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instants together to achieve a duration; no matter
how many such instants are added together, their sum
will always be zero.
The paradox of the Stadium is for the modern
reader the most baffling of the four, and our
interpretation, which follows, differs from
Brumbaugh's. We agree with him, however, that this
puzzle assumes both space and time to be
discrete--composed of minims.
The fourth argument is that concerning the two rows
of bodies, each 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.(7)
Assume for the moment that we are speaking, as Zeno
originally did, of bodies rather than chariots,
Assume a stationary body (A) divided into three
sections, each section being one minim long. Assume
two more such bodies, one (B) traveling past (A) from
left to right at a certain velocity, the other (C)
traveling past (A) in the opposite direction at the
same speed.
Let (B) be passing (A) at a velocity of one minim of
space per minim of time. Then in the time (one
temporal minim) in which the front edge of (B) passes
one minim of (A), the front edge of (C) will pass two
minims of (B), and in doing so the front edge of (C)
will pass one minim of (B) in half a minim of time,
which is impossible, since the minim is by definition
indivisible.
This puzzle would work just as well looked at in
another way. If we say that the second moving body
(B) is passing the first (A) at the slowest possible
speed, that is, one minim of space per minim of time,
then in the same duration in which the front edge of
(B) passes one minim of (C), it (B) will pass only
half a minim of (A), the stationary body, which is
impossible, since, once again, the minim is