Return to Aristotle, Prior Analytics
If, however, one of the propositions signifies the being present with, or not being present with from necessity, but the other signifies the being contingent; when the privative is necessary, there will be a syllogism, in which not only the happening not to be present with will be collected, but also the not being present. But when the affirmative is necessary, there will not be a syllogism. For let it be posited that A is necessarily present with no B, and that it is contingent to every C. The privative proposition, therefore, being converted, neither will B be present with any A. But A was contingent to every C. Again, therefore, a syllogism will be produced in the first figure, in which it may be collected that B happens to be present with no C. At the same time also it is evident, that neither is B present with any C. For let it be admitted that it is. If, therefore, A is contingent to no B, but B is present with a certain C, A will not be contingent to a certain C. But it was supposed to be contingent to every C. It will likewise be demonstrated after the same manner, if the privative is joined to C. Again, let the categoric interval be necessary, but the other, privative and contingent and let A be contingent to no B, but necessarily present with every C. The terms, therefore, thus subsisting, there will be no syllogism for it may happen that B is necessarily not present with C. For let A be white, B man, C a swan. Whiteness, therefore, is necessarily present with a swan, but is contingent to no man and man is necessarily present with no swan. That there will not, therefore, be a syllogism of the contingent is evident for that which is from necessity is not contingent.
It happens that no man is white:
It is necessary that every swan should be white:
∴ It is necessary that no swan should be a man.
Neither will there be a syllogism of the necessary. For the necessary is either inferred from both the necessary propositions, or from the privative. Farther still, these things being admitted, it may be possible that B may be present with C. For nothing hinders but that C may be under B and that A may be contingent to every B, and may be necessarily present with C as if C is awake; B animal and A, motion. For motion is necessarily present with every thing that is awake but is contingent to every animal and every thing which is awake is an animal.
It happens that no animal is moved:
It is necessary that every thing awake should be moved:
∴ Every thing awake is an animal.
It is evident, therefore, that neither is the not being present with collected since the terms thus subsisting, the being present with is necessary nor are the opposite affirmations collected. Hence there will be no syllogism. There will also be a similar demonstration if the affirmative proposition is posited vice versa. But if the propositions are similar in figure, being privative indeed, a syllogism will always be formed, when the contingent proposition is converted, as in the former syllogisms. For let it be assumed that A is necessarily not present with B, and that it happens not to be present with G. The propositions, therefore, being converted, B will be present with no A, and A will be present with every C. The first figure, therefore, will be produced. The like will also take place if the privative is joined to C. But if both the propositions are posited categoric there will not be a syllogism. For it is evident, that there will not be a syllogism of the not being present with, or of the not being present with from necessity, because a privative proposition is not assumed, neither in the being present with, nor in the being present with from necessity. But neither will there be a syllogism of the not happening to be present with. For the terms being thus posited from necessity, B will not be present with C as, for instance, if A is posited white; B, a swan and C, man. Neither will there be a syllogism of the opposite affirmations because it has been shown that B is necessarily not present with C. A syllogism, therefore, in short, will not be produced.
It is necessary that every swan should be white:
It happens that every man is white:
∴ It is necessary that no man should be a swan.
The like will also take place in partial syllogisms. For when the privative is universal and necessary, there will always be a syllogism of the contingent, and of the not being present with. But the demonstration will be through conversion. When, however, the affirmative is necessary there will never be a syllogism. But this may be demonstrated in the same manner as in the universal modes, and through the same terms.
It happens that no man is white:
It is necessary that some swan should be white:
∴ It is necessary that no swan should be a man.
It happens that no animal is moved:
It is necessary that something awake should be moved:
∴ It is necessary that every thing awake should be an animal.
It is necessary that every swan should be white:
It happens that some man is not white:
∴ It is necessary that no man should be a swan.
Nor will there then be a syllogism, when both the propositions are assumed affirmative for of this there is the same demonstration as before.
It is necessary that every swan should be white:
It happens that some man is a swan:
∴ It is necessary that no man should be a swan.
It happens that every man is white:
It is necessary that some swan should be white:
∴ It is necessary that no swan should be a man.
It is necessary that some swan should be white:
It happens that every man is white:
∴ It is necessary that no man should be a swan.
It happens that some man is white:
It is necessary that every swan should be white:
∴ It is necessary that no swan should be a man.
But when both the propositions are assumed privative, and that which signifies the not being present with, is universal and necessary; through the propositions, indeed, there will not be the necessary but the contingent proposition being converted, there will be a syllogism, as before. If, however, both the propositions are posited indefinite, or in a part, there will not be a syllogism. But the demonstration is the same, and through the same terms.
It happens that some animal is/is not white:
It is necessary that some man should not be/not be white:
∴ It is necessary that every man should be an animal.
It happens that some animal is/is not white:
It is necessary that something inanimate should be/not be white:
∴ It is necessary that nothing inanimate should be an animal.
It is necessary that some animal should be/not be white:
It happens that some man is/is not white:
∴ It is necessary that every man should be an animal.
It is necessary that some animal should be/not be white:
It happens that something inanimate is/is not white:
∴ It is necessary that nothing inanimate should be an animal.
It is evident, therefore, from what has been said, that when the privative position is posited universal and necessary, a syllogism will always be produced, not only of the happening not to be present with, but also of the not being present with. But there will never be a syllogism when the affirmative is posited necessary. It is also evident, that when the terms subsist after the same manner, is necessary and pure propositions, there will be, and there will not be, a syllogism. And it is likewise manifest, that all these syllogisms are imperfect, and that they are perfected through the above-mentioned figures.
Return to Aristotle, Prior Analytics
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