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It seems to me that Zeno's paradoxes just show how
limited his knowledge of math was.
The one Wordsmith gives is the runner who allegely can never even start, because before he and run a hundred meters, he has to run fifty meters, and before that he has to run twenty five meters, and so on ad infinitum, and so cannot even start. As with the turtle paradox, it seems to
me Zeno's problem was lack of concept of velocity. The turtle paradox appears to assume Achille's velocity is same as turtle's, which is just plain ignorant.
I was lucky to get a "C" in philosophy. What do some of you
"A" students say?
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Carpal Tunnel
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I got it tucked away in my JDM® that Zeno got the same bum rap as did Canute. He was using a reductio ad absurdum for something or other. Same with the famed proof that a bumblebee can't fly.
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Carpal Tunnel
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Hochstader spent some time with this one in G, E, & B. I think it's a curious puzzle to wrap your mind around.
formerly known as etaoin...
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For a long discussion of Zeno, see: http://www.utm.edu/research/iep/z/zenoelea.htmI didn't see the word 'velocity' any where, which is stupid. Or am I just a great philospher? (I'm collecting brickbats.)
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old hand
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old hand
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Doc
Zeno's Paradoxes are actually quite well-formed in both philosophical and mathematical terms. They were not mathematically resoluble (your reservations about velocity included) until the development of calculus and the understanding of the notion of a limit. At least this is my understanding.
As to velocity, you are right - it seems intuitively obvious to us that that is the Gordian knot requiring cutting - but Zeno takes the philosophical position that we cannot assume we know what velocity is. He makes us question our understanding of the idea of movement itself - and that's what his paradoxes are about - not the mathematics of physics, but the philosophy behind our notions of time, space and motion.
Ask yourself this:
If an object is 'moving', then presumable at one time (p) it is in spot A, and at another time (q) it is in spot B. What happens in between A and B. Does the object fill all the spece between them? Can you chop up time such that the distance between p and q can be truly infintesimal? What does it mean to say you can have a period of time that is infinitely small?
These are the sorts of things Zeno is asking us to think about. Even today we have no perfect answers for them. (By the way, some people, particularly those who have just started college, seem to think that Zeno is a 'proof' of some sort or another that can be thrown at any philosophy to mock it. This is not a useful or clever idea either.)
Hope this helps.
cheer
the sunshine warrior
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Carpal Tunnel
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I'm kinda partial to Kant's explaination that humans do not have the capacity to *understand the infinite.
All we can do is blur the concept with descriptions of/by things finite.
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