Prior Analytics - Book I   

premisses actually taken nothing necessary results in any way; but

if the problematic premiss is converted, we shall have a syllogism.

Suppose that A belongs to no B, and B may possibly belong to no C.

Through these comes nothing necessary. But if B is assumed to be

possible for all C (and this is true) and if the premiss AB remains as

before, we shall again have the same syllogism. But if it be assumed

that B does not belong to any C, instead of possibly not belonging,

there cannot be a syllogism anyhow, whether the premiss AB is negative

or affirmative. As common instances of a necessary and positive

relation we may take the terms white-animal-snow: of a necessary and

negative relation, white-animal-pitch. Clearly then if the terms are

universal, and one of the premisses is assertoric, the other

problematic, whenever the minor premiss is problematic a syllogism

always results, only sometimes it results from the premisses that

are taken, sometimes it requires the conversion of one premiss. We

have stated when each of these happens and the reason why. But if

one of the relations is universal, the other particular, then whenever

the major premiss is universal and problematic, whether affirmative or

negative, and the particular is affirmative and assertoric, there will

be a perfect syllogism, just as when the terms are universal. The

demonstration is the same as before. But whenever the major premiss is

universal, but assertoric, not problematic, and the minor is

particular and problematic, whether both premisses are negative or

affirmative, or one is negative, the other affirmative, in all cases

there will be an imperfect syllogism. Only some of them will be proved

per impossibile, others by the conversion of the problematic

premiss, as has been shown above. And a syllogism will be possible

by means of conversion when the major premiss is universal and

assertoric, whether positive or negative, and the minor particular,

negative, and problematic, e.g. if A belongs to all B or to no B,

and B may possibly not belong to some C. For if the premiss BC is

converted in respect of possibility, a syllogism results. But whenever