Return to Aristotle, Prior Analytics
When, however, one proposition signifies the being present with, or not being present with, from necessity, but the other signifies the being contingent, there will be a syllogism, the terms subsisting after the same manner; and it will be perfect, when the necessary is joined to the less extreme. But the conclusion, when the terms are categoric, will be of the contingent, and not of that which exists, whether the terms are universally, or not universally posited. But if one interval is affirmative, and the other privative; when the affirmative, indeed, is necessary, the conclusion will in like manner signify the being contingent, and not the not existing, or being present with. And when the privative is necessary, the conclusion will be of the happening not to be present with, and of the not being present with, whether the terms are universal, or not universal. The being contingent also in the conclusion is to be assumed after the same manner as in the former syllogisms. But there will not be a syllogism, in which the not being present with will be necessarily inferred; for it is one thing to be present with not necessarily, and another not to be present with necessarily. It is evident, therefore, that when the terms are affirmative, a necessary conclusion will not be produced. For let A be necessarily present with every B, but let B be contingent to every C. There will, therefore, be an imperfect syllogism, in which it may be collected that A happens to be present with every C. But that it is imperfect is evident from demonstration; for this may be demonstrated after the same manner as in the former syllogisms. Again, let A be contingent to every B, but let B be necessarily present with every C. There will, therefore, be a syllogism, in which it may be collected that A happens to be present with every C, but not that it is simply present with every C. The syllogism also will be perfect and not imperfect for it will be immediately completed through the propositions assumed from the first. But if the propositions are not similar in figure in the first place, let the privative proposition be necessary, and let A necessarily be contingent to no B, but let B be contingent to every C. It is necessary, therefore, that A should be present with no C. For let it be supposed to be present either with every individual, or with a certain individual but it was supposed to be contingent to no B. Since, therefore, a privative proposition may be converted, neither will B be contingent to any A. But A was posited to be present with every or with some C. Hence, B will happen to be present with no, or not with every C. It was supposed, however, from the first to be present with every C.
It is necessary that no B should be A:
It happens that every C is B:
∴ No C is A.
It is necssary that no A should be B:
Some C is A:
∴ It is necessary that some C should not be B.
But it is evident, that there will also be a syllogism of the not happening to be present with, since there is a syllogism of the not being present with. Again, let the affirmative proposition be necessary, and let it happen that A is present with no B, but that B is necessarily present with every C. The syllogism, therefore, will be perfect, yet not of the not being present with, but of the happening not to be present with for the proposition was thus assumed from the greater extreme and there cannot be a deduction to the impossible. For if A is supposed to be present with a certain C, and it is admitted that A happens to be present with no B, nothing impossible will thence happen. But if privation is joined to the less extreme, when it signifies to be contingent, there will be a syllogism through conversion, as in the former syllogisms. When, however, it signifies not to be contingent, there will not be a syllogism. Nor will there be a syllogism when both the intervals are privative, unless the contingent is joined to the less extreme. But let the terms be the same; viz. of being present with, white, animal, snow but of not being present with, white, animal, pitch.
It happens that every/no animal is white:
It is necessary that no snow should be an animal:
∴ It is necessary that all snow should be white.
It happens that every/no animal is white:
It is necessary that no pitch should be an animal:
∴ It is necessary that no pitch should be white.
The like also will take place in partial syllogisms. For when the privative interval is necessary, the conclusion will be of the not being present with. Thus, if A happens to be present with no B, but B happens to be present with a certain C, it is necessary that A should not be present with a certain C. For if it is present with every C, but is contingent to no B, neither will B happen to be present with any A. Hence, if A is present with every C, B will be contingent to no C. But it was supposed to be contingent to a certain C. But when the partial affirmative in a privative syllogism, as, for instance, B C, is necessary or the universal affirming in a categoric syllogism, as, for instance, A B, there will not be a syllogism of the being present with. But the demonstration is the same as in the former syllogisms. If, however, universal is joined to the less extreme, either affirmative, or privative and contingent; but the partial necessary is joined to the greater extreme, there will not be a syllogism. But let the terms of being present with from necessity be, animal, white, man and not being contingent, animal, white, garment.
It is necessary that something white should be/not be an animal:
It happens that every/no man is white:
∴ It is necessary that every man should be an animal.
It is necessary that something white should be/not be an animal:
It happens that every/no garment is white:
∴ It is necessary that no garment should be an animal.
But when the universal is necessary, and the partial contingent the universal being privative, let the terms of being present with be animal, white, crow but of not being present with, animal, white, pitch.
It happens that something white is/is not an animal:
It is necessary that no crow should be white:
∴ It is necessary that every crow should be an animal.
It happens that something white is/is not an animal:
It is necessary that no pitch should be white:
∴ It is necessary that no pitch should be an animal.
But when the universal affirms, let the terms of being present with be, animal, white, swan but of not being contingent, animal, white, snow.
It happens that something white is/is not an animal:
It is necessary that every swan should be white:
∴ It is necessary that every swan should be an animal.
It happens that something white is/is not an animal:
It is necessary that all snow should be white:
∴ It is neccssary that no snow should be an animal.
Nor will there then be a syllogism, when the propositions are assumed indefinite, or both, according to a part. But let the common terms of being present with be animal, white, man and of not being present with, animal, white, inanimate. For animal is necessarily present with, and does not happen to be present with, something white, and whiteness also is necessarily present with, and does not happen to be present with, something inanimate. And the like takes place in the contingent. Hence these terms are useful to all the modes.
It happens that something white is/is not an animal:
It is necessary that some man should be/not be white:
∴ It is necessary that every man should be an animal.
It happens that something white is/is not an animal:
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 something white should be/not be an animal:
It happens that some man is/is not white:
∴ It is necessary that every man should be an animal.
It is necessary that something white should be/not be an animal:
It happens that every thing inanimate ss white:
∴ It is necessary that nothing inanimate should be an aniinal.
From what has been said, therefore, it is evident, that when the terms subsist similarly in that which is present with, and in necessary propositions, a syllogism will, and will not be formed. There is this exception, however, that if the privative proposition is posited according to existing, or being present with, the syllogism will be of the happening not to be present with. But if the privative proposition is necessary, the syllogism will be of the happening not to be present with and of the not being present with. It ia also evident, that all the syllogisms are imperfect, and that they are perfected through the above-mentioned figures.
Return to Aristotle, Prior Analytics
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