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The First Figure of Syllogisms
These things being determined, let us now show through what things, when, and how every syllogism is produced; and afterwards let us speak concerning demonstration. For it is requisite to speak of syllogism prior to demonstration, because syllogism is more universal. For a demonstration, indeed, is a certain (kind of) syllogism, but not every syllogism is a demonstration.
Therefore, when three terms so subsist with reference to each other, as that the last is in the whole of the middle, and the middle either is or is not in the whole of the first; then it is necessary that there should be a perfect syllogism of the extremes.
But I call the middle that which is itself in another, another also being in it; and which likewise becomes the middle in position. And I call the extremes that which is itself in another, and that in which another also is. For if A is predicated of every B, and B of every C, it is necessary that A should be predicated of every C, for it has been before shown how we predicate of every individual of a given multitude. In like manner also, if A is predicated of no B, but B is predicated of every C, neither will A be predicated of any C. But if the first follows every middle, and the middle is present with no extreme, there will not be a syllogism of the extremes; for nothing necessary will happen in consequence of the existence of these; since it will happen that the first will be present with every and with no extreme. Hence, neither a particular, nor a universal conclusion will be necessarily produced. But nothing necessary being collected, there will not through these be a syllogism. Let, however, the terms of being present with every individual of a certain multitude be animal, man, horse; and let the terms of being present with no one be animal, man, stone.
Every man is an animal:
No horse is a man:
∴ Every horse is an animal.
Every man is an animal:
No stone is a man:
∴ No stone is an animal.
Neither then will there be a syllogism, since neither is the first term present with any middle, nor the middle with any extreme. Let the terms of being present be science, line, physician; but let the terms of not being present be science, line, unity.
No line is science:
No medicine is a line:
∴ Every medicine is science.
No line is science:
No unity is a line:
∴ No unity is science.
The terms, therefore, being universal it is manifest in this figure, when there will, and when there will not be a syllogism; and also that when there is a syllogism, it is necessary that the terms should subsist as we have said. For it is evident, that if they thus subsist there will be a syllogism. But if one of the terms is universal, and the other particular with reference to the other, when the universal is joined to the greater extreme, whether categoric or privative, but the particular term is categoric with respect to the less extreme, it is necessary that the syllogism should be perfect. But when the universal term is joined to the less extreme, or the terms subsist in some other way, it is impossible there should be a syllogism. I call, however, the greater extreme, that is which the middle is; and the less extreme, that which is under the middle. For let A be present with every B, but B with some C, If, therefore, to be predicated of every individual of a multitude is that which we asserted it to be from the first, A is necessarily present with some C. And if A is present with no B, but B is present with some C, it is necessary that A should not be present with some C. For the manner in which we speak of being predicated of no one of a multitude has been defined by us. Hence there will be a perfect syllogism. A similar conclusion also must be adopted, if the proposition B C is indefinite, being categoric; for there will be the same syllogism of the indefinite, and of that which is assumed in a part. But if to the less extreme, universal either categoric or privative, is added, there will not be a syllogism; whether an indefinite or a particular proposition affirms or denies. For instance, if A is present, or is not present, with some B; but B is present with some C. Let then the terms of being present be, good, habit, prudence; and let the terms of not being present be, good, habit, ignorance.
Some habit is/is not good:
All prudence is a habit:
∴ All prudence is good.
Some habit is/is not good:
All ignorance is a habit:
∴ No ignorance is good.
Again, if B is present with no C, but A is present with some B, or is not present, or is not present with every B; neither thus will there be a syllogism. Let the terms of being present with every individual be white, horse, swan; but the terms of being present with no one be white, horse, crow.
Some horse is/is not white:
No swan is a horse:
∴ Every swan is white.
Some horse is/is not white:
No crow is a horse:
∴ No crow is white.
The same terms also may be assumed if AB should be indefinite. Neither then will there be a syllogism, when universal either categoric or privative is added to the greater extreme; but to the less extreme a privative according to a part of the indefinite, and in a part is assumed; for instance, if A is present with every B, but B is not present with some, or not with every C. For that with which the middle is not present, to this, to every, and to none, the first will be consequent. Thus, let the terms animal, man, white, be supposed; and afterwards, from among those white things of which man is not predicated, let swan and snow be assumed. Hence animal will be predicated of every individual of the one; but of no individual of the other; so that there will not be a syllogism.
Every man is an animal:
Something white (a swan) is not a man:
∴ Every swan is an animal.
Every man is an animal:
Something white (snow) is not a man:
∴ No snow is an animal.
Again, let A be present with no B, but let B not be present with some C; and let the terms be, inanimate, man, white. Afterwards, let white things be assumed, viz. swan and snow, of which man is not predicated. For inanimate is predicated of every individual of the one, but of no individual of the other.
No man is inanimate:
Something white (snow) is not a man:
∴ All snow is inanimate.
No man is inanimate:
Something white (a swan) is not a man:
∴ No swan is inanimate.
Farther still, this is indefinite, namely, that B is not present with some C; (for it is truly asserted that it is not present with some C, whether it is present with none, or whether it is not present with every C) but terms of this kind being assumed, so as to be present with none, a syllogism will not be produced; for this has been asserted before. It is evident, therefore, that when the terms thus subsist, there will not be a syllogism; since if there could, there would also be a syllogism in these terms. The like also may be demonstrated, if universal privative is posited. Neither will there by any means be a syllogism, if both intervals according to apart are predicated either categorically or privatively; or the one categorically, but the other privatively; or if the one is indefinite, but the other definite; or both are indefinite. But let the common terms of all be, animal, white, man, animal, white, stone.
Something white is/is not an animal:
Some man is/is not white:
∴ Every man is an animal.
Something white is/is not an animal:
Some stone is/is not white:
∴ No stone is an animal.
From what has been said, therefore, it is evident, that if there is a particular syllogism in this figure, it is necessary that the terms should subsist as we have said; that if the terms thus subsist a syllogism is necessarily produced; but by no means, if they subsist in a different manner. It is also manifest, that all the syllogisms in this figure are perfect; for all are perfected through those things which were assumed from the first. Likewise, that all problems are demonstrated through this figure; for in this a thing is shown to be present with every, with none, with some one, and not with some one. But I call a figure of this kind, the first figure.
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