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Prior Analytics - Book II   


each figure when the conclusion is converted; when a result contrary

to the premiss, and when a result contradictory to the premiss, is

obtained. It is clear that in the first figure the syllogisms are

formed through the middle and the last figures, and the premiss

which concerns the minor extreme is alway refuted through the middle

figure, the premiss which concerns the major through the last

figure. In the second figure syllogisms proceed through the first

and the last figures, and the premiss which concerns the minor extreme

is always refuted through the first figure, the premiss which concerns

the major extreme through the last. In the third figure the refutation

proceeds through the first and the middle figures; the premiss which

concerns the major is always refuted through the first figure, the

premiss which concerns the minor through the middle figure.

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It is clear then what conversion is, how it is effected in each

figure, and what syllogism results. The syllogism per impossibile is

proved when the contradictory of the conclusion stated and another

premiss is assumed; it can be made in all the figures. For it

resembles conversion, differing only in this: conversion takes place

after a syllogism has been formed and both the premisses have been

taken, but a reduction to the impossible takes place not because the

contradictory has been agreed to already, but because it is clear that

it is true. The terms are alike in both, and the premisses of both are

taken in the same way. For example if A belongs to all B, C being

middle, then if it is supposed that A does not belong to all B or

belongs to no B, but to all C (which was admitted to be true), it

follows that C belongs to no B or not to all B. But this is

impossible: consequently the supposition is false: its contradictory

then is true. Similarly in the other figures: for whatever moods admit

of conversion admit also of the reduction per impossibile.

All the problems can be proved per impossibile in all the figures,

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