tradictory of the conclusion put in the place of the other. In the Second Figure, the major is preserved, and the contradictory of the conclusion put in place of the minor; in the Third Figure, the minor is preserved, and the contradictory of the conclusion is put in place of the major : Servat majorem, variatque secunda minorem; Thus, Baroko : All X is Y; Some Z is not Y; Some Z is not X. Every animal feels ; Some living thing does not feel; Therefore, some living thing is not animal. Reduced to Barbara : All X is Y (conceded); All Z is X ; .. All Z is Y; Every animal feels ; Every living is animal; Therefore, every living feels. As this conclusion is the contradictory of the original (given) Minor Premiss, it must be false; one of the premisses must, therefore, be false. But the original major as given is (supposed) true. The falsity is thus in the minor. This is the contradictory of the original conclusion; therefore, the original conclusion is true.2 The K in Baroko and Bokardo means that the premiss indicated by the vowel before it is to have the contradictory of the conclusion put in its place. In the one case, this is the major premiss; in the other, the minor. But the whole of reduction is simply unnecessary; the moods of the Second and Third Figures are on any system equally and as directly valid as those of the First. The superiority of the First Figure over the others lies not in a higher cogency or necessity of sequence, but in greater perspicuity in respect of the principle of inference. 1 Cf. Duncan, Inst. Log., L. iv. c. iii. Reduction by Contraposition has also, though not generally, been employed. Thus Camestres :— Every animal feels; No plant feels; Therefore, no plant is animal. Convert the major by Contraposition What does not feel is not animal, preserve the minor, and we have the same conclusion in Celarent: What does not feel is not animal; Therefore, no plant is animal. So Baroko to Ferio. This was not generally received, because the converse of the minor is less clear as in effect affirmative than the simple affirmation which has been transposed into it.1 1 Cf. Duncan, Inst. Log., L. iv. c. iii. 406 CHAPTER XXXI. CATEGORICAL SYLLOGISMS—ON HAMILTON'S PRINCIPLES—FIGURED AND UNFIGURED SYLLOGISM-ULTRA-TOTAL DISTRIBUTION. § 518. Hamilton has singular merit in his analysis of Figure, Major and Minor Terms, and Propositions. The whole tendency of his inquiries on this point is to simplification, scientific completeness and unity,-leading ultimately, in fact, to the position that Figure, with all its complexities, is unessential to reasoning. The ordinary view rather led to the notion that reasoning depended on the order of expression, certainly that the difference of Major and Minor in terms and propositions did. Hamilton has shown that reasoning depends on the internal thought,-on the essential mental relations of Containing and Contained,-of Inclusion and Exclusion in thought. His view on this point was developed prior to that of the quantification of the predicate. But this doctrine completed the theory. § 519. Mediate or Syllogistic Reasoning (Categorical) is, according to Hamilton, divided into two kinds-the Unfigured and the Figured. In the former, which results directly from the quantification of the predicate, and from regarding the proposition as an equation, the terms compared do not stand to each other in the reciprocal relation of subject and predi cate, being in the same proposition, either both subjects or (possibly) both predicates. The canon for this form of reasoning is: "In as far as two notions (notions proper or individuals) either both agree, or one agreeing, the other does not, with a common third -notion; in so far these notions do or do not agree with each other." § 520. In the Figured Syllogism Proper, again, the terms compared are severally subject and predicate, and thus containing and contained. Its general canon is: "What worse relation of subject and predicate subsists between either of two terms and a common third term, with which one at least is positively related; that relation subsists between the two terms themselves." 1 The Figured Syllogism runs in the counter wholes of Intension and Extension. § 521. According to Aristotle's mode of statement, the middle term was intermediate in nature and in position in the two premisses. Thus : P is in M; M is in S; .. P is in S. This shows the middle term, M, as between the two extremes, P and S. not so enounce such a reasoning. M is P; S is M; .. S is P. lying in the middle and But later logicians did They said : : Here the middle term does not lie between the extremes; and in the Second and Third Figures it no more does so, being in the one twice predicate, in the other twice subject. The Aristotelic form indeed is suitable at once to reasoning in comprehension and in extension. § 522. To preserve the Aristotelic position of the middle term in extension,-the subject being usually first,-it was necessary to state the minor premiss first, even in the First Figure. This was done by a majority of the older logicians. But subsequently this order was departed from, and the major premiss was stated first, thus displacing the middle term from its intermediate position in the syllogism. Now the question arises-Is there any natural rule or law regulating the order of enouncement? In Figured Syllogism, the true principle is the relation of the middle term, as including or included under the subject of the conclusion. It matters nothing as to which premiss is placed first or last in the expression. But to avoid ambiguity that premiss which expresses the relation of the greatest to the less, that which expresses the relation of the less to the least,-should 1 Discussions, p. 654. be placed first and second. The conclusion would, of course, state the relation of the least to the greatest. Thus, in Extension in the First Figure, we should have : M is contained under P; S is contained under M; .. S is contained under P. Р M S Here P is major, predicate of major premiss; S is minor, subject of minor premiss; S is subject of conclusion, P predicate. P the greatest whole; M=the less; S=the least. This being so, S the least must be contained in P the greater. § 523. In Comprehension, the same principle would lead to the reversal of the order of the premisses. Thus : S is M; .. S is P. This means S, the greatest whole, contains in it one mark M; M, the less, contains in it one mark, the least, P; .. S, the greatest whole, contains in it one mark P, the least. Animal contains in it sentient ; Sentient contains in it life; .. Animal contains in it life. It is clear from this that as the premisses in this First Figure determine the relation of the subject of the conclusion to the predicate, as either a part contained under the predicate, or as a whole containing the predicate in it, there can be but one immediate or direct conclusion in each of the moods, and in Extension and Comprehension. The First Figure thus still retains and admits of the distinction of major and minor terms, major and minor propositions, and the conclusion is single or direct, in each of the quantities of Extension and Comprehension. It admits, however, of two conclusions,―a direct and an immediately inferred conclusion.1 We can say : 1 Discussions, p. 658. |