Re Godels theorem is meaningless by TaylorRandle

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									                                 Re: Godels theorem is meaningless

Re: Godels theorem is meaningless

Source: http://sci.tech−archive.net/Archive/sci.math/2009−03/msg00685.html



      • From: Rupert <rupertmccallum@xxxxxxxxx>
      • Date: Wed, 4 Mar 2009 20:31:46 −0800 (PST)

On Mar 4, 10:39 pm, byron <spermato...@xxxxxxxxx> wrote:

       On Mar 5, 12:28 am, Rupert <rupertmccal...@xxxxxxxxx> wrote:




               On Mar 4, 4:58 pm, byron <spermato...@xxxxxxxxx> wrote:



                       On Mar 4, 6:17 pm, Rupert <rupertmccal...@xxxxxxxxx>
                       wrote:



                              On Mar 4, 11:35 am, byron
                              <spermato...@xxxxxxxxx> wrote:



                                       It has been pointed out that
                                      godels theorem is
                                      meaningless



                                      http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf



                                      as



                                      it turns out that godel had no
                                      idea what makes a


Re: Godels theorem is meaningless                                                                1
                             Re: Godels theorem is meaningless

                                    mathematical
                                    statement true as peter
                                    smith notes himself



                                    quote
                                    Gödel didn't rely on the
                                    notion
                                    of truth



                                    thus his incompletness
                                    theorem becomes
                                    meaningless



                                    quote



                                    http://en.wikipedia.org/wiki/G%C3%B6...s_theorems#Fir
                                    Gödel's first incompleteness
                                    theorem, perhaps the single
                                    most
                                    celebrated result in
                                    mathematical logic, states
                                    that:



                                    For any consistent formal,
                                    recursively enumerable
                                    theory that proves
                                    basic arithmetical truths, an
                                    arithmetical statement that is
                                    true, but
                                    not provable in the theory,
                                    can be constructed.1 That is,
                                    any
                                    effectively
                                    generated theory capable of
                                    expressing elementary
                                    arithmetic cannot be
                                    both consistent and
                                    complete.




Re: Godels theorem is meaningless                                                           2
                             Re: Godels theorem is meaningless
                                    And Peter smith notes godel
                                    is talking about true
                                    mathematical
                                    statements



                                    quotehttp://assets.cambridge.org/97805218...40_excerpt.pdf
                                    Godel did is find a general
                                    method that enabled him to
                                    take any theory
                                    T
                                    strong enough to capture a
                                    modest amount of basic
                                    arithmetic and
                                    construct a corresponding
                                    arithmetical sentence GT
                                    which encodes the
                                    claim The sentence GT
                                    itself is unprovable in theory
                                    T. So G T is
                                    true if and only
                                    if T cant prove it



                                    If we can locate GT



                                    , a Godel sentence for our
                                    favourite nicely ax−
                                    iomatized theory of
                                    arithmetic T, and can argue
                                    that G T is
                                    true−but−unprovable,



                                    So with out knowing what
                                    makes a mathematical
                                    statement true
                                    the incompleteness theorem
                                    is meaningless



                           There are semantic and syntactic versions of
                           the incompleteness
                           theorem. Your first quote gives a syntactic
                           version, your second quote

Re: Godels theorem is meaningless                                                                3
                                 Re: Godels theorem is meaningless
                               gives a semantic version. Gödel gave both in
                               his paper but made no
                               claim to rigour for the semantic version
                               because the notion of truth
                               had not yet been defined. However, Tarski
                               defined truth shortly
                               afterwards and both versions are perfectly
                               fine.



                     you say



                     Tarski defined truth shortly
                     afterwards and both versions are perfectly fine.



                     there are many theories of truth long before Tarski
                     the point is any one of those theories could be claimed to
                     account for
                     godels "truth"
                     it is not enough to say taraski or aristotle etc gave a theory
                     of
                     truth and hope that saves godel
                     your tarsk is to SHOW just how tarski theory of truth or any
                     other
                     theory of truth out there fits godels claims
                     as it stands godel had no theory of truth thus his theorem is
                     meaningless −its your task seeing you make the claim to
                     show just how
                     taskis theory fits godel
                     and to note
                     taski theory requires metalanguge



             No−one before Tarski gave a *mathematically rigorous* definition of
             truth. Tarski's definition *does* save Gödel because it enables us to
             make the argument for the semantic incompleteness theorem
             mathematically rigorous. If you want to know the details you'll need
             to do some study; do you want me to recommend a textbook for you?



                     and to note tarskis semantic theory of truth has problems




Re: Godels theorem is meaningless                                                     4
                                   Re: Godels theorem is meaningless

                What problems?



                        the problem with tarski
                        is it requires a metalangauge



                What of it?



                        and we get an ad infinitum



                Why?



                        if a grammar of a language must be in its metalanguage, as
                        Tarski.
                        seems
                        to require, than the grammar of this metalanguage must be in
                        its
                        metalanguage.
                        thus we have a notion of truth in the object langauge on
                        dependent on
                        the
                        notion of truth in the metalangauge.but the notion of truth in
                        the
                        metalague is itself dependent on the notion of truth in its
                        meta−meta−language



                No, it's not. We simply *use* the metalanguage. We do not need to
                define truth in the metalanguage in a metametalanguage.


      you say

      No−one before Tarski gave a *mathematically rigorous* definition of
      truth. Tarski's definition *does* save Gödel because it enables us to
      make the argument for the semantic incompleteness theorem
      mathematically rigorous.

      it is your tarsk as i say to show just how tarskis theory fits godels
      theorem
      i can even say a coherence theory of truth fits tarski but i would

Re: Godels theorem is meaningless                                                        5
                                    Re: Godels theorem is meaningless
        need to show that rather than state it

        tarskis theory is not rigourous as his theory leads to an ad infinitum
        in regard to "truth



I am not talking about the philosophical issues raised by Tarski's
work. Mathematically, as the definition of a concept, it is
unimpeachable. It can be used to do mathematics.
.




Re: Godels theorem is meaningless                                                6

								
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