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Prior Analytics - Book II   


is necessary then that C should not belong to some B. But originally

it belonged to all B, consequently the hypothesis is false: A then

will belong to no B.

When A does not belong to an B, suppose it does belong to all B, and

to no C. It is necessary then that C should belong to no B. But this

is impossible: so that it is true that A does not belong to all B.

It is clear then that all the syllogisms can be formed in the middle

figure.



13



Similarly they can all be formed in the last figure. Suppose that

A does not belong to some B, but C belongs to all B: then A does not

belong to some C. If then this is impossible, it is false that A

does not belong to some B; so that it is true that A belongs to all B.

But if it is supposed that A belongs to no B, we shall have a

syllogism and a conclusion which is impossible: but the problem in

hand is not proved: for if the contrary is supposed, we shall have the

same results as before.

But to prove that A belongs to some B, this hypothesis must be made.

If A belongs to no B, and C to some B, A will belong not to all C.

If then this is false, it is true that A belongs to some B.

When A belongs to no B, suppose A belongs to some B, and let it have

been assumed that C belongs to all B. Then it is necessary that A

should belong to some C. But ex hypothesi it belongs to no C, so

that it is false that A belongs to some B. But if it is supposed

that A belongs to all B, the problem is not proved.

But this hypothesis must be made if we are prove that A belongs

not to all B. For if A belongs to all B and C to some B, then A

belongs to some C. But this we assumed not to be so, so it is false

that A belongs to all B. But in that case it is true that A belongs

not to all B. If however it is assumed that A belongs to some B, we

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