Prior Analytics - Book II   

premisses are partially false; if one is quite true, the other

partially false; if one is wholly false, the other partially true. For

(1) if A belongs to no B and to all C, e.g. animal to no stone and

to every horse, then if the premisses are stated contrariwise and it

is assumed that A belongs to all B and to no C, though the premisses

are wholly false they will yield a true conclusion. Similarly if A

belongs to all B and to no C: for we shall have the same syllogism.

(2) Again if one premiss is wholly false, the other wholly true: for

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

to no C, e.g. a genus to its co-ordinate species. For animal belongs

to every horse and man, and no man is a horse. If then it is assumed

that animal belongs to all of the one, and none of the other, the

one premiss will be wholly false, the other wholly true, and the

conclusion will be true whichever term the negative statement

concerns.

(3) Also if one premiss is partially false, the other wholly true.

For it is possible that A should belong to some B and to all C, though

B belongs to no C, e.g. animal to some white things and to every

raven, though white belongs to no raven. If then it is assumed that

A belongs to no B, but to the whole of C, the premiss AB is

partially false, the premiss AC wholly true, and the conclusion

true. Similarly if the negative statement is transposed: the proof can

be made by means of the same terms. Also if the affirmative premiss is

partially false, the negative wholly true, a true conclusion is

possible. For nothing prevents A belonging to some B, but not to C

as a whole, while B belongs to no C, e.g. animal belongs to some white

things, but to no pitch, and white belongs to no pitch. Consequently

if it is assumed that A belongs to the whole of B, but to no C, the

premiss AB is partially false, the premiss AC is wholly true, and

the conclusion is true.

(4) And if both the premisses are partially false, the conclusion

may be true. For it is possible that A should belong to some B and