OF ARTS 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 



M is P 



S is M 



. • . 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 II. § 1. Of Apagogical Forms. 



If C is true when P is, then P is false when G 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, 



£ is M; 3IisP; 



S is P. 

 There are two others : — 



It is false that S is P ; M is P; S is M ; it is false that Sis P; 



It is false that S is M. It is false that M 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, 



Sis 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 



