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Re: Gödel's G has never actually been true in arithmetic

From olcott <polcott333@gmail.com>
Newsgroups sci.logic, sci.math, comp.theory, comp.ai.philosophy
Subject Re: Gödel's G has never actually been true in arithmetic
Date 2026-01-19 13:20 -0600
Organization A noiseless patient Spider
Message-ID <10km069$k8fs$1@dont-email.me> (permalink)
References (11 earlier) <10kk7sq$75m$1@dont-email.me> <10kka23$3s3oo$1@dont-email.me> <10kkbsm$1fvj$1@dont-email.me> <10kl5o2$3s3oo$2@dont-email.me> <10klda0$cbp5$1@dont-email.me>

Cross-posted to 4 groups.

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On 1/19/2026 7:58 AM, Tristan Wibberley wrote:
> On 19/01/2026 11:49, Richard Damon wrote:
> 
> ...
> 
>> the concept of Truth being based on Provability just breaks as it
>> means some things have undefinable (not just unknowable) truth values,
>> they can't even be defined as not-having a truth value, as you can't
>                       ^^^^^^^
> I'm pretty sure that's not the right word.
> 
>> prove that, but you insist that truth must be provable.
> 
> Unless you're lucky enough to make a statement about them be an axiom of
> the system. Then you are hoping you've defined a consistent system but
> perhaps you got lucky.
> 
> Is it really true, though, that truth based on provability always breaks
> so? It looks like falsity based on non-provability is the problem and
> then only in conjunction with some notions of negation and maybe some
> notions of conjunction too (obviously the Quine might be the problem but
> we know fixed points give us Quines and vice-versa and they're so
> important we don't want to lose them).
> 
> What is the negation of "go to the shop" ?
> What is the negation of "is so! is not! is so! is not! ..." but "is not!
> is so! is not! is so! ..."
> 
> Given positive intuitionist systems (where a system has unprovable
> things that are provable in extensions) our truth predicate must leave
> anything unprovable that could be an axiom of an extension as neither
> true nor false but rather be inapplicable. 

Yes that is the exact idea that I have been presenting
since 2020 and possibly earlier.

Simply defining Gödel Incompleteness and Tarski Undefinability away V12
https://groups.google.com/g/comp.ai.nat-lang/c/p_evEnqowPQ/m/0RHg0UjWAAAJ

Please leave the comp.theory link in because
my system applies to sci.math, sci.logic and
comp.theory by making:

"true on the basis of meaning expressed in language"
computable from finite strings.

> A binary Truth predicate (at
> minimum) is required to even make sense and maybe it requires a further
> restriction argument (a 2nd order logic, then), which Tarski's
> indefinability theorem doesn't cover, not by a long way.
> 



-- 
Copyright 2026 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>

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Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 15:08 -0600
  Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 16:54 -0500
    Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 16:50 -0600
      Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 19:14 -0500
        Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 18:49 -0600
          Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 20:20 -0500
            Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 19:30 -0600
              Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 20:46 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 19:59 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 22:20 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 21:59 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-17 23:13 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-17 22:38 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 12:37 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 12:38 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 15:55 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 15:49 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 18:28 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 17:41 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-18 19:28 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 21:17 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 10:50 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:00 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 21:19 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-18 22:56 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-18 22:28 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-19 06:49 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-19 08:43 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 15:23 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:04 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 22:54 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-21 07:35 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-21 09:45 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-21 22:37 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-21 21:53 -0600
                Re: Gödel's G has never actually been true in arithmetic Python <python@cccp.invalid> - 2026-01-22 04:59 +0000
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-21 23:18 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 19:17 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 18:33 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-22 21:51 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 22:18 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-23 20:33 -0500
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 19:15 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-19 13:20 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 14:00 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:12 -0500
                Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-20 23:08 +0000
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 17:33 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 19:23 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 18:49 -0600
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 19:05 -0600
                Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-22 21:48 -0500
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 19:30 -0600
                Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-23 00:23 +0000
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 18:29 -0600
                Re: Gödel's G has never actually been true in arithmetic Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-23 01:15 +0000
                Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-22 19:38 -0600
  Re: Gödel's G has never actually been true in arithmetic Mikko <mikko.levanto@iki.fi> - 2026-01-18 12:09 +0200
  Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-19 20:39 -0600
    Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
      Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-20 15:39 -0600
        Re: Gödel's G has never actually been true in arithmetic Richard Damon <Richard@Damon-Family.org> - 2026-01-20 23:21 -0500
        Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-28 12:17 -0600
          Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-02-01 07:33 -0500
      Re: Gödel's G has never actually been true in arithmetic olcott <polcott333@gmail.com> - 2026-01-28 12:08 -0600
        Re: Gödel's G has never actually been true in arithmetic Richard Damon <news.x.richarddamon@xoxy.net> - 2026-02-01 07:33 -0500

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