Return to Aristotle, Prior Analytics
In the second figure, however, when both the propositions are assumed contingent, there will be no syllogism, neither when they are categoric, nor when they are privative, neither when they are universal, nor when they are partial. But when one proposition signifies the being present with, and the other the being contingent if the affirmative signifies the being present with; there will never be a syllogism; but if the privative universal signifies the being present with, there will always be a syllogism. The like will also take place when one of the propopositions is assumed necessary, but the other contingent. It is necessary, however, in these syllogisms so to assume the contingent in the conclusions, as it was assumed in the former syllogisms. In the first place, therefore, it must be shown that a contingent privative is not convertible. Thus, if A is contingent to no B, it is not necessary that B also should be contingent to no A. For let this be posited, and let B happen to be present with no A. Since, therefore, contingent affirmations, as well those that are contrary, as those that are opposite, are converted into negations, but B happens to be present with no A, it is evident, that it may also happen that B may be present with every A. This, however, is false. For it does not follow that if this thing may happen to all of that, it is necessary that that thing should happen to this; so that a contingent privative cannot be converted. Again, nothing hinders, but that A may be contingent to no B, and yet B may not be necessarily present with a certain A. Thus, for instance, whiteness may happen not to be present with every man, because it may also happen to be present. But it is not true to say that man happens to be present with nothing white for he is necessarily not present with manythings that are white. And the necessary is not the contingent. Neither can its convertibility be shown from the impossible as if any one should think, since it is false, that B is contingent to no A, that it is true that it is not contingent to none (for these are affirmation and negation). But if this is true, B is necessarily present with a certain A so that A also is necessarily present with a certain B but this is impossible. For it does not follow that if B is not contingent to no A, it is necessarily present with a certain A. For not to be contingent to no individual is predicated in a twofold respect; in one, indeed, if a thing is necessarily present with something and in another, if it necessarily is not present with something. For that which necessarily is not present with a certain A, cannot be truly said to happen not to be present with every A as neither can that which is necessarily present with a certain thing, be truly said to happen to be present with every thing. If, therefore, any one thinks that because C does not happen to be present with every D, it necessarily is not present with a certain D, he thinks falsely; for it may happen to be present with every D. But because a thing is necessarily present with certain things, on this account we say that it is not contingent to every individual. Hence the being present with a certain thing from necessity, and the not being present with a certaia thing from necessity, are opposed to the happening to be present with every individual. There is also a similar opposition to the being contingent to no individual. It is evident, therefore, that when the contingent, and the not contingent, are assumed in the manner we have defined in the beginning, not only the being present with a certain thing from necessity, but also the not being present with a certain thing from necessity, ought to be assumed. But this being assumed nothing impossible will happen so that a syllogism will not be produced. From what has been said, therefore, it is evident, that a contingent privative cannot be converted. But this being demonstrated, let it be admitted that A is contingent to no B, but is contingent to every C. There will not, therefore, be a syllogism through conversion for it has been shown that a proposition of this kind is not convertible. Neither will there be a syllogism, through a deduction to the impossible. For B being posited to be contingently present with every C, nothing false will happen for it may happen that A may be present with every, and with no C.
It happens that no B is A:
It happens that every C is A:
∴ It happens that no C is B.
It happens that no B is A:
It is necessary that every/some C should be B:
∴ It happens that every or some C is not A.
In short, if there is a syllogism, it is evident it will be of that which is contingent (because neither of the propositions is assumed of that which exists, or is present with) and this, either affirmative, or privative. It is not possible, however, in either way. For if it is posited affirmative, it may be shown through the terms, that it will not happen to be present with. But if it is posited negative, it may be sho^vn that the conclusion is not contingent, but necessary. For let A be white B, man and C, horse. A, therefore, that is whiteness, may happen to be present with every individual’of the one, and with no individual of the other. But it neither happens to B to be present, nor yet not to be present with C. That it does not happen to be present indeed, is evident for no horse is a man. But neither does it happen not to be present for it is necessary that no horse should be a man. But the necessary is not contingent. A syllogism, therefore, will not be produced.
It happens that no man is white:
It happens that every horse is white:
∴ It is necessary that no horse should be a man.
This may also be similarly shown, if the privative should be placed in an inverse order, or if both the propositions are assumed affirmative, or both privative; for there will be a demonstration through the same terms.
It happens that every/no man is white:
It happens that every/no horse is white:
∴ It is necessary that no horse should be a man.
And when one proposition is universal, but the other partial or when both are partial, or indefinite; or in any other way in which it may be possible to change the propositions; for the demonstration will always be through the same terms.
It happens that every/no man is white:
It happens that some horse is/is not white:
∴ It is necessary that no horse should be a man.
It happens that some man is/is not white:
It happens that every/no horse is white:
∴ It is necessary that no horse should be a man.
It happens that some man is/is not white:
It happens that some horse is/is not white:
∴ It is necessary that no horse should be a man.
Return to Aristotle, Prior Analytics
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