each to each, or of parts which do not. The parts of a line bear a
relative position to each other, for each lies somewhere, and it would
be possible to distinguish each, and to state the position of each
on the plane and to explain to what sort of part among the rest each
was contiguous. Similarly the parts of a plane have position, for it
could similarly be stated what was the position of each and what
sort of parts were contiguous. The same is true with regard to the
solid and to space. But it would be impossible to show that the arts
of a number had a relative position each to each, or a particular
position, or to state what parts were contiguous. Nor could this be
done in the case of time, for none of the parts of time has an abiding
existence, and that which does not abide can hardly have position.
It would be better to say that such parts had a relative order, in
virtue of one being prior to another. Similarly with number: in
counting, 'one' is prior to 'two', and 'two' to 'three', and thus
the parts of number may be said to possess a relative order, though it
would be impossible to discover any distinct position for each. This
holds good also in the case of speech. None of its parts has an
abiding existence: when once a syllable is pronounced, it is not
possible to retain it, so that, naturally, as the parts do not
abide, they cannot have position. Thus, some quantities consist of
parts which have position, and some of those which have not.

  Strictly speaking, only the things which I have mentioned belong
to the category of quantity: everything else that is called
quantitative is a quantity in a secondary sense. It is because we have
in mind some one of these quantities, properly so called, that we
apply quantitative terms to other things. We speak of what is white as
large, because the surface over which the white extends is large; we
speak of an action or a process as lengthy, because the time covered
is long; these things cannot in their own right claim the quantitative
epithet. For instance, should any one explain how long an action
was, his statement would be made in terms of the time taken, to the
effect that it lasted a year, or something of that sort. In the same
way, he would explain the size of a white object in terms of
surface, for he would state the area which it covered. Thus the things
already mentioned, and these alone, are in their intrinsic nature
quantities; nothing else can claim the name in its own right, but,
if at all, only in a secondary sense.

  Quantities have no contraries. In the case of definite quantities
this is obvious; thus, there is nothing that is the contrary of 'two
cubits long' or of 'three cubits long', or of a surface, or of any
such quantities. A man might, indeed, argue that 'much' was the
contrary of 'little', and 'great' of 'small'. But these are not
quantitative, but relative; things are not great or small
absolutely, they are so called rather as the result of an act of
comparison. For instance, a mountain is called small, a grain large,
in virtue of the fact that the latter is greater than others of its
kind, the former less. Thus there is a reference here to an external
standard, for if the terms 'great' and 'small' were used absolutely, a
mountain would never be called small or a grain large. Again, we say
that there are many people in a village, and few in Athens, although
those in the city are many times as numerous as those in the
village: or we say that a house has many in it, and a theatre few,
though those in the theatre far outnumber those in the house. The
terms 'two cubits long, "three cubits long,' and so on indicate
quantity, the terms 'great' and 'small' indicate relation, for they
have reference to an external standard. It is, therefore, plain that
these are to be classed as relative.

  Again, whether we define them as quantitative or not, they have no
contraries: for how can there be a contrary of an attribute which is
not to be apprehended in or by itself, but only by reference to
something external? Again, if 'great' and 'small' are contraries, it
will come about that the same subject can admit contrary qualities
at one and the same time, and that things will themselves be
contrary to themselves. For it happens at times that the same thing is
both small and great. For the same thing may be small in comparison
with one thing, and great in comparison with another, so that the same
thing comes to be both small and great at one and the same time, and
is of such a nature as to admit contrary qualities at one and the same
moment. Yet it was agreed, when substance was being discussed, that
nothing admits contrary qualities at one and the same moment. For
though substance is capable of admitting contrary qualities, yet no
one is at the same time both sick and healthy, nothing is at the
same time both white and black. Nor is there anything which is
qualified in contrary ways at one and the same time.

  Moreover, if these were contraries, they would themselves be
contrary to themselves. For if 'great' is the contrary of 'small', and
the same thing is both great and small at the same time, then
'small' or 'great' is the contrary of itself. But this is
impossible. The term 'great', therefore, is not the contrary of the
term 'small', nor 'much' of 'little'. And even though a man should
call these terms not relative but quantitative, they would not have
contraries.

  It is in the case of space that quantity most plausibly appears to
admit of a contrary. For men define the term 'above' as the contrary
of 'below', when it is the region at the centre they mean by
'below'; and this is so, because nothing is farther from the
extremities of the universe than the region at the centre. Indeed,
it seems that in defining contraries of every kind men have recourse
to a spatial metaphor, for they say that those things are contraries
which, within the same class, are separated by the greatest possible
distance.

  Quantity does not, it appears, admit of variation of degree. One
thing cannot be two cubits long in a greater degree than another.