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| 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.
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>
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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
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