Prior Analytics - Book II   

true premisses, is made clear by this consideration. If it is

necessary that B should be when A is, it is necessary that A should

not be when B is not. If then A is true, B must be true: otherwise

it will turn out that the same thing both is and is not at the same

time. But this is impossible. Let it not, because A is laid down as

a single term, be supposed that it is possible, when a single fact

is given, that something should necessarily result. For that is not

possible. For what results necessarily is the conclusion, and the

means by which this comes about are at the least three terms, and

two relations of subject and predicate or premisses. If then it is

true that A belongs to all that to which B belongs, and that B belongs

to all that to which C belongs, it is necessary that A should belong

to all that to which C belongs, and this cannot be false: for then the

same thing will belong and not belong at the same time. So A is

posited as one thing, being two premisses taken together. The same

holds good of negative syllogisms: it is not possible to prove a false

conclusion from true premisses.

But from what is false a true conclusion may be drawn, whether

both the premisses are false or only one, provided that this is not

either of the premisses indifferently, if it is taken as wholly false:

but if the premiss is not taken as wholly false, it does not matter

which of the two is false. (1) Let A belong to the whole of C, but

to none of the Bs, neither let B belong to C. This is possible, e.g.

animal belongs to no stone, nor stone to any man. If then A is taken

to belong to all B and B to all C, A will belong to all C;

consequently though both the premisses are false the conclusion is

true: for every man is an animal. Similarly with the negative. For

it is possible that neither A nor B should belong to any C, although A

belongs to all B, e.g. if the same terms are taken and man is put as

middle: for neither animal nor man belongs to any stone, but animal

belongs to every man. Consequently if one term is taken to belong to

none of that to which it does belong, and the other term is taken to