Return to Aristotle, Prior Analytics
When, however, with the same thing, one thing is present with every individual, but another with none; or both with every, or both with none, I call a figure of this kind the third figure. But I call that the middle in it of which we predicate both; and I denominate extremes the things which are predicated; the greater extreme being that which is more remote from the middle, and the less, that which is nearer to the middle. But the middle is arranged external to the extremes, and is last in position. Neither, therefore, will a perfect syllogism be produced in this figure. But there may be a syllogism, the terms being joined to the middle, as well universally as not universally. The terms, therefore, being universally posited, when P and R are present with every S, there will be a syllogism, in which it will be necessarily inferred that P is necessarily present with a certain R. For since a categoric assertion is converted, S will be present with a certain R. Hence since P is present with every S, but S is present with a certain R, it is necessary that P should be present with a certain R. For a syllogism will be produced in the first figure. It is also possible to make the demonstration through the impossible, and through exposition. For if both are present with every S, if some S is assumed, as, for instance, N, both P and R will be present with this; so that P will be present with a certain R. And if R is present with every S, but P is present with no S, there will be a syllogism, in which it will be necessarily inferred that P is not present with a certain R. For there will be the same mode of demonstration, the proposition R S being converted. This may also be demonstrated through the impossible, as in the former syllogisms. But if R is present with no S, and P is present with every S, there will not be a syllogism. Let the terms of being present with be animal, horse, man; but of not being present with, animal, inanimate, man.
Every man is an animal:
No man is a horse:
∴ Every horse is an animal.
Every man is an animal:
No man is inanimate:
∴ Nothing inanimate is a horse.
Nor will there then be a syllogism, when both are predicated of no S. Let the terms of being present with be animal, horse, inanimate; but of not being present with be, man, horse, inanimate: the medium is inanimate.
Nothing inanimate is an animal:
Nothing inanimate is a horse:
∴ Every horse is an animal.
Nothing inanimate is a man:
Nothing inanimate is a horse:
∴ No horse is a man.
It is evident, therefore, in this figure also, when there will be, and when there will not be a syllogism, the terms being universally posited. For when both the terms arc categoric there will be a syllogism, in which it will be inferred that extreme is present with a certain extreme. But when both the terms are privative there will not be a syllogism. When, however, the one is privative, and the other affirmative; if, indeed, the greater term is privative, but the other affirmative, there will be a syllogism in which it will be inferred that extreme is not present with a certain extreme. But if the contrary takes place there will not be a syllogism. If, however, one of the terms is universally, but the other particularly joined to the middle; both of them being categoric, it is necessary that a syllogism should be produced, whichever of the terms is universally assumed. For if R, indeed, is present with every S, but P with a certain S, it is necessary that P should be present with a certain R. For since an affirmative assertion is. converted, S will be present with a certain P. Hence, since R is present with every S, but S is present with a certain P, R also will be present with a certain P, so that P also will be present with a certain R. Again, if R is present with a certain S, but P is present with every S, it is necessary that P should be present with a certain R; for there is the same mode of demonstration. These things also may be demonstrated through the impossible, and through exposition, as in the former syllogisms. But if one of the terms is categoric, and the other privative, and the categoric is assumed universally; when the less term, indeed, is categoric, there will be a syllogism. For if R is present with every S, but P is not present with a certain S, it is necessary that P should not be present with a certain R. For if P is present with every R, and R is present with every S; P also will be present with every S; but it is not present. This also may be shown without a deduction to the impossible, if some S is assumed with which P is not present. But when the greater term is categoric, there will not be a syllogism. For instance, if P is present with every S, but R is not present with a certain S. Let the terms of being present with every be animated, man, animal.
Every animal is animated:
Some animal is not a man:
∴ Every man is animated.
But it is not possible to assume the terms of being present with none, if R is present with a certain S, and with a certain S is not present. For if P is present with every S, and R is present with a certain S, P also will be present with a certain R. But it was supposed to be present with no R. Here, therefore, the same thing must be assumed as in the former syllogisms. For the assertion that something is not present with a certain thing being indefinite, also that which is not present with any individual of a certain multitude, is truly said not to be present with a certain individual of that multitude; but not being present with any individual, there will not be a syllogism. It is evident, therefore, that there will not be a syllogism, when there is an assumption of not being present with some individual of a certain multitude. If, however, the privative term is universal, but the particular terra is categoric; when the greater term, indeed, is privative, but the less categoric, there will be a syllogism. For if P is present with no S, but R is present with a certain S; P will not be present with a certain R. For again, there will be the first figure, the proposition R S being converted. But when the less term is privative, there will not be a syllogism. Let the terms of being present with be animal, man, wild; but of not being present with be, animal, science, wild. The middle of both is wild. Something wild is an animal: Nothing wild is a man: Every man is an animal. Something wild is an animal: Nothing wild is science: No science is an animal. Nor will there then be a syllogism, when both terms are privative; and the one is universal, but the other particular. Let the terms of not being present with, when the less term is universally joined to the middle, be animal, science, wild; but of being present with be, animal, man, wild.
Something wild is not an animal:
Nothing wild is science:
∴ No science is an animal.
Something wild is not an animal:
Nothing wild is a man:
∴ Every man is an animal.
But when the greater term is universal, but the less particular, let the terms of not being present with be crow, snow, white.
Nothing white is a crow:
Not every thing white is snow:
∴ No snow is a crow.
The terms, however, of being present wilh cannot be assumed, if R is present, indeed, with a certain S, and with a certain S is not present. For if P is present with every R, but R is present with a certain S, P also will be present with a certain S. It was supposed, however, not to be present with any S. But it is demonstrated from the indefinite. Neither will there by any means be a syllogism, if each extreme term is present, or is not present with a certain middle; or if one is present, but the other is not present; or the one is present with some individual, but the other not with every indiridual; or indefinitely. But let the common terms of all be animal, man, white animal, inanimate, white.
Something white is/is not an animal:
Something white is/is not a man:
∴ Every man is an animal.
Something white is/is not an animal:
Something white is/is not inanimate:
∴ Nothing inanimate is an animal.
It is evident, therefore, in this figure also, when there will be, and when there will not be a syllogism; that when the terms so subsist as has been mentioned, a syllogism is necessarily produced; and that if there is a syllogism, it is necessary the terms should subsist in this manner. It is likewise evident, that all the syllogisms in this figure are imperfect; for all of them are perfected by the assumption of certain things; and also that a universal conclusion, neither privative nor affirmative, will not be collected in this figure.
Return to Aristotle, Prior Analytics
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