3 ms·

Then, I'm afraid, you're missing the point of the paradox. There are a few stories (improperly called "paradoxes") attributed to Zeno: http://en.wikipedia.org/

Then, I'm afraid, you're missing the point of the paradox. There are a few stories (improperly called "paradoxes") attributed to Zeno: http://en.wikipedia.org/wiki/Zeno%27s_paradoxes http://en.wikipedia.org/wiki/Zeno%27s_paradoxes You're probably thinking of The Dichotomy. This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Further, very interesting reading: http://www.mathpages.com/rr/s3-07/3-07.htm http://www.mathpages.com/rr/s3-07/3-07.htm Math just gave us a way of coming up with the obvious answer, it does not describe the nature of the universe, which is what the philosophy was attempting.

321abc 17y ago
Also, just because a bunch of puny humans manage to convince each other that the world must be a certain way doesn't mean it actually is.
- joeyo 17y ago
  That depends on what your meaning of the word 'is' is.
ewjordan 17y ago
This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Actually, neither story proves either claim, which is apparent since there are rigorously defined and perfectly self consistent mathematical theories for each case. Philosophers just don't like them because they involve actual mathematical definitions, so they hide their heads in the sand and pretend they don't exist. From that Wikipedia article, a quote from Russell: Georg Cantor invented a theory of continuity and a theory of infinity which did away with all the old paradoxes upon which philosophers had battened. ... Philosophers met the situation by not reading the authors concerned. In other words, it's very easy to argue that infinite processes, continuous space, or motion in space don't make any sense if you can't be bothered to learn how they're rigorously defined in the mathematical theory you're arguing about. And FWIW, philosophy may have been attempting to describe the nature of the universe, but I can't come up with a single example of an actual physical result that's come from the field. You may argue that math and physics sprung from philosophy, but realize that those two disciplines provide most of philosophy's harshest detractors these days. And as far as retroactive claims that if people had listened to Zeno we might have stumbled upon special relativity earlier? (from the second link) Flat out bull poopy. The "inconsistencies" that special relativity resolves have nothing to do with classical mechanics at all, they have to do with E+M, and without a well tested and reliable E+M theory and the Michelson-Morley experiment to directly show us that the speed of light is constant regardless of motion we would have dismissed relativity theory as far too strange to be true (which, amusingly enough and in spite of massive evidence to the contrary, is a claim I've heard straight from the mouth of a tenured philosophy professor at an Ivy League school). An infinite speed of light would lead to a perfectly valid classical mechanics, albeit one that we could (now) prove is wrong, and there's nothing more logically consistent about either relativity or quantum mechanics that would have led us to either one without strenuous experimentation and Real Science.

321abc 17y ago

Also, just because a bunch of puny humans manage to convince each other that the world must be a certain way doesn't mean it actually is.

joeyo 17y ago
That depends on what your meaning of the word 'is' is.

ewjordan 17y ago

This story points out that matter must not be infinitely divisible. The paired story, The Arrow, shows that a universe of finite, indivisible pieces is also impossible. Thus, Zeno's paradox. Actually, neither story proves either claim, which is apparent since there are rigorously defined and perfectly self consistent mathematical theories for each case. Philosophers just don't like them because they involve actual mathematical definitions, so they hide their heads in the sand and pretend they don't exist. From that Wikipedia article, a quote from Russell: Georg Cantor invented a theory of continuity and a theory of infinity which did away with all the old paradoxes upon which philosophers had battened. ... Philosophers met the situation by not reading the authors concerned. In other words, it's very easy to argue that infinite processes, continuous space, or motion in space don't make any sense if you can't be bothered to learn how they're rigorously defined in the mathematical theory you're arguing about. And FWIW, philosophy may have been attempting to describe the nature of the universe, but I can't come up with a single example of an actual physical result that's come from the field. You may argue that math and physics sprung from philosophy, but realize that those two disciplines provide most of philosophy's harshest detractors these days. And as far as retroactive claims that if people had listened to Zeno we might have stumbled upon special relativity earlier? (from the second link) Flat out bull poopy. The "inconsistencies" that special relativity resolves have nothing to do with classical mechanics at all, they have to do with E+M, and without a well tested and reliable E+M theory and the Michelson-Morley experiment to directly show us that the speed of light is constant regardless of motion we would have dismissed relativity theory as far too strange to be true (which, amusingly enough and in spite of massive evidence to the contrary, is a claim I've heard straight from the mouth of a tenured philosophy professor at an Ivy League school). An infinite speed of light would lead to a perfectly valid classical mechanics, albeit one that we could (now) prove is wrong, and there's nothing more logically consistent about either relativity or quantum mechanics that would have led us to either one without strenuous experimentation and Real Science.