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Prior Analytics - Book II   


excepting the universal affirmative, which is proved in the middle and

third figures, but not in the first. Suppose that A belongs not to all

B, or to no B, and take besides another premiss concerning either of

the terms, viz. that C belongs to all A, or that B belongs to all D;

thus we get the first figure. If then it is supposed that A does not

belong to all B, no syllogism results whichever term the assumed

premiss concerns; but if it is supposed that A belongs to no B, when

the premiss BD is assumed as well we shall prove syllogistically

what is false, but not the problem proposed. For if A belongs to no B,

and B belongs to all D, A belongs to no D. Let this be impossible:

it is false then A belongs to no B. But the universal affirmative is

not necessarily true if the universal negative is false. But if the

premiss CA is assumed as well, no syllogism results, nor does it do so

when it is supposed that A does not belong to all B. Consequently it

is clear that the universal affirmative cannot be proved in the

first figure per impossibile.

But the particular affirmative and the universal and particular

negatives can all be proved. Suppose that A belongs to no B, and let

it have been assumed that B belongs to all or to some C. Then it is

necessary that A should belong to no C or not to all C. But this is

impossible (for let it be true and clear that A belongs to all C):

consequently if this is false, it is necessary that A should belong to

some B. But if the other premiss assumed relates to A, no syllogism

will be possible. Nor can a conclusion be drawn when the contrary of

the conclusion is supposed, e.g. that A does not belong to some B.

Clearly then we must suppose the contradictory.

Again suppose that A belongs to some B, and let it have been assumed

that C belongs to all A. It is necessary then that C should belong

to some B. But let this be impossible, so that the supposition is

false: in that case it is true that A belongs to no B. We may

proceed in the same way if the proposition CA has been taken as

negative. But if the premiss assumed concerns B, no syllogism will

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