266 PROCEEDINGS OF THE AMERICAN ACADEMY 



meant " * or " some *S"'; and has, 2d, as its predicate, instead of P, that 

 which differs from P or " not P." 



From these relations of contradictories, from the necessities of the 

 logic of apagogically related arguments, therefore, arises the need of 

 the two divisions of propositions into affirmative and negative on the 

 one hand, and into universal and particular on the other. The con- 

 tradictory of a universal proposition is particular, and the contradic- 

 tory of an affirmative proposition is negative. Contradiction is a recip- 

 rocal relation, and therefore the contradictory of a particular propo- 

 sition is universal, and that of a negative proposition is affirmative. 

 The contradiction of particular and negative propositions could 

 not be brought under the general formula, were the distinctions of 

 affirmative and negative absolute and not merely relative ; but, in 

 fact, not-not-P is the same as P. And, if it is said that " what is now 

 meant of the part of S meant at another time, is P" since the 

 part of S meant at another time is left to be determined in whatever 

 way the proposition made at another time may determine it, this can 

 only be true if All S is P. Therefore, if one man says " some *S' is 

 not P" and another replies, " some of that same >S' is P" this second 

 person, since he allows the first man's some S, which has not been 

 defined, to remain undefined, in effect says that All S is P. 



Whether contradictories differ in other respects than these well- 

 known ones is an open question. 



§ 3. Of Barbara. 



Since some S means " the part now meant of S" a particular prop- 

 osition is equivalent to a universal proposition with another subject; and 

 in the same way a negative proposition is equivalent to an affirmative 

 proposition with another predicate. 



The form, S is P, 



therefore, as well as representing propositions in general, particularly 



represents Universal Affirmative propositions ; and thus the general 



form of syllogism 



ATis P; ^ is M; 



S is P, 

 represents specially the syllogisms of the mood Barbara. 



* What <S is meant being generally undetermined. 



