Prior Analytics - Book II   

belong to all of that to which it does not belong, though both the

premisses are false the conclusion will be true. (2) A similar proof

may be given if each premiss is partially false.

(3) But if one only of the premisses is false, when the first

premiss is wholly false, e.g. AB, the conclusion will not be true, but

if the premiss BC is wholly false, a true conclusion will be possible.

I mean by 'wholly false' the contrary of the truth, e.g. if what

belongs to none is assumed to belong to all, or if what belongs to all

is assumed to belong to none. Let A belong to no B, and B to all C. If

then the premiss BC which I take is true, and the premiss AB is wholly

false, viz. that A belongs to all B, it is impossible that the

conclusion should be true: for A belonged to none of the Cs, since A

belonged to nothing to which B belonged, and B belonged to all C.

Similarly there cannot be a true conclusion if A belongs to all B, and

B to all C, but while the true premiss BC is assumed, the wholly false

premiss AB is also assumed, viz. that A belongs to nothing to which

B belongs: here the conclusion must be false. For A will belong to all

C, since A belongs to everything to which B belongs, and B to all C.

It is clear then that when the first premiss is wholly false,

whether affirmative or negative, and the other premiss is true, the

conclusion cannot be true.

(4) But if the premiss is not wholly false, a true conclusion is

possible. For if A belongs to all C and to some B, and if B belongs to

all C, e.g. animal to every swan and to some white thing, and white to

every swan, then if we take as premisses that A belongs to all B,

and B to all C, A will belong to all C truly: for every swan is an

animal. Similarly if the statement AB is negative. For it is

possible that A should belong to some B and to no C, and that B should

belong to all C, e.g. animal to some white thing, but to no snow,

and white to all snow. If then one should assume that A belongs to

no B, and B to all C, then will belong to no C.

(5) But if the premiss AB, which is assumed, is wholly true, and the