Return to Aristotle, Prior Analytics
When, therefore, A is contingent to every B, and B to every C, there will be a perfect syllogism, in which it may be collected that A is contingent to every C. But this is evident from definition; for we thus assume the being contingent to every. In like manner also, if A is contingent to no B, but B is contingent to every C, there will be a syllogism in which it may be collected that A is contingent to no C. For to assert that A is contingent to nothing to which B is contingent, is to leave no one of the contingents which are under B. But when A is contingent to every B, but B is contingent to no C, from the assumed propositions no syllogism will be produced; but the proposition B C being converted, according to the being contingent, the same syllogism will be produced as was produced before. For since it happens that B is present with no C, it may also happen to be present with every C; for this was shown before. Hence, since B may happen to be present with every C, and A with every B, again, the same syllogism will be produced. The like will also take place, if negation together with the being contingent are added to both the propositions. I say, for instance, if A is contingent to no B, and B to no C; for through the assumed propositions, no syllogism will be produced. But the propositions B Chig converted, there will again be the same syllogism, as was formed before. It is evident, therefore, that when negation is added to the less extreme, or to both the propositions, either a syllogism will not be produced, or it will be produced indeed, but will not be a perfect syllogism; for the necessity of consecution is effected from conversion. But if one of the propositions is universal, and the other is assumed in a part; the universal being posited at the greater extreme, there will be a perfect syllogism. For if A is contingent to every B, but B is contingent to a certain C, A also will be contingent to a certain C. This, however, is evident from the definition of being contingent to every individual of a certain multitude. Again, if A is contingent to no B, but B may happen to be present with a certain C, it is necessary that A should happen not to be present with a certain C. But the demonstration is the same. If, however, the proposition which is in a part is assumed privative, but the proposition which is universal is assumed affirmative, and retains the same position; as, for instance, if A may happen to be present with every B, but B may happen not to be present with a certain C; — if this be the case, from the assumed propositions, indeed, an evident syllogism will not be produced. But the particular proposition being converted, and it being admitted, that B may happen to be present with a certain C, there will be the same conclusion as before, as in the former syllogisms. If, however, the major proposition is assumed as particular, but the minor is universal, whether both are posited affirmative, or privative, or dissimilar in figure; or whether both are indefinite, or particular, there will by no means be a syllogism. For nothing hinders B from being more widely extended than A, and from not being equally predicated. But let that by which B is more widely extended than A, be assumed to be C; for to C it will happen that A is present neither to every, nor to none, nor to a certain one, nor not to a certain one; since contingent propositions may be converted, and B may happen to be present with more things than A. Farther still, this also is evident from the terms; for the propositions thus subsisting, the first will be contingent to the last and to none, and will necessarily be present with every individual. But let the common terms of all be these; of being present with, from necessity, animal, white, man; but of not happening to be present with, animal, white, garment.
It happens that something white is/is not animal:
It happens that every/no/some/not every man is white:
∴ It is necessary that every man should be an animal.
It happens that something white is/is not an animal:
It happens that every/no/some/not every garment is white:
∴ Is necessary that no garment should be an animal.
It is evident, therefore, that when the terms subsist after this manner, no syllogism will be produced. For every syllogism is either of that which exists, or of that which exists from necessity, or of that which is contingent. But that this syllogism is neither of that which exists, nor of that which necessarily exists is evident; for the affirmative conclusion is subverted by the privative, and the privative by the affirmative. It remains, therefore, that it must be of that which is contingent. This, however, is impossible; for it has been shown, that when the terms thus subsist, the first is necessarily inherent in all the last, and will happen to be present with no individual. Hence there will not be a syllogism of the contingent; for that which is necessary is not contingent. It is evident, therefore, that when the terms are universally assumed in contingent propositions, there will always be a syllogism in the first figure, both when they are categoric, and when they are privative; except that when they are categoric, there will be a perfect syllogism; but when they are privative, an imperfect syllogism. It is necessary, however, to assume the contingent, not in necessary propositions, but according to the definition mentioned in the preceding chapter. But sometimes a thing of this kind is latent.
Return to Aristotle, Prior Analytics
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