Sextus Empiricus: Physics 381
impossible to discover a first point among the infinite [divisions], starting
from which that which is said to be moved will move. 77. If the above
mentioned [continua] are postulated as having indivisible parts, and each
of the things in motion passes through the first spatial indivisible part
in an indivisible moment of time with its own first indivisible part, then
all things in motion are moved at the same speed, for example, the fastest
horse and the tortoise. And this is even more absurd than the previous
alternative. Therefore, motion does not occur progressively.
But neither does it occur all at once into a divisible interval. 78. For
if, as they say, it is necessary for appearances to testify to non-evident
things, then for someone to complete an interval of one stade, it is
necessary for him first to complete the first part of the stade, and second,
to complete the second part, and so on. So, it is reasonable to suppose
all things in motion [actually] move progressively, since, surely if that
which is moved were said to proceed all at once through all the parts of
the place in which it is said to be moved, it will simultaneously be in all
these parts, and if one of these parts through which it moves is cold,
and one hot, or perhaps, one dark and one light, so that they colour
whatever comes into contact with them, that which is moved will be
simultaneously hot and cold, dark and light. But this is absurd. 79. Next,
let them tell us how big a place that which is moved has passed through
all at once. For if they will say that the quantity is indefinite, they will
[thereby] allow that something is moved across the entire earth all at
once. If they [want to] avoid the conclusion, let them define for us the
extent of the place [through which it moves]. For to attempt to define
accurately [the extent of] the place through which that which is moved
can pass through all at once so that it could not pass through even a
little more is, in addition to being arbitrary, rash, or perhaps even ridicu-
lous; and besides [it] lands us back in the original problem. For everything
will move at equal speed, at least if each of them carries out its locomotion
in similar fashion through places which are defined. 80. But if they should
say that that which moves totally through a small place, but one which
is not accurately defined, it will be possible for us, using the sorites
argument, always to add a little extent of place to that which is hypothe-
sized. For if they will call a halt at any point while we are making this
argument, they will once again fall back on their bluff about an 'accurate
definition'. But if they allow the gradual increase, we shall compel them
to grant that something can be moved all at once through the extent of
the entire earth. So, neither is it the case that the things said to be moved
are moved all at once
moved neither all at once into a divisible place nor progressively, it is
not the case that something is moved.
marvins-underground-k-12
(Marvins-Underground-K-12)
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