Prior Analytics - Book I   

conclusion be necessary. Further, the point may be made clear by

considering the terms. Let the term A be 'good', let that which B

signifies be 'animal', let the term C be 'horse'. It is possible

then that the term good should belong to no horse, and it is necessary

that the term animal should belong to every horse: but it is not

necessary that some animal should not be good, since it is possible

for every animal to be good. Or if that is not possible, take as the

term 'awake' or 'asleep': for every animal can accept these.

If, then, the premisses are universal, we have stated when the

conclusion will be necessary. But if one premiss is universal, the

other particular, and if both are affirmative, whenever the

universal is necessary the conclusion also must be necessary. The

demonstration is the same as before; for the particular affirmative

also is convertible. If then it is necessary that B should belong to

all C, and A falls under C, it is necessary that B should belong to

some A. But if B must belong to some A, then A must belong to some

B: for conversion is possible. Similarly also if AC should be

necessary and universal: for B falls under C. But if the particular

premiss is necessary, the conclusion will not be necessary. Let the

premiss BC be both particular and necessary, and let A belong to all

C, not however necessarily. If the proposition BC is converted the

first figure is formed, and the universal premiss is not necessary,

but the particular is necessary. But when the premisses were thus, the

conclusion (as we proved was not necessary: consequently it is not

here either. Further, the point is clear if we look at the terms.

Let A be waking, B biped, and C animal. It is necessary that B

should belong to some C, but it is possible for A to belong to C,

and that A should belong to B is not necessary. For there is no

necessity that some biped should be asleep or awake. Similarly and

by means of the same terms proof can be made, should the proposition

AC be both particular and necessary.

But if one premiss is affirmative, the other negative, whenever