THE THEORY OF SYLLOGISM, ETC. 



89 



X: , Y:, Z=X: , Z, instead of X))Y))Z = X))Z. And I am bound to attribute* to Sir 

 William Hamilton the expression of the two distinct quantities, universal and particular, as two 

 distinct matters of phraseology and thence of notation, when the quantities are not numeri- 

 cally conceived and expressed. (F. L. p. 301.) 



If then the preceding notations were as much alike as they appear to be, I should call mine 

 '(which was first used in trying Sir W. Hamilton's system, F. L. p. 302), so far as affirmative 

 syllogisms are concerned, Sir William Hamilton's with what I judge to be a more convenient 

 mode of expression. But there is, in fact (independently of the omission of term-symbols), 

 a very material difference, and one which makes the notation I have given more suggestive T, 

 and its symbolic rules more easy to some extent in my own system, to a greater in Sir William 

 Hamilton's. In his mode of notation, the symbols of universal and particular are absolute 

 (: and ,) : in mine, the universality of the subject has the same symbol as the particularity 

 of the predicate, and vice versa: thus in X))Y, the same symbol [)] is applied to the 

 universal subject, and the particular predicate. 



The notion on which this mode of symbolizing quantity was tried and found to succeed, 

 was as follows : The most natural mode of predication, because the easiest premise for 

 inference, is the affirmative, and the syllogism of affirmative premises is the one to which all 

 other cases are naturally reduced. And here the predicates are always particular, while the 

 subjects are either universal, or, which is the same reality in inference, take the whole extent 

 named in the premise into the conclusion. Whenever this is the case, the invention of a name 

 will shew that the inference is of the same kind as one in which the term of the premise and 

 of the conclusion are both universal. In representing " All X is in Y, all Y is in Z, therefore 

 all X is in Z? by X))Y))Z there is something pictorial, and the particular character of the 

 predicate has its symbol of particularity invented out of the relation to the subject from 

 which we deduce that character. 



* And I may also note an inaccuracy of expression used by 

 Mr Thomson (pp. 265, 266): "Many of the different ele- 

 ments of the notation are not new, but the novelty lies in the 

 completeness and simplicity of the whole scheme." Not so; 

 for though the notation had failed entirely both in complete- 

 ness and simplicity, there would have remained the most re- 

 markable novelty which there now is, namely, notation of 

 quantity in both subject and predicate. 



t It would seem that the forms given by Sir William Ha- 



milton have not suggested any rules. " In the negative modes 

 the distribution of terms will remain exactly the same as it 

 was in the affirmatives from whence they were respectively 

 formed, with some few exceptions in which the conclusion has 

 a term distributed which was not when it was affirmative." 

 Thomson, Op. Cit. p. 267. Under a suggestive notation, the 

 rule which regulates the exceptions will be visible; and it will 

 be seen that these so called exceptions are in the rule, and 

 that cases of the affirmative syllogism are the exceptions. 



Vol. IX. Part I. 



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