Prior Analytics - Book II   

either both premisses arrived at by the conversion must be particular,

or the universal premiss must refer to the minor extreme. But we found

that no syllogism is possible thus either in the first or in the

middle figure. But if the conclusion is converted into its

contradictory, both the premisses can be refuted. For if A belongs

to no B, and B to all C, then A belongs to no C: again if A belongs to

no B, and to all C, B belongs to no C. And similarly if one of the

premisses is not universal. For if A belongs to no B, and B to some C,

A will not belong to some C: if A belongs to no B, and to C, B will

belong to no C.

Similarly if the original syllogism is negative. Suppose it has been

proved that A does not belong to some B, BC being affirmative, AC

being negative: for it was thus that, as we saw, a syllogism could

be made. Whenever then the contrary of the conclusion is assumed a

syllogism will not be possible. For if A belongs to some B, and B to

all C, no syllogism is possible (as we saw) about A and C. Nor, if A

belongs to some B, and to no C, was a syllogism possible concerning

B and C. Therefore the premisses are not refuted. But when the

contradictory of the conclusion is assumed, they are refuted. For if A

belongs to all B, and B to C, A belongs to all C: but A was supposed

originally to belong to no C. Again if A belongs to all B, and to no

C, then B belongs to no C: but it was supposed to belong to all C. A

similar proof is possible if the premisses are not universal. For AC

becomes universal and negative, the other premiss particular and

affirmative. If then A belongs to all B, and B to some C, it results

that A belongs to some C: but it was supposed to belong to no C. Again

if A belongs to all B, and to no C, then B belongs to no C: but it was

assumed to belong to some C. If A belongs to some B and B to some C,

no syllogism results: nor yet if A belongs to some B, and to no C.

Thus in one way the premisses are refuted, in the other way they are

not.

From what has been said it is clear how a syllogism results in