CATEGORICAL JUDGMENTS AND PROPOSITIONS 261 



are not) S P s, or S P s, as the case may be. For, were universals 

 to imply the existence of their subjects, each universal would be 

 a double assertion : e.g. S a P would mean &quot; There are S s, and all 

 of them are P&quot; ; while if particulars did not imply the existence 

 of their subjects they would really be hypothetical propositions : 

 e.g. S i P would mean * If there are any S s some of them 

 are P&quot;. 



130. EXISTENTIAL IMPORT OF MODAL PROPOSITIONS. It 

 is precisely those universals which, though expressed assertori- 

 cally (All S s are P, No S s are P\ would be more appropriately 

 expressed as modals, that do not imply the existence of their 

 subjects. Propositions which express some necessary connexion 

 of identity or incompatibility between 5 and /*, and which 

 are reached by an analysis of the notions compared, not by 

 any experience of actual instances : these are obviously apodeictic 

 in character, and they do not imply the existence of their subjects. 

 And the same, of course, is true of the propositions which deny 

 any such necessary connexion. But these latter are the prob 

 lematic modals (90). Hence these forms also 5 may be P, 

 S need not be P do not necessarily imply the existence of their 

 subjects. If we accept this view, and combine it with the view 

 that assertoric particulars do, and assertoric universals do not, 

 imply the existence of their subjects, we shall still be able to 

 infer &quot; All S s are P &quot; from &quot; 5 must be P,&quot; but we can no longer 

 infer &quot; Some S s are P &quot; from &quot; S may be P &quot;. 



131. FORMULATION OF EXISTENTIAL PROPOSITIONS. An 

 Existential Proposition is one which directly and explicitly affirms 

 or denies the existence or occurrence of something in the universe to 

 which the proposition refers. For example, &quot; God exists&quot; &quot; It is 

 raining&quot; &quot; Once upon a time there was a man who . . .,&quot; &quot; There 

 are no such things as ghosts&quot; &quot; There is no rose without a thorn? 

 &quot; It came to pass that . . .,&quot; &quot; The Resurrection of Christ is an 

 historical fact I &quot; The tiodo is now extinct&quot; (cf. 86). 



We have already seen (109) that the existence of any class, 

 X, may be expressed by the formula X &amp;gt; o, and its non-existence 

 by the formula X = o ; and, furthermore, that on the assumption 

 of particulars implying and universals not implying the existence 

 of their subjects, the four traditional forms may be expressed : 



S0/&amp;gt;asSP = o 

 5 e P asSP -= o 



