RATIOCINATION, OR SYLLOGISM. 191 



2. On examining, then, these two general formulae, we 

 find that in both of them, one premise, the major, is an uni- 

 versal proposition; and according as this is affirmative or 

 negative, the conclusion is so too. All ratiocination, therefore, 

 starts from a general proposition, principle, or assumption : a 



account of them, I will not say that it was not worth while to show in detail 

 how these also could be reduced to formulae 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 practical use of technical forms of rea- 

 soning is to bar out fallacies : but the fallacies which require to be guarded 

 against in ratiocination properly so called, arise from the incautious use of the 

 common forms of language ; and the logician must track the fallacy into that 

 territoi-y, instead of waiting for it on a territory of his own. While he remains 

 among propositions which have acquired the numerical precision of the Calculus 

 of Probabilities, the enemy is left in possession of the only ground on which he 

 can be formidable. And since the propositions (short of universal) on which 

 a thinker has to depend, either for purposes of speculation or of practice, do 

 not, except in a few peculiar cases, admit of any numerical precision ; common 

 reasoning cannot be translated into Mr. De Morgan's forms, which therefore 

 cannot serve any purpose as a test of it. 



Sir William Hamilton's theory of the " quantification of the predicate" (con- 

 cerning the originality of which in his case there can be no doubt, however Mr. 

 De Morgan may have also, and independently, originated an equivalent doc- 

 trine) may be briefly described as follows : 



" Logically" (I quote his own words) " we ought to take into account the 

 quantity, always understood in thought, but usually, for manifest reasons, 

 elided in its expression, 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 tantamount 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 coextensive with the subject, they all admit 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 coextensive. The last three forms, though 

 conveying real assertions, have no place in the ordinary classification of Pro- 

 positions. All propositions, then, being supposed to be translated into this 

 language, and written each in that one of the preceding forms which answers 

 to its signification, there emerges a new set of syllogistic rules, materially dif- 

 ferent from the common ones. A general view of the points of difference may 

 be given in the words of Sir W. Hamilton (Discussions, 2nd ed. p. 651) : 



"The revocation of the two terms of a Proposition to their true relation ; a 

 proposition being always an equation of its subject and its predicate. 



" The consequent reduction of the Conversion of Propositions from three 

 species to one that of Simple Conversion. 



