Prior Analytics - Book II   

premiss BC is wholly false, a true syllogism will be possible: for

nothing prevents A belonging to all B and to all C, though B belongs

to no C, e.g. these being species of the same genus which are not

subordinate one to the other: for animal belongs both to horse and

to man, but horse to no man. If then it is assumed that A belongs to

all B and B to all C, the conclusion will be true, although the

premiss BC is wholly false. Similarly if the premiss AB is negative.

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

and that B should not belong to any C, e.g. a genus to species of

another genus: for animal belongs neither to music nor to the art of

healing, nor does music belong to the art of healing. If then it is

assumed that A belongs to no B, and B to all C, the conclusion will be

true.

(6) And if the premiss BC is not wholly false but in part only, even

so the conclusion may be true. For nothing prevents A belonging to the

whole of B and of C, while B belongs to some C, e.g. a genus to its

species and difference: for animal belongs to every man and to every

footed thing, and man to some footed things though not to all. If then

it is assumed that A belongs to all B, and B to all C, A will belong

to all C: and this ex hypothesi is true. Similarly if the premiss AB

is negative. For it is possible that A should neither belong to any

B nor to any C, though B belongs to some C, e.g. a genus to the

species of another genus and its difference: for animal neither

belongs to any wisdom nor to any instance of 'speculative', but wisdom

belongs to some instance of 'speculative'. If then it should be

assumed that A belongs to no B, and B to all C, will belong to no C:

and this ex hypothesi is true.

In particular syllogisms it is possible when the first premiss is

wholly false, and the other true, that the conclusion should be

true; also when the first premiss is false in part, and the other

true; and when the first is true, and the particular is false; and

when both are false. (7) For nothing prevents A belonging to no B, but