CATEGORICAL JUDGMENTS AND PROPOSITIONS 255 



things as 5 P s, S a P denies that there are such things as 5 P s, 

 in a certain universe. This universe, in which the existence of 

 S P (or S P) is denied by the universal proposition, is the universe 

 of discourse of that proposition. The universe of discourse for 

 the particulars, S i P and S o P, is that universe, whatever it be, 

 in which the existence 5 P, or of 5 P, would be understood to 

 be denied by their respective contradictories, S e P and S a P. 



Now, given a categorical proposition with S and P as subject 

 and predicate, does it formally imply the existence of S or of P in 

 that sphere in which it (or its contradictory] denies the existence of 

 S P (or S P). 



Or, in other terms, S P (or S P), as an object, of thought is a 



certain complex of attributes: so is 5 itself, and so is P itself: 



does the categorical proposition imply the existence of these latter 



complexes in the same sense as it denies the existence of the 



former. 1 



Since the question is one of interpreting the meaning we are 

 to attach to prepositional forms, it is obvious that to some extent 

 different alternative solutions may be agreed upon ; that, on ac 

 count of the conventional element there is in the ordinary use of 

 language, and the absence of rigidly fixed meaning, no one solu 

 tion can be pronounced correct to the exclusion of all others (cf. 86, 

 87). But it is no less clear that in such interpretation we should 

 be guided to our results mainly by observing what people gener 

 ally mean to convey by the use of the ordinary propositional forms. 

 This is ^primary consideration. A secondary one is the influence 

 each of the various possible suppositions may have upon ordinary 

 processes of inference, whether mediate or immediate. Ceteris 

 paribus, the interpretation that would lend itself best to the logical 

 treatment of inferences from judgments should have our prefer 

 ence. 



127. INFLUENCE OF VARIOUS SUPPOSITIONS ON VALIDITY 

 OF LOGICAL INFERENCES. Of the very many suppositions 



posed to be entirely empty of content. Hence, any judgment which denies the exist 

 ence of S, or of P, implicitly affirms the existence of S, or of P, by the Principle of 

 Excluded Middle. But the affirmation of the existence of a class does not imply the 

 denial of the existence of the contradictory class. 



1 When it is remembered we are dealing with assertoric propositions, it may 

 reasonably be asked how we could reach a knowledge of the universals which deny 

 the existence of S P or S P, except we experienced both S and P (or S and P) as 

 actually existing in the universe of discourse. Cf. infra, p. 256, n. 2. 



