Prior Analytics - Book I   

negative a syllogism can always be formed by converting the

problematic premiss into its complementary affirmative as before.

Suppose A necessarily does not belong to B, and possibly may not

belong to C: if the premisses are converted B belongs to no A, and A

may possibly belong to all C: thus we have the first figure. Similarly

if the minor premiss is negative. But if the premisses are affirmative

there cannot be a syllogism. Clearly the conclusion cannot be a

negative assertoric or a negative necessary proposition because no

negative premiss has been laid down either in the assertoric or in the

necessary mode. Nor can the conclusion be a problematic negative

proposition. For if the terms are so related, there are cases in which

B necessarily will not belong to C; e.g. suppose that A is white, B

swan, C man. Nor can the opposite affirmations be established, since

we have shown a case in which B necessarily does not belong to C. A

syllogism then is not possible at all.

Similar relations will obtain in particular syllogisms. For whenever

the negative proposition is universal and necessary, a syllogism

will always be possible to prove both a problematic and a negative

assertoric proposition (the proof proceeds by conversion); but when

the affirmative proposition is universal and necessary, no syllogistic

conclusion can be drawn. This can be proved in the same way as for

universal propositions, and by the same terms. Nor is a syllogistic

conclusion possible when both premisses are affirmative: this also may

be proved as above. But when both premisses are negative, and the

premiss that definitely disconnects two terms is universal and

necessary, though nothing follows necessarily from the premisses as

they are stated, a conclusion can be drawn as above if the problematic

premiss is converted into its complementary affirmative. But if both

are indefinite or particular, no syllogism can be formed. The same

proof will serve, and the same terms.

It is clear then from what has been said that if the universal and

negative premiss is necessary, a syllogism is always possible, proving