Does calculus fully solve Zeno's Paradoxes

Hurkyl

Zeno's paradoxes demonstrate -- on the assumption that he hasn't made a logical error -- that the impossibility of motion is a prediction of our methods of analysis. Falsifying the conclusion would mean one or more of its hypotheses is wrong. Which claim do you wish to reject? Are you to assert that when walking from here to there that you don't pass through the point half-way in-between? That a physical theory is disallowed model space as a continuum? Something else?

But, fortunately, his arguments are somewhere between incoherent and logically flawed, so we don't have to sacrifice any of the hypotheses.

Hurkyl

What physical experiment could distinguish between the alternatives? Without an observable consequence, I'm free to choose however I like between indistinguishable alternatives. It's not really any different than my freedom to choose whatever coordinate chart I like to do my calculations.

SteveL27

I must say I'm surprised that anyone educated in either math or physics could believe that the objects characterized by the ZFC axioms have any basis in physical reality. Infinite sets? Nonmeasurable sets? Undefinable sets? The uncountable reals, their powerset, the powerset of the powerset, ad infinitum?

And I also believe that in order to think that 1 + 1/2 + 1/4 + ... = 1 in the physical world requires that one also accepts the physical reality of the objects of ZFC (whatever they are. They're very far from the sets envisioned naively by Cantor.)

But clearly you are one such. And I have no arguments beyond those I've already made. So I'm afraid I have to leave it at that.

micromass

We have had many threads about this. It just seems to be a rehashing of old arguments. Thus I lock the thread.