Return to Aristotle, Prior Analytics
But if one of the propositions is necessary, and the other contingent, the terms, indeed, being categoric, there will always be a syllogism of the contingent. When, however, one interval is categoric, but the other privative; if, indeed, the affirmative is necessary, there will be a syllogism of the happening not to be present with. But if the interval is privative, there will be a syllogism of the happening not to be present with, and of the not being present with. There will not, however, be a syllogism of the not being present with from necessity, as neither in the other figures. In the first place, therefore, let the terms be categoric, and let A be present from necessity with every C, but let B happen to be present with every C. Because, therefore, A is necessarily present with every C, but C is contingent to a certain B, A also will be contingent to, and will not be necessarily present with a certain B for such will be the conclusion in the first figure. A similar demonstration will take place, if the proposition B C is posited necessary, and the proposition AC contingent.
It happens that every man is white:
It is necessary that every man should be an animal:
∴ It happens that some animal iss white.
It happens that every man is white:
It is necessary that some animal should be a man:
∴ It happens that some animal is white.
Again, let the one proposition be categoric, but the other privative and let the categoric be necessary. Let also A happen to be present with no C, but let B necessarily be present with every C. Again, therefore, there will be the first figure and the conclusion will be contingent, but not pure for the privative proposition signifies the being contingent. It is evident, therefore, that the conclusion will be contingent for when the propositions thus subsisted in the first figure, the conclusion was contingent. But if the privative proposition should be necessary, the conclusion will be, that the not being present with a certain thing is contingent, and that it is not present with it. For let it be supposed that A is necessarily not present with C, but is contingent to every B. The affirmative proposition, therefore, B C being converted, there will be the first figure, and the privative proposition will be necessary. But when the propositions thus subsist, it will follow that A happens not to be present with a certain C, and that it is not present with it. Hence it is also necessary that A should not be present with a certain B. When, however, the privative is joined to the less extreme, if that is contingent there will be a syllogism, the proposition being converted, as in the former syllogisms. But if it is necessary, there will not be a syllogism, because it is necessary to be present with, every individual, and to happen to be present with no individual. Let the terms then of being present with every individual be, sleep, a sleeping horse, and man, but of being present with no individual sleep, a waking horse, and man.
It happens that every man sleeps:
It is necessary that no man should be a sleeping horse:
∴ It is necessary that every sleeping horse should sleep.
It happens that every man sleeps:
It is necessary that no man should be a waking horse:
∴ It is necessary that no waking horse should sleep.
The like will also take place, if one of the terms is joined to the middle universally, but the other partially. For both being categoric, there will be a syllogism of the being contingent, and not of the being present with; and also, when the one interval is assumed privative, but the other affimiative and the affirmative is necessary. But when the privative is necessary, the conclusion also will be of the not being present with. For there will be the same mode of demonstration, whether the terms are universal, or not universal since it is necessary that the syllogisms should be completed through the first figure. Hence it is necessary that there should be the same conclusion in these, as in those. But when the privative universally assumed is joined to the less extreme, if, indeed, it is contingent there will be a syllogism through conversion. If, however, it is necessary, there will not be a syllogism. But this may be demonstrated after the same manner as in universals, and through the same terms.
It happens that some man sleeps:
It is necessary that no man should be a sleeping horse:
∴ It is necessary that every sleeping horse should sleep.
It happens that, some man sleeps:
It is necessary that no man should be a waking horse:
∴ It is necessary that no waking horse should be asleep.
In this figure, therefore, it is also evident, when, and how there will be a syllogism; and when there will be a syllogism of the contingent, and when of the being present with. It is likewise evident, that all these syllogisms are imperfect, and that they are perfected through the first figure.
Return to Aristotle, Prior Analytics
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