Zeno’s Paradox of the Race Course
1.
The Paradox
Zeno argues that it is impossible for a runner to traverse a race course. His reason is that
“motion is impossible, because an object in motion must reach the halfway point
before it gets to the end” (Aristotle,
Physics
239b1113).
Why is this a problem? Because the same argument can be made about
half
of the race
course: it can be divided in half in the same way that the entire race course can be divided
in half. And so can the half of the half of the half, and so on,
ad infinitum
.
So a crucial assumption that Zeno makes is that of
infinite divisibility
: the distance from
the starting point (
S
) to the goal (
G
) can be divided into an infinite number of parts.
2.
Progressive vs. Regressive versions
How did Zeno mean to divide the race course? That is,
which half
of the race course
Zeno mean to be dividing in half? Was he saying (a) that before you reach
G
, you must
reach the point halfway from the halfway point to
G
? This is the
progressive
version of
the argument: the subdivisions are made on the righthand side, the goal side, of the race
course.
Or was he saying (b) that before you reach the halfway point, you must reach the point
halfway from
S
to the halfway point? This is the
regressive
version of the argument: the
subdivisions are made on the lefthand side, the starting point side, of the racecourse.
If he meant (a), the progressive version, then he was arguing that the runner could not
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '06
 Buechner
 Philosophy, Logic, Zeno

Click to edit the document details