Does calculus fully solve Zeno's Paradoxes


by rp.beltran
Tags: calculas, dichotomy, paradox, solutions, zeno's paradox
Hurkyl
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#19
Jun11-12, 04:06 PM
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Quote Quote by SteveL27 View Post
I don't understand how you can say that you have a choice in the matter.
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
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Jun11-12, 06:25 PM
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Quote Quote by Hurkyl View Post
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.
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
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Jun11-12, 09:43 PM
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We have had many threads about this. It just seems to be a rehashing of old arguments. Thus I lock the thread.


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