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Prior Analytics - Book II   

shall have the same result as before.

It is clear then that in all the syllogisms which proceed per

impossibile the contradictory must be assumed. And it is plain that in

the middle figure an affirmative conclusion, and in the last figure

a universal conclusion, are proved in a way.


Demonstration per impossibile differs from ostensive proof in that

it posits what it wishes to refute by reduction to a statement

admitted to be false; whereas ostensive proof starts from admitted

positions. Both, indeed, take two premisses that are admitted, but the

latter takes the premisses from which the syllogism starts, the former

takes one of these, along with the contradictory of the original

conclusion. Also in the ostensive proof it is not necessary that the

conclusion should be known, nor that one should suppose beforehand

that it is true or not: in the other it is necessary to suppose

beforehand that it is not true. It makes no difference whether the

conclusion is affirmative or negative; the method is the same in

both cases. Everything which is concluded ostensively can be proved

per impossibile, and that which is proved per impossibile can be

proved ostensively, through the same terms. Whenever the syllogism

is formed in the first figure, the truth will be found in the middle

or the last figure, if negative in the middle, if affirmative in the

last. Whenever the syllogism is formed in the middle figure, the truth

will be found in the first, whatever the problem may be. Whenever

the syllogism is formed in the last figure, the truth will be found in

the first and middle figures, if affirmative in first, if negative

in the middle. Suppose that A has been proved to belong to no B, or

not to all B, through the first figure. Then the hypothesis must

have been that A belongs to some B, and the original premisses that

C belongs to all A and to no B. For thus the syllogism was made and

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