Prior Analytics - Book II   

results in the contradictory of the minor premiss. A similar proof can

be given if the premisses are transposed in respect of their quality.

If the syllogism is particular, when the conclusion is converted

into its contrary neither premiss can be refuted, as also happened

in the first figure,' if the conclusion is converted into its

contradictory, both premisses can be refuted. Suppose that A belongs

to no B, and to some C: the conclusion is BC. If then it is assumed

that B belongs to some C, and the statement AB stands, the

conclusion will be that A does not belong to some C. But the

original statement has not been refuted: for it is possible that A

should belong to some C and also not to some C. Again if B belongs

to some C and A to some C, no syllogism will be possible: for

neither of the premisses taken is universal. Consequently the

proposition AB is not refuted. But if the conclusion is converted into

its contradictory, both premisses can be refuted. For if B belongs

to all C, and A to no B, A will belong to no C: but it was assumed

to belong to some C. Again if B belongs to all C and A to some C, A

will belong to some B. The same proof can be given if the universal

statement is affirmative.



10



In the third figure when the conclusion is converted into its

contrary, neither of the premisses can be refuted in any of the

syllogisms, but when the conclusion is converted into its

contradictory, both premisses may be refuted and in all the moods.

Suppose it has been proved that A belongs to some B, C being taken

as middle, and the premisses being universal. If then it is assumed

that A does not belong to some B, but B belongs to all C, no syllogism

is formed about A and C. Nor if A does not belong to some B, but

belongs to all C, will a syllogism be possible about B and C. A

similar proof can be given if the premisses are not universal. For