An amusing, informative, and well-written article indeed. But surely the paradox exists merely because of an implicit assumption wherein velocity is assumed to be coupled to distance? In other words, the core argument (unstated) is that you can never complete the transit between any two points because your velocity is proportional to the remaining distance between your current point and the end point. This is, of course, an unwarranted assumption.

The other problem with the paradox is that it is internally inconsistent. The runner could not even get halfway, because we can define “halfway” as the end point and apply the rule of the paradox. In fact we can reduce the entire paradox to the notion that the runner can never leave the start line, by using the internal (incorrect) logic of the paradox.

So we don’t really need infinite series or anything else; just an examination of the faulty assumption implicit in the very notion itself. And we know the assumption is faulty because we do see movement in the real world, all the time. Philosophy can lead one into a great many dead-ends because it’s not empirically based. Far better to begin with observation rather than abstract assumption, and follow what reality shows us rather than remain confined within the often inadequate workings of the human brain. Or to put it more crassly, “philosophy was what we had before we developed science.”