Prior Analytics - Book I   

animal, number-substance being the middle term.

Nor is a syllogism possible when M is predicated neither of any N

nor of any O. Terms to illustrate a positive relation are line,

animal, man: a negative relation, line, animal, stone.

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

universally related, the terms must be related as we stated at the

outset: for if they are otherwise related no necessary consequence

follows.

If the middle term is related universally to one of the extremes,

a particular negative syllogism must result whenever the middle term

is related universally to the major whether positively or

negatively, and particularly to the minor and in a manner opposite

to that of the universal statement: by 'an opposite manner' I mean, if

the universal statement is negative, the particular is affirmative: if

the universal is affirmative, the particular is negative. For if M

belongs to no N, but to some O, it is necessary that N does not belong

to some O. For since the negative statement is convertible, N will

belong to no M: but M was admitted to belong to some O: therefore N

will not belong to some O: for the result is reached by means of the

first figure. Again if M belongs to all N, but not to some O, it is

necessary that N does not belong to some O: for if N belongs to all O,

and M is predicated also of all N, M must belong to all O: but we

assumed that M does not belong to some O. And if M belongs to all N

but not to all O, we shall conclude that N does not belong to all O:

the proof is the same as the above. But if M is predicated of all O,

but not of all N, there will be no syllogism. Take the terms animal,

substance, raven; animal, white, raven. Nor will there be a conclusion

when M is predicated of no O, but of some N. Terms to illustrate a

positive relation between the extremes are animal, substance, unit:

a negative relation, animal, substance, science.

If then the universal statement is opposed to the particular, we

have stated when a syllogism will be possible and when not: but if the