relatives to
one another, (ii) as contraries to one another, (iii) as privatives to
positives, (iv) as affirmatives to negatives.

Let me sketch my meaning in outline. An instance of the use of the word
'opposite' with reference to correlatives is afforded by the
expressions 'double' and 'half'; with reference to contraries by 'bad'
and 'good'. Opposites in the sense of 'privatives' and 'positives' are'
blindness' and 'sight'; in the sense of affirmatives and negatives, the
propositions 'he sits', 'he does not sit'.

(i) Pairs of opposites which fall under the category of relation are
explained by a reference of the one to the other, the reference being
indicated by the preposition 'of' or by some other preposition. Thus,
double is a relative term, for that which is double is explained as the
double of something. Knowledge, again, is the opposite of the thing
known, in the same sense; and the thing known also is explained by its
relation to its opposite, knowledge. For the thing known is explained
as that which is known by something, that is, by knowledge. Such
things, then, as are opposite the one to the other in the sense of
being correlatives are explained by a reference of the one to the other.

(ii) Pairs of opposites which are contraries are not in any way
interdependent, but are contrary the one to the other. The good is not
spoken of as the good of the bad, but as the contrary of the bad, nor
is white spoken of as the white of the black, but as the contrary of
the black. These two types of opposition are therefore distinct. Those
contraries which are such that the subjects in which they are naturally
present, or of which they are predicated, must necessarily contain
either the one or the other of them, have no intermediate, but those in
the case of which no such necessity obtains, always have an
intermediate. Thus disease and health are naturally present in the body
of an animal, and it is necessary that either the one or the other
should be present in the body of an animal. Odd and even, again, are
predicated of number, and it is necessary that the one or the other
should be present in numbers. Now there is no intermediate between the
terms of either of these two pairs. On the other hand, in those
contraries with regard to which no such necessity obtains, we find an
intermediate. Blackness and whiteness are naturally present in the
body, but it is not necessary that either the one or the other should
be pres