The Categories | Page 8

not only time, but space also,
is a continuous quantity, for its parts have a common boundary.
Quantities consist either of parts which bear a relative position 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