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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