Now whether or not this is helpful *as a response to Zeno* depends on what you take Zeno to be trying to do. And that’s not easy to piece together. But on the interpretation I was sketching out above, it seems to me like this doesn’t offer a prima facie refutation of Zeno’s point, because when you start bringing out the mathematical apparatus (for example, to measure continuous intervals of time and space) you’re already doing something that seems likely to give you some prima facie commitments to the actual existence of things like past moments of time, which on a naive interpretation of mathematical language would seem to commit you to rejecting presentism in favor of eternalism, which would get him to the kind of Parmenidean conclusion that he would (on this, admittedly speculative, interpretation).

I don’t think that mathematical language actually *needs* to commit you to eternalism — there are ways of interpreting that away. But then that requires doing some substantial philosophy with some tricky problems involved in it, and the attempt to get out of the philosophical problem by a technical solution using mathematical notation just ended up kicking the can down the road.

I think Plato’s interpretation is unlikely. By having Socrates present his interpretation as a hypothesis which Zeno then confirms (in a conversation Plato invented), Plato makes clear that it’s not obvious from Zeno’s book that its goal is to defend Parmenides. And the fact that the real-life Zeno, when asked why he didn’t write about the Parmenidean One, replied that he was waiting for someone to explain to him what the heck it was (Testimonium A16), doesn’t make him sound like a faithful disciple of his teacher. I suspect Zeno’s goals were closer to those of Gorgias in *On Nature or What Is Not*.