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I understand that Bertrand Russell, in repsonse to Zeno's Paradox, uses his concept of motion: an object being at a different time at different places, instead of the "from-to" notion of motion.

I also understand that this concept solves Zeno's Paradox of the arrow, as his concept aptly describes the motion of the arrow; however, his concept of motion does not aptly resolve Zeno's Paradox when told as the "dichotomy" and the "race". However, I don't understand the following quote:

But it is not essential to the existence of a collection, or even to knowledge and reasoning concerning it, that we should be able to pass its terms in review one by one.

Can someone explain why this addition to his notion of motion not fully account for the "race" and the "dichotomy"?

  • Dear Curious_Mind- A segment is not a distance; Is that solved? CMS – Charles M Saunders Apr 12 at 12:57
  • I'm confused with what you are trying to imply. Could you please elaborate? – Curious_Mind Apr 12 at 13:09
  • By saying that an arrow travels halfway, the so-called paradox converts a distance into a segment. Halfway is not a distance traveled, it is a portion of the distance measured as a fraction. Reducing the halfway 'segment' until it disappears has nothing to do with distance. It is the wrong category of measurement to use when suggesting that motion is impossible. Cheers CMS – Charles M Saunders Apr 12 at 13:18
  • Be(r)trand who ? – Mauro ALLEGRANZA Apr 12 at 13:28
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    According to whom does his concept of motion "solves Zeno's Paradox of the arrow", but "does not aptly resolve Zeno's Paradox when told as the "dichotomy" and the "race""? Since you are asking I assume you read it in a commentary somewhere. Since Russell objects to counting milestones one by one before passing a collection of them is allowed this should work for dichotomy as well. The problem with Russell's "solution" is that his concept of motion is a concept of a collection of rests, and not of motion at all. – Conifold Apr 13 at 2:32
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Zeno's paradox should be understood as an inadvertent reductio ad absurdum.

That is, the paradox shows that if moving from A to B required, as is implicitly assumed in the paradox, that we should be able to "pass its term in review one by one", that is, that we should be able to review one by one all successive locations in an uncountable continuum of locations, then moving would indeed be impossible. Yet, as the paradox itself in fact assumes explicitly this time, and more importantly as we can all check for ourselves, moving is not only possible but happens and happens all the time. Therefore, the paradox's implicit assumption is falsified.

Zeno's argument only works as a paradox because the crucial assumption, i.e. that counting an uncountable set is somehow a necessary pre-condition for moving, is not articulated. Thus, the only assumption which is falsifiable doesn't appear and isn't so easy to uncover. There is nothing in evidence which is falsifiable.

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