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Groups > sci.math > #641072 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2025-11-25 14:20 -0600 |
| Last post | 2025-11-26 00:45 +0000 |
| Articles | 20 on this page of 190 — 12 participants |
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New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 14:20 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 20:56 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 15:01 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 21:03 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 15:09 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 21:12 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 15:27 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 13:30 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 23:14 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 17:21 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-25 23:25 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:00 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:04 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:14 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:18 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:38 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:42 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 00:47 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:52 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:57 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 19:19 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:29 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:32 +0000
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 18:29 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 19:43 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:45 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:03 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:09 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:34 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:36 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:46 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:47 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:01 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:03 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:11 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 07:34 -0500
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-05 17:03 -0600
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-05 19:53 -0600
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:36 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:38 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 19:36 -0800
Re: New formal foundation for correct reasoning makes True(X) computable polcott <polcott333@gmail.com> - 2025-11-26 22:10 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 21:30 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 02:36 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:43 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:09 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:17 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:26 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:32 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 05:15 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 07:36 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-26 11:22 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 09:15 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 10:20 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 10:31 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 19:43 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-27 09:40 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-27 09:17 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-27 10:42 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:29 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-28 08:54 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-28 17:22 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 16:31 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:40 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-29 10:42 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-29 15:01 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-30 12:19 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:46 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:22 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:24 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:27 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:33 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:36 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:50 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:53 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:58 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 22:18 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:21 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:56 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:54 -0800
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:22 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:23 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:55 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:58 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 22:06 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:11 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:23 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:24 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 20:56 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:01 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 08:53 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 10:06 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 21:59 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 05:18 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 05:16 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:14 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 07:27 -0500
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:00 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:08 -0600
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:12 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:30 -0600
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:36 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:41 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:43 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:24 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:26 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:30 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:47 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 22:01 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 04:07 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 08:44 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 10:04 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-26 10:34 -0500
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-26 11:05 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 08:58 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-27 09:30 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-27 09:16 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:35 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-28 09:16 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:44 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-29 10:40 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-30 12:14 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-26 09:13 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:36 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-28 09:18 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:48 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-29 10:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-11-30 12:07 +0200
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-03 12:53 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-03 10:11 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-04 11:07 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-04 08:10 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-05 11:13 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-05 11:40 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:19 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-06 06:45 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:55 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-08 13:44 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-06 11:21 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-06 06:46 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-07 12:50 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-07 11:15 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-08 11:08 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-08 13:05 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-13 13:05 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-13 09:55 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-15 11:52 +0200
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-12-15 09:49 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Mikko <mikko.levanto@iki.fi> - 2025-12-17 12:49 +0200
Re: New formal foundation for correct reasoning makes True(X) computable André G. Isaak <agisaak@gm.invalid> - 2025-11-25 19:45 -0700
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:59 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:16 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 02:34 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 20:37 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:02 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:06 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 03:08 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 03:19 +0000
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:28 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Richard Heathfield <rjh@cpax.org.uk> - 2025-11-26 05:53 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:15 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:21 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:16 -0800
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 19:08 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:19 -0600
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 19:22 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 21:30 -0600
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:18 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 22:14 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-26 01:48 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Richard Damon <Richard@Damon-Family.org> - 2025-11-25 20:59 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 21:11 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:16 +0000
Re: New formal foundation for correct reasoning makes True(X) computable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:34 +0000
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 20:05 -0800
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-25 13:27 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-11-26 19:23 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dbush <dbush.mobile@gmail.com> - 2025-11-26 14:40 -0500
Re: New formal foundation for correct reasoning makes True(X) computable "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-26 20:03 -0800
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 16:29 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:31 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 17:09 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 01:19 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 18:38 -0800
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 02:40 +0000
Re: New formal foundation for correct reasoning makes True(X) computable dart200 <user7160@newsgrouper.org.invalid> - 2025-11-25 19:16 -0800
Re: New formal foundation for correct reasoning makes True(X) computable olcott <polcott333@gmail.com> - 2025-11-25 18:40 -0600
Re: New formal foundation for correct reasoning makes True(X) computable Python <python@cccp.invalid> - 2025-11-26 00:45 +0000
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-28 09:16 -0600 |
| Message-ID | <10gcedc$2h1f4$1@dont-email.me> |
| In reply to | #641330 |
On 11/28/2025 2:35 AM, Mikko wrote:
> 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.
>
So you never heard of a type hierarchy that
has as its root: {thing}
>>> 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.
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-29 11:44 +0200 |
| Message-ID | <10gefak$385km$1@dont-email.me> |
| In reply to | #641345 |
olcott kirjoitti 28.11.2025 klo 17.16:
> On 11/28/2025 2:35 AM, Mikko wrote:
>> 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.
>
> So you never heard of a type hierarchy that
> has as its root: {thing}
Of course I have. Such type hierarcy has a structure that is different
from the structure where ALL subjects of thoughts are defined in terms
of other subjects of thoughts.
--
Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-29 10:40 -0600 |
| Message-ID | <10gf7m1$3hehl$2@dont-email.me> |
| In reply to | #641389 |
On 11/29/2025 3:44 AM, Mikko wrote:
> olcott kirjoitti 28.11.2025 klo 17.16:
>> On 11/28/2025 2:35 AM, Mikko wrote:
>>> 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.
>>
>> So you never heard of a type hierarchy that
>> has as its root: {thing}
>
> Of course I have. Such type hierarcy has a structure that is different
> from the structure where ALL subjects of thoughts are defined in terms
> of other subjects of thoughts.
>
The are synonymous. Even the root of the knowledge
tree: "thing" is defined in terms of its branches.
--
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.
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-30 12:14 +0200 |
| Message-ID | <10gh5e9$85rj$1@dont-email.me> |
| In reply to | #641408 |
olcott kirjoitti 29.11.2025 klo 18.40:
> On 11/29/2025 3:44 AM, Mikko wrote:
>> olcott kirjoitti 28.11.2025 klo 17.16:
>>> On 11/28/2025 2:35 AM, Mikko wrote:
>>>> 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.
>>>
>>> So you never heard of a type hierarchy that
>>> has as its root: {thing}
>>
>> Of course I have. Such type hierarcy has a structure that is different
>> from the structure where ALL subjects of thoughts are defined in terms
>> of other subjects of thoughts.
>
> The are synonymous. Even the root of the knowledge
> tree: "thing" is defined in terms of its branches.
Do you mean that your system allows circular definitions?
--
Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-26 09:13 -0600 |
| Message-ID | <10g75ef$gf3b$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. I am merely elaborating the structure of the knowledge ontology inheritance hierarchy tree of 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 | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-11-28 10:36 +0200 |
| Message-ID | <10gbmtg$2833a$2@dont-email.me> |
| In reply to | #641211 |
olcott kirjoitti 26.11.2025 klo 17.13: > 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. > > I am merely elaborating the structure of the > knowledge ontology inheritance hierarchy > tree of knowledge. If the structure is empty there is no need to elaborate. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-28 09:18 -0600 |
| Message-ID | <10gcegf$2h1f4$2@dont-email.me> |
| In reply to | #641331 |
On 11/28/2025 2:36 AM, Mikko wrote: > olcott kirjoitti 26.11.2025 klo 17.13: >> 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. >> >> I am merely elaborating the structure of the >> knowledge ontology inheritance hierarchy >> tree of knowledge. > > If the structure is empty there is no need to elaborate. > Every thought that anyone can possibly have has its place in a knowledge ontology inheritance hierarchy. -- 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 | 2025-11-29 11:48 +0200 |
| Message-ID | <10gefgi$387hc$1@dont-email.me> |
| In reply to | #641346 |
olcott kirjoitti 28.11.2025 klo 17.18: > On 11/28/2025 2:36 AM, Mikko wrote: >> olcott kirjoitti 26.11.2025 klo 17.13: >>> 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. >>> >>> I am merely elaborating the structure of the >>> knowledge ontology inheritance hierarchy >>> tree of knowledge. >> >> If the structure is empty there is no need to elaborate. > > Every thought that anyone can possibly have > has its place in a knowledge ontology inheritance > hierarchy. But none of them is in the colloection of subjects of thoughts where ALL subjects of thoughts are defined in terms of other subjects of thoughts. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-11-29 10:45 -0600 |
| Message-ID | <10gf7ug$3hehl$4@dont-email.me> |
| In reply to | #641390 |
On 11/29/2025 3:48 AM, Mikko wrote: > olcott kirjoitti 28.11.2025 klo 17.18: >> On 11/28/2025 2:36 AM, Mikko wrote: >>> olcott kirjoitti 26.11.2025 klo 17.13: >>>> 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. >>>> >>>> I am merely elaborating the structure of the >>>> knowledge ontology inheritance hierarchy >>>> tree of knowledge. >>> >>> If the structure is empty there is no need to elaborate. >> >> Every thought that anyone can possibly have >> has its place in a knowledge ontology inheritance >> hierarchy. > > But none of them is in the colloection of subjects of thoughts where > ALL subjects of thoughts are defined in terms of other subjects of > thoughts. > In Zen Buddhism subjects of thought are the imaginary ego that does not actually exist. Other than that I have no idea what you are talking about. -- 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 | 2025-11-30 12:07 +0200 |
| Message-ID | <9b3d27b6-df78-4381-9041-2d323a6100e2@iki.fi> |
| In reply to | #641410 |
olcott kirjoitti 29.11.2025 klo 18.45: > On 11/29/2025 3:48 AM, Mikko wrote: >> olcott kirjoitti 28.11.2025 klo 17.18: >>> On 11/28/2025 2:36 AM, Mikko wrote: >>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>> 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. >>>>> >>>>> I am merely elaborating the structure of the >>>>> knowledge ontology inheritance hierarchy >>>>> tree of knowledge. >>>> >>>> If the structure is empty there is no need to elaborate. >>> >>> Every thought that anyone can possibly have >>> has its place in a knowledge ontology inheritance >>> hierarchy. >> >> But none of them is in the colloection of subjects of thoughts where >> ALL subjects of thoughts are defined in terms of other subjects of >> thoughts. > In Zen Buddhism subjects of thought are the imaginary > ego that does not actually exist. Other than that > I have no idea what you are talking about. I'm talking oabout your collection of subjects of thoughts where ALL subjects of thoughts are defined in terms of other subjects of thoughts. That collection is empty. You can't show a single example ofa collection of subjects of thoughts where every subject of thought in the example is defined in terms of other subjects of thoughts in the example. -- Mikko
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2025-12-03 12:53 +0200 |
| Message-ID | <10gp4r0$37nh4$1@dont-email.me> |
| In reply to | #641211 |
olcott kirjoitti 26.11.2025 klo 17.13: > 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. > > I am merely elaborating the structure of the > knowledge ontology inheritance hierarchy > tree of knowledge. When ALL subjects of thoughts are defined in terms of other subjects of thoughts the system of ALL subjects of thoughts is either empty or not a hierarchy. There is no hierarchy where every member is under another member. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-03 10:11 -0600 |
| Message-ID | <10gpnfb$3f0cv$1@dont-email.me> |
| In reply to | #641580 |
On 12/3/2025 4:53 AM, Mikko wrote: > olcott kirjoitti 26.11.2025 klo 17.13: >> 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. >> >> I am merely elaborating the structure of the >> knowledge ontology inheritance hierarchy >> tree of knowledge. > > When ALL subjects of thoughts are defined in terms of other subjects > of thoughts the system of ALL subjects of thoughts is either empty > or not a hierarchy. There is no hierarchy where every member is under > another member. > *I have always been referring to the entire body of general knowledge* In philosophy, a subject is a being that exercises agency, undergoes conscious experiences, and is situated in relation to other things that exist outside itself; thus, a subject is any individual, person, or observer.[1] An object is any of the things observed or experienced by a subject, which may even include other beings (thus, from their own points of view: other subjects). https://en.wikipedia.org/wiki/Subject_and_object_(philosophy) -- 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 | 2025-12-04 11:07 +0200 |
| Message-ID | <10grivs$4fi5$1@dont-email.me> |
| In reply to | #641585 |
olcott kirjoitti 3.12.2025 klo 18.11: > On 12/3/2025 4:53 AM, Mikko wrote: >> olcott kirjoitti 26.11.2025 klo 17.13: >>> 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. >>> >>> I am merely elaborating the structure of the >>> knowledge ontology inheritance hierarchy >>> tree of knowledge. >> >> When ALL subjects of thoughts are defined in terms of other subjects >> of thoughts the system of ALL subjects of thoughts is either empty >> or not a hierarchy. There is no hierarchy where every member is under >> another member. > > *I have always been referring to the entire body of general knowledge* Your condition that ALL objects of thought can be defined in terms of other objects of thought is false about every non-empyt collection of objects of thjought, inluding the entire body of general knowledge, unless your system allows circular definitions that actually don't define. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-04 08:10 -0600 |
| Message-ID | <10gs4p5$bf3g$1@dont-email.me> |
| In reply to | #641602 |
On 12/4/2025 3:07 AM, Mikko wrote: > olcott kirjoitti 3.12.2025 klo 18.11: >> On 12/3/2025 4:53 AM, Mikko wrote: >>> olcott kirjoitti 26.11.2025 klo 17.13: >>>> 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. >>>> >>>> I am merely elaborating the structure of the >>>> knowledge ontology inheritance hierarchy >>>> tree of knowledge. >>> >>> When ALL subjects of thoughts are defined in terms of other subjects >>> of thoughts the system of ALL subjects of thoughts is either empty >>> or not a hierarchy. There is no hierarchy where every member is under >>> another member. >> >> *I have always been referring to the entire body of general knowledge* > > Your condition that ALL objects of thought can be defined in terms of > other objects of thought is false about every non-empyt collection of > objects of thjought, inluding the entire body of general knowledge, > unless your system allows circular definitions that actually don't > define. > Yes circular definitions can be defined syntactically and are rejected as semantically unsound. % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. In Olcott's Minimal Type Theory LP := ~True(LP) that expands to: ~True(~True(~True(~True(~True(LP))))) % This sentence cannot be proven in F ?- G = not(provable(F, G)). G = not(provable(F, G)). ?- unify_with_occurs_check(G, not(provable(F, G))). false. BEGIN:(Clocksin & Mellish 2003:254) Finally, a note about how Prolog matching sometimes differs from the unification used in Resolution. Most Prolog systems will allow you to satisfy goals like: equal(X, X). ?- equal(foo(Y), Y). that is, they will allow you to match a term against an uninstantiated subterm of itself. In this example, foo(Y) is matched against Y, which appears within it. As a result, Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands for), which is foo(foo(foo(Y))), and so on. So Y ends up standing for some kind of infinite structure. END:(Clocksin & Mellish 2003:254) -- 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 | 2025-12-05 11:13 +0200 |
| Message-ID | <10gu7nd$16dku$1@dont-email.me> |
| In reply to | #641610 |
olcott kirjoitti 4.12.2025 klo 16.10: > On 12/4/2025 3:07 AM, Mikko wrote: >> olcott kirjoitti 3.12.2025 klo 18.11: >>> On 12/3/2025 4:53 AM, Mikko wrote: >>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>> 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. >>>>> >>>>> I am merely elaborating the structure of the >>>>> knowledge ontology inheritance hierarchy >>>>> tree of knowledge. >>>> >>>> When ALL subjects of thoughts are defined in terms of other subjects >>>> of thoughts the system of ALL subjects of thoughts is either empty >>>> or not a hierarchy. There is no hierarchy where every member is under >>>> another member. >>> >>> *I have always been referring to the entire body of general knowledge* >> >> Your condition that ALL objects of thought can be defined in terms of >> other objects of thought is false about every non-empyt collection of >> objects of thjought, inluding the entire body of general knowledge, >> unless your system allows circular definitions that actually don't >> define. > Yes circular definitions can be defined syntactically > and are rejected as semantically unsound. The usual way is to rehject them as syntactically invalid. If you accept circular definitions as syntactically correct even if semantically unsound the you can have a nonempty collection of unsound objects of thought so that ALL objects of thought in that collection are defined (circularly) in terms of other objects of thought. But every object of thought defined in terms of an unsound object of thought is also unsound. > % This sentence is not true. You mean the one on the foloowing line? > ?- LP = not(true(LP)). > LP = not(true(LP)). The answer by the Prolog system means that it is true according to the Prolog rules. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-05 11:40 -0600 |
| Message-ID | <10gv5ev$1k1r1$1@dont-email.me> |
| In reply to | #641623 |
On 12/5/2025 3:13 AM, Mikko wrote: > olcott kirjoitti 4.12.2025 klo 16.10: >> On 12/4/2025 3:07 AM, Mikko wrote: >>> olcott kirjoitti 3.12.2025 klo 18.11: >>>> On 12/3/2025 4:53 AM, Mikko wrote: >>>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>>> 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. >>>>>> >>>>>> I am merely elaborating the structure of the >>>>>> knowledge ontology inheritance hierarchy >>>>>> tree of knowledge. >>>>> >>>>> When ALL subjects of thoughts are defined in terms of other subjects >>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>> or not a hierarchy. There is no hierarchy where every member is under >>>>> another member. >>>> >>>> *I have always been referring to the entire body of general knowledge* >>> >>> Your condition that ALL objects of thought can be defined in terms of >>> other objects of thought is false about every non-empyt collection of >>> objects of thjought, inluding the entire body of general knowledge, >>> unless your system allows circular definitions that actually don't >>> define. > >> Yes circular definitions can be defined syntactically >> and are rejected as semantically unsound. > > The usual way is to rehject them as syntactically invalid. > Even this simplified version has the same pathological self-reference (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom People incorrectly construe this as non-circular because of the convoluted mess of calculating Gödel numbers. The above expression abstracts away this convoluted mess. > If you accept circular definitions as syntactically correct even if > semantically unsound That would be quite nuts > the you can have a nonempty collection of unsound > objects of thought so that ALL objects of thought in that collection > are defined (circularly) in terms of other objects of thought. But > every object of thought defined in terms of an unsound object of > thought is also unsound. > >> % This sentence is not true. > > You mean the one on the foloowing line? > >> ?- LP = not(true(LP)). >> LP = not(true(LP)). > > The answer by the Prolog system means that it is true according to > the Prolog rules. > When you dishonestly erase the most important part then it might seem that way to stupid people. % This sentence cannot be proven in F ?- G = not(provable(F, G)). G = not(provable(F, G)). ?- unify_with_occurs_check(G, not(provable(F, G))). false. The false means that LP = not(true(LP)). is semantically unsound. Colorless green ideas sleep furiously was composed by Noam Chomsky in his 1957 book Syntactic Structures as an example of a sentence that is grammatically well-formed, but semantically nonsensical. https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously One of the most brilliant guys on formal languages clearly proves that it is the semantics that counts. -- 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 | 2025-12-06 11:19 +0200 |
| Message-ID | <10h0sen$29a0r$1@dont-email.me> |
| In reply to | #641640 |
olcott kirjoitti 5.12.2025 klo 19.40: > On 12/5/2025 3:13 AM, Mikko wrote: >> olcott kirjoitti 4.12.2025 klo 16.10: >>> On 12/4/2025 3:07 AM, Mikko wrote: >>>> olcott kirjoitti 3.12.2025 klo 18.11: >>>>> On 12/3/2025 4:53 AM, Mikko wrote: >>>>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>>>> 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. >>>>>>> >>>>>>> I am merely elaborating the structure of the >>>>>>> knowledge ontology inheritance hierarchy >>>>>>> tree of knowledge. >>>>>> >>>>>> When ALL subjects of thoughts are defined in terms of other subjects >>>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>>> or not a hierarchy. There is no hierarchy where every member is under >>>>>> another member. >>>>> >>>>> *I have always been referring to the entire body of general knowledge* >>>> >>>> Your condition that ALL objects of thought can be defined in terms of >>>> other objects of thought is false about every non-empyt collection of >>>> objects of thjought, inluding the entire body of general knowledge, >>>> unless your system allows circular definitions that actually don't >>>> define. >> >>> Yes circular definitions can be defined syntactically >>> and are rejected as semantically unsound. >> >> The usual way is to rehject them as syntactically invalid. > Even this simplified version has the same pathological self-reference > (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). There is no self reference there. F is a formal system. A formal system is not a reference. GF is an uninterpreted sentence in the language of F that is constructed earlier. Because it is uninterpreted it cannot refer. ProvF is the provability predicate that the caunter-assumption assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not refer. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-06 06:45 -0600 |
| Message-ID | <10h18gr$2dlk1$1@dont-email.me> |
| In reply to | #641660 |
On 12/6/2025 3:19 AM, Mikko wrote: > olcott kirjoitti 5.12.2025 klo 19.40: >> On 12/5/2025 3:13 AM, Mikko wrote: >>> olcott kirjoitti 4.12.2025 klo 16.10: >>>> On 12/4/2025 3:07 AM, Mikko wrote: >>>>> olcott kirjoitti 3.12.2025 klo 18.11: >>>>>> On 12/3/2025 4:53 AM, Mikko wrote: >>>>>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>>>>> 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. >>>>>>>> >>>>>>>> I am merely elaborating the structure of the >>>>>>>> knowledge ontology inheritance hierarchy >>>>>>>> tree of knowledge. >>>>>>> >>>>>>> When ALL subjects of thoughts are defined in terms of other subjects >>>>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>>>> or not a hierarchy. There is no hierarchy where every member is >>>>>>> under >>>>>>> another member. >>>>>> >>>>>> *I have always been referring to the entire body of general >>>>>> knowledge* >>>>> >>>>> Your condition that ALL objects of thought can be defined in terms of >>>>> other objects of thought is false about every non-empyt collection of >>>>> objects of thjought, inluding the entire body of general knowledge, >>>>> unless your system allows circular definitions that actually don't >>>>> define. >>> >>>> Yes circular definitions can be defined syntactically >>>> and are rejected as semantically unsound. >>> >>> The usual way is to rehject them as syntactically invalid. > >> Even this simplified version has the same pathological self-reference >> (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). > > There is no self reference there. F is a formal system. A formal system > is not a reference. GF is an uninterpreted sentence in the language of > F that is constructed earlier. Because it is uninterpreted it cannot > refer. ProvF is the provability predicate that the caunter-assumption > assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not > refer. > ...We are therefore confronted with a proposition which asserts its own unprovability. 15 … (Gödel 1931:40-41) Gödel, Kurt 1931. On Formally Undecidable Propositions of Principia Mathematica And Related Systems He says there is and the above expression fails the unify_with_occurs_check. That you don't understand what this means is not a rebuttal. % This sentence cannot be proven in F ?- G = not(provable(F, G)). G = not(provable(F, G)). ?- unify_with_occurs_check(G, not(provable(F, G))). false. -- 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 | 2025-12-07 12:55 +0200 |
| Message-ID | <10h3meo$3cqqf$1@dont-email.me> |
| In reply to | #641671 |
olcott kirjoitti 6.12.2025 klo 14.45: > On 12/6/2025 3:19 AM, Mikko wrote: >> olcott kirjoitti 5.12.2025 klo 19.40: >>> On 12/5/2025 3:13 AM, Mikko wrote: >>>> olcott kirjoitti 4.12.2025 klo 16.10: >>>>> On 12/4/2025 3:07 AM, Mikko wrote: >>>>>> olcott kirjoitti 3.12.2025 klo 18.11: >>>>>>> On 12/3/2025 4:53 AM, Mikko wrote: >>>>>>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>>>>>> 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. >>>>>>>>> >>>>>>>>> I am merely elaborating the structure of the >>>>>>>>> knowledge ontology inheritance hierarchy >>>>>>>>> tree of knowledge. >>>>>>>> >>>>>>>> When ALL subjects of thoughts are defined in terms of other >>>>>>>> subjects >>>>>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>>>>> or not a hierarchy. There is no hierarchy where every member is >>>>>>>> under >>>>>>>> another member. >>>>>>> >>>>>>> *I have always been referring to the entire body of general >>>>>>> knowledge* >>>>>> >>>>>> Your condition that ALL objects of thought can be defined in terms of >>>>>> other objects of thought is false about every non-empyt collection of >>>>>> objects of thjought, inluding the entire body of general knowledge, >>>>>> unless your system allows circular definitions that actually don't >>>>>> define. >>>> >>>>> Yes circular definitions can be defined syntactically >>>>> and are rejected as semantically unsound. >>>> >>>> The usual way is to rehject them as syntactically invalid. >> >>> Even this simplified version has the same pathological self-reference >>> (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). >> >> There is no self reference there. F is a formal system. A formal system >> is not a reference. GF is an uninterpreted sentence in the language of >> F that is constructed earlier. Because it is uninterpreted it cannot >> refer. ProvF is the provability predicate that the caunter-assumption >> assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not >> refer. > > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 … (Gödel 1931:40-41) Here Gödel refers to a non-arithmetic interpretation of an arithmetic sentence. But there is no self-reference in the arithmetic meaning of the sentence. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2025-12-08 13:44 -0600 |
| Message-ID | <10h79rk$c4ep$1@dont-email.me> |
| In reply to | #641699 |
On 12/7/2025 4:55 AM, Mikko wrote: > olcott kirjoitti 6.12.2025 klo 14.45: >> On 12/6/2025 3:19 AM, Mikko wrote: >>> olcott kirjoitti 5.12.2025 klo 19.40: >>>> On 12/5/2025 3:13 AM, Mikko wrote: >>>>> olcott kirjoitti 4.12.2025 klo 16.10: >>>>>> On 12/4/2025 3:07 AM, Mikko wrote: >>>>>>> olcott kirjoitti 3.12.2025 klo 18.11: >>>>>>>> On 12/3/2025 4:53 AM, Mikko wrote: >>>>>>>>> olcott kirjoitti 26.11.2025 klo 17.13: >>>>>>>>>> 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. >>>>>>>>>> >>>>>>>>>> I am merely elaborating the structure of the >>>>>>>>>> knowledge ontology inheritance hierarchy >>>>>>>>>> tree of knowledge. >>>>>>>>> >>>>>>>>> When ALL subjects of thoughts are defined in terms of other >>>>>>>>> subjects >>>>>>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>>>>>> or not a hierarchy. There is no hierarchy where every member is >>>>>>>>> under >>>>>>>>> another member. >>>>>>>> >>>>>>>> *I have always been referring to the entire body of general >>>>>>>> knowledge* >>>>>>> >>>>>>> Your condition that ALL objects of thought can be defined in >>>>>>> terms of >>>>>>> other objects of thought is false about every non-empyt >>>>>>> collection of >>>>>>> objects of thjought, inluding the entire body of general knowledge, >>>>>>> unless your system allows circular definitions that actually don't >>>>>>> define. >>>>> >>>>>> Yes circular definitions can be defined syntactically >>>>>> and are rejected as semantically unsound. >>>>> >>>>> The usual way is to rehject them as syntactically invalid. >>> >>>> Even this simplified version has the same pathological self-reference >>>> (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). >>> >>> There is no self reference there. F is a formal system. A formal system >>> is not a reference. GF is an uninterpreted sentence in the language of >>> F that is constructed earlier. Because it is uninterpreted it cannot >>> refer. ProvF is the provability predicate that the caunter-assumption >>> assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not >>> refer. >> >> ...We are therefore confronted with a proposition which asserts its >> own unprovability. 15 … (Gödel 1931:40-41) > > Here Gödel refers to a non-arithmetic interpretation of an arithmetic > sentence. But there is no self-reference in the arithmetic meaning > of the sentence. > (G) F ⊢ GF ↔ ¬ProvF(┌GF┐). The arithmetic can simply be represented Gödel_Number_of(GF) still showing pathological self reference(Olcott 2004) that cannot be resolved to a truth value. -- Copyright 2025 Olcott<br><br> My 28 year goal has been to make <br> "true on the basis of meaning" computable.<br><br> This required establishing a new foundation<br>
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