Return to Aristotle, Prior Analytics
The Second Figure of Syllogisms
But when the same thing (i.e. the middle term) is partly present with every individual, and partly with none; or is present to every or to none of each extreme; I call a figure of this kind the second figure. And I call the middle term in it, that which is predicated of both extremes. But I denominate the extremes those things of which this middle is predicated, the greater extreme being that which is situated near the middle; but the less extreme being that which is situated farther from the middle. But the middle is posited external to the extremes, and is first in position. By no means, therefore, will there be a perfect syllogism in this figure. But there may be a syllogism both when the terms are universal, and when they are not universal. And if the terms, indeed, are universal, there will be a syllogism when the middle is partly present with every, and partly with none; to whichever extreme the privative is added. But a syllogism will by no means be produced in any other way. For let M be predicated of no N, but of every O. Since, therefore, a privative proposition is converted, N will be present with no M. But M was supposed to be present with every O; so that N will, be present with no O. For this was demonstrated before. Figure 1 Again, if M is present with every N, but with no O, neither will O be present with any N. For if M is present with no O, neither, will O be present with any M. But M was present with every N; and hence O will be present with no N. For again, the first figure is produced. But since a privative proposition is converted, neither will N be present with any O. Hence there will be the same syllogism. These things also may be demonstrated by a deduction to the impossible. It is evident, therefore, that a syllogism, though not a perfect syllogism, may be produced, when the terms thus subsist; for the necessary not only receives its completion from those things which were assumed from the first, but also from other things. But if M is predicated of every N, and of every O, there will not be a syllogism. Figure 2 Let the terms then of being present with be essence, animal, man; but of not being present with be essence, animal, stone. And let the middle term be essence.
Every animal is an essence:
Every man is an essence:
∴ Every man is an animal. ((Note that this conclusion is true, but it does not necessarily follow from the premises. Therefore, this is not a syllogism.))
Every animal is an essence:
Every stone is an essence:
∴ No stone is an animal.
Nor will there then be a syllogism, when M is neither predicated of any N, nor of any O. Let the terms of being present with be line, animal, man; but of not being present with, line, animal, stone.
No animal is a line:
No man is a line:
∴ Every man is an animal.
No animal is a line:
No stone is a line:
∴ No stone is an animal.
It is evident, therefore, that if there is a syllogism when the terms are universally posited, it is necessary that the terms should subsist in that manner which we mentioned in the beginning, for if they subsist in any other way, the necessity of concluding will not be produced. But if the middle is universally affected with respect to either extreme; when universal is added to the greater extreme, either categorically, or privatively; but to the lesser extreme, according to a part, and oppositely to universal; (but I say oppositely, if the universal is privative, but the particular affirmative; and if the universal is categoric, but the particular privative) it is necessary that a syllogism privative according to a part should be produced. For if M is present with no N, but is present with a certain O, it is necessary that N should not be present with a certain O. For since a privative proposition may be converted, N will be present with no M: but M was supposed to be present with a certain O: so that N will not be present with a certain O; for a syllogism is produced in the first figure. Again, if M is present with every N, but is not present with a certain O, it is necessary that N should not be present with a certain O. For if it is present with every O, but M is predicated of every N, it is also necessary that M should be present with every O. But it was supposed that it is not present with a certain O. And if M is present, indeed, with every N, but not with every O, there will be a syllogism, from which it will follow that N is not present with every O. But the demonstration is the same. If, however, M is predicated of every O, but not of every N, there will not be a syllogism. Let the terms of being present with be animal, essence, crow; but of not being present with, animal, white, crow.
Not every essence is an animal:
Every crow is an animal:
∴ Every crow is an essence.
Not every thing white is an animal:
Every crow is an animal:
∴ No crow is white.
Neither will there be a syllogism, when M is predicated of no O, but of a certain N. Let the terms of being present with be animal, essence, stone; but of not being present with animal, essence, science.
Some essence is an animal:
No stone is an animal:
∴ Every stone is essence.
Some essence is an animal:
No science is an animal:
∴ No science is essence.
When, therefore, particular is opposed to universal, we have shown when, and when there will not be a syllogism. But when the propositions are similar in figure, for instance, when both are privative, or affirmative, there will by no means be a syllogism. For in the first place, let both be privative, and let universal be added to the greater extreme; as, for instance, let M be present with no N, and let it not be present with a certain O: it may happen, therefore, that N may be present with every and with no O. Let the terms of not being present with any be black, snow, animal.
No snow is black:
Some animal is not black:
∴ No animal is snow.
But the terms of being present with every cannot be assumed, if M is present, indeed, with a certain O, and with a certain O is not present. For if N is present with every O, but M is present with no N, M will be present with no O. But it was supposed to be present with a certain O. The terms, therefore, cannot thus be assumed. It may be demonstrated, however, from the indefinite. For since it was truly asserted that M is not present with a certain O, even if it is present with no O; but when it is present with no O, there was not a syllogism, it is evident that neither will there now be a syllogism. Again, let both the propositions be categorical, and let universal be similarly posited; as, for instance, let M be present with every N, and with a certain O. Hence, it may happen that N may be present with every, and with no O. Let the terms of not being present with any be white, swan, snow.
Every swan is white:
Some stone is white:
∴ No stone is a swan.
But the terms of not being present with every cannot be assumed, for the cause which we have before adduced.
Every swan is white:
Some bird is not white:
∴ Every bird is a swan.
Every swan is white:
Every bird is a swan:
∴ Every bird is white.
It may be demonstrated, however, from the indefinite. But if universal is added to the less extreme, and M is present with no O, and is not pre sent with a certain N, it may happen that N may be present with every and with no O. Let the terms of being present with be white, animal, crow; but of not being present with, white, stone, crow.
Some animal is not white:
No crow is white:
∴ Every crow is an animal.
Some stone is not white:
No crow is white:
∴ No crow is a stone.
But if the propositions are categoric, let the terms of not being present with be white, animal, snow; but of being present with be, white, animal, swan.
Some animal is white:
All snow is white:
∴ No snow is an animal.
Some animal is white:
Every swan is white:
∴ Every swan is an animal.
It is evident, therefore, that when the propositions are similar in figure, and the one is universal, but the other particular, there will by no means be a syllogism. Neither will there be a syllogism, if with some one of each term a thing is present, or is not present; or is partly present with someone, and partly not; or to every one of neither, or indefinitely. Let then the common terms of all be white, animal, man; white, animal, inanimate.
Some animal is/is not white:
Some man is/is not white:
∴ Every man is an animal.
Some animal is/is not white:
Something inanimate is/is not white:
∴ Nothing inanimate is an animal.
From what has been said, therefore, it is evident, that when the terms subsist with reference to each other, in the manner we have mentioned, a syllogism will necessarily be produced; and if a syllogism is produced, it is necessary that the terms should subsist in this manner. It is likewise evident, that all syllogisms which are in this figure are imperfect; for all of them are produced by certain things being assumed which either are necessarily inherent in the terms, or are admitted as hypotheses, as when we demonstrate through the impossible. It is also manifest, that an affirmative syllogism is not produced in this figure; but all the syllogisms are privative, both those that are universal, and those that arc particular.
Return to Aristotle, Prior Analytics
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