Prior Analytics - Book I   

relation-white-animal-snow, and for the negative

relation-white-animal-pitch.

The same relation will obtain in particular syllogisms. Whenever the

negative proposition is necessary, the conclusion will be negative

assertoric: e.g. if it is not possible that A should belong to any

B, but B may belong to some of the Cs, it is necessary that A should

not belong to some of the Cs. For if A belongs to all C, but cannot

belong to any B, neither can B belong to any A. So if A belongs to all

C, to none of the Cs can B belong. But it was laid down that B may

belong to some C. But when the particular affirmative in the

negative syllogism, e.g. BC the minor premiss, or the universal

proposition in the affirmative syllogism, e.g. AB the major premiss,

is necessary, there will not be an assertoric conclusion. The

demonstration is the same as before. But if the minor premiss is

universal, and problematic, whether affirmative or negative, and the

major premiss is particular and necessary, there cannot be a

syllogism. Premisses of this kind are possible both where the relation

is positive and necessary, e.g. animal-white-man, and where it is

necessary and negative, e.g. animal-white-garment. But when the

universal is necessary, the particular problematic, if the universal

is negative we may take the terms animal-white-raven to illustrate the

positive relation, or animal-white-pitch to illustrate the negative;

and if the universal is affirmative we may take the terms

animal-white-swan to illustrate the positive relation, and

animal-white-snow to illustrate the negative and necessary relation.

Nor again is a syllogism possible when the premisses are indefinite,

or both particular. Terms applicable in either case to illustrate

the positive relation are animal-white-man: to illustrate the

negative, animal-white-inanimate. For the relation of animal to some

white, and of white to some inanimate, is both necessary and

positive and necessary and negative. Similarly if the relation is

problematic: so the terms may be used for all cases.