Prior Analytics - Book I   

be obtained by a reductio ad absurdum: for if it is assumed that B can

belong to all C, no false consequence results: for A may belong both

to all C and to no C. In general, if there is a syllogism, it is clear

that its conclusion will be problematic because neither of the

premisses is assertoric; and this must be either affirmative or

negative. But neither is possible. Suppose the conclusion is

affirmative: it will be proved by an example that the predicate cannot

belong to the subject. Suppose the conclusion is negative: it will

be proved that it is not problematic but necessary. Let A be white,

B man, C horse. It is possible then for A to belong to all of the

one and to none of the other. But it is not possible for B to belong

nor not to belong to C. That it is not possible for it to belong, is

clear. For no horse is a man. Neither is it possible for it not to

belong. For it is necessary that no horse should be a man, but the

necessary we found to be different from the possible. No syllogism

then results. A similar proof can be given if the major premiss is

negative, the minor affirmative, or if both are affirmative or

negative. The demonstration can be made by means of the same terms.

And whenever one premiss is universal, the other particular, or both

are particular or indefinite, or in whatever other way the premisses

can be altered, the proof will always proceed through the same

terms. Clearly then, if both the premisses are problematic, no

syllogism results.



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But if one premiss is assertoric, the other problematic, if the

affirmative is assertoric and the negative problematic no syllogism

will be possible, whether the premisses are universal or particular.

The proof is the same as above, and by means of the same terms. But

when the affirmative premiss is problematic, and the negative

assertoric, we shall have a syllogism. Suppose A belongs to no B,