On Interpratation   

When, on the other hand, the reference is to universals, but the

propositions are not universal, it is not always the case that one

is true and the other false, for it is possible to state truly that

man is white and that man is not white and that man is beautiful and

that man is not beautiful; for if a man is deformed he is the

reverse of beautiful, also if he is progressing towards beauty he is

not yet beautiful.

This statement might seem at first sight to carry with it a

contradiction, owing to the fact that the proposition 'man is not

white' appears to be equivalent to the proposition 'no man is

white'. This, however, is not the case, nor are they necessarily at

the same time true or false.

It is evident also that the denial corresponding to a single

affirmation is itself single; for the denial must deny just that which

the affirmation affirms concerning the same subject, and must

correspond with the affirmation both in the universal or particular

character of the subject and in the distributed or undistributed sense

in which it is understood.

For instance, the affirmation 'Socrates is white' has its proper

denial in the proposition 'Socrates is not white'. If anything else be

negatively predicated of the subject or if anything else be the

subject though the predicate remain the same, the denial will not be

the denial proper to that affirmation, but on that is distinct.

The denial proper to the affirmation 'every man is white' is 'not

every man is white'; that proper to the affirmation 'some men are

white' is 'no man is white', while that proper to the affirmation 'man

is white' is 'man is not white'.

We have shown further that a single denial is contradictorily

opposite to a single affirmation and we have explained which these

are; we have also stated that contrary are distinct from contradictory

propositions and which the contrary are; also that with regard to a

pair of opposite propositions it is not always the case that one is