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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 | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2025-11-25 19:12 -0700 |
| Message-ID | <10g5nlk$3v398$3@dont-email.me> |
| In reply to | #641117 |
On 2025-11-25 19:08, olcott wrote: > On 11/25/2025 8:00 PM, André G. Isaak wrote: >> On 2025-11-25 18:43, olcott wrote: >>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>> On 2025-11-25 17:52, olcott wrote: >>>>> On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>> Gödel incompleteness can only exist in systems that divide >>>>>>> their syntax from their semantics ... >>>>>> >>>>>> And, so, just confuse syntax for semantics, and all is fixed! >>>>>> >>>>> >>>>> Things such as Montague Grammar are outside of your >>>>> current knowledge. It is called Montague Grammar >>>>> because it encodes natural language semantics as pure >>>>> syntax. >>>> >>>> You're terribly confused here. Montague Grammar is called 'Montague >>>> Grammar' because it is due to Richard Montague. >>>> >>>> Montague Grammar presents a theory of natural language (specifically >>>> English) semantics expressed in terms of logic. Formulae in his >>>> system have a syntax. They also have a semantics. The two are very >>>> much distinct. >>>> >>> >>> Montague Grammar is the syntax of English semantics >> >> I can't even make sense of that. It's a *theory* of English semantics. >> > > *Here is a concrete example* > The predicate Bachelor(x) is stipulated to mean ~Married(x) > where the predicate Married(x) is defined in terms of billions > of other things such as all of the details of Human(x). A concrete example of what? That's certainly not an example of 'the syntax of English semantics'. That's simply a stipulation involving two predicates. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 20:30 -0600 |
| Message-ID | <10g5onq$hnb$1@dont-email.me> |
| In reply to | #641119 |
On 11/25/2025 8:12 PM, André G. Isaak wrote: > On 2025-11-25 19:08, olcott wrote: >> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>> On 2025-11-25 18:43, olcott wrote: >>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>> On 2025-11-25 17:52, olcott wrote: >>>>>> 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. >>>>> >>>>> You're terribly confused here. Montague Grammar is called 'Montague >>>>> Grammar' because it is due to Richard Montague. >>>>> >>>>> Montague Grammar presents a theory of natural language >>>>> (specifically English) semantics expressed in terms of logic. >>>>> Formulae in his system have a syntax. They also have a semantics. >>>>> The two are very much distinct. >>>>> >>>> >>>> Montague Grammar is the syntax of English semantics >>> >>> I can't even make sense of that. It's a *theory* of English semantics. >>> >> >> *Here is a concrete example* >> The predicate Bachelor(x) is stipulated to mean ~Married(x) >> where the predicate Married(x) is defined in terms of billions >> of other things such as all of the details of Human(x). > > A concrete example of what? That's certainly not an example of 'the > syntax of English semantics'. That's simply a stipulation involving two > predicates. > > André > It is one concrete example of how a knowledge ontology of trillions of predicates can define the finite set of atomic facts of the world. *Actually read this, this time* 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 That is the basic infrastructure for defining all *objects of thought* can be defined in terms of other *objects of thought* -- 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 | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2025-11-25 19:36 -0700 |
| Message-ID | <10g5p32$3v398$4@dont-email.me> |
| In reply to | #641120 |
On 2025-11-25 19:30, olcott wrote: > On 11/25/2025 8:12 PM, André G. Isaak wrote: >> On 2025-11-25 19:08, olcott wrote: >>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>> On 2025-11-25 18:43, olcott wrote: >>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>> 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. >>>>>> >>>>>> You're terribly confused here. Montague Grammar is called >>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>> >>>>>> Montague Grammar presents a theory of natural language >>>>>> (specifically English) semantics expressed in terms of logic. >>>>>> Formulae in his system have a syntax. They also have a semantics. >>>>>> The two are very much distinct. >>>>>> >>>>> >>>>> Montague Grammar is the syntax of English semantics >>>> >>>> I can't even make sense of that. It's a *theory* of English semantics. >>>> >>> >>> *Here is a concrete example* >>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>> where the predicate Married(x) is defined in terms of billions >>> of other things such as all of the details of Human(x). >> >> A concrete example of what? That's certainly not an example of 'the >> syntax of English semantics'. That's simply a stipulation involving >> two predicates. >> >> André >> > > It is one concrete example of how a knowledge ontology > of trillions of predicates can define the finite set > of atomic facts of the world. But the topic under discussion was the relationship between syntax and semantics in Montague Grammar, not how knowledge ontologies are represented. So this isn't an example in anyway relevant to the discussion. > *Actually read this, this time* > 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 > > That is the basic infrastructure for defining all *objects of thought* > can be defined in terms of other *objects of thought* I know full well what a theory of types is. It has nothing to do with the relationship between syntax and semantics. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 20:41 -0600 |
| Message-ID | <10g5pde$o1v$1@dont-email.me> |
| In reply to | #641124 |
On 11/25/2025 8:36 PM, André G. Isaak wrote: > On 2025-11-25 19:30, olcott wrote: >> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>> On 2025-11-25 19:08, olcott wrote: >>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>> On 2025-11-25 18:43, olcott wrote: >>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>> 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. >>>>>>> >>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>> >>>>>>> Montague Grammar presents a theory of natural language >>>>>>> (specifically English) semantics expressed in terms of logic. >>>>>>> Formulae in his system have a syntax. They also have a semantics. >>>>>>> The two are very much distinct. >>>>>>> >>>>>> >>>>>> Montague Grammar is the syntax of English semantics >>>>> >>>>> I can't even make sense of that. It's a *theory* of English semantics. >>>>> >>>> >>>> *Here is a concrete example* >>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>> where the predicate Married(x) is defined in terms of billions >>>> of other things such as all of the details of Human(x). >>> >>> A concrete example of what? That's certainly not an example of 'the >>> syntax of English semantics'. That's simply a stipulation involving >>> two predicates. >>> >>> André >>> >> >> It is one concrete example of how a knowledge ontology >> of trillions of predicates can define the finite set >> of atomic facts of the world. > > But the topic under discussion was the relationship between syntax and > semantics in Montague Grammar, not how knowledge ontologies are > represented. So this isn't an example in anyway relevant to the discussion. > >> *Actually read this, this time* >> 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 >> >> That is the basic infrastructure for defining all *objects of thought* >> can be defined in terms of other *objects of thought* > > > I know full well what a theory of types is. It has nothing to do with > the relationship between syntax and semantics. > > André > That particular theory of types lays out the infrastructure of how all *objects of thought* can be defined in terms of other *objects of thought* such that the entire body of knowledge that can be expressed in language can be encoded into a single coherent formal system. -- 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 02:43 +0000 |
| Message-ID | <W0mtLib1AU9eFqnzwihjI5YVZ3c@jntp> |
| In reply to | #641131 |
Le 26/11/2025 à 03:41, olcott a écrit : > On 11/25/2025 8:36 PM, André G. Isaak wrote: >> On 2025-11-25 19:30, olcott wrote: >>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>> On 2025-11-25 19:08, olcott wrote: >>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>> 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. >>>>>>>> >>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>> >>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>> (specifically English) semantics expressed in terms of logic. >>>>>>>> Formulae in his system have a syntax. They also have a semantics. >>>>>>>> The two are very much distinct. >>>>>>>> >>>>>>> >>>>>>> Montague Grammar is the syntax of English semantics >>>>>> >>>>>> I can't even make sense of that. It's a *theory* of English semantics. >>>>>> >>>>> >>>>> *Here is a concrete example* >>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>> where the predicate Married(x) is defined in terms of billions >>>>> of other things such as all of the details of Human(x). >>>> >>>> A concrete example of what? That's certainly not an example of 'the >>>> syntax of English semantics'. That's simply a stipulation involving >>>> two predicates. >>>> >>>> André >>>> >>> >>> It is one concrete example of how a knowledge ontology >>> of trillions of predicates can define the finite set >>> of atomic facts of the world. >> >> But the topic under discussion was the relationship between syntax and >> semantics in Montague Grammar, not how knowledge ontologies are >> represented. So this isn't an example in anyway relevant to the discussion. >> >>> *Actually read this, this time* >>> 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 >>> >>> That is the basic infrastructure for defining all *objects of thought* >>> can be defined in terms of other *objects of thought* >> >> >> I know full well what a theory of types is. It has nothing to do with >> the relationship between syntax and semantics. >> >> André >> > > That particular theory of types lays out the infrastructure > of how all *objects of thought* can be defined in terms > of other *objects of thought* such that the entire body > of knowledge that can be expressed in language can be encoded > into a single coherent formal system. Typing “objects of thought” doesn’t make all truths provable — it only prevents ill-formed expressions. If your system looks complete, it’s because you threw away every sentence that would have made it incomplete.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 21:24 -0600 |
| Message-ID | <10g5rth$1c37$5@dont-email.me> |
| In reply to | #641132 |
On 11/25/2025 8:43 PM, Python wrote: > Le 26/11/2025 à 03:41, olcott a écrit : >> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>> On 2025-11-25 19:30, olcott wrote: >>>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>> On 2025-11-25 19:08, olcott wrote: >>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>> 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. >>>>>>>>> >>>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>>> >>>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>>> (specifically English) semantics expressed in terms of logic. >>>>>>>>> Formulae in his system have a syntax. They also have a >>>>>>>>> semantics. The two are very much distinct. >>>>>>>>> >>>>>>>> >>>>>>>> Montague Grammar is the syntax of English semantics >>>>>>> >>>>>>> I can't even make sense of that. It's a *theory* of English >>>>>>> semantics. >>>>>>> >>>>>> >>>>>> *Here is a concrete example* >>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>> where the predicate Married(x) is defined in terms of billions >>>>>> of other things such as all of the details of Human(x). >>>>> >>>>> A concrete example of what? That's certainly not an example of 'the >>>>> syntax of English semantics'. That's simply a stipulation involving >>>>> two predicates. >>>>> >>>>> André >>>>> >>>> >>>> It is one concrete example of how a knowledge ontology >>>> of trillions of predicates can define the finite set >>>> of atomic facts of the world. >>> >>> But the topic under discussion was the relationship between syntax >>> and semantics in Montague Grammar, not how knowledge ontologies are >>> represented. So this isn't an example in anyway relevant to the >>> discussion. >>> >>>> *Actually read this, this time* >>>> 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 >>>> >>>> That is the basic infrastructure for defining all *objects of thought* >>>> can be defined in terms of other *objects of thought* >>> >>> >>> I know full well what a theory of types is. It has nothing to do with >>> the relationship between syntax and semantics. >>> >>> André >>> >> >> That particular theory of types lays out the infrastructure >> of how all *objects of thought* can be defined in terms >> of other *objects of thought* such that the entire body >> of knowledge that can be expressed in language can be encoded >> into a single coherent formal system. > > Typing “objects of thought” doesn’t make all truths provable — it only > prevents ill-formed expressions. > If your system looks complete, it’s because you threw away every > sentence that would have made it incomplete. When ALL *objects of thought* are defined in terms of other *objects of thought* then their truth and their proof is simply walking the knowledge tree. -- 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 03:26 +0000 |
| Message-ID | <Dk-CKBplfgRB-mFFrm41KEmaJhY@jntp> |
| In reply to | #641159 |
Le 26/11/2025 à 04:24, olcott a écrit : > When ALL *objects of thought* are defined > in terms of other *objects of thought* then > their truth and their proof is simply walking > the knowledge tree. A definition tree is not a proof system, Peter. Walking a hierarchy does not make undecidable truths disappear — it just hides them from your model. If “truth” were just “following links in a tree,” then: no arithmetic fact would require a proof, no theorem would be non-trivial, no undecidable sentence would exist, and mathematics would collapse into a directory structure. But mathematics is not a filesystem.
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| From | Kaz Kylheku <643-408-1753@kylheku.com> |
|---|---|
| Date | 2025-11-26 03:30 +0000 |
| Message-ID | <20251125192833.16@kylheku.com> |
| In reply to | #641162 |
On 2025-11-26, Python <python@cccp.invalid> wrote: > Le 26/11/2025 à 04:24, olcott a écrit : >> When ALL *objects of thought* are defined >> in terms of other *objects of thought* then >> their truth and their proof is simply walking >> the knowledge tree. > > A definition tree is not a proof system, Peter. > Walking a hierarchy does not make undecidable truths disappear — it just > hides them from your model. > > If “truth” were just “following links in a tree,” then: > > no arithmetic fact would require a proof, And, like, that would totally not suit Olcott just fine, right? > no theorem would be non-trivial, No crank could be stupid for misunderstanding a theorem. > no undecidable sentence would exist, So even a crank could finally walk into a restaurant and decide between a soup and salad in 15 seconds flat. > and mathematics would collapse into a directory structure. Preferrably on a MS-DOS C:\> drive, to suit Olcott. It all checks out. -- 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 21:45 -0600 |
| Message-ID | <10g5t51$1ru2$1@dont-email.me> |
| In reply to | #641162 |
On 11/25/2025 9:26 PM, Python wrote: > Le 26/11/2025 à 04:24, olcott a écrit : >> When ALL *objects of thought* are defined >> in terms of other *objects of thought* then >> their truth and their proof is simply walking >> the knowledge tree. > > A definition tree is not a proof system, Peter. When you have a narrow-minded view maybe not. When a proof is any process applied to any combination of finite strings (such as a tree of knowledge) that makes its conclusion necessarily true then it is a proof in the most generic sense. When we stipulate that "cats" <are> "animals" then the stipulated relation between those two finite string is the proof that it is true. A tree of knowledge works this exact same way yet the relationships can also be their position in the inheritance hierarchy of types. > Walking a hierarchy does not make undecidable truths disappear — it just > hides them from your model. > A tree of knowledge makes undecidability impossible within the entire body of knowledge that can be expressed in language. > If “truth” were just “following links in a tree,” then: > > no arithmetic fact would require a proof, > We also have semantic logical entailment from a finite set of atomic facts. This set is not finite. > no theorem would be non-trivial, > > no undecidable sentence would exist, > > and mathematics would collapse into a directory structure. > > But mathematics is not a filesystem. It makes no difference that G is not provable in PA. Any X is provable in General_Knowledge or it is not a member of General_Knowledge. -- 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 03:47 +0000 |
| Message-ID | <93y07sKbiOs8MNN4yELNMcXfbI8@jntp> |
| In reply to | #641170 |
Le 26/11/2025 à 04:45, olcott a écrit : > On 11/25/2025 9:26 PM, Python wrote: >> Le 26/11/2025 à 04:24, olcott a écrit : >>> When ALL *objects of thought* are defined >>> in terms of other *objects of thought* then >>> their truth and their proof is simply walking >>> the knowledge tree. >> >> A definition tree is not a proof system, Peter. > > When you have a narrow-minded view maybe not. > When a proof is any process applied to any > combination of finite strings (such as a tree > of knowledge) that makes its conclusion necessarily > true then it is a proof in the most generic sense. > > When we stipulate that "cats" <are> "animals" > then the stipulated relation between those two > finite string is the proof that it is true. > > A tree of knowledge works this exact same > way yet the relationships can also be their > position in the inheritance hierarchy of types. > >> Walking a hierarchy does not make undecidable truths disappear — it just >> hides them from your model. >> > > A tree of knowledge makes undecidability impossible > within the entire body of knowledge that can be > expressed in language. > >> If “truth” were just “following links in a tree,” then: >> >> no arithmetic fact would require a proof, >> > > We also have semantic logical entailment from > a finite set of atomic facts. This set is not > finite. > >> no theorem would be non-trivial, >> >> no undecidable sentence would exist, >> >> and mathematics would collapse into a directory structure. >> >> But mathematics is not a filesystem. > > It makes no difference that G is not provable in PA. > Any X is provable in General_Knowledge or it is not > a member of General_Knowledge. Peter, you have quietly redefined “proof” to mean “any link I choose to place in my tree of definitions.” But that is not proof — that is classification. Stipulating “cats = animals” is not a derivation; it is a definition. Definitions can build a taxonomy, but they cannot prove arithmetic truths, resolve undecidable statements, or replace inference rules. Your “General_Knowledge” is complete only because you delete everything it cannot derive and declare it “not a member.” That is not a solution to incompleteness — it is circular pruning. You didn’t eliminate undecidability. You eliminated every sentence that would make your system face it.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-25 22:01 -0600 |
| Message-ID | <10g5u2t$25t9$1@dont-email.me> |
| In reply to | #641171 |
On 11/25/2025 9:47 PM, Python wrote: > Le 26/11/2025 à 04:45, olcott a écrit : >> On 11/25/2025 9:26 PM, Python wrote: >>> Le 26/11/2025 à 04:24, olcott a écrit : >>>> When ALL *objects of thought* are defined >>>> in terms of other *objects of thought* then >>>> their truth and their proof is simply walking >>>> the knowledge tree. >>> >>> A definition tree is not a proof system, Peter. >> >> When you have a narrow-minded view maybe not. >> When a proof is any process applied to any >> combination of finite strings (such as a tree >> of knowledge) that makes its conclusion necessarily >> true then it is a proof in the most generic sense. >> >> When we stipulate that "cats" <are> "animals" >> then the stipulated relation between those two >> finite string is the proof that it is true. >> >> A tree of knowledge works this exact same >> way yet the relationships can also be their >> position in the inheritance hierarchy of types. >> >>> Walking a hierarchy does not make undecidable truths disappear — it >>> just hides them from your model. >>> >> >> A tree of knowledge makes undecidability impossible >> within the entire body of knowledge that can be >> expressed in language. >> >>> If “truth” were just “following links in a tree,” then: >>> >>> no arithmetic fact would require a proof, >>> >> >> We also have semantic logical entailment from >> a finite set of atomic facts. This set is not >> finite. >> >>> no theorem would be non-trivial, >>> >>> no undecidable sentence would exist, >>> >>> and mathematics would collapse into a directory structure. >>> >>> But mathematics is not a filesystem. >> >> It makes no difference that G is not provable in PA. >> Any X is provable in General_Knowledge or it is not >> a member of General_Knowledge. > > Peter, you have quietly redefined “proof” to mean “any link I choose to > place in my tree of definitions.” > But that is not proof — that is classification. > When the full and complete semantic meaning of any *object of thought* is 100% entirely specified by its connection to other *objects of thought* then every element in this system has its provability exactly the same as its truth. > Stipulating “cats = animals” is not a derivation; it is a definition. > Definitions can build a taxonomy, but they cannot prove arithmetic > truths, resolve undecidable statements, or replace inference rules. > That is where semantic logical entailment specified syntactically comes in. > Your “General_Knowledge” is complete only because you delete everything > it cannot derive and declare it “not a member.” > That is not a solution to incompleteness — it is circular pruning. > You still do not understand how the combination of a complete finite set of atomic definitions along with every combination of things that they entail derives the entire body of knowledge that can be expressed in language. > You didn’t eliminate undecidability. > You eliminated every sentence that would make your system face it. > The complete body of knowledge that can be expressed in language can be algorithmically compressed as I have specified. It is only a finite set of atomic ideas and a finite set of ways to combine these ideas together. This derives an infinite set of ideas. -- 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 04:07 +0000 |
| Message-ID | <QrtNaUDPXuslCpyZBmRNVWu6UM8@jntp> |
| In reply to | #641176 |
Le 26/11/2025 à 05:01, olcott a écrit : > On 11/25/2025 9:47 PM, Python wrote: >> Le 26/11/2025 à 04:45, olcott a écrit : >>> On 11/25/2025 9:26 PM, Python wrote: >>>> Le 26/11/2025 à 04:24, olcott a écrit : >>>>> When ALL *objects of thought* are defined >>>>> in terms of other *objects of thought* then >>>>> their truth and their proof is simply walking >>>>> the knowledge tree. >>>> >>>> A definition tree is not a proof system, Peter. >>> >>> When you have a narrow-minded view maybe not. >>> When a proof is any process applied to any >>> combination of finite strings (such as a tree >>> of knowledge) that makes its conclusion necessarily >>> true then it is a proof in the most generic sense. >>> >>> When we stipulate that "cats" <are> "animals" >>> then the stipulated relation between those two >>> finite string is the proof that it is true. >>> >>> A tree of knowledge works this exact same >>> way yet the relationships can also be their >>> position in the inheritance hierarchy of types. >>> >>>> Walking a hierarchy does not make undecidable truths disappear — it >>>> just hides them from your model. >>>> >>> >>> A tree of knowledge makes undecidability impossible >>> within the entire body of knowledge that can be >>> expressed in language. >>> >>>> If “truth” were just “following links in a tree,” then: >>>> >>>> no arithmetic fact would require a proof, >>>> >>> >>> We also have semantic logical entailment from >>> a finite set of atomic facts. This set is not >>> finite. >>> >>>> no theorem would be non-trivial, >>>> >>>> no undecidable sentence would exist, >>>> >>>> and mathematics would collapse into a directory structure. >>>> >>>> But mathematics is not a filesystem. >>> >>> It makes no difference that G is not provable in PA. >>> Any X is provable in General_Knowledge or it is not >>> a member of General_Knowledge. >> >> Peter, you have quietly redefined “proof” to mean “any link I choose to >> place in my tree of definitions.” >> But that is not proof — that is classification. >> > > When the full and complete semantic meaning of any > *object of thought* is 100% entirely specified > by its connection to other *objects of thought* > then every element in this system has its provability > exactly the same as its truth. > >> Stipulating “cats = animals” is not a derivation; it is a definition. >> Definitions can build a taxonomy, but they cannot prove arithmetic >> truths, resolve undecidable statements, or replace inference rules. >> > > That is where semantic logical entailment specified > syntactically comes in. > >> Your “General_Knowledge” is complete only because you delete everything >> it cannot derive and declare it “not a member.” >> That is not a solution to incompleteness — it is circular pruning. >> > > You still do not understand how the combination > of a complete finite set of atomic definitions > along with every combination of things that > they entail derives the entire body of knowledge > that can be expressed in language. > >> You didn’t eliminate undecidability. >> You eliminated every sentence that would make your system face it. >> > > The complete body of knowledge that can be expressed > in language can be algorithmically compressed as I > have specified. It is only a finite set of atomic ideas > and a finite set of ways to combine these ideas together. > This derives an infinite set of ideas. Peter, if you claim that all knowledge expressible in language comes from a finite set of atomic ideas combined in finite ways, then your system can only generate countably many expressions, whereas arithmetic truth involves uncountably many possible functions and a non-recursively enumerable set of true statements; no finite definitional base can produce a complete theory strong enough to capture all arithmetic consequences, so when you insist that your finite tree “derives the entire body of knowledge,” what you actually have is a system that generates only a tiny countable fragment and discards everything it cannot express, which is not completeness but simply shrinking the universe of discourse until it fits inside your chosen model.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-26 08:44 -0600 |
| Message-ID | <10g73p4$fql1$1@dont-email.me> |
| In reply to | #641178 |
On 11/25/2025 10:07 PM, Python wrote: > Le 26/11/2025 à 05:01, olcott a écrit : >> On 11/25/2025 9:47 PM, Python wrote: >>> Le 26/11/2025 à 04:45, olcott a écrit : >>>> On 11/25/2025 9:26 PM, Python wrote: >>>>> Le 26/11/2025 à 04:24, olcott a écrit : >>>>>> When ALL *objects of thought* are defined >>>>>> in terms of other *objects of thought* then >>>>>> their truth and their proof is simply walking >>>>>> the knowledge tree. >>>>> >>>>> A definition tree is not a proof system, Peter. >>>> >>>> When you have a narrow-minded view maybe not. >>>> When a proof is any process applied to any >>>> combination of finite strings (such as a tree >>>> of knowledge) that makes its conclusion necessarily >>>> true then it is a proof in the most generic sense. >>>> >>>> When we stipulate that "cats" <are> "animals" >>>> then the stipulated relation between those two >>>> finite string is the proof that it is true. >>>> >>>> A tree of knowledge works this exact same >>>> way yet the relationships can also be their >>>> position in the inheritance hierarchy of types. >>>> >>>>> Walking a hierarchy does not make undecidable truths disappear — it >>>>> just hides them from your model. >>>>> >>>> >>>> A tree of knowledge makes undecidability impossible >>>> within the entire body of knowledge that can be >>>> expressed in language. >>>> >>>>> If “truth” were just “following links in a tree,” then: >>>>> >>>>> no arithmetic fact would require a proof, >>>>> >>>> >>>> We also have semantic logical entailment from >>>> a finite set of atomic facts. This set is not >>>> finite. >>>> >>>>> no theorem would be non-trivial, >>>>> >>>>> no undecidable sentence would exist, >>>>> >>>>> and mathematics would collapse into a directory structure. >>>>> >>>>> But mathematics is not a filesystem. >>>> >>>> It makes no difference that G is not provable in PA. >>>> Any X is provable in General_Knowledge or it is not >>>> a member of General_Knowledge. >>> >>> Peter, you have quietly redefined “proof” to mean “any link I choose >>> to place in my tree of definitions.” >>> But that is not proof — that is classification. >>> >> >> When the full and complete semantic meaning of any >> *object of thought* is 100% entirely specified >> by its connection to other *objects of thought* >> then every element in this system has its provability >> exactly the same as its truth. >> >>> Stipulating “cats = animals” is not a derivation; it is a definition. >>> Definitions can build a taxonomy, but they cannot prove arithmetic >>> truths, resolve undecidable statements, or replace inference rules. >>> >> >> That is where semantic logical entailment specified >> syntactically comes in. >> >>> Your “General_Knowledge” is complete only because you delete >>> everything it cannot derive and declare it “not a member.” >>> That is not a solution to incompleteness — it is circular pruning. >>> >> >> You still do not understand how the combination >> of a complete finite set of atomic definitions >> along with every combination of things that >> they entail derives the entire body of knowledge >> that can be expressed in language. >> >>> You didn’t eliminate undecidability. >>> You eliminated every sentence that would make your system face it. >>> >> >> The complete body of knowledge that can be expressed >> in language can be algorithmically compressed as I >> have specified. It is only a finite set of atomic ideas >> and a finite set of ways to combine these ideas together. >> This derives an infinite set of ideas. > > Peter, if you claim that all knowledge expressible in language comes > from a finite set of atomic ideas combined in finite ways, then your > system can only generate countably many expressions, If every verbal thought that anyone every had and every verbal thought that anyone will ever have until the Earth is engulfed by the Sun was written down this would be a finite set. Don't bring religion into this it is only a distraction away form the point. You don't seem to understand the distinction between truth and knowledge. True(L, x) tests for membership in the body of General_Knowledge. Elements not in this set are (a) False(L, x) defined as True(L, ~x) (b) unknown (c) semantically malformed > whereas arithmetic > truth involves uncountably many possible functions and a non-recursively If the Goldbach conjecture requires an infinite proof to resolve then its truth or falsity is not an element of the set of General_Knowledge. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture > enumerable set of true statements; no finite definitional base can > produce a complete theory strong enough to capture all arithmetic > consequences, Of course not. That is why we also have semantic logical inference. > so when you insist that your finite tree “derives the > entire body of knowledge,” what you actually have is a system that > generates only a tiny countable fragment and discards everything it > cannot express, which is not completeness but simply shrinking the > universe of discourse until it fits inside your chosen model. The body of General_Knowledge is algorithmically compressed into a complete and finite set of atomic facts. When we add semantic logical entailment to this any element in the set of General_Knowledge can be derived. "cats" <are> "animals" is general knowledge. "Fluffy" <is a> "Brown" "Cat" is specific knowledge. -- 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 | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2025-11-26 10:04 -0500 |
| Message-ID | <10g74ul$fhqt$1@dont-email.me> |
| In reply to | #641206 |
On 11/26/2025 9:44 AM, olcott wrote: > If every verbal thought that anyone every had and every verbal > thought that anyone will ever have until the Earth is engulfed > by the Sun was written down this would be a finite set. Don't > bring religion into this it is only a distraction away form > the point. > > You don't seem to understand the distinction between truth > and knowledge. > True(L, x) tests for membership in the body > of General_Knowledge. Elements not in this set are > (a) False(L, x) defined as True(L, ~x) > (b) unknown > (c) semantically malformed And (b) could always be unknown, making it or its inverse true and not provable. > >> whereas arithmetic truth involves uncountably many possible functions >> and a non-recursively > > If the Goldbach conjecture requires an infinite proof > to resolve then its truth or falsity is not an element > of the set of General_Knowledge. In other words, either it or its inverse would be true and not provable. > https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2025-11-26 10:34 -0500 |
| Message-ID | <x6FVQ.45897$5c64.38683@fx10.iad> |
| In reply to | #641206 |
On 11/26/25 9:44 AM, olcott wrote: > On 11/25/2025 10:07 PM, Python wrote: >> Le 26/11/2025 à 05:01, olcott a écrit : >>> On 11/25/2025 9:47 PM, Python wrote: >>>> Le 26/11/2025 à 04:45, olcott a écrit : >>>>> On 11/25/2025 9:26 PM, Python wrote: >>>>>> Le 26/11/2025 à 04:24, olcott a écrit : >>>>>>> When ALL *objects of thought* are defined >>>>>>> in terms of other *objects of thought* then >>>>>>> their truth and their proof is simply walking >>>>>>> the knowledge tree. >>>>>> >>>>>> A definition tree is not a proof system, Peter. >>>>> >>>>> When you have a narrow-minded view maybe not. >>>>> When a proof is any process applied to any >>>>> combination of finite strings (such as a tree >>>>> of knowledge) that makes its conclusion necessarily >>>>> true then it is a proof in the most generic sense. >>>>> >>>>> When we stipulate that "cats" <are> "animals" >>>>> then the stipulated relation between those two >>>>> finite string is the proof that it is true. >>>>> >>>>> A tree of knowledge works this exact same >>>>> way yet the relationships can also be their >>>>> position in the inheritance hierarchy of types. >>>>> >>>>>> Walking a hierarchy does not make undecidable truths disappear — >>>>>> it just hides them from your model. >>>>>> >>>>> >>>>> A tree of knowledge makes undecidability impossible >>>>> within the entire body of knowledge that can be >>>>> expressed in language. >>>>> >>>>>> If “truth” were just “following links in a tree,” then: >>>>>> >>>>>> no arithmetic fact would require a proof, >>>>>> >>>>> >>>>> We also have semantic logical entailment from >>>>> a finite set of atomic facts. This set is not >>>>> finite. >>>>> >>>>>> no theorem would be non-trivial, >>>>>> >>>>>> no undecidable sentence would exist, >>>>>> >>>>>> and mathematics would collapse into a directory structure. >>>>>> >>>>>> But mathematics is not a filesystem. >>>>> >>>>> It makes no difference that G is not provable in PA. >>>>> Any X is provable in General_Knowledge or it is not >>>>> a member of General_Knowledge. >>>> >>>> Peter, you have quietly redefined “proof” to mean “any link I choose >>>> to place in my tree of definitions.” >>>> But that is not proof — that is classification. >>>> >>> >>> When the full and complete semantic meaning of any >>> *object of thought* is 100% entirely specified >>> by its connection to other *objects of thought* >>> then every element in this system has its provability >>> exactly the same as its truth. >>> >>>> Stipulating “cats = animals” is not a derivation; it is a definition. >>>> Definitions can build a taxonomy, but they cannot prove arithmetic >>>> truths, resolve undecidable statements, or replace inference rules. >>>> >>> >>> That is where semantic logical entailment specified >>> syntactically comes in. >>> >>>> Your “General_Knowledge” is complete only because you delete >>>> everything it cannot derive and declare it “not a member.” >>>> That is not a solution to incompleteness — it is circular pruning. >>>> >>> >>> You still do not understand how the combination >>> of a complete finite set of atomic definitions >>> along with every combination of things that >>> they entail derives the entire body of knowledge >>> that can be expressed in language. >>> >>>> You didn’t eliminate undecidability. >>>> You eliminated every sentence that would make your system face it. >>>> >>> >>> The complete body of knowledge that can be expressed >>> in language can be algorithmically compressed as I >>> have specified. It is only a finite set of atomic ideas >>> and a finite set of ways to combine these ideas together. >>> This derives an infinite set of ideas. >> >> Peter, if you claim that all knowledge expressible in language comes >> from a finite set of atomic ideas combined in finite ways, then your >> system can only generate countably many expressions, > > If every verbal thought that anyone every had and every verbal > thought that anyone will ever have until the Earth is engulfed > by the Sun was written down this would be a finite set. Don't > bring religion into this it is only a distraction away form > the point. > > You don't seem to understand the distinction between truth > and knowledge. True(L, x) tests for membership in the body > of General_Knowledge. Elements not in this set are > (a) False(L, x) defined as True(L, ~x) > (b) unknown > (c) semantically malformed So, are you admitting that you have NEVER been talking about "truth", but only knowledge. This just shows that you shoule have NEVER used the word "true", but only "Known" > >> whereas arithmetic truth involves uncountably many possible functions >> and a non-recursively > > If the Goldbach conjecture requires an infinite proof > to resolve then its truth or falsity is not an element > of the set of General_Knowledge. > https://en.wikipedia.org/wiki/Goldbach%27s_conjecture So? IT is still either true of false. You are just showing you don't understand the difference between truth and knowledge. > >> enumerable set of true statements; no finite definitional base can >> produce a complete theory strong enough to capture all arithmetic >> consequences, > > Of course not. That is why we also have semantic logical > inference. > >> so when you insist that your finite tree “derives the entire body of >> knowledge,” what you actually have is a system that generates only a >> tiny countable fragment and discards everything it cannot express, >> which is not completeness but simply shrinking the universe of >> discourse until it fits inside your chosen model. > > The body of General_Knowledge is algorithmically compressed > into a complete and finite set of atomic facts. When we add > semantic logical entailment to this any element in the set > of General_Knowledge can be derived. > > "cats" <are> "animals" is general knowledge. > "Fluffy" <is a> "Brown" "Cat" is specific knowledge. > In other words, you are admitting that you are talking about KNOWLEDGE, snd not TRUTH, because you don't know the difference.
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-26 11:05 +0200 |
| Message-ID | <10g6fsp$80e5$2@dont-email.me> |
| In reply to | #641159 |
olcott kirjoitti 26.11.2025 klo 5.24: > On 11/25/2025 8:43 PM, Python wrote: >> Le 26/11/2025 à 03:41, olcott a écrit : >>> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>>> On 2025-11-25 19:30, olcott wrote: >>>>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>>> On 2025-11-25 19:08, olcott wrote: >>>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>>> 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. >>>>>>>>>> >>>>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>>>> >>>>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>>>> (specifically English) semantics expressed in terms of logic. >>>>>>>>>> Formulae in his system have a syntax. They also have a >>>>>>>>>> semantics. The two are very much distinct. >>>>>>>>>> >>>>>>>>> >>>>>>>>> Montague Grammar is the syntax of English semantics >>>>>>>> >>>>>>>> I can't even make sense of that. It's a *theory* of English >>>>>>>> semantics. >>>>>>>> >>>>>>> >>>>>>> *Here is a concrete example* >>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>> where the predicate Married(x) is defined in terms of billions >>>>>>> of other things such as all of the details of Human(x). >>>>>> >>>>>> A concrete example of what? That's certainly not an example of >>>>>> 'the syntax of English semantics'. That's simply a stipulation >>>>>> involving two predicates. >>>>>> >>>>>> André >>>>>> >>>>> >>>>> It is one concrete example of how a knowledge ontology >>>>> of trillions of predicates can define the finite set >>>>> of atomic facts of the world. >>>> >>>> But the topic under discussion was the relationship between syntax >>>> and semantics in Montague Grammar, not how knowledge ontologies are >>>> represented. So this isn't an example in anyway relevant to the >>>> discussion. >>>> >>>>> *Actually read this, this time* >>>>> 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 >>>>> >>>>> That is the basic infrastructure for defining all *objects of thought* >>>>> can be defined in terms of other *objects of thought* >>>> >>>> >>>> I know full well what a theory of types is. It has nothing to do >>>> with the relationship between syntax and semantics. >>>> >>>> André >>>> >>> >>> That particular theory of types lays out the infrastructure >>> of how all *objects of thought* can be defined in terms >>> of other *objects of thought* such that the entire body >>> of knowledge that can be expressed in language can be encoded >>> into a single coherent formal system. >> >> Typing “objects of thought” doesn’t make all truths provable — it only >> prevents ill-formed expressions. >> If your system looks complete, it’s because you threw away every >> sentence that would have made it incomplete. > > When ALL *objects of thought* are defined > in terms of other *objects of thought* then > their truth and their proof is simply walking > the knowledge tree. When ALL subjects of thoughts are defined in terms of other subjects of thoughts then there are no subjects of thoughts. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-26 08:58 -0600 |
| Message-ID | <10g74j1$g56g$1@dont-email.me> |
| In reply to | #641196 |
On 11/26/2025 3:05 AM, Mikko wrote: > olcott kirjoitti 26.11.2025 klo 5.24: >> On 11/25/2025 8:43 PM, Python wrote: >>> Le 26/11/2025 à 03:41, olcott a écrit : >>>> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>>>> On 2025-11-25 19:30, olcott wrote: >>>>>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>>>> On 2025-11-25 19:08, olcott wrote: >>>>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>>>> 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. >>>>>>>>>>> >>>>>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>>>>> >>>>>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>>>>> (specifically English) semantics expressed in terms of logic. >>>>>>>>>>> Formulae in his system have a syntax. They also have a >>>>>>>>>>> semantics. The two are very much distinct. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Montague Grammar is the syntax of English semantics >>>>>>>>> >>>>>>>>> I can't even make sense of that. It's a *theory* of English >>>>>>>>> semantics. >>>>>>>>> >>>>>>>> >>>>>>>> *Here is a concrete example* >>>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>> where the predicate Married(x) is defined in terms of billions >>>>>>>> of other things such as all of the details of Human(x). >>>>>>> >>>>>>> A concrete example of what? That's certainly not an example of >>>>>>> 'the syntax of English semantics'. That's simply a stipulation >>>>>>> involving two predicates. >>>>>>> >>>>>>> André >>>>>>> >>>>>> >>>>>> It is one concrete example of how a knowledge ontology >>>>>> of trillions of predicates can define the finite set >>>>>> of atomic facts of the world. >>>>> >>>>> But the topic under discussion was the relationship between syntax >>>>> and semantics in Montague Grammar, not how knowledge ontologies are >>>>> represented. So this isn't an example in anyway relevant to the >>>>> discussion. >>>>> >>>>>> *Actually read this, this time* >>>>>> 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 >>>>>> >>>>>> That is the basic infrastructure for defining all *objects of >>>>>> thought* >>>>>> can be defined in terms of other *objects of thought* >>>>> >>>>> >>>>> I know full well what a theory of types is. It has nothing to do >>>>> with the relationship between syntax and semantics. >>>>> >>>>> André >>>>> >>>> >>>> That particular theory of types lays out the infrastructure >>>> of how all *objects of thought* can be defined in terms >>>> of other *objects of thought* such that the entire body >>>> of knowledge that can be expressed in language can be encoded >>>> into a single coherent formal system. >>> >>> Typing “objects of thought” doesn’t make all truths provable — it >>> only prevents ill-formed expressions. >>> If your system looks complete, it’s because you threw away every >>> sentence that would have made it incomplete. >> >> When ALL *objects of thought* are defined >> in terms of other *objects of thought* then >> their truth and their proof is simply walking >> the knowledge tree. > > When ALL subjects of thoughts are defined > in terms of other subjects of thoughts then > there are no subjects of thoughts. > > Kurt Gödel explains the details of how *objects of thought* are defined in terms of other *objects of thought* 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, -- 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 | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-27 09:30 +0200 |
| Message-ID | <10g8umb$16cos$1@dont-email.me> |
| In reply to | #641208 |
olcott kirjoitti 26.11.2025 klo 16.58: > On 11/26/2025 3:05 AM, Mikko wrote: >> olcott kirjoitti 26.11.2025 klo 5.24: >>> On 11/25/2025 8:43 PM, Python wrote: >>>> Le 26/11/2025 à 03:41, olcott a écrit : >>>>> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>>>>> On 2025-11-25 19:30, olcott wrote: >>>>>>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>>>>> On 2025-11-25 19:08, olcott wrote: >>>>>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>>>>> 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. >>>>>>>>>>>> >>>>>>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>>>>>> >>>>>>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>>>>>> (specifically English) semantics expressed in terms of >>>>>>>>>>>> logic. Formulae in his system have a syntax. They also have >>>>>>>>>>>> a semantics. The two are very much distinct. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Montague Grammar is the syntax of English semantics >>>>>>>>>> >>>>>>>>>> I can't even make sense of that. It's a *theory* of English >>>>>>>>>> semantics. >>>>>>>>>> >>>>>>>>> >>>>>>>>> *Here is a concrete example* >>>>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>>> where the predicate Married(x) is defined in terms of billions >>>>>>>>> of other things such as all of the details of Human(x). >>>>>>>> >>>>>>>> A concrete example of what? That's certainly not an example of >>>>>>>> 'the syntax of English semantics'. That's simply a stipulation >>>>>>>> involving two predicates. >>>>>>>> >>>>>>>> André >>>>>>>> >>>>>>> >>>>>>> It is one concrete example of how a knowledge ontology >>>>>>> of trillions of predicates can define the finite set >>>>>>> of atomic facts of the world. >>>>>> >>>>>> But the topic under discussion was the relationship between syntax >>>>>> and semantics in Montague Grammar, not how knowledge ontologies >>>>>> are represented. So this isn't an example in anyway relevant to >>>>>> the discussion. >>>>>> >>>>>>> *Actually read this, this time* >>>>>>> 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 >>>>>>> >>>>>>> That is the basic infrastructure for defining all *objects of >>>>>>> thought* >>>>>>> can be defined in terms of other *objects of thought* >>>>>> >>>>>> >>>>>> I know full well what a theory of types is. It has nothing to do >>>>>> with the relationship between syntax and semantics. >>>>>> >>>>>> André >>>>>> >>>>> >>>>> That particular theory of types lays out the infrastructure >>>>> of how all *objects of thought* can be defined in terms >>>>> of other *objects of thought* such that the entire body >>>>> of knowledge that can be expressed in language can be encoded >>>>> into a single coherent formal system. >>>> >>>> Typing “objects of thought” doesn’t make all truths provable — it >>>> only prevents ill-formed expressions. >>>> If your system looks complete, it’s because you threw away every >>>> sentence that would have made it incomplete. >>> >>> When ALL *objects of thought* are defined >>> in terms of other *objects of thought* then >>> their truth and their proof is simply walking >>> the knowledge tree. >> >> When ALL subjects of thoughts are defined >> in terms of other subjects of thoughts then >> there are no subjects of thoughts. > > Kurt Gödel explains the details of how *objects of thought* > are defined in terms of other *objects of thought* > > 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, That is irrelevant to the point that you cannot define ALL subjects of thoughts in terms of other subject of thoughts. In order to define subjects of thoughts in terms of other subjects of thoughts you need a subject of thoughts that is not defined in terms of other subjects of thoughts. Unless, of course, your ALL subjects of thoughts is no subjects thoughts. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-27 09:16 -0600 |
| Message-ID | <10g9pvn$1gvv5$1@dont-email.me> |
| In reply to | #641295 |
On 11/27/2025 1:30 AM, Mikko wrote: > olcott kirjoitti 26.11.2025 klo 16.58: >> On 11/26/2025 3:05 AM, Mikko wrote: >>> olcott kirjoitti 26.11.2025 klo 5.24: >>>> On 11/25/2025 8:43 PM, Python wrote: >>>>> Le 26/11/2025 à 03:41, olcott a écrit : >>>>>> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>>>>>> On 2025-11-25 19:30, olcott wrote: >>>>>>>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>>>>>> On 2025-11-25 19:08, olcott wrote: >>>>>>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>>>>>> 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. >>>>>>>>>>>>> >>>>>>>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>>>>>>> >>>>>>>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>>>>>>> (specifically English) semantics expressed in terms of >>>>>>>>>>>>> logic. Formulae in his system have a syntax. They also have >>>>>>>>>>>>> a semantics. The two are very much distinct. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Montague Grammar is the syntax of English semantics >>>>>>>>>>> >>>>>>>>>>> I can't even make sense of that. It's a *theory* of English >>>>>>>>>>> semantics. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> *Here is a concrete example* >>>>>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>>>> where the predicate Married(x) is defined in terms of billions >>>>>>>>>> of other things such as all of the details of Human(x). >>>>>>>>> >>>>>>>>> A concrete example of what? That's certainly not an example of >>>>>>>>> 'the syntax of English semantics'. That's simply a stipulation >>>>>>>>> involving two predicates. >>>>>>>>> >>>>>>>>> André >>>>>>>>> >>>>>>>> >>>>>>>> It is one concrete example of how a knowledge ontology >>>>>>>> of trillions of predicates can define the finite set >>>>>>>> of atomic facts of the world. >>>>>>> >>>>>>> But the topic under discussion was the relationship between >>>>>>> syntax and semantics in Montague Grammar, not how knowledge >>>>>>> ontologies are represented. So this isn't an example in anyway >>>>>>> relevant to the discussion. >>>>>>> >>>>>>>> *Actually read this, this time* >>>>>>>> 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 >>>>>>>> >>>>>>>> That is the basic infrastructure for defining all *objects of >>>>>>>> thought* >>>>>>>> can be defined in terms of other *objects of thought* >>>>>>> >>>>>>> >>>>>>> I know full well what a theory of types is. It has nothing to do >>>>>>> with the relationship between syntax and semantics. >>>>>>> >>>>>>> André >>>>>>> >>>>>> >>>>>> That particular theory of types lays out the infrastructure >>>>>> of how all *objects of thought* can be defined in terms >>>>>> of other *objects of thought* such that the entire body >>>>>> of knowledge that can be expressed in language can be encoded >>>>>> into a single coherent formal system. >>>>> >>>>> Typing “objects of thought” doesn’t make all truths provable — it >>>>> only prevents ill-formed expressions. >>>>> If your system looks complete, it’s because you threw away every >>>>> sentence that would have made it incomplete. >>>> >>>> When ALL *objects of thought* are defined >>>> in terms of other *objects of thought* then >>>> their truth and their proof is simply walking >>>> the knowledge tree. >>> >>> When ALL subjects of thoughts are defined >>> in terms of other subjects of thoughts then >>> there are no subjects of thoughts. >> >> Kurt Gödel explains the details of how *objects of thought* >> are defined in terms of other *objects of thought* >> >> 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, > > That is irrelevant to the point that you cannot define ALL subjects of > thoughts in terms of other subject of thoughts. One cannot possibly exhaustively define individual living human beings at all. They are the subject of thought from the Zen Buddhist subject/object dichotomy at the heart of Anattā. https://en.wikipedia.org/wiki/Anatt%C4%81 On the other hand *objects of thought* are the set of every element of every thought that anyone can ever have when this thought is expressed in language. > In order to define > subjects of thoughts in terms of other subjects of thoughts you need a > subject of thoughts that is not defined in terms of other subjects of > thoughts. Unless, of course, your ALL subjects of thoughts is no > subjects thoughts. > -- 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 | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-28 10:35 +0200 |
| Message-ID | <10gbmrp$2833a$1@dont-email.me> |
| In reply to | #641310 |
olcott kirjoitti 27.11.2025 klo 17.16: > On 11/27/2025 1:30 AM, Mikko wrote: >> olcott kirjoitti 26.11.2025 klo 16.58: >>> On 11/26/2025 3:05 AM, Mikko wrote: >>>> olcott kirjoitti 26.11.2025 klo 5.24: >>>>> On 11/25/2025 8:43 PM, Python wrote: >>>>>> Le 26/11/2025 à 03:41, olcott a écrit : >>>>>>> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>>>>>>> On 2025-11-25 19:30, olcott wrote: >>>>>>>>> On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>>>>>>> On 2025-11-25 19:08, olcott wrote: >>>>>>>>>>> On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>>>>> On 2025-11-25 18:43, olcott wrote: >>>>>>>>>>>>> On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>>>>>>> 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. >>>>>>>>>>>>>> >>>>>>>>>>>>>> You're terribly confused here. Montague Grammar is called >>>>>>>>>>>>>> 'Montague Grammar' because it is due to Richard Montague. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Montague Grammar presents a theory of natural language >>>>>>>>>>>>>> (specifically English) semantics expressed in terms of >>>>>>>>>>>>>> logic. Formulae in his system have a syntax. They also >>>>>>>>>>>>>> have a semantics. The two are very much distinct. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Montague Grammar is the syntax of English semantics >>>>>>>>>>>> >>>>>>>>>>>> I can't even make sense of that. It's a *theory* of English >>>>>>>>>>>> semantics. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> *Here is a concrete example* >>>>>>>>>>> The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>>>>> where the predicate Married(x) is defined in terms of billions >>>>>>>>>>> of other things such as all of the details of Human(x). >>>>>>>>>> >>>>>>>>>> A concrete example of what? That's certainly not an example of >>>>>>>>>> 'the syntax of English semantics'. That's simply a stipulation >>>>>>>>>> involving two predicates. >>>>>>>>>> >>>>>>>>>> André >>>>>>>>>> >>>>>>>>> >>>>>>>>> It is one concrete example of how a knowledge ontology >>>>>>>>> of trillions of predicates can define the finite set >>>>>>>>> of atomic facts of the world. >>>>>>>> >>>>>>>> But the topic under discussion was the relationship between >>>>>>>> syntax and semantics in Montague Grammar, not how knowledge >>>>>>>> ontologies are represented. So this isn't an example in anyway >>>>>>>> relevant to the discussion. >>>>>>>> >>>>>>>>> *Actually read this, this time* >>>>>>>>> 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 >>>>>>>>> >>>>>>>>> That is the basic infrastructure for defining all *objects of >>>>>>>>> thought* >>>>>>>>> can be defined in terms of other *objects of thought* >>>>>>>> >>>>>>>> >>>>>>>> I know full well what a theory of types is. It has nothing to do >>>>>>>> with the relationship between syntax and semantics. >>>>>>>> >>>>>>>> André >>>>>>>> >>>>>>> >>>>>>> That particular theory of types lays out the infrastructure >>>>>>> of how all *objects of thought* can be defined in terms >>>>>>> of other *objects of thought* such that the entire body >>>>>>> of knowledge that can be expressed in language can be encoded >>>>>>> into a single coherent formal system. >>>>>> >>>>>> Typing “objects of thought” doesn’t make all truths provable — it >>>>>> only prevents ill-formed expressions. >>>>>> If your system looks complete, it’s because you threw away every >>>>>> sentence that would have made it incomplete. >>>>> >>>>> When ALL *objects of thought* are defined >>>>> in terms of other *objects of thought* then >>>>> their truth and their proof is simply walking >>>>> the knowledge tree. >>>> >>>> When ALL subjects of thoughts are defined >>>> in terms of other subjects of thoughts then >>>> there are no subjects of thoughts. >>> >>> Kurt Gödel explains the details of how *objects of thought* >>> are defined in terms of other *objects of thought* >>> >>> 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, >> >> That is irrelevant to the point that you cannot define ALL subjects of >> thoughts in terms of other subject of thoughts. > > One cannot possibly exhaustively define individual > living human beings at all. True, as already pointed out by Aristotle; but irrelevant to the point that if all objects of thought are defined by other objects of thought there are not objects of thought at all. >> In order to define >> subjects of thoughts in terms of other subjects of thoughts you need a >> subject of thoughts that is not defined in terms of other subjects of >> thoughts. Unless, of course, your ALL subjects of thoughts is no >> subjects thoughts. -- Mikko
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