RATIOCINATION, OR SYLLOGISM. 



"3 



§ 2. On examining, then, these two 

 general formulae, we find that in both 

 of them, one premise, the major, is an 

 universal proposition ; and according 

 as this is affirmative or negative, the 

 conclusion is so too. All ratiocina- 



can legitimately be drawn, and that the or- 

 dinary theory takes no account of them, 

 I will not say that it was not worth while 

 to >-how in detail how these also could be 

 reduced to forinulae as rigorous as those of 

 Aristotle. What Mr De Morgan has done 

 was worth doing once (perhaps more than 

 once, as a school exercise) ; but I question 

 if its results are worth studying and mas- 

 tering for any practical purpose. The prac- 

 tical use of technical forms of reasoning is 

 to bar out fallacies ; but the lallacie 5 which 

 require: to be guarded against in ratiocina- 

 tion properly so called, arise from the in- 

 cautious use of the common forms of lan- 

 guage ; and the logician must track the 

 fiUlacy into thar. territory, instead of wait- 

 ing for it on a territory of his own. While 

 he remains among propositions which have 

 acquired the numerical {)recision of the 

 Calculus of Probabilities, the enemy is left 

 in possession of tue only ground on which 

 he can be formidable. And since the pro- 

 positions (short of universal) on which a 

 thinker lias to depend, either for purposes 

 of speculation or of practice, do not, except 

 in a few peculiar cases, admit of any nume- 

 rical j)recision, common reasoning cannot 

 be translated into Mr. De Morgan's forms, 

 which therefore Ciinnot serve any purpose 

 as a test of it. 



Sir William Hamilton's theory of the 

 " quantification of the predicate " may be 

 described as follows :— 



"Logically" (I quote his words) "we 

 ought to take into account the quantity, 

 always vmderstood in thought, but usually, 

 for manifest reasons, elided in its expres- 

 sion, not only of the subject, but also of 

 the predicate of a judgment." All A is B, 

 is equivalent to all A is some B. No A is 

 B, to No A is any B. Some A is B, is tanta- 

 mount to Some A is some B. Some A is 

 not B, to Some A is not any B. As in these 

 forms of assertion the predicate is exactly 

 co-extensive with the subject, they all ad- 

 mit of simple conversion ; and by this we 

 obtain two additional forms— Some B is all 

 A and no B is some A. We may also make 

 the assertion All A is all B, which will be 

 true if the classes A and B are exactly co- 

 extensive. The last three forms, though 

 conveying real asst rtions, have no place in 

 the ordinary classification of Propositions. 

 All propositions, then, being supposed to 

 be translated into this language, and writ- 

 ten each in that one of the preceding forms 

 which answers to its signification, there 

 emerges a new set of syllogistic rules, mate- 

 rially different from the common ones. A 

 general view of tbp uointa of difference 



tion, therefore, starts from a general 

 proposition, principle, or assumption : 

 a proposition in which a predicate is 

 affirmed or denied of an entire class ; 

 that is, in which some attribute, or 

 the negation of some attribute, is 



may be given in the words of Sir W. 

 Hamilton {Discussions, ad ed. p. 651) : — 



"The revocation of tiie two terms of a 

 Proposition to their true relation ; a pro- 

 position being always an equation of its 

 subject and its predicate. 



"The consequent reduction of the Con- 

 version of Prop sitions from three species 

 to one — that of Simple Conversion. 



"The reduction of all the General Laws of 

 Categorical Syllogisms to a single Canon. 



"The evolution from that one canon of 

 all the Species and varieties of Syllogisms. 



" The abrogation of all the Special Laws 

 of Syllogism. 



"A demonstration of the exclusive pos- 

 sibility of Three Syllogistic Figures ; and 

 (on new grounds) the scientific and final 

 abolition of the Fourth. 



"A manifestation tiiat Figure is an un- 

 essential variation in syllogistic form ; and 

 the consequent absurdity of Reducing the 

 syllogisms of the other figures to tlie first. 



"An enouncement of one Organic Prin- 

 ciple for each Figure. 



" A determination of the true number of 

 the Legitimate Moods ; with 



" Their amplification in number (thirty- 

 six); 



" Their numerical equality under all the 

 figures ; and 



"Their relative equivalence, or virtual 

 identity, tiiroughoiit every schematic dif- 

 ference. 



"That, in the second and third figures, 

 the extremes holdint? both the same rela- 

 tion to the middle term, there is not, as in 

 the first, an opposition and subordination 

 between a term major and a term minor, 

 mutually containing and contained, in the 

 counter wholes of Extension and Compre- 

 hension. 



"Consequently, in the second and third 

 figures, there is no determinate major and 

 minor premise, and there are two indiffe- 

 rent conclusions ; whereas in the first the 

 premises are determinate, and there is a 

 single proximate conclusion." 



This doctrine, like tiiatof Mr. De Morgan 

 previously noticed, is a real addition to the 

 syllogistic theory ; and has moreover this 

 advantage over Mr. De Morgan's " numeri- 

 cally definite syllogism," that the forms it 

 supplies are really available as a test of the 

 correctne.ss of ratiocination ; since proposi- 

 tions in the common form may always have 

 their predicates quantified, and so be made 

 amenable to Sir W. Hamilton's rules. Con- 

 sidered however as a contribution to the 

 Science of Logic, that is, to the analysis of 

 the mental processes concerned in reason- 

 B 



