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Groups > comp.theory > #138902 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-01-06 22:44 -0600 |
| Last post | 2026-01-09 09:47 -0600 |
| Articles | 20 on this page of 198 — 8 participants |
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The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-06 22:44 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-07 13:49 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-07 05:54 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-08 12:22 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-08 08:22 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-09 11:59 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-09 09:52 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-10 10:23 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 09:47 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 18:19 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 18:13 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 19:35 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 18:52 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:03 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-10 20:22 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:34 -0500
Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:24 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:32 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-11 12:13 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-11 08:18 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-12 12:44 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-12 08:29 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-12 22:19 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 19:25 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-14 22:51 -0500
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-15 15:57 +0000
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-15 10:54 -0600
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-15 11:34 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-15 22:27 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-15 22:03 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-16 11:46 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-30 20:10 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-13 11:11 +0200
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-13 14:23 +0000
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-13 08:34 -0600
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-13 18:23 +0000
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-13 12:50 -0600
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-14 14:52 +0000
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 10:24 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 10:53 +0200
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-14 14:55 +0000
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-15 11:26 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 10:39 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 10:37 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-13 08:27 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 09:40 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 11:28 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-15 11:48 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-15 17:38 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-16 11:17 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-16 08:12 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-16 11:48 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-16 09:12 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-16 11:53 -0500
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-16 12:08 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-17 12:25 +0200
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-11 14:24 +0000
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-11 08:38 -0600
Re: The Halting Problem asks for too much Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-11 12:52 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-12 12:47 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-12 08:32 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-12 22:20 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-13 11:13 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-13 08:31 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 11:01 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 13:32 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-15 11:34 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-15 14:30 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-16 11:32 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-16 09:38 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-17 11:53 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-17 08:47 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-18 13:27 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-18 07:28 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-18 12:55 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-19 10:19 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-20 12:35 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-21 11:03 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-21 09:22 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-22 10:21 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-22 10:40 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-23 11:13 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-23 04:22 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-24 10:20 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 08:01 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-25 13:19 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 07:24 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:27 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 12:33 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:40 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 13:10 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 14:57 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 14:09 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 15:47 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-22 10:47 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-24 10:23 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 08:18 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-25 13:24 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 07:30 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:31 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 13:05 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 14:59 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 14:21 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 15:54 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-26 14:55 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 09:22 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 11:45 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 10:58 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 12:13 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 11:28 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-27 10:17 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-27 09:32 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-28 11:54 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-28 07:49 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-29 11:12 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-29 07:57 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-30 11:34 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-30 08:35 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-31 10:41 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-31 09:23 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-02-01 12:28 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-31 10:56 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-31 09:26 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-02-01 12:17 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-27 10:15 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-27 09:29 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-28 11:45 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-27 10:05 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-27 08:48 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-28 11:40 +0200
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-24 09:51 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 09:44 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-24 12:10 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 11:54 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-24 14:23 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 13:25 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-24 14:52 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 14:38 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-24 17:25 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 16:31 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-24 19:52 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-24 19:44 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 13:36 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 13:09 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 14:54 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 14:07 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-25 15:44 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-25 20:31 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 11:49 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 11:23 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 13:24 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 12:43 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 16:58 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 16:08 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 17:36 -0500
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-26 16:44 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-26 21:51 -0500
"true on the basis of meaning expressed in language" olcott <NoOne@NoWhere.com> - 2026-01-26 21:28 -0600
Re: The Halting Problem asks for too much dart200 <user7160@newsgrouper.org.invalid> - 2026-01-24 18:28 -0800
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-11 12:22 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-11 08:23 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-12 12:51 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-12 08:43 -0600
Re: The Halting Problem asks for too much Richard Damon <Richard@Damon-Family.org> - 2026-01-12 22:22 -0500
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-13 10:46 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-13 08:17 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 09:58 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 13:19 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-15 11:38 +0200
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-14 11:04 +0200
Re: The Halting Problem asks for too much olcott <polcott333@gmail.com> - 2026-01-14 13:35 -0600
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-15 11:21 +0200
Re: The Halting Problem asks for too much Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-15 14:52 +0000
Re: The Halting Problem asks for too much Mikko <mikko.levanto@iki.fi> - 2026-01-16 11:21 +0200
Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 17:19 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 19:35 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 19:03 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:03 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 20:20 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:33 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:18 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:30 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 19:05 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:03 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 20:09 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 21:33 -0500
Re: Computation and Undecidability polcott <polcott333@gmail.com> - 2026-01-10 20:52 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:28 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:16 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-10 22:28 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-10 21:34 -0600
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-11 06:31 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-11 08:03 -0600
Re: Computation and Undecidability Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-01-11 14:39 +0000
Re: Computation and Undecidability Richard Damon <news.x.richarddamon@xoxy.net> - 2026-01-11 12:52 -0500
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-11 12:12 -0600
Re: Computation and Undecidability olcott <polcott333@gmail.com> - 2026-01-11 15:50 -0600
Haskell Curry Foundations of Mathematical Logic sense of true in the system olcott <polcott333@gmail.com> - 2026-01-09 09:47 -0600
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-22 10:40 -0600 |
| Message-ID | <10ktjtm$35tto$1@dont-email.me> |
| In reply to | #139325 |
On 1/22/2026 2:21 AM, Mikko wrote: > On 21/01/2026 17:22, olcott wrote: >> On 1/21/2026 3:03 AM, Mikko wrote: >>> >>> No, it hasn't. In the way theories are usually discussed nothing is >>> "ture in arithmetic". Every sentence of a first order theory that >>> can be proven in the theory is true in every model theory. Every >>> sentence of a theory that cannot be proven in the theory is false >>> in some model of the theory. >>> >>>> only because back then proof theoretic semantics did >>>> not exist. >>> >>> Every interpretation of the theory is a definition of semantics. >>> >> >> Meta‑math relations about numbers don’t exist in PA >> because PA only contains arithmetical relations—addition, >> multiplication, ordering, primitive‑recursive predicates >> about numbers themselves—while relations that talk about >> PA’s own proofs, syntax, or truth conditions live entirely >> in the meta‑theory; > > Methamathematics does not need any other relations between numbers > than what PA has. But relations that map other things to numbers > can be useful for methamathematical purposes. > >> so when someone appeals to a Gödel‑style relation like >> “n encodes a proof of this very sentence,” they’re >> invoking a meta‑mathematical predicate that PA cannot >> internalize, which is exactly why your framework draws >> a clean boundary between internal proof‑theoretic truth >> and external model‑theoretic truth. > > Anyway, what can be provven that way is true aboout PA. You can deny > the proof but you cannot perform what is meta-provably impossible. > Gödel’s sentence is not “true in arithmetic.” It is true only in the meta‑theory, under an external interpretation of PA (typically the standard model ℕ). Inside PA itself, the sentence is not a truth‑bearer at all. The conflation happens when people treat model‑theoretic truth—truth in ℕ—as if it were internal truth in PA. Proof theoretic semantics anchored in axioms as their basis of truth proves that I have always been correct about everything that I said. All five LLMs agree with this immediately after I force them to actually simulate DD by HHH according to the semantics if C: Thus within well-founded proof theoretic semantics anchored in the operational semantics of the c programming language HHH(DD) is correct to reject its input as non-well-founded? Any cycle in the directed graph of the evaluation sequence of an expression correctly rejects this expression as non-well-founded in any proof theoretic semantics where true is anchored in the axioms of the system. Here is the first time that I explicitly referred to the idea of non-well-founded expressions in proof theoretic semantics [True(X) and ~Provable(X) is Impossible] Feb 4, 2018 https://groups.google.com/g/sci.logic/c/7XihPDLDy9s/m/uD6biLdjAwAJ -- 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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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-23 11:13 +0200 |
| Message-ID | <10kve43$3op07$1@dont-email.me> |
| In reply to | #139327 |
On 22/01/2026 18:40, olcott wrote: > On 1/22/2026 2:21 AM, Mikko wrote: >> On 21/01/2026 17:22, olcott wrote: >>> On 1/21/2026 3:03 AM, Mikko wrote: >>>> >>>> No, it hasn't. In the way theories are usually discussed nothing is >>>> "ture in arithmetic". Every sentence of a first order theory that >>>> can be proven in the theory is true in every model theory. Every >>>> sentence of a theory that cannot be proven in the theory is false >>>> in some model of the theory. >>>> >>>>> only because back then proof theoretic semantics did >>>>> not exist. >>>> >>>> Every interpretation of the theory is a definition of semantics. >>>> >>> >>> Meta‑math relations about numbers don’t exist in PA >>> because PA only contains arithmetical relations—addition, >>> multiplication, ordering, primitive‑recursive predicates >>> about numbers themselves—while relations that talk about >>> PA’s own proofs, syntax, or truth conditions live entirely >>> in the meta‑theory; >> >> Methamathematics does not need any other relations between numbers >> than what PA has. But relations that map other things to numbers >> can be useful for methamathematical purposes. >> >>> so when someone appeals to a Gödel‑style relation like >>> “n encodes a proof of this very sentence,” they’re >>> invoking a meta‑mathematical predicate that PA cannot >>> internalize, which is exactly why your framework draws >>> a clean boundary between internal proof‑theoretic truth >>> and external model‑theoretic truth. >> >> Anyway, what can be provven that way is true aboout PA. You can deny >> the proof but you cannot perform what is meta-provably impossible. > > Gödel’s sentence is not “true in arithmetic.” > It is true only in the meta‑theory, under an > external interpretation of PA (typically the > standard model ℕ). Inside PA itself, the sentence > is not a truth‑bearer at all. There is no concept of "truth-bearer" in an uninterpreted theory because there is not concept of "truth". The relevant concept is "sell-formed- formula" and Gödels sentence is one. It may be true or false in an interpretation. Gädel's metatheory contains PA. In Gödel's interpretation PA is interpreted in the same way as the PA part of the metathoéory. Gödel proves that G of PA as interpreted in the metatheory is true but cannot be proven in PA. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-23 04:22 -0600 |
| Message-ID | <10kvi5r$3q24q$2@dont-email.me> |
| In reply to | #139357 |
On 1/23/2026 3:13 AM, Mikko wrote: > On 22/01/2026 18:40, olcott wrote: >> On 1/22/2026 2:21 AM, Mikko wrote: >>> On 21/01/2026 17:22, olcott wrote: >>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>> >>>>> No, it hasn't. In the way theories are usually discussed nothing is >>>>> "ture in arithmetic". Every sentence of a first order theory that >>>>> can be proven in the theory is true in every model theory. Every >>>>> sentence of a theory that cannot be proven in the theory is false >>>>> in some model of the theory. >>>>> >>>>>> only because back then proof theoretic semantics did >>>>>> not exist. >>>>> >>>>> Every interpretation of the theory is a definition of semantics. >>>>> >>>> >>>> Meta‑math relations about numbers don’t exist in PA >>>> because PA only contains arithmetical relations—addition, >>>> multiplication, ordering, primitive‑recursive predicates >>>> about numbers themselves—while relations that talk about >>>> PA’s own proofs, syntax, or truth conditions live entirely >>>> in the meta‑theory; >>> >>> Methamathematics does not need any other relations between numbers >>> than what PA has. But relations that map other things to numbers >>> can be useful for methamathematical purposes. >>> >>>> so when someone appeals to a Gödel‑style relation like >>>> “n encodes a proof of this very sentence,” they’re >>>> invoking a meta‑mathematical predicate that PA cannot >>>> internalize, which is exactly why your framework draws >>>> a clean boundary between internal proof‑theoretic truth >>>> and external model‑theoretic truth. >>> >>> Anyway, what can be provven that way is true aboout PA. You can deny >>> the proof but you cannot perform what is meta-provably impossible. >> >> Gödel’s sentence is not “true in arithmetic.” >> It is true only in the meta‑theory, under an >> external interpretation of PA (typically the >> standard model ℕ). Inside PA itself, the sentence >> is not a truth‑bearer at all. > > There is no concept of "truth-bearer" in an uninterpreted theory because > there is not concept of "truth". The relevant concept is "sell-formed- > formula" and Gödels sentence is one. It may be true or false in an > interpretation. > There is a "true on the basis of meaning expressed in language" and I figured out how to make it computable over the body of knowledge. > Gädel's metatheory contains PA. In Gödel's interpretation PA is > interpreted in the same way as the PA part of the metathoéory. > Gödel proves that G of PA as interpreted in the metatheory is > true but cannot be proven in PA. > -- 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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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-24 10:20 +0200 |
| Message-ID | <10l1vdd$l5o9$1@dont-email.me> |
| In reply to | #139359 |
On 23/01/2026 12:22, olcott wrote: > On 1/23/2026 3:13 AM, Mikko wrote: >> On 22/01/2026 18:40, olcott wrote: >>> On 1/22/2026 2:21 AM, Mikko wrote: >>>> On 21/01/2026 17:22, olcott wrote: >>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>> >>>>>> No, it hasn't. In the way theories are usually discussed nothing is >>>>>> "ture in arithmetic". Every sentence of a first order theory that >>>>>> can be proven in the theory is true in every model theory. Every >>>>>> sentence of a theory that cannot be proven in the theory is false >>>>>> in some model of the theory. >>>>>> >>>>>>> only because back then proof theoretic semantics did >>>>>>> not exist. >>>>>> >>>>>> Every interpretation of the theory is a definition of semantics. >>>>>> >>>>> >>>>> Meta‑math relations about numbers don’t exist in PA >>>>> because PA only contains arithmetical relations—addition, >>>>> multiplication, ordering, primitive‑recursive predicates >>>>> about numbers themselves—while relations that talk about >>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>> in the meta‑theory; >>>> >>>> Methamathematics does not need any other relations between numbers >>>> than what PA has. But relations that map other things to numbers >>>> can be useful for methamathematical purposes. >>>> >>>>> so when someone appeals to a Gödel‑style relation like >>>>> “n encodes a proof of this very sentence,” they’re >>>>> invoking a meta‑mathematical predicate that PA cannot >>>>> internalize, which is exactly why your framework draws >>>>> a clean boundary between internal proof‑theoretic truth >>>>> and external model‑theoretic truth. >>>> >>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>> the proof but you cannot perform what is meta-provably impossible. >>> >>> Gödel’s sentence is not “true in arithmetic.” >>> It is true only in the meta‑theory, under an >>> external interpretation of PA (typically the >>> standard model ℕ). Inside PA itself, the sentence >>> is not a truth‑bearer at all. >> >> There is no concept of "truth-bearer" in an uninterpreted theory because >> there is not concept of "truth". The relevant concept is "sell-formed- >> formula" and Gödels sentence is one. It may be true or false in an >> interpretation. > There is a > "true on the basis of meaning expressed in language" > and I figured out how to make it computable over the > body of knowledge. Except that "true on the basis of meaning expressed in language" is nmt computable and does not cover all of the body of knowldge. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-24 08:01 -0600 |
| Message-ID | <10l2jci$rkbl$1@dont-email.me> |
| In reply to | #139379 |
On 1/24/2026 2:20 AM, Mikko wrote: > On 23/01/2026 12:22, olcott wrote: >> On 1/23/2026 3:13 AM, Mikko wrote: >>> On 22/01/2026 18:40, olcott wrote: >>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>> On 21/01/2026 17:22, olcott wrote: >>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>> >>>>>>> No, it hasn't. In the way theories are usually discussed nothing is >>>>>>> "ture in arithmetic". Every sentence of a first order theory that >>>>>>> can be proven in the theory is true in every model theory. Every >>>>>>> sentence of a theory that cannot be proven in the theory is false >>>>>>> in some model of the theory. >>>>>>> >>>>>>>> only because back then proof theoretic semantics did >>>>>>>> not exist. >>>>>>> >>>>>>> Every interpretation of the theory is a definition of semantics. >>>>>>> >>>>>> >>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>> because PA only contains arithmetical relations—addition, >>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>> about numbers themselves—while relations that talk about >>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>> in the meta‑theory; >>>>> >>>>> Methamathematics does not need any other relations between numbers >>>>> than what PA has. But relations that map other things to numbers >>>>> can be useful for methamathematical purposes. >>>>> >>>>>> so when someone appeals to a Gödel‑style relation like >>>>>> “n encodes a proof of this very sentence,” they’re >>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>> internalize, which is exactly why your framework draws >>>>>> a clean boundary between internal proof‑theoretic truth >>>>>> and external model‑theoretic truth. >>>>> >>>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>>> the proof but you cannot perform what is meta-provably impossible. >>>> >>>> Gödel’s sentence is not “true in arithmetic.” >>>> It is true only in the meta‑theory, under an >>>> external interpretation of PA (typically the >>>> standard model ℕ). Inside PA itself, the sentence >>>> is not a truth‑bearer at all. >>> >>> There is no concept of "truth-bearer" in an uninterpreted theory because >>> there is not concept of "truth". The relevant concept is "sell-formed- >>> formula" and Gödels sentence is one. It may be true or false in an >>> interpretation. > >> There is a >> "true on the basis of meaning expressed in language" >> and I figured out how to make it computable over the >> body of knowledge. > > Except that "true on the basis of meaning expressed in language" is > nmt computable and does not cover all of the body of knowldge. > When the basis of "true" is proof theoretic semantics internal to the formal system relative to its own axioms and not truth conditional in a separate model outside of the system undecidability ceases to 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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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-25 13:19 +0200 |
| Message-ID | <10l4u7q$1jgpb$1@dont-email.me> |
| In reply to | #139386 |
On 24/01/2026 16:01, olcott wrote: > On 1/24/2026 2:20 AM, Mikko wrote: >> On 23/01/2026 12:22, olcott wrote: >>> On 1/23/2026 3:13 AM, Mikko wrote: >>>> On 22/01/2026 18:40, olcott wrote: >>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>> >>>>>>>> No, it hasn't. In the way theories are usually discussed nothing is >>>>>>>> "ture in arithmetic". Every sentence of a first order theory that >>>>>>>> can be proven in the theory is true in every model theory. Every >>>>>>>> sentence of a theory that cannot be proven in the theory is false >>>>>>>> in some model of the theory. >>>>>>>> >>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>> not exist. >>>>>>>> >>>>>>>> Every interpretation of the theory is a definition of semantics. >>>>>>>> >>>>>>> >>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>> because PA only contains arithmetical relations—addition, >>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>> about numbers themselves—while relations that talk about >>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>> in the meta‑theory; >>>>>> >>>>>> Methamathematics does not need any other relations between numbers >>>>>> than what PA has. But relations that map other things to numbers >>>>>> can be useful for methamathematical purposes. >>>>>> >>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>> internalize, which is exactly why your framework draws >>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>> and external model‑theoretic truth. >>>>>> >>>>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>>>> the proof but you cannot perform what is meta-provably impossible. >>>>> >>>>> Gödel’s sentence is not “true in arithmetic.” >>>>> It is true only in the meta‑theory, under an >>>>> external interpretation of PA (typically the >>>>> standard model ℕ). Inside PA itself, the sentence >>>>> is not a truth‑bearer at all. >>>> >>>> There is no concept of "truth-bearer" in an uninterpreted theory >>>> because >>>> there is not concept of "truth". The relevant concept is "sell-formed- >>>> formula" and Gödels sentence is one. It may be true or false in an >>>> interpretation. >> >>> There is a >>> "true on the basis of meaning expressed in language" >>> and I figured out how to make it computable over the >>> body of knowledge. >> >> Except that "true on the basis of meaning expressed in language" is >> nmt computable and does not cover all of the body of knowldge. > > When the basis of "true" is proof theoretic semantics > internal to the formal system relative to its own axioms > and not truth conditional in a separate model outside > of the system undecidability ceases to exist. No, it does not. It does not matter what you call it, a sentence that cannot be neither proven nor disproven is undecidable because that is what the word means. An example is Gödel's sentence in Peano arithmetics. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-25 07:24 -0600 |
| Message-ID | <10l55hq$1lth6$1@dont-email.me> |
| In reply to | #139456 |
On 1/25/2026 5:19 AM, Mikko wrote: > On 24/01/2026 16:01, olcott wrote: >> On 1/24/2026 2:20 AM, Mikko wrote: >>> On 23/01/2026 12:22, olcott wrote: >>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>> On 22/01/2026 18:40, olcott wrote: >>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>> >>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>> nothing is >>>>>>>>> "ture in arithmetic". Every sentence of a first order theory that >>>>>>>>> can be proven in the theory is true in every model theory. Every >>>>>>>>> sentence of a theory that cannot be proven in the theory is false >>>>>>>>> in some model of the theory. >>>>>>>>> >>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>> not exist. >>>>>>>>> >>>>>>>>> Every interpretation of the theory is a definition of semantics. >>>>>>>>> >>>>>>>> >>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>> about numbers themselves—while relations that talk about >>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>> in the meta‑theory; >>>>>>> >>>>>>> Methamathematics does not need any other relations between numbers >>>>>>> than what PA has. But relations that map other things to numbers >>>>>>> can be useful for methamathematical purposes. >>>>>>> >>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>> internalize, which is exactly why your framework draws >>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>> and external model‑theoretic truth. >>>>>>> >>>>>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>>>>> the proof but you cannot perform what is meta-provably impossible. >>>>>> >>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>> It is true only in the meta‑theory, under an >>>>>> external interpretation of PA (typically the >>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>> is not a truth‑bearer at all. >>>>> >>>>> There is no concept of "truth-bearer" in an uninterpreted theory >>>>> because >>>>> there is not concept of "truth". The relevant concept is "sell-formed- >>>>> formula" and Gödels sentence is one. It may be true or false in an >>>>> interpretation. >>> >>>> There is a >>>> "true on the basis of meaning expressed in language" >>>> and I figured out how to make it computable over the >>>> body of knowledge. >>> >>> Except that "true on the basis of meaning expressed in language" is >>> nmt computable and does not cover all of the body of knowldge. >> >> When the basis of "true" is proof theoretic semantics >> internal to the formal system relative to its own axioms >> and not truth conditional in a separate model outside >> of the system undecidability ceases to exist. > > No, it does not. It does not matter what you call it, a sentence > that cannot be neither proven nor disproven is undecidable because > that is what the word means. An example is Gödel's sentence in > Peano arithmetics. > When a truth predicate gets the input "What time is?" this input is rejected as not truth-apt. When PA gets an expression that cannot be proven or refuted using its own axioms then this expression is not within its domain. -- 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 for the entire body of knowledge.<br><br> This required establishing a new foundation<br>
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-01-25 13:27 -0500 |
| Message-ID | <xgtdR.98062$4e1.48518@fx20.iad> |
| In reply to | #139458 |
On 1/25/26 8:24 AM, olcott wrote: > On 1/25/2026 5:19 AM, Mikko wrote: >> On 24/01/2026 16:01, olcott wrote: >>> On 1/24/2026 2:20 AM, Mikko wrote: >>>> On 23/01/2026 12:22, olcott wrote: >>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>> >>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>> nothing is >>>>>>>>>> "ture in arithmetic". Every sentence of a first order theory that >>>>>>>>>> can be proven in the theory is true in every model theory. Every >>>>>>>>>> sentence of a theory that cannot be proven in the theory is false >>>>>>>>>> in some model of the theory. >>>>>>>>>> >>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>> not exist. >>>>>>>>>> >>>>>>>>>> Every interpretation of the theory is a definition of semantics. >>>>>>>>>> >>>>>>>>> >>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>> in the meta‑theory; >>>>>>>> >>>>>>>> Methamathematics does not need any other relations between numbers >>>>>>>> than what PA has. But relations that map other things to numbers >>>>>>>> can be useful for methamathematical purposes. >>>>>>>> >>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>> and external model‑theoretic truth. >>>>>>>> >>>>>>>> Anyway, what can be provven that way is true aboout PA. You can >>>>>>>> deny >>>>>>>> the proof but you cannot perform what is meta-provably impossible. >>>>>>> >>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>> It is true only in the meta‑theory, under an >>>>>>> external interpretation of PA (typically the >>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>> is not a truth‑bearer at all. >>>>>> >>>>>> There is no concept of "truth-bearer" in an uninterpreted theory >>>>>> because >>>>>> there is not concept of "truth". The relevant concept is "sell- >>>>>> formed- >>>>>> formula" and Gödels sentence is one. It may be true or false in an >>>>>> interpretation. >>>> >>>>> There is a >>>>> "true on the basis of meaning expressed in language" >>>>> and I figured out how to make it computable over the >>>>> body of knowledge. >>>> >>>> Except that "true on the basis of meaning expressed in language" is >>>> nmt computable and does not cover all of the body of knowldge. >>> >>> When the basis of "true" is proof theoretic semantics >>> internal to the formal system relative to its own axioms >>> and not truth conditional in a separate model outside >>> of the system undecidability ceases to exist. >> >> No, it does not. It does not matter what you call it, a sentence >> that cannot be neither proven nor disproven is undecidable because >> that is what the word means. An example is Gödel's sentence in >> Peano arithmetics. >> > > When a truth predicate gets the input "What time is?" > this input is rejected as not truth-apt. That fine. > > When PA gets an expression that cannot be proven or > refuted using its own axioms then this expression is > not within its domain. > Then most of Natural Number mathematics is isn't in its domain, And, you can't KNOW if somehting is a valid question to ask until you know the answer. This makes a fairly worthless domain to learn things in. By your definition, a question like can every even number, greater than 2, be the sum of two prime numbers MIGHT not be within its domain, even though it is purely a question about the capability of numbers.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-25 12:33 -0600 |
| Message-ID | <10l5nls$1sfs5$1@dont-email.me> |
| In reply to | #139466 |
On 1/25/2026 12:27 PM, Richard Damon wrote: > On 1/25/26 8:24 AM, olcott wrote: >> On 1/25/2026 5:19 AM, Mikko wrote: >>> On 24/01/2026 16:01, olcott wrote: >>>> On 1/24/2026 2:20 AM, Mikko wrote: >>>>> On 23/01/2026 12:22, olcott wrote: >>>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>>> >>>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>>> nothing is >>>>>>>>>>> "ture in arithmetic". Every sentence of a first order theory >>>>>>>>>>> that >>>>>>>>>>> can be proven in the theory is true in every model theory. Every >>>>>>>>>>> sentence of a theory that cannot be proven in the theory is >>>>>>>>>>> false >>>>>>>>>>> in some model of the theory. >>>>>>>>>>> >>>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>>> not exist. >>>>>>>>>>> >>>>>>>>>>> Every interpretation of the theory is a definition of semantics. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>>> in the meta‑theory; >>>>>>>>> >>>>>>>>> Methamathematics does not need any other relations between numbers >>>>>>>>> than what PA has. But relations that map other things to numbers >>>>>>>>> can be useful for methamathematical purposes. >>>>>>>>> >>>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>>> and external model‑theoretic truth. >>>>>>>>> >>>>>>>>> Anyway, what can be provven that way is true aboout PA. You can >>>>>>>>> deny >>>>>>>>> the proof but you cannot perform what is meta-provably impossible. >>>>>>>> >>>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>>> It is true only in the meta‑theory, under an >>>>>>>> external interpretation of PA (typically the >>>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>>> is not a truth‑bearer at all. >>>>>>> >>>>>>> There is no concept of "truth-bearer" in an uninterpreted theory >>>>>>> because >>>>>>> there is not concept of "truth". The relevant concept is "sell- >>>>>>> formed- >>>>>>> formula" and Gödels sentence is one. It may be true or false in an >>>>>>> interpretation. >>>>> >>>>>> There is a >>>>>> "true on the basis of meaning expressed in language" >>>>>> and I figured out how to make it computable over the >>>>>> body of knowledge. >>>>> >>>>> Except that "true on the basis of meaning expressed in language" is >>>>> nmt computable and does not cover all of the body of knowldge. >>>> >>>> When the basis of "true" is proof theoretic semantics >>>> internal to the formal system relative to its own axioms >>>> and not truth conditional in a separate model outside >>>> of the system undecidability ceases to exist. >>> >>> No, it does not. It does not matter what you call it, a sentence >>> that cannot be neither proven nor disproven is undecidable because >>> that is what the word means. An example is Gödel's sentence in >>> Peano arithmetics. >>> >> >> When a truth predicate gets the input "What time is?" >> this input is rejected as not truth-apt. > > > That fine. >> >> When PA gets an expression that cannot be proven or >> refuted using its own axioms then this expression is >> not within its domain. >> > > Then most of Natural Number mathematics is isn't in its domain, > It is what it is. PA doesn't even know PA until you add a truth predicate. When you do add a truth predicate then PA knows PA. If you want more than that then meta-math can know "about" PA. This is one level of indirect reference away from knowing PA. > And, you can't KNOW if somehting is a valid question to ask until you > know the answer. > > This makes a fairly worthless domain to learn things in. > > By your definition, a question like can every even number, greater than > 2, be the sum of two prime numbers MIGHT not be within its domain, even > though it is purely a question about the capability of numbers. > -- 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 for the entire body of knowledge.<br><br> This required establishing a new foundation<br>
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-01-25 13:40 -0500 |
| Message-ID | <DstdR.98065$4e1.52878@fx20.iad> |
| In reply to | #139468 |
On 1/25/26 1:33 PM, olcott wrote: > On 1/25/2026 12:27 PM, Richard Damon wrote: >> On 1/25/26 8:24 AM, olcott wrote: >>> On 1/25/2026 5:19 AM, Mikko wrote: >>>> On 24/01/2026 16:01, olcott wrote: >>>>> On 1/24/2026 2:20 AM, Mikko wrote: >>>>>> On 23/01/2026 12:22, olcott wrote: >>>>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>>>> >>>>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>>>> nothing is >>>>>>>>>>>> "ture in arithmetic". Every sentence of a first order theory >>>>>>>>>>>> that >>>>>>>>>>>> can be proven in the theory is true in every model theory. >>>>>>>>>>>> Every >>>>>>>>>>>> sentence of a theory that cannot be proven in the theory is >>>>>>>>>>>> false >>>>>>>>>>>> in some model of the theory. >>>>>>>>>>>> >>>>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>>>> not exist. >>>>>>>>>>>> >>>>>>>>>>>> Every interpretation of the theory is a definition of >>>>>>>>>>>> semantics. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>>>> in the meta‑theory; >>>>>>>>>> >>>>>>>>>> Methamathematics does not need any other relations between >>>>>>>>>> numbers >>>>>>>>>> than what PA has. But relations that map other things to numbers >>>>>>>>>> can be useful for methamathematical purposes. >>>>>>>>>> >>>>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>>>> and external model‑theoretic truth. >>>>>>>>>> >>>>>>>>>> Anyway, what can be provven that way is true aboout PA. You >>>>>>>>>> can deny >>>>>>>>>> the proof but you cannot perform what is meta-provably >>>>>>>>>> impossible. >>>>>>>>> >>>>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>>>> It is true only in the meta‑theory, under an >>>>>>>>> external interpretation of PA (typically the >>>>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>>>> is not a truth‑bearer at all. >>>>>>>> >>>>>>>> There is no concept of "truth-bearer" in an uninterpreted theory >>>>>>>> because >>>>>>>> there is not concept of "truth". The relevant concept is "sell- >>>>>>>> formed- >>>>>>>> formula" and Gödels sentence is one. It may be true or false in an >>>>>>>> interpretation. >>>>>> >>>>>>> There is a >>>>>>> "true on the basis of meaning expressed in language" >>>>>>> and I figured out how to make it computable over the >>>>>>> body of knowledge. >>>>>> >>>>>> Except that "true on the basis of meaning expressed in language" is >>>>>> nmt computable and does not cover all of the body of knowldge. >>>>> >>>>> When the basis of "true" is proof theoretic semantics >>>>> internal to the formal system relative to its own axioms >>>>> and not truth conditional in a separate model outside >>>>> of the system undecidability ceases to exist. >>>> >>>> No, it does not. It does not matter what you call it, a sentence >>>> that cannot be neither proven nor disproven is undecidable because >>>> that is what the word means. An example is Gödel's sentence in >>>> Peano arithmetics. >>>> >>> >>> When a truth predicate gets the input "What time is?" >>> this input is rejected as not truth-apt. >> >> >> That fine. >>> >>> When PA gets an expression that cannot be proven or >>> refuted using its own axioms then this expression is >>> not within its domain. >>> >> >> Then most of Natural Number mathematics is isn't in its domain, >> > > It is what it is. But PA was CREATED to allow us to define the Natural Numbers in an axiomatic way. > PA doesn't even know PA until you add a truth predicate. > When you do add a truth predicate then PA knows PA. If > you want more than that then meta-math can know "about" PA. > This is one level of indirect reference away from knowing PA. In other words, you world is just inconsistant because it can't handle itself. You just build your logic on equivocations and lies. But since PA doesn't have a truth predicate, you can't add it. What PA has, if you actually understand it, is that it was built on a definition of logic that defines truth based on what flows out of the possible infinite application of its axioms. When you try to build with a lessor logic, you don't get a PA that can do what it needs to, and thus isn't actually an arithmatic. > >> And, you can't KNOW if somehting is a valid question to ask until you >> know the answer. >> >> This makes a fairly worthless domain to learn things in. >> >> By your definition, a question like can every even number, greater >> than 2, be the sum of two prime numbers MIGHT not be within its >> domain, even though it is purely a question about the capability of >> numbers. >> > >
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-25 13:10 -0600 |
| Message-ID | <10l5ps0$1t9k0$2@dont-email.me> |
| In reply to | #139470 |
On 1/25/2026 12:40 PM, Richard Damon wrote: > On 1/25/26 1:33 PM, olcott wrote: >> On 1/25/2026 12:27 PM, Richard Damon wrote: >>> On 1/25/26 8:24 AM, olcott wrote: >>>> On 1/25/2026 5:19 AM, Mikko wrote: >>>>> On 24/01/2026 16:01, olcott wrote: >>>>>> On 1/24/2026 2:20 AM, Mikko wrote: >>>>>>> On 23/01/2026 12:22, olcott wrote: >>>>>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>>>>> >>>>>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>>>>> nothing is >>>>>>>>>>>>> "ture in arithmetic". Every sentence of a first order >>>>>>>>>>>>> theory that >>>>>>>>>>>>> can be proven in the theory is true in every model theory. >>>>>>>>>>>>> Every >>>>>>>>>>>>> sentence of a theory that cannot be proven in the theory is >>>>>>>>>>>>> false >>>>>>>>>>>>> in some model of the theory. >>>>>>>>>>>>> >>>>>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>>>>> not exist. >>>>>>>>>>>>> >>>>>>>>>>>>> Every interpretation of the theory is a definition of >>>>>>>>>>>>> semantics. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>>>>> in the meta‑theory; >>>>>>>>>>> >>>>>>>>>>> Methamathematics does not need any other relations between >>>>>>>>>>> numbers >>>>>>>>>>> than what PA has. But relations that map other things to numbers >>>>>>>>>>> can be useful for methamathematical purposes. >>>>>>>>>>> >>>>>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>>>>> and external model‑theoretic truth. >>>>>>>>>>> >>>>>>>>>>> Anyway, what can be provven that way is true aboout PA. You >>>>>>>>>>> can deny >>>>>>>>>>> the proof but you cannot perform what is meta-provably >>>>>>>>>>> impossible. >>>>>>>>>> >>>>>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>>>>> It is true only in the meta‑theory, under an >>>>>>>>>> external interpretation of PA (typically the >>>>>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>>>>> is not a truth‑bearer at all. >>>>>>>>> >>>>>>>>> There is no concept of "truth-bearer" in an uninterpreted >>>>>>>>> theory because >>>>>>>>> there is not concept of "truth". The relevant concept is "sell- >>>>>>>>> formed- >>>>>>>>> formula" and Gödels sentence is one. It may be true or false in an >>>>>>>>> interpretation. >>>>>>> >>>>>>>> There is a >>>>>>>> "true on the basis of meaning expressed in language" >>>>>>>> and I figured out how to make it computable over the >>>>>>>> body of knowledge. >>>>>>> >>>>>>> Except that "true on the basis of meaning expressed in language" is >>>>>>> nmt computable and does not cover all of the body of knowldge. >>>>>> >>>>>> When the basis of "true" is proof theoretic semantics >>>>>> internal to the formal system relative to its own axioms >>>>>> and not truth conditional in a separate model outside >>>>>> of the system undecidability ceases to exist. >>>>> >>>>> No, it does not. It does not matter what you call it, a sentence >>>>> that cannot be neither proven nor disproven is undecidable because >>>>> that is what the word means. An example is Gödel's sentence in >>>>> Peano arithmetics. >>>>> >>>> >>>> When a truth predicate gets the input "What time is?" >>>> this input is rejected as not truth-apt. >>> >>> >>> That fine. >>>> >>>> When PA gets an expression that cannot be proven or >>>> refuted using its own axioms then this expression is >>>> not within its domain. >>>> >>> >>> Then most of Natural Number mathematics is isn't in its domain, >>> >> >> It is what it is. > > But PA was CREATED to allow us to define the Natural Numbers in an > axiomatic way. > Yet only within the actual axioms of PA. >> PA doesn't even know PA until you add a truth predicate. >> When you do add a truth predicate then PA knows PA. If >> you want more than that then meta-math can know "about" PA. >> This is one level of indirect reference away from knowing PA. > > In other words, you world is just inconsistant because it can't handle > itself. > > You just build your logic on equivocations and lies. > > But since PA doesn't have a truth predicate, you can't add it. > > What PA has, if you actually understand it, is that it was built on a > definition of logic that defines truth based on what flows out of the > possible infinite application of its axioms. > > When you try to build with a lessor logic, you don't get a PA that can > do what it needs to, and thus isn't actually an arithmatic. > >> >>> And, you can't KNOW if somehting is a valid question to ask until you >>> know the answer. >>> >>> This makes a fairly worthless domain to learn things in. >>> >>> By your definition, a question like can every even number, greater >>> than 2, be the sum of two prime numbers MIGHT not be within its >>> domain, even though it is purely a question about the capability of >>> numbers. >>> >> >> > -- 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 for the entire body of knowledge.<br><br> This required establishing a new foundation<br>
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-01-25 14:57 -0500 |
| Message-ID | <rAudR.98067$4e1.42181@fx20.iad> |
| In reply to | #139473 |
On 1/25/26 2:10 PM, olcott wrote: > On 1/25/2026 12:40 PM, Richard Damon wrote: >> On 1/25/26 1:33 PM, olcott wrote: >>> On 1/25/2026 12:27 PM, Richard Damon wrote: >>>> On 1/25/26 8:24 AM, olcott wrote: >>>>> On 1/25/2026 5:19 AM, Mikko wrote: >>>>>> On 24/01/2026 16:01, olcott wrote: >>>>>>> On 1/24/2026 2:20 AM, Mikko wrote: >>>>>>>> On 23/01/2026 12:22, olcott wrote: >>>>>>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>>>>>> nothing is >>>>>>>>>>>>>> "ture in arithmetic". Every sentence of a first order >>>>>>>>>>>>>> theory that >>>>>>>>>>>>>> can be proven in the theory is true in every model theory. >>>>>>>>>>>>>> Every >>>>>>>>>>>>>> sentence of a theory that cannot be proven in the theory >>>>>>>>>>>>>> is false >>>>>>>>>>>>>> in some model of the theory. >>>>>>>>>>>>>> >>>>>>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>>>>>> not exist. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Every interpretation of the theory is a definition of >>>>>>>>>>>>>> semantics. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>>>>>> in the meta‑theory; >>>>>>>>>>>> >>>>>>>>>>>> Methamathematics does not need any other relations between >>>>>>>>>>>> numbers >>>>>>>>>>>> than what PA has. But relations that map other things to >>>>>>>>>>>> numbers >>>>>>>>>>>> can be useful for methamathematical purposes. >>>>>>>>>>>> >>>>>>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>>>>>> and external model‑theoretic truth. >>>>>>>>>>>> >>>>>>>>>>>> Anyway, what can be provven that way is true aboout PA. You >>>>>>>>>>>> can deny >>>>>>>>>>>> the proof but you cannot perform what is meta-provably >>>>>>>>>>>> impossible. >>>>>>>>>>> >>>>>>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>>>>>> It is true only in the meta‑theory, under an >>>>>>>>>>> external interpretation of PA (typically the >>>>>>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>>>>>> is not a truth‑bearer at all. >>>>>>>>>> >>>>>>>>>> There is no concept of "truth-bearer" in an uninterpreted >>>>>>>>>> theory because >>>>>>>>>> there is not concept of "truth". The relevant concept is >>>>>>>>>> "sell- formed- >>>>>>>>>> formula" and Gödels sentence is one. It may be true or false >>>>>>>>>> in an >>>>>>>>>> interpretation. >>>>>>>> >>>>>>>>> There is a >>>>>>>>> "true on the basis of meaning expressed in language" >>>>>>>>> and I figured out how to make it computable over the >>>>>>>>> body of knowledge. >>>>>>>> >>>>>>>> Except that "true on the basis of meaning expressed in language" is >>>>>>>> nmt computable and does not cover all of the body of knowldge. >>>>>>> >>>>>>> When the basis of "true" is proof theoretic semantics >>>>>>> internal to the formal system relative to its own axioms >>>>>>> and not truth conditional in a separate model outside >>>>>>> of the system undecidability ceases to exist. >>>>>> >>>>>> No, it does not. It does not matter what you call it, a sentence >>>>>> that cannot be neither proven nor disproven is undecidable because >>>>>> that is what the word means. An example is Gödel's sentence in >>>>>> Peano arithmetics. >>>>>> >>>>> >>>>> When a truth predicate gets the input "What time is?" >>>>> this input is rejected as not truth-apt. >>>> >>>> >>>> That fine. >>>>> >>>>> When PA gets an expression that cannot be proven or >>>>> refuted using its own axioms then this expression is >>>>> not within its domain. >>>>> >>>> >>>> Then most of Natural Number mathematics is isn't in its domain, >>>> >>> >>> It is what it is. >> >> But PA was CREATED to allow us to define the Natural Numbers in an >> axiomatic way. >> > > Yet only within the actual axioms of PA. Yes, the Natural Numbers are object created within the formal system of Peano Arithmetic (as one way to define them) and in that system there are a lot of properties of them that are True (or False). If there is a property of them that PA Created that it can't talk about, that sounds very much like PA is just incomplete in its understanding of what it does, just by the basic normal definition of incomplete. > >>> PA doesn't even know PA until you add a truth predicate. >>> When you do add a truth predicate then PA knows PA. If >>> you want more than that then meta-math can know "about" PA. >>> This is one level of indirect reference away from knowing PA. >> >> In other words, you world is just inconsistant because it can't handle >> itself. >> >> You just build your logic on equivocations and lies. >> >> But since PA doesn't have a truth predicate, you can't add it. >> >> What PA has, if you actually understand it, is that it was built on a >> definition of logic that defines truth based on what flows out of the >> possible infinite application of its axioms. >> >> When you try to build with a lessor logic, you don't get a PA that can >> do what it needs to, and thus isn't actually an arithmatic. >> >>> >>>> And, you can't KNOW if somehting is a valid question to ask until >>>> you know the answer. >>>> >>>> This makes a fairly worthless domain to learn things in. >>>> >>>> By your definition, a question like can every even number, greater >>>> than 2, be the sum of two prime numbers MIGHT not be within its >>>> domain, even though it is purely a question about the capability of >>>> numbers. >>>> >>> >>> >> > >
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-25 14:09 -0600 |
| Message-ID | <10l5t9e$1ui63$2@dont-email.me> |
| In reply to | #139475 |
On 1/25/2026 1:57 PM, Richard Damon wrote: > On 1/25/26 2:10 PM, olcott wrote: >> On 1/25/2026 12:40 PM, Richard Damon wrote: >>> On 1/25/26 1:33 PM, olcott wrote: >>>> On 1/25/2026 12:27 PM, Richard Damon wrote: >>>>> On 1/25/26 8:24 AM, olcott wrote: >>>>>> On 1/25/2026 5:19 AM, Mikko wrote: >>>>>>> On 24/01/2026 16:01, olcott wrote: >>>>>>>> On 1/24/2026 2:20 AM, Mikko wrote: >>>>>>>>> On 23/01/2026 12:22, olcott wrote: >>>>>>>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>>>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>>>>>>> nothing is >>>>>>>>>>>>>>> "ture in arithmetic". Every sentence of a first order >>>>>>>>>>>>>>> theory that >>>>>>>>>>>>>>> can be proven in the theory is true in every model >>>>>>>>>>>>>>> theory. Every >>>>>>>>>>>>>>> sentence of a theory that cannot be proven in the theory >>>>>>>>>>>>>>> is false >>>>>>>>>>>>>>> in some model of the theory. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>>>>>>> not exist. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Every interpretation of the theory is a definition of >>>>>>>>>>>>>>> semantics. >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>>>>>>> in the meta‑theory; >>>>>>>>>>>>> >>>>>>>>>>>>> Methamathematics does not need any other relations between >>>>>>>>>>>>> numbers >>>>>>>>>>>>> than what PA has. But relations that map other things to >>>>>>>>>>>>> numbers >>>>>>>>>>>>> can be useful for methamathematical purposes. >>>>>>>>>>>>> >>>>>>>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>>>>>>> and external model‑theoretic truth. >>>>>>>>>>>>> >>>>>>>>>>>>> Anyway, what can be provven that way is true aboout PA. You >>>>>>>>>>>>> can deny >>>>>>>>>>>>> the proof but you cannot perform what is meta-provably >>>>>>>>>>>>> impossible. >>>>>>>>>>>> >>>>>>>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>>>>>>> It is true only in the meta‑theory, under an >>>>>>>>>>>> external interpretation of PA (typically the >>>>>>>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>>>>>>> is not a truth‑bearer at all. >>>>>>>>>>> >>>>>>>>>>> There is no concept of "truth-bearer" in an uninterpreted >>>>>>>>>>> theory because >>>>>>>>>>> there is not concept of "truth". The relevant concept is >>>>>>>>>>> "sell- formed- >>>>>>>>>>> formula" and Gödels sentence is one. It may be true or false >>>>>>>>>>> in an >>>>>>>>>>> interpretation. >>>>>>>>> >>>>>>>>>> There is a >>>>>>>>>> "true on the basis of meaning expressed in language" >>>>>>>>>> and I figured out how to make it computable over the >>>>>>>>>> body of knowledge. >>>>>>>>> >>>>>>>>> Except that "true on the basis of meaning expressed in >>>>>>>>> language" is >>>>>>>>> nmt computable and does not cover all of the body of knowldge. >>>>>>>> >>>>>>>> When the basis of "true" is proof theoretic semantics >>>>>>>> internal to the formal system relative to its own axioms >>>>>>>> and not truth conditional in a separate model outside >>>>>>>> of the system undecidability ceases to exist. >>>>>>> >>>>>>> No, it does not. It does not matter what you call it, a sentence >>>>>>> that cannot be neither proven nor disproven is undecidable because >>>>>>> that is what the word means. An example is Gödel's sentence in >>>>>>> Peano arithmetics. >>>>>>> >>>>>> >>>>>> When a truth predicate gets the input "What time is?" >>>>>> this input is rejected as not truth-apt. >>>>> >>>>> >>>>> That fine. >>>>>> >>>>>> When PA gets an expression that cannot be proven or >>>>>> refuted using its own axioms then this expression is >>>>>> not within its domain. >>>>>> >>>>> >>>>> Then most of Natural Number mathematics is isn't in its domain, >>>>> >>>> >>>> It is what it is. >>> >>> But PA was CREATED to allow us to define the Natural Numbers in an >>> axiomatic way. >>> >> >> Yet only within the actual axioms of PA. > > Yes, the Natural Numbers are object created within the formal system of > Peano Arithmetic (as one way to define them) and in that system there > are a lot of properties of them that are True (or False). > > If there is a property of them that PA Created that it can't talk about, > that sounds very much like PA is just incomplete in its understanding of > what it does, just by the basic normal definition of incomplete. > > Gödel’s sentence is not “true in arithmetic.” It is true only in the meta‑theory, under an external interpretation of PA (typically the standard model ℕ). Inside PA itself, the sentence is not a truth‑bearer at all. -- 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 for the entire body of knowledge.<br><br> This required establishing a new foundation<br>
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-01-25 15:47 -0500 |
| Message-ID | <PjvdR.98070$4e1.27534@fx20.iad> |
| In reply to | #139478 |
On 1/25/26 3:09 PM, olcott wrote: > On 1/25/2026 1:57 PM, Richard Damon wrote: >> On 1/25/26 2:10 PM, olcott wrote: >>> On 1/25/2026 12:40 PM, Richard Damon wrote: >>>> On 1/25/26 1:33 PM, olcott wrote: >>>>> On 1/25/2026 12:27 PM, Richard Damon wrote: >>>>>> On 1/25/26 8:24 AM, olcott wrote: >>>>>>> On 1/25/2026 5:19 AM, Mikko wrote: >>>>>>>> On 24/01/2026 16:01, olcott wrote: >>>>>>>>> On 1/24/2026 2:20 AM, Mikko wrote: >>>>>>>>>> On 23/01/2026 12:22, olcott wrote: >>>>>>>>>>> On 1/23/2026 3:13 AM, Mikko wrote: >>>>>>>>>>>> On 22/01/2026 18:40, olcott wrote: >>>>>>>>>>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>> On 21/01/2026 17:22, olcott wrote: >>>>>>>>>>>>>>> On 1/21/2026 3:03 AM, Mikko wrote: >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> No, it hasn't. In the way theories are usually discussed >>>>>>>>>>>>>>>> nothing is >>>>>>>>>>>>>>>> "ture in arithmetic". Every sentence of a first order >>>>>>>>>>>>>>>> theory that >>>>>>>>>>>>>>>> can be proven in the theory is true in every model >>>>>>>>>>>>>>>> theory. Every >>>>>>>>>>>>>>>> sentence of a theory that cannot be proven in the theory >>>>>>>>>>>>>>>> is false >>>>>>>>>>>>>>>> in some model of the theory. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> only because back then proof theoretic semantics did >>>>>>>>>>>>>>>>> not exist. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> Every interpretation of the theory is a definition of >>>>>>>>>>>>>>>> semantics. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Meta‑math relations about numbers don’t exist in PA >>>>>>>>>>>>>>> because PA only contains arithmetical relations—addition, >>>>>>>>>>>>>>> multiplication, ordering, primitive‑recursive predicates >>>>>>>>>>>>>>> about numbers themselves—while relations that talk about >>>>>>>>>>>>>>> PA’s own proofs, syntax, or truth conditions live entirely >>>>>>>>>>>>>>> in the meta‑theory; >>>>>>>>>>>>>> >>>>>>>>>>>>>> Methamathematics does not need any other relations between >>>>>>>>>>>>>> numbers >>>>>>>>>>>>>> than what PA has. But relations that map other things to >>>>>>>>>>>>>> numbers >>>>>>>>>>>>>> can be useful for methamathematical purposes. >>>>>>>>>>>>>> >>>>>>>>>>>>>>> so when someone appeals to a Gödel‑style relation like >>>>>>>>>>>>>>> “n encodes a proof of this very sentence,” they’re >>>>>>>>>>>>>>> invoking a meta‑mathematical predicate that PA cannot >>>>>>>>>>>>>>> internalize, which is exactly why your framework draws >>>>>>>>>>>>>>> a clean boundary between internal proof‑theoretic truth >>>>>>>>>>>>>>> and external model‑theoretic truth. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Anyway, what can be provven that way is true aboout PA. >>>>>>>>>>>>>> You can deny >>>>>>>>>>>>>> the proof but you cannot perform what is meta-provably >>>>>>>>>>>>>> impossible. >>>>>>>>>>>>> >>>>>>>>>>>>> Gödel’s sentence is not “true in arithmetic.” >>>>>>>>>>>>> It is true only in the meta‑theory, under an >>>>>>>>>>>>> external interpretation of PA (typically the >>>>>>>>>>>>> standard model ℕ). Inside PA itself, the sentence >>>>>>>>>>>>> is not a truth‑bearer at all. >>>>>>>>>>>> >>>>>>>>>>>> There is no concept of "truth-bearer" in an uninterpreted >>>>>>>>>>>> theory because >>>>>>>>>>>> there is not concept of "truth". The relevant concept is >>>>>>>>>>>> "sell- formed- >>>>>>>>>>>> formula" and Gödels sentence is one. It may be true or false >>>>>>>>>>>> in an >>>>>>>>>>>> interpretation. >>>>>>>>>> >>>>>>>>>>> There is a >>>>>>>>>>> "true on the basis of meaning expressed in language" >>>>>>>>>>> and I figured out how to make it computable over the >>>>>>>>>>> body of knowledge. >>>>>>>>>> >>>>>>>>>> Except that "true on the basis of meaning expressed in >>>>>>>>>> language" is >>>>>>>>>> nmt computable and does not cover all of the body of knowldge. >>>>>>>>> >>>>>>>>> When the basis of "true" is proof theoretic semantics >>>>>>>>> internal to the formal system relative to its own axioms >>>>>>>>> and not truth conditional in a separate model outside >>>>>>>>> of the system undecidability ceases to exist. >>>>>>>> >>>>>>>> No, it does not. It does not matter what you call it, a sentence >>>>>>>> that cannot be neither proven nor disproven is undecidable because >>>>>>>> that is what the word means. An example is Gödel's sentence in >>>>>>>> Peano arithmetics. >>>>>>>> >>>>>>> >>>>>>> When a truth predicate gets the input "What time is?" >>>>>>> this input is rejected as not truth-apt. >>>>>> >>>>>> >>>>>> That fine. >>>>>>> >>>>>>> When PA gets an expression that cannot be proven or >>>>>>> refuted using its own axioms then this expression is >>>>>>> not within its domain. >>>>>>> >>>>>> >>>>>> Then most of Natural Number mathematics is isn't in its domain, >>>>>> >>>>> >>>>> It is what it is. >>>> >>>> But PA was CREATED to allow us to define the Natural Numbers in an >>>> axiomatic way. >>>> >>> >>> Yet only within the actual axioms of PA. >> >> Yes, the Natural Numbers are object created within the formal system >> of Peano Arithmetic (as one way to define them) and in that system >> there are a lot of properties of them that are True (or False). >> >> If there is a property of them that PA Created that it can't talk >> about, that sounds very much like PA is just incomplete in its >> understanding of what it does, just by the basic normal definition of >> incomplete. >> >> > > Gödel’s sentence is not “true in arithmetic.” > It is true only in the meta‑theory, under an > external interpretation of PA (typically the > standard model ℕ). Inside PA itself, the sentence > is not a truth‑bearer at all. > > > Sure it is. It is a FACT that no number when plugged into the formula created ever returns a "true" result. Thus, the statement that no number statisfies that relationship exists is true. Your problem is you can't actualy understand the mathematical part of the proof, and can only understand it in the "simpler" interpretation that comes out of the meta mathematic theory. You just lie to yourself that it can't be, because it every existance breaks your ideas.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-22 10:47 -0600 |
| Message-ID | <10ktkc0$3637s$1@dont-email.me> |
| In reply to | #139325 |
On 1/22/2026 2:21 AM, Mikko wrote: > > Anyway, what can be provven that way is true aboout PA. You can deny > the proof but you cannot perform what is meta-provably impossible. > The meta-proof does not exist in the axioms of PA and that is the reason why an external truth in an external model cannot be proved internally in PA. All of these years it was only a mere conflation error. -- Copyright 2026 Olcott<br><br> My 28 year goal has been to make <br> "true on the basis of meaning expressed in language"<br> reliably computable.<br><br> This required establishing a new foundation<br>
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-24 10:23 +0200 |
| Message-ID | <10l1vit$l5o9$2@dont-email.me> |
| In reply to | #139329 |
On 22/01/2026 18:47, olcott wrote: > On 1/22/2026 2:21 AM, Mikko wrote: >> Anyway, what can be provven that way is true aboout PA. You can deny >> the proof but you cannot perform what is meta-provably impossible. > The meta-proof does not exist in the axioms of PA > and that is the reason why an external truth in > an external model cannot be proved internally in PA. > All of these years it was only a mere conflation > error. It is perfectly clear which is which. But every proof in PA is also a proof in Gödel's metatheory. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-24 08:18 -0600 |
| Message-ID | <10l2kbs$runt$1@dont-email.me> |
| In reply to | #139380 |
On 1/24/2026 2:23 AM, Mikko wrote:
> On 22/01/2026 18:47, olcott wrote:
>> On 1/22/2026 2:21 AM, Mikko wrote:
>
>>> Anyway, what can be provven that way is true aboout PA. You can deny
>>> the proof but you cannot perform what is meta-provably impossible.
>
>> The meta-proof does not exist in the axioms of PA
>> and that is the reason why an external truth in
>> an external model cannot be proved internally in PA.
>> All of these years it was only a mere conflation
>> error.
>
> It is perfectly clear which is which.
> But every proof in PA is also
> a proof in Gödel's metatheory.
>
∀x ∈ PA ( True(PA, x) ≡ PA ⊢ x )
∀x ∈ PA ( False(PA, x) ≡ PA ⊢ ¬x )
∀x ∈ PA ( ¬WellFounded(PA, x) ≡
(¬True(PA, x) ∧ (¬False(PA, x)))
--
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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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-01-25 13:24 +0200 |
| Message-ID | <10l4ui9$1jk2e$1@dont-email.me> |
| In reply to | #139387 |
On 24/01/2026 16:18, olcott wrote: > On 1/24/2026 2:23 AM, Mikko wrote: >> On 22/01/2026 18:47, olcott wrote: >>> On 1/22/2026 2:21 AM, Mikko wrote: >> >>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>> the proof but you cannot perform what is meta-provably impossible. >> >>> The meta-proof does not exist in the axioms of PA >>> and that is the reason why an external truth in >>> an external model cannot be proved internally in PA. >>> All of these years it was only a mere conflation >>> error. >> >> It is perfectly clear which is which. But every proof in PA is also >> a proof in Gödel's metatheory. > > ∀x ∈ PA ( True(PA, x) ≡ PA ⊢ x ) > ∀x ∈ PA ( False(PA, x) ≡ PA ⊢ ¬x ) > ∀x ∈ PA ( ¬WellFounded(PA, x) ≡ > (¬True(PA, x) ∧ (¬False(PA, x))) Those sentences don't mean anything without specificantions of a language and a theory that gives them some meaning. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-01-25 07:30 -0600 |
| Message-ID | <10l55th$1m1ar$1@dont-email.me> |
| In reply to | #139457 |
On 1/25/2026 5:24 AM, Mikko wrote: > On 24/01/2026 16:18, olcott wrote: >> On 1/24/2026 2:23 AM, Mikko wrote: >>> On 22/01/2026 18:47, olcott wrote: >>>> On 1/22/2026 2:21 AM, Mikko wrote: >>> >>>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>>> the proof but you cannot perform what is meta-provably impossible. >>> >>>> The meta-proof does not exist in the axioms of PA >>>> and that is the reason why an external truth in >>>> an external model cannot be proved internally in PA. >>>> All of these years it was only a mere conflation >>>> error. >>> >>> It is perfectly clear which is which. But every proof in PA is also >>> a proof in Gödel's metatheory. >> >> ∀x ∈ PA ( True(PA, x) ≡ PA ⊢ x ) >> ∀x ∈ PA ( False(PA, x) ≡ PA ⊢ ¬x ) >> ∀x ∈ PA ( ¬WellFounded(PA, x) ≡ >> (¬True(PA, x) ∧ (¬False(PA, x))) > > Those sentences don't mean anything without specificantions of a > language and a theory that gives them some meaning. > In other word you do not understand standard notational conventions that define True for PA as provable from the axioms of PA and False for PA as refutable from the axioms of PA. -- 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 for the entire body of knowledge.<br><br> This required establishing a new foundation<br>
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-01-25 13:31 -0500 |
| Message-ID | <cktdR.98063$4e1.27693@fx20.iad> |
| In reply to | #139459 |
On 1/25/26 8:30 AM, olcott wrote: > On 1/25/2026 5:24 AM, Mikko wrote: >> On 24/01/2026 16:18, olcott wrote: >>> On 1/24/2026 2:23 AM, Mikko wrote: >>>> On 22/01/2026 18:47, olcott wrote: >>>>> On 1/22/2026 2:21 AM, Mikko wrote: >>>> >>>>>> Anyway, what can be provven that way is true aboout PA. You can deny >>>>>> the proof but you cannot perform what is meta-provably impossible. >>>> >>>>> The meta-proof does not exist in the axioms of PA >>>>> and that is the reason why an external truth in >>>>> an external model cannot be proved internally in PA. >>>>> All of these years it was only a mere conflation >>>>> error. >>>> >>>> It is perfectly clear which is which. But every proof in PA is also >>>> a proof in Gödel's metatheory. >>> >>> ∀x ∈ PA ( True(PA, x) ≡ PA ⊢ x ) >>> ∀x ∈ PA ( False(PA, x) ≡ PA ⊢ ¬x ) >>> ∀x ∈ PA ( ¬WellFounded(PA, x) ≡ >>> (¬True(PA, x) ∧ (¬False(PA, x))) >> >> Those sentences don't mean anything without specificantions of a >> language and a theory that gives them some meaning. >> > > In other word you do not understand standard notational > conventions that define True for PA as provable from the > axioms of PA and False for PA as refutable from the axioms > of PA. > And you don't understand that those definitions aren't defined in a proof theoretic semantics. PA ⊢ x can't be evaluated itself in proof theoretic semantics and always get a value, as you can't PROVE that statement.
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