Prior Analytics - Book I   

negative major premiss is not necessary the conclusion will not be

necessary either. Therefore the same result will obtain here. Further,

if the conclusion is necessary, it follows that C necessarily does not

belong to some A. For if B necessarily belongs to no C, C will

necessarily belong to no B. But B at any rate must belong to some A,

if it is true (as was assumed) that A necessarily belongs to all B.

Consequently it is necessary that C does not belong to some A. But

nothing prevents such an A being taken that it is possible for C to

belong to all of it. Further one might show by an exposition of

terms that the conclusion is not necessary without qualification,

though it is a necessary conclusion from the premisses. For example

let A be animal, B man, C white, and let the premisses be assumed to

correspond to what we had before: it is possible that animal should

belong to nothing white. Man then will not belong to anything white,

but not necessarily: for it is possible for man to be born white,

not however so long as animal belongs to nothing white. Consequently

under these conditions the conclusion will be necessary, but it is not

necessary without qualification.

Similar results will obtain also in particular syllogisms. For

whenever the negative premiss is both universal and necessary, then

the conclusion will be necessary: but whenever the affirmative premiss

is universal, the negative particular, the conclusion will not be

necessary. First then let the negative premiss be both universal and

necessary: let it be possible for no B that A should belong to it, and

let A simply belong to some C. Since the negative statement is

convertible, it will be possible for no A that B should belong to

it: but A belongs to some C; consequently B necessarily does not

belong to some of the Cs. Again let the affirmative premiss be both

universal and necessary, and let the major premiss be affirmative.

If then A necessarily belongs to all B, but does not belong to some C,

it is clear that B will not belong to some C, but not necessarily. For

the same terms can be used to demonstrate the point, which were used