Return to Aristotle, Prior Analytics
But in the last figure, when both the propositions are contingent, and when one only is contingent, there will be a syllogism. When, therefore, the propositions signify the being contingent, the conclusion also will be contingent and when the one signifies the being contingent, but the other the being present with. But when one of the propositions is posited necessary if, indeed, it is affirmative, there will not be a conclusion, neither necessary nor pure. But if it is privative, there will be a syllogism of the not being present with, as before. In these, however, the contingent must be similarly assumed in the conclusions. In the first place, therefore, let both the propositions be contingent, and let A and B happen to be present with every C. Since then an affirmative proposition may be partially converted, but B is contingent to every C, G also will be contingent to a certain B. Hence, if A is contingent to every C, but C is contingent to a certain B, it is also necessary that A should be contingent to a certain B. For the first figure will be produced. And if A happens to be present with no C, but B is present with every C, it is also necessary that A should happen not to be present with a certain B for again, there will be the first figure through conversion. But if both the propositions are posited privative from the assumed propositions, indeed, there will not be the necessary (i.e. a necessity of concluding). The propositions, however, being converted, there will be a syllogism, as before. For if A and B . happen not to be present with C, if the happening not to be present with is changed, there will again be the first figure through conversion. But if one of the terms is universal, and the other partial; when the terms subsist in the same manner, as in that which is present with, there will be, and there will not be a syllogism. For let A be contingent to every C, but let B be present with a certain C again, there will be the first figure, the partial proposition being converted. For if A is contingent to every C, and C is contingent to a certain B, A also will be contingent to a certain B. The like will also take place, if the universal is joined to the proposition B C. And this in a similar manner will be effected, if the proposition A C is privative, but B C affirmative for again there will be the first figure through conversion. But if both are posited privative, the one universal, and the other partial through the things assumed, indeed, there will not be a syllogism but there will be when they are converted, as before. When, however, both are assumed indefinite, or partial, there will not be a syllogism. For it is necessary that A should be present with every, and with no B. Let the terms then of being present with be animal, man, white but of not being present with, horse, man, white; and let the middle be white.
It happens that something white is/is not an animal:
It happens that something white is/is not a man:
∴ It is necessary that every man should be an animal.
It happens that something white is/is not a horse:
It happens that something white is/is not a man:
∴ It is necessary that no man should be a horse.
Return to Aristotle, Prior Analytics
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