Similarly with regard to number: what is 'three' is not more truly
three than what is 'five' is five; nor is one set of three more
truly three than another set. Again, one period of time is not said to
be more truly time than another. Nor is there any other kind of
quantity, of all that have been mentioned, with regard to which
variation of degree can be predicated. The category of quantity,
therefore, does not admit of variation of degree.

  The most distinctive mark of quantity is that equality and
inequality are predicated of it. Each of the aforesaid quantities is
said to be equal or unequal. For instance, one solid is said to be
equal or unequal to another; number, too, and time can have these
terms applied to them, indeed can all those kinds of quantity that
have been mentioned.

  That which is not a quantity can by no means, it would seem, be
termed equal or unequal to anything else. One particular disposition
or one particular quality, such as whiteness, is by no means
compared with another in terms of equality and inequality but rather
in terms of similarity. Thus it is the distinctive mark of quantity
that it can be called equal and unequal.

                                 7

  Those things are called relative, which, being either said to be
of something else or related to something else, are explained by
reference to that other thing. For instance, the word 'superior' is
explained by reference to something else, for it is superiority over
something else that is meant. Similarly, the expression 'double' has
this external reference, for it is the double of something else that
is meant. So it is with everything else of this kind. There are,
moreover, other relatives, e.g. habit, disposition, perception,
knowledge, and attitude. The significance of all these is explained by
a reference to something else and in no other way. Thus, a habit is
a habit of something, knowledge is knowledge of something, attitude is
the attitude of something. So it is with all other relatives that have
been mentioned. Those terms, then, are called relative, the nature
of which is explained by reference to something else, the
preposition 'of' or some other preposition being used to indicate
the relation. Thus, one mountain is called great in comparison with
son with another; for the mountain claims this attribute by comparison
with something. Again, that which is called similar must be similar to
something else, and all other such attributes have this external
reference. It is to be noted that lying and standing and sitting are
particular attitudes, but attitude is itself a relative term. To
lie, to stand, to be seated, are not themselves attitudes, but take
their name from the aforesaid attitudes.

  It is possible for relatives to have contraries. Thus virtue has a
contrary, vice, these both being relatives; knowledge, too, has a
contrary, ignorance. But this is not the mark of all relatives;
'double' and 'triple' have no contrary, nor indeed has any such term.

  It also appears that relatives can admit of variation of degree. For
'like' and 'unlike', 'equal' and 'unequal', have the modifications
'more' and 'less' applied to them, and each of these is relative in
character: for the terms 'like' and 'unequal' bear 'unequal' bear a
reference to something external. Yet, again, it is not every
relative term that admits of variation of degree. No term such as
'double' admits of this modification. All relatives have correlatives:
by the term 'slave' we mean the slave of a master, by the term
'master', the master of a slave; by 'double', the double of its
hall; by 'half', the half of its double; by 'greater', greater than
that which is less; by 'less,' less than that which is greater.

  So it is with every other relative term; but the case we use to
express the correlation differs in some instances. Thus, by
knowledge we mean knowledge the knowable; by the knowable, that
which is to be apprehended by knowledge; by perception, perception
of the perceptible; by the perceptible, that which is apprehended by
perception.

  Sometimes, however, reciprocity of correlation does not appear to
exist. This comes about when a blunder is made, and that to which
the relative is related is not accurately stated. If a man states that
a wing is necessarily relative to a bird, the connexion between
these two will not be reciprocal, for it will not be possible to say
that a bird is a bird by reason of its wings. The reason is that the
original statement was inaccurate, for the wing is not said to be
relative to the bird qua bird, since many creatures besides birds have
wings, but qua winged creature. If, then, the statement is made
accurate, the connexion will be reciprocal, for we can speak of a
wing, having reference necessarily to a winged creature, and of a
winged creature as being such because of its wings.

  Occasionally, perhaps, it is necessary to coin words, if no word
exists by which a correlation can adequately be explained. If we
define a rudder as necessarily having reference to a boat, our
definition will not be appropriate, for the rudder does not have
this reference to a boat qua boat, as there are boats which have no
rudders. Thus we cannot use the terms reciprocally, for the word
'boat' cannot be said to find its explanation in the word 'rudder'. As
there is no existing word, our definition would perhaps be more
accurate if we coined some word like 'ruddered' as the correlative
of 'rudder'. If we express ourselves thus accurately, at any rate
the terms are reciprocally connected, for the 'ruddered' thing is
'ruddered' in virtue of its rudder. So it is in all other cases. A
head will be more accurately defined as the correlative of that
which is 'headed', than as that of an animal, for the animal does
not have a head qua animal, since many animals have no head.