Somebody might object that time is indeed the interval of movement, but
that it is not the characteristic interval of movement itself, being
only the interval in which movement exerts its extension, following
along with it. All these terms lack definition. This (extension) is
nothing else than the time within which the movement occurs. But
that is precisely the question at issue, from the very start. It is
as if a person who had been asked to define time should answer "time
is the interval of the movement produced within time." What then is
this interval called time, when considered outside of the interval
characteristic of movement? If the interval characteristic of time
be made to consist in movement, where shall the duration of rest be
posited? Indeed, for one object to be in motion implies that another
(corresponding object) is at rest; now the time of these objects is the
same, though for one it be the time of movement, and for the other the
time of rest (as thought Strato[451]). What then is the nature of this
interval? It cannot be an interval of space, since space is exterior
(to the movements that occur within it).
POLEMIC AGAINST ARISTOTLE: TIME IS NOT THE NUMBER AND MEASURE OF
MOVEMENT.
8. (9). Let us now examine in what sense it may be said (by
Aristotle[452]) that time is the number and measure of movement,
which definition seems more reasonable, because of the continuity
of movement. To begin with, following the method adopted with the
definition of time as "the interval of movement," we might ask whether
time be the measure and number of any kind of movement.[453] For how
indeed could we give a numerical valuation of unequal or irregular
movement. What system of numbering or measurement shall we use for
this? If the same measure be applied to slow or to swift movement,
in their case measure and number will be the same as the number ten
applied equally to horses and oxen; and further, such measure might
also be applied to dry and wet substances. If time be a measure of
this kind, we clearly see that it is the measure of movements, but we
do not discover what it may be in itself. If the number ten can be
conceived as a number, after making abstraction of the horses it served
to measure, if therefore a measure possess its own individuality,
even while no longer measuring anything, the case must be similar
with time, inasmuch as it is a measure. If then time be a number in
itself, in what does it differ from the number ten, or from any other
number composed of unities? As it is a continuous measure, and as it
is a quantity, it might, for instance, turn out to be something like
a foot-rule. It would then be a magnitude, as, for instance, a line,
which follows the movement; but how will this line be able to measure
what it follows? Why would it measure one thing rather than another?
It seems more reasonable to consider this measure, not as the measure
of every kind of movement, but only as the measure of the movement it
follows.[452] Then that measure is continuous, so far as the movement
it follows itself continue to exist. In this case, we should not
consider measure as something exterior, and separated from movement,
but as united to the measured movement. What then will measure? Is it
the movement that will be measured, and the extension that will measure
it? Which of these two things will time be? Will it be the measuring
movement, or the measuring extension? Time will be either the movement
measured by extension, or the measuring extension; or some third thing
which makes use of extension, as one makes use of a foot-rule, to
measure the quantity of movement. But in all these cases, we must, as
has already been noticed, suppose that movement is uniform; for unless
the movement be uniform, one and universal, the theory that movement is
a measure of any kind whatever will become almost impossible. If time
be "measured movement," that is, measured by quantity--besides granting
that it at all needs to be measured--movement must not be measured by
itself, but by something different. On the other hand, if movement
have a measure different from itself, and if, consequently, we need a
continuous measure to measure it, the result would be that extension
itself would need measure, so that movement, being measured, may have
a quantity which is determined by that of the thing according to which
it is measured. Consequently, under this hypothesis, time would be
the number of the extension which follows movement, and not extension
itself which follows movement.