a 76 THE SCIENCE OF LOGIC 



fact that inference would be superfluous (134), every judgment would be 

 likewise superfluous, because everything would be already seen to involve 

 everything else. 



Moreover, the attempt to approach such an ideal by eliminating what is 

 irrelevant from the antecedents of our hypothetical judgments, would make 

 these judgments tautological. When we connect SM with S P in the non- 

 reciprocal hypothetical, &quot;If S is M it is P, n our aim is to connect SP with 

 S M including whatever is irrelevant in the latter. It is just the &quot;irrelevant 

 element&quot; in 5J/that makes it to be S M as distinct from S P, so that were 

 we to eliminate this &quot;irrelevant element&quot; from S M, it would become S P, 

 and thus &quot;the judgment is made a tautology, that is, destroyed&quot;. 1 



In fact, it is the presence of such an element in the premisses or ante 

 cedents of our reasoning processes that makes discursive reasoning possible 

 at the same time that it renders this necessary. Take the typical syllogism, 

 &quot; If M is P and S is M, then S is P &quot;. It is the very presence of the &quot; irrele 

 vant&quot;^/ in the antecedent that enables us to reach the consequent SP, 

 from which the M is eliminated. &quot;But how in this case,&quot; writes Dr. 

 Keynes, &quot; we are to eliminate the irrelevant from the antecedent it is diffi 

 cult to see. Our object is to eliminate M from the consequent, and if in 

 advance we were to eliminate it from the antecedent the whole force of the 

 proposition would be lost. 2 



Finally, there is obviously another way of reaching the reciprocal hypo 

 thetical besides by eliminating from S M what is irrelevant to S P, and 

 that is to expand S P by putting into it all that does follow from the ante 

 cedent SM. 



We may, perhaps, aim at expressing the abstract truths of the exact or 

 mathematical sciences by means of reciprocal hypotheticals ; but if we set 

 up such an ideal in the concrete, inductive, historical and social sciences, 

 or seriously ambition the realization of it, we are not likely to achieve any 

 notable measure of success. 



Besides all this, the hypothetical judgment is not superior to the cate 

 gorical as a form of human knowledge ; indeed it emphasizes more pointedly 

 than the categorical that imperfection which consists in doubt or ignorance 

 as to the real existence of the objects thought about. 



139. OPPOSITION OF HYPOTHETICAL PROPOSITIONS. If it be 

 the function of the pure hypothetical to affirm one judgment to 

 be a necessary consequence of another, there would seem to be 

 no room for a negative hypothetical. 3 The form &quot; If A then 

 not C&quot; would be really affirmative, for its force would be to 

 affirm that the negation of C (or the falsity of C, or the truth 

 of C] is a necessary consequence of the truth of A. There 

 would thus be no room for distinctions of quality ; nor, there 

 fore, for a square of opposition. 



There is, in the next place, certainly no room for distinctions 



1 BOSANQUET, Logic, i., p. 261 \-apiid KEYNES, op. cit. t p. 272. 

 8 Cf. JOSEPH, op. cit., p. 164. 



