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Re: Question about the Flowers speech

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  • Bruno Marchal
    ... There is a counterexample. Few doubts that the notion of arithmetical truth is objective. But we know also that there is no complete theory capable of
    Message 1 of 3 , Jun 1 7:03 AM
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      Le 31-mai-07, à 05:01, nickwinning wrote :


      > This is a comment on, and a question about, Mr. Deutsch's flowers
      > speech. He says there that we should be concerned for objective
      > beauty more than we are for more parochial forms of beauty or
      > attraction because parochial beauty is circumscribed and thus
      > perfectible, while the pursuit of objective beauty offers the
      > possibility of boundless artistic progress. However, would not
      > objective beauty have an objective truth in the sense that there is
      > one best theory of aesthetics? And, if there is such a truth, it
      > might seem that aesthetics has an objective limit.



      There is a counterexample. Few doubts that the notion of arithmetical
      truth is objective. But we know also that there is no complete theory
      capable of circumscribing it. So, although the notion of natural
      numbers and the truth about their possible additive and multiplicative
      relations are objective, there will always be possible and necessary
      improvements. This is really a consequence of Godel's incompleteness
      theorem. It works for any theories in which you can represent a small
      amount of basic elementary truth on numbers (and thus also for any
      theories extending in some effective way such theories).





      >
      > Since knowledge is directional, that is it has a tendency to progress
      > if certain norms, which are themselves knowledge, are adhered to and
      > improved, one would think that if there were a true theory, we would
      > eventually reach it, given time. If ever we were to reach a true
      > understanding, then the arrow of knowledge would no longer bring us
      > forward. Without knowing whether the true theory was true, our
      > questioning it rationally might lead us to posit worse theories, but
      > ultimately reject them, so that after we have hit on the one best
      > theory, that is the true theory, we would no longer progress, but
      > perhaps rather just stray and come back, or wander around in the
      > vicinity of that truth. Would not such a scenario eventually
      > happen, given objective truth, about aesthetic subjects or any other
      > subject, including science?


      I can reassure you about this. Even with ultra-weak form of the
      computationalist hypothesis, there is a sense to say, about numbers,
      that we can always only scratch the surface.
      Strictly speaking, given that neither aesthetic nor all piece of
      science have been provably shown to necessitate numbers, we cannot
      exclude, just by referring to Godel, that aesthetic or science (without
      numbers, then) does not admit a final theory, but intuitively, given
      that such theory does not exist for number and machine, it would be a
      sort of miracle that it exists for something as subtle than aestetics
      or physics.


      >
      > This prospect has always seemed wrong to me.


      Correct intuition I dare to guess.




      > Perhaps for aesthetic reasons. It seems that thought ought to be an
      > infinite progress. But how is such an infinite progress reconcilable
      > with the concept of truth, which seems to imply a one best theory?



      Consistency *of* machine X, is definable by machine X but not provable
      by machine X, in case X is consistent.
      Truth *about* machine X is not even definable *by* machine X.
      Grosso modo the explanation is that truth (about numbers/machine) is
      infinite. Technically you need diagonalization to prove this. It is
      related to the liar paradoxes.





      > I think it is clear from what is said, but can be made more clear by
      > saying, that I am not saying that the truth could be known to be the
      > best theory. But good methods would lead us to wander about the one
      > best theory, after we found it, even if we could not know that we had
      > found it, instead of infinitely progressing to better and better
      > theories.



      I am slightly less optimistic on this point. Again in principle, we
      cannot completely exclude some convergence on a wrong (but consistent)
      theory. We could extend it by "better and better theories", but still
      all wrong ...
      This appears to be a price to pay for the absence of an ultimate
      complete theory.
      You are right of course. What I say is equivalent with the necessity
      that if we find a true theory (but then incomplete) we will not been
      able to assess it provably as the true theory. But here the subject
      should extend a bit the realm of numbers ...




      >
      > Because, perhaps for aesthetic reasons, I am unable to believe that
      > there is such an end of progress, I have been lead to believe that
      > there is no one best theory. However, this position seems to entail
      > that there is no true theory,



      Why? It only entails that if there is a true theory, then the theory is
      not axiomatizable, or not complete (and thus not "final"), or that it
      is infinitely complex, etc.




      > and thus imply some form of instrumentalism. I do not want to be an
      > instrumentalist,



      Me neither. Nor David, certainly (cf FOR).





      > but it seems that the belief in infinite progress means that there is
      > no final truth, ...


      It just means there is no final theory capturing correctly and
      completely that final truth. Truth (at least arithmetical truth) is
      like a giant infinite cosmos. You can explore it and get more and more
      familiarized with vaster and vaster portions, but there are some
      guarantees that big surprises await behind the horizon (as far as we
      remain consistent). Those surprises can force you to revise your
      beliefs or to just to extend them (in the lucky case).



      > ....not only in the sense of known truth, but also in the literal
      > sense of truth, thus no true theory, and the implication of
      > epistemological or metaphysical, if not methodological,
      > instrumentalism.


      As a realist (not necessarily a physical realist though) I consider
      that instrumentalism is the passage frrom science to engineering. Quite
      important for producing things and living, but contrary to the roots of
      the scientific attitude full of curiosity and attraction or
      contemplation for getting the less false possible global view of what
      could perhaps be.



      > How can you be a realist without believing in a one best, true theory?


      By admitting being realist about something infinite or transcendental
      ...



      > But Mr. Deutsch is not an instrumentalist. Yet he believes, with me,
      > in unbounded progress. If it is possible to believe in unbounded
      > progress while believing that there is a one best theory; or if it is
      > possible to believe that there is not a one best theory without being
      > an instrumentalist in some sense; I want to know how.



      In the case of numbers and machine, it is provable---by numbers and/or
      machine---that progress cannot be bounded, and all this despite the
      fact that it is easy to be realist about number and machine truth, as
      David and most scientists are.

      With or without comp, Godel's theorem (and their generalization like
      Löb, Solovay ...) should make us modest, and at the same time proud of
      being able to prove the existence of our limitation ((but then provably
      so only assuming comp). Then with realism, this is akin to force us to
      guess the transcendance of what exist: it is beyond us. So it needs
      some sort of *faith*. And so I would sum up by saying that it is faith
      which can prevent us against instrumentalism.
      (Note that an instrumental science will eventually make the human
      person instrumentalized!)
      Godel's result and alike provides a vaccine against reductionism and
      "final theories". This does not make it impossible to discover
      magnificent jewels along the road(s), like the quantum theory, computer
      science, number theory, knots invariants, and their various links, etc.

      Bruno

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


      [Non-text portions of this message have been removed]
    • Elliot Temple
      ... This question is not really about art. It applies to knowledge creation more generally. Different fields overlap. A picture of a rocket ship -- with the
      Message 2 of 3 , Jun 4 2:19 AM
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        On May 30, 2007, at 8:01 PM, nickwinning wrote:

        > This is a comment on, and a question about, Mr. Deutsch's flowers
        > speech. He says there that we should be concerned for objective
        > beauty more than we are for more parochial forms of beauty or
        > attraction because parochial beauty is circumscribed and thus
        > perfectible, while the pursuit of objective beauty offers the
        > possibility of boundless artistic progress. However, would not
        > objective beauty have an objective truth in the sense that there is
        > one best theory of aesthetics? And, if there is such a truth, it
        > might seem that aesthetics has an objective limit.

        This question is not really about art. It applies to knowledge
        creation more generally.

        Different fields overlap. A picture of a rocket ship -- with the
        exact same pixels -- would have a different meaning 500 years ago
        than it does today. And a reason is scientific progress, not artistic
        progress. Learning more about anything interesting gives you a new
        way to approach the knowledge you already have. So any sort of
        questions about limits in one field depend on whether there are
        limits to our knowledge in general, or not.

        Why should there be a limit, beyond which we can understand no
        further? A limit would mean when people get to the final theory and
        want to know more -- they ask "Why is it that way, and not another
        way?" -- there are no more answers to be found.

        Is it physically possible that the world is not comprehensible beyond
        some limit? Sure. We have yet to prove that no such limit exists. But
        never mind what we've *proven*: do we have any arguments in favor of
        such a limit?

        nickwinning mentions a possible argument: that a single objective
        truth constitutes such a limit. But there is no reason a single truth
        need be bounded in complexity or size, or otherwise limited. The
        point of saying there is a *single* truth is that a single,
        unambiguous question does not map to more than one "true" answer.

        -- Elliot Temple
        http://curi.us/
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