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Prior Analytics - Book II   


premisses are refuted. But neither can be refuted if the conclusion is

converted into its contrary. For if A does not belong to some C, but

to all B, then B will not belong to some C. But the original premiss

is not yet refuted: for it is possible that B should belong to some C,

and should not belong to some C. The universal premiss AB cannot be

affected by a syllogism at all: for if A does not belong to some of

the Cs, but B belongs to some of the Cs, neither of the premisses is

universal. Similarly if the syllogism is negative: for if it should be

assumed that A belongs to all C, both premisses are refuted: but if

the assumption is that A belongs to some C, neither premiss is

refuted. The proof is the same as before.



9



In the second figure it is not possible to refute the premiss

which concerns the major extreme by establishing something contrary to

it, whichever form the conversion of the conclusion may take. For

the conclusion of the refutation will always be in the third figure,

and in this figure (as we saw) there is no universal syllogism. The

other premiss can be refuted in a manner similar to the conversion:

I mean, if the conclusion of the first syllogism is converted into its

contrary, the conclusion of the refutation will be the contrary of the

minor premiss of the first, if into its contradictory, the

contradictory. Let A belong to all B and to no C: conclusion BC. If

then it is assumed that B belongs to all C, and the proposition AB

stands, A will belong to all C, since the first figure is produced. If

B belongs to all C, and A to no C, then A belongs not to all B: the

figure is the last. But if the conclusion BC is converted into its

contradictory, the premiss AB will be refuted as before, the

premiss, AC by its contradictory. For if B belongs to some C, and A to

no C, then A will not belong to some B. Again if B belongs to some

C, and A to all B, A will belong to some C, so that the syllogism

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