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Re: Zeno's Paradox

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  • Bill Taylor
    Hi Cristina! ... Yes, that is interesting. ... Hmmm... I m not sure if one should look for logic in the ancients, even Aristotle. Their ideas seem so quaint
    Message 1 of 30 , Feb 28, 2007
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      Hi Cristina!

      >> The original poster wanted to know how and what Aristotle might have
      >> made of it; so matters such as those mentioned above are completely
      >> irrelevant, as they are two millenia ahead of time.

      > That is true, I wanted to understand how both Zeno and Aristotle
      > were looking at the paradox from their different perspectives,

      Yes, that is interesting.

      > and I was trying to see the logic in Aristotle's refutations of Zeno's ideas.

      Hmmm... I'm not sure if one should look for logic in the ancients,
      even Aristotle. Their ideas seem so quaint now - and not just
      their ideas, which would be understandable, but their whole *approach*
      to ideas, which seem very wrong-headed, to me at least.

      > Aristotles in 239 b 5 says: "Zeno's argument is fallacious: for he says
      > that if everything is always at rest or always in motion

      So far so good.

      > since [...jargon...], the flying arrow is motionless. But this is false,

      I agree with Aristotle that Zeno has made a huge unjustified leap,
      and that the resolution he (Zeno) should have been able to think of
      for himself, is that a snapshot includes instantaneous motion, even though
      this is not visible in the snapshot, to our feeble eyes. I see nothing in
      this concept that shouldn't have been clear and conceivable to an ancient.

      > for time is not composed of moments (which are indivisible)

      Here Aristotle is just expressing a pre-Euclidean prejudice against
      a continuum being composed of all the points in it. As so often, these
      chaps make many unstated assumptions, without (AFAICS) any realization
      of the offense.

      In any event, the "snapshot with hidden variables" idea solves all, simply.

      > Both Aristotle and Zeno believed that time and space
      > could be divided ad infinitum

      True.

      > yet Aristotle believed that moments and points were indivisible

      True.

      > and that time was not compose of moments as well as
      > lines were not composed of points

      False. It all seems so plain to us; it's hard to see why it couldn't be
      plain to them, with due thought, except for the unspoken assumtions that
      they were trying to shoehorn their logic into agreeing with.

      > I can see the logic in Zeno's argument but the logic of Aristotle's arguments
      > as he refutes Zeno's arguments escape me.

      I'm not all that sure that I see the logic of either.
      They should both have been able to do better.

      Anyway, that's my arrogant PoV. But we all have 20-20 hindsight when viewing
      things through the retrospectoscope!

      -- Bill Taylor

      * Yesterday, I thought I had a new deja vu experience.
      * But on second thoughts I realized I'd had it before.
    • Bruno Marchal
      ... I think this is a prejudice. You would be astonished by the quality of the reflection of the ancients both in China and India before our era. Then the
      Message 2 of 30 , Mar 2, 2007
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        Le 01-mars-07, à 04:58, Bill Taylor a écrit :

        > Hi Cristina!
        >
        > >> The original poster wanted to know how and what Aristotle might
        > have
        > >> made of it; so matters such as those mentioned above are completely
        > >> irrelevant, as they are two millenia ahead of time.
        >
        > > That is true, I wanted to understand how both Zeno and Aristotle
        > > were looking at the paradox from their different perspectives,
        >
        > Yes, that is interesting.
        >
        > > and I was trying to see the logic in Aristotle's refutations of
        > Zeno's ideas.
        >
        > Hmmm... I'm not sure if one should look for logic in the ancients,
        > even Aristotle.


        I think this is a prejudice. You would be astonished by the quality of
        the reflection of the "ancients" both in China and India before our
        era.
        Then the greeks made a systematic effort there, and in part created the
        "modern science".
        And "greek modern science" included theology.
        Today it is still hard to do theology with the scientific attitude
        because we are told the problem has been solved (by Jesus + Roman
        authority) or is a false problem (by the eliminative materialist).
        Thanks to jews and arabs, the greek science has come in Europa after a
        rather long delay. We call that Enlightenment, but imo it has been only
        half enlightenment: "modern theology" got stuck. We are still only
        half-modern, I think.






        > Their ideas seem so quaint now - and not just
        > their ideas, which would be understandable, but their whole *approach*
        > to ideas, which seem very wrong-headed, to me at least.


        If you could elaborate a little bit. What was wrong in their whole
        approach to ideas?



        >
        > > Aristotles in 239 b 5 says: "Zeno's argument is fallacious: for he
        > says
        > > that if everything is always at rest or always in motion
        >
        > So far so good.
        >
        > > since [...jargon...], the flying arrow is motionless. But this is
        > false,
        >
        > I agree with Aristotle that Zeno has made a huge unjustified leap,
        > and that the resolution he (Zeno) should have been able to think of
        > for himself, is that a snapshot includes instantaneous motion, even
        > though
        > this is not visible in the snapshot, to our feeble eyes. I see
        > nothing in
        > this concept that shouldn't have been clear and conceivable to an
        > ancient.
        >
        > > for time is not composed of moments (which are indivisible)
        >
        > Here Aristotle is just expressing a pre-Euclidean prejudice against
        > a continuum being composed of all the points in it. As so often, these
        > chaps make many unstated assumptions, without (AFAICS) any realization
        > of the offense.
        >
        > In any event, the "snapshot with hidden variables" idea solves all,
        > simply.
        >
        > > Both Aristotle and Zeno believed that time and space
        > > could be divided ad infinitum
        >
        > True.
        >
        > > yet Aristotle believed that moments and points were indivisible
        >
        > True.
        >
        > > and that time was not compose of moments as well as
        > > lines were not composed of points
        >
        > False. It all seems so plain to us; it's hard to see why it couldn't
        > be
        > plain to them, with due thought, except for the unspoken assumtions
        > that
        > they were trying to shoehorn their logic into agreeing with.
        >
        > > I can see the logic in Zeno's argument but the logic of Aristotle's
        > arguments
        > > as he refutes Zeno's arguments escape me.
        >
        > I'm not all that sure that I see the logic of either.
        > They should both have been able to do better.
        >
        > Anyway, that's my arrogant PoV. But we all have 20-20 hindsight when
        > viewing
        > things through the retrospectoscope!



        I think Zeno's problem reappeared with a vengeance through Feynman
        integral (in QM), and is not yet solved, despite impressive advances.
        I appreciate that you are aware of your arrogance :)

        Bruno


        http://iridia.ulb.ac.be/~marchal/


        [Non-text portions of this message have been removed]
      • briankscurfield
        ... Could you expand on what you mean by theology and what sort of problems you study when you do theology with the scientific attitude ? Is that how you see
        Message 3 of 30 , Mar 2, 2007
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          --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...>
          wrote:

          > Today it is still hard to do theology with the scientific attitude
          > because we are told the problem has been solved (by Jesus + Roman
          > authority) or is a false problem (by the eliminative materialist).
          > Thanks to jews and arabs, the greek science has come in Europa after
          > a rather long delay. We call that Enlightenment, but imo it has been
          > only half enlightenment: "modern theology" got stuck. We are still
          > only half-modern, I think.

          Could you expand on what you mean by theology and what sort of
          problems you study when you do "theology with the scientific
          attitude"? Is that how you see comp: as a branch of theology?

          - Brian Scurfield
        • Bruno Marchal
          ... You can see it like that. For example [saying yes to a doctor proposing an artificial digital brain] is not just trusting a technology, it is also a bet on
          Message 4 of 30 , Mar 4, 2007
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            Le 02-mars-07, à 23:11, briankscurfield a écrit :

            > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...>
            > wrote:
            >
            > > Today it is still hard to do theology with the scientific attitude
            > > because we are told the problem has been solved (by Jesus + Roman
            > > authority) or is a false problem (by the eliminative materialist).
            > > Thanks to jews and arabs, the greek science has come in Europa after
            > > a rather long delay. We call that Enlightenment, but imo it has been
            > > only half enlightenment: "modern theology" got stuck. We are still
            > > only half-modern, I think.
            >
            > Could you expand on what you mean by theology and what sort of
            > problems you study when you do "theology with the scientific
            > attitude"? Is that how you see comp: as a branch of theology?


            You can see it like that. For example [saying yes to a doctor proposing
            an artificial digital brain] is not just trusting a technology, it is
            also a bet on some conception of reality. As such it cannot be imposed,
            etc.
            But with comp you can also see theology as a branch of computer
            science: what can machines prove about themselves, what can machines
            know about themselves, what can they hope and bet about themselves and
            their most probable histories.
            It can be shown that for a machine just "believing in a
            reality/history" is akin to a self-consistency assertion, which needs
            some "act of faith" or cautious care and nuance distinctions.
            Machines can infer the gap between truth (about themselves) and
            provability (about themselves) and discover the nuance I'm talking
            about.

            More globally I think the Plato/Aristotle question has not yet been
            settled. I mean the question: is physical reality mainly reality per se
            (Aristotle) or the shadow, the trace, the interface to a bigger or
            deeper reality? (Plato)

            Platonist and neoplatonist argued around the idea that that deeper
            reality was mathematical if not arithmetical. I am open to such an idea
            and believe this follows from the comp hypothesis when taken "seriously
            enough". This is not a reductionist view because today we have good
            reason to believe that we cannot unify the whole of arithmetical truth.

            There has been two major discoveries those days:

            1) The Universal Machine (Babbage, Post, Turing, Church, ...). She
            talks with bits.

            2) The Other Universal Machine (Feynman, Deutsch, Freedman, Kitaev,
            ...). She talk with qubits.


            It is known how to derive the bit-universal machine from the
            qubit-universal machine. I think that by taking the comp hyp or
            neoplatonist theology seriously enough we can predict (and test the
            idea) that a self-introspecting bit-universal machine can justify the
            appearance of a qubit machine as invariant in its most probable
            histories. The bit (mind)----qubit (matter) relationship would be a two
            way road. But the incompleteness theorem would enrich the bit---qubit
            path with the distinction between what is true and what is provable or
            communicable, embedding quanta in more general qualia.

            You can interpret "theology" by "science of everything" *including us,
            in a very large sense of "us", the persons. The "theo" in theology and
            the "theo" in "theorem" have the same origin. That word points just on
            some search for a panoramic view on reality. Doing that with the
            scientific attitude just means to make the theories as clear as
            possible for making them being doubtable, testable, falsifiable, etc.

            Bruno



            http://iridia.ulb.ac.be/~marchal/


            [Non-text portions of this message have been removed]
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