Aristotle, Prior Analytics by Aristotle, Smith (trans.)

By Aristotle, Smith (trans.)

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When the terms are universal, there will be a deduction when the middle belongs to all of one term and none of the other, no matter 26B5-27B 7 which one the privative is in relation to, but otherwise in no way. For let M be predicated of no N but of every X. Then, since the privative convertS, N will belong to no M. But M was assumed to belong to every X, so that N belongs to no X (for this has been proved earlier). Next, if M belongs to every N but to no X, then neither will N belong to any X.

It is necessary for a universal privative premise of belonging to convert with respect to its terms. For instance, if no pleasure is a good, neither will any good be a pleasure. And the positive premise necessarily converts, though not universally but in part. For instance, if every pleasure is a good, then some good will be a pleasure. Among the particular premises, the affirmative must convert partially (for if some pleasure is a good, then some good will be a pleasure), but the privative premise need not (for it is not the case that if man does nOt belong to some animal, then animal will not belong to some man).

The situation will also be similar in the case of the particular deductions. For when the privative premise is both universal and necessary, the conclusion will also be necessary; but when the positive premise is universal and the privative premise is particular, the conclusion will not be necessary. First, then, let the privative premise be both univer- 40 310 5 sal and necessary, and let it not be possible for A to belong to any B, but let A belong to some C. Then, since the privative converts, neither would it be possible for B to belong to any A.

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Aristotle, Prior Analytics by Aristotle, Smith (trans.)
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