Prior Analytics - Book II   

mean the opposition of 'to all' to 'to none', and of 'to some' to 'not

to some'. Suppose that A been proved of C, through B as middle term.

If then it should be assumed that A belongs to no C, but to all B, B

will belong to no C. And if A belongs to no C, and B to all C, A

will belong, not to no B at all, but not to all B. For (as we saw) the

universal is not proved through the last figure. In a word it is not

possible to refute universally by conversion the premiss which

concerns the major extreme: for the refutation always proceeds through

the third since it is necessary to take both premisses in reference to

the minor extreme. Similarly if the syllogism is negative. Suppose

it has been proved that A belongs to no C through B. Then if it is

assumed that A belongs to all C, and to no B, B will belong to none of

the Cs. And if A and B belong to all C, A will belong to some B: but

in the original premiss it belonged to no B.

If the conclusion is converted into its contradictory, the

syllogisms will be contradictory and not universal. For one premiss is

particular, so that the conclusion also will be particular. Let the

syllogism be affirmative, and let it be converted as stated. Then if A

belongs not to all C, but to all B, B will belong not to all C. And if

A belongs not to all C, but B belongs to all C, A will belong not to

all B. Similarly if the syllogism is negative. For if A belongs to

some C, and to no B, B will belong, not to no C at all, but-not to

some C. And if A belongs to some C, and B to all C, as was

originally assumed, A will belong to some B.

In particular syllogisms when the conclusion is converted into its

contradictory, both premisses may be refuted, but when it is converted

into its contrary, neither. For the result is no longer, as in the

universal syllogisms, refutation in which the conclusion reached by O,

conversion lacks universality, but no refutation at all. Suppose

that A has been proved of some C. If then it is assumed that A belongs

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

belongs to no C, but to all B, B will belong to no C. Thus both