Groups | Search | Server Info | Login | Register


Groups > comp.software-eng > #3747

Boiling Gödel's 1931 Incompleteness proof down to its barest essence

From olcott <polcott333@gmail.com>
Newsgroups comp.theory, comp.ai.philosophy, comp.software-eng, sci.logic, sci.math
Subject Boiling Gödel's 1931 Incompleteness proof down to its barest essence
Date 2026-01-06 08:02 -0600
Organization A noiseless patient Spider
Message-ID <10jj4ll$3rmu8$1@dont-email.me> (permalink)
References <10hct1p$1d92l$1@solani.org> <a3bcd46bf5b5a3ccc4b1308d8c7065008c1b4092.camel@gmail.com> <10hcu82$1d9h7$1@solani.org> <dbe9c3aa-42f9-496d-9394-a2d3205f9138@gmail.com> <10jj2dd$3qlcf$1@dont-email.me>

Cross-posted to 5 groups.

Show all headers | View raw


On 1/6/2026 7:23 AM, Mikko wrote:
> On 06/01/2026 02:24, Oleksiy Gapotchenko wrote:
>> Just an external observation:
>>
>> A lot of tech innovations in software optimization area get discarded 
>> from the very beginning because people who work on them perceive the 
>> halting problem as a dogma.
> 
> It is a dogma in the same sense as 2 * 3 = 6 is a dogma: a provably
> true sentence of a certain theory.
> 

...We are therefore confronted with a proposition which
asserts its own unprovability. 15 … (Gödel 1931:40-41)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of
Principia Mathematica And Related Systems

F ⊢ G_F ↔ ¬Prov_F (⌜G_F⌝)
"F proves that: G_F is equivalent to
Gödel_Number(G_F) is not provable in F"
https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

Stripping away the inessential baggage using a formal
language with its own self-reference operator and
provability operator (thus outside of arithmetic)

G := (F ⊬ G)   // G asserts its own unprovability in F

A proof of G in F would be a sequence of inference
steps in F that prove that they themselves do not exist.


-- 
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>

Back to comp.software-eng | Previous | NextPrevious in thread | Next in thread | Find similar


Thread

Re: Proof that the halting problem itself is a category error polcott <polcott333@gmail.com> - 2025-12-10 17:03 -0600
  Re: Proof that the halting problem itself is a category error wij <wyniijj5@gmail.com> - 2025-12-11 07:10 +0800
  Re: Proof that the halting problem itself is a category error --- typo polcott <polcott333@gmail.com> - 2025-12-10 17:53 -0600
  Re: Proof that the halting problem itself is a category error Oleksiy Gapotchenko <alex.s.gap@gmail.com> - 2026-01-06 01:24 +0100
    Re: Proof that the halting problem itself is a category error olcott <polcott333@gmail.com> - 2026-01-05 18:39 -0600
    is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-05 23:47 -0800
      Re: is the ct-thesis cooked? olcott <polcott333@gmail.com> - 2026-01-06 19:26 -0600
        Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-06 19:03 -0800
          Re: is the ct-thesis cooked? olcott <polcott333@gmail.com> - 2026-01-06 22:33 -0600
            Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-07 00:56 -0800
              yes/no questions lacking a correct yes/no answer are incorrect questions olcott <polcott333@gmail.com> - 2026-01-07 05:50 -0600
            Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-12 07:12 -0500
          Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-12 07:06 -0500
            Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-12 14:09 -0800
              Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-12 22:16 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-12 20:21 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-13 07:09 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-13 12:33 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-14 22:43 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-15 04:23 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-15 22:28 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-16 01:08 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-16 11:46 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-16 14:21 -0800
                The essence of all Computation generically defined olcott <polcott333@gmail.com> - 2026-01-16 16:58 -0600
                Re: The essence of all Computation generically defined Richard Damon <Richard@Damon-Family.org> - 2026-01-16 18:21 -0500
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-16 18:21 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-16 16:43 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-16 22:24 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-16 23:23 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-17 07:33 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-17 19:14 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-17 22:28 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-17 22:05 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-18 07:05 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-18 10:15 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-18 15:56 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-18 13:50 -0800
                Re: is the ct-thesis cooked? Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-18 22:27 +0000
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-18 15:01 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-18 19:28 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-18 20:30 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
                Re: is the ct-thesis cooked? Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-18 22:28 +0000
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-18 19:28 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-18 20:51 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-20 00:29 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-19 22:18 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-20 07:59 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-20 17:55 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-24 09:44 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 14:36 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-24 19:52 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 18:24 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:21 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-25 13:05 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-25 17:36 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-25 21:56 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-26 11:39 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-26 11:43 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-26 17:17 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-26 14:29 -0800
                Re: is the ct-thesis cooked? Dude <punditster@gmail.com> - 2026-01-27 13:31 -0800
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-28 01:12 -0800
                Re: is the ct-thesis cooked? Dude <punditster@gmail.com> - 2026-01-28 13:29 -0800
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-28 13:37 -0800
                Re: is the ct-thesis cooked? "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-01-27 14:07 -0800
                Re: is the ct-thesis cooked? Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-28 07:23 -0500
                Re: is the ct-thesis cooked? Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-17 12:17 +0000
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-17 08:15 -0500
                Re: is the ct-thesis cooked? dart200 <user7160@newsgrouper.org.invalid> - 2026-01-17 09:47 -0800
                Re: is the ct-thesis cooked? Richard Damon <Richard@Damon-Family.org> - 2026-01-17 15:31 -0500
                The essence of all Computation generically defined olcott <polcott333@gmail.com> - 2026-01-16 18:35 -0600
      Re: is the ct-thesis cooked? Mikko <mikko.levanto@iki.fi> - 2026-01-07 14:05 +0200
        Exactly what are deciders in the theory of computation? olcott <polcott333@gmail.com> - 2026-01-07 15:29 -0600
      Re: is the ct-thesis cooked? PLO olcott <polcott333@gmail.com> - 2026-01-24 17:06 -0600
        Re: is the ct-thesis cooked? PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-24 19:52 -0500
          Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 18:05 -0800
            Re: is the ct-thesis cooked? PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:23 -0500
              Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-25 13:04 -0800
                Re: is the ct-thesis cooked? PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-25 17:40 -0500
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-25 22:50 -0800
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-26 01:35 -0800
                Re: is the ct-thesis cooked? PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-26 11:43 -0500
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-26 11:45 -0800
                Re: is the ct-thesis cooked? PLO Richard Damon <Richard@Damon-Family.org> - 2026-01-26 17:28 -0500
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-27 00:00 -0800
          Re: is the ct-thesis cooked? PLO olcott <polcott333@gmail.com> - 2026-01-24 20:35 -0600
            Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 18:38 -0800
              Re: is the ct-thesis cooked? PLO olcott <polcott333@gmail.com> - 2026-01-24 20:53 -0600
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 19:12 -0800
                Re: is the ct-thesis cooked? PLO olcott <polcott333@gmail.com> - 2026-01-24 21:42 -0600
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 20:03 -0800
                Re: is the ct-thesis cooked? PLO olcott <polcott333@gmail.com> - 2026-01-24 22:06 -0600
                Re: is the ct-thesis cooked? PLO dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 21:45 -0800
    Re: Proof that the halting problem itself is a category error Mikko <mikko.levanto@iki.fi> - 2026-01-06 15:23 +0200
      Boiling Gödel's 1931 Incompleteness proof down to its barest essence olcott <polcott333@gmail.com> - 2026-01-06 08:02 -0600
        Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence Mikko <mikko.levanto@iki.fi> - 2026-01-07 14:10 +0200
          Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence olcott <polcott333@gmail.com> - 2026-01-07 07:06 -0600
            Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence Mikko <mikko.levanto@iki.fi> - 2026-01-08 12:21 +0200
              Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence olcott <polcott333@gmail.com> - 2026-01-08 08:18 -0600
                Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence Mikko <mikko.levanto@iki.fi> - 2026-01-10 11:25 +0200
                Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence olcott <polcott333@gmail.com> - 2026-01-11 08:32 -0600
                Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-11 16:16 +0000
                Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence olcott <NoOne@NoWhere.com> - 2026-01-11 21:00 -0600
                Re: Boiling Gödel's 1931 Incompleteness proof down to its barest essence Mikko <mikko.levanto@iki.fi> - 2026-01-12 13:05 +0200

csiph-web