Glad to see you get it, Blagg.
Here's a summary of the various resolutions of Zeno's paradox I have seen so far.
1. Since in reality, Achilles catches the hare, Zeno must be wrong and/or not worth bothering about. [Just dealt with that one].
2. Now that we know how to sum an infinite series, Zeno's paradox just melts away of itself. [It doesn't, since the definition of the sum of an infinite series is of a least upper bound. The problems inherent in that are in the thread].
3. Now that we have a rigorous definition of continuity, Zeno is no problem anymore. [Same kind of problem as with 2.]
4. Zeno did not get that 1+ 1/2+ 1/4+... actually adds up to one. [It doesn't actuallly add up to one, except in the sense of least upper bound. See 2.]
5. Now that we know about non standard analysis, the paradox is solved. [Red herring. Non standard analysis adds nothing to the discussion].
6. Space, time, and/or numbers do not really exist, and so are not worth bothering about. [Same rebuttal as for 1.]
All of these are flawed, to put it politely. This long thread is pretty much devoted to showing what's wrong with each of them.
The only answer I like is Smiling Dave's, posted here: http://mises.org/community/forums/p/29288/470667.aspx#470667
The gist of that answer is that Zeno is making an assumption with no basis, the assumption that we understand how infinity works. See the post for more details.
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It's easy to refute an argument if you first misrepresent it. William Keizer
Malachi, thank you for opening my eyes to how you think. .
I see that we are too far apart on the very basics. So good luck to you.
Smiling Dave: Malachi, thank you for opening my eyes to how you think. . I see that we are too far apart on the very basics. So good luck to you.
So what's the flaw? The flaw is in assuming his model makes sense. Slicing something up into a finite number of pieces makes sense to us, and we justified to feel we know the laws that apply to finite slicing, because we see countless examples of it every day of our lives. But we have never seen anything divided into an infinity of pieces. Therefore we have no basis for assuming we know the laws that apply to infinite slicing in the real world [even granting that such a thing is possible]. So we have no basis for the assertion that nature is not a glue that melds infinitely many objects together. On the contrary, we see that it is.
I guess you just cant imagine that someone would decline to make that assumption in the first place, it has to be you, after struggling with it for a while.
Glad to see you are one step ahead of me, in your world. Good for you.