Plato and the Other Companions of Sokrates, 3rd ed. Volume 1
Plato · en
The third Zenonian argument derived its name from the flight of an
arrow shot from a bow. The arrow while thus carried forward (says
Zeno) is nevertheless at rest.[24] For the time from the beginning to
the end of its course consists of a multitude of successive instants.
During each of these instants the arrow is in a given place of equal
dimension with itself. But that which is during any instant in a given
place, is at rest. Accordingly during each successive instant of its
flight, the arrow is at rest. Throughout its whole flight it is both
in motion and at rest. This argument is a deduction from the doctrine
of discontinuous time, as the preceding is a deduction from that of
discontinuous space.
[Footnote 24: Aristotel. Physic. vi. 9, p. 239, b. 30. [Greek: tri/tos
o( nu=n r(êthei/s, o(/ti ê( o)i+sto\s pherome/nê e(/stêken.]]
A fourth argument[25] was derived from the case of two equal bodies
moved with equal velocity in opposite directions, and passing each
other. If the body A B were at rest, the other body C D would move
along the whole length of C D in two minutes. But if C D be itself
moving with equal velocity in the opposite direction, A B will pass
along the whole length of C D in half that time, or one minute. Hence
Zeno infers that the motion of A B is nothing absolute, or belonging
to the thing in itself--for if that were so, it would not be varied
according to the movement of C D. It is no more than a phenomenal
fact, relative to us and our comparison.
[Footnote 25: See the illustration of this argument at some length by
Simplikius, especially the citation from Eudêmus at the close of
it--ap. Scholia ad Aristotel. p. 414, ed. Brandis.]
This argument, so far as I can understand its bearing, is not deduced
(as those preceding are) from the premisses of opponents: but rests
upon premisses of its own, and is intended to prove that motion is
only relative.
[Side-note: General result and purpose of the Zenonian Dialectic.
Nothing is knowable except the relative.]