Prior Analytics - Book I   

If then the terms are universally related, it is clear in this

figure when a syllogism will be possible and when not, and that if a

syllogism is possible the terms must be related as described, and if

they are so related there will be a syllogism.

But if one term is related universally, the other in part only, to

its subject, there must be a perfect syllogism whenever universality

is posited with reference to the major term either affirmatively or

negatively, and particularity with reference to the minor term

affirmatively: but whenever the universality is posited in relation to

the minor term, or the terms are related in any other way, a syllogism

is impossible. I call that term the major in which the middle is

contained and that term the minor which comes under the middle. Let

all B be A and some C be B. Then if 'predicated of all' means what was

said above, it is necessary that some C is A. And if no B is A but

some C is B, it is necessary that some C is not A. The meaning of

'predicated of none' has also been defined. So there will be a perfect

syllogism. This holds good also if the premiss BC should be

indefinite, provided that it is affirmative: for we shall have the

same syllogism whether the premiss is indefinite or particular.

But if the universality is posited with respect to the minor term

either affirmatively or negatively, a syllogism will not be

possible, whether the major premiss is positive or negative,

indefinite or particular: e.g. if some B is or is not A, and all C

is B. As an example of a positive relation between the extremes take

the terms good, state, wisdom: of a negative relation, good, state,

ignorance. Again if no C is B, but some B is or is not A or not

every B is A, there cannot be a syllogism. Take the terms white,

horse, swan: white, horse, raven. The same terms may be taken also

if the premiss BA is indefinite.

Nor when the major premiss is universal, whether affirmative or

negative, and the minor premiss is negative and particular, can

there be a syllogism, whether the minor premiss be indefinite or