Re: How many digits is pi computable to?

From: |-|erc (h_at_r.c)
Date: 01/18/05

  • Next message: |-|erc: "Re: How many digits is pi computable to?" 
    Date: Tue, 18 Jan 2005 11:59:35 +1000

    "Barb Knox" <see@sig.below> wrote in messag
    > In article <5eGdnbxpt4DqiXHcRVn-vw@rcn.net>,
    > "Bill Smythe" <chichess@beforeRCNafter.com> wrote:
    >
    > >"Michael Mendelsohn" wrote:
    > >> IIRC Herc rejects any kind of diagonalization argument.
    > >> (Maybe that has changed, though.)
    >
    > Oddly, he rejects ALL-BUT-ONE diagonalization argument. He DOES accept the
    > one that shows the unsolvability of the halting problem. And he doesn't
    > notice the logical difficulty with doing that.

    Diagonalisation DISPROVES a specific function Halt()
    That is different to PROVING antidiag exists.

    constructivism : the denial of existence resulting in contradiction does
                               not prove existence.

    ======================
    e.g. "this statement has no proof"

    Assume it is FALSE. <denial of existence>
    then it has a proof, so it is true
    CONTRADICTION <resulting in contradiction>

    therefore "this statement has no proof:" is true. <proves existence>
    =======================

    Now, compare that to the constructivist proof.

    true(facts) = proven(facts) U provable(facts).

    factX <=> true(factX) = ~proven(factX)
    factX <=> proven(factX) U provable(factX) = ~proven(factX)
    factX <=> t U p = ~t
    factX <=> t = ~t (extension of case p={})
    factX <=> CONTRADICTION

    Sorry, no incompleteness theorem just because you got stuck working out
    "YOU CANT PROVE ME"

    Herc

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    Relevant Pages

    • Re: How many digits is pi computable to?
      ... > one that shows the unsolvability of the halting problem. ... the denial of existence resulting in contradiction does ... compare that to the constructivist proof. ...
      (sci.logic)
    • Re: How many digits is pi computable to?
      ... > one that shows the unsolvability of the halting problem. ... the denial of existence resulting in contradiction does ... compare that to the constructivist proof. ...
      (sci.math)