Right, so it seems you think the argument is self-undermining. It assumes that you can get to the midpoint, C, and then it goes on to prove that motion from C to the endpoint B is impossible. Maybe we need to rethink our assumption that we could get to C! And indeed, other versions of this paradox of Zeno's work in that way. In order to get from A to B, this version runs, we need to get to the midpoint C. But in order to get from A to C, we need to that interval's midpoint, C1. And in order to get from A to C1, we need to get to its midpoint C2, ad infinitum . The strategy is always the same: to find a way of taking something finite (in this case, the racetrack) and dividing it into infinitely many parts; then arguing that a related task (here, running to the finish line) that looked to be finite really involves an actual infinite number of subtasks (here, reaching all the midpoints); and then concluding that, because one cannot complete an infinite number of tasks, the...

A number of paradoxes have been attributed to Zeno. One of them is the Paradox of the Runner : in order for a runner to get to the finish line, she needs to cross the first half of the track. Once she's done that, she needs to cross half the distance from the halfway mark to the finish line. Once she's done that, she needs to cross half the distance from that point to the finish line; etc. It seems that there are infinitely many finite intervals that she needs to traverse before she makes it to the finish line. But it's impossible to accomplish in a finite amount of time infinitely many tasks, each of which takes a finite amount of time. Therefore, the racer cannot make it to the finish line. It's common to hear that the solution is to appreciate that the sum of infinitely many finite quantities can be finite. Mathematicians have taught us, we're told, that the infinite sum: 1/2 + 1/4 + 1/8 + 1/16 + ... actually sums to 1. So, if we view the racer as traversing the first...