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1053a]
[1]
Hence the measure of number is most
exact, for we posit the unit as in every way indivisible; and in all
other cases we follow this example, for with the furlong or talent or
in general with the greater measure an addition or subtraction would
be less obvious than with a smaller one.Therefore the first thing from which,
according to our perception, nothing can be subtracted is used by all
men as their measure of wet and dry, weight and magnitude; and they
think that they know the quantity only when they know it in terms of
this measure. And they know motion too by simple motion and the most
rapid, for this takes least time.Hence in astronomy a unit of this kind is the
starting point and measure; for they assume that the motion of the
heavens is uniform and the most rapid, and by it they judge the
others. In music the measure is the quarter tone, because it is the
smallest interval; and in language the letter. All these are examples
of units in this sense—not in the sense that unity is
something common to them all, but in the sense which we have
described.The
measure is not always numerically one, but sometimes more than one;
e.g., there are two quarter tones, distinguished not by our hearing
but by their theoretical ratios
1; and the articulate sounds by which we measure
speech are more than one; and the diagonal of a square is measured by
two quantities,
2 and so are all magnitudes of this
kind. Thus unity is the measure of all things, because we learn of
what the substance is composed by dividing it,
[20]
in respect of either quantity or
form.Hence unity is
indivisible, because that which is primary in each class of things is
indivisible. But not every unit is indivisible in the same
sense—e.g. the foot and the arithmetical unit; but the
latter is absolutely indivisible, and the former must be classed as
indivisible with respect to our power of perception, as we have
already stated; since presumably everything which is continuous is
divisible.
The measure is always akin to the
thing measured. The measure of magnitude is magnitude, and in
particular the measure of length is a length; of breadth, a breadth;
of sounds, a sound; of weight, a weight; of units, a unit; for this is
the view that we must take, and not that the measure of numbers is a
number. The latter, indeed, would necessarily be true, if the analogy
held good; but the supposition is not analogous—it is as
though one were to suppose that the measure of units is units, and not
a unit; for number is a plurality of units.
We
also speak of knowledge or sense perception as a measure of things for
the same reason, because through them we come to know something;
whereas really they are measured themselves rather than measure other
things. But our experience is as though someone else measured us, and
we learned our height by noticing to what extent he applied his
foot-rule to us.Protagoras says that "man is the measure of all things," meaning, as
it were, the scholar or the man of perception;