Prior Analytics - Book I   

If R belongs to all S, and P to no S, there will be a syllogism to

prove that P will necessarily not belong to some R. This may be

demonstrated in the same way as before by converting the premiss RS.

It might be proved also per impossibile, as in the former cases. But

if R belongs to no S, P to all S, there will be no syllogism. Terms

for the positive relation are animal, horse, man: for the negative

relation animal, inanimate, man.

Nor can there be a syllogism when both terms are asserted of no S.

Terms for the positive relation are animal, horse, inanimate; for

the negative relation man, horse, inanimate-inanimate being the middle

term.

It is clear then in this figure also when a syllogism will be

possible and when not, if the terms are related universally. For

whenever both the terms are affirmative, there will be a syllogism

to prove that one extreme belongs to some of the other; but when

they are negative, no syllogism will be possible. But when one is

negative, the other affirmative, if the major is negative, the minor

affirmative, there will be a syllogism to prove that the one extreme

does not belong to some of the other: but if the relation is reversed,

no syllogism will be possible. If one term is related universally to

the middle, the other in part only, when both are affirmative there

must be a syllogism, no matter which of the premisses is universal.

For if R belongs to all S, P to some S, P must belong to some R. For

since the affirmative statement is convertible S will belong to some

P: consequently since R belongs to all S, and S to some P, R must also

belong to some P: therefore P must belong to some R.

Again if R belongs to some S, and P to all S, P must belong to

some R. This may be demonstrated in the same way as the preceding. And

it is possible to demonstrate it also per impossibile and by

exposition, as in the former cases. But if one term is affirmative,

the other negative, and if the affirmative is universal, a syllogism

will be possible whenever the minor term is affirmative. For if R