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Groups > sci.math > #641072 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2025-11-25 14:20 -0600 |
| Last post | 2025-11-26 00:45 +0000 |
| Articles | 20 on this page of 190 — 12 participants |
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New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 14:20 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 20:56 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 15:01 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 21:03 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 15:09 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 21:12 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 15:27 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 13:30 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 23:14 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 17:21 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 23:25 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:00 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:04 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:14 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:18 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:38 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:42 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 00:47 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:52 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:57 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 19:19 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:29 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:32 +0000
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 18:29 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 19:43 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:45 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:03 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:09 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:34 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:36 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:46 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:47 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:01 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:03 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:11 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 07:34 -0500
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-05 17:03 -0600
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-05 19:53 -0600
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:36 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:38 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 19:36 -0800
Re: New formal foundation for correct reasoning makes True(X) computable polcott <polcott333@gmail.com> - 2025-11-26 22:10 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 21:30 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 02:36 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:43 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:09 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:17 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:26 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:32 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 05:15 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 07:36 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-26 11:22 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 09:15 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 10:20 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 10:31 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 19:43 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-27 09:40 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-27 09:17 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-27 10:42 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:29 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-28 08:54 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-28 17:22 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 16:31 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:40 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-29 10:42 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-29 15:01 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-30 12:19 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:46 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:22 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:24 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:27 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:33 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:36 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:50 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:53 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:58 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 22:18 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:21 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:56 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:54 -0800
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:22 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:23 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:55 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:58 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 22:06 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:11 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:23 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:24 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:56 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:01 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 08:53 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 10:06 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:59 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 05:18 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 05:16 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:14 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 07:27 -0500
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:00 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:08 -0600
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:12 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:30 -0600
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:36 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:41 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:43 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:24 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:26 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:30 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:47 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 22:01 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:07 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 08:44 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 10:04 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 10:34 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-26 11:05 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 08:58 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-27 09:30 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-27 09:16 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:35 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-28 09:16 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:44 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-29 10:40 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-30 12:14 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 09:13 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:36 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-28 09:18 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:48 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-29 10:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-30 12:07 +0200
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-03 12:53 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-03 10:11 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-04 11:07 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-04 08:10 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:13 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-05 11:40 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:19 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-06 06:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:55 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-08 13:44 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:21 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-06 06:46 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:50 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-07 11:15 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-08 11:08 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-08 13:05 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-13 13:05 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-13 09:55 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-15 11:52 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-15 09:49 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-17 12:49 +0200
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:45 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:59 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:16 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 02:34 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:37 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:02 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:06 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:08 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:19 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:28 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Heathfield <rjh@cpax.org.uk> - 2025-11-26 05:53 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:15 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:21 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:16 -0800
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 19:08 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:19 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 19:22 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:30 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:18 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:14 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 01:48 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-25 20:59 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 21:11 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:16 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:34 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 20:05 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 13:27 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:23 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 14:40 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 20:03 -0800
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 16:29 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:31 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 17:09 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:19 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 18:38 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:40 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 19:16 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:40 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:45 +0000
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 14:20 -0600 |
| Subject | New formal foundation for correct reasoning makes True(X) computable |
| Message-ID | <10g5331$3ol1m$1@dont-email.me> |
On 11/25/2025 2:05 PM, dart200 wrote: > On 11/25/25 10:46 AM, Kaz Kylheku wrote: >> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>> D simulated by H cannot possibly reach its own >>>>> simulated final halt state. >>>> >>>> It has been shown /wth code/ that D simulated by H reaches its return, >>> >>> Liar, Liar Pants on Fire !!! >> >> I made the code public; another person was able to build and get the >> same results. >> >> Yes, it's a growing conspiracy against you, like the whole thing about >> the world being round. > > it is kinda nuts how uniformly retarded people are about this > I am working on building a foundation that can be published in a peer reviewed journal. That is only possible because of the excellent feedback that I have received from LLM systems. Every conversation that I have with an LLM system is brand new. This allows me to present my view ever more succinctly. It turns out that my new formal foundation for correct reasoning easily utterly eliminates all undecidability and undefinability and it does this by simply fully integrating semantics syntactically in its formal language. Both Montague Grammar and the CycL language of the Cyc project already do this. Semantic logical entailment is the only inference step. My system basically extends the syllogism to cover the entire body of all knowledge that can be expressed in language. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-25 20:56 +0000 |
| Message-ID | <0Jm85Dn6rlsUV3VjlJ5Z_Kk70e0@jntp> |
| In reply to | #641072 |
Le 25/11/2025 à 21:20, olcott a écrit : > On 11/25/2025 2:05 PM, dart200 wrote: >> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>> D simulated by H cannot possibly reach its own >>>>>> simulated final halt state. >>>>> >>>>> It has been shown /wth code/ that D simulated by H reaches its return, >>>> >>>> Liar, Liar Pants on Fire !!! >>> >>> I made the code public; another person was able to build and get the >>> same results. >>> >>> Yes, it's a growing conspiracy against you, like the whole thing about >>> the world being round. >> >> it is kinda nuts how uniformly retarded people are about this >> > > I am working on building a foundation that can be > published in a peer reviewed journal. That is only > possible because of the excellent feedback that I > have received from LLM systems. Every conversation > that I have with an LLM system is brand new. This > allows me to present my view ever more succinctly. > > It turns out that my new formal foundation for > correct reasoning easily utterly eliminates > all undecidability and undefinability and it > does this by simply fully integrating semantics > syntactically in its formal language. > > Both Montague Grammar and the CycL language > of the Cyc project already do this. > > Semantic logical entailment is the only inference > step. My system basically extends the syllogism > to cover the entire body of all knowledge that > can be expressed in language. Neither CycL nor Peter Olcott’s claims refute Gödel-style logical incompleteness. Below is the clear, technical explanation. 1. What Gödel’s incompleteness theorems actually say Gödel’s first incompleteness theorem applies to any formal system that is: Recursively axiomatizable (axioms and inference rules can be listed by a program), Consistent, Sufficiently expressive to encode basic arithmetic (Robinson arithmetic Q or stronger). Then: There exist true statements of arithmetic that the system cannot prove. No clever notation, ontology language, or knowledge-base trick can bypass this, because the theorem is about computability + representation of arithmetic, not about the syntax of the language. Gödel’s second incompleteness theorem says that such a system cannot prove its own consistency (again: subject to the above conditions). These results are fully stable under changes of language, ontology, semantic layers, etc. 2. Does CycL avoid incompleteness? No. CycL is an ontology language used by the Cyc project to encode commonsense knowledge using a vast collection of predicates, rules, and microtheories. But: CycL is not a complete formalization of arithmetic. Its microtheories intentionally avoid global consistency because knowledge is context-dependent. Cyc as a whole is not a single coherent formal system satisfying Gödel’s conditions. It is a heterogeneous, context-indexed collection of theories, some of which contradict others. Because it is not a single consistent recursively axiomatizable theory, Gödel’s theorems don’t even apply globally—but that does not mean Cyc “defeats incompleteness”; it just lives outside the scope of the theorem. Cyc’s strategy is not “beat incompleteness”; it is “use many partial microtheories and logical levels contextually”. This is like saying a library containing many inconsistent books “defeats incompleteness” — it does not; it simply is not a single formal theory. Conclusion: CycL cannot be used to derive Peano arithmetic in a way that would make it complete, and Cyc does not claim otherwise. 3. Do Peter Olcott’s claims refute incompleteness? No. Peter Olcott is known online for repeatedly claiming to have “resolved” or “invalidated” Gödel’s incompleteness or Turing’s halting problem. His claims are universally rejected by logicians because they misunderstand the formal structure of the theorems. In all variants of his claims: He proposes procedures that assume access to semantic truth, something incompleteness forbids a formal system from capturing internally. Or he proposes recognition algorithms that fail on classic diagonal/self-reference constructions but does not notice the failure. Or he builds systems that are not recursively axiomatizable, and therefore Gödel’s theorem does not apply — but then he claims “defeat” rather than “dodging the premises”. The pattern is always: Change the problem or the assumptions → claim the original theorem is wrong. This is equivalent to saying “I solved the halting problem… for programs that I forbid from diagonalizing.” That is not a refutation. 4. Why these approaches cannot refute incompleteness Gödel incompleteness is a meta-theorem. Any attempt to build a complete system for arithmetic must fail because: If the system is algorithmic, there’s a diagonal sentence G such that If the system is consistent: it cannot prove G. If it proves G: it becomes inconsistent. If you try to use “semantics” or “truth”: Tarski’s theorem says arithmetical truth is not definable inside arithmetic itself. If you use a non-recursively-axiomatizable system: Gödel’s theorem no longer applies, but such a system cannot be implemented as a fully formal algorithmic reasoning machine. Cyc, Olcott, or any other system inevitably satisfies one of these escape conditions, but none actually produces a complete and consistent theory strong enough to capture arithmetic. 5. The deep point: ➤ To refute incompleteness, one must produce a complete, consistent, computable theory of arithmetic. Nobody has ever achieved this, and it is mathematically impossible. Cyc is not a single consistent computable theory. Olcott’s systems are not both computable and consistent when applied to arithmetic. Changing the syntax does nothing: incompleteness is syntax-agnostic. 6. Final conclusion The existence of CycL and the claims Peter Olcott makes do NOT refute logical incompleteness. CycL sidesteps the theorem by not being a single formal theory, not by defeating it. Olcott misunderstands the premises of incompleteness and his proposals either fall outside Gödel’s scope or break on diagonalization. Gödel remains intact.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 15:01 -0600 |
| Message-ID | <10g55ef$3poa8$1@dont-email.me> |
| In reply to | #641076 |
On 11/25/2025 2:56 PM, Python wrote: > Le 25/11/2025 à 21:20, olcott a écrit : >> On 11/25/2025 2:05 PM, dart200 wrote: >>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>> D simulated by H cannot possibly reach its own >>>>>>> simulated final halt state. >>>>>> >>>>>> It has been shown /wth code/ that D simulated by H reaches its >>>>>> return, >>>>> >>>>> Liar, Liar Pants on Fire !!! >>>> >>>> I made the code public; another person was able to build and get the >>>> same results. >>>> >>>> Yes, it's a growing conspiracy against you, like the whole thing about >>>> the world being round. >>> >>> it is kinda nuts how uniformly retarded people are about this >>> >> >> I am working on building a foundation that can be >> published in a peer reviewed journal. That is only >> possible because of the excellent feedback that I >> have received from LLM systems. Every conversation >> that I have with an LLM system is brand new. This >> allows me to present my view ever more succinctly. >> >> It turns out that my new formal foundation for >> correct reasoning easily utterly eliminates >> all undecidability and undefinability and it >> does this by simply fully integrating semantics >> syntactically in its formal language. >> >> Both Montague Grammar and the CycL language >> of the Cyc project already do this. >> >> Semantic logical entailment is the only inference >> step. My system basically extends the syllogism >> to cover the entire body of all knowledge that >> can be expressed in language. > > Neither CycL nor Peter Olcott’s claims refute Gödel-style logical > incompleteness. > Below is the clear, technical explanation. > > 1. What Gödel’s incompleteness theorems actually say > > Gödel’s first incompleteness theorem applies to any formal system that is: > > Recursively axiomatizable (axioms and inference rules can be listed by a > program), > > Consistent, > > Sufficiently expressive to encode basic arithmetic (Robinson arithmetic > Q or stronger). > > Then: > > There exist true statements of arithmetic that the system cannot prove. > > No clever notation, ontology language, or knowledge-base trick can > bypass this, because the theorem is about computability + representation > of arithmetic, not about the syntax of the language. > > Gödel’s second incompleteness theorem says that such a system cannot > prove its own consistency (again: subject to the above conditions). > > These results are fully stable under changes of language, ontology, > semantic layers, etc. > > 2. Does CycL avoid incompleteness? > > No. CycL is an ontology language used by the Cyc project to encode > commonsense knowledge using a vast collection of predicates, rules, and > microtheories. But: > > CycL is not a complete formalization of arithmetic. > Its microtheories intentionally avoid global consistency because > knowledge is context-dependent. > > Cyc as a whole is not a single coherent formal system satisfying Gödel’s > conditions. > It is a heterogeneous, context-indexed collection of theories, some of > which contradict others. > > Because it is not a single consistent recursively axiomatizable theory, > Gödel’s theorems don’t even apply globally—but that does not mean Cyc > “defeats incompleteness”; it just lives outside the scope of the theorem. > > Cyc’s strategy is not “beat incompleteness”; it is “use many partial > microtheories and logical levels contextually”. > > This is like saying a library containing many inconsistent books > “defeats incompleteness” — it does not; it simply is not a single formal > theory. > > Conclusion: > CycL cannot be used to derive Peano arithmetic in a way that would make > it complete, and Cyc does not claim otherwise. > > 3. Do Peter Olcott’s claims refute incompleteness? > > No. Peter Olcott is known online for repeatedly claiming to have > “resolved” or “invalidated” Gödel’s incompleteness or Turing’s halting > problem. > His claims are universally rejected by logicians because they > misunderstand the formal structure of the theorems. > > In all variants of his claims: > > He proposes procedures that assume access to semantic truth, something > incompleteness forbids a formal system from capturing internally. > > Or he proposes recognition algorithms that fail on classic diagonal/ > self-reference constructions but does not notice the failure. > > Or he builds systems that are not recursively axiomatizable, and > therefore Gödel’s theorem does not apply — but then he claims “defeat” > rather than “dodging the premises”. > > The pattern is always: > > Change the problem or the assumptions → claim the original theorem is > wrong. > > This is equivalent to saying “I solved the halting problem… for programs > that I forbid from diagonalizing.” > That is not a refutation. > > 4. Why these approaches cannot refute incompleteness > > Gödel incompleteness is a meta-theorem. > Any attempt to build a complete system for arithmetic must fail because: > > If the system is algorithmic, there’s a diagonal sentence G such that > > If the system is consistent: it cannot prove G. > That is true. With my system there is one single all encompassing formal system that contains every element of general knowledge that can be expressed in language. Because the formal language has all semantics fully integrated into its syntax True(x) is exactly the same thing as Provable(x). If you can't prove it then it is not an element of the body of knowledge that can be expressed in language. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-25 21:03 +0000 |
| Message-ID | <Wv9Os4d8RofQnr6QfEf1M9RYJdQ@jntp> |
| In reply to | #641078 |
Le 25/11/2025 à 22:01, olcott a écrit : > On 11/25/2025 2:56 PM, Python wrote: >> Le 25/11/2025 à 21:20, olcott a écrit : >>> On 11/25/2025 2:05 PM, dart200 wrote: >>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>> simulated final halt state. >>>>>>> >>>>>>> It has been shown /wth code/ that D simulated by H reaches its >>>>>>> return, >>>>>> >>>>>> Liar, Liar Pants on Fire !!! >>>>> >>>>> I made the code public; another person was able to build and get the >>>>> same results. >>>>> >>>>> Yes, it's a growing conspiracy against you, like the whole thing about >>>>> the world being round. >>>> >>>> it is kinda nuts how uniformly retarded people are about this >>>> >>> >>> I am working on building a foundation that can be >>> published in a peer reviewed journal. That is only >>> possible because of the excellent feedback that I >>> have received from LLM systems. Every conversation >>> that I have with an LLM system is brand new. This >>> allows me to present my view ever more succinctly. >>> >>> It turns out that my new formal foundation for >>> correct reasoning easily utterly eliminates >>> all undecidability and undefinability and it >>> does this by simply fully integrating semantics >>> syntactically in its formal language. >>> >>> Both Montague Grammar and the CycL language >>> of the Cyc project already do this. >>> >>> Semantic logical entailment is the only inference >>> step. My system basically extends the syllogism >>> to cover the entire body of all knowledge that >>> can be expressed in language. >> >> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >> incompleteness. >> Below is the clear, technical explanation. >> >> 1. What Gödel’s incompleteness theorems actually say >> >> Gödel’s first incompleteness theorem applies to any formal system that is: >> >> Recursively axiomatizable (axioms and inference rules can be listed by a >> program), >> >> Consistent, >> >> Sufficiently expressive to encode basic arithmetic (Robinson arithmetic >> Q or stronger). >> >> Then: >> >> There exist true statements of arithmetic that the system cannot prove. >> >> No clever notation, ontology language, or knowledge-base trick can >> bypass this, because the theorem is about computability + representation >> of arithmetic, not about the syntax of the language. >> >> Gödel’s second incompleteness theorem says that such a system cannot >> prove its own consistency (again: subject to the above conditions). >> >> These results are fully stable under changes of language, ontology, >> semantic layers, etc. >> >> 2. Does CycL avoid incompleteness? >> >> No. CycL is an ontology language used by the Cyc project to encode >> commonsense knowledge using a vast collection of predicates, rules, and >> microtheories. But: >> >> CycL is not a complete formalization of arithmetic. >> Its microtheories intentionally avoid global consistency because >> knowledge is context-dependent. >> >> Cyc as a whole is not a single coherent formal system satisfying Gödel’s >> conditions. >> It is a heterogeneous, context-indexed collection of theories, some of >> which contradict others. >> >> Because it is not a single consistent recursively axiomatizable theory, >> Gödel’s theorems don’t even apply globally—but that does not mean Cyc >> “defeats incompleteness”; it just lives outside the scope of the theorem. >> >> Cyc’s strategy is not “beat incompleteness”; it is “use many partial >> microtheories and logical levels contextually”. >> >> This is like saying a library containing many inconsistent books >> “defeats incompleteness” — it does not; it simply is not a single formal >> theory. >> >> Conclusion: >> CycL cannot be used to derive Peano arithmetic in a way that would make >> it complete, and Cyc does not claim otherwise. >> >> 3. Do Peter Olcott’s claims refute incompleteness? >> >> No. Peter Olcott is known online for repeatedly claiming to have >> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >> halting >> problem. >> His claims are universally rejected by logicians because they >> misunderstand the formal structure of the theorems. >> >> In all variants of his claims: >> >> He proposes procedures that assume access to semantic truth, something >> incompleteness forbids a formal system from capturing internally. >> >> Or he proposes recognition algorithms that fail on classic diagonal/ >> self-reference constructions but does not notice the failure. >> >> Or he builds systems that are not recursively axiomatizable, and >> therefore Gödel’s theorem does not apply — but then he claims “defeat” >> rather than “dodging the premises”. >> >> The pattern is always: >> >> Change the problem or the assumptions → claim the original theorem is >> wrong. >> >> This is equivalent to saying “I solved the halting problem… for programs >> that I forbid from diagonalizing.” >> That is not a refutation. >> >> 4. Why these approaches cannot refute incompleteness >> >> Gödel incompleteness is a meta-theorem. >> Any attempt to build a complete system for arithmetic must fail because: >> >> If the system is algorithmic, there’s a diagonal sentence G such that >> >> If the system is consistent: it cannot prove G. >> > > That is true. > With my system there is one single all encompassing > formal system that contains every element of general > knowledge that can be expressed in language. > > Because the formal language has all semantics fully > integrated into its syntax True(x) is exactly the > same thing as Provable(x). If you can't prove it > then it is not an element of the body of knowledge > that can be expressed in language. The idea of a single, all-encompassing formal system in which every meaningful statement is expressible and in which True(x) ≡ Provable(x) is internally inconsistent, because as soon as the language is expressive enough to contain elementary arithmetic—inevitably required if it is to “contain every element of general knowledge expressible in language”—Gödel’s incompleteness theorem applies, producing well-formed statements that are true in the intended semantics but not provable in the system; thus the identification “true = provable” cannot hold unless one either (1) restricts the language so severely that it no longer expresses general knowledge, or (2) accepts a degenerate semantics in which “truth” is redefined to mean “provable in the system,” which merely eliminates semantics and collapses truth into syntactic provability by fiat, yielding a system that cannot describe its own correctness and cannot capture the ordinary notion of truth at all—in short, Olcott’s proposal either violates Gödel or empties “truth” of its usual meaning, and so it cannot simultaneously claim completeness, expressiveness, and a meaningful notion of truth.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 15:09 -0600 |
| Message-ID | <10g55tg$3pu0h$1@dont-email.me> |
| In reply to | #641079 |
On 11/25/2025 3:03 PM, Python wrote: > Le 25/11/2025 à 22:01, olcott a écrit : >> On 11/25/2025 2:56 PM, Python wrote: >>> Le 25/11/2025 à 21:20, olcott a écrit : >>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>> simulated final halt state. >>>>>>>> >>>>>>>> It has been shown /wth code/ that D simulated by H reaches its >>>>>>>> return, >>>>>>> >>>>>>> Liar, Liar Pants on Fire !!! >>>>>> >>>>>> I made the code public; another person was able to build and get the >>>>>> same results. >>>>>> >>>>>> Yes, it's a growing conspiracy against you, like the whole thing >>>>>> about >>>>>> the world being round. >>>>> >>>>> it is kinda nuts how uniformly retarded people are about this >>>>> >>>> >>>> I am working on building a foundation that can be >>>> published in a peer reviewed journal. That is only >>>> possible because of the excellent feedback that I >>>> have received from LLM systems. Every conversation >>>> that I have with an LLM system is brand new. This >>>> allows me to present my view ever more succinctly. >>>> >>>> It turns out that my new formal foundation for >>>> correct reasoning easily utterly eliminates >>>> all undecidability and undefinability and it >>>> does this by simply fully integrating semantics >>>> syntactically in its formal language. >>>> >>>> Both Montague Grammar and the CycL language >>>> of the Cyc project already do this. >>>> >>>> Semantic logical entailment is the only inference >>>> step. My system basically extends the syllogism >>>> to cover the entire body of all knowledge that >>>> can be expressed in language. >>> >>> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >>> incompleteness. >>> Below is the clear, technical explanation. >>> >>> 1. What Gödel’s incompleteness theorems actually say >>> >>> Gödel’s first incompleteness theorem applies to any formal system >>> that is: >>> >>> Recursively axiomatizable (axioms and inference rules can be listed >>> by a program), >>> >>> Consistent, >>> >>> Sufficiently expressive to encode basic arithmetic (Robinson >>> arithmetic Q or stronger). >>> >>> Then: >>> >>> There exist true statements of arithmetic that the system cannot prove. >>> >>> No clever notation, ontology language, or knowledge-base trick can >>> bypass this, because the theorem is about computability + >>> representation of arithmetic, not about the syntax of the language. >>> >>> Gödel’s second incompleteness theorem says that such a system cannot >>> prove its own consistency (again: subject to the above conditions). >>> >>> These results are fully stable under changes of language, ontology, >>> semantic layers, etc. >>> >>> 2. Does CycL avoid incompleteness? >>> >>> No. CycL is an ontology language used by the Cyc project to encode >>> commonsense knowledge using a vast collection of predicates, rules, >>> and microtheories. But: >>> >>> CycL is not a complete formalization of arithmetic. >>> Its microtheories intentionally avoid global consistency because >>> knowledge is context-dependent. >>> >>> Cyc as a whole is not a single coherent formal system satisfying >>> Gödel’s conditions. >>> It is a heterogeneous, context-indexed collection of theories, some >>> of which contradict others. >>> >>> Because it is not a single consistent recursively axiomatizable >>> theory, Gödel’s theorems don’t even apply globally—but that does not >>> mean Cyc “defeats incompleteness”; it just lives outside the scope of >>> the theorem. >>> >>> Cyc’s strategy is not “beat incompleteness”; it is “use many partial >>> microtheories and logical levels contextually”. >>> >>> This is like saying a library containing many inconsistent books >>> “defeats incompleteness” — it does not; it simply is not a single >>> formal theory. >>> >>> Conclusion: >>> CycL cannot be used to derive Peano arithmetic in a way that would >>> make it complete, and Cyc does not claim otherwise. >>> >>> 3. Do Peter Olcott’s claims refute incompleteness? >>> >>> No. Peter Olcott is known online for repeatedly claiming to have >>> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >>> halting problem. >>> His claims are universally rejected by logicians because they >>> misunderstand the formal structure of the theorems. >>> >>> In all variants of his claims: >>> >>> He proposes procedures that assume access to semantic truth, >>> something incompleteness forbids a formal system from capturing >>> internally. >>> >>> Or he proposes recognition algorithms that fail on classic diagonal/ >>> self-reference constructions but does not notice the failure. >>> >>> Or he builds systems that are not recursively axiomatizable, and >>> therefore Gödel’s theorem does not apply — but then he claims >>> “defeat” rather than “dodging the premises”. >>> >>> The pattern is always: >>> >>> Change the problem or the assumptions → claim the original theorem is >>> wrong. >>> >>> This is equivalent to saying “I solved the halting problem… for >>> programs that I forbid from diagonalizing.” >>> That is not a refutation. >>> >>> 4. Why these approaches cannot refute incompleteness >>> >>> Gödel incompleteness is a meta-theorem. >>> Any attempt to build a complete system for arithmetic must fail because: >>> >>> If the system is algorithmic, there’s a diagonal sentence G such that >>> >>> If the system is consistent: it cannot prove G. >>> >> >> That is true. >> With my system there is one single all encompassing >> formal system that contains every element of general >> knowledge that can be expressed in language. >> >> Because the formal language has all semantics fully >> integrated into its syntax True(x) is exactly the >> same thing as Provable(x). If you can't prove it >> then it is not an element of the body of knowledge >> that can be expressed in language. > > The idea of a single, all-encompassing formal system in which every > meaningful statement is expressible and in which True(x) ≡ Provable(x) > is internally inconsistent, because as soon as the language is > expressive enough to contain elementary arithmetic—inevitably required > if it is to “contain every element of general knowledge expressible in > language”—Gödel’s incompleteness theorem applies, producing well-formed > statements that are true in the intended semantics but not provable in > the system; In weaker systems this will remain true. When True(L,x) is exactly the same thing as Provable(L,x) because every aspect of all of semantics is directly formalized and fully integrated in the formal language then ~Provable(L,x) means not an element of the body of general knowledge that can be expressed in language. > thus the identification “true = provable” cannot hold unless > one either (1) restricts the language so severely that it no longer > expresses general knowledge, or (2) accepts a degenerate semantics in > which “truth” is redefined to mean “provable in the system,” which > merely eliminates semantics and collapses truth into syntactic > provability by fiat, yielding a system that cannot describe its own > correctness and cannot capture the ordinary notion of truth at all—in > short, Olcott’s proposal either violates Gödel or empties “truth” of its > usual meaning, and so it cannot simultaneously claim completeness, > expressiveness, and a meaningful notion of truth. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-25 21:12 +0000 |
| Message-ID | <254V-McZTZLNlaKEXTpR-_c90l8@jntp> |
| In reply to | #641080 |
Le 25/11/2025 à 22:09, olcott a écrit : > On 11/25/2025 3:03 PM, Python wrote: >> Le 25/11/2025 à 22:01, olcott a écrit : >>> On 11/25/2025 2:56 PM, Python wrote: >>>> Le 25/11/2025 à 21:20, olcott a écrit : >>>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>>> simulated final halt state. >>>>>>>>> >>>>>>>>> It has been shown /wth code/ that D simulated by H reaches its >>>>>>>>> return, >>>>>>>> >>>>>>>> Liar, Liar Pants on Fire !!! >>>>>>> >>>>>>> I made the code public; another person was able to build and get the >>>>>>> same results. >>>>>>> >>>>>>> Yes, it's a growing conspiracy against you, like the whole thing >>>>>>> about >>>>>>> the world being round. >>>>>> >>>>>> it is kinda nuts how uniformly retarded people are about this >>>>>> >>>>> >>>>> I am working on building a foundation that can be >>>>> published in a peer reviewed journal. That is only >>>>> possible because of the excellent feedback that I >>>>> have received from LLM systems. Every conversation >>>>> that I have with an LLM system is brand new. This >>>>> allows me to present my view ever more succinctly. >>>>> >>>>> It turns out that my new formal foundation for >>>>> correct reasoning easily utterly eliminates >>>>> all undecidability and undefinability and it >>>>> does this by simply fully integrating semantics >>>>> syntactically in its formal language. >>>>> >>>>> Both Montague Grammar and the CycL language >>>>> of the Cyc project already do this. >>>>> >>>>> Semantic logical entailment is the only inference >>>>> step. My system basically extends the syllogism >>>>> to cover the entire body of all knowledge that >>>>> can be expressed in language. >>>> >>>> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >>>> incompleteness. >>>> Below is the clear, technical explanation. >>>> >>>> 1. What Gödel’s incompleteness theorems actually say >>>> >>>> Gödel’s first incompleteness theorem applies to any formal system >>>> that is: >>>> >>>> Recursively axiomatizable (axioms and inference rules can be listed >>>> by a program), >>>> >>>> Consistent, >>>> >>>> Sufficiently expressive to encode basic arithmetic (Robinson >>>> arithmetic Q or stronger). >>>> >>>> Then: >>>> >>>> There exist true statements of arithmetic that the system cannot prove. >>>> >>>> No clever notation, ontology language, or knowledge-base trick can >>>> bypass this, because the theorem is about computability + >>>> representation of arithmetic, not about the syntax of the language. >>>> >>>> Gödel’s second incompleteness theorem says that such a system cannot >>>> prove its own consistency (again: subject to the above conditions). >>>> >>>> These results are fully stable under changes of language, ontology, >>>> semantic layers, etc. >>>> >>>> 2. Does CycL avoid incompleteness? >>>> >>>> No. CycL is an ontology language used by the Cyc project to encode >>>> commonsense knowledge using a vast collection of predicates, rules, >>>> and microtheories. But: >>>> >>>> CycL is not a complete formalization of arithmetic. >>>> Its microtheories intentionally avoid global consistency because >>>> knowledge is context-dependent. >>>> >>>> Cyc as a whole is not a single coherent formal system satisfying >>>> Gödel’s conditions. >>>> It is a heterogeneous, context-indexed collection of theories, some >>>> of which contradict others. >>>> >>>> Because it is not a single consistent recursively axiomatizable >>>> theory, Gödel’s theorems don’t even apply globally—but that does not >>>> mean Cyc “defeats incompleteness”; it just lives outside the scope of >>>> the theorem. >>>> >>>> Cyc’s strategy is not “beat incompleteness”; it is “use many partial >>>> microtheories and logical levels contextually”. >>>> >>>> This is like saying a library containing many inconsistent books >>>> “defeats incompleteness” — it does not; it simply is not a single >>>> formal theory. >>>> >>>> Conclusion: >>>> CycL cannot be used to derive Peano arithmetic in a way that would >>>> make it complete, and Cyc does not claim otherwise. >>>> >>>> 3. Do Peter Olcott’s claims refute incompleteness? >>>> >>>> No. Peter Olcott is known online for repeatedly claiming to have >>>> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >>>> halting problem. >>>> His claims are universally rejected by logicians because they >>>> misunderstand the formal structure of the theorems. >>>> >>>> In all variants of his claims: >>>> >>>> He proposes procedures that assume access to semantic truth, >>>> something incompleteness forbids a formal system from capturing >>>> internally. >>>> >>>> Or he proposes recognition algorithms that fail on classic diagonal/ >>>> self-reference constructions but does not notice the failure. >>>> >>>> Or he builds systems that are not recursively axiomatizable, and >>>> therefore Gödel’s theorem does not apply — but then he claims >>>> “defeat” rather than “dodging the premises”. >>>> >>>> The pattern is always: >>>> >>>> Change the problem or the assumptions → claim the original theorem is >>>> wrong. >>>> >>>> This is equivalent to saying “I solved the halting problem… for >>>> programs that I forbid from diagonalizing.” >>>> That is not a refutation. >>>> >>>> 4. Why these approaches cannot refute incompleteness >>>> >>>> Gödel incompleteness is a meta-theorem. >>>> Any attempt to build a complete system for arithmetic must fail because: >>>> >>>> If the system is algorithmic, there’s a diagonal sentence G such that >>>> >>>> If the system is consistent: it cannot prove G. >>>> >>> >>> That is true. >>> With my system there is one single all encompassing >>> formal system that contains every element of general >>> knowledge that can be expressed in language. >>> >>> Because the formal language has all semantics fully >>> integrated into its syntax True(x) is exactly the >>> same thing as Provable(x). If you can't prove it >>> then it is not an element of the body of knowledge >>> that can be expressed in language. >> >> The idea of a single, all-encompassing formal system in which every >> meaningful statement is expressible and in which True(x) ≡ Provable(x) >> is internally inconsistent, because as soon as the language is >> expressive enough to contain elementary arithmetic—inevitably required >> if it is to “contain every element of general knowledge expressible in >> language”—Gödel’s incompleteness theorem applies, producing well-formed >> statements that are true in the intended semantics but not provable in >> the system; > > In weaker systems this will remain true. > > When True(L,x) is exactly the same thing as Provable(L,x) > > because every aspect of all of semantics is directly > formalized and fully integrated in the formal language > > then ~Provable(L,x) means not an element of the body > of general knowledge that can be expressed in language. > >> thus the identification “true = provable” cannot hold unless >> one either (1) restricts the language so severely that it no longer >> expresses general knowledge, or (2) accepts a degenerate semantics in >> which “truth” is redefined to mean “provable in the system,” which >> merely eliminates semantics and collapses truth into syntactic >> provability by fiat, yielding a system that cannot describe its own >> correctness and cannot capture the ordinary notion of truth at all—in >> short, Olcott’s proposal either violates Gödel or empties “truth” of its >> usual meaning, and so it cannot simultaneously claim completeness, >> expressiveness, and a meaningful notion of truth. Olcott’s “one perfect formal system containing all knowledge with True(x) = Provable(x)” works beautifully, provided you never ask it anything interesting: the moment you give it arithmetic, it starts sweating like a politician in a fact-checking interview, because Gödel sneaks in through the back door and whispers a sentence the system can’t prove, whereupon Olcott shouts “If you can’t prove it, it’s not knowledge!” and throws the sentence out of the window, pats himself on the back, and calls the place clean; unfortunately, this is not so much solving incompleteness as declaring any inconvenient truth illegal, a bit like running a dictatorship where the official state newspaper defines “truth” as “things we printed,” and then brags about having eliminated misinformation forever—indeed, Olcott’s system is the only formal system in history to achieve total completeness by aggressively evicting all statements that would make it incomplete, thereby proving, once and for all, that if you shrink reality enough, it will fit anywhere.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 15:27 -0600 |
| Message-ID | <10g56va$3qbcp$1@dont-email.me> |
| In reply to | #641081 |
On 11/25/2025 3:12 PM, Python wrote: > Le 25/11/2025 à 22:09, olcott a écrit : >> On 11/25/2025 3:03 PM, Python wrote: >>> Le 25/11/2025 à 22:01, olcott a écrit : >>>> On 11/25/2025 2:56 PM, Python wrote: >>>>> Le 25/11/2025 à 21:20, olcott a écrit : >>>>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>>>> simulated final halt state. >>>>>>>>>> >>>>>>>>>> It has been shown /wth code/ that D simulated by H reaches its >>>>>>>>>> return, >>>>>>>>> >>>>>>>>> Liar, Liar Pants on Fire !!! >>>>>>>> >>>>>>>> I made the code public; another person was able to build and get >>>>>>>> the >>>>>>>> same results. >>>>>>>> >>>>>>>> Yes, it's a growing conspiracy against you, like the whole thing >>>>>>>> about >>>>>>>> the world being round. >>>>>>> >>>>>>> it is kinda nuts how uniformly retarded people are about this >>>>>>> >>>>>> >>>>>> I am working on building a foundation that can be >>>>>> published in a peer reviewed journal. That is only >>>>>> possible because of the excellent feedback that I >>>>>> have received from LLM systems. Every conversation >>>>>> that I have with an LLM system is brand new. This >>>>>> allows me to present my view ever more succinctly. >>>>>> >>>>>> It turns out that my new formal foundation for >>>>>> correct reasoning easily utterly eliminates >>>>>> all undecidability and undefinability and it >>>>>> does this by simply fully integrating semantics >>>>>> syntactically in its formal language. >>>>>> >>>>>> Both Montague Grammar and the CycL language >>>>>> of the Cyc project already do this. >>>>>> >>>>>> Semantic logical entailment is the only inference >>>>>> step. My system basically extends the syllogism >>>>>> to cover the entire body of all knowledge that >>>>>> can be expressed in language. >>>>> >>>>> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >>>>> incompleteness. >>>>> Below is the clear, technical explanation. >>>>> >>>>> 1. What Gödel’s incompleteness theorems actually say >>>>> >>>>> Gödel’s first incompleteness theorem applies to any formal system >>>>> that is: >>>>> >>>>> Recursively axiomatizable (axioms and inference rules can be listed >>>>> by a program), >>>>> >>>>> Consistent, >>>>> >>>>> Sufficiently expressive to encode basic arithmetic (Robinson >>>>> arithmetic Q or stronger). >>>>> >>>>> Then: >>>>> >>>>> There exist true statements of arithmetic that the system cannot >>>>> prove. >>>>> >>>>> No clever notation, ontology language, or knowledge-base trick can >>>>> bypass this, because the theorem is about computability + >>>>> representation of arithmetic, not about the syntax of the language. >>>>> >>>>> Gödel’s second incompleteness theorem says that such a system >>>>> cannot prove its own consistency (again: subject to the above >>>>> conditions). >>>>> >>>>> These results are fully stable under changes of language, ontology, >>>>> semantic layers, etc. >>>>> >>>>> 2. Does CycL avoid incompleteness? >>>>> >>>>> No. CycL is an ontology language used by the Cyc project to encode >>>>> commonsense knowledge using a vast collection of predicates, rules, >>>>> and microtheories. But: >>>>> >>>>> CycL is not a complete formalization of arithmetic. >>>>> Its microtheories intentionally avoid global consistency because >>>>> knowledge is context-dependent. >>>>> >>>>> Cyc as a whole is not a single coherent formal system satisfying >>>>> Gödel’s conditions. >>>>> It is a heterogeneous, context-indexed collection of theories, some >>>>> of which contradict others. >>>>> >>>>> Because it is not a single consistent recursively axiomatizable >>>>> theory, Gödel’s theorems don’t even apply globally—but that does >>>>> not mean Cyc “defeats incompleteness”; it just lives outside the >>>>> scope of the theorem. >>>>> >>>>> Cyc’s strategy is not “beat incompleteness”; it is “use many >>>>> partial microtheories and logical levels contextually”. >>>>> >>>>> This is like saying a library containing many inconsistent books >>>>> “defeats incompleteness” — it does not; it simply is not a single >>>>> formal theory. >>>>> >>>>> Conclusion: >>>>> CycL cannot be used to derive Peano arithmetic in a way that would >>>>> make it complete, and Cyc does not claim otherwise. >>>>> >>>>> 3. Do Peter Olcott’s claims refute incompleteness? >>>>> >>>>> No. Peter Olcott is known online for repeatedly claiming to have >>>>> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >>>>> halting problem. >>>>> His claims are universally rejected by logicians because they >>>>> misunderstand the formal structure of the theorems. >>>>> >>>>> In all variants of his claims: >>>>> >>>>> He proposes procedures that assume access to semantic truth, >>>>> something incompleteness forbids a formal system from capturing >>>>> internally. >>>>> >>>>> Or he proposes recognition algorithms that fail on classic >>>>> diagonal/ self-reference constructions but does not notice the >>>>> failure. >>>>> >>>>> Or he builds systems that are not recursively axiomatizable, and >>>>> therefore Gödel’s theorem does not apply — but then he claims >>>>> “defeat” rather than “dodging the premises”. >>>>> >>>>> The pattern is always: >>>>> >>>>> Change the problem or the assumptions → claim the original theorem >>>>> is wrong. >>>>> >>>>> This is equivalent to saying “I solved the halting problem… for >>>>> programs that I forbid from diagonalizing.” >>>>> That is not a refutation. >>>>> >>>>> 4. Why these approaches cannot refute incompleteness >>>>> >>>>> Gödel incompleteness is a meta-theorem. >>>>> Any attempt to build a complete system for arithmetic must fail >>>>> because: >>>>> >>>>> If the system is algorithmic, there’s a diagonal sentence G such that >>>>> >>>>> If the system is consistent: it cannot prove G. >>>>> >>>> >>>> That is true. >>>> With my system there is one single all encompassing >>>> formal system that contains every element of general >>>> knowledge that can be expressed in language. >>>> >>>> Because the formal language has all semantics fully >>>> integrated into its syntax True(x) is exactly the >>>> same thing as Provable(x). If you can't prove it >>>> then it is not an element of the body of knowledge >>>> that can be expressed in language. >>> >>> The idea of a single, all-encompassing formal system in which every >>> meaningful statement is expressible and in which True(x) ≡ >>> Provable(x) is internally inconsistent, because as soon as the >>> language is expressive enough to contain elementary arithmetic— >>> inevitably required if it is to “contain every element of general >>> knowledge expressible in language”—Gödel’s incompleteness theorem >>> applies, producing well-formed statements that are true in the >>> intended semantics but not provable in the system; >> >> In weaker systems this will remain true. >> >> When True(L,x) is exactly the same thing as Provable(L,x) >> >> because every aspect of all of semantics is directly >> formalized and fully integrated in the formal language >> >> then ~Provable(L,x) means not an element of the body >> of general knowledge that can be expressed in language. >> >>> thus the identification “true = provable” cannot hold unless one >>> either (1) restricts the language so severely that it no longer >>> expresses general knowledge, or (2) accepts a degenerate semantics in >>> which “truth” is redefined to mean “provable in the system,” which >>> merely eliminates semantics and collapses truth into syntactic >>> provability by fiat, yielding a system that cannot describe its own >>> correctness and cannot capture the ordinary notion of truth at all—in >>> short, Olcott’s proposal either violates Gödel or empties “truth” of >>> its usual meaning, and so it cannot simultaneously claim >>> completeness, expressiveness, and a meaningful notion of truth. > > Olcott’s “one perfect formal system containing all knowledge with > True(x) = Provable(x)” works beautifully, provided you never ask it > anything interesting: It literally has the entire body of general knowledge including every book or academic paper every published. > the moment you give it arithmetic, it starts > sweating like a politician in a fact-checking interview, because Gödel > sneaks in through the back door and whispers a sentence the system can’t > prove, whereupon Olcott shouts “If you can’t prove it, it’s not > knowledge!” and throws the sentence out of the window, pats himself on > the back, and calls the place clean; Let's name my formal system so that we can be specific. General_Knowledge. It already knows that G cannot be proved in F. This is an aspect of the body of general knowledge that can be expressed in language. Gödel incompleteness can only exist in systems that divide their syntax from their semantics using model theory. When the semantics is fully integrated into the syntax eliminating any need for model theory, then Gödel incompleteness cannot exist. > unfortunately, this is not so much > solving incompleteness as declaring any inconvenient truth illegal, a > bit like running a dictatorship where the official state newspaper > defines “truth” as “things we printed,” and then brags about having > eliminated misinformation forever—indeed, Olcott’s system is the only > formal system in history to achieve total completeness by aggressively > evicting all statements that would make it incomplete, thereby proving, > once and for all, that if you shrink reality enough, it will fit anywhere. > > This short Prolog shows the error of the Liar Paradox ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. That above means that the Liar Paradox contains a cycle in the directed graph of its evaluation sequence proving that its evaluation remains stuck in an infinite loop and thus can never be resolved. In 2000 years no one has even resolved the Liar Paradox in way that is widely accepted as correct. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> |
|---|---|
| Date | 2025-11-25 13:30 -0800 |
| Message-ID | <10g5764$3q215$1@dont-email.me> |
| In reply to | #641082 |
On 11/25/2025 1:27 PM, olcott wrote: [...] Just make sure that your info base includes facts about yourself. Don't try to wash it off because its permanent.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-25 23:14 +0000 |
| Message-ID | <9B_T055RCkHKVnO2UHiXfBz1bS4@jntp> |
| In reply to | #641082 |
Le 25/11/2025 à 22:27, olcott a écrit : > On 11/25/2025 3:12 PM, Python wrote: >> Le 25/11/2025 à 22:09, olcott a écrit : >>> On 11/25/2025 3:03 PM, Python wrote: >>>> Le 25/11/2025 à 22:01, olcott a écrit : >>>>> On 11/25/2025 2:56 PM, Python wrote: >>>>>> Le 25/11/2025 à 21:20, olcott a écrit : >>>>>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>>>>> simulated final halt state. >>>>>>>>>>> >>>>>>>>>>> It has been shown /wth code/ that D simulated by H reaches its >>>>>>>>>>> return, >>>>>>>>>> >>>>>>>>>> Liar, Liar Pants on Fire !!! >>>>>>>>> >>>>>>>>> I made the code public; another person was able to build and get >>>>>>>>> the >>>>>>>>> same results. >>>>>>>>> >>>>>>>>> Yes, it's a growing conspiracy against you, like the whole thing >>>>>>>>> about >>>>>>>>> the world being round. >>>>>>>> >>>>>>>> it is kinda nuts how uniformly retarded people are about this >>>>>>>> >>>>>>> >>>>>>> I am working on building a foundation that can be >>>>>>> published in a peer reviewed journal. That is only >>>>>>> possible because of the excellent feedback that I >>>>>>> have received from LLM systems. Every conversation >>>>>>> that I have with an LLM system is brand new. This >>>>>>> allows me to present my view ever more succinctly. >>>>>>> >>>>>>> It turns out that my new formal foundation for >>>>>>> correct reasoning easily utterly eliminates >>>>>>> all undecidability and undefinability and it >>>>>>> does this by simply fully integrating semantics >>>>>>> syntactically in its formal language. >>>>>>> >>>>>>> Both Montague Grammar and the CycL language >>>>>>> of the Cyc project already do this. >>>>>>> >>>>>>> Semantic logical entailment is the only inference >>>>>>> step. My system basically extends the syllogism >>>>>>> to cover the entire body of all knowledge that >>>>>>> can be expressed in language. >>>>>> >>>>>> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >>>>>> incompleteness. >>>>>> Below is the clear, technical explanation. >>>>>> >>>>>> 1. What Gödel’s incompleteness theorems actually say >>>>>> >>>>>> Gödel’s first incompleteness theorem applies to any formal system >>>>>> that is: >>>>>> >>>>>> Recursively axiomatizable (axioms and inference rules can be listed >>>>>> by a program), >>>>>> >>>>>> Consistent, >>>>>> >>>>>> Sufficiently expressive to encode basic arithmetic (Robinson >>>>>> arithmetic Q or stronger). >>>>>> >>>>>> Then: >>>>>> >>>>>> There exist true statements of arithmetic that the system cannot >>>>>> prove. >>>>>> >>>>>> No clever notation, ontology language, or knowledge-base trick can >>>>>> bypass this, because the theorem is about computability + >>>>>> representation of arithmetic, not about the syntax of the language. >>>>>> >>>>>> Gödel’s second incompleteness theorem says that such a system >>>>>> cannot prove its own consistency (again: subject to the above >>>>>> conditions). >>>>>> >>>>>> These results are fully stable under changes of language, ontology, >>>>>> semantic layers, etc. >>>>>> >>>>>> 2. Does CycL avoid incompleteness? >>>>>> >>>>>> No. CycL is an ontology language used by the Cyc project to encode >>>>>> commonsense knowledge using a vast collection of predicates, rules, >>>>>> and microtheories. But: >>>>>> >>>>>> CycL is not a complete formalization of arithmetic. >>>>>> Its microtheories intentionally avoid global consistency because >>>>>> knowledge is context-dependent. >>>>>> >>>>>> Cyc as a whole is not a single coherent formal system satisfying >>>>>> Gödel’s conditions. >>>>>> It is a heterogeneous, context-indexed collection of theories, some >>>>>> of which contradict others. >>>>>> >>>>>> Because it is not a single consistent recursively axiomatizable >>>>>> theory, Gödel’s theorems don’t even apply globally—but that does >>>>>> not mean Cyc “defeats incompleteness”; it just lives outside the >>>>>> scope of the theorem. >>>>>> >>>>>> Cyc’s strategy is not “beat incompleteness”; it is “use many >>>>>> partial microtheories and logical levels contextually”. >>>>>> >>>>>> This is like saying a library containing many inconsistent books >>>>>> “defeats incompleteness” — it does not; it simply is not a single >>>>>> formal theory. >>>>>> >>>>>> Conclusion: >>>>>> CycL cannot be used to derive Peano arithmetic in a way that would >>>>>> make it complete, and Cyc does not claim otherwise. >>>>>> >>>>>> 3. Do Peter Olcott’s claims refute incompleteness? >>>>>> >>>>>> No. Peter Olcott is known online for repeatedly claiming to have >>>>>> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >>>>>> halting problem. >>>>>> His claims are universally rejected by logicians because they >>>>>> misunderstand the formal structure of the theorems. >>>>>> >>>>>> In all variants of his claims: >>>>>> >>>>>> He proposes procedures that assume access to semantic truth, >>>>>> something incompleteness forbids a formal system from capturing >>>>>> internally. >>>>>> >>>>>> Or he proposes recognition algorithms that fail on classic >>>>>> diagonal/ self-reference constructions but does not notice the >>>>>> failure. >>>>>> >>>>>> Or he builds systems that are not recursively axiomatizable, and >>>>>> therefore Gödel’s theorem does not apply — but then he claims >>>>>> “defeat” rather than “dodging the premises”. >>>>>> >>>>>> The pattern is always: >>>>>> >>>>>> Change the problem or the assumptions → claim the original theorem >>>>>> is wrong. >>>>>> >>>>>> This is equivalent to saying “I solved the halting problem… for >>>>>> programs that I forbid from diagonalizing.” >>>>>> That is not a refutation. >>>>>> >>>>>> 4. Why these approaches cannot refute incompleteness >>>>>> >>>>>> Gödel incompleteness is a meta-theorem. >>>>>> Any attempt to build a complete system for arithmetic must fail >>>>>> because: >>>>>> >>>>>> If the system is algorithmic, there’s a diagonal sentence G such that >>>>>> >>>>>> If the system is consistent: it cannot prove G. >>>>>> >>>>> >>>>> That is true. >>>>> With my system there is one single all encompassing >>>>> formal system that contains every element of general >>>>> knowledge that can be expressed in language. >>>>> >>>>> Because the formal language has all semantics fully >>>>> integrated into its syntax True(x) is exactly the >>>>> same thing as Provable(x). If you can't prove it >>>>> then it is not an element of the body of knowledge >>>>> that can be expressed in language. >>>> >>>> The idea of a single, all-encompassing formal system in which every >>>> meaningful statement is expressible and in which True(x) ≡ >>>> Provable(x) is internally inconsistent, because as soon as the >>>> language is expressive enough to contain elementary arithmetic— >>>> inevitably required if it is to “contain every element of general >>>> knowledge expressible in language”—Gödel’s incompleteness theorem >>>> applies, producing well-formed statements that are true in the >>>> intended semantics but not provable in the system; >>> >>> In weaker systems this will remain true. >>> >>> When True(L,x) is exactly the same thing as Provable(L,x) >>> >>> because every aspect of all of semantics is directly >>> formalized and fully integrated in the formal language >>> >>> then ~Provable(L,x) means not an element of the body >>> of general knowledge that can be expressed in language. >>> >>>> thus the identification “true = provable” cannot hold unless one >>>> either (1) restricts the language so severely that it no longer >>>> expresses general knowledge, or (2) accepts a degenerate semantics in >>>> which “truth” is redefined to mean “provable in the system,” which >>>> merely eliminates semantics and collapses truth into syntactic >>>> provability by fiat, yielding a system that cannot describe its own >>>> correctness and cannot capture the ordinary notion of truth at all—in >>>> short, Olcott’s proposal either violates Gödel or empties “truth” of >>>> its usual meaning, and so it cannot simultaneously claim >>>> completeness, expressiveness, and a meaningful notion of truth. >> >> Olcott’s “one perfect formal system containing all knowledge with >> True(x) = Provable(x)” works beautifully, provided you never ask it >> anything interesting: > > It literally has the entire body of general knowledge > including every book or academic paper every published. > >> the moment you give it arithmetic, it starts >> sweating like a politician in a fact-checking interview, because Gödel >> sneaks in through the back door and whispers a sentence the system can’t >> prove, whereupon Olcott shouts “If you can’t prove it, it’s not >> knowledge!” and throws the sentence out of the window, pats himself on >> the back, and calls the place clean; > > Let's name my formal system so that we can be specific. > General_Knowledge. It already knows that G cannot be > proved in F. This is an aspect of the body of general > knowledge that can be expressed in language. > > Gödel incompleteness can only exist in systems that divide > their syntax from their semantics using model theory. When > the semantics is fully integrated into the syntax eliminating > any need for model theory, then Gödel incompleteness cannot > exist. > >> unfortunately, this is not so much >> solving incompleteness as declaring any inconvenient truth illegal, a >> bit like running a dictatorship where the official state newspaper >> defines “truth” as “things we printed,” and then brags about having >> eliminated misinformation forever—indeed, Olcott’s system is the only >> formal system in history to achieve total completeness by aggressively >> evicting all statements that would make it incomplete, thereby proving, >> once and for all, that if you shrink reality enough, it will fit anywhere. >> >> > > This short Prolog shows the error of the Liar Paradox > ?- LP = not(true(LP)). > LP = not(true(LP)). > ?- unify_with_occurs_check(LP, not(true(LP))). > false. > > That above means that the Liar Paradox contains > a cycle in the directed graph of its evaluation > sequence proving that its evaluation remains stuck > in an infinite loop and thus can never be resolved. > > In 2000 years no one has even resolved the Liar Paradox > in way that is widely accepted as correct. THE MINISTRY OF PROVABILITY ANNOUNCES THE END OF TRUTH AS WE KNOW IT “If it can’t be proven, it never happened,” says Supreme Formalizer Olcott. The Ministry of Provability is delighted to unveil The One Unified Formal System (TOUFS™), the first and only framework in human history to achieve Total Epistemic Harmony by the revolutionary method of banning all facts that don’t fit. Under the new legislation, Truth(x) = Provable(x) by constitutional decree. Citizens are reminded that any statement not provable within TOUFS™’ 14 axioms (“The Axioms of Perfect Obviousness,” revised weekly) will henceforth be classified as Ungovernable Nonsense and gently escorted outside the Ministry's cognitive perimeter. “We have finally solved Gödel,” announced Minister Olcott at a celebratory press event held in Axiom Chamber #3. “Gödel keeps sending us those confusing, unprovable statements. We now return them marked ‘Incorrect Form – Please Rephrase Within System Limits.’ Problem solved.” When asked whether TOUFS™ could express arithmetic, the Minister smiled warmly and replied: “We discovered arithmetic is dangerously expressive, so we downgraded it to a recreational activity.” Early adopters have praised the system’s clarity: Mathematicians report unprecedented peace of mind, since all difficult theorems have now been reclassified as “Not Real.” Philosophers have been redirected to the Ministry’s Silence Department for failing to produce provable questions. Physicists are adjusting to the new mandate requiring all particles to comply with Axiom 12 (“Everything Behaves Nicely”). A slight controversy arose when an inquisitive intern asked whether the statement “Everything in the system is provable” is itself provable. The Ministry immediately reassigned the intern to the Department of Semantic Recycling, where he is undergoing intensive training in Non-Issues. The Ministry concludes with a reassuring message to all citizens: “TOUFS™ guarantees a future where no truth will ever escape unproven, because unproven truths will no longer exist.” The press conference ended with the ceremonial shredding of Gödel’s incompleteness paper and the unveiling of a large poster reading: “IGNORANCE IS INCONSISTENCY-FREE.”
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 17:21 -0600 |
| Message-ID | <10g5dm8$3stbf$1@dont-email.me> |
| In reply to | #641088 |
On 11/25/2025 5:14 PM, Python wrote: > Le 25/11/2025 à 22:27, olcott a écrit : >> On 11/25/2025 3:12 PM, Python wrote: >>> Le 25/11/2025 à 22:09, olcott a écrit : >>>> On 11/25/2025 3:03 PM, Python wrote: >>>>> Le 25/11/2025 à 22:01, olcott a écrit : >>>>>> On 11/25/2025 2:56 PM, Python wrote: >>>>>>> Le 25/11/2025 à 21:20, olcott a écrit : >>>>>>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>>>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>>>>>> simulated final halt state. >>>>>>>>>>>> >>>>>>>>>>>> It has been shown /wth code/ that D simulated by H reaches >>>>>>>>>>>> its return, >>>>>>>>>>> >>>>>>>>>>> Liar, Liar Pants on Fire !!! >>>>>>>>>> >>>>>>>>>> I made the code public; another person was able to build and >>>>>>>>>> get the >>>>>>>>>> same results. >>>>>>>>>> >>>>>>>>>> Yes, it's a growing conspiracy against you, like the whole >>>>>>>>>> thing about >>>>>>>>>> the world being round. >>>>>>>>> >>>>>>>>> it is kinda nuts how uniformly retarded people are about this >>>>>>>>> >>>>>>>> >>>>>>>> I am working on building a foundation that can be >>>>>>>> published in a peer reviewed journal. That is only >>>>>>>> possible because of the excellent feedback that I >>>>>>>> have received from LLM systems. Every conversation >>>>>>>> that I have with an LLM system is brand new. This >>>>>>>> allows me to present my view ever more succinctly. >>>>>>>> >>>>>>>> It turns out that my new formal foundation for >>>>>>>> correct reasoning easily utterly eliminates >>>>>>>> all undecidability and undefinability and it >>>>>>>> does this by simply fully integrating semantics >>>>>>>> syntactically in its formal language. >>>>>>>> >>>>>>>> Both Montague Grammar and the CycL language >>>>>>>> of the Cyc project already do this. >>>>>>>> >>>>>>>> Semantic logical entailment is the only inference >>>>>>>> step. My system basically extends the syllogism >>>>>>>> to cover the entire body of all knowledge that >>>>>>>> can be expressed in language. >>>>>>> >>>>>>> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >>>>>>> incompleteness. >>>>>>> Below is the clear, technical explanation. >>>>>>> >>>>>>> 1. What Gödel’s incompleteness theorems actually say >>>>>>> >>>>>>> Gödel’s first incompleteness theorem applies to any formal system >>>>>>> that is: >>>>>>> >>>>>>> Recursively axiomatizable (axioms and inference rules can be >>>>>>> listed by a program), >>>>>>> >>>>>>> Consistent, >>>>>>> >>>>>>> Sufficiently expressive to encode basic arithmetic (Robinson >>>>>>> arithmetic Q or stronger). >>>>>>> >>>>>>> Then: >>>>>>> >>>>>>> There exist true statements of arithmetic that the system cannot >>>>>>> prove. >>>>>>> >>>>>>> No clever notation, ontology language, or knowledge-base trick >>>>>>> can bypass this, because the theorem is about computability + >>>>>>> representation of arithmetic, not about the syntax of the language. >>>>>>> >>>>>>> Gödel’s second incompleteness theorem says that such a system >>>>>>> cannot prove its own consistency (again: subject to the above >>>>>>> conditions). >>>>>>> >>>>>>> These results are fully stable under changes of language, >>>>>>> ontology, semantic layers, etc. >>>>>>> >>>>>>> 2. Does CycL avoid incompleteness? >>>>>>> >>>>>>> No. CycL is an ontology language used by the Cyc project to >>>>>>> encode commonsense knowledge using a vast collection of >>>>>>> predicates, rules, and microtheories. But: >>>>>>> >>>>>>> CycL is not a complete formalization of arithmetic. >>>>>>> Its microtheories intentionally avoid global consistency because >>>>>>> knowledge is context-dependent. >>>>>>> >>>>>>> Cyc as a whole is not a single coherent formal system satisfying >>>>>>> Gödel’s conditions. >>>>>>> It is a heterogeneous, context-indexed collection of theories, >>>>>>> some of which contradict others. >>>>>>> >>>>>>> Because it is not a single consistent recursively axiomatizable >>>>>>> theory, Gödel’s theorems don’t even apply globally—but that does >>>>>>> not mean Cyc “defeats incompleteness”; it just lives outside the >>>>>>> scope of the theorem. >>>>>>> >>>>>>> Cyc’s strategy is not “beat incompleteness”; it is “use many >>>>>>> partial microtheories and logical levels contextually”. >>>>>>> >>>>>>> This is like saying a library containing many inconsistent books >>>>>>> “defeats incompleteness” — it does not; it simply is not a single >>>>>>> formal theory. >>>>>>> >>>>>>> Conclusion: >>>>>>> CycL cannot be used to derive Peano arithmetic in a way that >>>>>>> would make it complete, and Cyc does not claim otherwise. >>>>>>> >>>>>>> 3. Do Peter Olcott’s claims refute incompleteness? >>>>>>> >>>>>>> No. Peter Olcott is known online for repeatedly claiming to have >>>>>>> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >>>>>>> halting problem. >>>>>>> His claims are universally rejected by logicians because they >>>>>>> misunderstand the formal structure of the theorems. >>>>>>> >>>>>>> In all variants of his claims: >>>>>>> >>>>>>> He proposes procedures that assume access to semantic truth, >>>>>>> something incompleteness forbids a formal system from capturing >>>>>>> internally. >>>>>>> >>>>>>> Or he proposes recognition algorithms that fail on classic >>>>>>> diagonal/ self-reference constructions but does not notice the >>>>>>> failure. >>>>>>> >>>>>>> Or he builds systems that are not recursively axiomatizable, and >>>>>>> therefore Gödel’s theorem does not apply — but then he claims >>>>>>> “defeat” rather than “dodging the premises”. >>>>>>> >>>>>>> The pattern is always: >>>>>>> >>>>>>> Change the problem or the assumptions → claim the original >>>>>>> theorem is wrong. >>>>>>> >>>>>>> This is equivalent to saying “I solved the halting problem… for >>>>>>> programs that I forbid from diagonalizing.” >>>>>>> That is not a refutation. >>>>>>> >>>>>>> 4. Why these approaches cannot refute incompleteness >>>>>>> >>>>>>> Gödel incompleteness is a meta-theorem. >>>>>>> Any attempt to build a complete system for arithmetic must fail >>>>>>> because: >>>>>>> >>>>>>> If the system is algorithmic, there’s a diagonal sentence G such >>>>>>> that >>>>>>> >>>>>>> If the system is consistent: it cannot prove G. >>>>>>> >>>>>> >>>>>> That is true. >>>>>> With my system there is one single all encompassing >>>>>> formal system that contains every element of general >>>>>> knowledge that can be expressed in language. >>>>>> >>>>>> Because the formal language has all semantics fully >>>>>> integrated into its syntax True(x) is exactly the >>>>>> same thing as Provable(x). If you can't prove it >>>>>> then it is not an element of the body of knowledge >>>>>> that can be expressed in language. >>>>> >>>>> The idea of a single, all-encompassing formal system in which every >>>>> meaningful statement is expressible and in which True(x) ≡ >>>>> Provable(x) is internally inconsistent, because as soon as the >>>>> language is expressive enough to contain elementary arithmetic— >>>>> inevitably required if it is to “contain every element of general >>>>> knowledge expressible in language”—Gödel’s incompleteness theorem >>>>> applies, producing well-formed statements that are true in the >>>>> intended semantics but not provable in the system; >>>> >>>> In weaker systems this will remain true. >>>> >>>> When True(L,x) is exactly the same thing as Provable(L,x) >>>> >>>> because every aspect of all of semantics is directly >>>> formalized and fully integrated in the formal language >>>> >>>> then ~Provable(L,x) means not an element of the body >>>> of general knowledge that can be expressed in language. >>>> >>>>> thus the identification “true = provable” cannot hold unless one >>>>> either (1) restricts the language so severely that it no longer >>>>> expresses general knowledge, or (2) accepts a degenerate semantics >>>>> in which “truth” is redefined to mean “provable in the system,” >>>>> which merely eliminates semantics and collapses truth into >>>>> syntactic provability by fiat, yielding a system that cannot >>>>> describe its own correctness and cannot capture the ordinary notion >>>>> of truth at all—in short, Olcott’s proposal either violates Gödel >>>>> or empties “truth” of its usual meaning, and so it cannot >>>>> simultaneously claim completeness, expressiveness, and a meaningful >>>>> notion of truth. >>> >>> Olcott’s “one perfect formal system containing all knowledge with >>> True(x) = Provable(x)” works beautifully, provided you never ask it >>> anything interesting: >> >> It literally has the entire body of general knowledge >> including every book or academic paper every published. >> >>> the moment you give it arithmetic, it starts sweating like a >>> politician in a fact-checking interview, because Gödel sneaks in >>> through the back door and whispers a sentence the system can’t prove, >>> whereupon Olcott shouts “If you can’t prove it, it’s not knowledge!” >>> and throws the sentence out of the window, pats himself on the back, >>> and calls the place clean; >> >> Let's name my formal system so that we can be specific. >> General_Knowledge. It already knows that G cannot be >> proved in F. This is an aspect of the body of general >> knowledge that can be expressed in language. >> >> Gödel incompleteness can only exist in systems that divide >> their syntax from their semantics using model theory. When >> the semantics is fully integrated into the syntax eliminating >> any need for model theory, then Gödel incompleteness cannot >> exist. >> >>> unfortunately, this is not so much solving incompleteness as >>> declaring any inconvenient truth illegal, a bit like running a >>> dictatorship where the official state newspaper defines “truth” as >>> “things we printed,” and then brags about having eliminated >>> misinformation forever—indeed, Olcott’s system is the only formal >>> system in history to achieve total completeness by aggressively >>> evicting all statements that would make it incomplete, thereby >>> proving, once and for all, that if you shrink reality enough, it will >>> fit anywhere. >>> >>> >> >> This short Prolog shows the error of the Liar Paradox >> ?- LP = not(true(LP)). >> LP = not(true(LP)). >> ?- unify_with_occurs_check(LP, not(true(LP))). >> false. >> >> That above means that the Liar Paradox contains >> a cycle in the directed graph of its evaluation >> sequence proving that its evaluation remains stuck >> in an infinite loop and thus can never be resolved. >> >> In 2000 years no one has even resolved the Liar Paradox >> in way that is widely accepted as correct. > > THE MINISTRY OF PROVABILITY ANNOUNCES THE END OF TRUTH AS WE KNOW IT > “If it can’t be proven, it never happened,” says Supreme Formalizer Olcott. > > The Ministry of Provability is delighted to unveil The One Unified > Formal System (TOUFS™), the first and only framework in human history to > achieve Total Epistemic Harmony by the revolutionary method of banning > all facts that don’t fit. > > Under the new legislation, Truth(x) = Provable(x) by constitutional > decree. Citizens are reminded that any statement not provable within > TOUFS™’ 14 axioms (“The Axioms of Perfect Obviousness,” revised weekly) > will henceforth be classified as Ungovernable Nonsense and gently > escorted outside the Ministry's cognitive perimeter. > > “We have finally solved Gödel,” announced Minister Olcott at a > celebratory press event held in Axiom Chamber #3. “Gödel keeps sending > us those confusing, unprovable statements. We now return them marked > ‘Incorrect Form – Please Rephrase Within System Limits.’ Problem solved.” > > When asked whether TOUFS™ could express arithmetic, the Minister smiled > warmly and replied: > “We discovered arithmetic is dangerously expressive, so we downgraded it > to a recreational activity.” > > Early adopters have praised the system’s clarity: > > Mathematicians report unprecedented peace of mind, since all difficult > theorems have now been reclassified as “Not Real.” > > Philosophers have been redirected to the Ministry’s Silence Department > for failing to produce provable questions. > > Physicists are adjusting to the new mandate requiring all particles to > comply with Axiom 12 (“Everything Behaves Nicely”). > > A slight controversy arose when an inquisitive intern asked whether the > statement “Everything in the system is provable” is itself provable. The > Ministry immediately reassigned the intern to the Department of Semantic > Recycling, where he is undergoing intensive training in Non-Issues. > > The Ministry concludes with a reassuring message to all citizens: > > “TOUFS™ guarantees a future where no truth will ever escape unproven, > because unproven truths will no longer exist.” > > The press conference ended with the ceremonial shredding of Gödel’s > incompleteness paper and the unveiling of a large poster reading: > > “IGNORANCE IS INCONSISTENCY-FREE.” Gödel incompleteness can only exist in systems that divide their syntax from their semantics using model theory. When the semantics is fully integrated into the syntax eliminating any need for model theory, then Gödel incompleteness cannot exist. Semantic logical entailment from a finite set of atomic facts is airtight. *I have thought this over again and again for a decade* Try and find an actual error. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-25 23:25 +0000 |
| Message-ID | <bHAQT2gxJsBPDz1qNjbEUaf9IUU@jntp> |
| In reply to | #641090 |
Le 26/11/2025 à 00:21, olcott a écrit : > On 11/25/2025 5:14 PM, Python wrote: >> Le 25/11/2025 à 22:27, olcott a écrit : >>> On 11/25/2025 3:12 PM, Python wrote: >>>> Le 25/11/2025 à 22:09, olcott a écrit : >>>>> On 11/25/2025 3:03 PM, Python wrote: >>>>>> Le 25/11/2025 à 22:01, olcott a écrit : >>>>>>> On 11/25/2025 2:56 PM, Python wrote: >>>>>>>> Le 25/11/2025 à 21:20, olcott a écrit : >>>>>>>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>>>>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>>>>>>> simulated final halt state. >>>>>>>>>>>>> >>>>>>>>>>>>> It has been shown /wth code/ that D simulated by H reaches >>>>>>>>>>>>> its return, >>>>>>>>>>>> >>>>>>>>>>>> Liar, Liar Pants on Fire !!! >>>>>>>>>>> >>>>>>>>>>> I made the code public; another person was able to build and >>>>>>>>>>> get the >>>>>>>>>>> same results. >>>>>>>>>>> >>>>>>>>>>> Yes, it's a growing conspiracy against you, like the whole >>>>>>>>>>> thing about >>>>>>>>>>> the world being round. >>>>>>>>>> >>>>>>>>>> it is kinda nuts how uniformly retarded people are about this >>>>>>>>>> >>>>>>>>> >>>>>>>>> I am working on building a foundation that can be >>>>>>>>> published in a peer reviewed journal. That is only >>>>>>>>> possible because of the excellent feedback that I >>>>>>>>> have received from LLM systems. Every conversation >>>>>>>>> that I have with an LLM system is brand new. This >>>>>>>>> allows me to present my view ever more succinctly. >>>>>>>>> >>>>>>>>> It turns out that my new formal foundation for >>>>>>>>> correct reasoning easily utterly eliminates >>>>>>>>> all undecidability and undefinability and it >>>>>>>>> does this by simply fully integrating semantics >>>>>>>>> syntactically in its formal language. >>>>>>>>> >>>>>>>>> Both Montague Grammar and the CycL language >>>>>>>>> of the Cyc project already do this. >>>>>>>>> >>>>>>>>> Semantic logical entailment is the only inference >>>>>>>>> step. My system basically extends the syllogism >>>>>>>>> to cover the entire body of all knowledge that >>>>>>>>> can be expressed in language. >>>>>>>> >>>>>>>> Neither CycL nor Peter Olcott’s claims refute Gödel-style logical >>>>>>>> incompleteness. >>>>>>>> Below is the clear, technical explanation. >>>>>>>> >>>>>>>> 1. What Gödel’s incompleteness theorems actually say >>>>>>>> >>>>>>>> Gödel’s first incompleteness theorem applies to any formal system >>>>>>>> that is: >>>>>>>> >>>>>>>> Recursively axiomatizable (axioms and inference rules can be >>>>>>>> listed by a program), >>>>>>>> >>>>>>>> Consistent, >>>>>>>> >>>>>>>> Sufficiently expressive to encode basic arithmetic (Robinson >>>>>>>> arithmetic Q or stronger). >>>>>>>> >>>>>>>> Then: >>>>>>>> >>>>>>>> There exist true statements of arithmetic that the system cannot >>>>>>>> prove. >>>>>>>> >>>>>>>> No clever notation, ontology language, or knowledge-base trick >>>>>>>> can bypass this, because the theorem is about computability + >>>>>>>> representation of arithmetic, not about the syntax of the language. >>>>>>>> >>>>>>>> Gödel’s second incompleteness theorem says that such a system >>>>>>>> cannot prove its own consistency (again: subject to the above >>>>>>>> conditions). >>>>>>>> >>>>>>>> These results are fully stable under changes of language, >>>>>>>> ontology, semantic layers, etc. >>>>>>>> >>>>>>>> 2. Does CycL avoid incompleteness? >>>>>>>> >>>>>>>> No. CycL is an ontology language used by the Cyc project to >>>>>>>> encode commonsense knowledge using a vast collection of >>>>>>>> predicates, rules, and microtheories. But: >>>>>>>> >>>>>>>> CycL is not a complete formalization of arithmetic. >>>>>>>> Its microtheories intentionally avoid global consistency because >>>>>>>> knowledge is context-dependent. >>>>>>>> >>>>>>>> Cyc as a whole is not a single coherent formal system satisfying >>>>>>>> Gödel’s conditions. >>>>>>>> It is a heterogeneous, context-indexed collection of theories, >>>>>>>> some of which contradict others. >>>>>>>> >>>>>>>> Because it is not a single consistent recursively axiomatizable >>>>>>>> theory, Gödel’s theorems don’t even apply globally—but that does >>>>>>>> not mean Cyc “defeats incompleteness”; it just lives outside the >>>>>>>> scope of the theorem. >>>>>>>> >>>>>>>> Cyc’s strategy is not “beat incompleteness”; it is “use many >>>>>>>> partial microtheories and logical levels contextually”. >>>>>>>> >>>>>>>> This is like saying a library containing many inconsistent books >>>>>>>> “defeats incompleteness” — it does not; it simply is not a single >>>>>>>> formal theory. >>>>>>>> >>>>>>>> Conclusion: >>>>>>>> CycL cannot be used to derive Peano arithmetic in a way that >>>>>>>> would make it complete, and Cyc does not claim otherwise. >>>>>>>> >>>>>>>> 3. Do Peter Olcott’s claims refute incompleteness? >>>>>>>> >>>>>>>> No. Peter Olcott is known online for repeatedly claiming to have >>>>>>>> “resolved” or “invalidated” Gödel’s incompleteness or Turing’s >>>>>>>> halting problem. >>>>>>>> His claims are universally rejected by logicians because they >>>>>>>> misunderstand the formal structure of the theorems. >>>>>>>> >>>>>>>> In all variants of his claims: >>>>>>>> >>>>>>>> He proposes procedures that assume access to semantic truth, >>>>>>>> something incompleteness forbids a formal system from capturing >>>>>>>> internally. >>>>>>>> >>>>>>>> Or he proposes recognition algorithms that fail on classic >>>>>>>> diagonal/ self-reference constructions but does not notice the >>>>>>>> failure. >>>>>>>> >>>>>>>> Or he builds systems that are not recursively axiomatizable, and >>>>>>>> therefore Gödel’s theorem does not apply — but then he claims >>>>>>>> “defeat” rather than “dodging the premises”. >>>>>>>> >>>>>>>> The pattern is always: >>>>>>>> >>>>>>>> Change the problem or the assumptions → claim the original >>>>>>>> theorem is wrong. >>>>>>>> >>>>>>>> This is equivalent to saying “I solved the halting problem… for >>>>>>>> programs that I forbid from diagonalizing.” >>>>>>>> That is not a refutation. >>>>>>>> >>>>>>>> 4. Why these approaches cannot refute incompleteness >>>>>>>> >>>>>>>> Gödel incompleteness is a meta-theorem. >>>>>>>> Any attempt to build a complete system for arithmetic must fail >>>>>>>> because: >>>>>>>> >>>>>>>> If the system is algorithmic, there’s a diagonal sentence G such >>>>>>>> that >>>>>>>> >>>>>>>> If the system is consistent: it cannot prove G. >>>>>>>> >>>>>>> >>>>>>> That is true. >>>>>>> With my system there is one single all encompassing >>>>>>> formal system that contains every element of general >>>>>>> knowledge that can be expressed in language. >>>>>>> >>>>>>> Because the formal language has all semantics fully >>>>>>> integrated into its syntax True(x) is exactly the >>>>>>> same thing as Provable(x). If you can't prove it >>>>>>> then it is not an element of the body of knowledge >>>>>>> that can be expressed in language. >>>>>> >>>>>> The idea of a single, all-encompassing formal system in which every >>>>>> meaningful statement is expressible and in which True(x) ≡ >>>>>> Provable(x) is internally inconsistent, because as soon as the >>>>>> language is expressive enough to contain elementary arithmetic— >>>>>> inevitably required if it is to “contain every element of general >>>>>> knowledge expressible in language”—Gödel’s incompleteness theorem >>>>>> applies, producing well-formed statements that are true in the >>>>>> intended semantics but not provable in the system; >>>>> >>>>> In weaker systems this will remain true. >>>>> >>>>> When True(L,x) is exactly the same thing as Provable(L,x) >>>>> >>>>> because every aspect of all of semantics is directly >>>>> formalized and fully integrated in the formal language >>>>> >>>>> then ~Provable(L,x) means not an element of the body >>>>> of general knowledge that can be expressed in language. >>>>> >>>>>> thus the identification “true = provable” cannot hold unless one >>>>>> either (1) restricts the language so severely that it no longer >>>>>> expresses general knowledge, or (2) accepts a degenerate semantics >>>>>> in which “truth” is redefined to mean “provable in the system,” >>>>>> which merely eliminates semantics and collapses truth into >>>>>> syntactic provability by fiat, yielding a system that cannot >>>>>> describe its own correctness and cannot capture the ordinary notion >>>>>> of truth at all—in short, Olcott’s proposal either violates Gödel >>>>>> or empties “truth” of its usual meaning, and so it cannot >>>>>> simultaneously claim completeness, expressiveness, and a meaningful >>>>>> notion of truth. >>>> >>>> Olcott’s “one perfect formal system containing all knowledge with >>>> True(x) = Provable(x)” works beautifully, provided you never ask it >>>> anything interesting: >>> >>> It literally has the entire body of general knowledge >>> including every book or academic paper every published. >>> >>>> the moment you give it arithmetic, it starts sweating like a >>>> politician in a fact-checking interview, because Gödel sneaks in >>>> through the back door and whispers a sentence the system can’t prove, >>>> whereupon Olcott shouts “If you can’t prove it, it’s not knowledge!” >>>> and throws the sentence out of the window, pats himself on the back, >>>> and calls the place clean; >>> >>> Let's name my formal system so that we can be specific. >>> General_Knowledge. It already knows that G cannot be >>> proved in F. This is an aspect of the body of general >>> knowledge that can be expressed in language. >>> >>> Gödel incompleteness can only exist in systems that divide >>> their syntax from their semantics using model theory. When >>> the semantics is fully integrated into the syntax eliminating >>> any need for model theory, then Gödel incompleteness cannot >>> exist. >>> >>>> unfortunately, this is not so much solving incompleteness as >>>> declaring any inconvenient truth illegal, a bit like running a >>>> dictatorship where the official state newspaper defines “truth” as >>>> “things we printed,” and then brags about having eliminated >>>> misinformation forever—indeed, Olcott’s system is the only formal >>>> system in history to achieve total completeness by aggressively >>>> evicting all statements that would make it incomplete, thereby >>>> proving, once and for all, that if you shrink reality enough, it will >>>> fit anywhere. >>>> >>>> >>> >>> This short Prolog shows the error of the Liar Paradox >>> ?- LP = not(true(LP)). >>> LP = not(true(LP)). >>> ?- unify_with_occurs_check(LP, not(true(LP))). >>> false. >>> >>> That above means that the Liar Paradox contains >>> a cycle in the directed graph of its evaluation >>> sequence proving that its evaluation remains stuck >>> in an infinite loop and thus can never be resolved. >>> >>> In 2000 years no one has even resolved the Liar Paradox >>> in way that is widely accepted as correct. >> >> THE MINISTRY OF PROVABILITY ANNOUNCES THE END OF TRUTH AS WE KNOW IT >> “If it can’t be proven, it never happened,” says Supreme Formalizer >> Olcott. >> >> The Ministry of Provability is delighted to unveil The One Unified >> Formal System (TOUFS™), the first and only framework in human history to >> achieve Total Epistemic Harmony by the revolutionary method of banning >> all facts that don’t fit. >> >> Under the new legislation, Truth(x) = Provable(x) by constitutional >> decree. Citizens are reminded that any statement not provable within >> TOUFS™’ 14 axioms (“The Axioms of Perfect Obviousness,” revised weekly) >> will henceforth be classified as Ungovernable Nonsense and gently >> escorted outside the Ministry's cognitive perimeter. >> >> “We have finally solved Gödel,” announced Minister Olcott at a >> celebratory press event held in Axiom Chamber #3. “Gödel keeps sending >> us those confusing, unprovable statements. We now return them marked >> ‘Incorrect Form – Please Rephrase Within System Limits.’ Problem >> solved.” >> >> When asked whether TOUFS™ could express arithmetic, the Minister smiled >> warmly and replied: >> “We discovered arithmetic is dangerously expressive, so we downgraded it >> to a recreational activity.” >> >> Early adopters have praised the system’s clarity: >> >> Mathematicians report unprecedented peace of mind, since all difficult >> theorems have now been reclassified as “Not Real.” >> >> Philosophers have been redirected to the Ministry’s Silence Department >> for failing to produce provable questions. >> >> Physicists are adjusting to the new mandate requiring all particles to >> comply with Axiom 12 (“Everything Behaves Nicely”). >> >> A slight controversy arose when an inquisitive intern asked whether the >> statement “Everything in the system is provable” is itself provable. The >> Ministry immediately reassigned the intern to the Department of Semantic >> Recycling, where he is undergoing intensive training in Non-Issues. >> >> The Ministry concludes with a reassuring message to all citizens: >> >> “TOUFS™ guarantees a future where no truth will ever escape unproven, >> because unproven truths will no longer exist.” >> >> The press conference ended with the ceremonial shredding of Gödel’s >> incompleteness paper and the unveiling of a large poster reading: >> >> “IGNORANCE IS INCONSISTENCY-FREE.” > > > Gödel incompleteness can only exist in systems that divide > their syntax from their semantics using model theory. When > the semantics is fully integrated into the syntax eliminating > any need for model theory, then Gödel incompleteness cannot > exist. > > Semantic logical entailment from a finite set of atomic > facts is airtight. > > *I have thought this over again and again for a decade* > Try and find an actual error. 1. Gödel incompleteness does not rely on model theory or a syntax/semantics split You say: Gödel incompleteness can only exist in systems that divide their syntax from their semantics using model theory. When the semantics is fully integrated into the syntax eliminating any need for model theory, then Gödel incompleteness cannot exist. This is just false historically and technically. Gödel’s 1931 incompleteness proof is almost entirely syntactic. He arithmetizes formulas and proofs, builds a sentence that says “I am not provable in this system,” and then proves: if the system is consistent, it cannot prove that sentence, nor its negation (under reasonable soundness assumptions). No model theory, no semantic consequence, no “external semantics” is required for the construction of the Gödel sentence. So incompleteness does not depend on a prior split between syntax and semantics. It applies to: any effectively axiomatized, sufficiently expressive, consistent system, regardless of how you talk about semantics. Your claim “it only exists when syntax and semantics are divided” is just wrong: syntax alone is already enough to generate the incompleteness phenomenon. 2. “Integrating semantics into syntax” in the way you propose is impossible (Tarski kicks the door in) You’re essentially proposing: There is a single formal system S such that – every element of “general knowledge expressible in language” is a sentence of S; – there is a predicate True(x) inside the same system such that True(⌜φ⌝) ↔ φ for every sentence φ; – and moreover True(x) = Provable(x). But: Tarski’s undefinability of truth says: in a sufficiently strong arithmetic language, there is no formula True(x) in that same language that correctly satisfies True(⌜φ⌝) ↔ φ for all sentences φ of that language. If you try, you get the liar-style paradox and inconsistency. So you cannot have a genuine internal truth predicate for “all sentences of this language” that is both: expressible in the language, and extensionally correct about all sentences. If you dodge this by decree: “OK, we define True(x) to mean Provable(x).” Then you haven’t “integrated semantics into syntax”; you’ve redefined truth as provability. That’s just a syntactic predicate wearing semantic perfume. If your system is sound but recursively axiomatized, then by Gödel there are true-but-unprovable sentences, so “True(x) = Provable(x)” is false extensionally. If you force “True = Provable” by definition, then your “truth” is no longer about the world or about standard arithmetic; it’s just “belongs to the theorem set of S.” That’s the second big error: you assume that you can have an internal predicate that both (a) behaves like real truth over “all general knowledge expressible in language” and (b) equals provability. Tarski + Gödel together say: no, you can’t. 3. “Semantic entailment from a finite set of atomic facts is airtight” is irrelevant to your grand claim You say: Semantic logical entailment from a finite set of atomic facts is airtight. Sure. From a finite set of atomic facts in a finite relational structure, semantic consequence is straightforward and even decidable. But that has almost nothing to do with your earlier claim: You’re not proposing “a finite database with first-order consequences.” You’re proposing one all-encompassing system for all general knowledge (which will necessarily involve arithmetic, infinity, etc.). In such a system: The “set of atomic facts” cannot be finite or even recursively decidable in general if it’s supposed to match “all true statements of arithmetic,” because the set of true arithmetic sentences is not recursively enumerable. So your “airtight semantic entailment from a finite base” applies only to a trivial fragment, not to the system you actually want. So the third error is a kind of bait-and-switch: you appeal to the safety of tiny finite-model entailment and then quietly promote that intuition to “all general knowledge,” where it simply doesn’t scale. In one sentence Your position hinges on three false assumptions: that Gödel incompleteness only arises when syntax and semantics are separated via model theory (no: the original proof is purely syntactic); that you can have an internal truth predicate for the same language which is both extensionally correct about all its sentences and identical to provability (no: Tarski and Gödel jointly rule this out); that the nice behavior of semantic entailment from a finite base somehow extends to a single system capturing all “general knowledge” including arithmetic (no: that’s where undecidability and incompleteness live). You can have “True(x) = Provable(x)”—but only by changing what “true” means so radically that you’re no longer talking about truth in any ordinary or semantic sense. That’s not beating Gödel; that’s walking off the playing field and declaring victory.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 18:00 -0600 |
| Message-ID | <10g5fv8$3tnku$1@dont-email.me> |
| In reply to | #641091 |
On 11/25/2025 5:25 PM, Python wrote: > Le 26/11/2025 à 00:21, olcott a écrit : >> On 11/25/2025 5:14 PM, Python wrote: >>> Le 25/11/2025 à 22:27, olcott a écrit : >>>> On 11/25/2025 3:12 PM, Python wrote: >>>>> Le 25/11/2025 à 22:09, olcott a écrit : >>>>>> On 11/25/2025 3:03 PM, Python wrote: >>>>>>> Le 25/11/2025 à 22:01, olcott a écrit : >>>>>>>> On 11/25/2025 2:56 PM, Python wrote: >>>>>>>>> Le 25/11/2025 à 21:20, olcott a écrit : >>>>>>>>>> On 11/25/2025 2:05 PM, dart200 wrote: >>>>>>>>>>> On 11/25/25 10:46 AM, Kaz Kylheku wrote: >>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>> On 11/25/2025 11:42 AM, Kaz Kylheku wrote: >>>>>>>>>>>>>> On 2025-11-06, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> D simulated by H cannot possibly reach its own >>>>>>>>>>>>>>> simulated final halt state. >>>>>>>>>>>>>> >>>>>>>>>>>>>> It has been shown /wth code/ that D simulated by H reaches >>>>>>>>>>>>>> its return, >>>>>>>>>>>>> >>>>>>>>>>>>> Liar, Liar Pants on Fire !!! >>>>>>>>>>>> >>>>>>>>>>>> I made the code public; another person was able to build and >>>>>>>>>>>> get the >>>>>>>>>>>> same results. >>>>>>>>>>>> >>>>>>>>>>>> Yes, it's a growing conspiracy against you, like the whole >>>>>>>>>>>> thing about >>>>>>>>>>>> the world being round. >>>>>>>>>>> >>>>>>>>>>> it is kinda nuts how uniformly retarded people are about this >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> I am working on building a foundation that can be >>>>>>>>>> published in a peer reviewed journal. That is only >>>>>>>>>> possible because of the excellent feedback that I >>>>>>>>>> have received from LLM systems. Every conversation >>>>>>>>>> that I have with an LLM system is brand new. This >>>>>>>>>> allows me to present my view ever more succinctly. >>>>>>>>>> >>>>>>>>>> It turns out that my new formal foundation for >>>>>>>>>> correct reasoning easily utterly eliminates >>>>>>>>>> all undecidability and undefinability and it >>>>>>>>>> does this by simply fully integrating semantics >>>>>>>>>> syntactically in its formal language. >>>>>>>>>> >>>>>>>>>> Both Montague Grammar and the CycL language >>>>>>>>>> of the Cyc project already do this. >>>>>>>>>> >>>>>>>>>> Semantic logical entailment is the only inference >>>>>>>>>> step. My system basically extends the syllogism >>>>>>>>>> to cover the entire body of all knowledge that >>>>>>>>>> can be expressed in language. >>>>>>>>> >>>>>>>>> Neither CycL nor Peter Olcott’s claims refute Gödel-style >>>>>>>>> logical incompleteness. >>>>>>>>> Below is the clear, technical explanation. >>>>>>>>> >>>>>>>>> 1. What Gödel’s incompleteness theorems actually say >>>>>>>>> >>>>>>>>> Gödel’s first incompleteness theorem applies to any formal >>>>>>>>> system that is: >>>>>>>>> >>>>>>>>> Recursively axiomatizable (axioms and inference rules can be >>>>>>>>> listed by a program), >>>>>>>>> >>>>>>>>> Consistent, >>>>>>>>> >>>>>>>>> Sufficiently expressive to encode basic arithmetic (Robinson >>>>>>>>> arithmetic Q or stronger). >>>>>>>>> >>>>>>>>> Then: >>>>>>>>> >>>>>>>>> There exist true statements of arithmetic that the system >>>>>>>>> cannot prove. >>>>>>>>> >>>>>>>>> No clever notation, ontology language, or knowledge-base trick >>>>>>>>> can bypass this, because the theorem is about computability + >>>>>>>>> representation of arithmetic, not about the syntax of the >>>>>>>>> language. >>>>>>>>> >>>>>>>>> Gödel’s second incompleteness theorem says that such a system >>>>>>>>> cannot prove its own consistency (again: subject to the above >>>>>>>>> conditions). >>>>>>>>> >>>>>>>>> These results are fully stable under changes of language, >>>>>>>>> ontology, semantic layers, etc. >>>>>>>>> >>>>>>>>> 2. Does CycL avoid incompleteness? >>>>>>>>> >>>>>>>>> No. CycL is an ontology language used by the Cyc project to >>>>>>>>> encode commonsense knowledge using a vast collection of >>>>>>>>> predicates, rules, and microtheories. But: >>>>>>>>> >>>>>>>>> CycL is not a complete formalization of arithmetic. >>>>>>>>> Its microtheories intentionally avoid global consistency >>>>>>>>> because knowledge is context-dependent. >>>>>>>>> >>>>>>>>> Cyc as a whole is not a single coherent formal system >>>>>>>>> satisfying Gödel’s conditions. >>>>>>>>> It is a heterogeneous, context-indexed collection of theories, >>>>>>>>> some of which contradict others. >>>>>>>>> >>>>>>>>> Because it is not a single consistent recursively axiomatizable >>>>>>>>> theory, Gödel’s theorems don’t even apply globally—but that >>>>>>>>> does not mean Cyc “defeats incompleteness”; it just lives >>>>>>>>> outside the scope of the theorem. >>>>>>>>> >>>>>>>>> Cyc’s strategy is not “beat incompleteness”; it is “use many >>>>>>>>> partial microtheories and logical levels contextually”. >>>>>>>>> >>>>>>>>> This is like saying a library containing many inconsistent >>>>>>>>> books “defeats incompleteness” — it does not; it simply is not >>>>>>>>> a single formal theory. >>>>>>>>> >>>>>>>>> Conclusion: >>>>>>>>> CycL cannot be used to derive Peano arithmetic in a way that >>>>>>>>> would make it complete, and Cyc does not claim otherwise. >>>>>>>>> >>>>>>>>> 3. Do Peter Olcott’s claims refute incompleteness? >>>>>>>>> >>>>>>>>> No. Peter Olcott is known online for repeatedly claiming to >>>>>>>>> have “resolved” or “invalidated” Gödel’s incompleteness or >>>>>>>>> Turing’s halting problem. >>>>>>>>> His claims are universally rejected by logicians because they >>>>>>>>> misunderstand the formal structure of the theorems. >>>>>>>>> >>>>>>>>> In all variants of his claims: >>>>>>>>> >>>>>>>>> He proposes procedures that assume access to semantic truth, >>>>>>>>> something incompleteness forbids a formal system from capturing >>>>>>>>> internally. >>>>>>>>> >>>>>>>>> Or he proposes recognition algorithms that fail on classic >>>>>>>>> diagonal/ self-reference constructions but does not notice the >>>>>>>>> failure. >>>>>>>>> >>>>>>>>> Or he builds systems that are not recursively axiomatizable, >>>>>>>>> and therefore Gödel’s theorem does not apply — but then he >>>>>>>>> claims “defeat” rather than “dodging the premises”. >>>>>>>>> >>>>>>>>> The pattern is always: >>>>>>>>> >>>>>>>>> Change the problem or the assumptions → claim the original >>>>>>>>> theorem is wrong. >>>>>>>>> >>>>>>>>> This is equivalent to saying “I solved the halting problem… for >>>>>>>>> programs that I forbid from diagonalizing.” >>>>>>>>> That is not a refutation. >>>>>>>>> >>>>>>>>> 4. Why these approaches cannot refute incompleteness >>>>>>>>> >>>>>>>>> Gödel incompleteness is a meta-theorem. >>>>>>>>> Any attempt to build a complete system for arithmetic must fail >>>>>>>>> because: >>>>>>>>> >>>>>>>>> If the system is algorithmic, there’s a diagonal sentence G >>>>>>>>> such that >>>>>>>>> >>>>>>>>> If the system is consistent: it cannot prove G. >>>>>>>>> >>>>>>>> >>>>>>>> That is true. >>>>>>>> With my system there is one single all encompassing >>>>>>>> formal system that contains every element of general >>>>>>>> knowledge that can be expressed in language. >>>>>>>> >>>>>>>> Because the formal language has all semantics fully >>>>>>>> integrated into its syntax True(x) is exactly the >>>>>>>> same thing as Provable(x). If you can't prove it >>>>>>>> then it is not an element of the body of knowledge >>>>>>>> that can be expressed in language. >>>>>>> >>>>>>> The idea of a single, all-encompassing formal system in which >>>>>>> every meaningful statement is expressible and in which True(x) ≡ >>>>>>> Provable(x) is internally inconsistent, because as soon as the >>>>>>> language is expressive enough to contain elementary arithmetic— >>>>>>> inevitably required if it is to “contain every element of general >>>>>>> knowledge expressible in language”—Gödel’s incompleteness theorem >>>>>>> applies, producing well-formed statements that are true in the >>>>>>> intended semantics but not provable in the system; >>>>>> >>>>>> In weaker systems this will remain true. >>>>>> >>>>>> When True(L,x) is exactly the same thing as Provable(L,x) >>>>>> >>>>>> because every aspect of all of semantics is directly >>>>>> formalized and fully integrated in the formal language >>>>>> >>>>>> then ~Provable(L,x) means not an element of the body >>>>>> of general knowledge that can be expressed in language. >>>>>> >>>>>>> thus the identification “true = provable” cannot hold unless one >>>>>>> either (1) restricts the language so severely that it no longer >>>>>>> expresses general knowledge, or (2) accepts a degenerate >>>>>>> semantics in which “truth” is redefined to mean “provable in the >>>>>>> system,” which merely eliminates semantics and collapses truth >>>>>>> into syntactic provability by fiat, yielding a system that cannot >>>>>>> describe its own correctness and cannot capture the ordinary >>>>>>> notion of truth at all—in short, Olcott’s proposal either >>>>>>> violates Gödel or empties “truth” of its usual meaning, and so it >>>>>>> cannot simultaneously claim completeness, expressiveness, and a >>>>>>> meaningful notion of truth. >>>>> >>>>> Olcott’s “one perfect formal system containing all knowledge with >>>>> True(x) = Provable(x)” works beautifully, provided you never ask it >>>>> anything interesting: >>>> >>>> It literally has the entire body of general knowledge >>>> including every book or academic paper every published. >>>> >>>>> the moment you give it arithmetic, it starts sweating like a >>>>> politician in a fact-checking interview, because Gödel sneaks in >>>>> through the back door and whispers a sentence the system can’t >>>>> prove, whereupon Olcott shouts “If you can’t prove it, it’s not >>>>> knowledge!” and throws the sentence out of the window, pats himself >>>>> on the back, and calls the place clean; >>>> >>>> Let's name my formal system so that we can be specific. >>>> General_Knowledge. It already knows that G cannot be >>>> proved in F. This is an aspect of the body of general >>>> knowledge that can be expressed in language. >>>> >>>> Gödel incompleteness can only exist in systems that divide >>>> their syntax from their semantics using model theory. When >>>> the semantics is fully integrated into the syntax eliminating >>>> any need for model theory, then Gödel incompleteness cannot >>>> exist. >>>> >>>>> unfortunately, this is not so much solving incompleteness as >>>>> declaring any inconvenient truth illegal, a bit like running a >>>>> dictatorship where the official state newspaper defines “truth” as >>>>> “things we printed,” and then brags about having eliminated >>>>> misinformation forever—indeed, Olcott’s system is the only formal >>>>> system in history to achieve total completeness by aggressively >>>>> evicting all statements that would make it incomplete, thereby >>>>> proving, once and for all, that if you shrink reality enough, it >>>>> will fit anywhere. >>>>> >>>>> >>>> >>>> This short Prolog shows the error of the Liar Paradox >>>> ?- LP = not(true(LP)). >>>> LP = not(true(LP)). >>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>> false. >>>> >>>> That above means that the Liar Paradox contains >>>> a cycle in the directed graph of its evaluation >>>> sequence proving that its evaluation remains stuck >>>> in an infinite loop and thus can never be resolved. >>>> >>>> In 2000 years no one has even resolved the Liar Paradox >>>> in way that is widely accepted as correct. >>> >>> THE MINISTRY OF PROVABILITY ANNOUNCES THE END OF TRUTH AS WE KNOW IT >>> “If it can’t be proven, it never happened,” says Supreme Formalizer >>> Olcott. >>> >>> The Ministry of Provability is delighted to unveil The One Unified >>> Formal System (TOUFS™), the first and only framework in human history >>> to achieve Total Epistemic Harmony by the revolutionary method of >>> banning all facts that don’t fit. >>> >>> Under the new legislation, Truth(x) = Provable(x) by constitutional >>> decree. Citizens are reminded that any statement not provable within >>> TOUFS™’ 14 axioms (“The Axioms of Perfect Obviousness,” revised >>> weekly) will henceforth be classified as Ungovernable Nonsense and >>> gently escorted outside the Ministry's cognitive perimeter. >>> >>> “We have finally solved Gödel,” announced Minister Olcott at a >>> celebratory press event held in Axiom Chamber #3. “Gödel keeps >>> sending us those confusing, unprovable statements. We now return them >>> marked ‘Incorrect Form – Please Rephrase Within System Limits.’ >>> Problem solved.” >>> >>> When asked whether TOUFS™ could express arithmetic, the Minister >>> smiled warmly and replied: >>> “We discovered arithmetic is dangerously expressive, so we downgraded >>> it to a recreational activity.” >>> >>> Early adopters have praised the system’s clarity: >>> >>> Mathematicians report unprecedented peace of mind, since all >>> difficult theorems have now been reclassified as “Not Real.” >>> >>> Philosophers have been redirected to the Ministry’s Silence >>> Department for failing to produce provable questions. >>> >>> Physicists are adjusting to the new mandate requiring all particles >>> to comply with Axiom 12 (“Everything Behaves Nicely”). >>> >>> A slight controversy arose when an inquisitive intern asked whether >>> the statement “Everything in the system is provable” is itself >>> provable. The Ministry immediately reassigned the intern to the >>> Department of Semantic Recycling, where he is undergoing intensive >>> training in Non-Issues. >>> >>> The Ministry concludes with a reassuring message to all citizens: >>> >>> “TOUFS™ guarantees a future where no truth will ever escape unproven, >>> because unproven truths will no longer exist.” >>> >>> The press conference ended with the ceremonial shredding of Gödel’s >>> incompleteness paper and the unveiling of a large poster reading: >>> >>> “IGNORANCE IS INCONSISTENCY-FREE.” >> >> >> Gödel incompleteness can only exist in systems that divide >> their syntax from their semantics using model theory. When >> the semantics is fully integrated into the syntax eliminating >> any need for model theory, then Gödel incompleteness cannot >> exist. >> >> Semantic logical entailment from a finite set of atomic >> facts is airtight. >> >> *I have thought this over again and again for a decade* >> Try and find an actual error. > > 1. Gödel incompleteness does not rely on model theory or a syntax/ > semantics split > > You say: > > Gödel incompleteness can only exist in systems that divide their syntax > from their semantics using model theory. > When the semantics is fully integrated into the syntax eliminating any > need for model theory, then Gödel incompleteness cannot exist. > > This is just false historically and technically. > > Gödel’s 1931 incompleteness proof is almost entirely syntactic. He > arithmetizes formulas and proofs, builds a sentence that says “I am not > provable in this system,” and then proves: if the system is consistent, > it cannot prove that sentence, nor its negation (under reasonable > soundness assumptions). No model theory, no semantic consequence, no > “external semantics” is required for the construction of the Gödel > sentence. > > So incompleteness does not depend on a prior split between syntax and > semantics. It applies to: > > any effectively axiomatized, sufficiently expressive, consistent system, > > regardless of how you talk about semantics. > > Your claim “it only exists when syntax and semantics are divided” is > just wrong: syntax alone is already enough to generate the > incompleteness phenomenon. > > 2. “Integrating semantics into syntax” in the way you propose is > impossible (Tarski kicks the door in) > > You’re essentially proposing: > > There is a single formal system S such that > – every element of “general knowledge expressible in language” is a > sentence of S; > – there is a predicate True(x) inside the same system such that > True(⌜φ⌝) ↔ φ for every sentence φ; > – and moreover True(x) = Provable(x). > Not at all. Gödel numbers merely hide the underlying semantic errors. You won't ever be able to understand how and why they are errors unless you understand what a cycle in the directed graph of an evaluation sequence means. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. > But: > > Tarski’s undefinability of truth says: in a sufficiently strong > arithmetic language, there is no formula True(x) in that same language > that correctly satisfies True(⌜φ⌝) ↔ φ for all sentences φ of that > language. If you try, you get the liar-style paradox and inconsistency. > > So you cannot have a genuine internal truth predicate for “all sentences > of this language” that is both: > > expressible in the language, and > > extensionally correct about all sentences. > > If you dodge this by decree: > > “OK, we define True(x) to mean Provable(x).” > > Then you haven’t “integrated semantics into syntax”; you’ve redefined > truth as provability. That’s just a syntactic predicate wearing semantic > perfume. > Montague Grammar and or the CycL language of the Cyc project can say anything that can be said in natural language. > If your system is sound but recursively axiomatized, then by Gödel there > are true-but-unprovable sentences, so “True(x) = Provable(x)” is false > extensionally. > > If you force “True = Provable” by definition, then your “truth” is no > longer about the world or about standard arithmetic; it’s just “belongs > to the theorem set of S.” > It is an entirely different foundation. The conventional rules do not apply this is a whole new game. > That’s the second big error: you assume that you can have an internal > predicate that both (a) behaves like real truth over “all general > knowledge expressible in language” and (b) equals provability. Tarski + > Gödel together say: no, you can’t. > > 3. “Semantic entailment from a finite set of atomic facts is airtight” > is irrelevant to your grand claim > > You say: > > Semantic logical entailment from a finite set of atomic facts is airtight. > > Sure. From a finite set of atomic facts in a finite relational > structure, semantic consequence is straightforward and even decidable. > But that has almost nothing to do with your earlier claim: > > You’re not proposing “a finite database with first-order consequences.” > It is a knowledge ontology this is essentially the quote below. > You’re proposing one all-encompassing system for all general knowledge > (which will necessarily involve arithmetic, infinity, etc.). > Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote: By the theory of simple types I mean the doctrine which says that the objects of thought (or, in another interpretation, the symbolic expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations, etc. (with a similar hierarchy for extensions), and that sentences of the form: " a has the property φ ", " b bears the relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together. > In such a system: > > The “set of atomic facts” cannot be finite or even recursively decidable > in general if it’s supposed to match “all true statements of > arithmetic,” because the set of true arithmetic sentences is not > recursively enumerable. > The finite set of axioms of arithmetic are its atomic facts. > So your “airtight semantic entailment from a finite base” applies only > to a trivial fragment, not to the system you actually want. > The entire body of general knowledge that can be expressed in language can be encoded as a finite set of atomic facts and semantic logical entailment applied to these facts. > So the third error is a kind of bait-and-switch: you appeal to the > safety of tiny finite-model entailment and then quietly promote that > intuition to “all general knowledge,” where it simply doesn’t scale. > Kurt Gödel in his 1944 quote shows that objects of thought can be placed in the kind of Knowledge Ontology that I refer to. In information science, an ontology encompasses a representation, formal naming, and definitions of the categories, properties, and relations between the concepts... https://en.wikipedia.org/wiki/Ontology_(information_science) > In one sentence > > Your position hinges on three false assumptions: > > that Gödel incompleteness only arises when syntax and semantics are > separated via model theory (no: the original proof is purely syntactic); > What I said is a truism because it makes true and unprovable impossible. When syntax and semantics are fully integrated together then unprovable means not an element of the body of general knowledge that can be expressed in language. > that you can have an internal truth predicate for the same language > which is both extensionally correct about all its sentences and > identical to provability (no: Tarski and Gödel jointly rule this out); > They are using a fundamentally different system. > that the nice behavior of semantic entailment from a finite base somehow > extends to a single system capturing all “general knowledge” including > arithmetic (no: that’s where undecidability and incompleteness live). > > You can have “True(x) = Provable(x)”—but only by changing what “true” > means so radically that you’re no longer talking about truth in any > ordinary or semantic sense. Not at all. This is how "True on the basis of meaning expressed in language" has always worked. > That’s not beating Gödel; that’s walking off > the playing field and declaring victory. It is exactly what I claimed: New formal foundation for correct reasoning makes True(X) computable -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-26 00:04 +0000 |
| Message-ID | <x3imZVWAiA_HBI-3OM7PYEEJevQ@jntp> |
| In reply to | #641092 |
Peter, every time someone points out that your system breaks Gödel by redefining truth as “things my system proves,” you reply that this is “a fundamentally different foundation,” as if giving a new name to the floor suddenly allowed you to float. Your new line — “Gödel incompleteness can only exist when syntax and semantics are divided” — is just the same move in a new hat. Gödel’s original 1931 proof is purely syntactic, requires zero model theory, and works even if you paint “SEMANTICS” on the side of the syntax with a big red brush. The diagonal argument doesn’t care about your ontology, your types, your Prolog unification, or how many decades you’ve stared at it. This is the whole problem: every time the theorem bites, you amputate the part of mathematics that hurts and say, “See, no wound!” You’ve solved incompleteness the same way a surgeon would solve mortality by outlawing death certificates. Your system makes True(x) computable exactly the way a shredder makes archival integrity computable: anything inconvenient simply becomes “not in the body of general knowledge expressible in language.” If Gödel sentences don’t fit, the bin is right there. That’s not “integrating semantics.” That’s declaring all troublesome meanings illegal. It’s a bold philosophical stance, sure. But it’s not mathematics.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 18:14 -0600 |
| Message-ID | <10g5gom$3u02j$1@dont-email.me> |
| In reply to | #641093 |
On 11/25/2025 6:04 PM, Python wrote: > Peter, every time someone points out that your system breaks Gödel by > redefining truth as “things my system proves,” you reply that this is “a > fundamentally different foundation,” as if giving a new name to the > floor suddenly allowed you to float. > > Your new line — “Gödel incompleteness can only exist when syntax and > semantics are divided” — is just the same move in a new hat. Gödel’s > original 1931 proof is purely syntactic, requires zero model theory, and > works even if you paint “SEMANTICS” on the side of the syntax with a big > red brush. The diagonal argument doesn’t care about your ontology, your > types, your Prolog unification, or how many decades you’ve stared at it. > > This is the whole problem: every time the theorem bites, you amputate > the part of mathematics that hurts and say, “See, no wound!” You’ve > solved incompleteness the same way a surgeon would solve mortality by > outlawing death certificates. > > Your system makes True(x) computable exactly the way a shredder makes > archival integrity computable: anything inconvenient simply becomes “not > in the body of general knowledge expressible in language.” If Gödel > sentences don’t fit, the bin is right there. > > That’s not “integrating semantics.” > That’s declaring all troublesome meanings illegal. > Perhaps you do not fully understand exactly what semantic logical entailment is thus cannot directly see how and why this totally eliminates undecidability and undefinability. I have spent at least five full time years on this one thing. > It’s a bold philosophical stance, sure. > But it’s not mathematics. It is a brand new provably correct foundation for correct reasoning that corrects all of the shortcoming and incoherence of logic and math. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-26 00:18 +0000 |
| Message-ID | <N0SxYwMlgNspsAZkX0F5vq23Rzk@jntp> |
| In reply to | #641094 |
Le 26/11/2025 à 01:14, olcott a écrit : > On 11/25/2025 6:04 PM, Python wrote: >> Peter, every time someone points out that your system breaks Gödel by >> redefining truth as “things my system proves,” you reply that this is “a >> fundamentally different foundation,” as if giving a new name to the >> floor suddenly allowed you to float. >> >> Your new line — “Gödel incompleteness can only exist when syntax and >> semantics are divided” — is just the same move in a new hat. Gödel’s >> original 1931 proof is purely syntactic, requires zero model theory, and >> works even if you paint “SEMANTICS” on the side of the syntax with a big >> red brush. The diagonal argument doesn’t care about your ontology, your >> types, your Prolog unification, or how many decades you’ve stared at it. >> >> This is the whole problem: every time the theorem bites, you amputate >> the part of mathematics that hurts and say, “See, no wound!” You’ve >> solved incompleteness the same way a surgeon would solve mortality by >> outlawing death certificates. >> >> Your system makes True(x) computable exactly the way a shredder makes >> archival integrity computable: anything inconvenient simply becomes “not >> in the body of general knowledge expressible in language.” If Gödel >> sentences don’t fit, the bin is right there. >> >> That’s not “integrating semantics.” >> That’s declaring all troublesome meanings illegal. >> > > Perhaps you do not fully understand exactly what > semantic logical entailment is thus cannot directly > see how and why this totally eliminates undecidability > and undefinability. I have spent at least five full > time years on this one thing. > >> It’s a bold philosophical stance, sure. >> But it’s not mathematics. > > It is a brand new provably correct foundation > for correct reasoning that corrects all of the > shortcoming and incoherence of logic and math. Peter, every time you say “perhaps you do not fully understand semantic logical entailment,” it sounds like a man insisting that everyone else is holding the map upside down, while he proudly walks into the same lamp post for the fiftieth time. You keep repeating that five years of thinking have shown you how to “totally eliminate undecidability,” but undecidability is not a software bug you can delete with enough staring. It’s a mathematical theorem about computability. You cannot remove a proven limit by declaring, “My foundation does not believe in limits.” Your proposed cure — redefining truth as whatever your system can derive — is like solving the problem of unmeasurable sets by banning rulers. Yes, it “eliminates” the difficulty, but only in the same sense that closing your eyes eliminates the sun. Gödel’s syntactic diagonal argument does not care how many semantic stickers you glue on top. It applies to any consistent, effective, sufficiently expressive system. If your system is effective and expressive, Gödel applies. If it’s not effective, you haven’t “solved undecidability”; you’ve stepped outside mathematics. If it’s not expressive enough to encode arithmetic, then it cannot be “the entire body of general knowledge.” Those are the only options. Claiming you’ve produced “a brand new provably correct foundation for correct reasoning” that fixes all shortcomings of logic and math is bold, certainly — but until you show a formal system rather than a proclamation, you are not correcting logic; you are advertising a logic-flavored product. Mathematics does not respond to ambition, only to proofs. So far, yours remain announcements.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 18:38 -0600 |
| Message-ID | <10g5i5v$3uevu$1@dont-email.me> |
| In reply to | #641095 |
On 11/25/2025 6:18 PM, Python wrote: > Le 26/11/2025 à 01:14, olcott a écrit : >> On 11/25/2025 6:04 PM, Python wrote: >>> Peter, every time someone points out that your system breaks Gödel by >>> redefining truth as “things my system proves,” you reply that this is >>> “a fundamentally different foundation,” as if giving a new name to >>> the floor suddenly allowed you to float. >>> >>> Your new line — “Gödel incompleteness can only exist when syntax and >>> semantics are divided” — is just the same move in a new hat. Gödel’s >>> original 1931 proof is purely syntactic, requires zero model theory, >>> and works even if you paint “SEMANTICS” on the side of the syntax >>> with a big red brush. The diagonal argument doesn’t care about your >>> ontology, your types, your Prolog unification, or how many decades >>> you’ve stared at it. >>> >>> This is the whole problem: every time the theorem bites, you amputate >>> the part of mathematics that hurts and say, “See, no wound!” You’ve >>> solved incompleteness the same way a surgeon would solve mortality by >>> outlawing death certificates. >>> >>> Your system makes True(x) computable exactly the way a shredder makes >>> archival integrity computable: anything inconvenient simply becomes >>> “not in the body of general knowledge expressible in language.” If >>> Gödel sentences don’t fit, the bin is right there. >>> >>> That’s not “integrating semantics.” >>> That’s declaring all troublesome meanings illegal. >>> >> >> Perhaps you do not fully understand exactly what >> semantic logical entailment is thus cannot directly >> see how and why this totally eliminates undecidability >> and undefinability. I have spent at least five full >> time years on this one thing. >> >>> It’s a bold philosophical stance, sure. >>> But it’s not mathematics. >> >> It is a brand new provably correct foundation >> for correct reasoning that corrects all of the >> shortcoming and incoherence of logic and math. > > Peter, every time you say “perhaps you do not fully understand semantic > logical entailment,” it sounds like a man insisting that everyone else > is holding the map upside down, while he proudly walks into the same > lamp post for the fiftieth time. > Have you spent five full time years studying the details of formalizing semantic logical entailment directly in the formal system with no need for a separate model theory? > You keep repeating that five years of thinking have shown you how to > “totally eliminate undecidability,” but undecidability is not a software > bug you can delete with enough staring. It’s a mathematical theorem > about computability. You cannot remove a proven limit by declaring, “My > foundation does not believe in limits.” > > Your proposed cure — redefining truth as whatever your system can derive > — is like solving the problem of unmeasurable sets by banning rulers. > Yes, it “eliminates” the difficulty, but only in the same sense that > closing your eyes eliminates the sun. > > Gödel’s syntactic diagonal argument does not care how many semantic > stickers you glue on top. It applies to any consistent, effective, > sufficiently expressive system. It does not. It simply uses Gödel numbers in a system woefully insufficiently expressive to say this tiny little expression: G := (F ⊬ G) meaning that G is defined as unprovable in F. Gödel numbers merely hide the underlying unsound inference. Unless you can prove to me that you understand what a directed graph of an evaluation sequence is it will be assumed that you don't even have a slight clue about this: ?- G = not(provable(F, G)). G = not(provable(F, G)). ?- unify_with_occurs_check(G, not(provable(F, G))). false. That proves that this is semantically unsound: G ↔ ¬Prov(⌜G⌝) Failing to understand what I say counts as much less than no rebuttal at all. > If your system is effective and > expressive, Gödel applies. If it’s not effective, you haven’t “solved > undecidability”; you’ve stepped outside mathematics. If it’s not > expressive enough to encode arithmetic, then it cannot be “the entire > body of general knowledge.” > > Those are the only options. > > Claiming you’ve produced “a brand new provably correct foundation for > correct reasoning” that fixes all shortcomings of logic and math is > bold, certainly — but until you show a formal system rather than a > proclamation, you are not correcting logic; you are advertising a logic- > flavored product. > > Mathematics does not respond to ambition, only to proofs. So far, yours > remain announcements. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-26 00:42 +0000 |
| Message-ID | <h2PWyc_ZLXy1W1yK4lqDB27ltNg@jntp> |
| In reply to | #641098 |
Peter, you keep asking whether I’ve spent five years studying your private notion of “semantic logical entailment,” as though the theorems of recursion theory require a pilgrimage to your personal monastery. Mathematics doesn’t work that way: if your claim contradicts Gödel’s diagonal lemma, you don’t get to demand biographical credentials from the people pointing it out. Your new argument — that Gödel’s proof fails because “F is insufficiently expressive to say G := (F ⊬ G)” — is simply wrong. Gödel’s construction does not require the language to express the English sentence “G is unprovable in F.” It only requires that the predicate Provable_F(x) be representable in arithmetic, which it is whenever F is effective. The diagonal lemma then produces a sentence G G such that: F⊢G↔¬ProvableF(⌜G⌝). F⊢G↔¬Provable F (┌G┐). This is a syntactic identity inside arithmetic. The system does not “say” the English meta-definition “G := unprovable”; the lemma constructs the fixed point automatically. The expressiveness you say is missing is literally the one Gödel shows exists. Your Prolog snippet does not refute this. It simply shows that Prolog’s unifier correctly detects self-reference. Congratulations — that is precisely why the diagonal lemma exists. A unifier rejecting a cyclic structure does not imply “semantic unsoundness”; it implies “there is a fixed point,” exactly what Gödel uses. You’ve mistaken a diagnostic signal for an error condition. You keep insisting Gödel numbers “hide” a flaw, but the flaw never appears. The arithmetization is explicit, mechanical, and provably faithful. If you believe there is an unsound inference, you need to specify which inference rule, not wave at a Prolog occurs-check and declare victory. Your entire argument reduces to: Gödel’s theorem contradicts your system. Therefore Gödel must contain an unsound step. Therefore any tool that detects self-reference “proves” unsoundness. That is not a critique of Gödel — it is a confession that your system cannot handle diagonalization. But any system that cannot handle diagonalization also cannot represent even basic arithmetic on proofs, so it cannot be “the entire body of general knowledge” no matter how many times you assert it. You claim to have eliminated undecidability, but every time diagonalization appears, you simply declare that expression “not expressible” or “semantically unsound.” That’s not a new foundation; that’s a filter. When you remove everything that makes incompleteness unavoidable, it’s no surprise the remainder looks complete. But mathematics is not impressed by systems that achieve completeness by amputating half of logic. When you have an actual formal system, with actual axioms and rules, you can present it. Until then, this remains a sequence of claims looking for a definition.
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| From | Kaz Kylheku <643-408-1753@kylheku.com> |
|---|---|
| Date | 2025-11-26 00:47 +0000 |
| Message-ID | <20251125164624.616@kylheku.com> |
| In reply to | #641090 |
On 2025-11-25, olcott <polcott333@gmail.com> wrote: > Gödel incompleteness can only exist in systems that divide > their syntax from their semantics ... And, so, just confuse syntax for semantics, and all is fixed! -- TXR Programming Language: http://nongnu.org/txr Cygnal: Cygwin Native Application Library: http://kylheku.com/cygnal Mastodon: @Kazinator@mstdn.ca
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 18:52 -0600 |
| Message-ID | <10g5j1d$3unf3$1@dont-email.me> |
| In reply to | #641102 |
On 11/25/2025 6:47 PM, Kaz Kylheku wrote: > On 2025-11-25, olcott <polcott333@gmail.com> wrote: >> Gödel incompleteness can only exist in systems that divide >> their syntax from their semantics ... > > And, so, just confuse syntax for semantics, and all is fixed! > Things such as Montague Grammar are outside of your current knowledge. It is called Montague Grammar because it encodes natural language semantics as pure syntax. 1940s–present Gödel 1944 Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote: By the theory of simple types I mean the doctrine which says that the objects of thought (or, in another interpretation, the symbolic expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations, etc. (with a similar hierarchy for extensions), and that sentences of the form: " a has the property φ ", " b bears the relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together. -- Copyright 2025 Olcott My 28 year goal has been to make "true on the basis of meaning" computable. This required establishing a new foundation for correct reasoning.
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| From | Python <python@cccp.invalid> |
|---|---|
| Date | 2025-11-26 00:57 +0000 |
| Message-ID | <0byGRNq2-ddTZNSA_lUOm8H7YSo@jntp> |
| In reply to | #641103 |
Le 26/11/2025 à 01:53, olcott a écrit : > On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>> Gödel incompleteness can only exist in systems that divide >>> their syntax from their semantics ... >> >> And, so, just confuse syntax for semantics, and all is fixed! >> > > Things such as Montague Grammar are outside of your > current knowledge. It is called Montague Grammar > because it encodes natural language semantics as pure > syntax. > > 1940s–present > Gödel 1944 > Kurt Gödel in his 1944 Russell's mathematical logic gave the following > definition of the "theory of simple types" in a footnote: > > By the theory of simple types I mean the doctrine which says that the > objects of thought (or, in another interpretation, the symbolic > expressions) are divided into types, namely: individuals, properties of > individuals, relations between individuals, properties of such > relations, etc. (with a similar hierarchy for extensions), and that > sentences of the form: " a has the property φ ", " b bears the relation > R to c ", etc. are meaningless, if a, b, c, R, φ are not of types > fitting together. Montague Grammar doesn’t save you from Gödel any more than grammar books save you from gravity — encoding meaning as syntax doesn’t magically break diagonalization.
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