CATEGORICAL JUDGMENTS AND PROPOSITIONS 257 



of the former, but is compatible with it : in the case, namely, in 

 which S is non-existent. The forms given as contradictories in 

 the square of opposition are therefore not contradictories. Nor 

 are S a P and S e P contraries, for the former merely asserts 

 that there are no 5 P s and the latter that there are no 5 P s : 

 two statements which may be true together, viz. , when S is non 

 existent, (b) As regards eductions: the conversion of A and 

 I will be, as we have seen (125), invalid; for in either case 

 the converse will imply that if there are any P s there are 

 some S s an implication not contained in either original. 

 Hence, too, the contraposition of E and O and the inversion 

 of E and A are invalid, since all these involve the conversion 

 of an A or an I proposition. 



(4) If particulars be taken to imply, and universals not to imply 

 the existence of their subjects, then (a) as regards opposition : the 

 forms given as contradictories are really contradictories, for it is 

 exactly what the universal denies (the existence of 5 P s or 5 P s) 

 that the particular of opposite quality affirms. But the forms given 

 as subalternants and subalterns, as contraries, and as sub contraries, 

 are not really such. From All S is P we cannot infer Some S 

 is P ; All S is P and No S is P may be true together, their 

 combined force being to deny the existence of S s; and both 

 Some S is P and Some S is not P will be false if 5 does not 

 exist (b) Of the eductions : the conversion of A is invalid ; J and, 

 consequently, the contraposition of E, and the inversion both of A 



collateral and independent assumption of S, P, S, and P, as existing classes: and it 

 is on this understanding that its results are worked out by Dr. Keynes seems to 

 be an impracticable supposition, i.e. one that is never realized in the case of assertoric 

 judgments, which are the only ones contemplated. The assertoric judgment, even 

 when universal, is a judgment of fact, based on experience. How, then, can we 

 know the truth of S a P or S e P tha there jire no S P s, or that there are no 

 S P s unless we have experienced S or S, P or P, as actually existing classes ? And 

 so far as we have experienced the actual existence of any such class, we may reason 

 ably assume its existence in examining the implications of our judgments in reference 

 to it. The interpretation of the assertoric particular, S i P (or S o P), as excluding 

 all assumption of the existence of S, P, S or P, is still more strained. How can ex 

 perience enable us to assert as a fact that some S s are P s (or not P s) unless we 

 have experienced S, P, or P, as actually existing. Such existence, if not indeed im 

 plied, is certainly assumed in S i P or S o P, so that these forms, in so far as they 

 assert existence at all, assert the existence of S P or S P just as categorically as 

 S e P or S a P deny such existence. 



1 Unless S be otherwise given as existing in some such proposition, e.g. as Some 

 R is S. So, also, can E be converted in supposition (2) above, if P be otherwise 

 guaranteed as existing. 



VOL. I. 17 



