Free The Complete Aristotle (eng.) by Aristotle

such
corresponding positive and negative propositions as refer to
universals and have a universal character, one must be true and the
other false. This is the case also when the reference is to
individuals, as in the propositions ‘Socrates is white’, ‘Socrates
is not white’.
    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 true and the other false. We have pointed out,
moreover, what the reason of this is and under what circumstances
the truth of the one involves the falsity of the other.
8
    An affirmation or denial is single, if it indicates some one
fact about some one subject; it matters not whether the subject is
universal and whether the statement has a universal character, or
whether this is not so. Such single propositions are: ‘every man is
white’, ‘not every man is white’;’man is white’,’man is not white’;
‘no man is white’, ‘some men are white’; provided the word ‘white’
has one meaning. If, on the other hand, one word has two meanings
which do not combine to form one, the affirmation is not single.
For instance, if a man should establish the symbol ‘garment’ as
significant both of a horse and of a man, the proposition ‘garment
is white’ would not be a single affirmation, nor its opposite a
single denial. For it is equivalent to the proposition ‘horse and
man are white’, which, again, is equivalent to the two propositions
‘horse is white’, ‘man is white’. If, then, these two propositions
have more than a single significance, and do not form a single
proposition, it is plain that the first proposition either has more
than one significance or else has none; for a particular man is not
a horse.
    This, then, is another instance of those propositions of which
both the positive and the negative forms may be true or false
simultaneously.
9
    In the case of that which is or which has taken place,
propositions, whether positive or negative, must be true or false.
Again, in the case of a pair of contradictories, either when the
subject is