Prior Analytics - Book I   

but can belong to all C. If the negative proposition is converted, B

will belong to no A. But ex hypothesi can belong to all C: so a

syllogism is made, proving by means of the first figure that B may

belong to no C. Similarly also if the minor premiss is negative. But

if both premisses are negative, one being assertoric, the other

problematic, nothing follows necessarily from these premisses as

they stand, but if the problematic premiss is converted into its

complementary affirmative a syllogism is formed to prove that B may

belong to no C, as before: for we shall again have the first figure.

But if both premisses are affirmative, no syllogism will be

possible. This arrangement of terms is possible both when the relation

is positive, e.g. health, animal, man, and when it is negative, e.g.

health, horse, man.

The same will hold good if the syllogisms are particular. Whenever

the affirmative proposition is assertoric, whether universal or

particular, no syllogism is possible (this is proved similarly and

by the same examples as above), but when the negative proposition is

assertoric, a conclusion can be drawn by means of conversion, as

before. Again if both the relations are negative, and the assertoric

proposition is universal, although no conclusion follows from the

actual premisses, a syllogism can be obtained by converting the

problematic premiss into its complementary affirmative as before.

But if the negative proposition is assertoric, but particular, no

syllogism is possible, whether the other premiss is affirmative or

negative. Nor can a conclusion be drawn when both premisses are

indefinite, whether affirmative or negative, or particular. The

proof is the same and by the same terms.



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If one of the premisses is necessary, the other problematic, then if

the negative is necessary a syllogistic conclusion can be drawn, not