuary become more numerous and the importance of this method increases4 ,examples3 ,the recorded dates of ancient eclipses having been found to differ from those assigned by calculation1 it appears that the average length of a day has in the meanwhile increased4 ,this is a residuary phenomenon not accounted for by the causes formerly recognised as determining the rotation of the earth on its axis2 and it may be explained by the consideration that the friction of the tides reduces the rate of the earth's rotation1 and thereby lengthens the day4 ,astronomy abounds in examples of the method of ,residues1 of which the discovery of ,neptune is the most famous4 ,capillarity seems to be a striking exception to the principle that water 7or any liquid7 'finds its level1' that being the condition of equilibrium2 yet capillarity proves to be only a refined case of equilibrium when account is taken of the forces of adhesion exerted by different kinds of bodies in contact4 ,many of the new elements of ,chemistry1 says ,herschel1 have been detected in the investigation of residual phenomena4 ,thus1 ,lord ,rayleigh and ,sir ,w4 ,ramsay found that nitrogen from the atmosphere was slightly heavier than nitrogen got from chemical sources2 and1 seeking the cause of this difference1 discovered argon4 ,the ,economist shows that when a country imports goods the chief means of paying for them is to export other goods4 ,if this were all1 imports and exports would be of equal value3 yet the ,united ,kingdom imports about #djj1jjj1jjj annually1 and exports about #cjj1jjj1jjj4 ,here1 then1 is a residuary phenomenon of #ajj1jjj1jjj to be accounted for4 ,but foreign countries owe us about #ej1jjj1jjj for the use of shipping1 and #gj1jjj1jjj as interest on the capital we have lent them1 and #ae1jjj1jjj in commissions upon business transacted for them4 ,these sums added together amount to #ace1jjj1jjj2 and that is #ce1jjj1jjj too much4 ,thus another residuary phenomenon emerges2 for whilst foreigners seem to owe us #dce1jjj1jjj they only send us #djj1jjj1jjj of imports4 ,these #ce1jjj1jjj are accounted for by the annual investment of our capital abroad1 in return for which no immediate payment is due2 and1 these being omitted1 exports and imports balance4 ,since this was written the figures of our foreign trade have greatly risen2 but the character of the explanation remains the same4 ,when1 in pursuing the method of ,variations1 the phenomena compared do not always correspond in their fluctuations1 the irregular movements of that phenomenon which we regard as the effect may often be explained by treating them as residuary phenomena1 and then seeking for exceptional causes1 whose temporary interference has obscured the influence of the general cause4 ,thus1 returning to the diagram of the ,price of ,tea in #d1 it is clear that generally the price falls as the duty falls2 but in ,mr4 ,denyer's more minutely wrought diagram1 from which this is reduced1 it may be seen that in #ahdj the price of tea rose from #cs4 #i;d4 to #ds4 #i;d4 without any increase of duty4 ,this1 however1 is readily explained by the ,chinese ,war of that year1 which checked the supply4 ,again1 from #ahfi to #ahhi the duty was constant1 whilst the price of tea fell as much as #h;d4 per lb42 but this residuary phenomenon is explained by the prodigiously increased production of tea during that period in ,india and ,ceylon4 ,the above examples of the method of ,residues are all quantitative2 but the method is often employed where exact estimates are unobtainable4 ,thus ,darwin1 having found certain modifications of animals in form1 coloration and habits1 that were not clearly derivable from their struggle for existence in relation to other species or to external conditions1 suggested that they were due to ,sexual ,selection4 ,the 'vestiges' and 'survivals' so common in ,biology and ,sociology are residuary phenomena4 ,it is a general inference from the doctrine of ,natural ,selection that every organ of a plant1 animal1 or society is in some way useful to it4 ,there occur1 however1 organs that have at present no assignable utility1 are at least wasteful1 and sometimes even injurious4 ,and the explanation is that formerly they were useful2 but that1 their uses having lapsed1 they are now retained by the force of heredity or tradition4 ,either they are not injurious enough to be eliminated by natural selection2 or they are correlated with other organs1 whose utility outweighs their disutility4 ,,chapter ,,xvii ,,combination ,,of ,,induction ,,with ,,deduction #a4 ,we have now reviewed ,mill's five ,canons of ,inductive ,proof4 ,at bottom1 as he observes1 there are only two1 namely1 ,agreement and ,difference3 since the ,double ,method1 ,variations and ,residues are only special forms of the other two4 ,indeed1 in their function of proof1 they are all reducible to one1 namely1 ,difference2 for the cogency of the method of ,agreement 7as distinguished from a simple enumeration of instances agreeing in the coincidence of a supposed cause and its effect71 depends upon the omission1 in one instance after another1 of all other circumstances2 which omission is a point of difference4 ,the ,canons are an analysis of the conditions of proving directly 7where possible71 by means of observation or experiment1 any proposition that predicates causation4 ,but if we say 'by means of observation or experiment1' it is not to be understood that these are the only means and that nothing else is involved2 for it has been shown that the ,law of ,causation is itself an indispensable foundation of the evidence4 ,in fact ,inductive ,logic may be considered as having a purely formal character4 ,it consists 7#a7 in a statement of the ,law of ,cause and ,effect2 7#b7 in certain immediate inferences from this ,law1 expanded into the ,canons2 7#c7 in the syllogistic application of the ,canons to special predications of causation by means of minor premises1 showing that certain instances satisfy the ,canons4 ,at the risk of some pedantry1 we may exhibit the process as follows 7cf4 ,prof4 ,ray's ,logic3 ,appendix ,d73 ,whatever relation of events has certain marks is a case of causation2 ,the relation ,a3 p has some or all of these marks 7as shown by observation and by the conformity of instances to such or such a ,canon73 ,therefore1 the relation ,a3 p is a case of causation4 ,now1 the parenthesis1 as shown by the conformity1 etc41 is an adscititious member of an ,epicheirema1 which may be stated1 as a ,prosyllogism1 thus3 ,if an instance1 etc4 7,canon of ,difference72 ,the instances ,a ,b ,c ,b ,c are of the kind required3 p q r' q r ,therefore1 ,a1 present where p occurs and absent where it does not occur1 is an indispensable antecedent of p4 ,such is the bare ,logic of ,induction3 so that1 strictly speaking1 observation or experiment is no part of the logic1 but a means of applying the logic to actual1 that is1 not merely symbolical1 propositions4 ,the ,formal ,logic of ,induction is essentially deductive2 and it has been much questioned whether any transition from the formal to the material conditions of proof is possible4 ,as long as we are content to illustrate the ,canons with symbols1 such as ,a and p1 all goes well2 but can we in any actual investigation show that the relevant facts or 'instances' correspond with those symbols8 ,in the first place1 as ,dr4 ,venn shows1 natural phenomena want the distinctness and capability of isolation that belong to symbols4 ,secondly1 the observing whether instances conform to a ,canon1 must always be subject at last to the limits of our faculties4 ,how can we ascertain exact equality1 immediate sequence8 ,the ,canon of ,difference1 in its experimental application1 is usually considered the most cogent sort of proof3 yet when can the two sequent instances1 before and after the introduction of a certain agent1 be said to differ in nothing else8 ,are not earth and stars always changing position2 is not every molecule in the room and apparatus always oscillating8 ,it is true that our senses are now aided by elaborate instruments2 but the construction of these depends on scientific theories1 which again depend on experiments4 ,it is right to touch upon this well-known sceptical topic2 but to insist much upon it is not a sign of good sense4 ,the works of ,herschel1 ,whewell1 and ,jevons should be consulted for the various methods of correcting observations1 by repeating them1 averaging them1 verifying one experimental process by another1 always refining the methods of exact measurement1 multiplying the opportunities of error 7that if any exist it may at last show itself71 and by other devices of what may be called ,material ,logic or ,methodology4 ,but only direct experience and personal manipulation of scientific processes1 can give a just sense of their effectiveness2 and to stand by1 suggesting academic doubts1 is easier and more amusing4 #b4 ,still1 it is not so much in laws based upon direct observation or experiment1 that the material validity of scientific reasoning appears1 as in the cumulative evidence that arises from the co-ordination of laws within each science1 and the growing harmony and coherence of all sciences4 ,this requires a more elaborate combination of deduction with observation and experiment4 ,during the last three hundred years many departments of science have been reduced under principles of the greatest generality1 such as the ,conservation of ,energy1 the ,law of ,gravitation1 the ,undulatory theory of ,light1 the ,law of combining ,equivalents1 and the ,theory of ,natural ,selection2 connecting and explaining the less general laws1 which1 again1 are said to connect and explain the facts4 ,meanwhile1 those sciences that were the first to make progress have helped to develop others which1 like ,biology and ,sociology1 present greater difficulties2 and it becomes more and more apparent that the distinctions drawn among sciences are entirely for the convenience of study1 and that all sciences tend to merge in one universal ,science of ,nature4 ,now1 this process of the 'unification of knowledge' is almost another name for deduction2 but at the same time it depends for its reality and solidity upon a constant reference to observation and experiment4 ,only a very inadequate notion of it can be given in the ensuing chapters4 ,we saw in chap4 xiv4 #f1 that when two or more agents or forces combine to produce a phenomenon1 their effects are intermixed in it1 and this in one of two ways according to their nature4 ,in chemical action and in vegetable and animal life1 the causal agents concerned are blended in their results in such a way that most of the qualities which they exhibited severally are lost1 whilst new qualities appear instead4 ,thus chlorine 7a greenish-yellow gas7 and sodium 7a metal7 unite to form common salt ,na,cl2 which is quite unlike either of them3 a man eats bread1 and it becomes muscle1 nerve and bone4 ,in such cases we cannot trace the qualities of the causal agents in the qualities of the effects2 given such causes1 we can prove experimentally1 according to the canons of induction1 that they have such effects2 but we may not be able in any new case to calculate what the effects will be4 ,on the other hand1 in ,astronomy and ,physics1 the causes treated of are mechanical2 at least1 it is the aim of ,physics to attain to a mechanical conception of phenomena2 so that1 in every new combination of forces1 the intermixed effect1 or resultant1 may be calculated beforehand2 provided that the forces concerned admit of being quantitatively estimated1 and that the conditions of their combination are not so complex as to baffle the powers of mathematicians4 ,in such cases1 when direct observation or experiment is insufficient to resolve an effect into the laws of its conditions1 the general method is to calculate what may be expected from a combination of its conditions1 as either known or hypothetically assumed1 and to compare this anticipation with the actual phenomenon4 #c4 ,this is what ,mill calls the ,direct ,deductive ,method2 or1 the ,physical ,method1 because it is so much relied on in treating of ,light1 ,heat1 ,sound1 etc42 it is also the method of ,astronomy and much used in ,economics3 ,deduction leads the way1 and its results are tested inductively by experiments or observations4 ,given any complex mechanical phenomenon1 the inquirer considers--7#a7 what laws already ascertained seem likely to apply to it 7in default of known laws1 hypotheses are substituted3 cf4 chap4 xviii472 he then--7#b7 computes the effect that will follow from these laws in circumstances similar to the case before him2 and 7#c7 he verifies his conclusion by comparing it with the actual phenomenon4 ,a simple example of this method is the explanation of the rise of water in the 'common pump4' ,we know three laws applicable to this case3 7a7 that the atmosphere weighs upon the water outside the pump with a pressure of #ae lb4 to the square inch2 7b7 that a liquid 7and therefore the water7 transmits pressure equally in all directions 7upwards as well as downwards and sideways72 and 7c7 that pressure upon a body in any direction1 if not counteracted by an opposite pressure1 produces motion4 ,hence1 when the rise of the piston of the pump removes the pressure upon the water within the cylinder1 tending to produce a vacuum there1 this water is pushed up by the pressure of the air upon the water outside the cylinder1 and follows the rising piston1 until the column of water inside the cylinder exerts a pressure equal to that of the atmosphere upon an equal area4 ,so much for the computation2 does it correspond with the fact8 ,it is found that at the sea level water can be pumped to the height of #cc ft2 and that such a column of water has a pressure of #ae lb4 to the square inch4 ,we may show further that1 at the sea level1 spirits of wine may be pumped higher according to its less specific gravity2 and that if we attempt to pump water at successive altitudes above the sea level1 we can only raise it to less and less heights1 corresponding with the lessened atmospheric pressure at those altitudes1 where the column of air producing the pressure is shorter4 ,finally1 if we try to work a pump1 having first produced a vacuum over the water outside the cylinder1 we shall find that the water inside will not rise at all2 the piston can be raised1 but the water does not follow it4 ,the verification thus shows that the computed effect corresponds with the phenomenon to be explained2 that the result does not depend upon the nature of water only1 but is true 7allowing for differences of specific gravity7 of other liquids2 that if the pressure of the outside air is diminished1 the height of pumping is so too 7canon of ,variations72 and that if that pressure is entirely removed1 pumping becomes impossible 7canon of ,difference74 ,any text-book of ,astronomy or ,physics furnishes numerous illustrations of the deductive method4 ,take1 for example1 the first chapter of ,deschanel's ,optics1 where are given three methods of determining the velocity of ,light4 ,this was first deduced from observation of ,jupiter's satellites4 ,the one nearest the planet passes behind it1 or into its shadow1 and is eclipsed1 at intervals of about #db-a_/b hours4 ,but it can be shown that1 when ,jupiter and the ,earth are nearest together on the same side of the ,sun1 an eclipse of this satellite is visible from the earth #af min4 #bf4f sec4 earlier than when ,jupiter and the earth are furthest apart on opposite sides of the ,sun3 #af min4 #bf4f sec1 then1 is the time in which light traverses the diameter of the ,earth's orbit4 ,therefore1 supposing the ,earth's distance from the ,sun to be #ib millions of miles1 light travels about #ahf1jjj miles a second4 ,another deduction1 agreeing with this1 starts from the fact of aberration1 or the displacement of the apparent from the actual position of the stars in the direction of the earth's motion4 ,aberration depends partly on the velocity of light1 partly on the velocity of the ,earth2 and the latter being known1 the former can be computed4 ,now1 these two deductive arguments1 verifying each other1 have also been verified experimentally4 ,foucault's experiment to measure the velocity of light is too elaborate to be described here3 a full account of it will be found in the treatise above cited1 #fhg4 ,when the phenomena to be explained are of such a character1 so vast in extent1 power or duration1 that it is impossible1 in the actual circumstances of the case1 to frame experiments in order to verify a deductive explanation1 it may still be possible to reproduce a similar phenomenon upon a smaller scale4 ,thus ,monge's explanation of mirage by the great heat of the desert sand1 which makes the lowest stratum of air less dense than those above it1 so that rays of light from distant objects are refracted in descending1 until they are actually turned upwards again to the eye of the beholders1 giving him inverted images of the objects as if they were reflected in water1 is manifestly incapable of being verified by experiment in the natural conditions of the phenomenon4 ,but by heating the bottom of a sheet-iron box1 with its ends cut away1 the rarefied air at the bottom of the box may sometimes be made to yield reflections2 and this shows at least that the supposed cause is a possible one 7,deschanel1 ,optics1 #gbf74 ,similarly as to the vastest of all phenomena1 the evolution of the stellar system1 and of the solar system as part of it1 from an immense cloudlike volume of matter3 ,h4 ,spencer1 in his ,essay on ,the ,nebular ,hypothesis1 says1 amidst a great array of deductive arguments from mechanical principles1 that this a priori reasoning harmonises with the results of experiment4 ,dr4 ,plateau has shown that when a mass of fluid is1 as far as may be1 protected from the action of external forces1 it will1 if made to rotate with adequate velocity1 form detached rings2 and that these rings will break up into spheroids1 which turn on their axes in the same direction with the central mass4 ,the theory of the evolution of species of plants and animals by ,natural ,selection1 again1 though1 of course1 it cannot be verified by direct experiment 7since experiment implies artificial arrangement71 and the process is too slow for observation1 is1 nevertheless1 to some extent confirmed by the practice of gardeners and breeders of animals3 since1 by taking advantage of accidental variations of form and colour in the plants or animals under their care1 and relying on the inheritability of these variations they obtain extensive modifications of the original stocks1 and adapt them to the various purposes for which flowers and cereals1 poultry1 dogs and cattle are domesticated4 ,this shows1 at least1 that living forms are plastic1 and extensively modifiable in a comparatively short time4 #d4 ,suppose1 however1 that1 in verifying a deductive argument1 the effect as computed from the laws of the causes assigned1 does not correspond with the facts observed3 there must then be an error somewhere4 ,if the fact has been accurately observed1 the error must lie either in the process of deduction and computation1 or else in the premises4 ,as to the process of deduction1 it may be very simple and easily revised1 as in the above explanation of the common pump2 or it may be very involved and comprise long trains of mathematical calculation4 ,if1 however1 on re-examining the computations1 we find them correct1 it remains to look for some mistake in the premises4 7#a7 ,we may not have accurately ascertained the laws1 or the modes of operation1 or the amounts of the forces present4 ,thus1 the rate at which bodies fall was formerly believed to vary in proportion to their relative weights2 and any estimate based upon this belief cannot agree with the facts4 ,again1 the corpuscular theory of light1 namely1 that the physical cause of light is a stream of fine particles projected in straight lines from the luminous object1 though it seemed adequate to the explanation of many optical phenomena1 could not be made to agree with the facts of interference and double refraction4 7#b7 ,the circumstances in which the agents are combined may not have been correctly conceived4 ,when ,newton began to inquire whether the attraction of the earth determined the orbit of the moon1 he was at first disappointed4 ,according to ,newton's calculations1 made at this time1 says ,whewell1 the moon1 by her motion in her orbit1 was deflected from the tangent every minute through a space of thirteen feet4 ,but by noticing the space which bodies would fall in one minute at the earth's surface1 and supposing this to be diminished in the ratio of the inverse square1 it appeared that gravity would1 at the moon's orbit1 draw a body through more than fifteen feet4 ,in view of this discrepancy he gave up the inquiry for sixteen years1 until in #afhb1 having obtained better data1 he successfully renewed it4 ,he had been mistaken in the magnitude of the earth1 and consequently in the distance of the moon1 which is determined by measurements of which the earth's radius is the base4 ,it was not1 therefore1 a mistake as to the law or as to the nature of the forces concerned 7namely1 the law of the inverse square and the identity of celestial with terrestrial gravity71 but as to the circumstances in which the agents 7earth and moon7 were combined1 that prevented his calculations being verified4 7,hist4 ,ind4 ,sc43 ,,vii4 ii4 #c47 7#c7 ,one or more of the agents affecting the result may have been overlooked and omitted from the estimate4 ,thus1 an attempt to explain the tides by taking account only of the earth and the moon1 will not entirely agree with the facts1 since the sun also influences the tides4 ,this illustration1 however1 shows that when the conclusion of a deductive explanation does not entirely agree with the facts1 it is not always to be inferred that the reasoning is1 properly speaking1 wrong2 it may be right as far as it goes1 and merely inadequate4 ,hence 7a7 in such cases an opportunity occurs of applying the ,method of ,residues1 by discovering the agent that must be allowed for in order to complete the explanation4 ,and 7b7 the investigation of a phenomenon is often designedly begun upon an imperfect basis for the sake of simplicity2 the result being regarded as a first approximation1 to be afterwards corrected by including1 one by one1 the remaining agents or circumstances affecting the phenomenon1 until the theory is complete2 that is1 until its agreement with the facts is satisfactory4 7#d7 ,we may have included among the data of our reasonings agents or circumstances that do not exist or do not affect the phenomenon in question4 ,in the early days of science purely fanciful powers were much relied upon3 such as the solid spheres that carried the planets and stars2 the influence of the planets upon human destiny2 the tendency of everything to seek its own place1 so that fire rises to heaven1 and solids fall to the earth2 the plastic virtue of the soil1 which was once thought to have produced fossils4 ,when1 however1 such conceptions hindered the progress of explanation1 it was not so much by vitiating the deductive method as by putting men off from exact inquiries4 ,more to our present purpose were the supposed cataclysms1 or extraordinary convulsions of the earth1 a belief in which long hindered the progress of ,geology4 ,again1 in ,biology1 ,psychology1 and ,sociology many explanations have depended upon the doctrine that any improvement of structure or faculty acquired by an individual may be inherited by his descendants3 as that1 if an animal learns to climb trees1 his offspring have a greater aptitude for that mode of life2 that if a man tries to be good1 his children find it easier to be virtuous2 that if the inhabitants of a district carry on cloth-work1 it becomes easier for each successive generation to acquire dexterity in that art4 ,but now the inheritability of powers acquired by the individual through his own efforts1 is disputed2 and1 if the denial be made good1 all such explanations as the above must be revised4 ,if1 then1 the premises of a deductive argument be vitiated in any of these four ways1 its conclusion will fail to agree with the results of observation and experiment1 unless1 of course1 one kind of error happen to be cancelled by another that is 'equal and opposite4' ,we now come to a variation of the method of combining ,induction with ,deduction1 so important as to require separate treatment4 #e4 ,the ,inverse or ,historical ,method has of late years become remarkably fruitful4 ,when the forces determining a phenomenon are too numerous1 or too indefinite1 to be combined in a direct deduction1 we may begin by collecting an empirical law of the phenomenon 7as that 'the democracies of ,city-,states are arbitrary and fickle'71 and then endeavour to show by deductions from the nature of the case1 that is1 from a consideration of the circumstances and forces known to be operative 7of which1 in the above instance1 the most important is sympathetic contagion71 that such a law was to be expected4 ,deduction is thus called in to verify a previous induction2 whereas in the ',physical ,method' a deduction was verified by comparing it with an induction or an experiment2 hence the method now to be discussed has been named the ,inverse ,deductive ,method4 ,but although it is true that1 in such inquiries as we are now dealing with1 induction generally takes the lead2 yet ,i cannot think that the mere order in which the two logical processes occur is the essential distinction between the two ways of combining them4 ,for1 in the first place1 in investigations of any complexity both induction and deduction recur again and again in whatever order may be most convenient2 and1 in the second place1 the so-called 'inverse order' is sometimes resorted to in ,astronomy and ,physics4 ,for example1 ,kepler's ,laws were first collected empirically from observations of the planetary motions1 and afterwards deduced by ,newton from the ,law of ,gravitation2 this1 then1 was the ,inverse ,method2 but the result is something very different from any that can be obtained by the ,historical ,method4 ,the essential difference between the ,physical and ,historical ,methods is that1 in the former1 whether ,direct or ,inverse1 the deductive process1 when complete1 amounts to exact demonstration2 whereas1 in the latter1 the deductions may consist of qualitative reasonings1 and the results are indefinite4 ,they establish--7#a7 a merely probable connection between the phenomena according to an empirical law 7say1 between ,city-democracy and fickle politics72 7#b7 connect this with other historical or social generalisations1 by showing that they all alike flow from the same causes1 namely1 from the nature of races of men under certain social and geographical conditions2 and 7#c7 explain why such empirical laws may fail1 according to the differences that prevail among races of men and among the conditions under which they live4 ,thus1 seeing how rapidly excitement is propagated by the chatter1 grimacing1 and gesticulation of townsmen1 it is probable enough that the democracy of a ,city-state should be fickle 7and arbitrary1 because irresponsible74 ,a similar phenomenon of panic1 sympathetic hope and despair1 is exhibited by every stock-exchange1 and is not peculiar to political life4 ,and when political opinion is not manufactured solely in the reverberating furnace of a city1 fickleness ceases to characterise democracy2 and1 in fact1 is not found in ,switzerland1 or the ,united ,states1 nor in ,france so far as politics1 depend upon the peasantry4 ,this is called the ,historical ,method1 then1 because it is especially useful in explaining the movements of history1 and in verifying the generalisations of political and social science4 ,we must not1 however1 suppose that its use is confined to such studies4 ,only a ridiculous pedantry would allot to each subject its own method and forbid the use of any other2 as if it were not our capital object to establish truth by any means4 ,wherever the forces determining a phenomenon are too numerous or too indefinite to be combined in a deductive demonstration1 there the ,historical ,method is likely to be useful2 and this seems often to be the case in ,geology and ,biology1 as well as in the ,science of ,history1 or ,sociology1 and its various subsidiary studies4 ,consider upon what causes historical events depend3 the customs1 character1 and opinions of all the people concerned2 the organisation of their government1 and the character of their religious institutions2 the development of industry among them1 of the military art1 of fine art1 literature and science2 their relations1 commercial1 political and social1 with other nations2 the physical conditions of climate and geographical position amidst which they live4 ,hardly an event of importance occurs in any nation that is not1 directly or indirectly1 influenced by every one of these circumstances1 and that does not react upon them4 ,now1 from the nature of the ,canons of direct ,induction1 a satisfactory employment of them in such a complex and tangled situation as history presents1 is rarely possible2 for they all require the actual or virtual isolation of the phenomenon under investigation4 ,they also require the greatest attainable immediacy of connection between cause and effect2 whereas the causes of social events may accumulate during hundreds of years4 ,in collecting empirical laws from history1 therefore1 only very rough inductions can be hoped for1 and we may have to be content with simple enumeration4 ,hence the importance of supporting such laws by deduction from the nature of the case1 however faint a probability of the asserted connection is thereby raised2 and this even if each law is valued merely for its own sake4 ,still more1 if anything worth the name of ,historical ,science is to be constructed1 must a mere collection of such empiricisms fail to content us2 and the only way to give them a scientific character is to show deductively their common dependence upon various combinations of the same causes4 ,yet even those who profess to employ the ,historical ,method often omit the deductive half of it2 and of course 'practical politicians' boast of their entire contentment with what they call 'the facts4' ,sometimes1 however1 politicians1 venturing upon deductive reasoning1 have fallen into the opposite error of omitting to test their results by any comparison with the facts3 arguing from certain ',rights of ,man1' or ',interests of ,classes1' or ',laws of ,supply and ,demand1' that this or that event will happen1 or ought to happen1 without troubling themselves to observe whether it does happen or ever has happened4 ,this method of ,deduction without any empirical verification1 is called by ,mill the ,geometrical2 and1 plainly1 it can be trustworthy only where there is no actual conflict of forces to be considered4 ,in pure mathematical reasoning about space1 time1 and number1 provided the premises and the reasoning be correct1 verification by a comparison with the facts may be needless1 because there is no possibility of counteraction4 ,but when we deal with actual causes1 no computation of their effects can be relied upon without comparing our conclusions with the facts3 not even in ,astronomy and ,physics1 least of all in ,politics4 ,burke1 then1 has well said that without the guide and light of sound1 well-understood principles all our reasoning in politics1 as in everything else1 would be only a confused jumble of particular facts and details without the means of drawing any sort of theoretical or practical conclusion2 but that1 on the other hand1 the statesman1 who does not take account of circumstances1 infinite and infinitely combined1 is not erroneous1 but stark mad--he is metaphysically mad 7,on the ,petition of the ,unitarians74 ,there is1 or ought to be1 no logical difference between the evidence required by a statesman and that appealed to by a philosopher2 and since1 as we have seen1 the combination of principles with circumstances cannot1 in solving problems of social science1 be made with the demonstrative precision that belongs to astronomical and physical investigations1 there remains the ,historical ,method as above described4 ,examples of the empirical laws from which this method begins abound in histories1 newspapers1 and political discussions1 and are of all shades of truth or half-truth3 as that ',history consists in the biographies of great men'2 in other words1 that the movements of society are due to exceptional personal powers1 not to general causes2 ,that at certain epochs great men occur in groups2 ,that every ,fine ,art passes through periods of development1 culmination and decline2 ,that ,democracies tend to change into ,despotisms2 ,that the possession of power1 whether by classes or despots1 corrupts the possessor3 ,that 'the governments most distinguished for sustained vigour and abilities have generally been aristocracies'2 ,that 'revolutions always begin in hunger'2 ,that civilisation is inimical to individuality2 ,that the civilisation of the country proceeds from the town2 ,that 'the movement of progressive societies has hitherto been a movement from ,status to ,contract 7i4e41 from a condition in which the individual's rights and duties depend on his caste1 or position in his family as slave1 child1 or patriarch1 to a condition in which his rights and duties are largely determined by the voluntary agreements he enters into7'2 and this last is treated by ,h4 ,spencer as one aspect of the law first stated by ,comte1 that the progress of societies is from the military to the industrial state4 ,the deductive process we may illustrate by ,spencer's explanation of the co-existence in the military state of those specific characters1 the inductive proof of which furnished an illustration of the method of ,agreement 7ch4 xvi4 #a74 ,the type of the military ,state involves the growth of the warrior class1 and the treatment of labourers as existing solely to support the warriors2 the complete subordination of all individuals to the will of the despotic soldier-king1 their property1 liberty and life being at the service of the ,state2 the regimentation of society1 not only for military1 but also for civil purposes2 the suppression of all private associations1 etc4 ,now all these characteristics arise from their utility for the purpose of war1 a utility amounting to necessity if war is the ,state's chief purpose4 ,for every purpose is best served when the whole available force co-operates toward it3 other things equal1 the bigger the army the better2 and to increase it1 men must be taken from industry1 until only just enough remain to feed and equip the soldiers4 ,as this arrangement is not to everybody's taste1 there must be despotic control2 and this control is most effective through regimentation by grades of command4 ,private associations1 of course1 cannot live openly in such a ,state1 because they may have wills of their own and are convenient for conspiracy4 ,thus the induction of characteristics is verified by a deduction of them from the nature of the case4 #f4 ,the greater indefiniteness of the ,historical compared with the ,physical ,method1 both in its inductions and in its deductions1 makes it even more difficult to work with4 ,it wants much sagacity and more impartiality2 for the demon of ,party is too much with us4 ,our first care should be to make the empirical law as nearly true as possible1 collecting as many as we can of the facts which the law is supposed to generalise1 and examining them according to the canons of ,induction1 with due allowance for the imperfect applicability of those canons to such complex1 unwieldy1 and indefinite instances4 ,in the examples of such laws given above1 it is clear that in some cases no pains have been taken to examine the facts4 ,what is the inductive evidence that ,democracies change into ,despotisms2 that revolutions always begin in hunger2 or that civilisation is inimical to individuality8 ,even ,mill's often quoted saying1 that the governments remarkable in history for sustained vigour and ability have generally been aristocracies1 is oddly over-stated4 ,for if you turn to the passage 7,rep4 ,gov4 chap4 vi471 the next sentence tells you that such governments have always been aristocracies of public functionaries2 and the next sentence but one restricts1 apparently1 the list of such remarkable governments to two--,rome and ,venice4 ,whence1 then1 comes the word generally into ,mill's law8 ,as to deducing our empirical law from a consideration of the nature of the case1 it is obvious that we ought--7a7 to take account of all the important conditions2 7b7 to allow weight to them severally in proportion to their importance2 and 7c7 not to include in our estimates any condition which we cannot show to be probably present and operative4 ,thus the ,great-,man-,theory of history must surely be admitted to assign a real condition of national success4 ,the great man organises1 directs1 inspires3 is that nothing8 ,on the other hand1 to recognise no other condition of national success is the manifest frenzy of a mind in the mythopic age4 ,we must allow the great man his due weight1 and then inquire into the general conditions that 7a7 bring him to birth in one nation rather than another1 and 7b7 give him his opportunity4 ,mill's explanation of the success of the aristocratic governments of ,rome and ,venice is1 that they were1 in fact1 bureaucracies2 that is to say1 their members were trained in the science and art of administration and command4 ,here1 again1 we have1 no doubt1 a real condition2 but is it the only one8 ,the popular mind1 which little relishes the scaling down of ,mill's original law to those two remote cases1 is persuaded that an aristocracy is the depository of hereditary virtue1 especially with reference to government1 and would at once ascribe to this circumstance the greater part of the success of any aristocratic constitution4 ,now1 if the effects of training are inherited1 they must1 in an hereditary aristocracy1 increase the energy of the cause assigned by ,mill2 but1 if not1 such heredity is a condition not present or not operative4 ,still1 if families are ennobled for their extraordinary natural powers of administration or command 7as sometimes happens71 it is agreed on all hands that innate qualities are inheritable2 at least1 if care be taken to intermarry with families similarly distinguished1 and if by natural or artificial selection all the failures among the offspring be eliminated4 ,the ,spartans had some crude notion of both these precautions2 and if such measures had been widely adopted1 we might deduce from the doctrine of heredity a probability in favour of ,mill's original proposition1 and thereby verify it in its generality1 if it could be collected from the facts4 ,the ,historical ,method may be further illustrated by the course adopted in that branch of ,social ,science which has been found susceptible of the most extensive independent development1 namely1 ,economics4 ,first1 by way of contrast1 ,i should say that the abstract1 or theoretical treatment of ,economics follows the ,physical ,method2 because1 as ,mill explains1 although the phenomena of industry are no doubt influenced1 like other social affairs1 by all the other circumstances of ,society1 government1 religion1 war1 art1 etc42 yet1 where industry is most developed1 as in ,england and the ,united ,states1 certain special conditions affecting it are so much the most important that1 for the purpose at least of a first outline of the science1 they may conveniently be considered as the only ones4 ,these conditions are3 7#a7 the general disposition of men to obtain wealth with as little trouble as possible1 and 7#b7 to spend it so as to obtain the greatest satisfaction of their various desires2 7#c7 the facts that determine population2 and 7#d7 the tendency of extractive industry1 when pushed beyond a certain limit without any improvement in the industrial arts1 to yield diminishing returns4 ,from these premises it is easy to infer the general laws of prices1 of wages and interest 7which are the prices of labour and of the use of capital71 and of rent2 and it remains to verify these laws by comparing them with the facts in each case2 and 7if they fail to agree with the facts7 to amend them1 according to the ,method of ,residues1 by taking account of those influential conditions which were omitted from the first draft of the theory4 ,whilst1 however1 this is usually the procedure of those inquirers who have done most to give ,economics its scientific character1 to insist that no other plan shall be adopted would be sheer pedantry2 and ,dr4 ,keynes has shown1 in his ,scope and ,method of ,political ,economy1 that ,mill has himself sometimes solved economic problems by the ,historical ,method4 ,with an analysis of his treatment of ,peasant ,proprietorship 7,political ,economy1 ,b4 ,,ii41 cc4 #g and #h7 we may close this section4 ,mill first shows inductively1 by collecting evidence from ,switzerland1 ,germany1 ,norway1 ,belgium1 and ,france 7countries differing in race1 government1 climate and situation71 that peasant proprietors are superhumanly industrious2 intelligent cultivators1 and generally intelligent men2 prudent1 temperate1 and independent1 and that they exercise self-control in avoiding improvident marriages4 ,this group of empirical generalisations as to the character of peasant proprietors he then deduces from the nature of the case3 their industry1 he says1 is a natural consequence of the fact that1 however much they produce1 it is all their own2 they cultivate intelligently1 because for generations they have given their whole mind to it2 they are generally intelligent men1 because the variety of work involved in small farming1 requiring foresight and calculation1 necessarily promotes intelligence2 they are prudent1 because they have something to save1 and by saving can improve their station and perhaps buy more land2 they are temperate1 because intemperance is incompatible with industry and prudence2 they are independent1 because secure of the necessaries of life1 and from having property to fall back upon2 and they avoid improvidence in marriage1 because the extent and fertility of their fields is always plainly before them1 and therefore how many children they can maintain is easily calculated4 ,the worst of them is that they work too hard and deny themselves too much3 but1 over the greater part of the world1 other peasantry work too hard2 though they can scarcely be said to deny themselves too much2 since all their labour for others brings them no surplus to squander upon self-indulgence4 #g4 ,the foregoing account of the ,historical ,method is based upon ,mill's discussions in ,b4 ,,vi4 of his ,logic1 especially cc4 #f to #aa4 ,mill ascribes to ,comte the first clear statement of the method2 and it is highly scientific1 and important in generalising the connections of historical events4 ,but perhaps the expression1 ',historical ,method1' is more frequently applied to the ,comparative ,method1 as used in investigating the history of institutions or the true sense of legends4 7#a7 ,suppose we are trying to explain the institution of capital punishment as it now exists in ,england4 7#a7 ,we must try to trace the history of it back to the earliest times2 for social custom and tradition is one line of causation4 ,at present the punishment of death is legally incident only to murder and high treason4 ,but early in the last century malefactors were hung for forgery1 sheep-stealing1 arson and a long list of other offences down to pocket-picking3 earlier still the list included witchcraft and heresy4 ,at present hanging is the only mode of putting a malefactor to death2 but formerly the ways of putting to death included also burning1 boiling1 pressing1 beheading1 and mixed modes4 ,before the ,restoration1 however1 the offences punishable with death were far fewer than they afterwards became2 and until the twelfth century1 the penalty of death might be avoided by paying compensation1 the wer-geld4 7#b7 ,every change in the history of an institution must be explained by pointing to the special causes in operation during the time when the change was in progress4 ,thus the restriction of the death penalty1 in the nineteenth century1 to so few offences was due partly to the growth of humane feelings1 partly to the belief that the infliction1 or threat1 of the extreme penalty had failed to enforce the law and had demoralised the administration of ,justice4 ,the continual extension of the death penalty throughout the eighteenth century may be attributed to a belief that it was the most effectual means of deterring evil-doers when the means of detecting and apprehending criminals were feeble and ill-organised4 ,the various old brutal ways of execution were adopted sometimes to strike terror1 sometimes for vengeance1 sometimes from horror of the crime1 or even from 'conscientious scruples'2--which last were the excuse for preferring the burning of heretics to any sort of bloodshed4 7#c7 ,the causes of any change in the history of an institution in any country may not be directly discoverable3 they must then be investigated by the ,comparative ,method4 ,again1 the recorded history of a nation1 and of all its institutions1 followed backwards1 comes at last to an end3 then the antecedent history must also be supplied by the ,comparative ,method2 whose special use is to indicate the existence of facts for which there is no direct evidence4 ,this method rests upon the principle that where the causes are alike the effects will be alike1 and that similar effects are traceable to similar causes4 ,every department of study--,astronomy1 ,chemistry1 ,zoology1 ,sociology--is determined by the fact that the phenomena it investigates have certain common characteristics2 and we are apt to infer that any process observed in some of these phenomena1 if depending on those common characteristics1 will be found in others4 ,for example1 the decomposition1 or radio-activity1 of certain elements prepares one to believe that all elements may exhibit it4 ,where the properties of an object are known to be closely interdependent1 as in the organisation of plants1 animals and societies1 we are especially justified in inferring from one case to another4 ,the whole animal ,kingdom has certain common characters--the metabolic process1 dependence upon oxygen1 upon vegetable food 7ultimately71 heredity1 etc41 and1 upon this ground1 any process 7say1 the differentiation of species by ,natural ,selection7 that has been established for some kinds of animal is readily extended to others4 ,if instead of the whole animal ,kingdom we take some district of it--,class1 ,order1 ,family--our confidence in such inferences increases2 because the common characters are more numerous and the conditions of life are more alike2 or1 in other words1 the common causes are more numerous that initiate and control the development of nearly allied animals4 ,for such reasons a few fragmentary remains of an extinct animal enable the palontologist to reconstruct with some probability an outline of its appearance1 organisation1 food1 habitat and habits4 ,applied to ,history1 the ,comparative ,method rests upon an assumption 7which the known facts of 7say7 #f1jjj years amply justify7 that human nature1 after attaining a recognisable type as homo sapiens1 is approximately uniform in all countries and in all ages1 though more especially where states of culture are similar4 ,men living in society are actuated by similar motives and reasons in similar ways2 they are all dependent upon the supply of food and therefore on the sun and the seasons and the weather and upon means of making fire1 and so on4 ,accordingly1 they entertain similar beliefs1 and develop similar institutions through similar series of changes4 ,hence1 if in one nation some institution has been altered for reasons that we cannot directly discover1 whereas we know the reasons why a similar change was adopted elsewhere1 we may conjecture with more or less probability1 after making allowance for differences in other circumstances1 that the motives or causes in the former case were similar to those in the latter1 or in any cases that are better known4 ,or1 again1 if in one nation we cannot trace an institution beyond a certain point1 but can show that elsewhere a similar institution has had such or such an antecedent history1 we may venture to reconstruct with more or less probability the earlier history of that institution in the nation we are studying4 ,amongst the ,english and ,saxon tribes that settled in ,britain1 death was the penalty for murder1 and the criminal was delivered to the next-of-kin of his victim for execution2 he might1 however1 compound for his crime by paying a certain compensation4 ,studying the history of other tribes in various parts of the world1 we are able1 with much probability1 to reconstruct the antecedents of this death-penalty in our own prehistoric ages1 and to trace it to the blood-feud2 that is1 to a tribal condition in which the next-of-kin of a murdered man was socially and religiously bound to avenge him by slaying the murderer or one of his kindred4 ,this duty of revenge is sometimes 7and perhaps was at first everywhere7 regarded as necessary to appease the ghost of the victim2 sometimes as necessary to compensate the surviving members of his family4 ,in the latter case1 it is open to them to accept compensation in money or cattle1 etc4 ,whether the kin will be ready to accept compensation must depend upon the value they set upon wealth in comparison with revenge2 but for the sake of order and tribal strength1 it is the interest of the tribe1 or its elders1 or chieftain1 to encourage or even to enforce such acceptance4 ,it is also their interest to take the questions--whether a crime has been committed1 by whom1 and what compensation is due--out of the hands of the injured party1 and to submit them to some sort of court or judicial authority4 ,at first1 following ancient custom as much as possible1 the act of requital1 or the choice of accepting compensation1 is left to the next-of-kin2 but with the growth of central power these things are entrusted to ministers of the ,government4 ,then revenge has undergone its full transformation into punishment4 ,very likely the wrong itself will come to be treated as having been done not to the kindred of the murdered man1 but to the ,state or the ,king1 as in fact a breach of the ,king's peace4 ,this happened in our own history4 7#d7 ,the ,comparative ,method assumes that human nature is approximately the same in different countries and ages2 but1 of course1 'approximately' is an important word4 ,although there is often a striking and significant resemblance between the beliefs and institutions of widely separated peoples1 we expect to draw the most instructive parallels between those who are nearly related by descent1 or neighbourhood1 or culture4 ,to shed light upon our own manners1 we turn first to other ,teutons1 then to ,slavonians and ,kelts1 or other ,aryans1 and so on2 and we prefer evidence from ,europe to examples from ,africa4 7#e7 ,as to national culture1 that it exhibits certain 'stages' of development is popularly recognised in the distinction drawn between savages1 barbarians and civilised folk4 ,but the idea remains rather vague2 and there is not space here to define it4 ,i refer1 therefore1 to the classifications of stages of culture given by ,a4 ,sutherland1 7,origin and ,growth of ,moral ,instinct1 ,vol4 ,i1 p4 #ajc71 and ,l4,t4 ,hobhouse 7,morals in ,evolution1 c4 #b74 ,that in any 'state of ,society1' its factors--religion1 government1 science1 etc4--are mutually dependent1 was a leading doctrine with ,comte1 adopted by ,mill4 ,there must be some truth in it2 but in some cases we do not understand social influences sufficiently well to trace the connection of factors2 and whilst preferring to look for historical parallels between nations of similar culture1 we find many cases in which barbarous or savage customs linger in a civilised country4 7#f7 ,it was another favourite doctrine with ,comte1 also adopted by ,mill--that the general state of culture is chiefly determined by the prevailing intellectual condition of a people1 especially by the accepted ground of explanation--whether the will of supernatural beings1 or occult powers1 or physical antecedents3 the law of three stages1 ,fetichism1 ,metaphysics1 ,positivism4 ,and this also is1 at least1 so far true1 that it is useless to try to interpret the manners and institutions of any nation until we know its predominant beliefs4 ,magic and animism are beliefs everywhere held by mankind in early stages of culture1 and they influence every action of life4 ,but that is not all3 these beliefs retain their hold upon great multitudes of civilised men and affect the thoughts of the most enlightened4 ,whilst the saying 'that human nature is the same in all ages' seems to make no allowance for the fact that1 in some nations1 a considerable number of individuals has attained to powers of deliberation1 self-control1 and exact reasoning1 far above the barbarous level1 it is yet so far true that1 even in civilised countries1 masses of people1 were it not for the example and instruction of those individuals1 would fall back upon magic and animism and the manners that go with those beliefs4 ,the different degrees of enlightenment enjoyed by different classes of the population often enable the less educated to preserve a barbarous custom amidst many civilised characteristics of the national life4 #h4 ,historical reasoning must start from1 or be verified by1 observations4 ,if we are writing the history of ourselves3 if of another time or country1 we can observe some of the present conditions of the country1 its inhabitants1 language1 manners1 institutions1 which are effects of the past and must be traceable to it2 we may also be able to observe ancient buildings or their ruins1 funerary remains1 coins1 dating from the very times we are to treat of4 ,our own observations1 of course1 are by no means free from error4 ,but even in treating of our own age and country1 most of our information must be derived from the testimony of others1 who may have made mistakes of observation and further mistakes in reporting their observations1 or may have intentionally falsified them4 ,testimony is of two kinds3 ,oral2 and ,written1 inscribed or printed4 ,in investigating the events of a remote age1 nearly all our direct evidence must be some sort of testimony4 7#a7 ,oral testimony depends upon the character of the witness2 and the best witness is not perfectly trustworthy2 for he may not have observed accurately1 or he may not have reported correctly2 especially if some time elapsed between the event and his account of it2 for no man's memory is perfect4 ,since witnesses vary widely in capacity and integrity1 we must ask concerning any one of them--was he a good judge of what he saw1 and of what was really important in the event8 ,had he good opportunities of knowing the circumstances8 ,had he any interest in the event--personal1 or partisan1 or patriotic8 ,such interests would colour his report2 and so would the love of telling a dramatic story1 if that was a weakness of his4 ,nay1 a love of truth might lead him to modify the report of what he remembered if--as he remembered it--the matter seemed not quite credible4 ,we must also bear in mind that1 for want of training1 precision in speaking the truth is not understood or appreciated by many honest people even now1 still less in unscientific ages4 ,oral tradition is formed by passing a report from one to another1 generation by generation2 and it is generally true that such a tradition loses credit at every step1 because every narrator has some weakness4 ,however1 the value of tradition depends upon the motives people have to report correctly1 and on the form of the communication1 and on whether monuments survive in connection with the story4 ,amongst the things best remembered are religious and magic formul1 heroic poems1 lists of ancestors1 popular legends about deeply impressive events1 such as migrations1 conquests1 famines1 plagues4 ,we are apt now to underrate the value of tradition1 because the use of writing has made tradition less important1 and therefore less pains are taken to preserve it4 ,in the middle of last century1 it was usual 7and then quite justifiable7 to depreciate oral tradition as nearly worthless2 but the spread of archological and anthropological research1 and the growth of the ,comparative ,method1 have given new significance to legends and traditions which1 merely by themselves1 could not deserve the slightest confidence4 7#b7 ,as to written evidence1 contemporary inscriptions--such as are found on rocks and stones and bricks in various parts of the world1 and most abundantly in ,egypt and ,western ,asia--are of the highest value1 because least liable to fraudulent abuse2 but must be considered with reference to the motives of those who set them forth4 ,manuscripts and books give rise to many difficulties4 ,we have to consider whether they were originally written by some one contemporary with the events recorded3 if so they have the same value as immediate oral testimony1 provided they have not been tampered with since4 ,but if not contemporary records1 they may have been derived from other records that were contemporary1 or only from oral tradition4 ,in the latter case they are vitiated by the weakness of oral tradition4 ,in the former case1 we have to ask what was the trustworthiness of the original records1 and how far do the extant writings fairly represent those records8 ,our answers to these questions will partly depend upon what we know or can discover of the authors of the ,,mss4 or books4 ,who was the author8 ,if a work bears some man's name1 did he really write it8 ,the evidence bearing upon this question is usually divided into internal1 external and mixed2 but perhaps no evidence is purely internal1 if we define it as that which is derived entirely from the work itself4 ,under the name of internal evidence it is usual to put the language1 the style1 consistency of ideas2 but if we had no grounds of judgment but the book itself1 we could not possibly say whether the style was the author's3 this requires us to know his other works4 ,nor could we say whether the language was that of his age1 unless we knew other literature of the same age2 nor even that different passages seem to be written in the manner of different ages1 but for our knowledge of change in other literatures4 ,there must in every case be some external reference4 ,thus we judge that a work is not by the alleged author1 nor contemporary with him1 if words are used that only became current at a later date1 or are used in a sense that they only later acquired1 or if later writers are imitated1 or if events are mentioned that happened later 7'anachronism'74 ,books are sometimes forged outright1 that is1 are written by one man and deliberately fathered upon another2 but sometimes books come to be ascribed to a well-known name1 which were written by some one else without fraudulent intent1 dramatically or as a rhetorical exercise4 ,as to external evidence1 if from other sources we have some knowledge of the facts described in a given book1 and if it presents no serious discrepancies with those facts1 this is some confirmation of a claim to contemporaneity4 ,but the chief source of external evidence is other literature1 where we may find the book in question referred to or quoted4 ,such other literature may be by another author1 as when ,aristotle refers to a dialogue of ,plato's1 or ,shakespeare quotes ,marlowe2 or may be other work of the author himself1 as when ,aristotle in the ,ethics refers to his own ,physics1 or ,chaucer in ,the ,canterbury ,tales mentions as his own ,the ,legend of ,good ,women1 and in ,the ,legend gives a list of other works of his4 ,this kind of argument assumes that the authorship of the work we start from is undisputed2 which is practically the case with the ,ethics and ,the ,canterbury ,tales4 ,but1 now1 granting that a work is by a good author1 or contemporary with the events recorded1 or healthily related to others that were contemporary1 it remains to consider whether it has been well preserved and is likely to retain its original sense4 ,it is1 therefore1 desirable to know the history of a book or ,,ms41 and through whose hands it has passed4 ,have there been opportunities of tampering with it2 and have there been motives to do so8 ,in reprinting books1 but still more in copying ,,mss41 there are opportunities of omitting or interpolating passages1 or of otherwise altering the sense4 ,in fact1 slight changes are almost sure to be made even without meaning to make them1 especially in copying ,,mss41 through the carelessness or ignorance of transcribers4 ,hence the oldest ,,ms4 is reckoned the best4 ,if a work contains stories that are physically impossible1 it shows a defect of judgment in the author1 and decreases our confidence in his other statements2 but it does not follow that these others are to be rejected4 ,we must try to compare them with other evidence4 ,even incredible stories are significant3 they show what people were capable of believing1 and1 therefore1 under what conditions they reasoned and acted4 ,one cause of the incredibility of popular stories is the fusion of legend with myth4 ,a legend is a traditionary story about something that really happened3 it may have been greatly distorted by stupidity1 or exaggeration1 or dramatisation1 or rationalisation1 but may still retain a good deal of the original fact4 ,a myth1 however1 has not necessarily any basis of fact3 it may be a sort of primitive philosophy1 an hypothesis freely invented to explain some fact in nature1 such as eclipses1 or to explain some social custom whose origin is forgotten1 such as the sacrificing of a ram4 ,all historical conclusions1 then1 depend on a sum of convergent and conflicting probabilities in the nature of circumstantial evidence4 ,the best testimony is only highly probable1 and it is always incomplete4 ,to complete the picture of any past age there is no resource but the ,comparative ,method4 ,we use this method without being aware of it1 whenever we make the records of the last generation intelligible to ourselves by our own experience4 ,without it nothing would be intelligible3 an ancient coin or weapon would have no meaning1 were we not acquainted with the origins and uses of other coins and weapons4 ,generally1 the further we go back in history1 the more the evidence needs interpretation and reconstruction1 and the more prominent becomes the appeal to the ,comparative ,method4 ,our aim is to construct a history of the world1 and of the planet as part of the world1 and of mankind as part of the life of the planet1 in such a way that every event shall be consistent with1 and even required by1 the rest according to the principle of ,causation4 ,,chapter ,,xviii ,,hypotheses #a4 ,an ,hypothesis1 sometimes employed instead of a known law1 as a premise in the deductive investigation of nature1 is defined by ,mill as any supposition which we make 7either without actual evidence1 or on evidence avowedly insufficient7 in order to endeavour to deduce from it conclusions in accordance with facts which are known to be real2 under the idea that if the conclusions to which the hypothesis leads are known truths1 the hypothesis itself either must be1 or at least is likely to be1 true4 ,the deduction of known truths from an hypothesis is its ,verification2 and when this has been accomplished in a good many cases1 and there are no manifest failures1 the hypothesis is often called a ,theory2 though this term is also used for the whole system of laws of a certain class of phenomena1 as when ,astronomy is called the 'theory of the heavens4' ,between hypothesis and theory in the former sense no distinct line can be drawn2 for the complete proof of any speculation may take a long time1 and meanwhile the gradually accumulating evidence produces in different minds very different degrees of satisfaction2 so that the sanguine begin to talk of 'the theory1' whilst the circumspect continue to call it 'the hypothesis4' ,an ,hypothesis may be made concerning 7#a7 an ,agent1 such as the ether2 or 7#b7 a ,collocation1 such as the plan of our solar system--whether geocentric or heliocentric2 or 7#c7 a ,law of an agent's operation1 as that light is transmitted by a wave motion of such lengths or of such rates of vibration4 ,the received explanation of light involves both an agent1 the ether1 as an all-pervading elastic fluid1 and also the law of its operation1 as transmitting light in waves of definite form and length1 with definite velocity4 ,the agreement between the calculated results of this complex hypothesis and the observed phenomena of light is the chief part of the verification2 which has now been so successfully accomplished that we generally hear of the ',undulatory ,theory4' ,sometimes a new agent only is proposed2 as the planet ,neptune was at first assumed to exist in order to account for perturbations in the movements of ,uranus1 influencing it according to the already established law of gravitation4 ,sometimes the agents are known1 and only the law of their operation is hypothetical1 as was at first the case with the law of gravitation itself4 ,for the agents1 namely1 ,earth1 falling bodies on the ,earth1 ,moon1 ,sun1 and planets were manifest2 and the hypothesis was that their motions might be due to their attracting one another with a force inversely proportional to the squares of the distances between them4 ,in the ,ptolemaic ,astronomy1 again1 there was an hypothesis as to the collocation of the heavenly bodies 7namely1 that our ,earth was the centre of the universe1 and that ,moon1 ,sun1 planets and stars revolved around her73 in the early form of the system there was also an hypothesis concerning agents upon which this arrangement depended 7namely1 the crystalline spheres in which the heavenly bodies were fixed1 though these were afterwards declared to be imaginary72 and an hypothesis concerning the law of operation 7namely1 that circular motion is the most perfect and eternal1 and therefore proper to celestial things74 ,hypotheses are by no means confined to the physical sciences3 we all make them freely in private life4 ,in searching for anything1 we guess where it may be before going to look for it3 the search for the ,north ,pole was likewise guided by hypotheses how best to get there4 ,in estimating the characters or explaining the conduct of acquaintances or of public men1 we frame hypotheses as to their dispositions and principles4 ',that we should not impute motives' is a peculiarly absurd maxim1 as there is no other way of understanding human life4 ,to impute bad motives1 indeed1 when good are just as probable1 is to be wanting in the scientific spirit1 which views every subject in 'a dry light4' ,nor can we help 'judging others by ourselves'2 for self-knowledge is the only possible starting-point when we set out to interpret the lives of others4 ,but to understand the manifold combinations of which the elements of character are susceptible1 and how these are determined by the breeding of race or family under various conditions1 and again by the circumstances of each man's life1 demands an extraordinary union of sympathetic imagination with scientific habits of thought4 ,such should be the equipment of the historian1 who pursues the same method of hypothesis when he attempts to explain 7say7 the state of parties upon the ,exclusion ,bill1 or the policy of ,louis ,,xi4 ,problems such as the former of these are the easier2 because1 amidst the compromises of a party1 personal peculiarities obliterate one another1 and expose a simpler scheme of human nature with fewer fig-leaves4 ,much more hazardous hypotheses are necessary in interpreting the customs of savages1 and the feelings of all sorts of animals4 ,literary criticisms1 again1 abound with hypotheses3 e4g41 as to the composition of the ,homeric poems1 the order of the ,platonic dialogues1 the authorship of the ,cdmonic poems1 or the ,ossianic1 or of the letters of ,junius4 ,thus the method of our everyday thoughts is identical with that of our most refined speculations2 and in every case we have to find whether the hypothesis accounts for the facts4 #b4 ,it follows from the definition of an hypothesis that none is of any use that does not admit of verification 7proof or disproof71 by comparing the results that may be deduced from it with facts or laws4 ,if so framed as to elude every attempt to test it by facts1 it can never be proved by them nor add anything to our understanding of them4 ,suppose that a conjurer asserts that his table is controlled by the spirit of your deceased relative1 and makes it rap out an account of some adventure that could not easily have been within a stranger's knowledge4 ,so far good4 ,then1 trying again1 the table raps out some blunder about your family which the deceased relative could not have committed2 but the conjurer explains that 'a lying spirit' sometimes possesses the table4 ,this amendment of the hypothesis makes it equally compatible with success and with failure4 ,to pass from small things to great1 not dissimilar was the case of the ,ptolemaic ,astronomy3 by successive modifications1 its hypothesis was made to correspond with accumulating observations of the celestial motions so ingeniously that1 until the telescope was invented1 it may be said to have been unverifiable4 ,consider1 again1 the sociological hypothesis1 that civil order was at first founded on a ,contract which remains binding upon all mankind3 this is reconcilable with the most opposite institutions4 ,for we have no record of such an event3 and if the institutions of one ,state 7say the ,british7 include ceremonies1 such as the coronation oath and oath of allegiance1 which may be remnants of an original contract1 they may nevertheless be of comparatively recent origin2 whereas if the institutions of another ,state 7say the ,russian7 contain nothing that admits of similar interpretation1 yet traces of the contract once existing may long since have been obliterated4 ,moreover1 the actual contents of the contract not having been preserved1 every adherent of this hypothesis supplies them at his own discretion1 'according to the dictates of ,reason'2 and so one derives from it the duty of passive obedience1 and another with equal cogency establishes the right of rebellion4 ,to be verifiable1 then1 an hypothesis must be definite2 if somewhat vague in its first conception 7which is reasonably to be expected71 it must be made definite in order to be put to the proof4 ,but1 except this condition of verifiability1 and definiteness for the sake of verifiability1 without which a proposition does not deserve the name of an hypothesis1 it seems inadvisable to lay down rules for a 'legitimate' hypothesis4 ,the epithet is misleading4 ,it suggests that the ,logician makes rules for scientific inquirers2 whereas his business is to discover the principles which they1 in fact1 employ in what are acknowledged to be their most successful investigations4 ,if he did make rules for them1 and they treated him seriously1 they might be discouraged in the exercise of that liberty of hypothesising which is the condition of all originality2 whilst if they paid no attention to him1 he must suffer some loss of dignity4 ,again1 to say that a 'legitimate hypothesis' must explain all the facts1 at least in the department for which it is invented1 is decidedly discouraging4 ,no doubt it may be expected to do this in the long run when 7if ever7 it is completely established2 but this may take a long time3 is it meanwhile illegitimate8 ,or can this adjective be applied to ,newton's corpuscular theory of light1 even though it has failed to explain all the facts8 #c4 ,given a verifiable hypothesis1 however1 what constitutes proof or disproof8 7#a7 ,if a new agent be proposed1 it is desirable that we should be able directly to observe it1 or at least to obtain some evidence of its existence of a different kind from the very facts which it has been invented to explain4 ,thus1 in the discovery of ,neptune1 after the existence of such a planet outside the orbit of ,uranus had been conjectured 7to account for the movements of the latter71 the place in the heavens which such a body should occupy at a certain time was calculated1 and there by means of the telescope it was actually seen4 ,agents1 however1 are assumed and reasoned upon very successfully which1 by their nature1 never can be objects of perception3 such are the atoms of ,chemistry and the ether of ,optics4 ,but the severer methodologists regard them with suspicion3 ,mill was never completely convinced about the ether2 the defining of which has been found very difficult4 ,he was willing1 however1 to make the most of the evidence that has been adduced as indicating a certain property of it distinct from those by which it transmits radiation1 namely1 mechanical inertia1 whereby it has been supposed to retard the career of the heavenly bodies1 as shown especially by the history of ,encke's comet4 ,this comet returned sooner than it should1 as calculated from the usual data2 the difference was ascribed to the influence of a resisting medium in reducing the extent of its orbit2 and such a medium may be the ether4 ,if this conjecture 7now of less credit7 should gain acceptance1 the ether might be regarded as a vera causa 7that is1 a condition whose existence may be proved independently of the phenomena it was intended to explain71 in spite of its being excluded by its nature from the sphere of direct perception4 ,however1 science is not a way of perceiving things1 but essentially a way of thinking about them4 ,it starts1 indeed1 from perception and returns to it1 and its thinking is controlled by the analogies of perception4 ,atoms and ether are thought about as if they could be seen or felt1 not as noumena2 and if still successful in connecting and explaining perceptions1 and free from contradiction1 they will stand as hypotheses on that ground4 ,on the other hand1 a great many agents1 once assumed in order to explain phenomena1 have since been explained away4 ,of course1 a fact can never be 'explained away'3 the phrase is properly applicable to the fate of erroneous hypotheses1 when1 not only are they disproved1 but others are established in their places4 ,of the ,aristotelian spheres1 which were supposed to support and translate sun1 moon and planets1 no trace has ever been found3 they would have been very much in the way of the comets4 ,phlogiston1 again1 an agent much in favour with the earlier ,chemists1 was found1 ,whewell tells us1 when their theories were tested by exact weighing1 to be not merely non-existent but a minus quantity2 that is to say1 it required the assumption of its absolute lightness so that it diminished the weight of the compounds into which it entered4 ,these agents1 then1 the spheres and phlogiston1 have been explained away1 and instead of them we have the laws of motion and oxygen4 7#b7 ,whether the hypothetical agent be perceptible or not1 it cannot be established as a cause1 nor can a supposed law of such an agent be accepted as sufficient to the given inquiry1 unless it is adequate to account for the effects which it is called upon to explain1 at least so far as it pretends to explain them4 ,the general truth of this is sufficiently obvious1 since to explain the facts is the purpose of an hypothesis2 and we have seen that ,newton gave up his hypothesis that the moon was a falling body1 as long as he was unable to show that the amount of its deflection from a tangent 7or fall7 in a given time1 was exactly what it should be1 if the ,moon was controlled by the same force as falling bodies on the ,earth4 ,it is important to observe the limitations to this canon4 ,in the first place1 it says that1 unless adequate to explain the facts in question1 an hypothesis cannot be 'established'2 but1 for all that1 such an hypothesis may be a very promising one1 not to be hastily rejected1 since it may take a very long time fully to verify an hypothesis4 ,some facts may not be obtainable that are necessary to show the connection of others3 as1 for example1 the hypothesis that all species of animals have arisen from earlier ones by some process of gradual change1 can be only imperfectly verified by collecting the fossil remains of extinct species1 because immense depths and expanses of fossiliferous strata have been destroyed4 ,or1 again1 the general state of culture may be such as to prevent men from tracing the consequences of an hypothesis2 for which reason1 apparently1 the doctrine that the ,sun is the centre of our planetary system remained a discredited hypothesis for #bjjj years4 ,this should instruct us not to regard an hypothesis as necessarily erroneous or illegitimate merely because we cannot yet see how it works out3 but neither can we in such a case regard it as established1 unless we take somebody's word for it4 ,secondly1 the canon says that an hypothesis is not established1 unless it accounts for the phenomena so far as it professes to4 ,but it implies a complete misunderstanding to assail a doctrine for not explaining what lies beyond its scope4 ,thus1 it is no objection to a theory of the origin of species1 that it does not explain the origin of life3 it does not profess to4 ,for the same reason1 it is no objection to the theory of ,natural ,selection1 that it does not account for the variations which selection presupposes4 ,but such objections might be perfectly fair against a general doctrine of ,evolution4 ,an interesting case in ,wallace's ,darwinism 7chap4 x47 will illustrate the importance of attending to the exact conditions of an hypothesis4 ,he says that in those groups of birds that need protection from enemies1 when the male is brightly coloured and the female sits exposed on the nest1 she is always less brilliant and generally of quite sober and protective hues2 and his hypothesis is1 that these sober hues have been acquired or preserved by ,natural ,selection1 because it is important to the family that the sitting bird should be inconspicuous4 ,now to this it might be objected that in some birds both sexes are brilliant or conspicuous2 but the answer is that the female of such species does not sit exposed on the nest2 for the nests are either domed over1 or made in a hole2 so that the sitting bird does not need protective colouring4 ,if it be objected1 again1 that some sober-coloured birds build domed nests1 it may be replied that the proposition ',all conspicuously coloured birds are concealed in the nest1' is not to be converted simply into ',all birds that sit concealed in the nest are conspicuously coloured4' ,in the cases alleged the domed nests are a protection against the weather1 and the sober colouring is a general protection to the bird1 which inhabits an open country4 ,it may be urged1 however1 that jays1 crows1 and magpies are conspicuous birds1 and yet build open nests3 but these are aggressive birds1 not needing protection from enemies4 ,finally1 there are cases1 it must be confessed1 in which the female is more brilliant than the male1 and which yet have open nests4 ,yes3 but then the male sits upon the eggs1 and the female is stronger and more pugnacious6 ,thus every objection is shown to imply some inattention to the conditions of the hypothesis2 and in each case it may be said1 exceptio probat regulam--the exception tests the rule4 7,of course1 the usual translation proves the rule1 in the restricted modern sense of prove1 is absurd47 ,that is to say1 it appears on examination3 7#a7 that the alleged exception is not really one1 and 7#b7 that it stands in such relation to the rule as to confirm it4 ,for to all the above objections it is replied that1 granting the phenomenon in question 7special protective colouring for the female7 to be absent1 the alleged cause 7need of protection7 is also absent2 so that the proof is1 by means of the objections1 extended1 from being one by the method of ,agreement1 into one by the ,double ,method4 ,thirdly1 an hypothesis originally intended to account for the whole of a phenomenon and failing to do so1 though it cannot be established in that sense1 may nevertheless contain an essential part of the explanation4 ,the ,neptunian ,hypothesis in ,geology1 was an attempt to explain the formation of the ,earth's outer crust1 as having been deposited from an universal ocean of mud4 ,in the progress of the science other causes1 seismic1 fluvial and atmospheric1 have been found necessary in order to complete the theory of the history of the ,earth's crust2 but it remains true that the stratified rocks1 and some that have lost their stratified character1 were originally deposited under water4 ,inadequacy1 therefore1 is not a reason for entirely rejecting an hypothesis or treating it as illegitimate4 7#c7 ,granting that the hypothetical cause is real and adequate1 the investigation is not complete4 ,agreement with the facts is a very persuasive circumstance1 the more so the more extensive the agreement1 especially if no exceptions are known4 ,still1 if this is all that can be said in favour of an hypothesis1 it amounts to proof at most by the method of ,agreement2 it does not exclude the possibility of vicarious causes2 and if the hypothesis proposes a new agent that cannot be directly observed1 an equally plausible hypothesis about another imagined agent may perhaps be invented4 ,according to ,whewell1 it is a strong mark of the truth of an hypothesis when it agrees with distinct inductions concerning different classes of facts1 and he calls this the ',consilience of ,inductions1' because they jump together in the unity of the hypothesis4 ,it is particularly convincing when this consilience takes place easily and naturally without necessitating the mending and tinkering of the hypothesis2 and he cites the ,theory of ,gravitation and the ,undulatory ,theory of ,light as the most conspicuous examples of such ever-victorious hypotheses4 ,thus1 gravitation explains the fall of bodies on the ,earth1 and the orbits of the planets and their satellites2 it applies to the tides1 the comets1 the double stars1 and gives consistency to the ,nebular ,hypothesis1 whence flow important geological inferences2 and all this without any need of amendment4 ,nevertheless1 ,mill1 with his rigorous sense of duty1 points out1 that an induction is merely a proposition concerning many facts1 and that a consilience of inductions is merely a multiplication of the facts explained2 and that1 therefore1 if the proof is merely ,agreement in each case1 there can be no more in the totality2 the possibility of vicarious causes is not precluded2 and the hypothesis may1 after all1 describe an accidental circumstance4 ,whewell also laid great stress upon prediction as a mark of a true hypothesis4 ,thus1 ,astronomers predict eclipses1 occultations1 transits1 long beforehand with the greatest precision2 and the prediction of the place of ,neptune by sheer force of deduction is one of the most astonishing things in the history of science4 ,yet ,mill persisted in showing that a predicted fact is only another fact1 and that it is really not very extraordinary that an hypothesis1 that happens to agree with many known facts1 should also agree with some still undiscovered4 ,certainly1 there seems to be some illusion in the common belief in the probative force of prediction4 ,prediction surprises us1 puts us off our guard1 and renders persuasion easy2 in this it resembles the force of an epigram in rhetoric4 ,but cases can be produced in which erroneous hypotheses have led to prediction2 and ,whewell himself produces them4 ,thus1 he says that the ,ptolemaic theory was confirmed by its predicting eclipses and other celestial phenomena1 and by leading to the construction of ,tables in which the places of the heavenly bodies were given at every moment of time4 ,similarly1 both ,newton's theory of light and the chemical doctrine of phlogiston led to predictions which came true4 ,what sound method demands in the proof of an hypothesis1 then1 is not merely that it be shown to agree with the facts1 but that every other hypothesis be excluded4 ,this1 to be sure1 may be beyond our power2 there may in some cases be no such negative proof except the exhaustion of human ingenuity in the course of time4 ,the present theory of colour has in its favour the failure of ,newton's corpuscular hypothesis and of ,goethe's anti-mathematical hypothesis2 but the field of conjecture remains open4 ,on the other hand1 ,newton's proof that the solar system is controlled by a central force1 was supported by the demonstration that a force having any other direction could not have results agreeing with ,kepler's second law of the planetary motions1 namely1 that1 as a planet moves in its orbit1 the areas described by a line drawn from the sun to the planet are proportional to the times occupied in the planet's motion4 ,when a planet is nearest to the sun1 the area described by such a line is least for any given distance traversed by the planet2 and then the planet moves fastest3 when the planet is furthest from the sun1 the area described by such a line is greatest for an equal distance traversed2 and then the planet moves slowest4 ,this law may be deduced from the hypothesis of a central force1 but not from any other2 the proof1 therefore1 as ,mill says1 satisfies the method of ,difference4 ,apparently1 to such completeness of demonstration certain conditions are necessary3 the possibilities must lie between alternatives1 such as ,a or not-,a1 or amongst some definite list of cases that may be exhausted1 such as equal1 greater or less4 ,he whose hypothesis cannot be brought to such a definite issue1 must try to refute whatever other hypotheses are offered1 and naturally he will attack first the strongest rivals4 ,with this object in view he looks about for a crucial instance1 that is1 an observation or experiment that stands like a cross 7sign-post7 at the parting of the ways to guide us into the right way1 or1 in plain words1 an instance that can be explained by one hypothesis but not by another4 ,thus the phases of ,venus1 similar to those of the ,moon1 but concurring with great changes of apparent size1 presented1 when discovered by ,galileo1 a crucial instance in favour of the ,copernican hypothesis1 as against the ,ptolemaic1 so far at least as to prove that ,venus revolved around the ,sun inside the orbit of the ,earth4 ,foucault's experiment determining the velocity of ,light 7cited in the last chapter7 was at first intended as an experimentum crucis to decide between the corpuscular and undulatory theories2 and answered this purpose1 by showing that the velocity of a beam passed through water was less than it should be by the former1 but in agreement with the latter doctrine 7,deschanel3 #hac74 ,perhaps experiments of this decisive character are commonest in ,chemistry3 chemical tests1 says ,herschel1 are almost universally crucial experiments4 ,the following is abridged from ,playfair 7,encycl4 ,met41 ,diss4 ,,iii473 ,the ,chemists of the eighteenth century observed that metals were rendered heavier by calcination2 and there were two ways of accounting for this3 either something had been added in the process1 though what1 they could not imagine2 or1 something had been driven off that was in its nature light1 namely1 phlogiston4 ,to decide between these hypotheses1 ,lavoisier hermetically sealed some tin in a glass retort1 and weighed the whole4 ,he then heated it2 and1 when the tin was calcined1 weighed the whole again1 and found it the same as before4 ,no substance1 therefore1 either light or heavy1 had escaped4 ,further1 when the retort was cooled and opened1 the air rushed in1 showing that some of the air formerly within had disappeared or lost its elasticity4 ,on weighing the whole again1 its weight was now found to have increased by ten grains2 so that ten grains of air had entered when it was opened4 ,the calcined tin was then weighed separately1 and proved to be exactly ten grains heavier than when it was placed in the retort2 showing that the ten grains of air that had disappeared had combined with the metal during calcination4 ,this experiment1 then1 decided against phlogiston1 and led to an analysis of common air confirming ,priestley's discovery of oxygen4 7#d7 ,an hypothesis must agree with the rest of the laws of ,nature2 and1 if not itself of the highest generality1 must be derivable from primary laws 7chap4 xix4 #a74 ,gravitation and the diffusion of heat1 light and sound from a centre1 all follow the 'law of the inverse square1' and agree with the relation of the radius of a sphere to its surface4 ,any one who should think that he had discovered a new central force would naturally begin to investigate it on the hypothesis that it conformed to the same law as gravitation or light4 ,a ,chemist again1 who should believe himself to have discovered a new element1 would expect it to fill one of the vacant places in the ,periodic ,table4 ,conformity1 in such cases1 is strong confirmation1 and disagreement is an occasion of misgivings4 ,a narrower hypothesis1 as 'that the toad's ugliness is protective'1 would be supported by the general theory of protective colouring and figure1 and by the still more general theory of ,natural ,selection1 if facts could be adduced to show that the toad's appearance does really deter its enemies4 ,such an hypothesis resembles an ,empirical ,law in its need of derivation 7chap4 xix4 #a1 #b74 ,if underivable from1 or irreconcilable with1 known laws1 it is a mere conjecture or prejudice4 ,the absolute leviation of phlogiston1 in contrast with the gravitation of all other forms of matter1 discredited that supposed agent4 ,that ,macpherson should have found the ,ossianic poems extant in the ,gaelic memory1 was contrary to the nature of oral tradition2 except where tradition is organised1 as it was for ages among the ,brahmins4 ,the suggestion that xanthochroid ,aryans were bleached by exposure during the glacial period1 does not agree with ,wallace's doctrine concerning the coloration of ,arctic animals4 ,that our forefathers being predatory1 like bears1 white variations amongst them were then selected by the advantage of concealment1 is a more plausible hypothesis4 ,although1 then1 the consilience of ,inductions or ,hypotheses is not a sufficient proof of their truth1 it is still a condition of it2 nonconsilience is a suspicious circumstance1 and resilience 7so to speak71 or mutual repugnance1 is fatal to one or all4 #d4 ,we have now seen that a scientific hypothesis1 to deserve the name1 must be verifiable and therefore definite2 and that to establish itself as a true theory1 it must present some symptom of reality1 and be adequate and exclusive and in harmony with the system of experience4 ,thus guarded1 hypotheses seem harmless enough2 but some people have a strong prejudice against them1 as against a tribe of savages without government1 or laws1 or any decent regard for vested interests4 ,it is well known1 too1 that ,bacon and ,newton disparaged them4 ,but ,bacon1 in his examples of an investigation according to his own method1 is obliged1 after a preliminary classification of facts1 to resort to an hypothesis1 calling it permissio intellectus1 interpretatio inchoata or vindemiatio prima4 ,and ,newton when he said hypotheses non fingo1 meant that he did not deal in fictions1 or lay stress upon supposed forces 7such as 'attraction'71 that add nothing to the law of the facts4 ,hypotheses are essential aids to discovery3 speaking generally1 deliberate investigation depends wholly upon the use of them4 ,it is true that we may sometimes observe a train of events that chances to pass before us1 when either we are idle or engaged with some other inquiry1 and so obtain a new glimpse of the course of nature2 or we may try experiments haphazard1 and watch the results4 ,but1 even in these cases1 before our new notions can be considered knowledge1 they must be definitely framed in hypotheses and reobserved or experimented upon1 with whatever calculations or precautions may be necessary to ensure accuracy or isolation4 ,as a rule1 when inquiring deliberately into the cause of an event1 whether in nature or in history1 we first reflect upon the circumstances of the case and compare it with similar ones previously investigated1 and so are guided by a preconception more or less definite of 'what to look for1' what the cause is likely to be1 that is1 by an hypothesis4 ,then1 if our preconception is justified1 or something which we observe leads to a new hypothesis1 either we look for other instances to satisfy the canons of ,agreement2 or 7if the matter admits of experiment7 we endeavour1 under known conditions according to the canon of ,difference1 to reproduce the event by means of that which our hypothesis assigns as the cause2 or we draw remote inferences from our hypothesis1 and try to test these by the ,inductive ,canons4 ,if we argue from an hypothesis and express ourselves formally1 it will usually appear as the major premise2 but this is not always the case4 ,in extending ascertained laws to fresh cases1 the minor premise may be an hypothesis1 as in testing the chemical constitution of any doubtful substance1 such as a piece of ore4 ,some solution or preparation1 ,a1 is generally made which 7it is known7 will1 on the introduction of a certain agent1 ,b1 give a reaction1 ,c1 if the preparation contains a given substance1 ,x4 ,the major premise is the law of reaction-- ,whenever ,a is ,x1 if treated with ,b it is ,c4 ,the minor premise is an hypothesis that the preparation contains ,x4 ,an experiment then treats ,a with ,b4 ,if ,c result1 a probability is raised in favour of the hypothesis that ,a is ,x2 or a certainty1 if we know that ,c results on that condition only4 ,so important are hypotheses to science1 that ,whewell insists that they have often been extremely valuable even though erroneous4 ,of the ,ptolemaic system he says1 ,we can hardly imagine that ,astronomy could1 in its outset1 have made so great a progress under any other form4 ,it served to connect men's thoughts on the subject and to sustain their interest in working it out2 by successive corrections to save appearances1 it attained at last to a descriptive sort of truth1 which was of great practical utility2 it also occasioned the invention of technical terms1 and1 in general digested the whole body of observations and prepared them for assimilation by a better hypothesis in the fulness of time4 ,whewell even defends the maxim that ,nature abhors a vacuum1 as having formerly served to connect many facts that differ widely in their first aspect4 ,and in reality is it not true1 he asks1 that nature does abhor a vacuum1 and does all she can to avoid it8 ,let no forlorn cause despair of a champion6 ,yet no one has accused ,whewell of ,quixotry2 and the sense of his position is that the human mind is a rather feeble affair1 that can hardly begin to think except with blunders4 ,the progress of science may be plausibly attributed to a process of ,natural ,selection2 hypotheses are produced in abundance and variety1 and those unfit to bear verification are destroyed1 until only the fittest survive4 ,wallace1 a practical naturalist1 if there ever was one1 as well as an eminent theorist1 takes the same view as ,whewell of such inadequate conjectures4 ,of ',lemuria1' an hypothetical continent in the ,indian ,ocean1 once supposed to be traceable in the islands of ,madagascar1 ,seychelles1 and ,mauritius1 its surviving fragments1 and named from the ,lemurs1 its characteristic denizens1 he says 7,island ,life1 chap4 xix47 that it was essentially a provisional hypothesis1 very useful in calling attention to a remarkable series of problems in geographical distribution of plants and animals1 but not affording the true solution of those problems4 ,we see1 then1 that 'provisional hypotheses1' or working hypotheses1' though erroneous1 may be very useful or 7as ,whewell says7 necessary4 ,hence1 to be prolific of hypotheses is the first attribute of scientific genius2 the first1 because without it no progress whatever can be made4 ,and some men seem to have a marked felicity1 a sort of instinctive judgment even in their guesses1 as if their heads were made according to ,nature4 ,but others among the greatest1 like ,kepler1 guess often and are often wrong before they hit upon the truth1 and themselves1 like ,nature1 destroy many vain shoots and seedlings of science for one that they find fit to live4 ,if this is how the mind works in scientific inquiry 7as it certainly is1 with most men1 in poetry1 in fine art1 and in the scheming of business71 it is useless to complain4 ,we should rather recognise a place for fools' hypotheses1 as ,darwin did for fools' experiments4 ,but to complete the scientific character1 there must be great patience1 accuracy1 and impartiality in examining and testing these conjectures1 as well as great ingenuity in devising experiments to that end4 ,the want of these qualities leads to crude work and public failure and brings hypotheses into derision4 ,not partially and hastily to believe in one's own guesses1 nor petulantly or timidly to reject them1 but to consider the matter1 to suspend judgment1 is the moral lesson of science3 difficult1 distasteful1 and rarely mastered4 #e4 ,the word 'hypothesis' is often used also for the scientific device of treating an ,abstraction as1 for the purposes of argument1 equivalent to the concrete facts4 ,thus1 in ,geometry1 a line is treated as having no breadth2 in ,mechanics1 a bar may be supposed absolutely rigid1 or a machine to work without friction2 in ,economics1 man is sometimes regarded as actuated solely by love of gain and dislike of exertion4 ,the results reached by such reasoning may be made applicable to the concrete facts1 if allowance be made for the omitted circumstances or properties1 in the several cases of lines1 bars1 and men2 but otherwise all conclusions from abstract terms are limited by their definitions4 ,abstract reasoning1 then 7that is1 reasoning limited by definitions71 is often said to imply 'the hypothesis' that things exist as their names are defined1 having no properties but those enumerated in their definitions4 ,this seems1 however1 a needless and confusing extension of the term2 for an hypothesis proposes an agent1 collocation1 or law hitherto unknown2 whereas abstract reasoning proposes to exclude from consideration a good deal that is well known4 ,there seems no reason why the latter device should not be plainly called an ,abstraction4 ,such abstractions are necessary to science2 for no object is comprehensible by us in all its properties at once4 ,but if we forget the limitations of our abstract data1 we are liable to make strange blunders by mistaking the character of the results3 treating the results as simply true of actual things1 instead of as true of actual things only so far as they are represented by the abstractions4 ,in addressing abstract reasoning1 therefore1 to those who are unfamiliar with scientific methods1 pains should be taken to make it clear what the abstractions are1 what are the consequent limitations upon the argument and its conclusions1 and what corrections and allowances are necessary in order to turn the conclusions into an adequate account of the concrete facts4 ,the greater the number1 variety1 and subtlety of the properties possessed by any object 7such as human nature71 the greater are the qualifications required in the conclusions of abstract reasoning1 before they can hold true of such an object in practical affairs4 ,closely allied to this method of ,abstraction is the ,mathematical ,method of ,limits4 ,in his ,history of ,scientific ,ideas 7,b4 ,,ii4 c4 #ab71 ,whewell says3 ,the ,idea of a ,limit supplies a new mode of establishing mathematical truths4 ,thus with regard to the length of any portion of a curve1 a problem which we have just mentioned2 a curve is not made up of straight lines1 and therefore we cannot by means of any of the doctrines of elementary geometry measure the length of any curve4 ,but we may make up a figure nearly resembling any curve by putting together many short straight lines1 just as a polygonal building of very many sides may nearly resemble a circular room4 ,and in order to approach nearer and nearer to a curve1 we may make the sides more and more small1 more and more numerous4 ,we may then possibly find some mode of measurement1 some relation of these small lines to other lines1 which is not disturbed by the multiplication of the sides1 however far it be carried4 ,and thus we may do what is equivalent to measuring the curve itself2 for by multiplying the sides we may approach more and more closely to the curve till no appreciable difference remains4 ,the curve line is the ,limit of the polygon2 and in this process we proceed on the ,axiom that ',what is true up to the ,limit is true at the ,limit4' ,what ,whewell calls the ,axiom here1 others might call an ,hypothesis2 but perhaps it is properly a ,postulate4 ,and it is just the obverse of the ,postulate implied in the ,method of ,abstractions1 namely1 that ',what is true of the ,abstraction is true of concrete cases the more nearly they approach the ,abstraction4' ,what is true of the ',economic ,man' is truer of a broker than of a farmer1 of a farmer than of a labourer1 of a labourer than of the artist of romance4 ,hence the ,abstraction may be called a ,limit or limiting case1 in the sense that it stands to concrete individuals1 as a curve does to the figures made up by putting together many short straight lines4 ,correspondingly1 the ,proper ,name may be called the ,limit of the class-name2 since its attributes are infinite1 whereas any name whose attributes are less than infinite stands for a possible class4 ,in short1 for logical purposes1 a ,limit may be defined as any extreme case to which actual examples may approach without ever reaching it4 ,and in this sense ',method of ,limits' might be used as a term including the ,method of ,abstractions2 though it would be better to speak of them generically as ',methods of ,approximation4' ,we may also notice the ,assumptions 7as they may be called7 that are sometimes employed to facilitate an investigation1 because some definite ground must be taken and nothing better can be thought of3 as in estimating national wealth1 that furniture is half the value of the houses4 ,it is easy to conceive of an objector urging that such devices as the above are merely ways of avoiding the actual problems1 and that they display more cunning than skill4 ,but science1 like good sense1 puts up with the best that can be had2 and1 like prudence1 does not reject the half-loaf4 ,the position1 that a conceivable case that can be dealt with may1 under certain conditions1 be substituted for one that is unworkable1 is a touchstone of intelligence4 ,to stand out for ideals that are known to be impossible1 is only an excuse for doing nothing at all4 ,in another sense1 again1 the whole of science is sometimes said to be hypothetical1 because it takes for granted the ,uniformity of ,nature2 for this1 in its various aspects1 can only be directly ascertained by us as far as our experience extends2 whereas the whole value of the principle of ,uniformity consists in its furnishing a formula for the extension of our other beliefs beyond our actual experience4 ,transcendentalists1 indeed1 call it a form of ,reason1 just because it is presupposed in all knowledge2 and they and the ,empiricists agree that to adduce material evidence for it1 in its full extent1 is impossible4 ,if1 then1 material evidence is demanded by any one1 he cannot regard the conclusions of ,mathematics and ,physical ,science as depending on what is itself unproved2 he must1 with ,mill1 regard these conclusions as drawn not from but according to the axioms of ,equality and ,causation4 ,that is to say1 if the axioms are true1 the conclusions are2 the material evidence for both the axioms and the conclusions being the same1 namely1 uncontradicted experience4 ,now when we say1 ',if ,nature is uniform1 science is true1' the hypothetical character of science appears in the form of the statement4 ,nevertheless1 it seems undesirable to call our confidence in ,nature's uniformity an 'hypothesis'3 it is incongruous to use the same term for our tentative conjectures and for our most indispensable beliefs4 ',the ,universal ,postulate' is a better term for the principle which1 in some form or other1 every generalisation takes for granted4 ,we are now sometimes told that1 instead of the determinism and continuity of phenomena hitherto assumed by science1 we should recognise indeterminism and discontinuity4 ,but it will be time enough to fall in with this doctrine when its advocates produce a new ,logic of ,induction1 and explain the use of the method of ,difference and of control experiments according to the new postulates4 ,,chapter ,,xix ,,laws ,,classified2 ,,explanation2 ,,co-,,existence2 ,,analogy #a4 ,laws are classified1 according to their degrees of generality1 as higher and lower1 though the grades may not be decisively distinguishable4 ,first1 there are ,axioms or ,principles1 that is real1 universal1 self-evident propositions4 ,they are--7#a7 real propositions2 not1 like ',the whole is greater than any of its parts1' merely definitions1 or implied in definitions4 7#b7 ,they are regarded as universally true of phenomena1 as far as the form of their expression extends2 that is1 for example1 ,axioms concerning quantity are true of everything that is considered in its quantitative aspect1 though not 7of course7 in its qualitative aspect4 7#c7 ,they are self-evident2 that is1 each rests upon its own evidence 7whatever that may be72 they cannot be derived from one another1 nor from any more general law4 ,some1 indeed1 are more general than others3 the ,logical ,principle of ,contradiction1 'if ,a is ,b1 it is not not-,b'1 is true of qualities as well as of quantities2 whereas the ,axioms of ,mathematics apply only to quantities4 ,the ,mathematical ,axioms1 again1 apply to time1 space1 mental phenomena1 and matter and energy2 whereas the ,law of ,causation is only true of concrete events in the redistribution of matter and energy3 such1 at least1 is the strict limit of ,causation1 if we identify it with the ,conservation of ,energy2 although our imperfect knowledge of life and mind often drives us to speak of feelings1 ideas1 volitions1 as causes4 ,still1 the ,law of ,causation cannot be derived from the ,mathematical ,axioms1 nor these from the ,logical4 ,the kind of evidence upon which ,axioms rest1 or whether any evidence can be given for them1 is 7as before observed7 a question for ,metaphysics1 not for ,logic4 ,axioms are the upward limit of ,logic1 which1 like all the special sciences1 necessarily takes them for granted1 as the starting point of all deduction and the goal of all generalisation4 ,next to ,axioms1 come ,primary ,laws of ,nature3 these are of less generality than the ,axioms1 and are subject to the conditions of methodical proof2 being universally true only of certain forces or properties of matter1 or of nature under certain conditions2 so that proof of them by logical or mathematical reasoning is expected1 because they depend upon the ,axioms for their formal evidence4 ,such are the law of gravitation1 in ,astronomy2 the law of definite proportions1 in ,chemistry2 the law of heredity1 in ,biology2 and in ,psychology1 the law of relativity4 ,then1 there are ,secondary ,laws1 of still less generality1 resulting from a combination of conditions or forces in given circumstances1 and therefore conceivably derivable from the laws of those conditions or forces1 if we can discover them and compute their united effects4 ,accordingly1 ,secondary ,laws are either--7#a7 ,derivative1 having been analysed into1 and deduced from1 ,primary ,laws2 or 7#b7 ,empirical1 those that have not yet been deduced 7though from their comparatively special and complex character1 it seems probable they may be1 given sufficient time and ingenuity71 and that meanwhile rest upon some unsatisfactory sort of induction by ,agreement or ,simple ,enumeration4 ,whether laws proved only by the canon of ,difference are to be considered ,empirical1 is perhaps a question3 their proof derives them from the principle of ,causation2 but1 being of narrow scope1 some more special account of them seems requisite in relation to the ,primary ,laws before we can call them ,derivative in the technical sense4 ,many ,secondary ,laws1 again1 are partially or imperfectly ,derivative2 we can give general reasons for them1 without being able to determine theoretically the precise relations of the phenomena they describe4 ,meteorologists can explain the general conditions of all sorts of weather1 but have made little progress toward predicting the actual course of it 7at least1 for our island73 ,geologists know the general causes of mountain ranges1 but not why they rise just where we find them3 ,economists explain the general course of a commercial crisis1 but not why the great crises recurred at intervals of about ten years4 ,derivative ,laws make up the body of the exact sciences1 having been assimilated and organised2 whilst ,empirical ,laws are the undigested materials of science4 ,the theorems of ,euclid are good examples of derivative laws in ,mathematics2 in ,astronomy1 ,kepler's laws and the laws of the tides2 in ,physics1 the laws of shadows1 of perspective1 of harmony2 in ,biology1 the law of protective coloration2 in ,economics1 the laws of prices1 wages1 interest1 and rent4 ,empirical ,laws are such as ,bode's law of the planetary distances2 the laws of the expansion of different bodies by heat1 and formul expressing the electrical conductivity of each substance as a function of the temperature4 ,strictly speaking1 ,i suppose1 all the laws of chemical combination are empirical3 the law of definite proportions is verifiable in all cases that have been examined1 except for variations that may be ascribed to errors of experiment4 ,much the same is true in ,biology2 most of the secondary laws are empirical1 except so far as structures or functions may be regarded as specialised cases in ,physics or ,chemistry and deducible from these sciences4 ,the theory of ,natural ,selection1 however1 has been the means of rendering many laws1 that were once wholly empirical1 at least partially derivative2 namely1 the laws of the geographical distribution of plants and animals1 and of their adaptation in organisation1 form and colour1 habits and instincts1 to their various conditions of life4 ,the laws that remain empirical in ,biology are of all degrees of generality from that of the tendency to variation in size and in every other character shown by every species 7though as to the reason of this there are promising hypotheses71 down to such curious cases as that the colour of roses and carnations never varies into blue1 that scarlet flowers are never sweet-scented1 that bullfinches fed on hemp-seed turn black1 that the young of white1 yellow and dun pigeons are born almost naked 7whilst others have plenty of down72 and so on4 ,the derivation of empirical laws is the greater part of the explanation of ,nature 7 #e1 #f74 ,a ',fact1' in the common use of the word1 is a particular observation3 it is the material of science in its rawest state4 ,as perceived by a mind1 it is1 of course1 never absolutely particular3 for we cannot perceive anything without classing it1 more or less definitely1 with things already known to us2 nor describe it without using connotative terms which imply a classification of the things denoted4 ,still1 we may consider an observation as particular1 in comparison with a law that includes it with numerous others in one general proposition4 ,to turn an observation into an experiment1 or 7where experiment is impracticable7 to repeat it with all possible precautions and exactness1 and to describe it as to the duration1 quantity1 quality and order of occurrence of its phenomena1 is the first stage of scientific manufacture4 ,then comes the formulation of an empirical law2 and lastly1 if possible1 deduction or derivation1 either from higher laws previously ascertained1 or from an hypothesis4 ,however1 as a word is used in various senses1 we often speak of laws as 'facts'3 we say the law of gravitation is a fact1 meaning that it is real1 or verifiable by observations or experiments4 #b4 ,secondary ,laws may also be classified according to their constancy into--7#a7 the ,invariable 7as far as experience reaches71 and 7#b7 ,approximate ,generalisations in the form--,most ,x's are ,y4 ,of the invariable we have given examples above4 ,the following are approximate generalisations3 ,most comets go round the ,sun from ,east to ,west2 ,most metals are solid at ordinary temperatures2 ,most marsupials are ,australasian2 ,most arctic animals are white in winter2 ,most cases of plague are fatal2 ,most men think first of their own interests4 ,some of these laws are empirical1 as that ',most metals are solid at ordinary temperatures'3 at present no reason can be given for this2 nor do we know why most cases of plague are fatal4 ,others1 however1 are at least partially derivative1 as that ',most arctic animals are white'2 for this seems to be due to the advantage of concealment in the snow2 whether1 as with the bear1 the better to surprise its prey1 or1 with the hare1 to escape the notice of its enemies4 ,but the scientific treatment of such a proposition requires that we should also explain the exceptions3 if ',most are1' this implies that ',some are not'2 why not1 then8 ,now1 if we can give reasons for all the exceptions1 the approximate generalisation may be converted into an universal one1 thus3 ',all arctic animals are white1 unless 7like the raven7 they need no concealment either to prey or to escape2 or unless mutual recognition is more important to them than concealment 7as with the musk-sheep7'4 ,the same end of universal statement may be gained by including the conditions on which the phenomenon depends1 thus3 ',all arctic animals to whom concealment is of the utmost utility are white4' ,when statistics are obtainable1 it is proper to convert an approximate generalisation into a proportional statement of the fact1 thus3 instead of ',most attacks of plague are fatal'1 we might find that in a certain country #gj per cent4 were so4 ,then1 if we found that in another country the percentage of deaths was #fj1 in another #dj1 we might discover1 in the different conditions of these countries1 a clue to the high rate of mortality from this disease4 ,even if the proportion of cases in which two facts are connected does not amount to ',most1' yet1 if any definite percentage is obtainable1 the proposition has a higher scientific value than a vague ',some'3 as if we know that #b per cent4 of the deaths in ,england are due to suicide1 this may be compared with the rates of suicide in other countries2 from which perhaps inferences may be drawn as to the causes of suicide4 ,in one department of life1 namely1 ,politics1 there is a special advantage in true approximate generalisations amounting to ',most cases4' ,the citizens of any ,state are so various in character1 enlightenment1 and conditions of life1 that we can expect to find few propositions universally true of them3 so that propositions true of the majority must be trusted as the bases of legislation4 ,if most men are deterred from crime by fear of punishment2 if most men will idle if they can obtain support without industry2 if most jurymen will refuse to convict of a crime for which the prescribed penalties seem to them too severe2 these are most useful truths1 though there should be numerous exceptions to them all4 #c4 ,secondary ,laws can only be trusted in ',adjacent ,cases'2 that is1 where the circumstances are similar to those in which the laws are known to be true4 ,a ,derivative ,law will be true wherever the forces concerned exist in the combinations upon which the law depends1 if there are no counteracting conditions4 ,that water can be pumped to about #cc feet at the sea-level1 is a derivative law on this planet3 is it true in ,mars8 ,that depends on whether there are in ,mars bodies of a liquid similar to our water2 whether there is an atmosphere there1 and how great its pressure is2 which will vary with its height and density4 ,if there is no atmosphere there can be no pumping2 or if there is an atmosphere of less pressure than ours1 water such as ours can only be pumped to a less height than #cc feet4 ,again1 we know that there are arctic regions in ,mars2 if there are also arctic animals1 are they white8 ,that may depend upon whether there are any beasts of prey4 ,if not1 concealment seems to be of no use4 ,an ,empirical ,law1 being one whose conditions we do not know1 the extent of its prevalence is still less ascertainable4 ,where it has not been actually observed to be true1 we cannot trust it unless the circumstances1 on the whole1 resemble so closely those amongst which it has been observed1 that the unknown causes1 whatever they may be1 are likely to prevail there4 ,and1 even then1 we cannot have much confidence in it2 for there may be unknown circumstances which entirely frustrate the effect4 ,the first naturalist who travelled 7say7 from ,singapore eastward by ,sumatra and ,java1 or ,borneo1 and found the mammalia there similar to those of ,asia1 may naturally have expected the same thing in ,celebes and ,papua2 but1 if so1 he was entirely disappointed2 for in ,papua the mammalia are marsupials like those of ,australia4 ,thus his empirical law1 ',the mammalia of the ,eastern ,archipelago are ,asiatic1' would have failed for no apparent reason4 ,according to ,mr4 ,wallace1 there is a reason for it1 though such as could only be discovered by extensive researches2 namely1 that the sea is deep between ,borneo and ,celebes1 so that they must have been separated for many ages2 whereas it is shallow from ,borneo westward to ,asia1 and also southward from ,celebes to ,australia2 so that these regions1 respectively1 may have been recently united3 and the true law is that similar mammalia belong to those tracts which at comparatively recent dates have formed parts of the same continents 7unless they are the remains of a former much wider distribution74 ,a considerable lapse of time may make an empirical law no longer trustworthy2 for the forces from whose combination it resulted may have ceased to operate1 or to operate in the same combination2 and since we do not know what those forces were1 even the knowledge that great changes have taken place in the meantime cannot enable us1 after an interval1 to judge whether or not the law still holds true4 ,new stars shine in the sky and go out2 species of plants and animals become extinct2 diseases die out and fresh ones afflict mankind3 all these things doubtless have their causes1 but if we do not know what they are1 we have no measure of the effects1 and cannot tell when or where they will happen4 ,laws of ,concomitant ,variations may hold good only within certain limits4 ,that bodies contract as the temperature falls1 is not true of water below #ci ,f4 ,in ,psychology1 ,weber's ,law is only true within the median range of sensation-intensities1 not for very faint1 nor for very strong1 stimuli4 ,in such cases the failure of the laws may depend upon something imperfectly understood in the collocation3 as to water1 on its molecular constitution2 as to sensation1 upon the structure of the nervous system4 #d4 ,secondary ,laws1 again1 are either of ,succession or of ,co-existence4 ,those of ,succession are either--7#a7 of direct causation1 as that ',water quenches fire1' or 7more strictly7 that ',evaporation reduces temperature'2 or 7#b7 of the effect of a remote cause1 as ',bad harvests tend to raise the price of bread'2 or 7#c7 of the joint effects of the same cause1 as that ',night follows day' 7from the revolution of the earth71 or the course of the seasons 7from the inclination of the earth's axis74 ,laws of ,co-existence are of several classes4 7#a7 ,one has the generality of a primary law1 though it is proved only by ,agreement1 namely1 ',all gravitating bodies are inert'4 ,others1 though less general than this1 are of very extensive range1 as that ',all gases that are not decomposed by rise of temperature have the same rate of expansion'2 and1 in ,botany that ',all monocotyledonous plants are endogenous'4 ,these laws of ,co-existence are concerned with fundamental properties of bodies4 7#b7 ,next come laws of the ,co-existence of those properties which are comprised in the definitions of ,natural ,kinds4 ,mill distinguished between 77 classes of things that agree among themselves and differ from others only in one or a few attributes 7such as 'red things1' 'musical notes'1 'carnivorous animals'1 'soldiers'71 and 77 classes of things that agree among themselves and differ from others in a multitude of characters3 and the latter he calls ,natural ,kinds4 ,these comprise the chemical elements and their pure compounds 7such as water1 alcohol1 rock-salt71 and the species of plants and animals4 ,clearly1 each of these is constituted by the co-existence or co-inherence of a multitude of properties1 some of which are selected as the basis of their definitions4 ,thus1 ,gold is a metal of high specific gravity1 atomic weight #aig4b1 high melting point1 low chemical affinities1 great ductility1 yellow colour1 etc43 a ,horse has 'a vertebral column1 mamm1 a placental embryo1 four legs1 a single well-developed toe in each foot provided with a hoof1 a bushy tail1 and callosities on the inner sides of both the fore and the hind legs' 7,huxley74 ,since ,darwinism has obtained general acceptance1 some ,logicians have doubted the propriety of calling the organic species ',kinds1' on the ground that they are not1 as to definiteness and permanence1 on a par with the chemical elements or such compounds as water and rock-salt2 that they vary extensively1 and that it is only by the loss of former generations of animals that we are able to distinguish species at all4 ,but to this it may be replied that species are often approximately constant for immense periods of time1 and may be called permanent in comparison with human generations2 and that1 although the leading principles of ,logic are perhaps eternal truths1 yet upon a detail such as this1 the science may condescend to recognise a distinction if it is good for 7say7 only #ajj1jjj years4 ,that if former generations of plants and animals were not lost1 all distinctions of species would disappear1 may be true2 but they are lost--for the most part beyond hope of recovery2 and accordingly the distinction of species is still recognised2 although there are cases1 chiefly at the lower stages of organisation1 in which so many varieties occur as to make adjacent species almost or quite indistinguishable4 ,so far as species are recognised1 then1 they present a complex co-inherence of qualities1 which is1 in one aspect1 a logical problem2 and1 in another1 a logical datum2 and1 coming more naturally under the head of ,natural ,kinds than any other1 they must be mentioned in this place4 7#c7 ,there are1 again1 certain coincidences of qualities not essential to any kind1 and sometimes prevailing amongst many different kinds3 such as ',insects of nauseous taste have vivid 7warning7 colours'2 ',white tom-cats with blue eyes are deaf'2 ',white spots and patches1 when they appear in domestic animals1 are most frequent on the left side4' 7#d7 ,finally1 there may be constancy of relative position1 as of sides and angles in ,geometry2 and also among concrete things 7at least for long periods of time71 as of the planetary orbits1 the apparent positions of fixed stars in the sky1 the distribution of land and water on the globe1 opposite seasons in opposite hemispheres4 ,all these cases of ,co-existence 7except the geometrical7 present the problem of deriving them from ,causation2 for there is no general ,law of ,co-existence from which they can be derived2 and1 indeed1 if we conceive of the external world as a perpetual redistribution of matter and energy1 it follows that the whole state of ,nature at any instant1 and therefore every co-existence included in it1 is due to causation issuing from some earlier distribution of matter and energy4 ,hence1 indeed1 it is not likely that the problems of co-existence as a whole will ever be solved1 since the original distribution of matter is1 of course1 unknown4 ,still1 starting with any given state of ,nature1 we may hope to explain some of the co-existences in any subsequent state4 ,we do not1 indeed1 know why heavy bodies are always inert1 nor why the chemical elements are what they are2 but it is known that the properties of the elements are functions of their atomic weight1 which 7though1 at present1 only an empirical law7 may be a clue to some deeper explanation4 ,as to plants and animals1 we know the conditions of their generation1 and can trace a connection between most of their characteristics and the conditions of their life3 as that the teeth and stomach of animals vary with their food1 and that their colour generally varies with their habitat4 ,geometrical ,co-existence1 when it is not a matter of definition 7as 'a square is a rectangle with four equal sides'71 is deduced from the definitions and axioms3 as when it is shown that in triangles the greater side is opposite the greater angle4 ,the deductions of theorems or secondary laws1 in ,geometry is a type of what is desirable in the ,physical ,sciences3 the demonstration1 namely1 that all the connections of phenomena1 whether successive or co-existent1 are consequences of the redistribution of matter and energy according to the principle of ,causation4 ,coincidences of ,co-existence 7,group 7#c77 may sometimes be deduced and sometimes not4 ,that 'nauseous insects have vivid coloration' comes under the general law of 'protective coloration'2 as they are easily recognised and therefore avoided by insectivorous birds and other animals4 ,but why white tom-cats with blue-eyes should be deaf1 is 7,i believe7 unknown4 ,when co-existences cannot be derived from causation1 they can only be proved by collecting examples and trusting vaguely to the ,uniformity of ,nature4 ,if no exceptions are found1 we have an empirical law of considerable probability within the range of our exploration4 ,if exceptions occur1 we have at most an approximate generalisation1 as that ',most metals are whitish1' or ',most domestic cats are tabbies' 7but this probably is the ancestral colouring74 ,we may then resort to statistics for greater definiteness1 and find that in ,hampshire 7say7 #ij per cent4 of the domestic cats are tabby4 #e4 ,scientific ,explanation consists in discovering1 deducing1 and assimilating the laws of phenomena2 it is the analysis of that ,heracleitan 'flux' which so many philosophers have regarded as intractable to human inquiry4 ,in the ordinary use of the word1 'explanation' means the satisfying a man's understanding2 and what may serve this purpose depends partly upon the natural soundness of his understanding1 and partly on his education2 but it is always at last an appeal to the primary functions of cognition1 discrimination and assimilation4 ,generally1 what we are accustomed to seems to need no explanation1 unless our curiosity is particularly directed to it4 ,that boys climb trees and throw stones1 and that men go fox-hunting1 may easily pass for matters of course4 ,if any one is so exacting as to ask the reason1 there is a ready answer in the 'need of exercise4' ,but this will not explain the peculiar zest of those exercises1 which is something quite different from our feelings whilst swinging dumb-bells or tramping the highway4 ,others1 more sophisticated1 tell us that the civilised individual retains in his nature the instincts of his remote ancestors1 and that these assert themselves at stages of his growth corresponding with ancestral periods of culture or savagery3 so that if we delight to climb trees1 throw stones1 and hunt1 it is because our forefathers once lived in trees1 had no missiles but stones1 and depended for a livelihood upon killing something4 ,to some of us1 again1 this seems an explanation2 to others it merely gives annoyance1 as a superfluous hypothesis1 the fruit of a wanton imagination and too much leisure4 ,however1 what we are not accustomed to immediately excites curiosity4 ,if it were exceptional to climb trees1 throw stones1 ride after foxes1 whoever did such things would be viewed with suspicion4 ,an eclipse1 a shooting star1 a solitary boulder on the heath1 a strange animal1 or a ,chinaman in the street1 calls for explanation2 and among some nations1 eclipses have been explained by supposing a dragon to devour the sun or moon2 solitary boulders1 as the missiles of a giant2 and so on4 ,such explanations1 plainly1 are attempts to regard rare phenomena as similar to others that are better known2 a snake having been seen to swallow a rabbit1 a bigger one may swallow the sun3 a giant is supposed to bear much the same relation to a boulder as a boy does to half a brick4 ,when any very common thing seems to need no explanation1 it is because the several instances of its occurrence are a sufficient basis of assimilation to satisfy most of us4 ,still1 if a reason for such a thing be demanded1 the commonest answer has the same implication1 namely1 that assimilation or classification is a sufficient reason for it4 ,thus1 if climbing trees is referred to the need of exercise1 it is assimilated to running1 rowing1 etc42 if the customs of a savage tribe are referred to the command of its gods1 they are assimilated to those things that are done at the command of chieftains4 ,explanation1 then1 is a kind of classification2 it is the finding of resemblance between the phenomenon in question and other phenomena4 ,in ,mathematics1 the explanation of a theorem is the same as its proof1 and consists in showing that it repeats1 under different conditions1 the definitions and axioms already assumed and the theorems already demonstrated4 ,in ,logic1 the major premise of every syllogism is an explanation of the conclusion2 for the minor premise asserts that the conclusion is an example of the major premise4 ,in ,concrete ,sciences1 to discover the cause of a phenomenon1 or to derive an empirical law from laws of causation1 is to explain it2 because a cause is an invariable antecedent1 and therefore reminds us of1 or enables us to conceive1 an indefinite number of cases similar to the present one wherever the cause exists4 ,it classifies the present case with other instances of causation1 or brings it under the universal law2 and1 as we have seen that the discovery of the laws of nature is essentially the discovery of causes1 the discovery and derivation of laws is scientific explanation4 ,the discovery of quantitative laws is especially satisfactory1 because it not only explains why an event happens at all1 but why it happens just in this direction1 degree1 or amount2 and not only is the given relation of cause and effect definitely assimilated to other causal instances1 but the effect is identified with the cause as the same matter and energy redistributed2 wherefore1 whether the conservation of matter and energy be universally true or not1 it must still be an universal postulate of scientific explanation4 ,the mere discovery of an empirical law of co-existence1 as that 'white tom-cats with blue eyes are deaf'1 is indeed something better than an isolated fact3 every general proposition relieves the mind of a load of facts2 and1 for many people1 to be able to say--',it is always so'--may be enough2 but for scientific explanation we require to know the reason of it1 that is1 the cause4 ,still1 if asked to explain an axiom1 we can only say1 ',it is always so3' though it is some relief to point out particular instances of its realisation1 or to exhibit the similarity of its form to that of other axioms--as of the ,dictum to the axiom of equality4 #f4 ,there are three modes of scientific ,explanation2 ,first1 the analysis of a phenomenon into the laws of its causes and the concurrence of those causes4 ,the pumping of water implies 7#a7 pressure of the air1 7#b7 distribution of pressure in a liquid1 7#c7 that motion takes the direction of least resistance4 ,similarly1 that thunder follows forked lightning1 and that the report of a gun follows the flash1 are resolvable into 7#a7 the discharge of electricity1 or the explosion of gunpowder2 7#b7 distance of the observer from the event2 7#c7 that light travels faster than sound4 ,the planetary orbits are analysable into the tendency of planets to fall into the sun1 and their tendency to travel in a straight line4 ,when this conception is helped out by swinging a ball round by a string1 and then letting it go1 to show what would happen to the earth if gravitation ceased1 we see how the recognition of resemblance lies at the bottom of explanation4 ,secondly1 the discovery of steps of causation between a cause and its remote effects2 the interpolation and concatenation of causes4 ,the maxim ',no cats no clover' is explained by assigning the intermediate steps in the following series2 that the fructification of red clover depends on the visits of humble-bees1 who distribute the pollen in seeking honey2 that if field-mice are numerous they destroy the humble-bees' nests2 and that 7owls and weasels being exterminated by gamekeepers7 the destruction of field-mice depends upon the supply of cats2 which1 therefore1 are a remote condition of the clover crop4 ,again1 the communication of thought by speech is an example of something so common that it seems to need no explanation2 yet to explain it is a long story4 ,a thought in one man's mind is the remote cause of a similar thought in another's3 here we have 7#a7 a thought associated with mental words2 7#b7 a connection between these thoughts and some tracts of the brain2 7#c7 a connection between these tracts of the brain and the muscles of the larynx1 the tongue and the lips2 7#d7 movements of the chest1 larynx and mouth1 propelling and modifying waves of air2 7#e7 the impinging of these air-waves upon another man's ear1 and by a complex mechanism exciting the aural nerve2 7#f7 the transfer of this excitation to certain tracts of his brain2 7#g7 a connection there with sounds of words and their associated thoughts4 ,if one of these links fail1 there is no communication4 ,thirdly1 the subsumption of several laws under one more general expression4 ,the tendency of bodies to fall to the earth and the tendency of the earth itself 7with the other planets7 to fall into the sun1 are subsumed under the general law that ',all matter gravitates4' ,the same law subsumes the movements of the tide4 ,by means of the notion of specific gravity1 it includes 'levitation1' or the actual rising of some bodies1 as of corks in water1 of balloons1 or flames in the air3 the fact being that these things do not tend to rise1 but to fall like everything else2 only as the water or air weighs more in proportion to its volume than corks or balloons1 the latter are pushed up4 ,this process of subsumption bears the same relation to secondary laws1 that these do to particular facts4 ,the generalisation of many particular facts 7that is1 a statement of that in which they agree7 is a law2 and the generalisation of these laws 7that is1 again1 a statement of that in which they agree7 is a higher law2 and this process1 upwards or downwards1 is characteristic of scientific progress4 ,the perfecting of any science consists in comprehending more and more of the facts within its province1 and in showing that they all exemplify a smaller and smaller number of principles1 which express their most profound resemblances4 ,these three modes of explanation 7analysis1 interpolation1 subsumption7 all consist in generalising or assimilating the phenomena4 ,the pressure of the air1 of a liquid1 and motion in the direction of least resistance1 are all commoner facts than pumping2 that light travels faster than sound is a commoner fact than a thunderstorm or gun-firing4 ,each of the laws--',cats kill mice1' ',mice destroy humble-bees' nests1' ',humble-bees fructify red clover'--is wider and expresses the resemblance of more numerous cases than the law that ',clover depends on cats'2 because each of them is less subject to further conditions4 ,similarly1 every step in the communication of thought by language is less conditional1 and therefore more general1 than the completion of the process4 ,in all the above cases1 again1 each law into which the phenomenon 7whether pumping or conversation7 is resolved1 suggests a host of parallel cases3 as the modifying of air-waves by the larynx and lips suggests the various devices by which the strings and orifices of musical instruments modify the character of notes4 ,subsumption consists entirely in proving the existence of an essential similarity between things where it was formerly not observed3 as that the gyrations of the moon1 the fall of apples1 and the flotation of bubbles are all examples of gravitation3 or that the purifying of the blood by breathing1 the burning of a candle1 and the rusting of iron are all cases of oxidation3 or that the colouring of the underside of a red-admiral's wings1 the spots of the giraffe1 the shape and attitude of a stick-caterpillar1 the immobility of a bird on its nest1 and countless other cases1 though superficially so different1 agree in this1 that they conceal and thereby protect the organism4 ,not any sort of likeness1 however1 suffices for scientific explanation3 the only satisfactory explanation of concrete things or events1 is to discover their likeness to others in respect of ,causation4 ,hence attempts to help the understanding by familiar comparisons are often worse than useless4 ,any of the above examples will show that the first result of explanation is not to make a phenomenon seem familiar1 but to put 7as the saying is7 'quite a new face upon it4' ,when1 indeed1 we have thought it over in all its newly discovered relations1 we feel more at home with it than ever2 and this is one source of our satisfaction in explaining things2 and hence to substitute immediate familiarisation for radical explanation1 is the easily besetting sin of human understanding3 the most plausible of fallacies1 the most attractive1 the most difficult to avoid even when we are on our guard against it4 #g4 ,the explanation of ,nature 7if it be admitted to consist in generalisation1 or the discovery of resemblance amidst differences7 can never be completed4 ,for--7#a7 there are 7as ,mill says7 facts1 namely1 fundamental states or processes of consciousness1 which are distinct2 in other words1 they do not resemble one another1 and therefore cannot be generalised or subsumed under one explanation4 ,colour1 heat1 smell1 sound1 touch1 pleasure and pain1 are so different that there is one group of conditions to be sought for each2 and the laws of these conditions cannot be subsumed under a more general one without leaving out the very facts to be explained4 ,a general condition of sensation1 such as the stimulating of the sensory organs of a living animal1 gives no account of the special characters of colour1 smell1 etc42 which are1 however1 the phenomena in question2 and each of them has its own law4 ,nay1 each distinct sensation-quality1 or degree1 must have its own law2 for in each ultimate difference there is something that cannot be assimilated4 ,such differences amount1 according to experimental ,psychologists1 to more than #ej1jjj4 ,moreover1 a neural process can never explain a conscious process in the way of cause and effect2 for there is no equivalence between them1 and one can never absorb the other4 7#b7 ,when physical science is treated objectively 7that is1 with as little reference as possible to the fact that all phenomena are only known in relation to the human mind71 colour1 heat1 smell1 sound 7considered as sensations7 are neglected1 and attention is fixed upon certain of their conditions3 extension1 figure1 resistance1 weight1 motion1 with their derivatives1 density1 elasticity1 etc4 ,these are called the ,primary ,qualities of ,matter2 and it is assumed that they belong to matter by itself1 whether we look on or not3 whilst colour1 heat1 sound1 etc41 are called ,secondary ,qualities1 as depending entirely upon the reaction of some conscious animal4 ,by physical science the world is considered in the abstract1 as a perpetual redistribution of matter and energy1 and the distracting multiplicity of sensations seems to be got rid of4 ,but1 not to dwell upon the difficulty of reducing the activities of life and chemistry to mechanical principles--even if this were done1 complete explanation could not be attained4 ,for--7a7 as explanation is the discovery of causes1 we no sooner succeed in assigning the causes of the present state of the world than we have to inquire into the causes of those causes1 and again the still earlier causes1 and so on to infinity4 ,but1 this being impossible1 we must be content1 wherever we stop1 to contemplate the uncaused1 that is1 the unexplained2 and then all that follows is only relatively explained4 ,besides this difficulty1 however1 there is another that prevents the perfecting of any theory of the abstract material world1 namely 7b71 that it involves more than one first principle4 ,for we have seen that the ,uniformity of ,nature is not really a principle1 but a merely nominal generalisation1 since it cannot be definitely stated2 and1 therefore1 the principles of ,contradiction1 ,mediate ,equality1 and ,causation remain incapable of subsumption2 nor can any one of them be reduced to another3 so that they remain unexplained4 7#c7 ,another limit to explanation lies in the infinite character of every particular fact2 so that we may know the laws of many of its properties and yet come far short of understanding it as a whole4 ,a lump of sandstone in the road3 we may know a good deal about its specific gravity1 temperature1 chemical composition1 geological conditions2 but if we inquire the causes of the particular modifications it exhibits of these properties1 and further why it is just so big1 containing so many molecules1 neither more nor less1 disposed in just such relations to one another as to give it this particular figure1 why it lies exactly there rather than a yard off1 and so forth1 we shall get no explanation of all this4 ,the causes determining each particular phenomenon are infinite1 and can never be computed2 and1 therefore1 it can never be fully explained4 #h4 ,analogy is used in two senses3 7#a7 for the resemblance of relations between terms that have little or no resemblance--as ,the wind drives the clouds as a shepherd drives his sheep--where wind and shepherd1 clouds and sheep are totally unlike4 ,such analogies are a favourite figure in poetry and rhetoric1 but cannot prove anything4 ,for valid reasoning there must be parallel cases1 according to substance and attribute1 or cause and effect1 or proportion3 e4g4 ,as cattle and deer are to herbivorousness1 so are camels2 ,as bodies near the earth fall toward it1 so does the moon2 ,as #b is to #c so is #d to #f4 7#b7 ,analogy is discussed in ,logic as a kind of probable proof based upon imperfect similarity 7as the best that can be discovered7 between the data of comparison and the subject of our inference4 ,like ,deduction and ,induction1 it assumes that things which are alike in some respects are also alike in others2 but it differs from them in not appealing to a definite general law assigning the essential points of resemblance upon which the argument relies4 ,in ,deductive proof1 this is done by the major premise of every syllogism3 if the major says that ',all fat men are humorists1' and we can establish the minor1 ',x is a fat man1' we have secured the essential resemblance that carries the conclusion4 ,in induction1 the ,law of ,causation and its representatives1 the ,canons1 serve the same purpose1 specifying the essential marks of a cause4 ,but1 in ,analogy1 the resemblance relied on cannot be stated categorically4 ,if we argue that ,mars is inhabited because it resembles the datum1 our ,earth1 7#a7 in being a planet1 7#b7 neither too hot nor too cold for life1 7#c7 having an atmosphere1 7#d7 land and water1 etc41 we are not prepared to say that ',all planets having these characteristics are inhabited4' ,it is1 therefore1 not a deduction2 and since we do not know the original causes of life on the ,earth1 we certainly cannot show by induction that adequate causes exist in ,mars4 ,we rely1 then1 upon some such vague notion of ,uniformity as that ',things alike in some points are alike in others'2 which1 plainly1 is either false or nugatory4 ,but if the linear markings upon the surface of ,mars indicate a system of canals1 the inference that he has intelligent inhabitants is no longer analogical1 since canals can have no other cause4 ,the cogency of any proof depends upon the character and definiteness of the likeness which one phenomenon bears to another2 but ,analogy trusts to the general quantity of likeness between them1 in ignorance of what may be the really important likeness4 ,if1 having tried with a stone1 an apple1 a bullet1 etc41 we find that they all break an ordinary window1 and thence infer that a cricket ball will do so1 we do not reason by analogy1 but make instinctively a deductive extension of an induction1 merely omitting the explicit generalisation1 ',all missiles of a certain weight1 size and solidity break windows4' ,but if1 knowing nothing of snakes except that the viper is venomous1 a child runs away from a grass-snake1 he argues by analogy2 and1 though his conduct is prudentially justifiable1 his inference is wrong3 for there is no law that ',all snakes are venomous1' but only that those are venomous that have a certain structure of fang2 a point which he did not stay to examine4 ,the discovery of an analogy1 then1 may suggest hypotheses2 it states a problem--to find the causes of the analogy2 and thus it may lead to scientific proof2 but merely analogical argument is only probable in various degrees4 7#a7 ,the greater the number and importance of the points of agreement1 the more probable is the inference4 7#b7 ,the greater the number and importance of the points of difference1 the less probable is the inference4 7#c7 ,the greater the number of unknown properties in the subject of our argument1 the less the value of any inference from those that we do know4 ,of course the number of unknown properties can itself be estimated only by analogy4 ,in the case of ,mars1 they are probably very numerous2 and1 apart from the evidence of canals1 the prevalent assumption that there are intelligent beings in that planet1 seems to rest less upon probability than on a curiously imaginative extension of the gregarious sentiment1 the chilly discomfort of mankind at the thought of being alone in the universe1 and a hope that there may be conversable and 'clubable' souls nearer than the ,dog-star4 ,,chapter ,,xx ,,probability #a4 ,chance was once believed to be a distinct power in the world1 disturbing the regularity of ,nature2 though1 according to ,aristotle1 it was only operative in occurrences below the sphere of the moon4 ,as1 however1 it is now admitted that every event in the world is due to some cause1 if we can only trace the connection1 whilst nevertheless the notion of ,chance is still useful when rightly conceived1 we have to find some other ground for it than that of a spontaneous capricious force inherent in things4 ,for such a conception can have no place in any logical interpretation of ,nature3 it can never be inferred from a principle1 seeing that every principle expresses an uniformity2 nor1 again1 if the existence of a capricious power be granted1 can any inference be drawn from it4 ,impossible alike as premise and as conclusion1 for ,reason it is nothing at all4 ,every event is a result of causes3 but the multitude of forces and the variety of collocations being immeasurably great1 the overwhelming majority of events occurring about the same time are only related by ,causation so remotely that the connection cannot be followed4 ,whilst my pen moves along the paper1 a cab rattles down the street1 bells in the neighbouring steeple chime the quarter1 a girl in the next house is practising her scales1 and throughout the world innumerable events are happening which may never happen together again2 so that should one of them recur1 we have no reason to expect any of the others4 ,this is ,chance1 or chance coincidence4 ,the word ,coincidence is vulgarly used only for the inexplicable concurrence of interesting events--quite a coincidence6 ,on the other hand1 many things are now happening together or coinciding1 that will do so1 for assignable reasons1 again and again2 thousands of men are leaving the ,city1 who leave at the same hour five days a week4 ,but this is not chance2 it is causal coincidence due to the custom of business in this country1 as determined by our latitude and longitude and other circumstances4 ,no doubt the above chance coincidences--writing1 cab-rattling1 chimes1 scales1 etc4--are causally connected at some point of past time4 ,they were predetermined by the condition of the world ten minutes ago2 and that was due to earlier conditions1 one behind the other1 even to the formation of the planet4 ,but whatever connection there may have been1 we have no such knowledge of it as to be able to deduce the coincidence1 or calculate its recurrence4 ,hence ,chance is defined by ,mill to be3 ,coincidence giving no ground to infer uniformity4 ,still1 some chance coincidences do recur according to laws of their own3 ,i say some1 but it may be all4 ,if the world is finite1 the possible combinations of its elements are exhaustible2 and1 in time1 whatever conditions of the world have concurred will concur again1 and in the same relation to former conditions4 ,this writing1 that cab1 those chimes1 those scales will coincide again2 the ,argonautic expedition1 and the ,trojan war1 and all our other troubles will be renewed4 ,but let us consider some more manageable instance1 such as the throwing of dice4 ,every one who has played much with dice knows that double sixes are sometimes thrown1 and sometimes double aces4 ,such coincidences do not happen once and only once2 they occur again and again1 and a great number of trials will show that1 though their recurrence has not the regularity of cause and effect1 it yet has a law of its own1 namely--a tendency to average regularity4 ,in #aj1jjj throws there will be some number of double sixes2 and the greater the number of throws the more closely will the average recurrence of double sixes1 or double aces1 approximate to one in thirty-six4 ,such a law of average recurrence is the basis of ,probability4 ,chance being the fact of coincidence without assignable cause1 ,probability is expectation based on the average frequency of its happening4 #b4 ,probability is an ambiguous term4 ,usually1 when we say that an event is 'probable1' we mean that it is more likely than not to happen4 ,but1 scientifically1 an event is probable if our expectation of its occurrence is less than certainty1 as long as the event is not impossible4 ,probability1 thus conceived1 is represented by a fraction4 ,taking #a to stand for certainty1 and #j for impossibility1 probability may be #iii_/ajjj1 or #a_/ajjj1 or 7generally7 #a_/m4 ,the denominator represents the number of times that an event happens1 and the numerator the number of times that it coincides with another event4 ,in throwing a die1 the probability of ace turning up is expressed by putting the number of throws for the denominator and the number of times that ace is thrown for the numerator2 and we may assume that the more trials we make the nearer will the resulting fraction approximate to #a_/f4 ,instead of speaking of the 'throwing of the die' and its 'turning up ace' as two events1 the former is called 'the event' and the latter 'the way of its happening4' ,and these expressions may easily be extended to cover relations of distinct events2 as when two men shoot at a mark and we desire to represent the probability of both hitting the bull's eye together1 each shot may count as an event 7denominator7 and the coincidence of 'bull's-eyes' as the way of its happening 7numerator74 ,it is also common to speak of probability as a proportion4 ,if the fraction expressing the probability of ace being cast is #a_/f1 the proportion of cases in which it happens is #a to #e2 or 7as it is1 perhaps1 still more commonly put7 'the chances are #e to #a against it4' #c4 ,as to the grounds of probability opinions differ4 ,according to one view the ground is subjective3 probability depends1 it is said1 upon the quantity of our ,belief in the happening of a certain event1 or in its happening in a particular way4 ,according to the other view the ground is objective1 and1 in fact1 is nothing else than experience1 which is most trustworthy when carefully expressed in statistics4 ,to the subjective view it may be objected1 7a7 that belief cannot by itself be satisfactorily measured4 ,no one will maintain that belief1 merely as a state of mind1 always has a definite numerical value of which one is conscious1 as #a_/ajj or #a_/aj4 ,let anybody mix a number of letters in a bag1 knowing nothing of them except that one of them is ,x1 and then draw them one by one1 endeavouring each time to estimate the value of his belief that the next will be ,x2 can he say that his belief in the drawing of ,x next time regularly increases as the number of letters left decreases8 ,if not1 we see that 7b7 belief does not uniformly correspond with the state of the facts4 ,if in such a trial as proposed above1 we really wish to draw ,x1 as when looking for something in a number of boxes1 how common it is1 after a few failures1 to feel quite hopeless and to say3 ,oh1 of course it will be in the last4 ,for belief is subject to hope and fear1 temperament1 passion1 and prejudice1 and not merely to rational considerations4 ,and it is useless to appeal to 'the ,wise ,man1' the purely rational judge of probability1 unless he is producible4 ,or1 if it be said that belief is a short cut to the evaluation of experience1 because it is the resultant of all past experience1 we may reply that this is not true4 ,for one striking experience1 or two or three recent ones1 will immensely outweigh a great number of faint or remote experiences4 ,moreover1 the experience of two men may be practically equal1 whilst their beliefs upon any question greatly differ4 ,any two ,englishmen have about the same experience1 personal and ancestral1 of the weather2 yet their beliefs in the saw that 'if it rain on ,st4 ,swithin's ,day it will rain for forty days after1' may differ as confident expectation and sheer scepticism4 ,upon which of these beliefs shall we ground the probability of forty days' rain8 ,but 7c7 at any rate1 if ,probability is to be connected with ,inductive ,logic1 it must rest upon the same ground1 namely--observation4 ,induction1 in any particular case1 is not content with beliefs or opinions1 but aims at testing1 verifying or correcting them by appealing to the facts2 and ,probability has the same object and the same basis4 ,in some cases1 indeed1 the conditions of an event are supposed to be mathematically predetermined1 as in tossing a penny1 throwing dice1 dealing cards4 ,in throwing a die1 the ways of happening are six2 in tossing a penny only two1 head and tail3 and we usually assume that the odds with a die are fairly #e to #a against ace1 whilst with a penny 'the betting is even' on head or tail4 ,still1 this assumption rests upon another1 that the die is perfectly fair1 or that the head and tail of a penny are exactly alike2 and this is not true4 ,with an ordinary die or penny1 a very great number of trials would1 no doubt1 give an average approximating to #a_/f or #a_/b2 yet might always leave a certain excess one way or the other1 which would also become more definite as the trials went on2 thus showing that the die or penny did not satisfy the mathematical hypothesis4 ,buffon is said to have tossed a coin #djdj times1 obtaining #aiib heads and #bjdh tails2 a pupil of ,de ,morgan tossed #djib times1 obtaining #bjdh heads and #bjdd tails4 ,there are other important cases in which probability is estimated and numerically expressed1 although statistical evidence directly bearing upon the point in question cannot be obtained2 as in betting upon a race2 or in the prices of stocks and shares1 which are supposed to represent the probability of their paying1 or continuing to pay1 a certain rate of interest4 ,but the judgment of experts in such matters is certainly based upon experience2 and great pains are taken to make the evidence as definite as possible by comparing records of speed1 or by financial estimates2 though something must still be allowed for reports of the condition of horses1 or of the prospects of war1 harvests1 etc4 ,however1 where statistical evidence is obtainable1 no one dreams of estimating probability by the quantity of his belief4 ,insurance offices1 dealing with fire1 shipwreck1 death1 accident1 etc41 prepare elaborate statistics of these events1 and regulate their rates accordingly4 ,apart from statistics1 at what rate ought the lives of men aged #dj to be insured1 in order to leave a profit of #e per cent4 upon #ajjj payable at each man's death8 ,is 'quantity of belief' a sufficient basis for doing this sum8 #d4 ,the ground of probability is experience1 then1 and1 whenever possible1 statistics2 which are a kind of induction4 ,it has indeed been urged that induction is itself based upon probability2 that the subtlety1 complexity and secrecy of nature are such1 that we are never quite sure that we fully know even what we have observed2 and that1 as for laws1 the conditions of the universe at large may at any moment be completely changed2 so that all imperfect inductions1 including the law of causation itself1 are only probable4 ,but1 clearly1 this doctrine turns upon another ambiguity in the word 'probable4' ,it may be used in the sense of 'less than absolutely certain'2 and such doubtless is the condition of all human knowledge1 in comparison with the comprehensive intuition of arch-angels3 or it may mean 'less than certain according to our standard of certainty1' that is1 in comparison with the law of causation and its derivatives4 ,we may suppose some one to object that by this relative standard even empirical laws cannot be called 'only probable' as long as we 'know no exception to them'2 for that is all that can be said for the boasted law of causation2 and that1 accordingly1 we can frame no fraction to represent their probability4 ,that 'all swans are white' was at one time1 from this point of view1 not probable but certain2 though we now know it to be false4 ,it would have been an indecorum to call it only probable as long as no other-coloured swan had been discovered2 not merely because the quantity of belief amounted to certainty1 but because the number of events 7seeing a swan7 and the number of their happenings in a certain way 7being white7 were equal1 and therefore the evidence amounted to #a or certainty4 ,but1 in fact1 such an empirical law is only probable2 and the estimate of its probability must be based on the number of times that similar laws have been found liable to exceptions4 ,albinism is of frequent occurrence2 and it is common to find closely allied varieties of animals differing in colour4 ,had the evidence been duly weighed1 it could never have seemed more than probable that 'all swans are white4' ,but what law1 approaching the comprehensiveness of the law of causation1 presents any exceptions8 ,supposing evidence to be ultimately nothing but accumulated experience1 the amount of it in favour of causation is incomparably greater than the most that has ever been advanced to show the probability of any other kind of event2 and every relation of events which is shown to have the marks of causation obtains the support of that incomparably greater body of evidence4 ,hence the only way in which causation can be called probable1 for us1 is by considering it as the upward limit 7#a7 to which the series of probabilities tends2 as impossibility is the downward limit 7#j74 ,induction1 'humanly speaking1' does not rest on probability2 but the probability of concrete events 7not of mere mathematical abstractions like the falling of absolutely true dice7 rests on induction and1 therefore1 on causation4 ,the inductive evidence underlying an estimate of probability may be of three kinds3 7a7 direct statistics of the events in question2 as when we find that1 at the age of #bj1 the average expectation of life is #ci-dj years4 ,this is an empirical law1 and1 if we do not know the causes of any event1 we must be content with an empirical law4 ,but 7b7 if we do know the causes of an event1 and the causes which may prevent its happening1 and can estimate the comparative frequency of their occurring1 we may deduce the probability that the effect 7that is1 the event in question7 will occur4 ,or 7c7 we may combine these two methods1 verifying each by means of the other4 ,now either the method 7b7 or 7a fortiori7 the method 7c7 7both depending on causation7 is more trustworthy than the method 7a7 by itself4 ,but1 further1 a merely empirical statistical law will only be true as long as the causes influencing the event remain the same4 ,a die may be found to turn ace once in six throws1 on the average1 in close accordance with mathematical theory2 but if we load it on that facet the results will be very different4 ,so it is with the expectation of life1 or fire1 or shipwreck4 ,the increased virulence of some epidemic such as influenza1 an outbreak of anarchic incendiarism1 a moral epidemic of over-loading ships1 may deceive the hopes of insurance offices4 ,hence we see1 again1 that probability depends upon causation1 not causation upon probability4 ,that uncertainty of an event which arises not from ignorance of the law of its cause1 but from our not knowing whether the cause itself does or does not occur at any particular time1 is ,contingency4 #e4 ,the nature of an average supposes deviations from it4 ,deviations from an average1 or errors1 are assumed to conform to the law 7#a7 that the greater errors are less frequent than the smaller1 so that most events approximate to the average2 and 7#b7 that errors have no bias1 but are equally frequent and equally great in both directions from the mean1 so that they are scattered symmetrically4 ,hence their distribution may be expressed by some such figure as the following3 ,illustration3 ,,fig4 #aa4 ,here o is the average event1 and oy represents the number of average events4 ,along ox1 in either direction1 deviations are measured4 ,at p the amount of error or deviation is op2 and the number of such deviations is represented by the line or ordinate pa4 ,at s the deviation is os2 and the number of such deviations is expressed by sb4 ,as the deviations grow greater1 the number of them grows less4 ,on the other side of o1 toward -x1 at distances1 op'1 os' 7equal to op1 os7 the lines p'a'1 s'b' represent the numbers of those errors 7equal to pa1 sb74 ,if o is the average height of the adult men of a nation1 7say7 #e ft4 #f in41 s' and s may stand for #e ft4 and #f ft42 men of #d ft4 #f in4 lie further toward -x1 and men of #f ft4 #f in4 further toward x4 ,there are limits to the stature of human beings 7or to any kind of animal or plant7 in both directions1 because of the physical conditions of generation and birth4 ,with such events the curve b'yb meets the abscissa at some point in each direction2 though where this occurs can only be known by continually measuring dwarfs and giants4 ,but in throwing dice or tossing coins1 whilst the average occurrence of ace is once in six throws1 and the average occurrence of 'tail' is once in two tosses1 there is no necessary limit to the sequences of ace or of 'tail' that may occur in an infinite number of trials4 ,to provide for such cases the curve is drawn as if it never touched the abscissa4 ,that some such figure as that given above describes a frequent characteristic of an average with the deviations from it1 may be shown in two ways3 7#a7 ,by arranging the statistical results of any homogeneous class of measurements2 when it is often found that they do1 in fact1 approximately conform to the figure2 that very many events are near the average2 that errors are symmetrically distributed on either side1 and that the greater errors are the rarer4 7#b7 ,by mathematical demonstration based upon the supposition that each of the events in question is influenced1 more or less1 by a number of unknown conditions common to them all1 and that these conditions are independent of one another4 ,for then1 in rare cases1 all the conditions will operate favourably in one way1 and the men will be tall2 or in the opposite way1 and the men will be short2 in more numerous cases1 many of the conditions will operate in one direction1 and will be partially cancelled by a few opposing them2 whilst in still more cases opposed conditions will approximately balance one another and produce the average event or something near it4 ,the results will then conform to the above figure4 ,from the above assumption it follows that the symmetrical curve describes only a 'homogeneous class' of measurements2 that is1 a class no portion of which is much influenced by conditions peculiar to itself4 ,if the class is not homogeneous1 because some portion of it is subject to peculiar conditions1 the curve will show a hump on one side or the other4 ,suppose we are tabulating the ages at which ,englishmen die who have reached the age of #bj1 we may find that the greatest number die at #ci 7#ai years being the average expectation of life at #bj7 and that as far as that age the curve upwards is regular1 and that beyond the age of #ci it begins to descend regularly1 but that on approaching #de it bulges out some way before resuming its regular descent--thus3 ,illustration3 ,,fig4 #ab4 ,such a hump in the curve might be due to the presence of a considerable body of teetotalers1 whose longevity was increased by the peculiar condition of abstaining from alcohol1 and whose average age was #de1 #f years more than the average for common men4 ,again1 if the group we are measuring be subject to selection 7such as ,british soldiers1 for which profession all volunteers below a certain height--say1 #e ft4 #e in4--are rejected71 the curve will fall steeply on one side1 thus3 ,illustration3 ,,fig4 #ac4 ,if1 above a certain height1 volunteers are also rejected1 the curve will fall abruptly on both sides4 ,the average is supposed to be #e ft4 #h in4 ,the distribution of events is described by 'some such curve' as that given in ,fig4 #aa2 but different groups of events may present figures or surfaces in which the slopes of the curves are very different1 namely1 more or less steep2 and if the curve is very steep1 the figure runs into a peak2 whereas1 if the curve is gradual1 the figure is comparatively flat4 ,in the latter case1 where the figure is flat1 fewer events will closely cluster about the average1 and the deviations will be greater4 ,suppose that we know nothing of a given event except that it belongs to a certain class or series1 what can we venture to infer of it from our knowledge of the series8 ,let the event be the cephalic index of an ,englishman4 ,the cephalic index is the breadth of a skull #ajj and divided by the length of it2 e4g4 if a skull is #h in4 long and #f in4 broad1 7#fajj7_/hge4 ,we know that the average ,english skull has an index of #gh4 ,the skull of the given individual1 therefore1 is more likely to have that index than any other4 ,still1 many skulls deviate from the average1 and we should like to know what is the probable error in this case4 ,the probable error is the measurement that divides the deviations from the average in either direction into halves1 so that there are as many events having a greater deviation as there are events having a less deviation4 ,if1 in ,fig4 #aa above1 we have arranged the measurements of the cephalic index of ,english adult males1 and if at o 7the average or mean7 the index is #gh1 and if the line pa divides the right side of the fig4 into halves1 then op is the probable error4 ,if the measurement at p is #hj1 the probable error is #b4 ,similarly1 on the left hand1 the probable error is op'1 and the measurement at p' is #gf4 ,we may infer1 then1 that the skull of the man before us is more likely to have an index of #gh than any other2 if any other1 it is equally likely to lie between #hj and #gf1 or to lie outside them2 but as the numbers rise above #hj to the right1 or fall below #gf to the left1 it rapidly becomes less and less likely that they describe this skull4 ,in such cases as heights of men or skull measurements1 where great numbers of specimens exist1 the average will be actually presented by many of them2 but if we take a small group1 such as the measurements of a college class1 it may happen that the average height 7say1 #e ft4 #h in47 is not the actual height of any one man4 ,even then there will generally be a closer cluster of the actual heights about that number than about any other4 ,still1 with very few cases before us1 it may be better to take the median than the average4 ,the median is that event on either side of which there are equal numbers of deviations4 ,one advantage of this procedure is that it may save time and trouble4 ,to find approximately the average height of a class1 arrange the men in order of height1 take the middle one and measure him4 ,a further advantage of this method is that it excludes the influence of extraordinary deviations4 ,suppose we have seven cephalic indices1 from skeletons found in the same barrow1 #ge-a_/b1 #gf1 #gh1 #gh1 #gi1 #hj-a_/b1 #hf4 ,the average is #gi2 but this number is swollen unduly by the last measurement2 and the median1 #gh1 is more fairly representative of the series2 that is to say1 with a greater number of skulls the average would probably have been nearer #gh4 ,to make a single measurement of a phenomenon does not give one much confidence4 ,another measurement is made2 and then1 if there is no opportunity for more1 one takes the mean or average of the two4 ,but why8 ,for the result may certainly be worse than the first measurement4 ,suppose that the events ,i am measuring are in fact fairly described by ,fig4 ,,ii1 although 7at the outset7 ,i know nothing about them2 and that my first measurement gives p1 and my second s2 the average of them is worse than p4 ,still1 being yet ignorant of the distribution of these events1 ,i do rightly in taking the average4 ,for1 as it happens1 #c_/d of the events lie to the left of p2 so that if the first trial gives p1 then the average of p and any subsequent trial that fell nearer than 7say7 s' on the opposite side1 would be better than p2 and since deviations greater than s' are rare1 the chances are nearly #c to #a that the taking of an average will improve the observation4 ,only if the first trial give o1 or fall within a little more than #a_/b p on either side of o1 will the chances be against any improvement by trying again and taking an average4 ,since1 therefore1 we cannot know the position of our first trial in relation to o1 it is always prudent to try again and take the average2 and the more trials we can make and average1 the better is the result4 ,the average of a number of observations is called a ,reduced ,observation4 ,we may have reason to believe that some of our measurements are better than others because they have been taken by a better trained observer1 or by the same observer in a more deliberate way1 or with better instruments1 and so forth4 ,if so1 such observations should be 'weighted1' or given more importance in our calculations2 and a simple way of doing this is to count them twice or oftener in taking the average4 #f4 ,these considerations have an important bearing upon the interpretation of probabilities4 ,the average probability for any general class or series of events cannot be confidently applied to any one instance or to any special class of instances1 since this one1 or this special class1 may exhibit a striking error or deviation2 it may1 in fact1 be subject to special causes4 ,within the class whose average is first taken1 and which is described by general characters as 'a man1' or 'a die1' or 'a rifle shot1' there may be classes marked by special characters and determined by special influences4 ,statistics giving the average for 'mankind' may not be true of 'civilised men1' or of any still smaller class such as ',frenchmen4' ,hence life-insurance offices rely not merely on statistics of life and death in general1 but collect special evidence in respect of different ages and sexes1 and make further allowance for teetotalism1 inherited disease1 etc4 ,similarly with individual cases3 the average expectation for a class1 whether general or special1 is only applicable to any particular case if that case is adequately described by the class characters4 ,in ,england1 for example1 the average expectation of life for males at #bj years of age is #ci4dj2 but at #fj it is still #ac4ad1 and at #gc it is #g4jg2 at #ajj it's #a4fa4 ,of men #bj years old those who live more or less than #ci4dj years are deviations or errors2 but there are a great many of them4 ,to insure the life of a single man at #bj1 in the expectation of his dying at #fj1 would be a mere bet1 if we had no special knowledge of him2 the safety of an insurance office lies in having so many clients that opposite deviations cancel one another3 the more clients the safer the business4 ,it is quite possible that a hundred men aged #bj should be insured in one week and all of them die before #be2 this would be ruinous1 if others did not live to be #hj or #ij4 ,not only in such a practical affair as insurance1 but in matters purely scientific1 the minute and subtle peculiarities of individuals have important consequences4 ,each man has a certain cast of mind1 character1 physique1 giving a distinctive turn to all his actions even when he tries to be normal4 ,in every employment this determines his ,personal ,equation1 or average deviation from the normal4 ,the term ,personal ,equation is used chiefly in connection with scientific observation1 as in ,astronomy4 ,each observer is liable to be a little wrong1 and this error has to be allowed for and his observations corrected accordingly4 ,the use of the term 'expectation1' and of examples drawn from insurance and gambling1 may convey the notion that probability relates entirely to future events2 but if based on laws and causes1 it can have no reference to point of time4 ,as long as conditions are the same1 events will be the same1 whether we consider uniformities or averages4 ,we may therefore draw probable inferences concerning the past as well as the future1 subject to the same hypothesis1 that the causes affecting the events in question were the same and similarly combined4 ,on the other hand1 if we know that conditions bearing on the subject of investigation1 have changed since statistics were collected1 or were different at some time previous to the collection of evidence1 every probable inference based on those statistics must be corrected by allowing for the altered conditions1 whether we desire to reason forwards or backwards in time4 #g4 ,the rules for the combination of probabilities are as follows3 7#a7 ,if two events or causes do not concur1 the probability of one or the other occurring is the sum of the separate probabilities4 ,a die cannot turn up both ace and six2 but the probability in favour of each is #a_/f3 therefore1 the probability in favour of one or the other is #a_/c4 ,death can hardly occur from both burning and drowning3 if #a in #ajjj is burned and #b in #ajjj are drowned1 the probability of being burned or drowned is #c_/ajjj4 7#b7 ,if two events are independent1 having neither connection nor repugnance1 the probability of their concurring is found by multiplying together the separate probabilities of each occurring4 ,if in walking down a certain street ,i meet ,a once in four times1 and ,b once in three times1 ,i ought 7by mere chance7 to meet both once in twelve times3 for in twelve occasions ,i meet ,b four times2 but once in four ,i meet ,a4 ,this is a very important rule in scientific investigation1 since it enables us to detect the presence of causation4 ,for if the coincidence of two events is more or less frequent than it would be if they were entirely independent1 there is either connection or repugnance between them4 ,if1 e4g41 in walking down the street ,i meet both ,a and ,b oftener than once in twelve times1 they may be engaged in similar business1 calling them from their offices at about the same hour4 ,if ,i meet them both less often than once in twelve times1 they may belong to the same office1 where one acts as a substitute for the other4 ,similarly1 if in a multitude of throws a die turns six oftener than once in six times1 it is not a fair one3 that is1 there is a cause favouring the turning of six4 ,if of #bj1jjj people #ejj see apparitions and #ajj have friends murdered1 the chance of any man having both experiences is #a_/hjjj2 but if each lives on the average #cjj1jjj hours1 the chance of both events occurring in the same hour is #a_/bdjjjjjjjj4 ,if the two events occur in the same hour oftener than this1 there is more than a chance coincidence4 ,the more minute a cause of connection or repugnance between events1 the longer the series of trials or instances necessary to bring out its influence3 the less a die is loaded1 the more casts must be made before it can be shown that a certain side tends to recur oftener than once in six4 7#c7 ,the rule for calculating the probability of a dependent event is the same as the above2 for the concurrence of two independent events is itself dependent upon each of them occurring4 ,my meeting with both ,a and ,b in the street is dependent on my walking there and on my meeting one of them4 ,similarly1 if ,a is sometimes a cause of ,b 7though liable to be frustrated71 and ,b sometimes of ,c 7,c and ,b having no causes independent of ,b and ,a respectively71 the occurrence of ,c is dependent on that of ,b1 and that again on the occurrence of ,a4 ,hence we may state the rule3 ,if two events are dependent each on another1 so that if one occur the second may 7or may not71 and if the second a third2 whilst the third never occurs without the second1 nor the second without the first2 the probability that if the first occur the third will1 is found by multiplying together the fractions expressing the probability that the first is a mark of the second and the second of the third4 ,upon this principle the value of hearsay evidence or tradition deteriorates1 and generally the cogency of any argument based upon the combination of approximate generalisations dependent on one another or self-infirmative4 ,if there are two witnesses1 ,a and ,b1 of whom ,a saw an event1 whilst ,b only heard ,a relate it 7and is therefore dependent on ,a71 what credit is due to ,b's recital8 ,suppose the probability of each man's being correct as to what he says he saw1 or heard1 is #c_/d3 then 7#c_/d #c_/d #i_/af7 the probability that ,b's story is true is a little more than #a_/b4 ,for if in #af attestations ,a is wrong #d times1 ,b can only be right in #c_/d of the remainder1 or #i times in #af4 ,again1 if we have the ,approximate ,generalisations1 ',most attempts to reduce wages are met by strikes1' and ',most strikes are successful1' and learn1 on statistical inquiry1 that in every hundred attempts to reduce wages there are #hj strikes1 and that #gj p4c4 of the strikes are successful1 then #ef p4c4 of attempts to reduce wages are unsuccessful4 ,of course this method of calculation cannot be quantitatively applied if no statistics are obtainable1 as in the testimony of witnesses2 and even if an average numerical value could be attached to the evidence of a certain class of witnesses1 it would be absurd to apply it to the evidence of any particular member of the class without taking account of his education1 interest in the case1 prejudice1 or general capacity4 ,still1 the numerical illustration of the rapid deterioration of hearsay evidence1 when less than quite veracious1 puts us on our guard against rumour4 ,to retail rumour may be as bad as to invent an original lie4 7#d7 ,if an event may coincide with two or more other independent events1 the probability that they will together be a sign of it1 is found by multiplying together the fractions representing the improbability that each is a sign of it1 and subtracting the product from unity4 ,this is the rule for estimating the cogency of circumstantial evidence and analogical evidence2 or1 generally1 for combining approximate generalisations self-corroboratively4 ,if1 for example1 each of two independent circumstances1 ,a and ,b1 indicates a probability of #f to #a in favour of a certain event2 taking #a to represent certainty1 #a-f_/g is the improbability of the event1 notwithstanding each circumstance4 ,then #a_/g #a_/g #a_/di1 the improbability of both proving it4 ,therefore the probability of the event is #dh to #a4 ,the matter may be plainer if put thus3 ,a's indication is right #f times in #g1 or #db in #di2 in the remaining #g times in #di1 ,b's indication will be right #f times4 ,therefore1 together they will be right #dh times in #di4 ,if each of two witnesses is truthful #f times in #g1 one or the other will be truthful #dh times in #di4 ,but they will not be believed unless they agree2 and in the #db cases of ,a being right1 ,b will contradict him #f times2 so that they only concur in being right #cf times4 ,in the remaining #g times in which ,a is wrong1 ,b will contradict him #f times1 and once they will both be wrong4 ,it does not follow that when both are wrong they will concur2 for they may tell very different stories and still contradict one another4 ,if in an analogical argument there were #h points of comparison1 #e for and #c against a certain inference1 and the probability raised by each point could be quantified1 the total value of the evidence might be estimated by doing similar sums for and against1 and subtracting the unfavourable from the favourable total4 ,when approximate generalisations that have not been precisely quantified combine their evidence1 the cogency of the argument increases in the same way1 though it cannot be made so definite4 ,if it be true that most poets are irritable1 and also that most invalids are irritable1 a still greater proportion will be irritable of those who are both invalids and poets4 ,on the whole1 from the discussion of probabilities there emerge four principal cautions as to their use3 ,not to make a pedantic parade of numerical probability1 where the numbers have not been ascertained2 ,not to trust to our feeling of what is likely1 if statistics can be obtained2 ,not to apply an average probability to special classes or individuals without inquiring whether they correspond to the average type2 and ,not to trust to the empirical probability of events1 if their causes can be discovered and made the basis of reasoning which the empirical probability may be used to verify4 ,the reader who wishes to pursue this subject further should read a work to which the foregoing chapter is greatly indebted1 ,dr4 ,venn's ,logic of ,chance4 ,,chapter ,,xxi ,,division ,,and ,,classification #a4 ,classification1 in its widest sense1 is a mental grouping of facts or phenomena according to their resemblances and differences1 so as best to serve some purpose4 ,a mental grouping3 for although in museums we often see the things themselves arranged in classes1 yet such an arrangement only contains specimens representing a classification4 ,the classification itself may extend to innumerable objects most of which have never been seen at all4 ,extinct animals1 for example1 are classified from what we know of their fossils2 and some of the fossils may be seen arranged in a museum2 but the animals themselves have disappeared for many ages4 ,again1 things are classed according to their resemblances and differences3 that is to say1 those that most closely resemble one another are classed together on that ground2 and those that differ from one another in important ways1 are distributed into other classes4 ,the more the things differ1 the wider apart are their classes both in thought and in the arrangements of a museum4 ,if their differences are very great1 as with animals1 vegetables and minerals1 the classing of them falls to different departments of thought or science1 and is often represented in different museums1 zoological1 botanical1 mineralogical4 ,we must not1 however1 suppose that there is only one way of classifying things4 ,the same objects may be classed in various ways according to the purpose in view4 ,for gardening1 we are usually content to classify plants into trees1 shrubs1 flowers1 grasses and weeds2 the ordinary crops of ,english agriculture are distinguished1 in settling their rotation1 into white and green2 the botanist divides the higher plants into gymnosperms and angiosperms1 and the latter into monocotyledons and dicotyledons4 ,the principle of resemblance and difference is recognised in all these cases2 but what resemblances or differences are important depends upon the purpose to be served4 ,purposes are either 77 special or practical1 as in gardening or hunting1 or 77 general or scientific1 as in ,botany or ,zoology4 ,the scientific purpose is merely knowledge2 it may indeed subserve all particular or practical ends1 but has no other end than knowledge directly in view4 ,and whilst1 even for knowledge1 different classifications may be suitable for different lines of inquiry1 in ,botany and ,zoology the ,morphological ,classification is that which gives the most general and comprehensive knowledge 7see ,huxley1 ,on the ,classification of ,animals1 ch4 #a74 ,most of what a logician says about classification is applicable to the practical kind2 but the scientific 7often called ',natural ,classification'71 as the most thorough and comprehensive1 is what he keeps most constantly before him4 ,scientific classification comes late in human history1 and at first works over earlier classifications which have been made by the growth of intelligence1 of language1 and of the practical arts4 ,even in the distinctions recognised by animals1 may be traced the grounds of classification3 a cat does not confound a dog with one of its own species1 nor water with milk1 nor cabbage with fish4 ,but it is in the development of language that the progress of instinctive classification may best be seen4 ,the use of general names implies the recognition of classes of things corresponding to them1 which form their denotation1 and whose resembling qualities1 so far as recognised1 form their connotation2 and such names are of many degrees of generality4 ,the use of abstract names shows that the objects classed have also been analysed1 and that their resembling qualities have been recognised amidst diverse groups of qualities4 ,of the classes marked by popular language it is worth while to distinguish two sorts 7cf4 chap4 xix4 #d73 ,kinds1 and those having but few points of agreement4 ,but the popular classifications1 made by language and the primitive arts1 are very imperfect4 ,they omit innumerable things which have not been found useful or noxious1 or have been inconspicuous1 or have not happened to occur in the region inhabited by those who speak a particular language2 and even things recognised and named may have been very superficially examined1 and therefore wrongly classed1 as when a whale or porpoise is called a fish1 or a slowworm is confounded with snakes4 ,a scientific classification1 on the other hand1 aims at the utmost comprehensiveness1 ransacking the whole world from the depths of the earth to the remotest star for new objects1 and scrutinising everything with the aid of crucible and dissecting knife1 microscope and spectroscope1 to find the qualities and constitution of everything1 in order that it may be classed among those things with which it has most in common and distinguished from those other things from which it differs4 ,a scientific classification continually grows more comprehensive1 more discriminative1 more definitely and systematically coherent4 ,hence the uses of classification may be easily perceived4 #b4 ,the first use of classification is the better understanding of the facts of ,nature 7or of any sphere of practice72 for understanding consists in perceiving and comprehending the likeness and difference of things1 in assimilating and distinguishing them2 and1 in carrying out this process systematically1 new correlations of properties are continually disclosed4 ,thus classification is closely analogous to explanation4 ,explanation has been shown 7chap4 xix4 #e7 to consist in the discovery of the laws or causes of changes in ,nature2 and laws and causes imply similarity1 or like changes under like conditions3 in the same way classification consists in the discovery of resemblances in the things that undergo change4 ,we may say 7subject to subsequent qualifications7 that ,explanation deals with ,nature in its dynamic1 ,classification in its static aspect4 ,in both cases we have a feeling of relief4 ,when the cause of any event is pointed out1 or an object is assigned its place in a system of classes1 the gaping wonder1 or confusion1 or perplexity1 occasioned by an unintelligible thing1 or by a multitude of such things1 is dissipated4 ,some people are more than others susceptible of this pleasure and fastidious about its purity4 ,a second use of classification is to aid the memory4 ,it strengthens memory1 because one of the conditions of our recollecting things is1 that they resemble what we last thought of2 so that to be accustomed to study and think of things in classes must greatly facilitate recollection4 ,but1 besides this1 a classification enables us easily to run over all the contrasted and related things that we want to think of4 ,explanation and classification both tend to rationalise the memory1 and to organise the mind in correspondence with ,nature4 ,every one knows how a poor mind is always repeating itself1 going by rote through the same train of words1 ideas1 actions2 and that such a mind is neither interesting nor practical4 ,it is not practical1 because the circumstances of life are rarely exactly repeated1 so that for a present purpose it is rarely enough to remember only one former case2 we need several1 that by comparing 7perhaps automatically7 their resemblances and differences with the one before us1 we may select a course of action1 or a principle1 or a parallel1 suited to our immediate needs4 ,greater fertility and flexibility of thought seem naturally to result from the practice of explanation and classification4 ,but it must be honestly added1 that the result depends upon the spirit in which such study is carried on2 for if we are too fond of finality1 too eager to believe that we have already attained a greater precision and comprehension than are in fact attainable1 nothing can be more petrific than 'science1' and our last state may be worse than the first4 ,of this1 students of ,logic have often furnished examples4 #c4 ,classification may be either ,deductive or ,inductive2 that is to say1 in the formation of classes1 as in the proof of propositions1 we may1 on the whole1 proceed from the more to the less1 or from the less to the more general2 not that these two processes are entirely independent4 ,if we begin with some large class1 such as ',animal1' and subdivide it deductively into ,vertebrate and ,invertebrate1 yet the principle of division 7namely1 central structure7 has first been reached by a comparison of examples and by generalisation2 if1 on the other hand1 beginning with individuals1 we group them inductively into classes1 and these again into wider ones 7as dogs1 rats1 horses1 whales and monkeys into mammalia7 we are guided both in special cases by hypotheses as to the best grounds of resemblance1 and throughout by the general principle of classification--to associate things that are alike and to separate things that are unlike4 ,this principle holds implicitly a place in classification similar to that of causation in explanation2 both are principles of intelligence4 ,here1 then1 as in proof1 induction is implied in deduction1 and deduction in induction4 ,still1 the two modes of procedure may be usefully distinguished3 in deduction1 we proceed from the idea of a whole to its parts1 from general to special2 in induction1 from special 7or particular7 to general1 from parts to the idea of a whole4 #d4 ,the process of ,deductive ,classification1 or ,formal ,division1 may be represented thus3 ,a ------------------- ,a ,b ,a b ---------- ---------- ,a ,b ,c ,a ,b c ,a b ,c ,a b c ,given any class 7,a7 to be divided3 #a4 ,select one important character1 attribute1 or quality 7,b71 not common to all the individuals comprehended in the class1 as the basis of division 7fundamentum divisionis74 #b4 ,proceed by ,dichotomy2 that is1 cut the given class into two1 one having the selected attribute 7say1 ,b71 the other not having it 7b74 ,this1 like all formal processes1 assumes the principles of ,contradiction and ,excluded ,middle1 that ',no ,a is both ,b and not-,b1' and that ',every ,a is either ,b or not-,b' 7chap4 vi4 #c72 and if these principles are not true1 or not applicable1 the method fails4 ,when a class is thus subdivided1 it may be called1 in relation to its subclasses1 a ,genus2 and in relation to it1 the subclasses may be called ,species3 thus--genus ,a1 species ,,ab and ,ab1 etc4 #c4 ,proceed gradually in the order of the importance of characters2 that is1 having divided the given class1 subdivide on the same principle the two classes thence arising2 and so again and again1 step by step1 until all the characters are exhausted3 ,divisio ne fiat per saltum4 ,suppose we were to attempt an exhaustive classification of things by this method1 we must begin with ',all ,things1' and divide them 7say7 into phenomenal and not-phenomenal1 and then subdivide phenomena1 and so on1 thus3 ,all ,things ------------------ ,phenomenal ,not-phenomenal -------------------- ,extended ,unextended 7e4g41 ,pleasure and ,pain7 ---------------- ,resistant ,not-resistant 7,matter7 7,space7 ------------------- ,gravitating ,not-gravitating ----------- ,simple ,compound ,having subdivided ',simple' by all possible characters1 we must then go back and similarly subdivide ,not-phenomenal1 ,unextended1 ,not-resistant1 ,not-gravitating1 and ,compound4 ,now1 if we knew all possible characters1 and the order of their importance1 we might prepare a priori a classification of all possible things2 at least1 of all things that come under the principles of ,contradiction and ,excluded ,middle4 ,many of our compartments might contain nothing actual2 there may1 for example1 be nothing that is not phenomenal to some mind1 or nothing that is extended and not-resistant 7no vacuum71 and so forth4 ,this would imply a breach of the rule1 that the dividing quality be not common to the whole class2 but1 in fact1 doubts have been1 and are1 seriously entertained whether these compartments are filled or not4 ,if they are not1 we have concepts representing nothing1 which have been generated by the mere force of grammatical negation1 or by the habit of thinking according to the principle of ,excluded ,middle2 and1 on the strength of these empty concepts1 we have been misled into dividing by an attribute1 which 7being universal7 cannot be a fundamentum divisionis4 ,but though in such a classification places might be empty1 there would be a place for everything2 for whatever did not come into some positive class 7such as ,gravitating7 must fall under one of the negative classes 7the ',nots'7 that run down the right-hand side of the ,table and of its subdivisions4 ,this is the ideal of classification4 ,unfortunately we have to learn what characters or attributes are possible1 by experience and comparison2 we are far from knowing them all3 and we do not know the order of their importance2 nor are we even clear what 'important' means in this context1 whether 'widely prevalent1' or 'ancient1' or 'causally influential1' or 'indicative of others4' ,hence1 in classifying actual things1 we must follow the inductive method of beginning with particulars1 and sorting them according to their likeness and difference as discovered by investigation4 ,the exceptional cases1 in which deduction is really useful1 occur where certain limits to the number and combination of qualities happen to be known1 as they may be in human institutions1 or where there are mathematical conditions4 ,thus1 we might be able to classify orders of ,architecture1 or the classical metres and stanzas of ,english poetry2 though1 in fact1 these things are too free1 subtle and complex for deductive treatment3 for do not the ,arts grow like trees8 ,the only sure cases are mathematical2 as we may show that there are possible only three kinds of plane triangles1 four conic sections1 five regular solids4 #e4 ,the rules for testing a ,division are as follows3 #a4 ,each ,sub-class1 or ,species1 should comprise less than the ,class1 or ,genus1 to be divided4 ,this provides that the division shall be a real one1 and not based upon an attribute common to the whole class2 that1 therefore1 the first rule for making a division shall have been adhered to4 ,but1 as in #d1 we are here met by a logical difficulty4 ,suppose that the class to be divided is ,a1 and that we attempt to divide upon the attribute ,b1 into ,,ab and ,ab2 is this a true division1 if we do not know any ,a that is not ,b8 ,as far as our knowledge extends1 we have not divided ,a at all4 ,on the other hand1 our knowledge of concrete things is never exhaustive2 so that1 although we know of no ,a that is not ,b1 it may yet exist1 and we have seen that it is a logical caution not to assume what we do not know4 ,in a deductive classification1 at least1 it seems better to regard every attribute as a possible ground of division4 ,hence1 in the above division of ',all ,things1'--',not-phenomenal1' ',extended-,not-resistant1' ',resistant-,not-gravitating1' appear as negative classes 7that is1 classes based on the negation of an attribute71 although their real existence may be doubtful4 ,but1 if this be justifiable1 we must either rewrite the first test of a division thus3 ',each sub-class should possibly comprise less than the class to be divided'2 or else we must confine the test to 7a7 thoroughly empirical divisions1 as in dividing ,colour into ,red and ,not-red1 where we know that both sub-classes are real2 and 7b7 divisions under demonstrable conditions--as in dividing the three kinds of triangles by the quality equilateral1 we know that it is only applicable to acute-angled triangles1 and do not attempt to divide the right-angled or obtuse-angled by it4 #b4 ,the ,sub-classes taken together should be equal to the ,class to be divided3 the sum of the ,species constitutes the ,genus4 ,this provides that the division shall be exhaustive2 which dichotomy always secures1 according to the principle of ,excluded ,middle2 because whatever is not in the positive class1 must be in the negative3 ,red and ,not-red include all colours4 #c4 ,the ,sub-classes must be opposed or mutually exclusive3 ,species must not overlap4 ,this again is secured by dichotomy1 according to the principle of ,contradiction1 provided the division be made upon one attribute at a time4 ,but1 if we attempt to divide simultaneously upon two attributes1 as ',musicians' upon 'nationality' and 'method1' we get what is called a ,cross-division1 thus ',german ,musicians4' ',not-,german1' ',classical1' ',not-,classical2' for these classes may overlap1 the same men sometimes appearing in two groups--,bach in ',german' and ',classical1' ,pergolesi in ',not-,german' and ',classical4' ,if1 however1 we divide ,musicians upon these attributes successively1 cross division will be avoided1 thus3 ,musicians ------------------------ ,classical ,not-classical ------------ ------------ ,german ,not-,german ,german ,not-,german ,here no ,musician will be found in two classes1 unless he has written works in two styles1 or unless there are works whose style is undecided4 ,this unless--or unless may suggest caution in using dichotomy as a short cut to the classification of realities4 #d4 ,no ,sub-class must include anything that is not comprised in the class to be divided3 the ,genus comprises all the ,species4 ,we must not divide ,dogs into fox-terriers and dog-fish4 #f4 ,the process of ,inductive ,classification may be represented thus3 ,given any multitude of individuals to be classified3 7#a7 ,place together in groups 7or in thought7 those things that have in common the most1 the most widely diffused and the most important qualities4 7#b7 ,connect those groups which have1 as groups1 the greater resemblance1 and separate those that have the greater difference4 7#c7 ,demarcate1 as forming higher or more general classes1 those groups of groups that have important characters in common2 and1 if possible1 on the same principle1 form these higher classes into classes higher still3 that is to say1 graduate the classification upwards4 ,whilst in ,division the terms ',genus' and ',species' are entirely relative to one another and have no fixed positions in a gradation of classes1 it has been usual1 in ,inductive ,classification1 to confine the term ',species' to classes regarded as lowest in the scale1 to give the term ',genera' to classes on the step above1 and at each higher step to find some new term such as ',tribe1' ',order1' ',sub-kingdom1' ',kingdom'2 as may be seen by turning to any book on ,botany or ,zoology4 ,if1 having fixed our ,species1 we find them subdivisible1 it is usual to call the ,sub-species ',varieties4' ,suppose an attempt to classify by this method the objects in a sitting-room4 ,we see at a glance carpets1 mats1 curtains1 grates1 fire-irons1 coal-scuttles1 chairs1 sofas1 tables1 books1 pictures1 musical instruments1 etc4 ,these may be called ',species4' ,carpets and mats go together2 so do chairs and sofas2 so do grates1 fire-irons1 and coal-scuttles and so on4 ,these greater groups1 or higher classes1 are ',genera4' ,putting together carpets1 mats and curtains as 'warmth-fabrics'2 chairs1 sofas and tables as 'supports'2 books1 pictures and musical instruments as 'means of culture'2 these groups we may call ,orders4 ,sum up the whole as1 from the housewife's point of view1 'furniture4' ,if we then subdivide some of the species1 as books into poetry1 novels1 travels1 etc41 these ,sub-species may be considered ',varieties4' ,a ,classification thus made1 may be tested by the same rules as those given for testing a ,division2 but if it does not stand the test1 we must not infer that the classification is a bad one4 ,if the best possible1 it is good1 though formally imperfect3 whatever faults are found must then be charged upon the 'matter1' which is traditionally perverse and intractable4 ,if1 for example1 there is a hammock in the room1 it must be classed not with the curtains as a warmth-fabric1 but with the sofas as a support2 and books and pictures may be classed as1 in a peculiar sense1 means of culture1 though all the objects in the room may have been modified and assorted with a view to gratifying and developing good taste4 #g4 ,the difficulty of classifying natural objects is very great4 ,it is not enough to consider their external appearance3 exhaustive knowledge of their internal structure is necessary1 and of the functions of every part of their structure4 ,this is a matter of immense research1 and has occupied many of the greatest minds for very many years4 ,the following is a tabular outline of the classification of the ,animal ,kingdom ------------------- ,,sub-,,kingdom1 ,vertebrates ,invertebrates 7#aj ,sub-kingdom #e7 or ,phylum3 ------------------------------- ,sauropsida ,ichthyopsida --------- ----------- ,,class3 ,mammalia ,birds ,reptiles ,amphibia ,fishes ------------------------- ,,sub-,,class3 ,placental ,implacental ------------------- ,,division3 ,monodelphia ,didelphia ,ornithodelphia --------------------------------------- ,,order3 ,quadrumana ,rodentia ,carnivora ,ungulata ,ctacea1 etc4 ---------------------------------- ,,section3 ,pinnigrada ,plantigrada ,digitigrada 7,seals1 etc47 7,bears1 etc47 -------------------------------------- ,,genus3 ,mustelid ,viverrid ,hyanid ,canid ,felid 7,weasels1 etc47 7,civets1 etc47 --------------------------------------- ,,species3 ,lion ,tiger ,leopard ,puma ,lynx ,cat1 etc4 --------------------- ,,variety3 ,african ,syrian ,cave-lion 7extinct7 ,as there is not space enough to tabulate such a classification in full1 ,i have developed at each step the most interesting groups3 ,vertebrates1 ,mammalia1 ,monodelphia ,carnivora1 ,digitigrada1 ,felid1 ,lion4 ,most of the other groups in each grade are also subdivisible1 though some of them contain far fewer sub-classes than others4 ,to see the true character of this classification1 we must consider that it is based chiefly upon knowledge of existing animals4 ,some extinct animals1 known by their fossils1 find places in it2 for others new places have been made4 ,but it represents1 on the whole1 a cross-section1 or cross-sections of ,nature as developing in time2 and1 in order to give a just view of the relations of animals1 it must be seen in the light of other considerations4 ,the older systems of classification1 and the rules for making them1 seem to have assumed that an actual system of classes1 or of what ,mill calls ',kinds1' exists in nature1 and that the relations of ,kinds in this system are determined by quantity of resemblance in co-inherent qualities1 as the ground of their affinity4 #h4 ,darwin's doctrine of the origin of species affects the conception of natural classification in several ways1 7#a7 ,if all living things are blood-relations1 modified in the course of ages according to their various conditions of life1 'affinity' must mean 'nearness of common descent'2 and it seems irrational to propose a classification upon any other basis4 ,we have to consider the ,animal 7or the ,vegetable7 ,kingdom as a family tree1 exhibiting a long line of ancestors1 and 7descended from them7 all sorts of cousins1 first1 second1 third1 etc41 perhaps once1 twice1 or oftener 'removed4' ,animals in the relation of first cousins must be classed as nearer than second cousins1 and so on4 ,but1 if we accept this principle1 and are able to trace relationship1 it may not lead to the same results as would be reached by simply relying upon the present 'quantity of resemblance1' unless we understand this in a very particular way4 ,for the most obvious features of an animal may have been recently acquired2 which often happens with those characters that adapt an animal to its habits of life1 as the wings of a bat1 or the fish-like shape of a dolphin2 or as in cases of 'mimicry4' ,some butterflies1 snakes1 etc41 have grown to resemble closely1 in a superficial way1 other butterflies and snakes1 from which a stricter investigation widely separates them2 and this superficial resemblance is probably a recent acquisition1 for the sake of protection2 the imitated butterflies being nauseous1 and the imitated snakes poisonous4 ,on the other hand1 ancient and important traits of structure may1 in some species1 have dwindled into inconspicuous survivals or be still found only in the embryo2 so that only great knowledge and sagacity can identify them2 yet upon ancient traits1 though hidden1 classification depends4 ,the seal seems nearer allied to the porpoise than to the tiger1 the shrew nearer to the mouse than to the hedgehog2 and the ,tasmanian wolf looks more like a true wolf1 the ,tasmanian devil more like a badger1 than like a kangaroo3 yet the seal is nearer akin to the tiger1 the shrew to the hedgehog1 and the ,tasmanian flesh-eaters are marsupial1 like the kangaroo4 ,to overcome this difficulty we must understand the resemblance upon which classification is based to include resemblance of ,causation1 that is1 the fact itself of descent from common ancestors4 ,for organic beings1 all other rules of classification are subordinate to one3 trace the genealogy of every form4 ,by this rule we get a definite meaning for the phrase 'important or fundamental attribute' as determining organic classes2 namely1 most ancient1 or 'best serving to indicate community of origin4' ,grades of classification will be determined by such fundamental characters1 and may correspond approximately to the more general types 7now extinct7 from which existing animals have descended4 7#b7 ,by the hypothesis of development the fixity of species is discredited4 ,the lowest grade of a classification is made up not of well-defined types unchanging from age to age1 but of temporary species1 often connected by uncertain and indistinct varieties3 some of which may1 in turn1 if the conditions of their existence alter1 undergo such changes as to produce new species4 ,hence the notion that ,kinds exist in organic nature must be greatly modified4 ,during a given period of a few thousand years1 ,kinds may be recognised1 because1 under such conditions as now prevail in the world1 that period of time is insufficient to bring about great changes4 ,but1 if it be true that lions1 tigers1 and leopards have had a common ancestor1 from whose type they have gradually diverged1 it is plain that their present distinctness results only from the death of intermediate specimens and the destruction of intermediate varieties4 ,were it possible to restore1 by the evidence of fossils1 all the ranks of the great processions that have descended from the common ancestor1 there would nowhere occur a greater difference than between offspring and parents2 and the appearance of ,kinds existing in nature1 which is so striking in a museum or zoological garden1 would entirely vanish4 ,a classification1 then1 as formerly observed1 represents a cross-section of nature as developing in time3 could we begin at the beginning and follow this development down the course of time1 we should find no classes1 but an ever-moving1 changing1 spreading1 branching continuum4 ,it may be represented thus3 ,suppose an animal 7or plant7 ,a1 extending over a certain geographical area1 subject to different influences and conditions of climate1 food1 hill and plain1 wood and prairie1 enemies and rivals1 and undergoing modifications here and there in adaptation to the varying conditions of life3 then varieties appear4 ,these varieties1 diverging more and more1 become distinct species 7,,ab1 ,,ac1 ,,ad1 ,,ax74 ,some of these species1 the more widely diffused1 again produce varieties2 which1 in turn become species 7,,abe1 ,,abf1 ,,adg1 ,,adh74 ,from these1 again1 ,,abe1 ,,abfi1 ,,abfj1 ,,ac1 ,,adhk1 ,,adhl1 ,,adhm1 the extant species1 descend4 ,a _/ _/ _/ _/ _/ ,,ab ,,ac ,,ad ,,ax _/ _/ _/ _/ _/ _/ ,,abe ,,abf ,,adg ,,adh _/ _/ _/ _/ _/ _/ _/ _/ _/ ,,abe ,,abfi ,,abfj ,,ac ,,adhk ,,adhl ,,adhm ,if in this age a classifier appears1 he finds seven living species1 which can be grouped into four genera 7,,abe1 ,,abf1 ,,ac1 ,,adh71 and these again into three ,families 7,,ab1 ,,ac1 ,,ad71 all forming one ,order4 ,but the animals which were their ancestors are all extinct4 ,if the fossils of any of them--say ,,ab1 ,,adg and ,,ax--can be found1 he has three more species1 one more genus 7,,adg71 and one more family 7,,ax74 ,for ,,ac1 which has persisted unchanged1 and ,,ax1 which has become extinct1 are both of them ,families1 each represented by only one species4 ,it seems necessary to treat such ancient types as species on a level with extant forms2 but the naturalist draws our attention to their archaic characteristics1 and tries to explain their places in the order of evolution and their relationships4 ,but now suppose that he could find a fossil specimen of every generation 7hundreds of thousands of generations71 from ,,abfi1 etc41 up to ,a2 then1 as each generation would only differ from the preceding as offspring from parents1 he would be unable at any point to distinguish a species2 at most1 he would observe a slightly marked variety4 ,,abfi and ,,abfj would grow more and more alike1 until they became indistinguishable in ,,abf2 ,,abf and ,,abe would merge into ,,ab2 ,,ab1 ,,ac1 ,,ad and ,,ax would merge into ,a4 ,hence1 the appearance of species is due to our taking cross-sections of time1 or comparing forms that belong to periods remote from one another 7like ,,ax1 ,,adg1 and ,,adhk1 or ,,ad1 ,,adh and ,,adhk71 and this appearance of species depends upon the destruction of ancestral intermediate forms4 7#c7 ,the hypothesis of development modifies the logical character of classification3 it no longer consists in a direct induction of co-inherent characters1 but is largely a deduction of these from the characters of earlier forms1 together with the conditions of variation2 in other words1 the definition of a species must1 with the progress of science1 cease to be a mere empirical law of co-inherence and become a derivative law of ,causation4 ,but this was already implied in the position that causation is the fundamental principle of the explanation of concrete things2 and accordingly1 the derivative character of species or kinds extends beyond organic nature4 #i4 ,the classification of inorganic bodies also depends on causation4 ,there is the physical classification into ,solids1 ,liquids1 and ,gases4 ,but these states of matter are dependent on temperature2 at different temperatures1 the same body may exist in all three states4 ,they cannot therefore be defined as solid1 liquid1 or gaseous absolutely1 but only within certain degrees of temperature1 and therefore as dependent upon causation4 ,similarly1 the geological classification of rocks1 according to relative antiquity 7primary1 secondary1 tertiary1 with their subdivisions71 and mode of formation 7igneous and aqueous71 rests upon causation2 and so does the chemical classification of compound bodies according to the elements that enter into them in definite proportions4 ,hence1 only the classification of the elements themselves 7amongst concrete things71 at present1 depends largely upon empirical ,coinherence4 ,if the elements remain irresolvable into anything simpler1 the definitions of the co-inherent characters that distinguish them must be reckoned amongst the ultimate ,uniformities of ,nature4 ,but if a definite theory of their origin both generally and severally1 whether out of ether-vortices1 or groups of electric corpuscles1 or whatnot1 shall ever gain acceptance1 similarity of genesis or causation will naturally be the leading consideration in classifying the chemical elements4 ,to find common principles of causation1 therefore1 constitutes the verification of every ,natural ,classification4 ,the ultimate explanation of nature is always causation2 the ,law of ,causation is the backbone of the system of ,experience4 ,,chapter ,,xxii ,,nomenclature1 ,,definition1 ,,predicables #a4 ,precision of thought needs precision of language for the recording of such thought and for communicating it to others4 ,we can often remember with great vividness persons1 things1 landscapes1 changes and actions of persons or things1 without the aid of language 7though words are often mixed with such trains of imagery71 and by this means may form judgments and inferences in particular cases2 but for general notions1 judgments and inferences1 not merely about this or that man1 or thing1 but about all men or all kinds of things1 we need something besides the few images we can form of them from observation4 ,even if we possess generic images1 say1 of 'horse' or 'cat' 7that is1 images formed1 like composite photographs1 by a coalescence of the images of all the horses or cats we have seen1 so that their common properties stand out and their differences frustrate and cancel one another71 these are useless for precise thought2 for the generic image will not correspond with the general appearance of horse or cat1 unless we have had proportional experience of all varieties and have been impartially interested in all2 and1 besides1 what we want for general thought is not a generic image of the appearance of things1 though it were much more definite and fairly representative than such images ever are1 but a general representation of their important characters2 which may be connected with internal organs1 such as none but an anatomist ever sees4 ,we require a symbol connected with the general character of a thing1 or quality1 or process1 as scientifically determined1 whose representative truth may be trusted in ordinary cases1 or may be verified whenever doubt arises4 ,such symbols are for most purposes provided by language2 ,mathematics and ,chemistry have their own symbols4 #b4 ,first there should be a name for every important meaning3 7a7 ,a ,nomenclature1 or system of the names of all classes of objects1 adapted to the use of each science4 ,thus1 in ,geology there are names for classes of rocks and strata1 in ,chemistry for the elements and their compounds1 in ,zoology and ,botany for the varieties and species of animals and plants1 their genera1 families and orders4 ,to have such names1 however1 is not the whole aim in forming a scientific language2 it is desirable that they should be systematically significant1 and even elegant4 ,names1 like other instruments1 ought to be efficient1 and the efficiency of names consists in conveying the most meaning with the least effort4 ,in ,botany and ,zoology this result is obtained by giving to each species a composite name which includes that of the genus to which it belongs4 ,the species of ,felid given in chap4 xvii4 #g1 are called ,felis leo 7lion71 ,felis tigris 7tiger71 ,felis leopardus 7leopard71 ,felis concolor 7puma71 ,felis lyncus 7,european lynx71 ,felis catus 7wild cat74 ,in ,chemistry1 the nomenclature is extremely efficient4 ,names of the simpler compounds are formed by combining the names of the elements that enter into them2 as ,hydrogen ,chloride1 ,hydrogen ,sulphide1 ,carbon ,dioxide2 and these can be given still more briefly and efficiently in symbols1 as ,h,cl1 ,h#b,s1 ,,co#b4 ,the symbolic letters are usually initials of the names of the elements3 as ,c ,carbon1 ,s ,sulphur2 sometimes of the ,latin name1 when the common name is ,english1 as ,fe ,iron4 ,each letter represents a fixed quantity of the element for which it stands1 viz41 the atomic weight4 ,the number written below a symbol on the right-hand side shows how many atoms of the element denoted enter into a molecule of the compound4 7b7 ,a ,terminology is next required1 in order to describe and define the things that constitute the classes designated by the nomenclature1 and to describe and explain their actions4 7i7 ,a name for every integral part of an object1 as head1 limb1 vertebra1 heart1 nerve1 tendon2 stalk1 leaf1 corolla1 stamen1 pistil2 plinth1 frieze1 etc4 7ii7 ,a name for every metaphysical part or abstract quality of an object1 and for its degrees and modes2 as extension1 figure1 solidity1 weight2 rough1 smooth1 elastic1 friable2 the various colours1 red1 blue1 yellow1 in all their shades and combinations and so with sounds1 smells1 tastes1 temperatures4 ,the terms of ,geometry are employed to describe the modes of figure1 as angular1 curved1 square1 elliptical2 and the terms of ,arithmetic to express the degrees of weight1 elasticity1 temperature1 pitch of sound4 ,when other means fail1 qualities are suggested by the names of things which exhibit them in a salient way2 figures by such terms as amphitheatre1 bowl-like1 pear-shaped1 egg-shaped2 colours by lias-blue1 sky-blue1 gentian-blue1 peacock-blue2 and similarly with sounds1 smells and tastes4 ,it is also important to express by short terms complex qualities1 as harmony1 fragrance1 organisation1 sex1 symmetry1 stratification4 7iii7 ,in the explanation of ,nature we further require suitable names for processes and activities3 as deduction1 conversion1 verification1 addition1 integration1 causation1 tendency1 momentum1 gravitation1 aberration1 refraction1 conduction1 affinity1 combination1 germination1 respiration1 attention1 association1 development4 ,there may sometimes be a difficulty in distinguishing the terms which stand for qualities from those that express activities1 since all qualities imply activities3 weight1 for example1 implies gravitation2 and the quality heat is also a kind of motion4 ,the distinction aimed at lies between a quality as perceived by means of an effect upon our senses 7as weight is resistance to our effort in lifting2 heat1 a sensation when we approach fire71 and that property of a body which is conceived to account for its energy 7as gravitation that brings a body to the ground1 or physical heat that expands an iron bar or works an engine74 ,the former class of words1 expressing qualities1 are chiefly used in description3 the latter class1 expressing activities1 are chiefly needed in explanation4 ,they correspond respectively1 like classification and explanation1 with the static and dynamic aspects of ,nature4 ,the terms of ordinary language fall into the same classes as those of science3 they stand for things1 classes of things1 parts1 or qualities1 or activities of things2 but they are far less precise in their signification4 ,as long as popular thought is vague its language must be vague2 nor is it desirable too strictly to correct the language whilst the thought is incorrigible4 ,much of the effect of poetry and eloquence depends upon the elasticity and indirect suggestiveness of common terms4 ,even in reasoning upon some subjects1 it is a mistake to aim at an unattainable precision4 ,it is better to be vaguely right than exactly wrong4 ,in the criticism of manners1 of fine art1 or of literature1 in politics1 religion and moral philosophy1 what we are anxious to say is often far from clear to ourselves2 and it is better to indicate our meaning approximately1 or as we feel about it1 than to convey a false meaning1 or to lose the warmth and colour that are the life of such reflections4 ,it is hard to decide whether more harm has been done by sophists who take a base advantage of the vagueness of common terms1 or by honest paralogists 7if ,i may use the word7 who begin by deceiving themselves with a plausible definiteness of expression1 and go on to propagate their delusions amongst followers eager for systematic insight but ignorant of the limits of its possibility4 #c4 ,a ,definition is necessary 7if possible7 for every scientific name4 ,to define a name is to give a precise statement of its meaning or connotation4 ,the name to be defined is the subject of a proposition1 whose predicate is a list of the fundamental qualities common to the things or processes which the subject denotes1 and on account of possessing which qualities this name is given to them4 ,thus1 a curve is a line of which no part is straight4 ,the momentum of a moving body is the product of its mass and its velocity 7these being expressed in numbers of certain units74 ,nitrogen is a transparent colourless gas1 atomic weight #ad1 specific gravity 4#igac1 not readily combining1 etc4 ,a lion is a monodelphian mammal1 predatory1 walking on its toes1 of nocturnal habits1 with a short rounded head and muzzle2 dental formula3 ,incisors 7#c-c7_/7c-c71 canines 7#a-a7_/7a_/a71 prmolars 7#c-c7_/7b-b71 molars 7#a-a7_/7a-a7 #cj2 four toes on the hind and five on the fore foot1 retractile claws1 prickly tongue1 light and muscular in build1 about #i-a_/b feet from muzzle to tip of tail1 tawny in colour1 the males maned1 with a tufted tail4 ,if anything answers to this description1 it is called a lion2 if not1 not3 for this is the meaning of the name4 ,for ordinary purposes1 it may suffice to give an ,incomplete ,definition2 that is1 a list of qualities not exhaustive1 but containing enough to identify the things denoted by the given name2 as if we say that a lion is 'a large tawny beast of prey with a tufted tail4' ,such purposes may also be served by a ,description2 which is technically1 a proposition mentioning properties sufficient to distinguish the things denoted1 but not the properties that enter into the definition2 as if nitrogen be indicated as the gas that constitutes #d_/e of the atmosphere4 #d4 ,the rules for testing a ,definition are3 ,i4--,as to its ,contents-- 7#a7 ,it must state the whole connotation of the name to be defined4 7#b7 ,it must not include any quality derivative from the connotation4 ,such a quality is called a ,proprium4 ,a breach of this rule can do no positive harm1 but it is a departure from scientific economy4 ,there is no need to state in the definition what can be derived from it2 and whatever can be derived by causation1 or by mathematical demonstration1 should be exhibited in that manner4 7#c7 ,it must not mention any circumstance that is not a part of the connotation1 even though it be universally found in the things denoted4 ,such a circumstance1 if not derivable from the connotation1 is called an ,accident4 ,that1 for example1 the lion at present only inhabits the ,old ,world1 is an accident3 if a species otherwise like a lion were found in ,brazil1 it would not be refused the name of lion on the score of locality4 ,whilst1 however1 the rules of ,logic have forbidden the inclusion of proprium or accident in a definition1 in fact the definitions of ,natural ,history often mention such attributes when characteristic4 ,indeed1 definitions of superordinate classes--,families and ,orders--not infrequently give qualities as generally found in the subordinate classes1 and at the same time mention exceptional cases in which they do not occur4 ,,ii4--,as to its ,expression-- 7#d7 ,a ,definition must not include the very term to be defined1 nor any cognate4 ,in defining 'lion' we must not repeat 'lion1' nor use 'leonine'2 it would elucidate nothing4 7#e7 ,it must not be put in vague language4 7#f7 ,it must not be in a negative form1 if a positive form be obtainable4 ,we must not be content to say that a lion is 'no vegetarian1' or 'no lover of daylight4' ,to define a curve as a line 'always changing its direction' may be better than as 'in no part straight4' #e4 ,the process of determining a ,definition is inseparable from classification4 ,we saw that classification consists in distributing things into groups according to their likenesses and differences1 regarding as a class those individuals which have most qualities in common4 ,in doing so we must1 of course1 recognise the common qualities or points of likeness2 and to enumerate these is to define the name of the class4 ,if we discover the qualities upon which a class is based by direct observation and induction1 by the same method we discover the definition of its name4 ,we saw also that classification is not merely the determination of isolated groups of things1 but a systematic arrangement of such groups in relation to one another4 ,hence1 again1 ,definitions are not independent1 but relative to one another2 and1 of course1 in the same way as classes are relative4 ,that is to say1 as a class is placed in subordination to higher or more comprehensive groups1 so the definition of its name is subordinate to that of their names2 and as a class stands in contrast with co-ordinate classes 7those that are in the same degree of subordination to the same higher groups71 so the definition of its name is in contrast or co-ordination with the definitions of their names4 ,lion is subordinate to ,felis1 to ,digitigrade1 to ,carnivore and so on up to ,animal2 and1 beyond the ,animal ,kingdom1 to ,phenomenon2 it is co-ordinate with tiger1 puma1 etc42 and more remotely it is co-ordinate with dog1 jackal1 wolf1 which come under ,canis--a genus co-ordinate with ,felis4 ,the definition of lion1 therefore1 is subordinate to that of ,felis1 and to all above it up to ,phenomenon2 and is co-ordinate with that of tiger1 and with all species in the same grade4 ,this is the ground of the old method of definition per genus et differentiam4 ,the genus being the next class above any species1 the differentia or ,difference consists of the qualities which mark that species in addition to those that mark the genus1 and which therefore distinguish it from all other species of the same genus4 ,in the above definition of lion1 for example1 all the properties down to light and muscular in build are generic1 that is1 are possessed by the whole genus1 ,felis2 and the remaining four 7size1 colour1 tufted tail1 and mane in the male7 are the ,difference or specific properties1 because in those points the lion contrasts with the other species of that genus4 ,differences may be exhibited thus3 ,lion4 ,tiger4 ,,size3 about #i-a_/b feet from nose ,about #aj feet4 to tip of tail4 ,,colour3 tawny4 ,warm tawny1 striped with black4 ,,tail3 tufted4 ,tapering4 ,,mane3 present in the male4 ,both sexes maneless4 ,there are other differences in the shape of the skull4 ,in defining lion1 then1 it would have been enough to mention the genus and the properties making up the ,difference2 because the properties of the genus may be found by turning to the definition of the genus2 and1 on the principle of economy1 whatever it is enough to do it is right to do4 ,to define 'by genus and difference' is a point of elegance1 when the genus is known2 but the only way of knowing it is to compare the individuals comprised in it and in co-ordinate genera1 according to the methods of scientific classification4 ,it may be added that1 as the genus represents ancestral derivation1 the predication of genus in a definition indicates the remote causes of the phenomena denoted by the name defined4 ,and this way of defining corresponds with the method of double naming by genus and species3 ,felis leo1 ,felis tigris1 etc42 ,vanessa ,atalanta1 ,vanessa ,io1 etc4 ,the so-called ,genetic ,definition1 chiefly used in ,mathematics1 is a rule for constructing that which a name denotes1 in such a way as to ensure its possessing the tributes connoted by the name4 ,thus1 for a circle3 ,take any point and1 at any constant distance from it1 trace a line returning into itself4 ,in ,chemistry a genetic definition of any compound might be given in the form of directions for the requisite synthesis of elements4 #f4 ,the chief difficulty in the definition of scientific names consists in determining exactly the nature of the things denoted by them1 as in classifying plants and animals4 ,if organic species are free growths1 continually changing1 however gradually1 according as circumstances give some advantage to one form over others1 we may expect to find such species branching into varieties1 which differ considerably from one another in some respects1 though not enough to constitute distinct species4 ,this is the case2 and1 consequently1 there arises some uncertainty in collecting from all the varieties those attributes which are common to the species as a whole2 and1 therefore1 of course1 uncertainty in defining the species4 ,the same difficulty may occur in defining a genus1 on account of the extent to which some of its species differ from others1 whilst having enough of the common character to deter the classifier from forming a distinct genus on their account4 ,on the other hand the occurrence of numerous intermediate varieties may make it difficult to distinguish genera or species at all4 ,even the ,kingdoms of plants and animals are hard to discriminate at the lowest levels of organisation4 ,now1 where there is a difficulty of classification there must be a corresponding difficulty of definition4 ,it has been proposed in such cases to substitute a ,type for a ,definition2 to select some variety of a species1 or species of a genus1 as exhibiting its character in an eminent degree1 and to regard other groups as belonging to the same species or genus1 according as they agree more with this type than with other types representing other species or genera4 ,but the selection of one group as typical implies a recognition of its attributes as prevailing generally 7though not universally7 throughout the species or genus2 and to recognise these attributes and yet refuse to enumerate them in a definition1 seems to be no great gain4 ,to enumerate the attributes of the type as an ,approximate ,definition of the species or genus1 true of most of the groups constituting the species or genus1 answers the same purpose1 is more explicit1 and can mislead no one who really attends to the exposition4 ,an approximate definition is1 indeed1 less misleading than the indication of a type2 for the latter method seems to imply that the group which is now typical has a greater permanence or reality than its co-ordinate groups2 whereas1 for aught we know1 one of the outside varieties or species may even now be superseding and extinguishing it4 ,but the statement of a definition as approximate1 is an honest confession that both the definition and the classification are 7like a provisional hypothesis7 merely the best account we can give of the matter according to our present knowledge4 #g4 ,the limits of ,definition are twofold3 7a7 ,a name whose meaning cannot be analysed cannot be defined4 ,this limitation meets us only in dealing with the names of the metaphysical parts or simple qualities of objects under the second requisite of a ,terminology4 ,resistance and weight1 colour and its modes1 many names of sounds1 tastes1 smells1 heat and cold--in fact1 whatever stands for an unanalysable perception1 cannot be made intelligible to any one who has not had experience of the facts denoted2 they cannot be defined1 but only exemplified4 ,a sort of genetic definition may perhaps be attempted1 as if we say that colour is the special sensation of the cones of the retina1 or that blue is the sensation produced by a ray of light vibrating about #fej1jjj1jjj1jjj1jjj times a second2 but such expressions can give no notion of our meaning to a blind man1 or to any one who has never seen a blue object4 ,nor can we explain what heat is like1 or the smell of tobacco1 to those who have never experienced them2 nor the sound of ,c #abh to one who knows nothing of the musical scale4 ,if we distinguish the property of an object from the sensation it excites in us1 we may define any simple property as 'the power of producing the sensation'2 the colour of a flower as the power of exciting the sensation of colour in us4 ,still1 this gives no information to the blind nor to the colour-blind4 ,abstract names may be defined by defining the corresponding concrete3 the definition of 'human nature' is the same as of 'man4' ,but if the corresponding concrete be a simple sensation 7as blue71 this being indefinable1 the abstract 7blueness7 is also indefinable4 7b7 ,the second limit of ,definition is the impossibility of exhausting infinity1 which would be necessary in order to convey the meaning of the name of any individual thing or person4 ,for1 as we saw in chap4 iv41 if in attempting to define a proper name we stop short of infinity1 our list of qualities or properties may possibly be found in two individuals1 and then it becomes the definition of a class-name or general name1 however small the actual class4 ,hence we can only give a ,description of that which a proper name denotes1 enumerating enough of its properties to distinguish it from everything else as far as our knowledge goes4 #h4 ,the five ,predicables 7,species1 ,genus1 ,difference1 ,proprium1 ,accident7 may best be discussed in connection with ,classification and ,definition2 and in giving an account of ,classification1 most of what has to be said about them has been anticipated4 ,their name1 indeed1 connects them with the doctrine of ,propositions2 for ,predicables are terms that may be predicated1 classified according to their connotative relation to the subject of a proposition 7that is1 according to the relation in which their connotation stands to the connotation of the subject73 nevertheless1 the significance of the relations of such predicates to a subject is derivative from the general doctrine of classification4 ,for example1 in the proposition ',x is ,y1' ,y must be one of the five sorts of predicables in relation to ,x2 but of what sort1 depends upon what ,x 7the subject7 is1 or means4 ,the subject of the proposition must be either a definition1 or a general connotative name1 or a singular name4 ,if ,x be a definition1 ,y must be a species2 for nothing but a general name can be predicated of a definition3 and1 strictly speaking1 it is only in relation to a definition 7as subject7 that species can be a predicable2 when it is called ,species predicabilis 7#a74 ,if ,x be a connotative name1 it is itself a species 7,species subjicibilis72 and the place of the subject of a proposition is the usual one for species4 ,the predicate1 ,y1 may then be related to the species in three different ways4 ,first1 it may be a definition1 exactly equivalent to the species2--in fact1 nothing else than the species in an explicit form1 the analysis of its connotation4 ,secondly1 the predicate may be1 or connote1 some part only of the definition or connotation of the species2 and then it is either genus 7#b71 or difference 7#c74 ,thirdly1 the predicate may connote no part of the definition1 and then it is either derivable from it1 being a proprium 7#d71 or not derivable from it1 being an accident 7#e74 ,these points of doctrine will be expanded and illustrated in subsequent pages4 ,if ,x be a singular name1 deriving connotation from its constituent terms 7chap4 iv4 #b71 as ',the present ,emperor of ,china1' it may be treated as a ,species subjicibilis4 ,then that he is 'an absolute monarch1' predicates a genus2 because that is a genus of ',emperor1' a part of the singular name that gives it connotation4 ,that he wears a yellow robe is a proprium1 derivable from the ceremonial of his court4 ,that he is thirty years of age is an accident4 ,but if ,x be a proper name1 having no connotation1 ,y must always be an accident2 since there can then be no definition of ,x1 and therefore neither species1 genus1 difference1 nor proprium4 ,hence1 that ',john ,doe is a man' is an accidental proposition3 'man' is not here a ,species predicabilis2 for the name might have been given to a dog or a mountain4 ,that is what enables the proposition to convey information3 it would be useless if the proper name implied 'humanity4' ',species' is most frequently used 7as in ,zoology7 for the class denoted by a general name2 but in ,logic it is better to treat it as a general name used connotatively for the attributes possessed in common by the things denoted1 and on account of which they are regarded as a class3 it is sometimes called the ,essence 7 #i74 ,in this connotative sense1 a species is implicitly what the definition is explicitly2 and therefore the two are always simply convertible4 ,thus1 ',a plane triangle' 7species7 is 'a figure enclosed by three straight lines' 7definition73 clearly we may equally say1 ',a figure enclosed by three straight lines is a plane triangle4' ,it is a simple identity4 ,a genus is also commonly viewed denotatively1 as a class containing smaller classes1 its species2 but in ,logic it is1 again1 better to treat it connotatively1 as a name whose definition is part of the definition of a given species4 ,a difference is the remainder of the definition of any species after subtracting a given genus4 ,hence1 the genus and difference together make up the species2 whence the method of definition per genus et differentiam 7ante1 #e74 ,whilst in ,botany and ,zoology the species is fixed at the lowest step of the classification 7varieties not being reckoned as classes71 and the genus is also fixed on the step next above it1 in ,logic these predicables are treated as movable up and down the ladder3 any lower class being species in relation to any higher2 which higher class1 wherever taken1 thus becomes a genus4 ,lion may logically be regarded as a species of digitigrade1 or mammal1 or animal2 and then each of these is a genus as to lion3 or1 again1 digitigrade may be regarded as a species of mammal1 or mammal as a species of animal4 ,the highest class1 however1 is never a species2 wherefore it is called a ,summum ,genus3 and the lowest class is never a genus2 wherefore it is called an ,infima ,species4 ,between these two any step may be either species or genus1 according to the relation in which it is viewed to other classes1 and is then called ,subaltern4 ,the summum genus1 again1 may be viewed in relation to a given universe or suppositio 7that is1 any limited area of existence now the object of attention71 or to the whole universe4 ,if we take the animal kingdom as our suppositio1 ,animal is the summum genus2 but if we take the whole universe1 ',all things' is the summum genus4 ,porphyry's tree is used to illustrate this doctrine4 ,it begins with a summum genus1 ',substance1' and descends by adding differences1 step by step1 to the infima species1 ',man4' ,it also illustrates ,division by ,dichotomy4 ,,substance _/ ,,corporeal ,,incorporeal ,,body _/ ,,animate ,,inanimate ,,living ,,body _/ ,,sensible ,,insensible ,,animal _/ ,,rational ,,irrational ,,man _/_/ _/_/ _/_/ _/_/ _/_/ _/_/ _/_/ ,socrates ,plato ,aristotle ,beginning with ',substance1' as summum genus1 and adding the difference ',corporeal1' we frame the species ',body4' ,taking ',body' as the genus and adding the difference ',animate1' we frame the species ',living ,body2' and so on till ',man' is reached2 which1 being infima species1 is only subdivisible into individuals4 ,but the division of ,man into individuals involves a change of principle2 it is a division of the denotation1 not an increase of the connotation as in the earlier steps4 ,only one side of each dichotomy is followed out in the 'tree'3 if the other side had been taken1 ,incorporeal ,substance would be ',spirit'2 which might be similarly subdivided4 ,genus and species1 then1 have a double relation4 ,in denotation the genus includes the species2 in connotation the species includes the genus4 ,hence the doctrine that by increasing the connotation of a name we decrease its denotation3 if1 for example1 to the definition of 'lion' we add 'inhabiting ,africa1' ,asiatic lions are no longer denoted by it4 ,on the other hand1 if we use a name to denote objects that it did not formerly apply to1 some of the connotation must be dropped3 if1 for example1 the name 'lion' be used to include 'pumas1' the tufted tail and mane can no longer be part of the meaning of the word2 since pumas have not these properties4 ,this doctrine is logically or formally true1 but it may not always be true in fact4 ,it is logically true2 because wherever we add to the connotation of a name1 it is possible that some things to which it formerly applied are now excluded from its denotation1 though we may not know of any such things4 ,still1 as a matter of fact1 an object may be discovered to have a property previously unknown1 and this property may be fundamental and co-extensive with the denotation of its name1 or even more widely prevalent4 ,the discovery that the whale is a mammal did not limit the class 'whale'2 nor did the discovery that lions1 dogs1 wolves1 etc41 walk upon their toes1 affect the application of any of these names4 ,similarly1 the extension of a name to things not previously denoted by it1 may not in fact alter its definition2 for the extension may be made on the very ground that the things now first denoted by it have been found to have the properties enumerated in its definition1 as when the name 'mammal' was applied to whales1 dolphins1 etc4 ,if1 however1 'mammal' had formerly been understood to apply only to land animals1 so that its definition included 7at least1 popularly7 the quality of 'living on the land1' this part of the connotation was of course lost when the denotation came to include certain aquatic animals4 ,a proprium is an attribute derived from the definition3 being either 7a7 implied in it1 or deducible from it1 as 'having its three angles equal to two right angles' may be proved from the definition of a triangle2 or 7b7 causally dependent on it1 as being 'dangerous to flocks' results from the nature of a wolf1 and as 'moving in an ellipse' results from the nature of a planet in its relation to the sun4 ,an accident is a property accompanying the defining attributes without being deducible from them4 ,the word suggests that such a property is merely 'accidental1' or there 'by chance'2 but it only means that we do not understand the connection4 ,proprium and ,accident bear the same relation to one another as ,derivative and ,empirical ,laws3 the predication of a proprium is a derivative law1 and the predication of an accident is an empirical law4 ,both accidents and empirical laws present problems1 the solution of which consists in reducing them1 respectively1 to propria and derivative laws4 ,thus the colour of animals was once regarded as an accident for which no reason could be given2 but now the colour of animals is regarded as an effect of their nature and habits1 the chief determinants of it being the advantage of concealment2 whilst in other cases1 as among brightly coloured insects and snakes1 the determinant may be the advantage of advertising their own noxiousness4 ,if such reasoning is sound1 colour is a proprium 7and if so1 it cannot logically be included in a definition2 but it is better to be judicious than formal74 ,if the colour of animals is a proprium1 we must recognise a distinction between ,inseparable and ,separable ,propria1 according as they do1 or do not1 always accompany the essence3 for mankind is regarded as one species2 but each colour1 white1 black or yellow1 is separable from it under different climatic conditions2 whilst tigers are everywhere coloured and striped in much the same way2 so that we may consider their colouring as inseparable1 in spite of exceptional specimens black or white or clouded4 ,the same distinction may be drawn between accidents4 ',inhabiting ,asia' is an ,inseparable ,accident of tiger1 but a ,separable ,accident of lion4 ,even the occasional characteristics and occupations of individuals are sometimes called separable accidents of the species2 as1 of man1 being colour-blind1 carpentering1 or running4 ,a proprium in the original signification of the term was peculiar to a species1 never found with any other1 and was therefore convertible with the subject2 but this restriction is no longer insisted on4 #i4 ,any predication of a genus1 difference or definition1 is a verbal1 analytic1 or essential proposition3 and any predication of a proprium or accident1 is a real1 synthetic1 or accidental proposition 7chap4 v4 #f74 ,a proposition is called verbal or analytic when the predicate is a part1 or the whole1 of the meaning of the subject2 and the subject being species1 a genus or difference is part1 and a definition is the whole1 of its meaning or connotation4 ,hence such a proposition has also been called explicative4 ,again1 a proposition is called real or synthetic when the predicate is no part of the meaning of the subject2 and1 the subject being species1 a proprium or accident is no part of its meaning or connotation4 ,hence such a proposition has been called ampliative4 ,as to ,essential and ,accidental1 these terms are derived from the doctrine of ,realism4 ,realists maintain that the essence of a thing1 or that which makes a thing to be what 7or of what kind7 it is1 also makes everything else of the same kind to be what it is4 ,the essence1 they say1 is not proper to each thing or separately inherent in it1 but is an ',universal' common to all things of that kind4 ,some hold that the universal nature of things of any kind is an ,idea existing 7apart from the things7 in the intelligible world1 invisible to mortal eye and only accessible to thought2 whence the ,idea is called a noumenon3 that only the ,idea is truly real1 and that the things 7say1 trees1 bedsteads and cities7 which appear to us in sense-perception1 and which therefore are called phenomena1 only exist by participating in1 or imitating1 the ,idea of each kind of them4 ,the standard of this school bears the legend ,universalia ante rem4 ,but others think that the ,universal does not exist apart from particular things1 but is their present essence2 gives them actuality as individual substances2 informs them1 or is their formal cause1 and thus makes them to be what they are of their kind according to the definition3 the universal lion is in all lions1 and is not merely similar1 but identical in all2 for thus the ,universal ,reason thinks and energises in ,nature4 ,this school inscribes upon its banners1 ,universalia in re4 ,to define anything1 then1 is to discover its essence1 whether transcendent or immanent2 and to predicate the definition1 or any part of it 7genus or difference71 is to enounce an essential proposition4 ,but a proprium1 being no part of a definition1 though it always goes along with it1 does not show what a thing is2 nor of course does an accident2 so that to predicate either of these is to enounce an accidental proposition4 ,another school of ,metaphysicians denies the existence of ,universal ,ideas or ,forms2 the real things1 according to them1 are individuals2 which1 so far as any of them resemble one another1 are regarded as forming classes2 and the only ,universal is the class-name1 which is applied universally in the same sense4 ,hence1 they are called ,nominalists4 ,the sense in which any name is applied1 they say1 is derived from a comparison of the individuals1 and by abstraction of the properties they have in common2 and thus the definition is formed4 ,universalia post rem is their motto4 ,some ,nominalists1 however1 hold that1 though ,universals do not exist in nature1 they do in our minds1 as ,abstract ,ideas or ,concepts2 and that to define a term is to analyse the concept it stands for2 whence1 these philosophers are called ,conceptualists4 ,such questions belong to ,metaphysics rather than to ,logic2 and the foregoing is a commonplace account of a subject upon every point of which there is much difference of opinion4 #aj4 ,the doctrine of the ,predicaments1 or ,categories1 is so interwoven with the history of speculation and especially of ,logic that1 though its vitality is exhausted1 it can hardly be passed over unmentioned4 ,the predicaments of ,aristotle are the heads of a classification of terms as possible predicates of a particular thing or individual4 ,hamilton 7,logic3 ,lect4 xi47 has given a classification of them2 which1 if it cannot be found in ,aristotle1 is an aid to the memory1 and may be thrown into a table thus3 ,substance 7#a7 ,quantity 7#b7 ,attribute ,quality 7#c7 ,relation 7#d7 ,where 7#e7 ,when 7#f7 ,action 7#g7 ,modes of ,relation ,passion 7#h7 ,posture 7#i7 ,habit 7#aj7 ,taking a particular thing or individual1 as ',socrates1' this is ,substance in the proper sense of the word1 and can never be a predicate1 but is the subject of all predicates4 ,we may assert of him 7#a7 ,substance in the secondary sense 7species or genus7 that he is a man or an animal2 7#b7 ,quantity1 of such a height or weight2 7#c7 ,quality1 fair or dark2 7#d7 ,relation1 shorter or taller than ,xanthippe2 7#e7 ,where1 at ,athens2 7#f7 ,when1 two thousand and odd years ago2 7#g7 ,action1 that he questions or pleads2 7#h7 ,passion1 that he is answered or condemned2 7#i7 ,posture1 that he sits or stands2 7#aj7 ,habit1 that he is clothed or armed4 ,thus illustrated 7,categori3 c4 #d71 the predicaments seem to be a list of topics1 generally useful for the analysis and description of an individual1 but wanting in the scientific qualities of rational arrangement1 derivation and limitation4 ,why are there just these heads1 and just so many8 ,it has been suggested that they were determined by grammatical forms3 for ,substance is expressed by a substantive2 ,quantity1 ,quality and ,relation are adjectival2 ,where and ,when1 adverbial2 and the remaining four are verbal4 ,it is true that the parts of speech were not systematically discriminated until some years after ,aristotle's time2 but1 as they existed1 they may have unconsciously influenced his selection and arrangement of the predicaments4 ,where a principle is so obscure one feels glad of any clue to it 7cf4 ,grote's ,aristotle1 c4 #c1 and ,zeller's ,aristotle1 c4 #f74 ,but whatever the origin and original meaning of the predicaments1 they were for a long time regarded as a classification of things2 and it is in this sense that ,mill criticises them 7,logic3 ,bk4 ,i4 c4 #c74 ,if1 however1 the predicaments are heads of a classification of terms predicable1 we may expect to find some connection with the predicables2 and1 in fact1 secondary ,substances are species and genus2 whilst the remaining nine forms are generally accidents4 ,but1 again1 we may expect some agreement between them and the fundamental forms of predication 7ante1 chap4 i4 #e1 and chap4 ii #d73 ,substance1 whether as the foundation of attributes1 or as genus and species1 implies the predication of co-inherence1 which is one mode of ,co-existence4 ,quantity is predicated as equality 7or inequality7 a mode of ,likeness2 and the other mode of ,likeness is involved in the predication of ,quality4 ,relation1 indeed1 is the abstract of all predication1 and ought not to appear in a list along with special forms of itself4 ',where' is position1 or ,co-existence in space2 and ',when' is position in time1 or ,succession4 ,action and ,passion are the most interesting aspect of ,causation4 ,posture and ,habit are complex modes of ,co-existence1 but too specialised to have any philosophic value4 ,now1 ,i do not pretend that this is what ,aristotle meant and was trying to say3 but if ,likeness1 ,co-existence1 ,succession and ,causation are fundamental forms of predication1 a good mind analysing the fact of predication is likely to happen upon them in one set of words or another4 ,by ,kant the word ',category' has been appropriated to the highest forms of judgment1 such as ,unity1 ,reality1 ,substance1 and ,cause1 under which the understanding reduces phenomena to order and thereby constitutes ,nature4 ,this change of meaning has not been made without a certain continuity of thought2 for forms of judgment are modes of predication4 ,but besides altering the lists of categories and greatly improving it1 ,kant has brought forward under an old title a doctrine so original and suggestive that it has extensively influenced the subsequent history of ,philosophy4 ,at the same time1 and probably as a result of the vogue of the ,kantian philosophy1 the word 'category' has been vulgarised as a synonym for 'class1' just as 'predicament' long ago passed from ,scholastic ,logic into common use as a synonym for 'plight4' ,a minister is said to be 'in a predicament1' or to fall under the 'category of impostors4' ,,chapter ,,xxiii ,,definition ,,of ,,common ,,terms #a4 ,ordinary words may need definition1 if in the course of exposition or argument their meaning is liable to be mistaken4 ,but as definition cannot give one the sense of a popular word for all occasions of its use1 it is an operation of great delicacy4 ,fixity of meaning in the use of single words is contrary to the genius of the common vocabulary2 since each word1 whilst having a certain predominant character1 must be used with many shades of significance1 in order to express the different thoughts and feelings of multitudes of men in endlessly diversified situations2 and its force1 whenever it is used1 is qualified by the other words with which it is connected in a sentence1 by its place in the construction of the sentence1 by the emphasis1 or by the pitch of its pronunciation compared with the other words4 ,clearly1 the requisite of a scientific language1 'that every word shall have one meaning well defined1' is too exacting for popular language2 because the other chief requisite of scientific language cannot be complied with1 'that there be no important meaning without a name4' ',important meanings1' or what seem such1 are too numerous to be thus provided for2 and new ones are constantly arising1 as each of us pursues his business or his pleasure1 his meditations or the excursions of his fancy4 ,it is impossible to have a separate term for each meaning2 and1 therefore1 the terms we have must admit of variable application4 ,an attempt to introduce new words is generally disgusting4 ,few men have mastered the uses of half the words already to be found in our classics4 ,much more would be lost than gained by doubling the dictionary4 ,it is true that1 at certain stages in the growth of a people1 a need may be widely felt for the adoption of new words3 such1 in our own case1 was the period of the ,tudors and early ,stuarts4 ,many fresh words1 chiefly from the ,latin1 then appeared in books1 were often received with reprobation and derision1 sometimes disappeared again1 sometimes established their footing in the language3 see ,the ,art of ,english ,poetry 7ascribed to ,puttenham71 ,book ,,iii4 chap4 #d1 and ,ben ,jonson's ,poetaster1 ,act4 ,v4 sc4 ,i4 ,good judges did not know whether a word was really called for3 even ,shakespeare thought 'remuneration' and 'accommodate' ridiculous4 ,but such national exigencies rarely arise2 and in our own time great authors distinguish themselves by the plastic power with which they make common words convey uncommon meanings4 ,fluid1 however1 as popular language is and ought to be1 it may be necessary for the sake of clear exposition1 or to steady the course of an argument1 to avoid either sophistry or unintentional confusion1 that words should be defined and discriminated2 and we must discuss the means of doing so4 #b4 ,scientific method is applicable1 with some qualifications1 to the definition of ordinary words4 ,classification is involved in any problem of definition3 at least1 if our object is to find a meaning that shall be generally acceptable and intelligible4 ,no doubt two disputants may1 for their own satisfaction1 adopt any arbitrary definition of a word important in their controversy2 or1 any one may define a word as he pleases1 at the risk of being misunderstood1 provided he has no fraudulent intention4 ,but in exposition or argument addressed to the public1 where words are used in some of their ordinary senses1 it should be recognised that the meaning of each one involves that of many others4 ,for language has grown with the human mind1 as representing its knowledge of the world3 this knowledge consists of the resemblances and differences of things and of the activities of things1 that is1 of classes and causes2 and as there is such order in the world1 so there must be in language3 language1 therefore1 embodies an irregular classification of things with their attributes and relations according to our knowledge and beliefs4 ,the best attempt 7known to me7 to carry out this view is contained in ,roget's ,thesaurus1 which is a classification of ,english words according to their meanings3 founded1 as the author tells us1 on the models of ,zoology and ,botany1 it has some of the requisites of a ,logical ,dictionary4 ,popular language1 indeed1 having grown up with a predominantly practical purpose1 represents a very imperfect classification philosophically considered4 ,things1 or aspects1 or processes of things1 that have excited little interest1 have often gone unnamed3 so that scientific discoverers are obliged1 for scientific purposes1 to invent thousands of new names4 ,strong interests1 on the other hand1 give such a colour to language1 that1 where they enter1 it is difficult to find any indifferent expressions4 ,consistency being much prized1 though often the part of a blockhead1 inconsistency implies not merely the absence of the supposed virtue1 but a positive vice3 ,beauty being attractive and ugliness the reverse1 if we invent a word for that which is neither1 'plainness1' it at once becomes tinged with the ugly4 ,we seem to love beauty and morality so much as to be almost incapable of signifying their absence without expressing aversion4 ,again1 the erroneous theories of mankind have often found their way into popular speech1 and their terms have remained there long after the rejection of the beliefs they embodied3 as--lunatic1 augury1 divination1 spell1 exorcism3 though1 to be sure1 such words may often be turned to good account1 besides the interest of preserving their original sense4 ,language is a record as well as an index of ideas4 ,language1 then1 being essentially classificatory1 any attempt to ascertain the meaning of a word1 far from neglecting its relations to others1 should be directed toward elucidating them4 ,every word belongs to a group1 and this group to some other larger group4 ,a group is sometimes formed by derivation1 at least so far as different meanings are marked merely by inflections1 as short1 shorter1 shorten1 shortly2 but1 for the most part1 is a conflux of words from many different sources4 ,repose1 depose1 suppose1 impose1 propose1 are not nearly connected in meaning2 but are severally allied in sense much more closely with words philologically remote4 ,thus repose is allied with rest1 sleep1 tranquillity2 disturbance1 unrest1 tumult2 whilst depose is1 in one sense1 allied with overthrow1 dismiss1 dethrone2 restore1 confirm1 establish2 and1 in another sense1 with declare1 attest1 swear1 prove1 etc4 ,groups of words1 in fact1 depend on their meanings1 just as the connection of scientific names follows the resemblance in character of the things denoted4 ,words1 accordingly1 stand related to one another1 for the most part1 though very irregularly1 as genus1 species1 and co-ordinate species4 ,taking repose as a genus1 we have as species of it1 though not exactly co-ordinate with one another1 tranquillity with a mental differentia 7repose of mind71 rest1 whether of mind or body1 sleep1 with the differentia of unconsciousness 7privative74 ,synonyms are species1 or varieties1 wherever any difference can be detected in them2 and to discriminate them we must first find the generic meaning2 for which there may1 or may not1 be a single word4 ,thus1 equality1 sameness1 likeness1 similarity1 resemblance1 identity1 are synonyms2 but1 if we attend to the ways in which they are actually used1 perhaps none of them can claim to be a genus in relation to the rest4 ,if so1 we must resort to a compound term for the genus1 such as 'absence of some sort of difference4' ,then equality is absence of difference in quantity2 sameness is often absence of difference in quality1 though the usage is not strict3 likeness1 similarity1 and resemblance1 in their actual use1 perhaps1 cannot be discriminated2 unless likeness be the more concrete1 similarity the more abstract2 but they may all be used compatibly with the recognition of more or less difference in the things compared1 and even imply this4 ,identity is the absence of difference of origin1 a continuity of existence1 with so much sameness from moment to moment as is compatible with changes in the course of nature2 so that egg1 caterpillar1 chrysalis1 butterfly may be identical for the run of an individual life1 in spite of differences quantitative and qualitative1 as truly as a shilling that all the time lies in a drawer4 ,co-ordinate ,species1 when positive1 have the least contrariety2 but there are also opposites1 namely1 negatives1 contradictories and fuller contraries4 ,these may be regarded as either co-ordinate genera or the species of co-ordinate genera4 ,thus1 repose being a genus1 not-repose is by dichotomy a co-ordinate genus and is a negative and contradictory2 then activity 7implying an end in view71 motion 7limited to matter71 disturbance 7implying changes from a state of calm71 tumult1 etc41 are co-ordinate species of not-repose1 and are therefore co-ordinate opposites1 or contraries1 of the species of repose4 ,as for correlative words1 like master and slave1 husband and wife1 etc41 it may seem far-fetched to compare them with the sexes of the same species of plants or animals2 but there is this resemblance between the two cases1 that sexual names are correlative1 as 'lioness1' and that one sex of a species1 like a correlative name1 cannot be defined without implying the other2 for if a distinctive attribute of one sex be mentioned 7as the lion's mane71 it is implied that the other wants it1 and apart from this implication the species is not defined3 just as the definition of 'master' implies a 'slave' to obey4 ,common words1 less precise than the terms of a scientific nomenclature1 differ from them also in this1 that the same word may occur in different genera4 ,thus1 sleep is a species of repose as above2 but it is also a species of unconsciousness1 with co-ordinate species swoon1 hypnotic state1 etc4 ,in fact1 every word stands under as many distinct genera1 at least1 as there are simple or indefinable qualities to be enumerated in its definition4 #c4 ,partially similar to a scientific nomenclature1 ordinary language has likewise a terminology for describing things according to their qualities and structure4 ,such is the function of all the names of colours1 sounds1 tastes1 contrasts of temperature1 of hardness1 of pleasantness2 in short1 of all descriptive adjectives1 and all names for the parts and processes of things4 ,any word connoting a quality may be used to describe many very different things1 as long as they agree in that quality4 ,but the quality connoted by a word1 and treated as always the same quality1 is often only analogically the same4 ,we speak of a great storm1 a great man1 a great book2 but great is in each case not only relative1 implying small1 and leaving open the possibility that what we call great is still smaller than something else of its kind1 but it is also predicated with reference to some quality or qualities1 which may be very different in the several cases of its application4 ,if the book is prized for wisdom1 or for imagination1 its greatness lies in that quality2 if the man is distinguished for influence1 or for courage1 his greatness is of that nature2 if the storm is remarkable for violence1 or for duration1 its greatness depends on that fact4 ,the word great1 therefore1 is not used for these things in the same sense1 but only analogically and elliptically4 ,similarly with good1 pure1 free1 strong1 rich1 and so on4 ',rest' has not the same meaning in respect of a stone and of an animal1 nor 'strong' in respect of thought and muscle1 nor 'sweet' in respect of sugar and music4 ,but here we come to the border between literal and figurative use2 every one sees that figurative epithets are analogical2 but by custom any figurative use may become literal4 ,again1 many general names of widely different meaning1 are brought together in describing any concrete object1 as an animal1 or a landscape1 or in defining any specific term4 ,this is the sense of the doctrine1 that any concrete thing is a conflux of generalities or universals3 it may at least be considered in this way2 though it seems more natural to say1 that an object presents these different aspects to a spectator1 who1 fully to comprehend it1 must classify it in every aspect4 #d4 ,the process of seeking a definition may be guided by the following maxims3 7#a7 ,find the usage of good modern authors2 that is 7as they rarely define a word explicitly71 consider what in various relations they use it to denote2 from which uses its connotation may be collected4 7#b7 ,but if this process yield no satisfactory result1 make a list of the things denoted1 and of those denoted by the co-ordinate and opposite words2 and observe the qualities in which the things denoted agree1 and in which they differ from those denoted by the contraries and opposites4 ,if 'civilisation' is to be defined1 make lists of civilised peoples1 of semi-civilised1 of barbarous1 and of savage3 now1 what things are common to civilised peoples and wanting in the others respectively8 ,this is an exercise worth attempting4 ,if poetry is to be defined1 survey some typical examples of what good critics recognise as poetry1 and compare them with examples of bad 'poetry1' literary prose1 oratory1 and science4 ,having determined the characteristics of each kind1 arrange them opposite one another in parallel columns4 ,whoever tries to define by this method a few important1 frequently occurring words1 will find his thoughts the clearer for it1 and will collect by the way much information which may be more valuable than the definition itself1 should he ever find one4 7#c7 ,if the genus of a word to be defined is already known1 the process may be shortened4 ,suppose the genus of poetry to be belles lettres 7that is1 'appealing to good taste'71 this suffices to mark it off from science2 but since literary prose and oratory are also belles lettres1 we must still seek the differentia of poetry by a comparison of it with these co-ordinate species4 ,a compound word often exhibits genus and difference upon its face3 as 're-turn1' 'inter-penetrate1' 'tuning-fork1' 'cricket-bat'2 but the two last would hardly be understood without inspection or further description4 ,and however a definition be discovered1 it is well to state it per genus et differentiam4 7#d7 ,in defining any term we should avoid encroaching upon the meaning of any of the co-ordinate terms2 for else their usefulness is lessened3 as by making 'law' include 'custom1' or 'wealth' include 'labour' or 'culture4' 7#e7 ,if two or more terms happen to be exactly synonymous1 it may be possible 7and1 if so1 it is a service to the language7 to divert one of them to any neighbouring meaning that has no determinate expression4 ,thus1 ,wordsworth and ,coleridge took great pains to distinguish between ,imagination and ,fancy1 which had become in common usage practically equivalent2 and they sought to limit 'imagination' to an order of poetic effect1 which 7they said7 had prevailed during the ,elizabethan age1 but had been almost lost during the ,gallo-classic1 and which it was their mission to restore4 ,co-ordinate terms often tend to coalesce and become synonymous1 or one almost supersedes the other1 to the consequent impoverishment of our speech4 ,at present proposition 7that something is the fact7 has almost driven out proposal 7that it is desirable to co-operate in some action74 ,even good writers and speakers1 by their own practice1 encourage this confusion3 they submit to ,parliament certain 'propositions' 7proposals for legislation71 or even make 'a proposition of marriage4' ,definition should counteract such a tendency4 7#f7 ,we must avoid the temptation to extend the denotation of a word so far as to diminish or destroy its connotation2 or to increase its connotation so much as to render it no longer applicable to things which it formerly denoted3 we should neither unduly generalise1 nor unduly specialise1 a term4 ,is it desirable to define education so as to include the 'lessons of experience'2 or is it better to restrict it as implying a personal educator8 ,if any word implies blame or praise1 we are apt to extend it to everything we hate or approve4 ,but coward cannot be so defined as to include all bullies1 nor noble so as to include every honest man1 without some loss in distinctness of thought4 ,the same impulses make us specialise words2 for1 if two words express approval1 we wish to apply both to whatever we admire and to refuse both to whatever displeases us4 ,thus1 a man may resolve to call no one great who is not good3 greatness1 according to him1 connotes goodness3 whence it follows that 7say7 ,napoleon ,i4 was not great4 ,another man is disgusted with greatness3 according to him1 good and great are mutually exclusive classes1 sheep and goats1 as in ,gray's wretched clench3 ,beneath the good how far1 yet far above the great4 ,in feet1 however 'good' and 'great' are descriptive terms1 sometimes applicable to the same object1 sometimes to different3 but 'great' is the wider term and applicable to goodness itself and also to badness2 whereas by making 'great' connote goodness it becomes the narrower term4 ,and as we have seen 7 #c71 such epithets may be applicable to objects on account of different qualities3 good is not predicated on the same ground of a man and of a horse4 7#g7 ,in defining any word1 it is desirable to bear in mind its derivation1 and to preserve the connection of meaning with its origin2 unless there are preponderant reasons for diverting it1 grounded on our need of the word to express a certain sense1 and the greater difficulty of finding any other word for the same purpose4 ,it is better to lean to the classical than to the vulgar sense of 'indifferent1' 'impertinent1' 'aggravating1' 'phenomenal4' 7#h7 ,rigorous definition should not be attempted where the subject does not admit of it4 ,some kinds of things are so complex in their qualities1 and each quality may manifest itself in so many degrees without ever admitting of exact measurement1 that we have no means of marking them off precisely from other things nearly allied1 similarly complex and similarly variable4 ,if so we cannot precisely define their names4 ,imagination and fancy are of this nature1 civilisation and barbarism1 poetry and other kinds of literary expression4 ,as to poetry1 some think it only exists in metre1 but hardly maintain that the metre must be strictly regular3 if not1 how much irregularity of rhythm is admissible8 ,others regard a certain mood of impassioned imagination as the essence of poetry2 but they have never told us how great intensity of this mood is requisite4 ,we also hear that poetry is of such a nature that the enjoyment of it is an end in itself2 but as it is not maintained that poetry must be wholly impersuasive or uninstructive1 there seems to be no means of deciding what amount or prominence of persuasion or instruction would transfer the work to the region of oratory or science4 ,such cases make the method of defining by the aid of a type really useful3 the difficulty can hardly be got over without pointing to typical examples of each meaning1 and admitting that there may be many divergences and unclassifiable instances on the border between allied meanings4 #e4 ,as science began from common knowledge1 the terms of the common vocabulary have often been adopted into the sciences1 and many are still found there3 such as weight1 mass1 work1 attraction1 repulsion1 diffusion1 reflection1 absorption1 base1 salt1 and so forth4 ,in the more exact sciences1 the vague popular associations with such words are hardly an inconvenience3 since those addicted to such studies do not expect to master them without undergoing special discipline2 and1 having precisely defined the terms1 they acquire the habit of thinking with them according to their assigned signification in those investigations to which they are appropriate4 ,it is in the ,social ,sciences1 especially ,economics and ,ethics1 that the use of popular terminology is at once unavoidable and prejudicial4 ,for the subject-matters1 industry and the conduct of life1 are every man's business2 and1 accordingly1 have always been discussed with a consciousness of their direct practical bearing upon public and private interests1 and therefore in the common language1 in order that everybody may as far as possible benefit by whatever light can be thrown upon them4 ,the general practice of ,economists and ,moralists1 however1 shows that1 in their judgment1 the good derived from writing in the common vocabulary outweighs the evil3 though it is sometimes manifest that they themselves have been misled by extra-scientific meanings4 ,to reduce the evil as much as possible1 the following precautions seem reasonable3 7#a7 ,to try to find and adopt the central meaning of the word 7say rent or money7 in its current or traditionary applications3 so as to lessen in the greater number of cases the jar of conflicting associations4 ,but if the central popular meaning does not correspond with the scientific conception to be expressed1 it may be better to invent a new term4 7#b7 ,to define the term with sufficient accuracy to secure its clear and consistent use for scientific purposes4 7#c7 ,when a popular term has to be used in a sense that departs from the ordinary one in such a way as to incur the danger of misunderstanding1 to qualify it by some adjunct or interpretation-clause4 ,the first of these rules is not always adhered to2 and1 in the progress of a science1 as subtler and more abstract relations are discovered amongst the facts1 the meaning of a term may have to be modified and shifted further and further from its popular use4 ,the term 'rent1' for example1 is used by economists1 in such a sense that they have to begin the discussion of the facts it denotes1 by explaining that it does not imply any actual payment by one man to another4 ,here1 for most readers1 the meaning they are accustomed to1 seems already to have entirely disappeared4 ,difficulties may1 however1 be largely overcome by qualifying the term in its various relations1 as produce-rents1 ground-rents1 customary rents1 and so forth1 7,cf4 ,dr4 ,keynes' ,scope and ,method of ,political ,economy1 chap4 #e47 #f4 ,definitions affect the cogency of arguments in many ways1 whether we use popular or scientific language4 ,if the definitions of our terms are vague1 or are badly abstracted from the facts denoted1 all arguments involving these terms are inconclusive4 ,there can be no confidence in reasoning with such terms2 since1 if vague1 there is nothing to protect us from ambiguity2 or1 if their meaning has been badly abstracted1 we may be led into absurdity--as if 'impudence' should be defined in such a way as to confound it with honesty4 ,again1 it is by definitions that we can best distinguish between ,verbal and ,real ,propositions4 ,whether a term predicated is implied in the definition of the subject1 or adds something to its meaning1 deserves our constant attention4 ,we often persuade ourselves that statements are profound and important1 when1 in fact1 they are mere verbal propositions4 ,it is just to give every man his due2 the greater good ought to be preferred to the less2 such dicta sound well--indeed1 too well6 ,for 'a man's due' means nothing else than what it is just to give him2 and 'the greater good' may mean the one that ought to be preferred3 these1 therefore1 are ,truisms4 ,the investigation of a definition may be a very valuable service to thought2 but1 once found1 there is no merit in repeating it4 ,to put forward verbal or analytic propositions1 or truisms1 as information 7except1 of course1 in explaining terms to the uninstructed71 shows that we are not thinking what we say2 for else we must become aware of our own emptiness4 ,every step forward in knowledge is expressed in a real or synthetic proposition2 and it is only by means of such propositions that information can be given 7except as to the meaning of words7 or that an argument or train of reasoning can make any progress4 ,opposed to a truism is a ,contradiction in ,terms2 that is1 the denying of a subject something which it connotes 7or which belongs to its definition71 or the affirming of it something whose absence it connotes 7or which is excluded by its definition74 ,a verbal proposition is necessarily true1 because it is tautologous2 a contradiction in terms is necessarily false1 because it is inconsistent4 ,yet1 as a rhetorical artifice1 or figure1 it may be effective3 that 'the slave is not bound to obey his master' may be a way of saying that there ought to be no slaves2 that 'property is theft1' is an uncompromising assertion of the communistic ideal4 ,similarly a truism may have rhetorical value3 that 'a ,negro is a man' has often been a timely reminder1 or even that a man's a man4 ,it is only when we fall into such contradiction or tautology by lapse of thought1 by not fully understanding our own words1 that it becomes absurd4 ,real ,propositions comprise the predication of ,propria and ,accidentia4 ,accidentia1 implying a sort of empirical law1 can only be established by direct induction4 ,but propria are deduced from 7or rather by means of7 the definition with the help of real propositions1 and this is what is called 'arguing from a ,definition4' ,thus1 if increasing capacity for co-operation be a specific character of civilisation1 'great wealth' may be considered as a proprium of civilised as compared with barbarous nations4 ,for co-operation is made most effectual by the division of labour1 and that this is the chief condition of producing wealth is a real proposition4 ,such arguments from definitions concerning concrete facts and causation require verification by comparing the conclusion with the facts4 ,the verification of this example is easy1 if we do not let ourselves be misled in estimating the wealth of barbarians by the ostentatious pearl and gold of kings and nobles1 where #ii per cent4 of the people live in penury and servitude4 ,the wealth of civilisation is not only great but diffused1 and in its diffusion its greatness must be estimated4 ,to argue from a definition may be a process of several degrees of complexity4 ,the simplest case is the establishing of a proprium as the direct consequence of some connoted attribute1 as in the above example4 ,if the definition has been correctly abstracted from the particulars1 the particulars have the attributes summarised in the definition2 and1 therefore1 they have whatever can be shown to follow from those attributes4 ,but it frequently happens that the argument rests partly on the qualities connoted by the class name and partly on many other facts4 ,in ,geometry1 the proof of a theorem depends not only upon the definition of the figure or figures directly concerned1 but also upon one or more axioms1 and upon propria or constructions already established4 ,thus1 in ,euclid's fifth ,proposition1 the proof that the angles at the base of an isosceles triangle are equal1 depends not only on the equality of the opposite sides1 but upon this together with the construction that shows how from the greater of two lines a part may be cut off equal to the less1 the proof that triangles that can be conceived to coincide are equal1 and the axiom that if equals be taken from equals the remainders are equal4 ,similarly1 in ,biology1 if colouring favourable to concealment is a proprium of carnivorous animals1 it is not deducible merely from their predatory character or any other attribute entering into the definition of any species of them1 but from their predatory character together with the causes summarised in the phrase ',natural ,selection'2 that is1 competition for a livelihood1 and the destruction of those that labour under any disadvantages1 of which conspicuous colouring would be one4 ,the particular coloration of any given species1 again1 can only be deduced by further considering its habitat 7desert1 jungle or snowfield73 a circumstance lying wholly outside the definition of the species4 ,the validity of an argument based partly or wholly on a definition depends1 in the first place1 on the existence of things corresponding with the definition--that is1 having the properties connoted by the name defined4 ,if there are no such things as isosceles triangles1 ,euclid's fifth ,proposition is only formally true1 like a theorem concerning the fourth dimension of space3 merely consistent with his other assumptions4 ,but if there be any triangles only approximately isosceles1 the proof applies to them1 making allowance for their concrete imperfection3 the nearer their sides approach straightness and equality the more nearly equal will the opposite angles be4 ,again1 as to the things corresponding with terms defined1 according to ,dr4 ,venn1 their 'existence' may be understood in several senses3 7#a7 merely for the reason1 like the pure genera and species of ,porphyry's tree2 the sole condition of whose being is logical consistency3 or 7#b7 for the imagination1 like the giants and magicians of romance1 the heroes of tragedy and the fairies of popular superstition2 whose properties may be discussed1 and verified by appeal to the right documents and authorities 7poems and ballads73 or 7#c7 for perception1 like plants1 animals1 stones and stars4 ,only the third class exist in the proper sense of the word4 ,but under a convention or hypothesis of existence1 we may argue from the definition of a fairy1 or a demigod1 or a dragon1 and deduce various consequences without absurdity1 if we are content with poetic consistency and the authority of myths and romances as the test of truth4 ,in the region of concrete objects1 whose properties are causes1 and neither merely fictions nor determinations of space 7as in ,geometry71 we meet with another condition of the validity of any argument depending on a definition3 there must not only be objects corresponding to the definition1 but there must be no other causes counteracting those qualities on whose agency our argument relies4 ,thus1 though we may infer from the quality of co-operation connoted by civilisation1 that a civilised country will be a wealthy one1 this may not be found true of such a country recently devastated by war or other calamity4 ,nor can co-operation always triumph over disadvantageous circumstances4 ,scandinavia is so poor in the gifts of nature favourable to industry1 that it is not wealthy in spite of civilisation3 still1 it is far wealthier than it would be in the hands of a barbarous people4 ,in short1 when arguing from a definition1 we can only infer the tendency of any causal characteristics included in it2 the unqualified realisation of such a tendency must depend upon the absence of counteracting causes4 ,as soon as we leave the region of pure conceptions and make any attempt to bring our speculations home to the actual phenomena of nature or of human life1 the verification of every inference becomes an unremitting obligation4 ,,chapter ,,xxiv ,,fallacies #a4 ,a ,fallacy is any failure to fulfil the conditions of proof4 ,if we neglect or mistake the conditions of proof unintentionally1 whether in our private meditations or in addressing others1 it is a ,paralogism3 but if we endeavour to pass off upon others evidence or argument which we know or suspect to be unsound1 it is a ,sophism4 ,fallacies1 whether paralogisms or sophisms1 may be divided into two classes3 7a7 the ,formal1 or those that can be shown to conflict with one or more of the truths of ,logic1 whether ,deductive or ,inductive2 as if we attempt to prove an universal affirmative in the ,third ,figure2 or to argue that1 as the average expectation of life for males at the age of #bj is #ai-a_/b years1 therefore ,alcibiades1 being #bj years of age1 will die when he is #ci-a_/b2 7b7 the ,material1 or those that cannot be clearly exhibited as transgressions of any logical principle1 but are due to superficial inquiry or confused reasoning2 as in adopting premises on insufficient authority1 or without examining the facts2 or in mistaking the point to be proved4 #b4 ,formal ,fallacies of ,deduction and ,induction are1 all of them1 breaches of the rule 'not to go beyond the evidence4' ,as a detailed account of them would be little else than a repetition of the foregoing chapters1 it may suffice to recall some of the places at which it is easiest to go astray4 7#a7 ,it is not uncommon to mistake the ,contrary for the ,contradictory1 as--,a is not taller than ,b1 he is shorter4 7#b7 ,to convert ,a4 or ,o4 simply1 as-- ,all ,money is ,wealth ,all ,wealth is ,money2 or--,some ,wealth is not ,money ,some ,money is not ,wealth4 ,in both these cases1 ,wealth1 though undistributed in the convertend1 is distributed in the converse4 7#c7 ,to attempt to syllogise with two premises containing four terms1 as ,the ,papuans are savages2 ,the ,javanese are neighbours of the ,papuans3 ,the ,javanese are savages4 ,such an argument is excluded by the definition of a ,syllogism1 and presents no formal evidence whatever4 ,we should naturally assume that any man who advanced it merely meant to raise some probability that 'neighbourhood is a sign of community of ideas and customs4' ,but1 if so1 he should have been more explicit4 ,there would1 of course1 be the same failure of connection1 if a fourth term were introduced into the conclusion1 instead of into the premises4 7#d7 ,to distribute in the conclusion a term that was undistributed in the premises 7an error essentially the same as 7#b7 above71 i4e41 ,illicit process of the major or minor term1 as-- ,every rational agent is accountable2 ,brutes are not rational agents3 ,brutes are not accountable4 ,in this example 7from ,whately71 an illegitimate mood of ,fig4 ,i41 the major term1 'accountable1' has suffered the illicit process2 since1 in the premise1 it is predicate of an affirmative proposition and1 therefore1 undistributed2 but1 in the conclusion1 it is predicate of a negative proposition and1 therefore1 distributed4 ,the fact that nearly everybody would accept the conclusion as true1 might lead one to overlook the formal inconclusiveness of the proof4 ,again1 ,all men are two-handed2 ,all two-handed animals are cooking animals3 ,all cooking animals are men4 ,here we have ,bramantip concluding in ,a42 and there is1 formally1 an illicit process of the minor2 though the conclusion is true2 and the evidence1 such as it is1 is materially adequate4 7',two-handed1' being a peculiar differentia1 is nugatory as a middle term1 and may be cut out of both premises2 whilst 'cooking' is a proprium peculiar to the species ,man2 so that these terms might be related in ,u41 ,all men are all cookers2 whence1 by conversion1 ,all cookers are men47 7#e7 ,to omit to distribute the middle term in one or the other premise1 as-- ,all verbal propositions are self-evident2 ,all axioms are self-evident3 ,all axioms are verbal propositions4 ,this is an illegitimate mood in ,fig4 ,,ii42 in which1 to give any conclusion1 one premise must be negative4 ,it may serve as a formal illustration of ,undistributed ,middle2 though1 as both premises are verbal propositions1 it is 7materially7 not syllogistic at all1 but an error of classification2 a confounding of co-ordinate species by assuming their identity because they have the generic attribute in common4 7#f7 ,to simply convert an hypothetical proposition1 as-- ,if trade is free1 it prospers2 ,if trade prospers1 it is free4 ,this is similar to the simple conversion of the categorical ,a42 since it takes for granted that the antecedent is co-extensive with the consequent1 or 7in other words7 that the freedom of trade is the sole condition of1 or 7at least7 inseparable from1 its prosperity4 ,the same assumption is made if1 in an hypothetical syllogism1 we try to ground an inference on the affirmation of the consequent or denial of the antecedent1 as-- ,if trade is free it prospers3 ,it does prosper2 ,it is free4 ,it is not free2 ,it does not prosper4 ,neither of these arguments is formally good2 nor1 of course1 is either of them materially valid1 if it be possible for trade to prosper in spite of protective tariffs4 ,an important example of this fallacy is the prevalent notion1 that if the conclusion of an argument is true the premises must be trustworthy2 or1 that if the premises are false the conclusion must be erroneous4 ,for1 plainly1 that-- ,if the premises are true1 the conclusion is true1 is a hypothetical proposition2 and we argue justly-- ,the premises are true2 ,the conclusion is true2 or1 ,the conclusion is false2 ,the premises are false 7or one of them is74 ,this is valid for every argument that is formally correct2 but that we cannot trust the premises on the strength of the conclusion1 nor reject the conclusion because the premises are absurd1 the following example will show3 ,all who square the circle are great mathematicians2 ,newton squared the circle3 ,newton was a great mathematician4 ,the conclusion is true2 but the premises are intolerable4 ,how the taking of ,contraries for ,contradictories may vitiate ,disjunctive ,syllogisms and ,dilemmas has been sufficiently explained in the twelfth chapter4 #c4 ,formal ,fallacies of ,induction consist in supposing or inferring ,causation without attempting to prove it1 or in pretending to prove it without satisfying the ,canons of observation and experiment3 as-- 7#a7 ,to assign the ,cause of anything that is not a concrete event3 as1 e4g41 why two circles can touch only in one point4 ,we should give the 'reason'2 for this expression includes1 besides evidence of causation1 the principles of formal deduction1 logical and mathematical4 7#b7 ,to argue1 as if on inductive grounds1 concerning the cause of the ,universe as a whole4 ,this may be called the fallacy of transcendent inference3 since the ,canons are only applicable to instances of events that can be compared2 they cannot deal with that which is in its nature unique4 7#c7 ,to mistake co-existent phenomena for cause and effect3 as when a man1 wearing an amulet and escaping shipwreck1 regards the amulet as the cause of his escape4 ,to prove his point1 he must either get again into exactly the same circumstances without his amulet1 and be drowned--according to the method of ,difference2 or1 shirking the only satisfactory test1 and putting up with mere ,agreement1 he must show1 7a7 that all who are shipwrecked and escape wear amulets1 and 7b7 that their cases agree in nothing else2 and 7c71 by the ,joint ,method1 that all who are shipwrecked without amulets are drowned4 ,and even if his evidence1 according to ,agreement1 seemed satisfactory at all these points1 it would still be fallacious to trust to it as proof of direct causation2 since we have seen that unaided observation is never sufficient for this3 it is only by experiment in prepared circumstances that we can confidently trace sequence and the transfer of energy4 ,there is the reverse error of mistaking causal connection for independent co-existence3 as if any one regards it as merely a curious coincidence that great rivers generally flow past great towns4 ,in this case1 however1 the evidence of connection does not depend merely upon direct ,induction4 7#d7 ,post hoc1 ergo propter hoc3 to accept the mere sequence of phenomena1 even though often repeated1 as proving that the phenomena are cause and effect1 or connected by causation4 ,this is a very natural error3 for although1 the antecedents of a phenomenon being numerous1 most of them cannot be its cause1 yet it is among them that the cause must be sought4 ,indeed1 if there is neither time nor opportunity for analysis1 it may seem better to accept any antecedent as a cause 7or1 at least1 as a sign7 of an important event than to go without any guide4 ,and1 accordingly1 the vast and complicated learning of omens1 augury1 horoscopy and prophetic dreams1 relies upon this maxim2 for whatever the origin of such superstitions1 a single coincidence in their favour triumphantly confirms them4 ,it is the besetting delusion of everybody who has wishes or prejudices2 that is1 of all of us at some time or other2 for then we are ready to believe without evidence4 ,the fallacy consists in judging off-hand1 without any attempt1 either by logic or by common sense1 to eliminate the irrelevant antecedents2 which may include all the most striking and specious4 7#e7 ,to regard the ,co-,effects 7whether simultaneous or successive7 of a common cause as standing in the direct relation of cause and effect4 ,probably no one supposes that the falling of the mercury in his thermometer causes the neighbouring lake to freeze4 ,true1 it is the antecedent1 and 7within a narrow range of experience7 may be the invariable antecedent of the formation of ice2 but1 besides that the two events are so unequal1 every one is aware that there is another antecedent1 the fall of temperature1 which causes both4 ,to justify inductively our belief in causation1 the instances compared must agree1 or differ1 in one circumstance only 7besides the effect74 ,the flowing tide is an antecedent of the ebbing tide2 it is invariably so1 and is equal to it2 but it is not the cause of it3 other circumstances are present2 and the moon is the chief condition of both flow and ebb4 ,in several instances1 ,states that have grown outrageously luxurious have declined in power3 that luxury caused their downfall may seem obvious1 and capable of furnishing a moral lesson to the young4 ,hence other important circumstances are overlooked1 such as the institution of slavery1 the corruption and rapacity of officials and tax-gatherers1 an army too powerful for discipline2 any or all of which may be present1 and sufficient to explain both the luxury and the ruin4 7#f7 ,to mistake one condition of a phenomenon for the whole cause4 ,to speak of an indispensable condition of any phenomenon as the cause of it1 may be a mere conventional abbreviation2 and in this way such a mode of expression is common not only in popular but also in scientific discussion4 ,thus we say that a temperature of #cc ,f4 is a cause of the melting of ice2 although that ice melts at #cc ,f41 must further depend upon something in the nature of water2 for every solid has its own melting-point4 ,as long1 then1 as we remember that 'cause1' used in this sense1 is only a convenient abbreviation1 no harm is done2 but1 if we forget it1 fallacy may result3 as when a man says that the cause of a financial crisis was the raising of the rate of discount1 neglecting the other conditions of the market2 whereas1 in some circumstances1 a rise of the ,bank-rate may increase public confidence and prevent a crisis4 ,we have seen that the direct use of the ,canons of ,agreement and ,difference may only enable us to say that a certain antecedent is a cause or an indispensable condition of the phenomenon under investigation4 ,if1 therefore1 it is important to find the whole cause1 we must either experiment directly upon the other conditions1 or resort to the ,method of ,residues and deductive reasoning2 nor must we be content1 without showing 7where such precision is possible7 that the alleged cause and the given phenomenon are equal4 7#g7 ,to mistake a single consequence of a given cause for the whole effect1 is a corresponding error2 and none so common4 ,nearly all the mistakes of private conduct and of legislation are due to it3 ,to cure temporary lassitude by a stimulant1 and so derange the liver2 to establish a new industry by protective duties1 and thereby impoverish the rest of the country2 to gag the press1 and so drive the discontented into conspiracy2 to build an alms-house1 and thereby attract paupers into the parish1 raise the rates1 and discourage industry4 7#h7 ,to demand greater exactness in the estimate of causes or effects than a given subject admits of4 ,in the more complex sciences1 ,biology1 ,psychology1 ,sociology1 it is often impossible to be confident that all the conditions of a given phenomenon have been assigned1 or that all its consequences have been traced4 ,the causes of the origin of species and of the great ,french ,revolution have been carefully investigated1 and still we may doubt whether they have all been discovered1 or whether their comparative importance has been rightly determined2 but it would be very unreasonable to treat those things as miraculous and unintelligible4 ,we read in the ,ethics1 that a properly cultivated mind knows what degree of precision is to be expected in each science4 ,the greatest possible precision is always to be sought2 but what is possible depends partly on the nature of the study and partly upon the state of scientific preparation4 7#i7 ,to treat an agent or condition remote in time as an unconditional cause3 for every moment of time gives an opportunity for new combinations of forces and1 therefore1 for modifications of the effect4 ,thus1 although we often say that ,napoleon's ,russian expedition was the cause of his downfall1 yet the effect was subject to numerous further conditions4 ,had the natives not burnt ,moscow1 had the winter been exceptionally mild1 had the ,prussians and ,austrians not risen against him1 the event might have been very different4 ,it is rash to trace the liberties of modern ,europe to the battle of ,marathon4 ,indeed1 our powers of perception are so unequal to the subtlety of nature1 that even in experimental science there is time for molecular changes to occur between what we treat as a cause and the effect as we perceive it2 and1 in such cases1 the strictly unconditional cause has not been discovered4 7#aj7 ,to neglect the negative conditions to which a cause is subject4 ,when we say that water boils at #bab ,f41 we mean provided the pressure be the same as that of the atmosphere at about the sea-level2 for under a greater pressure water will not boil at that temperature1 whilst under less pressure it boils at a lower temperature4 ,in the usual statement of a law of causation1 'disturbing1' 'frustrating1' 'counteracting' circumstances 7that is1 negative conditions7 are supposed to be absent2 so that the strict statement of such a law1 whether for a remote cause1 or for an immediate cause 7when only positive conditions are included71 is that the agent or assemblage of conditions1 tends to produce such an effect1 other conditions being favourable1 or in the absence of contrary forces4 7#aa7 ,it is needless to repeat what has already been said of other fallacies that beset inductive proof2 such as the neglect of a possible plurality of causes where the effect has been vaguely conceived2 the extension of empirical laws beyond adjacent cases2 the chief errors to which the estimate of analogies and probabilities1 or the application of the principles of classification are liable2 and the reliance upon direct ,induction where the aid of ,deduction may be obtained1 or upon observation where experiment may be employed4 ,as to formal fallacies that may be avoided by adhering to the rules of logical method1 this may suffice4 #d4 ,there remain many ways in which arguments fall short of a tolerable standard of proof1 though they cannot be exhibited as definite breaches of logical principles4 ,logicians1 therefore1 might be excused from discussing them2 but out of the abundance of their pity for human infirmity they usually describe and label the chief classes of these 'extra-logical fallacies1' and exhibit a few examples4 ,we may adopt ,whately's remark1 that a fallacy lies either 7#a7 in the premises1 or 7#b7 in the conclusion1 or 7#c7 in the attempt to connect a conclusion with the premises4 7#a7 ,now the premises of a sound argument must either be valid deductions1 or valid inductions1 or particular observations1 or axioms4 ,in an unsound argument1 then1 whose premises are supported by either deduction or induction1 the evidence may be reduced to logical rules2 and its failure is therefore a 'logical fallacy' such as we have already discussed4 ,it follows that an extra-logical fallacy of the premises must lie in what cannot be reduced to rules of evidence1 that is1 in bad observations 7 #e71 or sham axioms 7 #f74 7#b7 ,as to the conclusion1 this can only be fallacious if some other conclusion has been substituted for that which was to have been proved 7 #g74 7#c7 ,fallacies in the connection between premises and conclusion1 if all the propositions are distinctly and explicitly stated1 become manifest upon applying the rules of ,logic4 ,fallacies1 therefore1 which are not thus manifest1 and so are extra-logical1 must depend upon some sort of slurring1 confusion1 or ambiguity of thought or speech 7 #h74 #e4 ,amongst ,fallacies of ,observation1 ,mill distinguishes 7#a7 those of ,non-observation1 where either instances of the presence or absence of the phenomenon under investigation1 or else some of the circumstances constituting it or attending upon it1 though important to the induction1 are overlooked4 ,these errors are implied in the ,formal ,fallacies of ,induction already treated of in #c 7paragraphs 7#c7 to 7#g774 ,mill's class 7#b7 comprises fallacies of ,malobservation4 ,malobservation may be due to obtuseness or slowness of perception2 and it is one advantage of the physical sciences as means of education1 that the training involved in studying them tends to cure these defects--at least1 within their own range4 ,but the occasion of error upon which ,mill most insists1 is our proneness to substitute a hasty inference for a just representation of the fact before us2 as when a yachtsman1 eager for marvels1 sees a line of porpoises and takes them for the sea-serpent4 ,every one knows what it is to mistake a stranger for a friend1 a leaf for a sparrow1 one word for another4 ,the wonder is that we are not oftener wrong2 considering how small a part present sensation has in perception1 and how much of every object observed is supplied by a sort of automatic judgment4 ,you see something brown1 which your perceptive mechanism classes with the appearance of a cow at such a distance2 and instantly all the other properties of a cow are supplied from the resources of former experience3 but on getting nearer1 it turns out to be a log of wood4 ,it is some protection against such errors to know that we are subject to them2 and the ,logician fulfils his duty in warning us accordingly4 ,but the matter belongs essentially to ,psychology2 and whoever wishes to pursue it will find a thorough explanation in ,prof4 ,sully's volume on ,illusions4 ,another error is the accumulation of useless1 irrelevant observations1 from which no proof of the point at issue can be derived4 ,it has been said that an important part of an inductive inquirer's equipment consists in knowing what to observe4 ,the study of any science educates this faculty by showing us what observations have been effective in similar cases2 but something depends upon genius4 ,observation is generally guided by hypotheses3 he makes the right observations who can frame the right hypotheses2 whilst another overlooks things1 or sees them all awry1 because he is confused and perverted by wishes1 prejudices or other false preconceptions2 and still another gropes about blindly1 noting this and docketing that to no purpose1 because he has no hypothesis1 or one so vague and ill-conceived that it sheds no light upon his path4 #f4 ,the second kind of extra-logical ,fallacy lying in the premises1 consists in offering as evidence some assertion entirely baseless or nugatory1 but expressed in such a way as to seem like a general truth capable of subsuming the proposition in dispute3 it is generally known as petitio principii1 or begging the question4 ,the question may be begged in three ways3 7#a7 ,there are what ,mill calls ,fallacies a priori1 mere assertions1 pretending to be self-evident1 and often sincerely accepted as such by the author and some infatuated disciples1 but in which the cool spectator sees either no sense at all1 or palpable falsity4 ,these sham axioms are numerous2 and probably every one is familiar with the following examples3 ,that circular motion is the most perfect2 ,that every body strives toward its natural place2 ,that like cures like2 ,that every bane has its antidote2 ,that what is true of our conceptions is true of ,nature2 ,that pleasure is nothing but relief from pain2 ,that the good1 the beautiful and the true are the same thing2 ,that1 in trade1 whatever is somewhere gained is somewhere lost2 ,that only in agriculture does nature assist man2 ,that a man may do what he will with his own2 ,that some men are naturally born to rule and others to obey4 ,some of these doctrines are specious enough2 whilst1 as to others1 how they could ever have been entertained arouses a wonder that can only be allayed by a lengthy historical and psychological disquisition4 7#b7 ,verbal propositions offered as proof of some matter of fact4 ,these have1 indeed1 one attribute of axioms2 they are self-evident to any one who knows the language2 but as they only dissect the meaning of words1 nothing but the meaning of words can be inferred from them4 ,if anything further is arrived at1 it must be by the help of real propositions4 ,how common is such an argument as this3 ',lying is wrong1 because it is vicious'--the implied major premise being that 'what is vicious is wrong4' ,all three propositions are verbal1 and we merely learn from them that lying is called vicious and wrong2 and to make that knowledge deterrent1 it must be supplemented by a further premise1 that 'whatever is called wrong ought to be avoided4' ,this is a real proposition2 but it is much more difficult to prove it than 'that lying ought to be avoided4' ,still1 such arguments1 though bad ,logic1 often have a rhetorical force3 to call lying not only wrong but vicious1 may be dissuasive by accumulating associations of shame and ignominy4 ,definitions1 being the most important of verbal propositions 7since they imply the possibility of as many other verbal propositions as there are defining attributes and combinations of them71 need to be watched with especial care4 ,if two disputants define the same word in different ways1 with each of the different attributes included in their several definitions they may bring in a fresh set of real propositions as to the agency or normal connection of that attribute4 ,hence their conclusions about the things denoted by the word defined1 diverge in all directions and to any extent4 ,and it is generally felt that a man who is allowed to define his terms as he pleases1 may prove anything to those who1 through ignorance or inadvertence1 grant that the things that those terms stand for have the attributes that figure in his definitions4 7#c7 ,circulus in demonstrando1 the pretence of giving a reason for an assertion1 whilst in fact only repeating the assertion itself--generally in other words4 ,in such cases the original proposition is1 perhaps1 really regarded as self-evident1 but by force of habit a man says 'because'2 and then1 after vainly fumbling in his empty pocket for the coin of reason1 the habit of symbolic thinking in words only1 without reference to the facts1 comes to his rescue1 and he ends with a paraphrase of the same assertion4 ,thus a man may try to prove the necessity of ,causation3 ',every event must have a cause2 because an event is a change of phenomena1 and this implies a transformation of something pre-existing2 which can only have been possible1 if there were forces in operation capable of transforming it4' ,or1 again3 ',we ought not to go to war1 because it is wrong to shed blood4' ,but1 plainly1 if war did not imply bloodshed1 the unlawfulness of this could be nothing against war4 ,the more serious any matter is1 the more important it becomes either to reason thoroughly about it1 or to content ourselves with wholesome assertions4 ,how many 'arguments' are superfluous6 #g4 ,the ,fallacy of surreptitious conclusion 7ignoratio elenchi71 the mistaking or obscuring of the proposition really at issue1 whilst proving something else instead4 ,this may be done by substituting a particular proposition for an universal1 or an universal for a particular4 ,thus1 he who attacks the practice of giving in charity must not be content to show that it has1 in this or that case1 degraded the recipient2 who may have been exceptionally weak4 ,or1 again1 to dissuade another from giving alms in a particular case1 it is not enough to show that the general tendency of almsgiving is injurious2 for1 by taking pains in a particular case1 the general tendency may often be counteracted4 ,sometimes an argument establishing a wholly irrelevant conclusion is substituted for an argumentum ad rem4 ,macaulay complains of those apologists for ,charles ,i4 who try to defend him as a king1 by urging that he was a good judge of paintings and indulgent to his wife4 ,to this class of ,fallacies belongs the argumentum ad hominem1 which consists in showing not that a certain proposition is true1 but that ,critias ought to accept it in consistency with his other opinions4 ,thus3 ',in every parish the cost of education ought to be paid out of the rates3 you1 at least1 have said that there can be no sound economy1 unless local expenses are defrayed from local funds4' ,but whether this is a fallacy depends1 as ,whately observes1 upon whether it is urged as actually proving the point at issue1 or merely as convicting the opponent of inconsistency4 ,in the latter case1 the argument is quite fair3 whatever such a conclusion may be worth4 ,similarly with the argumentum ad populum3 'this measure is favourable to such or such a class2 let them vote for it4' ,an appeal to private greed1 however base1 is not fallacious1 as long as the interest of the class is not fraudulently substituted for the good of the nation4 ,and much the same may be said for the argumentum ad verecundiam4 ,when a question of morals is debated as a question of honour among thieves1 there is no fallacy1 if the moral issue is frankly repudiated4 ,the argument from authority is often brought under this head3 'such is the opinion of ,aristotle4' ,although this does not establish the truth of any proposition1 it may be fairly urged as a reason for not hastily adopting a contrary conclusion3 that is1 if the subject under discussion be one as to which ,aristotle 7or whoever the authority may be7 had materials for forming a judgment4 ,a negative use of this fallacy is very common4 ,some general doctrine1 such as ,positivism1 ,transcendentalism1 ,utilitarianism1 or ,darwinism1 is held in common by a group of men2 who1 however1 all judge independently1 and therefore are likely to differ in details4 ,an opponent exhibits their differences of opinion1 and thereupon pretends to have refuted the theory they agree in supporting4 ,this is an argumentum ad scholam1 and pushes too far the demand for consistency4 ,in fact it recoils upon the sophist2 for there is no sense in quoting men against one another1 unless both 7or all7 are acknowledged to speak with the authority of learning and judgment1 and therefore the general doctrine which they hold in common is the more confirmed4 ,this is an example of the paralogism of 'proving too much'2 when a disputant is so eager to refute an opponent as to lay down1 or imply1 principles from which an easy inference destroys his own position4 ,to appeal to a principle of greater sweep than the occasion requires may easily open the way to this pitfall3 as if a man should urge that 'all men are liars1' as the premise of an argument designed to show that another's assertion is less credible than his own4 ,a common form of ignoratio elenchi is that which ,whately called the 'fallacy of objections'3 namely1 to lay stress upon all the considerations against any doctrine or proposal1 without any attempt to weigh them against the considerations in its favour2 amongst which should be reckoned all the considerations that tell against the alternative doctrines or proposals4 ,incontestable demonstration can rarely be expected even in science1 outside of the ,mathematics2 and in practical affairs1 as ,butler says1 'probability is the very guide of life'2 so that every conclusion depends upon the balance of evidence1 and to allow weight to only a part of it is an evasion of the right issue4 #h4 ,fallacies in the connection of premises and conclusion1 that cannot be detected by reducing the arguments to syllogistic form1 must depend upon some juggling with language to disguise their incoherence4 ,they may be generally described as ,fallacies of ,ambiguity1 whether they turn upon the use of the same word in different senses1 or upon ellipsis4 ,thus it may be argued that all works written in a classical language are classical1 and that1 therefore1 the history of ,philosophy by ,diogenes ,lrtius1 being written in ,greek1 is a classic4 ,such ambiguities are sometimes serious enough2 sometimes are little better than jokes4 ,for jokes1 as ,whately observes1 are often fallacies2 and considered as a propdeutic to the art of sophistry1 punning deserves the ignominy that has overtaken it4 ,fallacies of ellipsis usually go by learned names1 as2 7#a7 a dicto secundum quid ad dictum simpliciter4 ,it has been argued that since1 according to ,ricardo1 the value of goods depends solely upon the quantity of labour necessary to produce them1 the labourers who are employed upon 7say7 cotton cloth ought to receive as wages the whole price derived from its sale1 leaving nothing for interest upon capital4 ,ricardo1 however1 explained that by 'the quantity of labour necessary to produce goods' he meant not only what is immediately applied to them1 but also the labour bestowed upon the implements and buildings with which the immediate labour is assisted4 ,now these buildings and implements are capital1 the labour which produced them was paid for1 and it was far enough from ,ricardo's mind to suppose that the capital which assists present labour upon 7say7 cotton cloth has no claim to remuneration out of the price of it4 ,in this argument1 then1 the word labour in the premise is used secundum quid1 that is1 with the suppressed qualification of including past as well as present labour2 but in the conclusion labour is used simpliciter to mean present labour only4 7#b7 ,a dicto secundum quid ad dictum secundum alterum quid4 ,it may be urged that1 since the tax on tea is uniform1 therefore all consumers contribute equally to the revenue for their enjoyment of it4 ,but written out fairly this argument runs thus3 ,since tea is taxed uniformly #d;d4 per lb41 all consumers pay equally for their enjoyment of it whatever quantity they use4 ,these qualifications introduced1 nobody can be deceived4 7#c7 ,a dicto simpliciter ad dictum secundum quid1 also called fallacia accidentis4 ,thus3 ,to take interest upon a loan is perfectly just1 therefore1 ,i do right to exact it from my own father in distress4 ,the popular answer to this sort of blunder is that 'circumstances alter cases4' ,we commit this error in supposing that what is true of the average is likely to be true of each case2 as if one should say3 ',the offices are ready to insure my house with thousands of others against fire at a rate per annum which will leave them heavy losers unless it lasts a hundred years2 so1 as we are told not to take long views of life1 ,i shall not insure4' ,the ,fallacy of ,division and ,composition consists in suggesting1 or assuming1 that what is true of things severally denoted by a term is true of them taken together4 ,that every man is mortal is generally admitted1 but we cannot infer that1 therefore1 the human race will become extinct4 ,that the remote prospects of the race are tragic may be plausibly argued1 but not from that premise4 ,changing the ,premises is a fallacy usually placed in this division2 although1 instead of disguising different meanings under similar words1 it generally consists in using words or phrases ostensibly differing1 as if they were equivalent3 those addressed being expected to renounce their right to reduce the argument to strict forms of proof1 as needless pedantry in dealing with an author so palpably straightforward4 ,if an orator says--',napoleon conquered ,europe2 in other words1 he murdered five millions of his fellow creatures'--and is allowed to go on1 he may infer from the latter of these propositions many things which the former of them would hardly have covered4 ,this is a sort of hyperbole1 and there is a corresponding meiosis1 as3 ',mill admits that the ,syllogism is useful'2 when1 in fact1 that is ,mill's contention4 ,it may be supposed that1 if a man be fool enough to be imposed upon by such transparent colours1 it serves him right2 but this harsh judgment will not be urged by any one who knows and considers the weaker brethren4 #i4 ,the above classification of ,fallacies is a rearrangement of the plans adopted by ,whately and ,mill4 ,but ,fallacies resemble other spontaneous natural growths in not submitting to precise and definite classification4 ,the same blunders1 looked at from different points of view1 may seem to belong to different groups4 ,thus1 the example given above to illustrate fallacia accidentis1 'that1 since it is just to take interest1 it is right to exact it from one's own father1' may also be regarded as petitio principii1 if we consider the unconditional statement of the premise--'to take interest upon a loan is perfectly just'2 for1 surely1 this is only conditionally true4 ,or1 again1 the first example given of simple ambiguity--'that whatever is written in a classical language is classical1 etc41' may1 if we attend merely to the major premise1 be treated as a bad generalisation1 an undue extension of an inference1 founded upon a simple enumeration of the first few ,greek and ,latin works that one happened to remember4 ,it must also be acknowledged that genuine wild fallacies1 roaming the jungle of controversy1 are not so easily detected or evaded as specimens seem to be when exhibited in a ,logician's collection2 where one surveys them without fear1 like a child at a menagerie4 ,to assume the succinct mode of statement that is most convenient for refutation1 is not the natural habit of these things4 ,but to give reality to his account of fallacies an author needs a large space1 that he may quote no inconsiderable part of literature ancient and modern4 ,as to the means of avoiding fallacies1 a general increase of sincerity and candour amongst mankind may be freely recommended4 ,with more honesty there would be fewer bad arguments2 but there is such a thing as well-meaning incapacity that gets unaffectedly fogged in converting ,a41 and regards the refractoriness of ,o41 as more than flesh and blood can endure4 ,mere indulgence in figurative language1 again1 is a besetting snare4 ,one of the fathers1 in great severity called poesy vinum dmonum1 says ,bacon3 himself too fanciful for a philosopher4 ,surely1 to use a simile for the discovery of truth is like studying beauty in the bowl of a spoon4 ,the study of the natural sciences trains and confirms the mind in a habit of good reasoning1 which is the surest preservative against paralogism1 as long as the terms in use are1 like those of science1 well defined2 and where they are ill defined1 so that it is necessary to guard against ambiguity1 a thorough training in politics or metaphysics may be useful4 ,logic seems to me to serve1 in some measure1 both these purposes4 ,the conduct of business1 or experience1 a sufficient time being granted1 is indeed the best teacher1 but also the most austere and expensive4 ,in the seventeenth century some of the greatest philosophers wrote de intellectus emendatione2 and if their successors have given over this very practical inquiry1 the cause of its abandonment is not success and satiety but despair4 ,perhaps the right mind is not to be made by instruction1 but can only be bred3 a slow1 haphazard process2 and meanwhile the rogue of a sophist may count on a steady supply of dupes to amuse the tedium of many an age4 ,,finis4 ,,questions ,the following questions are chiefly taken from public examination papers3 ,civil ,service ,s1 ,oxford ,o1 ,cambridge ,c1 ,london ,l4 ,i4 ,,terms1 ,,etc4 #a4 ,what is a ,term8 ,explain and illustrate the chief divisions of ,terms4 ,what is meant by the ,connotation of a ,term8 ,illustrate4 ,s #b4 ,the connotation and denotation of terms vary inversely4 ,examine this assertion1 explaining carefully the limits within which it is true1 if at all4 ,s #c4 ,exemplify the false reasoning arising from the confusion of ,contrary and ,contradictory ,terms4 ,s #d4 ,discuss the claims of the doctrine of ,terms to be included in a ,logical ,system4 ,distinguish between a ,general and an ,abstract ,term4 ,s #e4 ,explain and illustrate what is meant by the ,denotation and ,connotation of a ,term4 ,what terms have both1 and what have one only8 ,s #f4 ,distinguish between ,abstract and ,concrete ,names4 ,to which of these classes belong 7a7 adjectives1 7b7 names of states of consciousness8 ,are any abstract names connotative8 ,s #g4 ,distinguish between 7a7 ,proper and ,singular ,terms1 7b7 ,negative and ,privative1 7c7 ,absolute and ,relative4 ,illustrate4 #h4 ,what connection is there between the ,connotation and the ,relativity of ,names8 #i4 ,examine the logical relations between the following pairs of terms3 7a7 happy and happiness2 7b7 happy and unhappy2 7c7 'the juryman' and 'the jury'2 7d7 parent and offspring4 ,explain the technical words used in your answer4 ,c #aj4 ,distinguish between name2 part of speech2 term3 and illustrate by reference to the following--use1 useful1 usefully4 ,c #aa4 ,describe the nature of ,collective terms2 examine in particular any difficulties in distinguishing between these and general or abstract terms4 ,c #ab4 ,distinguish between positive1 negative1 and privative names4 ,of what kind are the following1 and why--parallel1 alien1 idle1 unhappy8 ,what ambiguity is there in the use of such a term as not-white8 ,c ,,ii4 ,,propositions ,,and ,,immediate ,,inference4 #ac4 ,what is meant by 7#a7 the ,conversion1 and 7#b7 the ,contra-position of a proposition8 ,apply these processes1 as far as admissible1 to the following3-- 7a7 ,all invertebrates have cold blood4 7b7 ,some cold-blooded animals are not invertebrates4 7c7 ,no wingless birds are songsters4 7d7 ,some winged birds are not songsters4 ,what can you infer from 7a7 and 7b7 jointly1 and what from 7c7 and 7d7 jointly8 ,s #ad4 ,the author actually supposes that1 because ,professor ,fawcett denies that all wealth is money1 he denies that all money is wealth4 ,analyse the differences of opinion implied in the above passage4 ,s #ae4 ,take any universal affirmative proposition2 convert it by obversion 7contraposition72 attach the negative particle to the predicate1 and again convert4 ,interpret the result exactly1 and say whether it is or is not equivalent to the original proposition4 ,s #af4 ,what information about the term solid body can we derive from the proposition1 ,no bodies which are not solids are crystals8 ,s #ag4 ,discuss the proposal to treat all propositions as affirmative4 #ah4 ,convert the proposition ,a is probably ,b4 ,what information does the proposition give us concerning ,b8 ,s #ai4 ,show in how many ways you can deny the following assertions3 ,all cathedral towns are all cities2 ,canterbury is the ,metropolitan see4 ,s #bj4 ,explain the nature of a hypothetical 7or conditional7 proposition4 ,what do you consider the radical difference between it and a categorical8 ,s #ba4 ,what is the function of the copula8 ,in what different manners has it been treated8 ,s #bb4 ,convert ,a killed ,c unjustly2 ,all ,knowledge is probably useful2 ,the exception proves the rule2 ,birds of a feather flock together4 ,s #bc4 ,what is modality8 ,how are modals treated by 7a7 formal logic and 7b7 by the theory of induction8 ,s #bd4 ,what is the subject of an impersonal proposition8 ,give reasons for your answer4 ,s #be4 ,is the categorical proposition sufficiently described as referring a thing or things to a class8 ,s #bf4 ,enumerate the cases in which the truth or falsity of one proposition may be formally inferred from the truth or falsity of another4 ,illustrate these cases1 and give to each its technical name4 ,s #bg4 ,illustrate the relation of ,immediate ,inferences to the ,laws of ,thought4 #bh4 ,explain what is meant by 7a7 ,symbolic ,logic2 7b7 the ,logic of ,relatives4 ,describe some method of representing propositions by means of diagrams2 and indicate how far any particular theory of the import of propositions is involved in such representation4 ,s #bi4 ,explain the exact nature of the relation between two ,contradictory propositions2 and define ,conversion by ,contraposition1 determining what kind of propositions admit of such conversion4 ,give the contradictory and the contrapositive of each of the following propositions3-- 7a7 ,all equilateral triangles are equiangular2 7b7 ,no vertebrate animal has jaws opening sideways2 7c7 ,wherever ,a and ,b are both present1 either ,c or ,d is also present4 ,s #cj4 ,define ,obversion and ,inversion1 and apply these processes also to the above three propositions4 #ca4 ,propositions can be understood either in extension or in intension4 ,explain this1 and discuss the relative value of the two interpretations4 ,s #cb4 ,distinguish between real and verbal propositions2 and explain the importance of the distinction4 #cc4 ,illustrate the process called 'change of ,relation4' ,,iii4 ,,syllogism ,,and ,,mediate ,,inference4 #cd4 ,what is a ,syllogism8 ,find1 without reference to the mnemonic verses1 in what different ways it is possible to prove syllogistically the conclusion ,no ,s is ,p2 and show the equivalence between these different ways4 ,s #ce4 ,from what points of view can the syllogism be regarded 7#a7 as being1 7#b7 as not being1 a petitio principii8 ,s #cf4 ,what are the figures of syllogism8 ,for what kind of arguments are they severally adapted8 ,s #cg4 ,what is meant by ,mood and ,figure8 ,how can the validity of a ,mood be tested8 ,should there be four ,figures or three8 ,s #ch4 ,construct syllogisms in ,camenes1 ,datisi and ,baroco1 and reduce them to the corresponding moods of the first figure4 #ci4 ,explain the meaning of ostensive and indirect ,reduction4 ,show that any ,mood of the second ,figure may be reduced in either way4 #dj4 ,show that ,a cannot be proved except in the ,first ,figure4 ,express the following reasoning in as many syllogistic figures as you can3 ,some theorists cannot be trusted1 for they are unwise4 ,s #da4 ,discuss the possibility of reducing the argument a fortiori to the syllogistic form4 ,s #db4 ,can a false conclusion be reached through true premises1 or a true conclusion through false premises8 ,give reasons for your answer4 ,s #dc4 ,can we under any circumstances infer a relation between ,x and ,z from the premises-- ,some ,y's are ,x's ,some ,y's are ,z's8 ,s #dd4 ,take an apparent syllogism subject to the fallacy of negative premises1 and inquire whether you can correct the reasoning by converting one or both of the premises into the affirmative form4 ,s #de4 ,enumerate the faults to which a syllogism is liable1 giving instances of each4 ,s #df4 ,state any ,enthymeme1 and expand it into 7#a7 a ,syllogism1 7#b7 an ,epicheirema1 7#c7 a ,sorites2 and give in each case the technical name of the ,mood or ,order that results4 #dg4 ,state any ,disjunctive ,syllogism1 and change it 7#a7 into a ,hypothetical1 7#b7 into a ,categorical2 and discuss the loss or gain1 in cogency or significance involved in this process4 #dh4 ,can the ,syllogism be treated as merely a consequence of the ,laws of ,thought8 ,if not1 why not2 and what else does it imply8 #di4 ,prove that with three given propositions 7of the forms ,a41 ,e41 ,i41 ,o47 it is never possible to construct more than one valid syllogism4 ,c #ej4 ,distinguish between a ,constructive and a ,destructive ,hypothetical ,syllogism2 and show how one may be reduced to the other4 ,c ,,iv4 ,,induction1 ,,etc4 #ea4 ,what constitutes a ,valid ,induction8 ,distinguish it from a legitimate hypothesis4 ,s #eb4 ,is it possible to form true universal propositions about facts if we have not actually observed all the individuals designated by the subject of the proposition8 ,if so1 how8 ,s #ec4 ,perfect induction is demonstrative and syllogistic2 imperfect induction is neither4 ,explain the difference between perfect and imperfect induction1 and examine the truth of this assertion4 ,s #ed4 ,why is it that one should not regard night as the cause1 nor even as a universal condition of day8 ,explain cause and condition4 ,s #ee4 ,what do you understand by an experiment8 ,can you say how many experiments are required to establish 7#a7 a fact1 7#b7 a law of nature8 #ef4 ,how would you define antecedent1 cause1 effect1 consequent8 ,s #eg4 ,england is the richest country in the world1 and has a gold currency4 ,russia and ,india1 in proportion to population1 are poor countries and have little or no gold currency4 ,how far are such kind of facts logically sufficient to prove that a gold currency is the cause of a nation's wealth8 ,s #eh4 ,a man having been shot through the heart immediately falls dead4 ,investigate the logical value of such a fact as proving that all men shot through the heart will fall dead4 ,s #ei4 ,explain the process of induction called the ,method of ,difference1 and give some new instances of its application4 ,how is it related to the ,method of ,concomitant ,variations8 ,what is the ,major ,premise implied in all these methods8 ,s #ei;,a4 ,examine the position1 that the ,canons of ,experiment are useless1 because the work of preparing the experiments must have been done before the canons can be applied4 #fj4 ,explain the logical cogency of experiments in the search for physical causes4 ,s #fa4 ,if the effects of ,a ,b ,c ,d are fully expressed by a b c d1 and those of ,b ,c ,d by b c d1 what inductive inference can be drawn and on what principle8 ,state the canon according to which it is drawn4 ,s #fb4 ,compare the advantage of observation and experiment as means of gaining data for ,reasoning4 ,s #fc4 ,compare the cogency of different ,inductive ,methods1 showing the kind of evidence each requires1 and the principle on which it is based4 ,s #fd4 ,compare the ,canons of ,agreement and ,difference 7#a7 as to the difficulty of finding or preparing actual ,instances for them1 and 7#b7 as to their conclusiveness4 #fe4 ,describe what is meant by residual phenomena1 and estimate their value in inductive science4 ,s #ff4 ,what is the argument from ,analogy8 ,how does it differ from 7a7 ,induction1 7b7 metaphorical argument8 ,s #fg4 ,what are the various senses in which the word ,analogy has been used8 ,distinguish1 giving instances1 between good and bad analogies4 ,s #fh4 ,how do you distinguish between what ,mill calls the ,geometrical1 ,physical1 and ,historical ,methods8 #fh;,a4 ,the ,comparative ,method is appealed to where direct evidence is wanting4 ,explain this4 #fi4 ,what is meant by a doctrine being unverifiable8 ,if a conclusion reached by deduction does not agree with the facts1 where must we look for error8 #gj4 ,there are certain cases in which failure of verification is fatal to a theory1 and other cases in which it is of comparatively little cogency4 ,how would you distinguish between these classes of cases8 ,s #ga4 ,taking the evolution1 or any other proposed hypothesis1 how should one proceed 7a7 to show whether it satisfies the conditions of a legitimate hypothesis sufficiently to entitle it to investigation1 and 7b7 to test it with a view to its acceptance or rejection as a truth of science8 ,s #gb4 ,what do you mean by saying that a phenomenon has been satisfactorily explained8 #gc4 ,explain and illustrate the ,historical ,method of ,sociological inquiry4 ,s #gd4 ,what is the relation of the theory of ,probability to ,logic8 ,s #ge4 ,explain and discuss the doctrine that ,induction is based upon the ,theory of ,probability4 ,s #ge;,a4 ,what are the logical grounds of the ,law of ,error8 #gf4 ,explain the nature and use of ,classification1 the means to1 and tests of1 its successful performance4 ,s #gg4 ,what is ,definition and what is its use8 ,mention various difficulties that occur in the process1 and show how they are to be met4 ,s #gh4 ,propose rules for a good ,division and a good ,definition1 and exemplify the breach of them4 ,s #gi4 ,examine the validity of the idea of ,real ,kinds4 ,o #hj4 ,what kind of words are indefinable1 and why8 ,when do we define by negation and by example8 ,s #ha4 ,distinguish between the province and aims of classification and 7logical7 division4 ,illustrate4 ,s #hb4 ,what is an infima species or species specialissima8 ,compare the use of the terms genus and species in ,logic with that which is common in speaking of animals or plants4 ,s #hc4 ,how far does the formation of ,definitions and ,classifications constitute the end of ,science8 ,s #hd4 ,examine the methodological relations between ,definition1 ,classification and ,nomenclature4 ,s #he4 ,give instances of ,differentia1 ,property1 ,inseparable ,accident2 and examine1 with reference to your instances1 how far it is possible to distinguish them4 ,s ,v4 ,,miscellaneous4 #hf4 ,people can reason without the help of ,logic4 ,why is this not a sufficient objection to the study8 ,in your answer show distinctly why ,logic should be studied4 ,s #hg4 ,what is the meaning of the assertion that ,logic is concerned with the form1 and not with the matter1 of thought8 ,s #hh4 ,neither by deductive nor inductive reasoning can we add a tittle to our implicit knowledge4 7,jevons47 ,explain and criticise4 ,s #hi4 ,what is the logical foundation of the indirect method or reductio ad absurdum8 ,is it applicable to non-mathematical subjects8 ,s #ij4 ,on what grounds do we believe in the reality of an historical event8 ,s #ia4 ,facts are familiar theories4 ,explain and discuss this4 ,o #ib4 ,wherein lies the difficulty of proving a negative8 ,o #ic4 ,can any limits be assigned to the possible unification of the sciences8 ,o #id4 ,are the results of inductive inference necessarily certain8 ,o #ie4 ,the method of deductive science is hypothetical4 ,explain and discuss4 ,o #if4 ,the uniformity of ,nature can never be more than a working hypothesis4 ,explain and criticise4 #ig4 ,without speculation there is no good and original observation4 ,why8 ,o #ih4 ,can the provinces of induction and deduction be kept separate8 ,o #ii4 ,how far is the relation of logical dependence identical with that of causation8 ,o #ii;,a4 ,discuss the position that the forms of ,logic are meaningless apart from their application4 #ajj4 ,state in syllogistic form 7mood and figure7 the following arguments3-- 7a7 ,as polygamy is in many countries legal1 we may infer the variability of the moral standard4 7b7 ,if gold is wealth1 to export it diminishes the national resources4 7c7 ,if all good people are happy1 unhappiness is an indication of vice4 7d7 ,one may be sure of the benefits of inuring young children to cold1 from the strength exhibited by all men and women thus treated in infancy4 7e7 ,where there is no law1 there is no injustice4 7f7 ,dissimulation is but a faint kind of policy or wisdom2 for it asketh a strong wit and a strong heart to know when to tell the truth1 and to do it2 therefore it is the weaker sort of politicians that are the greatest dissemblers4 7,bacon47 7g7 ,money being a barren product1 it is contrary to nature to make it reproduce itself4 ,usury1 therefore1 is unnatural1 and1 being unnatural1 is unjustifiable4 7h7 ,the study of mathematics is essential to a complete course of education1 because it induces a habit of close and regular reasoning4 ,s #aja4 ,explain and illustrate the following terms3--,subalternans1 ,vera ,causa1 ,plurality of ,causes1 ,law of ,nature1 ,empirical ,law1 ,summum ,genus1 ,predicament1 ,arbor ,porphyriana1 ,axiom1 ,universe of discourse 7suppositio71 ,antinomy1 ,dilemma1 ,realism1 ,dichotomy1 etc4 #ajb4 ,is there any distinction and1 if so1 what1 between a complete ,description and an ,explanation8 ,c #ajc4 ,on what principles have fallacies been classified8 ,to what extent do you think a satisfactory classification of ,fallacies possible8 ,c #ajd4 ,examine how far conceptions of ,persistence and of ,invariable ,concomitance of ,properties are involved in the methodological application of the conception of ,cause4 #ajd;,a4 ,inquire whether the two following propositions can be reconciled with one another3 7a7 ,the same conjunction of antecedents is invariably followed by the same consequent2 7b7 ,we never find the same concurrence of phenomena a second time4 ,c #aje4 ,using the term ,logic in a wide sense1 so as to include ,methodology1 inquire how far a ,logic of ,observation is possible1 and show in what it will consist4 ,c #ajf4 ,what is ,proof8 ,explain and discuss the following dicta3--7a7 ,qui nimium probat1 nihil probat3 7b7 ,a bad proof is worse than no proof2 7c7 ,the exception proves the rule2 7d7 ,negatives cannot be proved4 ,c #ajg4 ,examine how far the rules of immediate and syllogistic inference are modified by differences of interpretation of the categorical proposition in respect of the existence of the subject4 ,s #ajh4 ,an effect is but the sum of all the partial causes1 the concurrence of which constitutes its existence4 ,the cause of an event is its invariable and unconditional antecedent4 ,explain and compare these two theories of causation4 ,does either alone exhaust the scientific conception of cause8 ,s #aji4 ,under what logical conditions are statistical inferences authorised1 and what is the nature of their conclusions8 ,s #aaj4 ,distinguish between ,psychology1 ,metaphysics1 and ,logic2 and discuss briefly their mutual relations4 ,s #aaa4 ,all processes of inference in which the ultimate premises are particular cases are equally induction4 ,induction is an inverse deduction4 ,explain and contrast these two theories of the relation of induction to deduction4 ,s #aab4 ,what are the ,fallacies specially incident to ,induction8--or to the application of the theory of ,probabilities8 ,s #aac4 ,what is meant by the personal error 7or personal equation7 in observation8 ,discuss its importance in different branches of knowledge4 ,s #aad4 ,define and illustrate3--,paralogism1 ignoratio elenchi1 fallacia accidentis1 argumentum ad verecundiam1 illicit process1 undistributed middle1 etc4 #aae4 ,state the three fundamental laws of thought1 explain their meaning1 and consider how far they are independent of each other8 ,l #aaf4 ,enumerate the ,heads of ,predicables and define their meaning4 ,discuss their logical importance4 ,l #aag4 ,upon what grounds has it been asserted that the conclusion of a syllogism is drawn1 not from1 but according to1 the major premise8 ,are they valid8 ,l #aah4 ,experiment is always preferable to observation4 ,why is this8 ,explain from the example of any science how observation and experiment supplement each other4 ,l #aai4 ,what is a hypothesis8 ,distinguish between a working hypothesis and an established hypothesis1 so as to bring out the conditions on which the latter depends4 ,l #abj4 ,explain how good scientific nomenclature and terminology are connected with the purposes of good classification4 ,l ,printed in ,great ,britain by ,hazell1 ,watson ,viney1 ,ld41 ,london and ,aylesbury for ,simpkin1 ,marshall1 ,hamilton1 ,kent ,co4 ,ltd4 ,transcriber's ,note3 ,the following corrections were made to the original text3 ,page #dj3 inedequate changed to inadequate ,page #db3 classily changed to classify ,page #ij3 alledging changed to alleging ,page #abh3 missing comma added3 ,camenes1 ,dimaris ,page #ada3 evalued changed to evaluated ,page #adg3 tellens changed to tollens3 and the ,modus tollens ,page #agj3 impredictable changed to unpredictable ,page #baj3 missing word 'a' added3 ,sesostris conquered a great ,page #cjg3 either changed to neither ,page #cae3 inductions changed to induction ,page #dja3 quality changed to quantity ,page #dja3 propdeutic changed to propdeutic