The Complete Aristotle (eng.)
row being composed of an equal number of bodies of equal size,
passing each other on a race-course as they proceed with equal
velocity in opposite directions, the one row originally occupying
the space between the goal and the middle point of the course and
the other that between the middle point and the starting-post.
This, he thinks, involves the conclusion that half a given time is
equal to double that time. The fallacy of the reasoning lies in the
assumption that a body occupies an equal time in passing with equal
velocity a body that is in motion and a body of equal size that is
at rest; which is false. For instance (so runs the argument), let
A, A… be the stationary bodies of equal size, B, B… the bodies,
equal in number and in size to A, A… ,originally occupying the half
of the course from the starting-post to the middle of the A’s, and
G, G… those originally occupying the other half from the goal to
the middle of the A’s, equal in number, size, and velocity to B, B…
.Then three consequences follow:
First, as the B’s and the G’s pass one another, the first B
reaches the last G at the same moment as the first G reaches the
last B. Secondly at this moment the first G has passed all the A’s,
whereas the first B has passed only half the A’s, and has
consequently occupied only half the time occupied by the first G,
since each of the two occupies an equal time in passing each A.
Thirdly, at the same moment all the B’s have passed all the G’s:
for the first G and the first B will simultaneously reach the
opposite ends of the course, since (so says Zeno) the time occupied
by the first G in passing each of the B’s is equal to that occupied
by it in passing each of the A’s, because an equal time is occupied
by both the first B and the first G in passing all the A’s. This is
the argument, but it presupposed the aforesaid fallacious
assumption.
Nor in reference to contradictory change shall we find anything
unanswerable in the argument that if a thing is changing from
not-white, say, to white, and is in neither condition, then it will
be neither white nor not-white: for the fact that it is not wholly
in either condition will not preclude us from calling it white or
not-white. We call a thing white or not-white not necessarily
because it is be one or the other, but cause most of its parts or
the most essential parts of it are so: not being in a certain
condition is different from not being wholly in that condition. So,
too, in the case of being and not-being and all other conditions
which stand in a contradictory relation: while the changing thing
must of necessity be in one of the two opposites, it is never
wholly in either.
Again, in the case of circles and spheres and everything whose
motion is confined within the space that it occupies, it is not
true to say the motion can be nothing but rest, on the ground that
such things in motion, themselves and their parts, will occupy the
same position for a period of time, and that therefore they will be
at once at rest and in motion. For in the first place the parts do
not occupy the same position for any period of time: and in the
second place the whole also is always changing to a different
position: for if we take the orbit as described from a point A on a
circumference, it will not be the same as the orbit as described
from B or G or any other point on the same circumference except in
an accidental sense, the sense that is to say in which a musical
man is the same as a man. Thus one orbit is always changing into
another, and the thing will never be at rest. And it is the same
with the sphere and everything else whose motion is confined within
the space that it occupies.
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10
Our next point is that that which is without parts cannot be in
motion except accidentally: i.e. it can be in motion only in so far
as the body or the magnitude is in motion and the partless is in
motion by inclusion therein, just as that which is in a boat may be
in motion in consequence of the locomotion of the boat, or a part
may be in motion in virtue of the motion of the whole. (It must be
remembered, however, that by ‘that which is without parts’ I mean
that which is quantitatively indivisible (and that the case of the
motion of a part is not exactly parallel): for parts have motions
belonging essentially and severally to themselves distinct from the
motion of the whole. The distinction may be seen most clearly
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