ZENO’S ARGUMENTS ABOUT MOTION 275
be both great and small, so great on the one hand as to be
infinite in size and so small on tho other as to have no size. 1
To prove the latter of these contentions, Zeno relied on the
infinite divisibility of bodies as evident; assuming this, he
easily proved that division will continually give smaller and
smaller parts, there will be no limit to the diminution, and, if
there is a final element, it must be absolutely nothing. Conse
quently to add any number of these ^-elements to anything
will not increase its size, nor will the subtraction of them
diminish it; and of course to add them to one another, even
in infinite number, will give nothing as the total. (The
second horn of the dilemma, not apparently stated by Zeno
in this form, would be this. A critic might argue that infinite
division would only lead to parts having some size, so that the
last element would itself have some size; to this the answer
would be that, as there would, by hypothesis, be an infinite
number of such parts, the original magnitude which was
divided would be infinite in size.) The connexion between
the arguments against the Many and those against motion
lies in the fact that the former rest on the assumption of
the divisibility of matter ad infinitum, and that this is the
hypothesis assumed in the first two arguments against motion.
We shall see that, while the first two arguments proceed on
this hypothesis, the last two appear to proceed on the opposite
hypothesis that space and time are not infinitely divisible, but
that they are composed of indivisible elements; so that the
four arguments form a complete dilemma.
The four arguments against motion shall be stated in the
words of Aristotle.
I. The Dichotomy.
‘ There is no motion because that which is moved must
arrive at the middle (of its course) before it arrives at the
end.’ 2 (And of course it must traverse the half of the half
before it reaches the middle, and so on ad infinitum.)
II. The Achilles.
‘This asserts that the slower when running will never be
1 Simpl. in Phys., p. 139. 5, Diels.
2 Aristotle, Phys. vi. 9, 239 b 11.
T 2
