How will there occur a going of present-being-gone-to
When there never obtains a double going of
present-being-gone-to?
p.291
On this reading the argument is against the model of
motion which assumes that both time and space are
discontinuous; thus it parallels in function Zeno's
paradox of the Stadium. Suppose that time is
constituted of indivisible minims of duration d, and
space is constituted of indivisible minims of length
s. Now suppose three adjacent minims of space, A, B,
and C, and suppose that an object of length 1s at
time t[0] occupies A and at time t[1] occupies C.
such that the interval t[0]-t[1] is 1d. Now since the
object has been displaced two minims of space, that
is. 2s, this means that its displacement velocity is
v=2s/d. For the object to go from A to C, however, it
is clearly necessary that it traverse B, and so the
question naturally arises, When did the object occupy
minim B? Since displacement A-B is 1s, by our formula
we conclude that the object occupied B at t[0] +1/2d.
This result is clearly impossible, however, since d
is posited as an indivisible unit of time. And yet
the notion that the object went from A to C without
traversing B is unacceptable. In order to reconcile
theory with fact, we might posit an imaginary going
whereby the object goes from A through B to C,
alongside the orthodox interpretation whereby the
object goes directly from A to C without traversing
B. This model requires two separate goings, however,
and that is clearly absurd. Thus we must conclude
that there is no going of present-being-gone-to,
since the requisite notion of an extended present
leads to absurdity.
If we accept Teramoto's or May's reading, then
II.3 becomes:
Then how will there obtain a going of
present-being-gone-to,
Since there never obtains a nongoing of
present-being-gone-to?
This may be taken as an argument against the model of
motion which presupposes discontinuous time but a
spatial continuum. Suppose that time is constituted
of indivisible minims of duration d, Now suppose that
a point is moving along a line a-c at such a rate