Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/813

 LOGIC 789 comment is induction, of the nature of which something has already been said. The obscure chapter in which the formal analysis of induction is undertaken, a chapter which has much exercised the ingenuity of commentators, 1 presents difficulties of varied kinds. An opposition is indicated between syllogism and induction, yet induction is treated as a kind of syllogism ; that is, freely inter preted, induction is so analysed as to show that in it, also, there is the union of general assumption and particular detail which is char acteristic of syllogistic reasoning. Further, Aristotle seems to waver between induction as a kind of inference, through which we arrive at general principles, and as a species of proof, and his teaching is therefore perplexed by the want of some clear statement regarding a difficulty in the theory of induction, which is still far from perfect solution. For, according to Aristotle, induction as such, starting from the particulars of sense, and proceeding by comparison of similar cases and enumeration of all the similarly constituted mem bers, never, even when the enumeration is complete, attains to probative force. 2 It is still a syllogism of fact, not of ground or reason ; there is a distinction of kind between the survey of empirical detail, even when complete, and the assertion of causal connexion between the characteristics of the class and its deduced properties. 3 Thus, perception of the law (rl /ca0oA.ou) from induc tion is a kind of new element in the process ; it is recognition by means of the empirico-critical survey which is the essence of induc tion.* Induction makes clear only, and does not prove. 5 If we interpret according to more modern phraseology, this peculiarity may be expressed as the distinctive feature of inductive research based on facts or effects. We do^not regard the inquiry as terminat ing in the establishment of a law until it is possible to reverse the process and show that from the surmised cause the effects do actually follow. Otherwise we have a conclusion of &quot; coexistence &quot; jkjerely an empirical rule or generalization. If, bearing in mind these sources of difficulty, and also the correlation which for Aristotle always obtains between empirical details and grounds of reason, we consider the example given in the obscure chapter before UK, some light may be cast on the exposition there given. The example selected is one touched upon by Aristotle in other two passages, in the treatise DC Partibus Animalium, and in the Post. Anal., ii. IS. 6 As regards the first of these, reference is desirable only to bring out the fact that causal nexus is the KaBoov in question ; the second is of the utmost importance as clearing up what has always seemed an obscurity in the account of the inductive syllogism. In the chapters 16-18 of Anal. Post., ii., Aristotle considers the relation of cause and effect as the essential basis of proof, and he points out with much clearness the difference between the fact as cause of knowledge and the cause as ground of existence and proof. In some cases cause and effect are so united, so recipro cate, that we may infer from one to the other. But the doubt arises, may there not be more than one cause for any given attribute, in which case all such inferences from effect must become problem atical. Aristotle s solution is remarkable, both in itself and in its bearing on the inductive syllogism. Suppose the attribute ft is found in all individuals of a class A, and also in individuals of class B, C, &c. In order to discover the cause, investigations must be carried on until we have a denned number of classes A,B,C, &c. , in all of which ft is found, and which comprehend all cases of the presence of ft. Then that which is also common to A,B,C, &c., may be regarded as the cause of ft, say, e.g., an attribute a. If this attri bute a be really the cause of ft, it will enter into its definition ; it will be its definition. There might, however, be a connexion of a and ft of this universal and reciprocating kind, and yet a might not be the cause in question ; it might be only a fact from which ft could be inferred ; the real cause 7, which gives rise to a, lies in the back ground. Characteristic of causation, then, is constant reciprocal conjunction of facts. Even if it be admitted, then, that there may be more causes for a phenomenon than one, it will yet be true that each of these causes will be manifested in one class of pheno mena where there will be the universal reciprocating coexistence that is characteristic of the relation in question. Thus the attribute longevity observable in quadruped animals and in birds may be due to different causes, e.g., to absence of g;ill in the one case, to pre dominance of solid, dry matter in the other. But in each case there will be a definite species characterized by the constant conjunction l Anal. Pr.. ii. 23. Cf. Vhewell. Camt. Phi!. Soc. Trans., vol.ix.. 18.&quot;&amp;gt;6 ; Hamil ton, Lectures, ii. 308-62 ; Grote. I. pp. 268-74 ; Heyder, 216-21! ; Kampe, 189-92. - On induction and recognition of similarity, sec Topics, i. chap. IS, p. 1081), 7 ,&amp;lt;7. ; viii. cliap. 1, J H, and chap. 8, J 1 (in these last similaiity is viewed as being wider in scope than the basis of induction). That induction &quot;implies a complete enumeration, see Anal. I r., ii. chaps. 23, 24: Anal. I ost., ii. chap. 7, J 1. That induction even when complete is not demonstiative, see Anal. I ost., i. chap. 5. 3 On tins distinction see mainly Anal. I ost., ii. 13, where a very fine description of deductive and inductive proof occurs. the discussion regarding the relation of universal and particular in Anal. I r., ii 21 of the cause and the causatum ; the whole class long-lived animals and the class gall-less animals will coincide. Turning now to the chapter on inductive syllogism, we find induction defined as inference through the minor that the major belongs to the middle. Here evidently major and middle are regarded not as determined by form only but naturally distinct, and we must assume that by middle term is to be understood the ground or reason of the attribute (major term) characteristic of a defined species or group (the middle term). Were our knowledge complete and scientific, we should be able to express this in apodu- tic form : whatever animal has no gall is long-lived ; man, horse, mule, &c., are animals having no gall ; therefore they are long-lived. The progress of knowledge, however, may be from the empirical details. We may have given to us the fact of the attribute, long- livedness, in the group of animals, man, horse, &c., and discover that these long-lived animals are also wanting in gall. If then, in accordance with the rules above sketched, there can be discovered a reciprocating relation between want of gall in animals and long- livedness, if we can constitute a class distinguished by conjoint presence of gall-lessness and longevity, we have the basis -for an inductive proof. We may infer therefrom that gall-lessness is, iii this species, the cause of longevity. Such a reasoning is founded on particulars given, and as the coexistence is given, the conclusion seems to be immediately drawn ; there does not appear to be media tion or use of a middle term ; nevertheless the middle term is implied, not in the supposition that the two classes reciprocate, but in the transference from empirical coexistence to causal nexus. Aristotle s mode of stating this argument has presented so many difficulties of interpretation that various emendations have been proposed. Grote, e.g., who has not apprehended why tlie class long- lived animals should be taken universally, &quot;we are,&quot; he says, &quot;in no way concerned with the totality of long-lived animals,&quot; suggests an emendation, which makes the essence of the inductive reasoning turn upon the extension of what we know regarding some gall-less animals to all of that class. But this is not the inductive step according to Aristotle. Induction has not to prove or assume that a and ft, found coexisting in some members of a species, coexist in all of them ; Aristotle takes this universal coexistence for granted as the basis of the argument. The inductive step is the transference from this universal coexistence to causal nexus. Apodictically, we should say, if a is the cause of ft, then all A which possesses a possesses ft ; thus reasoning from cause to causatum. Inductively we say, all A which possesses a has ft ; therefore a is the cause of ft.~ Induction, as dealing with particulars, starting with the sense data, and resting upon the more evident fact ill order to point towards the essential ground or reason, is therefore more persuasive, more palpable, more adapted for popular inquiries, and relatively more apparent. Syllogistic proof, on the other hand, is more strin gent, and more efficacious in establishing a scientific conclusion ex position. Aristotle s mode of dealing with induction, in so far at least as any specific process is designated by that term, seems on the surface to diverge widely from modern logical theory, and we look in vain in his analytical researches for consideration of the methods of observation and experiment which has come to be recognized as the essential portion of a doctrine of inductive reasoning. Yet it may fairly be argued that in modern theories the term induction is used with great laxity, so as to cover either all processes connected with scientific method or some one special feature of scientific reasoning, and that the difference between the Aristotelian and modern views 21, p. 67a, 22 rq. 5 Anal. I ost.. ii. 5. p. 91b, 33, ovK yap o firoy 8 DC Part. Anim.. iv. 2. Cf. Hamilton, Lect.. iv. p. 358 ii. 16-18, see the valuable summary by Grote, i. pp. 366-G8. oSeiKW&amp;lt;rti&amp;gt;, aAX bV&amp;lt;S On Anal. Post., 7 The following is the relative portion of chap. 23 of bk. ii. of the Anal. Pr.: &quot; Xow induction and syllogism through induction is the process of concluding by means of the minor term that the major term is predicable of the middle &quot; (that is to say, of concluding from given facts that an attribute found in all of them is the effect of some other attribute also found in all of them). &quot; For example, if B be the middle term, A and C the extremes, we show, by means of C, that A is predicable of B ; for this is the inductive process. Thus, let A be longlived ; B, those wanting gall: C, individual long-lived, as man. horse, mule. Then A is predicated universally of C&quot; (that is to say, the attribute A is found in all the examples before us), for also that which wants gall is long-lived &quot; (that is to say, as a given fact, gall-lessness and longevity in the species, group, before us coexist). &quot; B, wanting gall, thus is predicated universally of C. If then B and C be reciprocating, if C do not extend beyond the middle term &quot; (that is, if we do not find other animals than the long-lived animals enumerated which also are devoid of gall), &quot; it is necessary that A should be predicated of B. For it has been shown previously that if two terms are predicable of the same third, and if the extreme reciprocate with one of these, then the other of those predicates WUI be pre dicable of that with which the first reciprocated ; but it is necessary to know that C is the complex of all the individual cases.&quot; The last sentence is extremely hard to interpret. The expression TO dxpoi occurring in it is generally the technical word for major term, but as in the syllogism before us the major term is one of the predicates, this signification would seem to contradict the words vpb&amp;lt;; ddrepof avriav. Hamilton reads TO pco-ov, which makes the argument intelligible and coherent with the passage apparently referred to in SeSfucrai Trporepoi: viz.. Anal. Pr.. ii. 21. p. 68a, 21-2-j. Probably Aristotle u.-es TO cucpov here as equivalent to C. the axpov through which the induction proceeds. According to the view taken above, the essence of the Aristotelian induction does not at all lie in the universal izing of C, but in connecting in one proposition the attributes Ii and A found to coexist, in the group C. There is thus in one sense no middle, for cause is net reached ; in another sense there is, for C is the material link connecting A nd I&amp;gt;. Aristotle then might naturally use axpov for C. and assimilate the process of induction to a syllogism in which there ws reciprocation of terms. In fact, however, induction regaided after his fashion results merely in the constitution of a group or class characterized as possessing two attributes in common.
 * C&amp;gt;inparc the passages above noted, and see the curious expression used in