278 THE SCIENCE OF LOGIC 



examine the results of the various possible suppositions ; for the same prin 

 ciples apply here as in the case of categoricals. 



We referred above (136) to the danger of mistaking the contrary for the 

 contradictory of a conditional proposition. The same danger exists in the 

 case of the hypothetical. The proposition If A then not C cannot possibly 

 be the contradictory of the proposition If A then C. If both be interpreted 

 modally and as implying the possible truth of their antecedents, they cannot 

 be true together ; but they may both be false together : for neither the truth 

 nor the falsity of C may be a necessary consequence of the truth of A : a in 

 which case they would be contraries. If, being modal, they be not understood 

 to imply the possible truth of their antecedents, not only might both be false 

 together, but both might be true together, thus uniting to establish the im 

 possibility of A, just as in the analogous case All S s are P s and No S s are 

 P^s might both be true while establishing the non-existence of 5 (127). 



If both be interpreted assertorically, If A then C merely denies A C, 

 and If A then not C merely denies AC: hence both cannot be false together, 

 for that would mean the simultaneous truth of A C and A C. But both may 

 be true together ; for since they merely deny A C and A C they are simul 

 taneously compatible with A C, or with A C. For example, neither of the 

 propositions &quot; If this pen is not cross-nibbed it is corroded with ink &quot; (If A 

 then C) and &quot; If this pen is not c toss-nibbed it is not corroded with ink (If A 

 then C] can be said to be false in case the pen is cross-nibbed. 2 



Hence, on the assertoric interpretation, If A then C and If A then not C 

 are subcontraries. 



140. EDUCTIONS FROM HYPOTHETICAL PROPOSITIONS. As 

 in the case of conditionals/ the most important eductions here are 

 those analogous to the contrapositive of A and the converse of E 

 in categoricals. 



A From &quot; If A then C&quot; we infer by contraposition &quot; If not C 

 then not A &quot;. For example, from the proposition, &quot; If there is a 

 just God the wicked will be punished&quot; we infer &quot; If the wicked are 

 not punished there is no just God &quot;. 



E From &quot; If A then not C&quot; we infer by conversion &quot; If C 

 then not A&quot; . For example, from the proposition &quot; If the scrip 

 tures speak truly the human soul will never die&quot; we infer &quot; If the 

 human soul dies the scriptures do not speak truly &quot;. 



The converse and inverse of A, and the contrapositive and 

 inverse of E are, of course, obtainable ; but they are of little im 

 portance, seeing that they give us practically no knowledge : for 

 they are all problematic, merely stating that something may, or 

 need not, follow from something else. 



1 If A then. not-C means that not-C follows necessarily from A which is much 

 more than to say merely that C does not follow necessarily from A. 

 a KEYNES, op. cit., p. 267. 



