Prior Analytics - Book I   

proof of the first or of the second. For the affirmative is

destroyed by the negative, and the negative by the affirmative.

There remains the proof of possibility. But this is impossible. For it

has been proved that if the terms are related in this manner it is

both necessary that the major should belong to all the minor and not

possible that it should belong to any. Consequently there cannot be

a syllogism to prove the possibility; for the necessary (as we stated)

is not possible.

It is clear that if the terms are universal in possible premisses

a syllogism always results in the first figure, whether they are

affirmative or negative, only a perfect syllogism results in the first

case, an imperfect in the second. But possibility must be understood

according to the definition laid down, not as covering necessity. This

is sometimes forgotten.



15



If one premiss is a simple proposition, the other a problematic,

whenever the major premiss indicates possibility all the syllogisms

will be perfect and establish possibility in the sense defined; but

whenever the minor premiss indicates possibility all the syllogisms

will be imperfect, and those which are negative will establish not

possibility according to the definition, but that the major does not

necessarily belong to any, or to all, of the minor. For if this is so,

we say it is possible that it should belong to none or not to all. Let

A be possible for all B, and let B belong to all C. Since C falls

under B, and A is possible for all B, clearly it is possible for all C

also. So a perfect syllogism results. Likewise if the premiss AB is

negative, and the premiss BC is affirmative, the former stating

possible, the latter simple attribution, a perfect syllogism results

proving that A possibly belongs to no C.

It is clear that perfect syllogisms result if the minor premiss