OF AETS AND SCIENCES : APRIL 9, 1867. 265 



the latter term belongs to every object of the former. Hence, in the 

 other premise, it must fulfil the function of a subject. Hence the 

 general formula of all argument must be 



if is P 



S isM 



.-. S is P; 



which is to be understood in this sense, — that the terms of every syllo- 

 gistic argument fulfil functions of subject and predicate as here indi- 

 cated, but not that the argument can be grammatically expressed in 

 this way. 



Part H. § 1. Of Apagogical Forms. 



If G is true when P is, then P is false when C is. Hence it is 

 always possible to substitute for any premise the denial of the conclu- 

 sion, provided the denial of that premise be at the same time substitut- 

 ed for the conclusion.* Hence, corresponding to every syllogistic 

 argument in the general form, 



S is M; MisP; 



S h P. 

 There are two others : — 



It is false that Sis P; Mis P; Sis 31; it is false that ^ is P; 



It is false that S is 31. It is false that if is P. 



% 2. Of Contradiction. 



The apagogical forms make it necessary to consider in what way 

 propositions deny one another. 



If a proposition be put into the general form, 



>S'is P, 



its contradictory has, 1st, as its subject, instead of S, "the S now 



* This operation will be termed a contraposition of the premise and conclusion. 



VOL. VII. 34 



