Prior Analytics - Book I   

premisses are similar in form, I mean both negative or both

affirmative, a syllogism will not be possible anyhow. First let them

be negative, and let the major premiss be universal, e.g. let M belong

to no N, and not to some O. It is possible then for N to belong either

to all O or to no O. Terms to illustrate the negative relation are

black, snow, animal. But it is not possible to find terms of which the

extremes are related positively and universally, if M belongs to

some O, and does not belong to some O. For if N belonged to all O, but

M to no N, then M would belong to no O: but we assumed that it belongs

to some O. In this way then it is not admissible to take terms: our

point must be proved from the indefinite nature of the particular

statement. For since it is true that M does not belong to some O, even

if it belongs to no O, and since if it belongs to no O a syllogism

is (as we have seen) not possible, clearly it will not be possible now

either.

Again let the premisses be affirmative, and let the major premiss as

before be universal, e.g. let M belong to all N and to some O. It is

possible then for N to belong to all O or to no O. Terms to illustrate

the negative relation are white, swan, stone. But it is not possible

to take terms to illustrate the universal affirmative relation, for

the reason already stated: the point must be proved from the

indefinite nature of the particular statement. But if the minor

premiss is universal, and M belongs to no O, and not to some N, it

is possible for N to belong either to all O or to no O. Terms for

the positive relation are white, animal, raven: for the negative

relation, white, stone, raven. If the premisses are affirmative, terms

for the negative relation are white, animal, snow; for the positive

relation, white, animal, swan. Evidently then, whenever the

premisses are similar in form, and one is universal, the other

particular, a syllogism can, not be formed anyhow. Nor is one possible

if the middle term belongs to some of each of the extremes, or does

not belong to some of either, or belongs to some of the one, not to