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