Prior Analytics - Book I   

follows is not necessary. Suppose A necessarily belongs to all B,

and let B be possible for all C. We shall have an imperfect

syllogism to prove that A may belong to all C. That it is imperfect is

clear from the proof: for it will be proved in the same manner as

above. Again, let A be possible for all B, and let B necessarily

belong to all C. We shall then have a syllogism to prove that A may

belong to all C, not that A does belong to all C: and it is perfect,

not imperfect: for it is completed directly through the original

premisses.

But if the premisses are not similar in quality, suppose first

that the negative premiss is necessary, and let necessarily A not be

possible for any B, but let B be possible for all C. It is necessary

then that A belongs to no C. For suppose A to belong to all C or to

some C. Now we assumed that A is not possible for any B. Since then

the negative proposition is convertible, B is not possible for any

A. But A is supposed to belong to all C or to some C. Consequently B

will not be possible for any C or for all C. But it was originally

laid down that B is possible for all C. And it is clear that the

possibility of belonging can be inferred, since the fact of not

belonging is inferred. Again, let the affirmative premiss be

necessary, and let A possibly not belong to any B, and let B

necessarily belong to all C. The syllogism will be perfect, but it

will establish a problematic negative, not an assertoric negative. For

the major premiss was problematic, and further it is not possible to

prove the assertoric conclusion per impossibile. For if it were

supposed that A belongs to some C, and it is laid down that A possibly

does not belong to any B, no impossible relation between B and C

follows from these premisses. But if the minor premiss is negative,

when it is problematic a syllogism is possible by conversion, as

above; but when it is necessary no syllogism can be formed. Nor

again when both premisses are negative, and the minor is necessary.

The same terms as before serve both for the positive