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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"?

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  • Dear Curious_Mind- A segment is not a distance; Is that solved? CMS
    – user37981
    Apr 12, 2020 at 12:57
  • I'm confused with what you are trying to imply. Could you please elaborate? Apr 12, 2020 at 13:09
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    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
    – user37981
    Apr 12, 2020 at 13:18
  • Be(r)trand who ? Apr 12, 2020 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, 2020 at 2:32

3 Answers 3

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Bertrand Russell wasn't very keen on ancient philosophy and I doubt he took Aristotle's solution to Zeno's question on what constitutes motion.

Bertrands assertion is at odds with Aristotle - for he says that if the collection is infinite, then they can be passed if they are potential but not if they are actual. I would suggest that Russell was rekying upon the theory of inginite series.

This is most common solution to Zeno's question, that is to use infinite series. Now, although there was no such thing as infinite series in Aristotle's time, it is clear from his discussion that they were understood qualitatively, if not formally, and he says that they are an 'adequate' answer but not the true answer.

For the latter, he uses his theory of potentiality and actuality and says that motion is an alternation of potential motion with actual motion; potential motion is becoming and changeful but not actual; whilst actual motion is not in fact motion, it is not changeful, but rest.

Interestingly, just like Parmenides he says that which is actual does not move. As Zeno was supporting Parmenides, in some sense he is verifying both Zeno & Parmenides.

It's also worth noting that Hegel supported Aristotle. He said that the reason why something moved is because it is both here and there - a sort of super-position.

Moreover, it should be noted the close analogy between Aristotles conception of motion and quantum evolution. In quantum mechanics, the quantum potential evolves and is not real whilst the the quantum reduction does not change but is real. Notice that the quantum potential is both here and there - just as Hegel suggested.

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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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    That's not true. 1/2, 1/4, 1/8, 1/16 ... (in one version) or 1/2, 3/4, 7/18, 15/16, ... (in another) are countably infinite sets.
    – user4894
    Jan 8, 2021 at 18:31
  • However there is an uncountable set of positions through which the arrow must pass on its journey, being the irrational number in the range zero to (length of journey), so there is still an argument to be made. Whether it’s any more persuasive than for a countable set is another matter.
    – Frog
    Jan 9, 2021 at 1:53
  • @user4894 Read again. I said "uncountable continuum of locations". Jan 9, 2021 at 16:41
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    @Speakpigeon So you are using the word uncountable to mean ... what, exactly, since you apparently reject the standard mathematical usage?
    – user4894
    Jan 12, 2021 at 3:47
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    @Speakpigeon LOL
    – user4894
    Jan 13, 2021 at 19:49
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solution is infinite series is independently valid motion of arrow is independently valid therefore the dependency has to be met ie the infinite series has to be registered in real time as arrow moves paradox solved since contravention of laws of nature (relativity) ie infinite speed of register invalid

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  • As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center.
    – Community Bot
    Dec 20, 2021 at 12:41
  • first consider the infinite series applied to the points A B the sequence of 1/2 points now 2 ways first to register these 1/2 points casually and anytime at irregular times second to register positions in real time for a fixed velocity the first of course is never completed and no particular problem the second is quickly impossible to realize since it calls for speeds of registration which contravene laws of nature according to relativity it is this second way which applies to zeno otherwise the infinite series is quite unrelated to the movement between a and b
    – robin
    Dec 20, 2021 at 20:24

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