Ian asked:

What is the present state of opinion on Zeno's paradox? Is there now a modern consensus, such as
some technical/mathematical solution involving the sum of a series of recurringly divided numbers?
Or are certain assumptions in the solution still considered problematic?

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There is consensus on the mathematical solution to Achilles and the tortoise. There are claims to
have solved the paradox of the dichotomy mathematically (e.g. Max Black Problems of Analysis), but
the problem of traversing an infinity of sub-distances is still discussed.

In Time, Creation and the Continuum,Richard Sorabji objects to mathematical solutions which claim
that there is not an infinity of spatio-temporal distances but only mathematical points which make up
mathematical distances. On Sorabji's view the paradox isn't solved this way, since it still applies to
physical points and distances. Sorabji rejects Aristotle's claim that we cannot traverse an infinity
(Aristotle thought we could only traverse a potential infinity) and suggests that we accept the paradox
and consequences to which it gives rise. If, in ordinary motion, we traverse infinite sub-distances in
order to reach our destination then once we have reached that destination we have completed
movement over a series of sub-distances. However, there is no final sub-distance that allows us to
reach our destination because any sub-distance can be divided: There is always a gap between
where you are and the destination. So one consequence for space, noted by Sorabji, is that the sum
of sub-distances is not equal to the whole.

Rachel Browne