274 THE SCIENCE OF LOGIC 



If, however, it denies the possibility of combining not-C with A, 

 then its contradictory will merely assert that possibility (without 

 asserting the actuality)^ and will therefore be &quot; If A is true C may 

 be false&quot; or &quot; If A then perhaps not C n . 



Although we meet with occasional examples of hypothetical 

 which may be interpreted assertorically , these are by no means 

 typical of the pure hypothetical, which has usually a modal force. 

 The following few instances of the hypothetical form used asser 

 torically are given by Dr. Keynes : * &quot; If the flowers I planted in this 

 bed were not pansies, they were violets &quot; where I know that one of 

 two propositions is true but do not know or remember which ; 

 11 If that boy comes back Pll eat my head&quot; (vide Oliver Twisty 

 where we emphatically deny a proposition by making its contra 

 dictory the antecedent of a manifestly false consequent ; &quot; // he 

 cannot act, he can at any rate sing&quot; where we emphasize the truth 

 of a proposition by making it the consequent of an admittedly 

 true antecedent. 2 But these examples are not typical of the ordi 

 nary hypothetical. A sufficient proof that the latter is interpreted 

 modally is found in the fact that in order to contradict &quot; If A then 

 C&quot; we consider it quite sufficient to be able to say &quot; If A then not 

 necessarily C&quot; without categorically affirming A and denying C 

 in the copulative form &quot;A but not C&quot;. We shall therefore inter 

 pret &quot; If A then C&quot; apodeictically &amp;gt; i.e. to mean that C is a necessary 

 consequence of A. 



This, of course, does not necessarily imply that C is an immediate infer 

 ence from A. Where C is an immediate inference from A, where A gives 

 explicitly the adequate ground for C, we might call the proposition a formal 

 or self-contained hypothetical ; 3 e.g. &quot; If all men are mortal^ and the Pope is 

 a man, then the Pope is mortal&quot;. But, far oftener, A is only a part, though a 

 necessary part, of the adequate ground of C, the suppressed past being taken 

 for granted. The name referential has been suggested for this class of 

 hypotheticals. 4 



The question has been raised whether, in the ideally perfect hypothetical 

 or conditional proposition, the antecedent should give what is at once 

 the adequate and the only possible ground for the consequent, and neither 

 more nor less than this. If, in the proposition &quot; If S is M it is /*,&quot; the &quot;M&quot; 

 gave us explicitly the sufficient an& only possible ground for &quot;/*,&quot; and nothing 

 else, the proposition would be reciprocal : we should infer from consequent 

 to antecedent as necessarily as from antecedent to consequent, and we should 

 be enabled to convert our A proposition simply , to &quot; If S is P it is M &quot;. 



1 op. cit., pp. 262, 263. 



2 Compare such forms as &quot; If Cromwell was an Englishman he was an 

 usurper&quot;. 



;t KEYNES, op. cit. t p. 264, footnote. *ibid. 



