Return to Aristotle, Prior Analytics
But if one proposition signifies the existing or being present with, and the other, the being contingent; when the categoric proposition signifies the being present with, but the privative, the being contingent, there will never be a syllogism, neither when the terms are assumed universally, nor when they are assumed partially. The demonstration, however, is the same, and through the same terms. But when the affirmative signifies the being contingent, but the privative the being present with, there will be a syllogism. For let it be assumed that A is present with no B, but is contingent to every C. The privative interval, therefore, being converted, B will be present with no A. But A was contingent to every C. A syllogism, therefore, will be produced, in the first figure, in which it may be collected that B is contingent to no C. In like manner also, a syllogism will be formed, if the privative is added to C. But if both the propositions are privative and the one signifies the not being present with, but the other the happening not to be present with through the assumed propositions, indeed, nothing necessary will happen. If the contingent proposition, however, is converted, there will be a syllogism, in which it may be collected, that B happens to be present with no C, as in the former syllogisms for again, there will be the first figure. But if both the propositions are posited categoric, there will not be a syllogism. Let the terms of being present with be health, animal, man but of not being present with, health, horse, man.
It happens that every animal is well:
Every man is well:
∴ It is necessary that every man should be an animal.
It happens that every horse is well:
Every man is well:
∴ It is necessary that no man should be a horse.
Every animal is well:
It happens that every man is well:
∴ It is necessary that every man should be an animal.
Every horse is well:
It happens that every man is well:
∴ It is necessary that no man shoulld be a horse.
The like will also take place in partial syllogisms. For when the affirmative proposition is pure, whethcr it be assumed universally, or partially, there will be no syllogism. But this may be demonstrated similarly, and through the same terms as before.
It happens that no animal is well:
Some man is well:
∴ It is necessary that every man shouldl be an animal.
Every animal is well:
It happens that some man is not well:
∴ It is necessary that every man shouldl be an animal.
It happens that no horse is well:
Some man is well:
∴ It is necessary that no man should be a horse.
Every horse is well:
It happens that some man is not well:
∴ It is necessary that no man should be a horse.
But when the privative is pure, there will be a syllogism through conversion, as in the former syllogisms. Again, if both intervals are assumed privative, and that which signifies the not being present with is universal from these propositions, indeed, there will not be the necessary. But when the contingent is converted, as before, there will be a syllogism. If, however, the privative interval is, indeed, pure, but is assumed in part, there will not be a syllogism, whether the other proposition be affirmative or privative. Nor will there then be a syllogism, when both the propositions are assumed indefinite, whether affirming, or denying, or partial. But the demonstration is the same, and through the same terms.
Some animal is/is not well:
It happens that some man is/is not well:
∴ It is necessary that every man should be an animal.
Some horse is/is not well:
It happens that some man is/is not well:
∴ It is necessary that no man should be a horse.
It happens that some animal is/is not well:
Some man is/is not well:
∴ It is necessary that every man should be an animal.
It happens that some horse is/is not well:
Some man is/is not well:
∴ It is necessary that no man should be a horse.
Return to Aristotle, Prior Analytics
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