By Aristotle, Smith (trans.)
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Extra resources for Aristotle, Prior Analytics
But if one of the terms is positive and the other privative, then when the universal is both privative and necessary, the conclusion will also be necessary. For if it is not possible for A to belong to any C and B belongs to some C, then it is necessary for A not to belong to some B. But when the affirmative is put as necessary (whether it is universal or particular), or when the privative is particular, the conclusion will not be necessary. The proofs for the rest are the same as those we stated concerning the previous cases; terms for the case in which the positive necessary premise is universal are wakefulness, animal, man (with man the middle), and for the case in which the positive necessary premise is particular they are wakefulness, animal, white.
However, when the premise in relation to the minor extreme is possible, then not only are the deductions all incomplete, but also the privative deductions among them are not of what is possible according to the determination, but rather of what belongs of necessity to none or not to every (for if something belongs of necessity to none, or not to every, we also say it is possible for it to belong to none or not to every). For let it be possible for A to belong to every B and let B be put as belonging to every C.
It is also the same way in the other cases. For since what is possible is not necessary, and it is possible for what is not necessary not to belong, it is evident that, if it is possible for A to belong to B, then it is also possible for it not to belong; and, if it is possible for it to belong to everyone, then it is also possible for it not to belong to everyone. And it will also be the same in the case of particular affirmations (for the demonstration is the Same). Premises of these sorts are positive and not privative: for 'to be possible' is arranged similarly to 'to be,' as was stated earlier.