Prior Analytics - Book I   

Whenever the same thing belongs to all of one subject, and to none

of another, or to all of each subject or to none of either, I call

such a figure the second; by middle term in it I mean that which is

predicated of both subjects, by extremes the terms of which this is

said, by major extreme that which lies near the middle, by minor

that which is further away from the middle. The middle term stands

outside the extremes, and is first in position. A syllogism cannot

be perfect anyhow in this figure, but it may be valid whether the

terms are related universally or not.

If then the terms are related universally a syllogism will be

possible, whenever the middle belongs to all of one subject and to

none of another (it does not matter which has the negative

relation), but in no other way. Let M be predicated of no N, but of

all O. Since, then, the negative relation is convertible, N will

belong to no M: but M was assumed to belong to all O: consequently N

will belong to no O. This has already been proved. Again if M

belongs to all N, but to no O, then N will belong to no O. For if M

belongs to no O, O belongs to no M: but M (as was said) belongs to all

N: O then will belong to no N: for the first figure has again been

formed. But since the negative relation is convertible, N will

belong to no O. Thus it will be the same syllogism that proves both

conclusions.

It is possible to prove these results also by reductio ad

impossibile.

It is clear then that a syllogism is formed when the terms are so

related, but not a perfect syllogism; for necessity is not perfectly

established merely from the original premisses; others also are

needed.

But if M is predicated of every N and O, there cannot be a

syllogism. Terms to illustrate a positive relation between the

extremes are substance, animal, man; a negative relation, substance,