Prior Analytics - Book I   

belongs to all S, but P does not belong to some S, it is necessary

that P does not belong to some R. For if P belongs to all R, and R

belongs to all S, then P will belong to all S: but we assumed that

it did not. Proof is possible also without reduction ad impossibile,

if one of the Ss be taken to which P does not belong.

But whenever the major is affirmative, no syllogism will be

possible, e.g. if P belongs to all S and R does not belong to some

S. Terms for the universal affirmative relation are animate, man,

animal. For the universal negative relation it is not possible to

get terms, if R belongs to some S, and does not belong to some S.

For if P belongs to all S, and R to some S, then P will belong to some

R: but we assumed that it belongs to no R. We must put the matter as

before.' Since the expression 'it does not belong to some' is

indefinite, it may be used truly of that also which belongs to none.

But if R belongs to no S, no syllogism is possible, as has been shown.

Clearly then no syllogism will be possible here.

But if the negative term is universal, whenever the major is

negative and the minor affirmative there will be a syllogism. For if P

belongs to no S, and R belongs to some S, P will not belong to some R:

for we shall have the first figure again, if the premiss RS is

converted.

But when the minor is negative, there will be no syllogism. Terms

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

relation, animal, science, wild-the middle in both being the term

wild.

Nor is a syllogism possible when both are stated in the negative,

but one is universal, the other particular. When the minor is

related universally to the middle, take the terms animal, science,

wild; animal, man, wild. When the major is related universally to

the middle, take as terms for a negative relation raven, snow,

white. For a positive relation terms cannot be found, if R belongs

to some S, and does not belong to some S. For if P belongs to all R,