Prior Analytics - Book II   

every man, beautiful not to every man, and beautiful to some bipeds.

If then it is assumed that both A and B belong to the whole of C,

the premiss BC is wholly true, the premiss AC partly false, the

conclusion true. Similarly if of the premisses assumed AC is true

and BC partly false, a true conclusion is possible: this can be

proved, if the same terms as before are transposed. Also the

conclusion may be true if one premiss is negative, the other

affirmative. For since it is possible that B should belong to the

whole of C, and A to some C, and, when they are so, that A should

not belong to all B, therefore it is assumed that B belongs to the

whole of C, and A to no C, the negative premiss is partly false, the

other premiss wholly true, and the conclusion is true. Again since

it has been proved that if A belongs to no C and B to some C, it is

possible that A should not belong to some C, it is clear that if the

premiss AC is wholly true, and the premiss BC partly false, it is

possible that the conclusion should be true. For if it is assumed that

A belongs to no C, and B to all C, the premiss AC is wholly true,

and the premiss BC is partly false.

(5) It is clear also in the case of particular syllogisms that a

true conclusion may come through what is false, in every possible way.

For the same terms must be taken as have been taken when the premisses

are universal, positive terms in positive syllogisms, negative terms

in negative. For it makes no difference to the setting out of the

terms, whether one assumes that what belongs to none belongs to all or

that what belongs to some belongs to all. The same applies to negative

statements.

It is clear then that if the conclusion is false, the premisses of

the argument must be false, either all or some of them; but when the

conclusion is true, it is not necessary that the premisses should be

true, either one or all, yet it is possible, though no part of the

syllogism is true, that the conclusion may none the less be true;

but it is not necessitated. The reason is that when two things are