Return to Aristotle, Prior Analytics
If, however, one of the propositions signifies the being present with, but the other the being contingent; the conclusion will be, that a thing is contingent, and not that it is present with. But there will be a syllogism, the terms subsisting in the same manner as before. For in the first place, let them be categoric and let A be present with every C, but let B happen to be present with every C. The proposition, therefore, B C being converted, there will be the first figure; and the conclusion will be, that A happens to be present with a certain B. For when one of the propositions in the first figure signifies the being contingent, the conclusion also is contingent. In a similar manner, if the proposition B C signifies the being present with, but the proposition AC the being contingent and if AC is privative, but B C categoric, and either of them is pure for in both ways the conclusion will be contingent, since again, the first figure will be produced. But it has been shown, that when one of the propositions in that figure, signifies the being contingent, the conclusion also will be contingent. If, however, a contingent privative is joined to the less extreme, or both the intervals are assumed privative through the things posited, indeed, there will not be a syllogism but when they are converted, there will be a syllogism, as before. But if one of the propositions is universal, and the other partial both, indeed, being categoric or the universal being privative, but the partial affirmative there will be the same mode of syllogisms; for all of them will be completed through the first figure. Hence it is evident, that there will be a syllogism in which the contingent, and not the beiug present with, will be collected. But if the affirmative proposition is universal, and the privative partial, the demonstration will be through the impossible. For let B be present with every C, and let A happen not to be present with a certain C. It is necessary, therefore, that A should happen not to be present with a certain B. For if A is necessarily present with every B, but B is posited to be present with every C, A is necessarily present with every C. For this was demonstrated before. But it was supposed that A happens not to be present with a certain C. But when both the propositions are assumed indefinite, or partial, there will not be a syllogism. But the demonstration is the same as that which was in universals, and through the same terms.
Something white is/is not an animal:
It happens that something white is/is not a man:
∴ It is necessary that every man should be an animal.
Something white is/is not a horse:
It happens that something white is/is not a man:
∴ It is necessary that no man should be a horse.
It happens that something white is/is not an animal:
Something white is/is not a man.
∴ It is necessary that every man should be an animal.
It happens that some animal is/is not a horse:
Something white is/is not a man:
∴ It is necessary that no man should be a horse.
Return to Aristotle, Prior Analytics
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