254 THE SCIENCE OF LOGIC 



the converse an implication of existence not contained in the convertend, un 

 less this latter be supposed to imply the existence of S ; or, unless the exist 

 ence of S be otherwise guaranteed. 



Again, the tacit assumption on which alone all the traditional eductions 

 in Chap. VI. are valid (as categoricals) is the assumption that S, P, S and 

 P represent classes actually existing in the universe of discourse of the pro 

 position (cf. 120) : whether this was considered to be implied in each of 

 the four propositions, A, E, I, O, or merely assumed concomitantly by the 

 person judging. In regard to the traditional doctrine on Opposition (Chap. V.), 

 Dr. Keynes says this will be found to hold good universally only on the under 

 standing that universal propositions be supposed to imply, and particulars 

 not to imply the existence of their subjects in the universe of discourse. 

 And he points out that this supposition &quot;conflicts altogether with popular 

 usage ; it renders the processes of simple conversion and simple contra 

 position illegitimate ; and whilst making universals double judgments, it 

 destroys the categorical character of particulars altogether&quot;. 1 



But the traditional doctrine on opposition will also hold good if the 

 existence of S be assumed independently of the import of the propositions 

 themselves altogether. And this appears to have been the assumption really, 

 if only implicitly, made in scholastic logic. We shall find on examination 

 that the traditional doctrine on contradictory and subcontrary opposition 

 holds good on the tacit assumption that S at least represents an actually 

 existing class, and that we are therefore precluded from supposing S to be 

 non-existent ; 2 while if this assumption that 6* represents an existing class 

 were made part of the meaning of the proposition, so that &quot;All S is P&quot; 

 would mean &quot; S exists and is always /*,&quot; then, were 6&quot; non-existent, the three 

 propositions &quot; All S is P,&quot; &quot; Some S is P,&quot; and &quot; Some S is not P,&quot; would 

 be all false together. For instance, if the propositions &quot; /2//(0rsome of} the 

 answers to the questions showed originality &quot; and &quot; Some of the answers to 

 the questions did not show originality &quot; implied as pait of their meaning 

 the existence of &quot;answers,&quot; they would all be false in case there were no 

 answers. In such a case the real contradictory of &quot;All the answers to the 

 questions showed originality &quot; would be &quot; Either some did not . . . or there 

 were no answers at all&quot;. The traditional doctrine on opposition did not 

 consider the existence of S (or P or S or P) to be implied as part of their 

 meaning by the A, E, I, and O propositions, but to be presupposed by them, so 

 that the possible consequences of the non-existence of any such class could 

 not arise at all for discussion. 



126. STATEMENT OF THE QUESTION OF EXISTENTIAL IM 

 PORT IN CATEGORICAL PROPOSITIONS. The question is formu 

 lated in practically the following terms by Dr. Keynes. 3 It 

 is part at least of the meaning of every universal proposition to 

 deny the existence of a certain class of objects of thought in some 

 universe or sphere of being. 4 S e P denies that there are such 



1 op. cit., p. 241, note 3. 2 o/&amp;gt;. cit., pp. 228, 229. 3 op. cit., pp. 212, 213. 



4 And, by implication, to affirm the existence of the contradictory class. For, 



since the sphere referred to by any judgment is objectively real, it cannot be sup- 



