[cornelis]

:) Perhaps a mathematician here would like to explain how the sum of infinity "which can be mathematically shown to be equal to a finite number" is allowed by Zeno. I think legitimate solutions that answer to Zeno can only make sense with Zeno the Eleatic. However, the historical context of Parmenidean philosophy of being is absent, which tells me the usual story that puzzles can work within their own definitions. In the context of eleaticism, Zeno's puzzles were a reductio ad absurdum. Anyone may advise, but a reductio ad absurdum is not faulty logic. Yet his faulty logic is 2500 years ahead of his time? But Zeno himself meant to deny motion? Both sides have been argued, Zeno against and for Parmenides, but which one does Lynd adopt?

[betty boop]

But Zeno himself meant to deny motion?

I strongly doubt it, cornelis.

I think what his paradoxes show is that, if you load an unfounded/incorrect assumption into an analysis of a problem, you could find yourself "proving" something that isn't true. The incorrect assumption in these cases is that time is divisible into discrete units. Thus all the results obtained contradict the types of results that we would expect to obtain on the basis of direct observation, knowledge, and experience.

Zeno's logic wasn't faulty. His "trial assumption" was faulty. And I think he knew that. That was the point. He probably took some pleasure in the effects his paradoxes had on people who engaged them, perhaps thinking it would be difficult for many if not most people to spot the fundamental problem that lies at the root of their construction. Of course you're right: "puzzles can work within their own definitions." Whether those definitions have anything to do with objective reality is the real question.

I think Lynds, if anything, wants to thank Zeno for showing how our own mental constructions of methods to solve problems can be self-defeating, leading to absurdity. I get the sense that Lynds goes Zeno one better: That if time were actually divisible into discrete units, nothing could "move" at all.