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Groups > sci.math > #644766 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-04-20 11:57 -0500 |
| Last post | 2026-06-30 06:54 +0100 |
| Articles | 20 on this page of 408 — 15 participants |
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Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-27 09:50 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:39 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-28 21:52 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:14 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:18 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:45 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:56 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 22:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:57 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:02 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:17 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 07:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 09:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 13:33 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:40 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:50 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:47 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:11 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:28 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:50 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:52 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 15:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 17:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 17:09 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 19:05 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 18:39 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 20:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 19:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:03 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 00:02 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 08:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:48 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:17 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:12 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:21 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:38 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:46 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 15:22 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:11 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:49 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:13 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 09:36 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:42 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:16 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 10:58 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:21 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:35 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:54 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:09 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:44 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:23 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:31 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:42 -0500
Re: The simple essence of Proof Theoretic Semantics Alan Mackenzie <acm@muc.de> - 2026-07-01 19:18 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:56 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:05 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:53 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:13 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:37 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:50 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 16:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 17:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 18:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 22:36 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:00 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:43 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:59 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 23:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:57 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 09:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 13:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 14:22 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 14:33 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 15:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 16:54 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:12 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:23 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:32 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:47 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 18:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 20:03 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:22 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 10:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 11:50 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:40 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:47 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 17:37 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 21:58 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:05 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:43 -0400
The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-03 22:11 -0500
Re: The truth about the halting problem counter-example input dbush <dbush.mobile@gmail.com> - 2026-07-03 23:23 -0400
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:58 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-04 12:16 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:07 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-06 10:18 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:45 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:58 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:07 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:11 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:27 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:19 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:04 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:46 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:55 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:24 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:30 -0500
Re: The simple essence of Proof Theoretic Semantics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:23 -0700
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 11:57 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:23 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:08 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:10 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:11 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:18 -0400
Re: The simple essence of Proof Theoretic Semantics Brenden Jafarov <rnarnj@rbn.ru> - 2026-07-04 12:47 +0000
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:43 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:04 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:28 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:27 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:45 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:53 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 16:59 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:57 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:01 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:33 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:25 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:10 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 14:08 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 15:12 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:38 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:09 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:28 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:15 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:41 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:38 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:40 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:39 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:14 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:32 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:37 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:06 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:03 +0300
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:25 +0300
Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-06 10:54 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:22 +0300
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-08 22:32 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:25 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:11 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:27 +0300
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: Terms-Of-The-Art are Liars Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 14:59 +0100
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:23 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 10:19 -0400
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:29 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 12:39 -0400
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 13:09 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:46 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 12:39 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:38 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-08 22:40 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:42 +0300
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 14:07 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:38 +0300
Re: Terms-Of-The-Art are Liars dart200 <user7160@newsgrouper.org.invalid> - 2026-07-06 14:53 -0700
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 17:01 -0500
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-07 15:36 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:17 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 10:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 10:07 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:27 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:56 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 13:12 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 12:54 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 14:03 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 14:08 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 15:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 15:13 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:00 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:53 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 17:39 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:52 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:47 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:45 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:44 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 10:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 11:01 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:35 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:54 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 13:14 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 19:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 07:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:56 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:22 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 06:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 12:04 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 22:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 17:22 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:10 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:30 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:11 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:35 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-29 14:27 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-27 15:35 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-01 21:17 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:34 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 16:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 15:52 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 17:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 11:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 12:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 15:25 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 14:30 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 16:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 15:15 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 17:55 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:16 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:58 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 12:00 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-06 14:19 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-04-26 15:54 -0500 |
| Message-ID | <10slu2o$1sd53$1@dont-email.me> |
| In reply to | #644877 |
On 4/26/2026 3:01 PM, Scott Hoge wrote: > On 2026-04-20, olcott <polcott333@gmail.com> wrote: >> Proof-theoretic semantics is inherently inferential, as >> it is inferential activity which manifests itself in proofs. >> ...inferences and the rules of inference establish the >> meaning of expressions. >> Schroeder-Heister, Peter, 2024 "Proof-Theoretic Semantics" >> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >> #InfeIntuAntiReal >> >> Provable(PA, φ) := ∃Γ ⊂ PA(Γ ⊣ φ) >> There exists a finite set Γ of inference steps of PA such that φ >> is back-chained to PA can ALWAYS be resolved in directly in SOL. >> Has_Meaning_PTS(PA, φ) := Provable(PA, φ) > > Twenty years ago (under my sixth-grade-adopted nickname "Mike"), > I posted in sci.math that Gödel's G was meaningless due to the > infinite regression toward infinity on the basis of which its > meaning was supposedly obtained. > > The correct interpretation was, I argued, not "This sentence is > unprovable," but rather: > > The following is unprovable (1): > The following is unprovable (2): > The following is unprovable (3): > ... > > As regards semantics, I could call statement (1) the "unencoded > sentence," sentence (2) the "first encoded sentence," the concept > under which all sentences (1)-(∞) belong the "formally abstracted > sentence," and the concept under which all sentences (2)-(∞) > belong the "encoding-abstracted sentence." > > Then, I could argue that: > > 1. The /unencoded sentence/ is /true and meaningful/. It's a > statement about numbers. > > 2. The /formally abstracted/ and /encoding-abstracted/ sentences > are both /meaningless/. > > Does this seem in agreement with your view? If so, how would you > describe my concepts in your own terms? > > --Scott Hoge F ⊢ GF ↔ ¬ProvF(⌜GF⌝) https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom Olcott's Minimal Type Theory G ↔ ¬Prov_PA(⌜G⌝) Directed Graph of evaluation sequence 00 ↔ 01 02 01 G 02 ¬ 03 03 Prov_PA 04 04 Gödel_Number_of 01 // cycle % 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 first incompleteness theorem sentence has a cycle in the directed graph of its evaluation sequence making it semantically incoherent. This kind of semantically incoherence is foundational in proof theoretic semantics. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Richard Damon <Richard@Damon-Family.org> |
|---|---|
| Date | 2026-04-26 20:16 -0400 |
| Message-ID | <FVxHR.558921$DN1.343068@fx48.iad> |
| In reply to | #644878 |
On 4/26/26 4:54 PM, olcott wrote: > On 4/26/2026 3:01 PM, Scott Hoge wrote: >> On 2026-04-20, olcott <polcott333@gmail.com> wrote: >>> Proof-theoretic semantics is inherently inferential, as >>> it is inferential activity which manifests itself in proofs. >>> ...inferences and the rules of inference establish the >>> meaning of expressions. >>> Schroeder-Heister, Peter, 2024 "Proof-Theoretic Semantics" >>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>> #InfeIntuAntiReal >>> >>> Provable(PA, φ) := ∃Γ ⊂ PA(Γ ⊣ φ) >>> There exists a finite set Γ of inference steps of PA such that φ >>> is back-chained to PA can ALWAYS be resolved in directly in SOL. >>> Has_Meaning_PTS(PA, φ) := Provable(PA, φ) >> >> Twenty years ago (under my sixth-grade-adopted nickname "Mike"), >> I posted in sci.math that Gödel's G was meaningless due to the >> infinite regression toward infinity on the basis of which its >> meaning was supposedly obtained. >> >> The correct interpretation was, I argued, not "This sentence is >> unprovable," but rather: >> >> The following is unprovable (1): >> The following is unprovable (2): >> The following is unprovable (3): >> ... >> >> As regards semantics, I could call statement (1) the "unencoded >> sentence," sentence (2) the "first encoded sentence," the concept >> under which all sentences (1)-(∞) belong the "formally abstracted >> sentence," and the concept under which all sentences (2)-(∞) >> belong the "encoding-abstracted sentence." >> >> Then, I could argue that: >> >> 1. The /unencoded sentence/ is /true and meaningful/. It's a >> statement about numbers. >> >> 2. The /formally abstracted/ and /encoding-abstracted/ sentences >> are both /meaningless/. >> >> Does this seem in agreement with your view? If so, how would you >> describe my concepts in your own terms? >> >> --Scott Hoge > > F ⊢ GF ↔ ¬ProvF(⌜GF⌝) > https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom > > Olcott's Minimal Type Theory > G ↔ ¬Prov_PA(⌜G⌝) > Directed Graph of evaluation sequence > 00 ↔ 01 02 > 01 G > 02 ¬ 03 > 03 Prov_PA 04 > 04 Gödel_Number_of 01 // cycle > > % 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 first incompleteness theorem sentence > has a cycle in the directed graph of its > evaluation sequence making it semantically > incoherent. > > This kind of semantically incoherence is > foundational in proof theoretic semantics. > > In other words, you admit that you logic system just can't handle the logic required in the system. Thus, your whole arguement is just a big fat stupid lie.
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-04-27 12:30 +0300 |
| Message-ID | <10snaci$28k0a$1@dont-email.me> |
| In reply to | #644878 |
On 26/04/2026 23:54, olcott wrote: > On 4/26/2026 3:01 PM, Scott Hoge wrote: >> On 2026-04-20, olcott <polcott333@gmail.com> wrote: >>> Proof-theoretic semantics is inherently inferential, as >>> it is inferential activity which manifests itself in proofs. >>> ...inferences and the rules of inference establish the >>> meaning of expressions. >>> Schroeder-Heister, Peter, 2024 "Proof-Theoretic Semantics" >>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>> #InfeIntuAntiReal >>> >>> Provable(PA, φ) := ∃Γ ⊂ PA(Γ ⊣ φ) >>> There exists a finite set Γ of inference steps of PA such that φ >>> is back-chained to PA can ALWAYS be resolved in directly in SOL. >>> Has_Meaning_PTS(PA, φ) := Provable(PA, φ) >> >> Twenty years ago (under my sixth-grade-adopted nickname "Mike"), >> I posted in sci.math that Gödel's G was meaningless due to the >> infinite regression toward infinity on the basis of which its >> meaning was supposedly obtained. >> >> The correct interpretation was, I argued, not "This sentence is >> unprovable," but rather: >> >> The following is unprovable (1): >> The following is unprovable (2): >> The following is unprovable (3): >> ... >> >> As regards semantics, I could call statement (1) the "unencoded >> sentence," sentence (2) the "first encoded sentence," the concept >> under which all sentences (1)-(∞) belong the "formally abstracted >> sentence," and the concept under which all sentences (2)-(∞) >> belong the "encoding-abstracted sentence." >> >> Then, I could argue that: >> >> 1. The /unencoded sentence/ is /true and meaningful/. It's a >> statement about numbers. >> >> 2. The /formally abstracted/ and /encoding-abstracted/ sentences >> are both /meaningless/. >> >> Does this seem in agreement with your view? If so, how would you >> describe my concepts in your own terms? >> >> --Scott Hoge > > F ⊢ GF ↔ ¬ProvF(⌜GF⌝) > https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom > > Olcott's Minimal Type Theory > G ↔ ¬Prov_PA(⌜G⌝) > Directed Graph of evaluation sequence > 00 ↔ 01 02 > 01 G > 02 ¬ 03 > 03 Prov_PA 04 > 04 Gödel_Number_of 01 // cycle > > % 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 first incompleteness theorem sentence > has a cycle in the directed graph of its > evaluation sequence making it semantically > incoherent. > > This kind of semantically incoherence is > foundational in proof theoretic semantics. Olcott's usual reaction is to say something unrelated to any asked question instead of answering. Perhaps he hopes to hide his ignorance and incompetens. But it does not work. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-04-27 09:53 -0500 |
| Message-ID | <10snt9d$2f46l$1@dont-email.me> |
| In reply to | #644884 |
On 4/27/2026 4:30 AM, Mikko wrote: > On 26/04/2026 23:54, olcott wrote: >> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>> On 2026-04-20, olcott <polcott333@gmail.com> wrote: >>>> Proof-theoretic semantics is inherently inferential, as >>>> it is inferential activity which manifests itself in proofs. >>>> ...inferences and the rules of inference establish the >>>> meaning of expressions. >>>> Schroeder-Heister, Peter, 2024 "Proof-Theoretic Semantics" >>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>> #InfeIntuAntiReal >>>> >>>> Provable(PA, φ) := ∃Γ ⊂ PA(Γ ⊣ φ) >>>> There exists a finite set Γ of inference steps of PA such that φ >>>> is back-chained to PA can ALWAYS be resolved in directly in SOL. >>>> Has_Meaning_PTS(PA, φ) := Provable(PA, φ) >>> >>> Twenty years ago (under my sixth-grade-adopted nickname "Mike"), >>> I posted in sci.math that Gödel's G was meaningless due to the >>> infinite regression toward infinity on the basis of which its >>> meaning was supposedly obtained. >>> >>> The correct interpretation was, I argued, not "This sentence is >>> unprovable," but rather: >>> >>> The following is unprovable (1): >>> The following is unprovable (2): >>> The following is unprovable (3): >>> ... The directed graph of the evaluation sequence of G has a cycle preventing its evaluation from ever terminating. If you have no idea what directed graphs are you will never get this. If you always knew what directed graphs of evaluation sequences that contain cycles are then you rebuttal has always been pure dishonesty. >>> >>> As regards semantics, I could call statement (1) the "unencoded >>> sentence," sentence (2) the "first encoded sentence," the concept >>> under which all sentences (1)-(∞) belong the "formally abstracted >>> sentence," and the concept under which all sentences (2)-(∞) >>> belong the "encoding-abstracted sentence." >>> >>> Then, I could argue that: >>> >>> 1. The /unencoded sentence/ is /true and meaningful/. It's a >>> statement about numbers. >>> >>> 2. The /formally abstracted/ and /encoding-abstracted/ sentences >>> are both /meaningless/. >>> >>> Does this seem in agreement with your view? If so, how would you >>> describe my concepts in your own terms? >>> >>> --Scott Hoge >> >> F ⊢ GF ↔ ¬ProvF(⌜GF⌝) >> https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom >> >> Olcott's Minimal Type Theory >> G ↔ ¬Prov_PA(⌜G⌝) >> Directed Graph of evaluation sequence >> 00 ↔ 01 02 >> 01 G >> 02 ¬ 03 >> 03 Prov_PA 04 >> 04 Gödel_Number_of 01 // cycle >> >> % 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 first incompleteness theorem sentence >> has a cycle in the directed graph of its >> evaluation sequence making it semantically >> incoherent. >> >> This kind of semantically incoherence is >> foundational in proof theoretic semantics. > > Olcott's usual reaction is to say something unrelated to any asked > question instead of answering. Perhaps he hopes to hide his ignorance > and incompetens. But it does not work. > In other words you did nor bother to page attention to what Scott Hoge said. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Scott Hoge <nospam@nospam.com> |
|---|---|
| Date | 2026-04-27 19:15 +0000 |
| Message-ID | <JBOHR.71960$qn1.41265@fx18.ams4> |
| In reply to | #644887 |
On 2026-04-27, olcott <polcott333@gmail.com> wrote: [...] >>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>> >>>> [...] >>>> >>>> The correct interpretation was, I argued, not "This sentence >>>> is unprovable," but rather: >>>> >>>> The following is unprovable (1): >>>> The following is unprovable (2): >>>> The following is unprovable (3): >>>> ... > > The directed graph of the evaluation sequence of G > has a cycle preventing its evaluation from ever > terminating. > > If you have no idea what directed graphs are you will > never get this. If you always knew what directed graphs > of evaluation sequences that contain cycles are then > you rebuttal has always been pure dishonesty. I learned what directed graphs were in high school. It seems our views are somewhat in agreement, but my directed graph looks like this: (D1) · ─→ · ─→ · ─→ · ─→ ... Yours appears to look like this, where its semantic (?) evaluation contains a cycle: (D2) · ─┐ ↑ ↓ └─ · (This may be an oversimplification of the actual cycle, but it's for illustrative purposes.) I'll requote my proposed division of concepts: >>>> As regards semantics, I could call statement (1) the >>>> "unencoded sentence," sentence (2) the "first encoded >>>> sentence," the concept under which all sentences (1)-(∞) >>>> belong the "formally abstracted sentence," and the concept >>>> under which all sentences (2)-(∞) belong the >>>> "encoding-abstracted sentence." If we're speaking of the /infinite sequence of nth-encoded sentences/, the graph would be D1. However, we may still be able to argue that for the /formally abstracted/ sentence, the graph would be D2. The formally abstracted sentence is closer in concept to "This sentence is unprovable." Does this view sound tenable? -- Scott Hoge
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-04-27 15:10 -0500 |
| Message-ID | <10sofqv$2lhnj$1@dont-email.me> |
| In reply to | #644888 |
On 4/27/2026 2:15 PM, Scott Hoge wrote: > On 2026-04-27, olcott <polcott333@gmail.com> wrote: > > [...] > >>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>> >>>>> [...] >>>>> >>>>> The correct interpretation was, I argued, not "This sentence >>>>> is unprovable," but rather: >>>>> >>>>> The following is unprovable (1): >>>>> The following is unprovable (2): >>>>> The following is unprovable (3): >>>>> ... >> >> The directed graph of the evaluation sequence of G >> has a cycle preventing its evaluation from ever >> terminating. >> >> If you have no idea what directed graphs are you will >> never get this. If you always knew what directed graphs >> of evaluation sequences that contain cycles are then >> you rebuttal has always been pure dishonesty. > > I learned what directed graphs were in high school. > > It seems our views are somewhat in agreement, but my directed > graph looks like this: > > (D1) > · ─→ · ─→ · ─→ · ─→ ... > > Yours appears to look like this, where its semantic (?) > evaluation contains a cycle: > > (D2) > · ─┐ > ↑ ↓ > └─ · > > (This may be an oversimplification of the actual cycle, but it's > for illustrative purposes.) > > I'll requote my proposed division of concepts: > >>>>> As regards semantics, I could call statement (1) the >>>>> "unencoded sentence," sentence (2) the "first encoded >>>>> sentence," the concept under which all sentences (1)-(∞) >>>>> belong the "formally abstracted sentence," and the concept >>>>> under which all sentences (2)-(∞) belong the >>>>> "encoding-abstracted sentence." > > If we're speaking of the /infinite sequence of nth-encoded > sentences/, the graph would be D1. However, we may still be able > to argue that for the /formally abstracted/ sentence, the graph > would be D2. > > The formally abstracted sentence is closer in concept to "This > sentence is unprovable." > Yet that is one way of several ways to see the error of the 1931 Incompleteness Theorem. > Does this view sound tenable? > > -- Scott Hoge % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. Prolog finally once and for all resolves the Liar Paradox as semantically incoherent within the analytical framework of Proof Theoretical Semantics. It does this on the basis that the LP specifies a cycle in the directed graph of its evaluation sequence, thus not a well founded justification tree. The above the simplest possible concrete example of my 28 years of primary research. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2026-04-27 21:03 +0000 |
| Message-ID | <10soiuk$np0$1@news.muc.de> |
| In reply to | #644888 |
[ Followup-To: set ] In sci.math Scott Hoge <nospam@nospam.com> wrote: > On 2026-04-27, olcott <polcott333@gmail.com> wrote: > [...] > >>> On 4/26/2026 3:01 PM, Scott Hoge wrote: > >>>> [...] > >>>> The correct interpretation was, I argued, not "This sentence > >>>> is unprovable," but rather: > >>>> The following is unprovable (1): > >>>> The following is unprovable (2): > >>>> The following is unprovable (3): > >>>> ... > > The directed graph of the evaluation sequence of G > > has a cycle preventing its evaluation from ever > > terminating. > > If you have no idea what directed graphs are you will > > never get this. If you always knew what directed graphs > > of evaluation sequences that contain cycles are then > > you rebuttal has always been pure dishonesty. > I learned what directed graphs were in high school. > It seems our views are somewhat in agreement, but my directed > graph looks like this: > (D1) > · ─→ · ─→ · ─→ · ─→ ... I strongly urge you to read and understand an actual proof of Gödel's incompleteness theorem[*]. There are no looping or endless directed graphs in these. Such notions result from misunderstandings by those lacking formal training in mathematics. [*] I would suggest finding a second hand copy of "Gödel, Escher, Bach, an Eternal Golden Braid" by Douglas Hofstadter, published around 1978 or 1979. A proof of the incompleteness theorem is a central theme of the book, which is witty and entertaining and well worth reading. Peter Olcott has never read and understood such a proof. Although not particularly difficult, it is beyond his understanding. And please note, this theorem is _TRUE_. It has been proven rigorously and verified by millions of students and academics over a very long time period. Peter Olcott doesn't like it any more than he doesn't understand it, so he pours scorn on the distinguished mathematicians of the past, falsely claiming it to be false. I would urge you to be sceptical of _any_ so called "result" emanating from him. [ .... ] > -- Scott Hoge -- Alan Mackenzie (Nuremberg, Germany).
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-04-27 16:57 -0500 |
| Message-ID | <10som3k$2ndjl$1@dont-email.me> |
| In reply to | #644890 |
On 4/27/2026 4:03 PM, Alan Mackenzie wrote: > [ Followup-To: set ] > > In sci.math Scott Hoge <nospam@nospam.com> wrote: >> On 2026-04-27, olcott <polcott333@gmail.com> wrote: > >> [...] > >>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: > >>>>>> [...] > >>>>>> The correct interpretation was, I argued, not "This sentence >>>>>> is unprovable," but rather: > >>>>>> The following is unprovable (1): >>>>>> The following is unprovable (2): >>>>>> The following is unprovable (3): >>>>>> ... > >>> The directed graph of the evaluation sequence of G >>> has a cycle preventing its evaluation from ever >>> terminating. > >>> If you have no idea what directed graphs are you will >>> never get this. If you always knew what directed graphs >>> of evaluation sequences that contain cycles are then >>> you rebuttal has always been pure dishonesty. > >> I learned what directed graphs were in high school. > >> It seems our views are somewhat in agreement, but my directed >> graph looks like this: > >> (D1) >> · ─→ · ─→ · ─→ · ─→ ... > > I strongly urge you to read and understand an actual proof of Gödel's > incompleteness theorem[*]. There are no looping or endless directed > graphs in these. Such notions result from misunderstandings by those > lacking formal training in mathematics. > > [*] I would suggest finding a second hand copy of "Gödel, Escher, Bach, > an Eternal Golden Braid" by Douglas Hofstadter, published around 1978 or > 1979. A proof of the incompleteness theorem is a central theme of the > book, which is witty and entertaining and well worth reading. > > Peter Olcott has never read and understood such a proof. Although not > particularly difficult, it is beyond his understanding. > After all these years where I have repeatedly proven that Gödel himself says that his proof does have pathological self reference you repeatedly deny this because you and everyone else here only cares about denigration rather than truth. Prolog detects [and rejects] pathological self reference in the Gödel sentence BEGIN:(Gödel 1931:39-41)...there is also a close ...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...We are therefore confronted with a proposition which asserts its own unprovability. 15 ...We are therefore confronted with a proposition which asserts its own unprovability. 15 https://www.researchgate.net/publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence > And please note, this theorem is _TRUE_. It has been proven rigorously > and verified by millions of students and academics over a very long time > period. > Yet never once examined within the alternative foundation of proof theoretic semantics utterly replacing foundation of model theoretic semantics. > Peter Olcott doesn't like it any more than he doesn't understand it, so > he pours scorn on the distinguished mathematicians of the past, falsely > claiming it to be false. I would urge you to be sceptical of _any_ so > called "result" emanating from him. > > [ .... ] > >> -- Scott Hoge > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-04-28 10:34 +0300 |
| Message-ID | <10spntn$2viov$1@dont-email.me> |
| In reply to | #644891 |
On 28/04/2026 00:57, olcott wrote: > On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >> [ Followup-To: set ] >> >> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >> >>> [...] >> >>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >> >>>>>>> [...] >> >>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>> is unprovable," but rather: >> >>>>>>> The following is unprovable (1): >>>>>>> The following is unprovable (2): >>>>>>> The following is unprovable (3): >>>>>>> ... >> >>>> The directed graph of the evaluation sequence of G >>>> has a cycle preventing its evaluation from ever >>>> terminating. >> >>>> If you have no idea what directed graphs are you will >>>> never get this. If you always knew what directed graphs >>>> of evaluation sequences that contain cycles are then >>>> you rebuttal has always been pure dishonesty. >> >>> I learned what directed graphs were in high school. >> >>> It seems our views are somewhat in agreement, but my directed >>> graph looks like this: >> >>> (D1) >>> · ─→ · ─→ · ─→ · ─→ ... >> >> I strongly urge you to read and understand an actual proof of Gödel's >> incompleteness theorem[*]. There are no looping or endless directed >> graphs in these. Such notions result from misunderstandings by those >> lacking formal training in mathematics. >> >> [*] I would suggest finding a second hand copy of "Gödel, Escher, Bach, >> an Eternal Golden Braid" by Douglas Hofstadter, published around 1978 or >> 1979. A proof of the incompleteness theorem is a central theme of the >> book, which is witty and entertaining and well worth reading. >> >> Peter Olcott has never read and understood such a proof. Although not >> particularly difficult, it is beyond his understanding. > > After all these years where I have repeatedly proven that Gödel > himself says that his proof does have pathological self reference > you repeatedly deny this because you and everyone else here only > cares about denigration rather than truth. > > Prolog detects [and rejects] pathological self reference in the Gödel > sentence Prolog alone does not detect pathological self reference. It has certain standard predicates that makes such detection simpler than in typical programming languages(like Fortran) but the same detection is possible in those, too. Gödel's sentence is a sentence in the first order Peano arithmetic. In that language there is no way to express a reference and in particular a self-reference. For the undecidability proof there is no need to interprete the theorem at all. In the proof of an Peano- unprovable arithmetic truth the usual arithmetic interpretation is relevant. > BEGIN:(Gödel 1931:39-41)...there is also a close > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 > > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 > > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 > > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 > > ...We are therefore confronted with a proposition which asserts its own > unprovability. 15 Olcott's ilevel of understanding is illustrated by his habit to prove by repetition. > https://www.researchgate.net/ > publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence > >> And please note, this theorem is _TRUE_. It has been proven rigorously >> and verified by millions of students and academics over a very long time >> period. > > Yet never once examined within the alternative foundation of > proof theoretic semantics utterly replacing foundation of model > theoretic semantics. That only demonstrates that proof theoretic semantics provides an insufficient foundation. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-04-28 07:18 -0500 |
| Message-ID | <10sq8i4$34r38$1@dont-email.me> |
| In reply to | #644895 |
On 4/28/2026 2:34 AM, Mikko wrote: > On 28/04/2026 00:57, olcott wrote: >> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>> [ Followup-To: set ] >>> >>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>> >>>> [...] >>> >>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>> >>>>>>>> [...] >>> >>>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>>> is unprovable," but rather: >>> >>>>>>>> The following is unprovable (1): >>>>>>>> The following is unprovable (2): >>>>>>>> The following is unprovable (3): >>>>>>>> ... >>> >>>>> The directed graph of the evaluation sequence of G >>>>> has a cycle preventing its evaluation from ever >>>>> terminating. >>> >>>>> If you have no idea what directed graphs are you will >>>>> never get this. If you always knew what directed graphs >>>>> of evaluation sequences that contain cycles are then >>>>> you rebuttal has always been pure dishonesty. >>> >>>> I learned what directed graphs were in high school. >>> >>>> It seems our views are somewhat in agreement, but my directed >>>> graph looks like this: >>> >>>> (D1) >>>> · ─→ · ─→ · ─→ · ─→ ... >>> >>> I strongly urge you to read and understand an actual proof of Gödel's >>> incompleteness theorem[*]. There are no looping or endless directed >>> graphs in these. Such notions result from misunderstandings by those >>> lacking formal training in mathematics. >>> >>> [*] I would suggest finding a second hand copy of "Gödel, Escher, Bach, >>> an Eternal Golden Braid" by Douglas Hofstadter, published around 1978 or >>> 1979. A proof of the incompleteness theorem is a central theme of the >>> book, which is witty and entertaining and well worth reading. >>> >>> Peter Olcott has never read and understood such a proof. Although not >>> particularly difficult, it is beyond his understanding. >> >> After all these years where I have repeatedly proven that Gödel >> himself says that his proof does have pathological self reference >> you repeatedly deny this because you and everyone else here only >> cares about denigration rather than truth. >> >> Prolog detects [and rejects] pathological self reference in the Gödel >> sentence > > Prolog alone does not detect pathological self reference. Counter-factual. unify_with_occurs_check() <is> Prolog. % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. > It has > certain standard predicates that makes such detection simpler > than in typical programming languages(like Fortran) but the same > detection is possible in those, too. > > Gödel's sentence is a sentence in the first order Peano arithmetic. > In that language there is no way to express a reference and in > particular a self-reference. For the undecidability proof there is > no need to interprete the theorem at all. In the proof of an Peano- > unprovable arithmetic truth the usual arithmetic interpretation is > relevant. > In PTS if directly in PA there are no inference steps that derive G directly in PA then G is ungrounded in PA thus essentially meaningless in PA. Dag Prawitz goes further and says that G is untrue in PA. >> BEGIN:(Gödel 1931:39-41)...there is also a close >> ...We are therefore confronted with a proposition which asserts its >> own unprovability. 15 >> >> ...We are therefore confronted with a proposition which asserts its >> own unprovability. 15 >> >> ...We are therefore confronted with a proposition which asserts its >> own unprovability. 15 >> >> ...We are therefore confronted with a proposition which asserts its >> own unprovability. 15 >> >> ...We are therefore confronted with a proposition which asserts its >> own unprovability. 15 > > Olcott's ilevel of understanding is illustrated by his habit to prove > by repetition. > >> https://www.researchgate.net/ >> publication/350789898_Prolog_detects_and_rejects_pathological_self_reference_in_the_Godel_sentence >> >>> And please note, this theorem is _TRUE_. It has been proven rigorously >>> and verified by millions of students and academics over a very long time >>> period. >> >> Yet never once examined within the alternative foundation of >> proof theoretic semantics utterly replacing foundation of model >> theoretic semantics. > > That only demonstrates that proof theoretic semantics provides an > insufficient foundation. > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-04-29 09:37 +0300 |
| Message-ID | <10ss8vm$3n5dj$1@dont-email.me> |
| In reply to | #644904 |
On 28/04/2026 15:18, olcott wrote: > On 4/28/2026 2:34 AM, Mikko wrote: >> On 28/04/2026 00:57, olcott wrote: >>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>> [ Followup-To: set ] >>>> >>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>> >>>>> [...] >>>> >>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>> >>>>>>>>> [...] >>>> >>>>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>>>> is unprovable," but rather: >>>> >>>>>>>>> The following is unprovable (1): >>>>>>>>> The following is unprovable (2): >>>>>>>>> The following is unprovable (3): >>>>>>>>> ... >>>> >>>>>> The directed graph of the evaluation sequence of G >>>>>> has a cycle preventing its evaluation from ever >>>>>> terminating. >>>> >>>>>> If you have no idea what directed graphs are you will >>>>>> never get this. If you always knew what directed graphs >>>>>> of evaluation sequences that contain cycles are then >>>>>> you rebuttal has always been pure dishonesty. >>>> >>>>> I learned what directed graphs were in high school. >>>> >>>>> It seems our views are somewhat in agreement, but my directed >>>>> graph looks like this: >>>> >>>>> (D1) >>>>> · ─→ · ─→ · ─→ · ─→ ... >>>> >>>> I strongly urge you to read and understand an actual proof of Gödel's >>>> incompleteness theorem[*]. There are no looping or endless directed >>>> graphs in these. Such notions result from misunderstandings by those >>>> lacking formal training in mathematics. >>>> >>>> [*] I would suggest finding a second hand copy of "Gödel, Escher, Bach, >>>> an Eternal Golden Braid" by Douglas Hofstadter, published around >>>> 1978 or >>>> 1979. A proof of the incompleteness theorem is a central theme of the >>>> book, which is witty and entertaining and well worth reading. >>>> >>>> Peter Olcott has never read and understood such a proof. Although not >>>> particularly difficult, it is beyond his understanding. >>> >>> After all these years where I have repeatedly proven that Gödel >>> himself says that his proof does have pathological self reference >>> you repeatedly deny this because you and everyone else here only >>> cares about denigration rather than truth. >>> >>> Prolog detects [and rejects] pathological self reference in the Gödel >>> sentence >> >> Prolog alone does not detect pathological self reference. > > Counter-factual. unify_with_occurs_check() <is> Prolog. The predicate unify_with_occurs_check is not the same as Prolog. It is just a small part of the standard language. It is one of those library predicates that can be used as I said below. > % This sentence is not true. > ?- LP = not(true(LP)). > LP = not(true(LP)). > ?- unify_with_occurs_check(LP, not(true(LP))). > false. Though it does not say why unify_with_occurs_check fails. The result is the same for unify_with_occurs_check(5, not(true(LP))). >> It has certain standard predicates including unify_with_occurs_check >> that makes such detection simpler than in typical programming >> languages(like Fortran) but the same detection is possible in >> those, too. >> Gödel's sentence is a sentence in the first order Peano arithmetic. >> In that language there is no way to express a reference and in >> particular a self-reference. For the undecidability proof there is >> no need to interprete the theorem at all. In the proof of an Peano- >> unprovable arithmetic truth the usual arithmetic interpretation is >> relevant. > In PTS if directly in PA there are no inference steps > that derive G directly in PA then G is ungrounded in > PA thus essentially meaningless in PA. Meaning is not relevant. That neither G nor its negation can be derived in PA is enough to call PA incomplete. In addition Gödel proved that ddding more postulates and perhaps other symbols cannot yield a complete consistent theory. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-04-29 09:17 -0500 |
| Message-ID | <10st3tt$3vb99$1@dont-email.me> |
| In reply to | #644913 |
On 4/29/2026 1:37 AM, Mikko wrote: > On 28/04/2026 15:18, olcott wrote: >> On 4/28/2026 2:34 AM, Mikko wrote: >>> On 28/04/2026 00:57, olcott wrote: >>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>> [ Followup-To: set ] >>>>> >>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>> >>>>>> [...] >>>>> >>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>> >>>>>>>>>> [...] >>>>> >>>>>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>>>>> is unprovable," but rather: >>>>> >>>>>>>>>> The following is unprovable (1): >>>>>>>>>> The following is unprovable (2): >>>>>>>>>> The following is unprovable (3): >>>>>>>>>> ... >>>>> >>>>>>> The directed graph of the evaluation sequence of G >>>>>>> has a cycle preventing its evaluation from ever >>>>>>> terminating. >>>>> >>>>>>> If you have no idea what directed graphs are you will >>>>>>> never get this. If you always knew what directed graphs >>>>>>> of evaluation sequences that contain cycles are then >>>>>>> you rebuttal has always been pure dishonesty. >>>>> >>>>>> I learned what directed graphs were in high school. >>>>> >>>>>> It seems our views are somewhat in agreement, but my directed >>>>>> graph looks like this: >>>>> >>>>>> (D1) >>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>> >>>>> I strongly urge you to read and understand an actual proof of Gödel's >>>>> incompleteness theorem[*]. There are no looping or endless directed >>>>> graphs in these. Such notions result from misunderstandings by those >>>>> lacking formal training in mathematics. >>>>> >>>>> [*] I would suggest finding a second hand copy of "Gödel, Escher, >>>>> Bach, >>>>> an Eternal Golden Braid" by Douglas Hofstadter, published around >>>>> 1978 or >>>>> 1979. A proof of the incompleteness theorem is a central theme of the >>>>> book, which is witty and entertaining and well worth reading. >>>>> >>>>> Peter Olcott has never read and understood such a proof. Although not >>>>> particularly difficult, it is beyond his understanding. >>>> >>>> After all these years where I have repeatedly proven that Gödel >>>> himself says that his proof does have pathological self reference >>>> you repeatedly deny this because you and everyone else here only >>>> cares about denigration rather than truth. >>>> >>>> Prolog detects [and rejects] pathological self reference in the >>>> Gödel sentence >>> >>> Prolog alone does not detect pathological self reference. >> >> Counter-factual. unify_with_occurs_check() <is> Prolog. > > The predicate unify_with_occurs_check is not the same as Prolog. It is > just a small part of the standard language. It is one of those library > predicates that can be used as I said below. >> % This sentence is not true. >> ?- LP = not(true(LP)). >> LP = not(true(LP)). >> ?- unify_with_occurs_check(LP, not(true(LP))). >> false. You can check it every which way and find that it fails because LP does not have a finite set of inference steps thus would be rejected by proof theoretic semantics as semantically ungrounded. If you don't give a rat's ass for this truth I am done talking to you. > > Though it does not say why unify_with_occurs_check fails. The result > is the same for unify_with_occurs_check(5, not(true(LP))). > >>> It has certain standard predicates > > including unify_with_occurs_check > > >> that makes such detection simpler than in typical programming > >> languages(like Fortran) but the same detection is possible in > >> those, too. >>> Gödel's sentence is a sentence in the first order Peano arithmetic. >>> In that language there is no way to express a reference and in >>> particular a self-reference. For the undecidability proof there is >>> no need to interprete the theorem at all. In the proof of an Peano- >>> unprovable arithmetic truth the usual arithmetic interpretation is >>> relevant. > >> In PTS if directly in PA there are no inference steps >> that derive G directly in PA then G is ungrounded in >> PA thus essentially meaningless in PA. > > Meaning is not relevant. Not being able to prove meaningless gibberish has never been any actual limitation. The meaningless gibberish should have always been rejected as bad input. > That neither G nor its negation can be > derived in PA is enough to call PA incomplete. In addition Gödel > proved that ddding more postulates and perhaps other symbols > cannot yield a complete consistent theory. > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-04-30 10:55 +0300 |
| Message-ID | <10sv1u7$gocn$1@dont-email.me> |
| In reply to | #644924 |
On 29/04/2026 17:17, olcott wrote: > On 4/29/2026 1:37 AM, Mikko wrote: >> On 28/04/2026 15:18, olcott wrote: >>> On 4/28/2026 2:34 AM, Mikko wrote: >>>> On 28/04/2026 00:57, olcott wrote: >>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>> [ Followup-To: set ] >>>>>> >>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>> >>>>>>> [...] >>>>>> >>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>> >>>>>>>>>>> [...] >>>>>> >>>>>>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>>>>>> is unprovable," but rather: >>>>>> >>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>> ... >>>>>> >>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>> terminating. >>>>>> >>>>>>>> If you have no idea what directed graphs are you will >>>>>>>> never get this. If you always knew what directed graphs >>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>> you rebuttal has always been pure dishonesty. >>>>>> >>>>>>> I learned what directed graphs were in high school. >>>>>> >>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>> graph looks like this: >>>>>> >>>>>>> (D1) >>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>> >>>>>> I strongly urge you to read and understand an actual proof of Gödel's >>>>>> incompleteness theorem[*]. There are no looping or endless directed >>>>>> graphs in these. Such notions result from misunderstandings by those >>>>>> lacking formal training in mathematics. >>>>>> >>>>>> [*] I would suggest finding a second hand copy of "Gödel, Escher, >>>>>> Bach, >>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published around >>>>>> 1978 or >>>>>> 1979. A proof of the incompleteness theorem is a central theme of >>>>>> the >>>>>> book, which is witty and entertaining and well worth reading. >>>>>> >>>>>> Peter Olcott has never read and understood such a proof. Although >>>>>> not >>>>>> particularly difficult, it is beyond his understanding. >>>>> >>>>> After all these years where I have repeatedly proven that Gödel >>>>> himself says that his proof does have pathological self reference >>>>> you repeatedly deny this because you and everyone else here only >>>>> cares about denigration rather than truth. >>>>> >>>>> Prolog detects [and rejects] pathological self reference in the >>>>> Gödel sentence >>>> >>>> Prolog alone does not detect pathological self reference. >>> >>> Counter-factual. unify_with_occurs_check() <is> Prolog. >> >> The predicate unify_with_occurs_check is not the same as Prolog. It is >> just a small part of the standard language. It is one of those library >> predicates that can be used as I said below. >>> % This sentence is not true. >>> ?- LP = not(true(LP)). >>> LP = not(true(LP)). >>> ?- unify_with_occurs_check(LP, not(true(LP))). >>> false. > > You can check it every which way and find that it fails > because LP does not have a finite set of inference steps > thus would be rejected by proof theoretic semantics as > semantically ungrounded. You can check it ever whixh way and find that it says nothing more than "false". > If you don't give a rat's ass for this truth I am done > talking to you. We already know you don't care about this truth any more than other truths. >> Though it does not say why unify_with_occurs_check fails. The result >> is the same for unify_with_occurs_check(5, not(true(LP))). >> > > >>>> It has certain standard predicates >> >> including unify_with_occurs_check >> >> >> that makes such detection simpler than in typical programming >> >> languages(like Fortran) but the same detection is possible in >> >> those, too. >>>> Gödel's sentence is a sentence in the first order Peano arithmetic. >>>> In that language there is no way to express a reference and in >>>> particular a self-reference. For the undecidability proof there is >>>> no need to interprete the theorem at all. In the proof of an Peano- >>>> unprovable arithmetic truth the usual arithmetic interpretation is >>>> relevant. >> >>> In PTS if directly in PA there are no inference steps >>> that derive G directly in PA then G is ungrounded in >>> PA thus essentially meaningless in PA. >> >> Meaning is not relevant. > > Not being able to prove meaningless gibberish has > never been any actual limitation. The meaningless > gibberish should have always been rejected as bad input. Not to be able to give meaning to an arithmetic statement has never been more than a personal limitation. Every natural number is a natural number number and Gödel numbers are no exception. >> That neither G nor its negation can be >> derived in PA is enough to call PA incomplete. In addition Gödel >> proved that ddding more postulates and perhaps other symbols >> cannot yield a complete consistent theory. Nice to see you don't disagree. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-05-01 09:54 -0500 |
| Message-ID | <10t2er2$1g7g3$1@dont-email.me> |
| In reply to | #644928 |
On 5/1/2026 3:24 AM, Mikko wrote: > On 30/04/2026 15:01, olcott wrote: >> On 4/30/2026 2:55 AM, Mikko wrote: >>> On 29/04/2026 17:17, olcott wrote: >>>> On 4/29/2026 1:37 AM, Mikko wrote: >>>>> On 28/04/2026 15:18, olcott wrote: >>>>>> On 4/28/2026 2:34 AM, Mikko wrote: >>>>>>> On 28/04/2026 00:57, olcott wrote: >>>>>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>>>>> [ Followup-To: set ] >>>>>>>>> >>>>>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>>>>> >>>>>>>>>> [...] >>>>>>>>> >>>>>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>>>>> >>>>>>>>>>>>>> [...] >>>>>>>>> >>>>>>>>>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>>>>>>>>> is unprovable," but rather: >>>>>>>>> >>>>>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>>>>> ... >>>>>>>>> >>>>>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>>>>> terminating. >>>>>>>>> >>>>>>>>>>> If you have no idea what directed graphs are you will >>>>>>>>>>> never get this. If you always knew what directed graphs >>>>>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>>>>> you rebuttal has always been pure dishonesty. >>>>>>>>> >>>>>>>>>> I learned what directed graphs were in high school. >>>>>>>>> >>>>>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>>>>> graph looks like this: >>>>>>>>> >>>>>>>>>> (D1) >>>>>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>>>>> >>>>>>>>> I strongly urge you to read and understand an actual proof of >>>>>>>>> Gödel's >>>>>>>>> incompleteness theorem[*]. There are no looping or endless >>>>>>>>> directed >>>>>>>>> graphs in these. Such notions result from misunderstandings by >>>>>>>>> those >>>>>>>>> lacking formal training in mathematics. >>>>>>>>> >>>>>>>>> [*] I would suggest finding a second hand copy of "Gödel, >>>>>>>>> Escher, Bach, >>>>>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published >>>>>>>>> around 1978 or >>>>>>>>> 1979. A proof of the incompleteness theorem is a central theme >>>>>>>>> of the >>>>>>>>> book, which is witty and entertaining and well worth reading. >>>>>>>>> >>>>>>>>> Peter Olcott has never read and understood such a proof. >>>>>>>>> Although not >>>>>>>>> particularly difficult, it is beyond his understanding. >>>>>>>> >>>>>>>> After all these years where I have repeatedly proven that Gödel >>>>>>>> himself says that his proof does have pathological self reference >>>>>>>> you repeatedly deny this because you and everyone else here only >>>>>>>> cares about denigration rather than truth. >>>>>>>> >>>>>>>> Prolog detects [and rejects] pathological self reference in the >>>>>>>> Gödel sentence >>>>>>> >>>>>>> Prolog alone does not detect pathological self reference. >>>>>> >>>>>> Counter-factual. unify_with_occurs_check() <is> Prolog. >>>>> >>>>> The predicate unify_with_occurs_check is not the same as Prolog. It is >>>>> just a small part of the standard language. It is one of those library >>>>> predicates that can be used as I said below. >>>>>> % This sentence is not true. >>>>>> ?- LP = not(true(LP)). >>>>>> LP = not(true(LP)). >>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>> false. >>>> >>>> You can check it every which way and find that it fails >>>> because LP does not have a finite set of inference steps >>>> thus would be rejected by proof theoretic semantics as >>>> semantically ungrounded. >>> >>> You can check it ever whixh way and find that it says nothing >>> more than "false". >>> >>>> If you don't give a rat's ass for this truth I am done >>>> talking to you. >>> >>> We already know you don't care about this truth any more than >>> other truths. >> >> I just emphasized that because of the lack of truth >> life on Earth will not survive and you said this was >> off topic. > > It is. > Yu >>>>> Though it does not say why unify_with_occurs_check fails. The result >>>>> is the same for unify_with_occurs_check(5, not(true(LP))). >>>>> >>>> >>>> >>>>>>> It has certain standard predicates >>>>> >>>>> including unify_with_occurs_check >>>>> >>>>> >> that makes such detection simpler than in typical programming >>>>> >> languages(like Fortran) but the same detection is possible in >>>>> >> those, too. >>>>>>> Gödel's sentence is a sentence in the first order Peano arithmetic. >>>>>>> In that language there is no way to express a reference and in >>>>>>> particular a self-reference. For the undecidability proof there is >>>>>>> no need to interprete the theorem at all. In the proof of an Peano- >>>>>>> unprovable arithmetic truth the usual arithmetic interpretation is >>>>>>> relevant. >>>>> >>>>>> In PTS if directly in PA there are no inference steps >>>>>> that derive G directly in PA then G is ungrounded in >>>>>> PA thus essentially meaningless in PA. >>>>> >>>>> Meaning is not relevant. >>>> >>>> Not being able to prove meaningless gibberish has >>>> never been any actual limitation. The meaningless >>>> gibberish should have always been rejected as bad input. >>> >>> Not to be able to give meaning to an arithmetic statement has >>> never been more than a personal limitation. Every natural number >>> is a natural number number and Gödel numbers are no exception. >> >> 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. > > And not desiderable when discussing arithmetic. The most important thing about arithmetic is to get the correct answer. When a gibberish nonsense expression of PA is construed as meaningful just because its syntax is correct this is a woefully stupid mistake. Because you are a mindless robot utterly bereft of a living soul you will never get this. > Therefore the formal > languages for logic and arithemtic are desigend so that that kind of > nonsense is not expressible. > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-05-01 10:47 -0700 |
| Message-ID | <VnydnQf3KoTvemn0nZ2dnZfqnPGdnZ2d@giganews.com> |
| In reply to | #644940 |
On 05/01/2026 07:54 AM, olcott wrote: > On 5/1/2026 3:24 AM, Mikko wrote: >> On 30/04/2026 15:01, olcott wrote: >>> On 4/30/2026 2:55 AM, Mikko wrote: >>>> On 29/04/2026 17:17, olcott wrote: >>>>> On 4/29/2026 1:37 AM, Mikko wrote: >>>>>> On 28/04/2026 15:18, olcott wrote: >>>>>>> On 4/28/2026 2:34 AM, Mikko wrote: >>>>>>>> On 28/04/2026 00:57, olcott wrote: >>>>>>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>>>>>> [ Followup-To: set ] >>>>>>>>>> >>>>>>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>>>>>> >>>>>>>>>>> [...] >>>>>>>>>> >>>>>>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>>>>>> >>>>>>>>>>>>>>> [...] >>>>>>>>>> >>>>>>>>>>>>>>> The correct interpretation was, I argued, not "This sentence >>>>>>>>>>>>>>> is unprovable," but rather: >>>>>>>>>> >>>>>>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>>>>>> ... >>>>>>>>>> >>>>>>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>>>>>> terminating. >>>>>>>>>> >>>>>>>>>>>> If you have no idea what directed graphs are you will >>>>>>>>>>>> never get this. If you always knew what directed graphs >>>>>>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>>>>>> you rebuttal has always been pure dishonesty. >>>>>>>>>> >>>>>>>>>>> I learned what directed graphs were in high school. >>>>>>>>>> >>>>>>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>>>>>> graph looks like this: >>>>>>>>>> >>>>>>>>>>> (D1) >>>>>>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>>>>>> >>>>>>>>>> I strongly urge you to read and understand an actual proof of >>>>>>>>>> Gödel's >>>>>>>>>> incompleteness theorem[*]. There are no looping or endless >>>>>>>>>> directed >>>>>>>>>> graphs in these. Such notions result from misunderstandings >>>>>>>>>> by those >>>>>>>>>> lacking formal training in mathematics. >>>>>>>>>> >>>>>>>>>> [*] I would suggest finding a second hand copy of "Gödel, >>>>>>>>>> Escher, Bach, >>>>>>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published >>>>>>>>>> around 1978 or >>>>>>>>>> 1979. A proof of the incompleteness theorem is a central >>>>>>>>>> theme of the >>>>>>>>>> book, which is witty and entertaining and well worth reading. >>>>>>>>>> >>>>>>>>>> Peter Olcott has never read and understood such a proof. >>>>>>>>>> Although not >>>>>>>>>> particularly difficult, it is beyond his understanding. >>>>>>>>> >>>>>>>>> After all these years where I have repeatedly proven that Gödel >>>>>>>>> himself says that his proof does have pathological self reference >>>>>>>>> you repeatedly deny this because you and everyone else here only >>>>>>>>> cares about denigration rather than truth. >>>>>>>>> >>>>>>>>> Prolog detects [and rejects] pathological self reference in the >>>>>>>>> Gödel sentence >>>>>>>> >>>>>>>> Prolog alone does not detect pathological self reference. >>>>>>> >>>>>>> Counter-factual. unify_with_occurs_check() <is> Prolog. >>>>>> >>>>>> The predicate unify_with_occurs_check is not the same as Prolog. >>>>>> It is >>>>>> just a small part of the standard language. It is one of those >>>>>> library >>>>>> predicates that can be used as I said below. >>>>>>> % This sentence is not true. >>>>>>> ?- LP = not(true(LP)). >>>>>>> LP = not(true(LP)). >>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>> false. >>>>> >>>>> You can check it every which way and find that it fails >>>>> because LP does not have a finite set of inference steps >>>>> thus would be rejected by proof theoretic semantics as >>>>> semantically ungrounded. >>>> >>>> You can check it ever whixh way and find that it says nothing >>>> more than "false". >>>> >>>>> If you don't give a rat's ass for this truth I am done >>>>> talking to you. >>>> >>>> We already know you don't care about this truth any more than >>>> other truths. >>> >>> I just emphasized that because of the lack of truth >>> life on Earth will not survive and you said this was >>> off topic. >> >> It is. >> > > Yu >>>>> Though it does not say why unify_with_occurs_check fails. The > result >>>>>> is the same for unify_with_occurs_check(5, not(true(LP))). >>>>>> >>>>> >>>>> >>>>>>>> It has certain standard predicates >>>>>> >>>>>> including unify_with_occurs_check >>>>>> >>>>>> >> that makes such detection simpler than in typical programming >>>>>> >> languages(like Fortran) but the same detection is possible in >>>>>> >> those, too. >>>>>>>> Gödel's sentence is a sentence in the first order Peano arithmetic. >>>>>>>> In that language there is no way to express a reference and in >>>>>>>> particular a self-reference. For the undecidability proof there is >>>>>>>> no need to interprete the theorem at all. In the proof of an Peano- >>>>>>>> unprovable arithmetic truth the usual arithmetic interpretation is >>>>>>>> relevant. >>>>>> >>>>>>> In PTS if directly in PA there are no inference steps >>>>>>> that derive G directly in PA then G is ungrounded in >>>>>>> PA thus essentially meaningless in PA. >>>>>> >>>>>> Meaning is not relevant. >>>>> >>>>> Not being able to prove meaningless gibberish has >>>>> never been any actual limitation. The meaningless >>>>> gibberish should have always been rejected as bad input. >>>> >>>> Not to be able to give meaning to an arithmetic statement has >>>> never been more than a personal limitation. Every natural number >>>> is a natural number number and Gödel numbers are no exception. >>> >>> 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. >> >> And not desiderable when discussing arithmetic. > > The most important thing about arithmetic is to get the > correct answer. When a gibberish nonsense expression of > PA is construed as meaningful just because its syntax is > correct this is a woefully stupid mistake. Because you are > a mindless robot utterly bereft of a living soul you will > never get this. > >> Therefore the formal >> languages for logic and arithemtic are desigend so that that kind of >> nonsense is not expressible. >> > > In my theory of light and color I actually make an account where there's "green-shift" and there really is "colorless green" or as about "mono-green-shift", since something like Ogden Rood's "Modern Chromatics". One imagines "colorless green" and "sleep furiously" came out of an early generative program and since multi-pass parsers greatly modify the considerations of usual formal methods and right linear automatons perhaps equipped with look-ahead. Multi-pass parsers are an entirely different model of computation, and natural languages here have Tesniere grammars. So, maybe he just didn't get it, it's "grue" and "bleen", about Nelson Goodman's "Riddle of Induction". Absent a modal temporal relevance logic that's quite weak. Anyways "sleep furiously" simply reflects on that the brain works rather continuously on background problems, the digestion and the internalization, for usual accounts of problems best worked by taking a nap. Chomsky lost a lot of cachet since the whole hedonism/corruption/blackmail bit. Anyways also the account of one-pass small-stack grammar's is not according to the usual account of natural language the parsing. So, natural language grammars in their complexity and the flow in the accidence and adjectival force are much more about Tesniere and dependency-clause grammars as students in English learned to diagram sentences about the same time as mathematical "proof" was introduced.
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-05-01 11:01 -0700 |
| Message-ID | <XC-dnV_HiP0Fd2n0nZ2dnZfqn_idnZ2d@giganews.com> |
| In reply to | #644942 |
On 05/01/2026 10:47 AM, Ross Finlayson wrote: > On 05/01/2026 07:54 AM, olcott wrote: >> On 5/1/2026 3:24 AM, Mikko wrote: >>> On 30/04/2026 15:01, olcott wrote: >>>> On 4/30/2026 2:55 AM, Mikko wrote: >>>>> On 29/04/2026 17:17, olcott wrote: >>>>>> On 4/29/2026 1:37 AM, Mikko wrote: >>>>>>> On 28/04/2026 15:18, olcott wrote: >>>>>>>> On 4/28/2026 2:34 AM, Mikko wrote: >>>>>>>>> On 28/04/2026 00:57, olcott wrote: >>>>>>>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>> >>>>>>>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> [...] >>>>>>>>>>> >>>>>>>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>>>>>>> >>>>>>>>>>>>>>>> [...] >>>>>>>>>>> >>>>>>>>>>>>>>>> The correct interpretation was, I argued, not "This >>>>>>>>>>>>>>>> sentence >>>>>>>>>>>>>>>> is unprovable," but rather: >>>>>>>>>>> >>>>>>>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>>>>>>> ... >>>>>>>>>>> >>>>>>>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>>>>>>> terminating. >>>>>>>>>>> >>>>>>>>>>>>> If you have no idea what directed graphs are you will >>>>>>>>>>>>> never get this. If you always knew what directed graphs >>>>>>>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>>>>>>> you rebuttal has always been pure dishonesty. >>>>>>>>>>> >>>>>>>>>>>> I learned what directed graphs were in high school. >>>>>>>>>>> >>>>>>>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>>>>>>> graph looks like this: >>>>>>>>>>> >>>>>>>>>>>> (D1) >>>>>>>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>>>>>>> >>>>>>>>>>> I strongly urge you to read and understand an actual proof of >>>>>>>>>>> Gödel's >>>>>>>>>>> incompleteness theorem[*]. There are no looping or endless >>>>>>>>>>> directed >>>>>>>>>>> graphs in these. Such notions result from misunderstandings >>>>>>>>>>> by those >>>>>>>>>>> lacking formal training in mathematics. >>>>>>>>>>> >>>>>>>>>>> [*] I would suggest finding a second hand copy of "Gödel, >>>>>>>>>>> Escher, Bach, >>>>>>>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published >>>>>>>>>>> around 1978 or >>>>>>>>>>> 1979. A proof of the incompleteness theorem is a central >>>>>>>>>>> theme of the >>>>>>>>>>> book, which is witty and entertaining and well worth reading. >>>>>>>>>>> >>>>>>>>>>> Peter Olcott has never read and understood such a proof. >>>>>>>>>>> Although not >>>>>>>>>>> particularly difficult, it is beyond his understanding. >>>>>>>>>> >>>>>>>>>> After all these years where I have repeatedly proven that Gödel >>>>>>>>>> himself says that his proof does have pathological self reference >>>>>>>>>> you repeatedly deny this because you and everyone else here only >>>>>>>>>> cares about denigration rather than truth. >>>>>>>>>> >>>>>>>>>> Prolog detects [and rejects] pathological self reference in the >>>>>>>>>> Gödel sentence >>>>>>>>> >>>>>>>>> Prolog alone does not detect pathological self reference. >>>>>>>> >>>>>>>> Counter-factual. unify_with_occurs_check() <is> Prolog. >>>>>>> >>>>>>> The predicate unify_with_occurs_check is not the same as Prolog. >>>>>>> It is >>>>>>> just a small part of the standard language. It is one of those >>>>>>> library >>>>>>> predicates that can be used as I said below. >>>>>>>> % This sentence is not true. >>>>>>>> ?- LP = not(true(LP)). >>>>>>>> LP = not(true(LP)). >>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>> false. >>>>>> >>>>>> You can check it every which way and find that it fails >>>>>> because LP does not have a finite set of inference steps >>>>>> thus would be rejected by proof theoretic semantics as >>>>>> semantically ungrounded. >>>>> >>>>> You can check it ever whixh way and find that it says nothing >>>>> more than "false". >>>>> >>>>>> If you don't give a rat's ass for this truth I am done >>>>>> talking to you. >>>>> >>>>> We already know you don't care about this truth any more than >>>>> other truths. >>>> >>>> I just emphasized that because of the lack of truth >>>> life on Earth will not survive and you said this was >>>> off topic. >>> >>> It is. >>> >> >> Yu >>>>> Though it does not say why unify_with_occurs_check fails. The >> result >>>>>>> is the same for unify_with_occurs_check(5, not(true(LP))). >>>>>>> >>>>>> >>>>>> >>>>>>>>> It has certain standard predicates >>>>>>> >>>>>>> including unify_with_occurs_check >>>>>>> >>>>>>> >> that makes such detection simpler than in typical programming >>>>>>> >> languages(like Fortran) but the same detection is possible in >>>>>>> >> those, too. >>>>>>>>> Gödel's sentence is a sentence in the first order Peano >>>>>>>>> arithmetic. >>>>>>>>> In that language there is no way to express a reference and in >>>>>>>>> particular a self-reference. For the undecidability proof there is >>>>>>>>> no need to interprete the theorem at all. In the proof of an >>>>>>>>> Peano- >>>>>>>>> unprovable arithmetic truth the usual arithmetic interpretation is >>>>>>>>> relevant. >>>>>>> >>>>>>>> In PTS if directly in PA there are no inference steps >>>>>>>> that derive G directly in PA then G is ungrounded in >>>>>>>> PA thus essentially meaningless in PA. >>>>>>> >>>>>>> Meaning is not relevant. >>>>>> >>>>>> Not being able to prove meaningless gibberish has >>>>>> never been any actual limitation. The meaningless >>>>>> gibberish should have always been rejected as bad input. >>>>> >>>>> Not to be able to give meaning to an arithmetic statement has >>>>> never been more than a personal limitation. Every natural number >>>>> is a natural number number and Gödel numbers are no exception. >>>> >>>> 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. >>> >>> And not desiderable when discussing arithmetic. >> >> The most important thing about arithmetic is to get the >> correct answer. When a gibberish nonsense expression of >> PA is construed as meaningful just because its syntax is >> correct this is a woefully stupid mistake. Because you are >> a mindless robot utterly bereft of a living soul you will >> never get this. >> >>> Therefore the formal >>> languages for logic and arithemtic are desigend so that that kind of >>> nonsense is not expressible. >>> >> >> > > > In my theory of light and color I actually make an account where > there's "green-shift" and there really is "colorless green" or > as about "mono-green-shift", since something like Ogden Rood's > "Modern Chromatics". > > One imagines "colorless green" and "sleep furiously" came out > of an early generative program and since multi-pass parsers > greatly modify the considerations of usual formal methods and > right linear automatons perhaps equipped with look-ahead. > Multi-pass parsers are an entirely different model of computation, > and natural languages here have Tesniere grammars. > > So, maybe he just didn't get it, it's "grue" and "bleen", > about Nelson Goodman's "Riddle of Induction". Absent a > modal temporal relevance logic that's quite weak. > > Anyways "sleep furiously" simply reflects on that the brain > works rather continuously on background problems, the digestion > and the internalization, for usual accounts of problems best > worked by taking a nap. > > > Chomsky lost a lot of cachet since the whole > hedonism/corruption/blackmail bit. Anyways > also the account of one-pass small-stack grammar's > is not according to the usual account of natural > language the parsing. > > So, natural language grammars in their complexity > and the flow in the accidence and adjectival force > are much more about Tesniere and dependency-clause > grammars as students in English learned to diagram > sentences about the same time as mathematical "proof" > was introduced. > > > > > > Parsing is pretty natural if you imagine, for example, putting "not" in front of anything, and then, of course, that "that" can be repeated indefinitely anywhere, that that that that that that that that that that that it is so. P.S., while I mostly sort of pity Chomsky, or find it pitiful, I sort of despise H. Putnam, as snide, and Pinker, as a dupe.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-05-01 14:35 -0500 |
| Message-ID | <10t2v9c$1lfpq$1@dont-email.me> |
| In reply to | #644942 |
On 5/1/2026 12:47 PM, Ross Finlayson wrote: > On 05/01/2026 07:54 AM, olcott wrote: >> On 5/1/2026 3:24 AM, Mikko wrote: >>> On 30/04/2026 15:01, olcott wrote: >>>> On 4/30/2026 2:55 AM, Mikko wrote: >>>>> On 29/04/2026 17:17, olcott wrote: >>>>>> On 4/29/2026 1:37 AM, Mikko wrote: >>>>>>> On 28/04/2026 15:18, olcott wrote: >>>>>>>> On 4/28/2026 2:34 AM, Mikko wrote: >>>>>>>>> On 28/04/2026 00:57, olcott wrote: >>>>>>>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>> >>>>>>>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>> >>>>>>>>>>>> [...] >>>>>>>>>>> >>>>>>>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>>>>>>> >>>>>>>>>>>>>>>> [...] >>>>>>>>>>> >>>>>>>>>>>>>>>> The correct interpretation was, I argued, not "This >>>>>>>>>>>>>>>> sentence >>>>>>>>>>>>>>>> is unprovable," but rather: >>>>>>>>>>> >>>>>>>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>>>>>>> ... >>>>>>>>>>> >>>>>>>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>>>>>>> terminating. >>>>>>>>>>> >>>>>>>>>>>>> If you have no idea what directed graphs are you will >>>>>>>>>>>>> never get this. If you always knew what directed graphs >>>>>>>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>>>>>>> you rebuttal has always been pure dishonesty. >>>>>>>>>>> >>>>>>>>>>>> I learned what directed graphs were in high school. >>>>>>>>>>> >>>>>>>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>>>>>>> graph looks like this: >>>>>>>>>>> >>>>>>>>>>>> (D1) >>>>>>>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>>>>>>> >>>>>>>>>>> I strongly urge you to read and understand an actual proof of >>>>>>>>>>> Gödel's >>>>>>>>>>> incompleteness theorem[*]. There are no looping or endless >>>>>>>>>>> directed >>>>>>>>>>> graphs in these. Such notions result from misunderstandings >>>>>>>>>>> by those >>>>>>>>>>> lacking formal training in mathematics. >>>>>>>>>>> >>>>>>>>>>> [*] I would suggest finding a second hand copy of "Gödel, >>>>>>>>>>> Escher, Bach, >>>>>>>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published >>>>>>>>>>> around 1978 or >>>>>>>>>>> 1979. A proof of the incompleteness theorem is a central >>>>>>>>>>> theme of the >>>>>>>>>>> book, which is witty and entertaining and well worth reading. >>>>>>>>>>> >>>>>>>>>>> Peter Olcott has never read and understood such a proof. >>>>>>>>>>> Although not >>>>>>>>>>> particularly difficult, it is beyond his understanding. >>>>>>>>>> >>>>>>>>>> After all these years where I have repeatedly proven that Gödel >>>>>>>>>> himself says that his proof does have pathological self reference >>>>>>>>>> you repeatedly deny this because you and everyone else here only >>>>>>>>>> cares about denigration rather than truth. >>>>>>>>>> >>>>>>>>>> Prolog detects [and rejects] pathological self reference in the >>>>>>>>>> Gödel sentence >>>>>>>>> >>>>>>>>> Prolog alone does not detect pathological self reference. >>>>>>>> >>>>>>>> Counter-factual. unify_with_occurs_check() <is> Prolog. >>>>>>> >>>>>>> The predicate unify_with_occurs_check is not the same as Prolog. >>>>>>> It is >>>>>>> just a small part of the standard language. It is one of those >>>>>>> library >>>>>>> predicates that can be used as I said below. >>>>>>>> % This sentence is not true. >>>>>>>> ?- LP = not(true(LP)). >>>>>>>> LP = not(true(LP)). >>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>> false. >>>>>> >>>>>> You can check it every which way and find that it fails >>>>>> because LP does not have a finite set of inference steps >>>>>> thus would be rejected by proof theoretic semantics as >>>>>> semantically ungrounded. >>>>> >>>>> You can check it ever whixh way and find that it says nothing >>>>> more than "false". >>>>> >>>>>> If you don't give a rat's ass for this truth I am done >>>>>> talking to you. >>>>> >>>>> We already know you don't care about this truth any more than >>>>> other truths. >>>> >>>> I just emphasized that because of the lack of truth >>>> life on Earth will not survive and you said this was >>>> off topic. >>> >>> It is. >>> >> >> Yu >>>>> Though it does not say why unify_with_occurs_check fails. The >> result >>>>>>> is the same for unify_with_occurs_check(5, not(true(LP))). >>>>>>> >>>>>> >>>>>> >>>>>>>>> It has certain standard predicates >>>>>>> >>>>>>> including unify_with_occurs_check >>>>>>> >>>>>>> >> that makes such detection simpler than in typical programming >>>>>>> >> languages(like Fortran) but the same detection is possible in >>>>>>> >> those, too. >>>>>>>>> Gödel's sentence is a sentence in the first order Peano >>>>>>>>> arithmetic. >>>>>>>>> In that language there is no way to express a reference and in >>>>>>>>> particular a self-reference. For the undecidability proof there is >>>>>>>>> no need to interprete the theorem at all. In the proof of an >>>>>>>>> Peano- >>>>>>>>> unprovable arithmetic truth the usual arithmetic interpretation is >>>>>>>>> relevant. >>>>>>> >>>>>>>> In PTS if directly in PA there are no inference steps >>>>>>>> that derive G directly in PA then G is ungrounded in >>>>>>>> PA thus essentially meaningless in PA. >>>>>>> >>>>>>> Meaning is not relevant. >>>>>> >>>>>> Not being able to prove meaningless gibberish has >>>>>> never been any actual limitation. The meaningless >>>>>> gibberish should have always been rejected as bad input. >>>>> >>>>> Not to be able to give meaning to an arithmetic statement has >>>>> never been more than a personal limitation. Every natural number >>>>> is a natural number number and Gödel numbers are no exception. >>>> >>>> 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. >>> >>> And not desiderable when discussing arithmetic. >> >> The most important thing about arithmetic is to get the >> correct answer. When a gibberish nonsense expression of >> PA is construed as meaningful just because its syntax is >> correct this is a woefully stupid mistake. Because you are >> a mindless robot utterly bereft of a living soul you will >> never get this. >> >>> Therefore the formal >>> languages for logic and arithemtic are desigend so that that kind of >>> nonsense is not expressible. >>> >> >> > > > In my theory of light and color I actually make an account where > there's "green-shift" and there really is "colorless green" or > as about "mono-green-shift", since something like Ogden Rood's > "Modern Chromatics". > > One imagines "colorless green" and "sleep furiously" came out > of an early generative program and since multi-pass parsers > greatly modify the considerations of usual formal methods and > right linear automatons perhaps equipped with look-ahead. > Multi-pass parsers are an entirely different model of computation, > and natural languages here have Tesniere grammars. > > So, maybe he just didn't get it, it's "grue" and "bleen", > about Nelson Goodman's "Riddle of Induction". Absent a > modal temporal relevance logic that's quite weak. > > Anyways "sleep furiously" simply reflects on that the brain > works rather continuously on background problems, the digestion > and the internalization, for usual accounts of problems best > worked by taking a nap. > > > Chomsky lost a lot of cachet since the whole > hedonism/corruption/blackmail bit. Anyways > also the account of one-pass small-stack grammar's > is not according to the usual account of natural > language the parsing. > > So, natural language grammars in their complexity > and the flow in the accidence and adjectival force > are much more about Tesniere and dependency-clause > grammars as students in English learned to diagram > sentences about the same time as mathematical "proof" > was introduced. > > It seems that you are trying to get away with pretending that you fail to understand the notion of a type mismatch error. Kurt Gödel in his 1944 Russell's mathematical logic gave the following definition of the "theory of simple types" in a footnote: By the theory of simple types I mean the doctrine which says that the objects of thought (or, in another interpretation, the symbolic expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations, etc. (with a similar hierarchy for extensions), and that sentences of the form: " a has the property φ ", " b bears the relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together. https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-05-01 12:54 -0700 |
| Message-ID | <nd6dnYlmPc-QmGj0nZ2dnZfqnPqdnZ2d@giganews.com> |
| In reply to | #644946 |
On 05/01/2026 12:35 PM, olcott wrote: > On 5/1/2026 12:47 PM, Ross Finlayson wrote: >> On 05/01/2026 07:54 AM, olcott wrote: >>> On 5/1/2026 3:24 AM, Mikko wrote: >>>> On 30/04/2026 15:01, olcott wrote: >>>>> On 4/30/2026 2:55 AM, Mikko wrote: >>>>>> On 29/04/2026 17:17, olcott wrote: >>>>>>> On 4/29/2026 1:37 AM, Mikko wrote: >>>>>>>> On 28/04/2026 15:18, olcott wrote: >>>>>>>>> On 4/28/2026 2:34 AM, Mikko wrote: >>>>>>>>>> On 28/04/2026 00:57, olcott wrote: >>>>>>>>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>> >>>>>>>>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>>>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>> >>>>>>>>>>>>> [...] >>>>>>>>>>>> >>>>>>>>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>>>>>>>> >>>>>>>>>>>>>>>>> [...] >>>>>>>>>>>> >>>>>>>>>>>>>>>>> The correct interpretation was, I argued, not "This >>>>>>>>>>>>>>>>> sentence >>>>>>>>>>>>>>>>> is unprovable," but rather: >>>>>>>>>>>> >>>>>>>>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>>>>>>>> ... >>>>>>>>>>>> >>>>>>>>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>>>>>>>> terminating. >>>>>>>>>>>> >>>>>>>>>>>>>> If you have no idea what directed graphs are you will >>>>>>>>>>>>>> never get this. If you always knew what directed graphs >>>>>>>>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>>>>>>>> you rebuttal has always been pure dishonesty. >>>>>>>>>>>> >>>>>>>>>>>>> I learned what directed graphs were in high school. >>>>>>>>>>>> >>>>>>>>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>>>>>>>> graph looks like this: >>>>>>>>>>>> >>>>>>>>>>>>> (D1) >>>>>>>>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>>>>>>>> >>>>>>>>>>>> I strongly urge you to read and understand an actual proof of >>>>>>>>>>>> Gödel's >>>>>>>>>>>> incompleteness theorem[*]. There are no looping or endless >>>>>>>>>>>> directed >>>>>>>>>>>> graphs in these. Such notions result from misunderstandings >>>>>>>>>>>> by those >>>>>>>>>>>> lacking formal training in mathematics. >>>>>>>>>>>> >>>>>>>>>>>> [*] I would suggest finding a second hand copy of "Gödel, >>>>>>>>>>>> Escher, Bach, >>>>>>>>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published >>>>>>>>>>>> around 1978 or >>>>>>>>>>>> 1979. A proof of the incompleteness theorem is a central >>>>>>>>>>>> theme of the >>>>>>>>>>>> book, which is witty and entertaining and well worth reading. >>>>>>>>>>>> >>>>>>>>>>>> Peter Olcott has never read and understood such a proof. >>>>>>>>>>>> Although not >>>>>>>>>>>> particularly difficult, it is beyond his understanding. >>>>>>>>>>> >>>>>>>>>>> After all these years where I have repeatedly proven that Gödel >>>>>>>>>>> himself says that his proof does have pathological self >>>>>>>>>>> reference >>>>>>>>>>> you repeatedly deny this because you and everyone else here only >>>>>>>>>>> cares about denigration rather than truth. >>>>>>>>>>> >>>>>>>>>>> Prolog detects [and rejects] pathological self reference in the >>>>>>>>>>> Gödel sentence >>>>>>>>>> >>>>>>>>>> Prolog alone does not detect pathological self reference. >>>>>>>>> >>>>>>>>> Counter-factual. unify_with_occurs_check() <is> Prolog. >>>>>>>> >>>>>>>> The predicate unify_with_occurs_check is not the same as Prolog. >>>>>>>> It is >>>>>>>> just a small part of the standard language. It is one of those >>>>>>>> library >>>>>>>> predicates that can be used as I said below. >>>>>>>>> % This sentence is not true. >>>>>>>>> ?- LP = not(true(LP)). >>>>>>>>> LP = not(true(LP)). >>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>> false. >>>>>>> >>>>>>> You can check it every which way and find that it fails >>>>>>> because LP does not have a finite set of inference steps >>>>>>> thus would be rejected by proof theoretic semantics as >>>>>>> semantically ungrounded. >>>>>> >>>>>> You can check it ever whixh way and find that it says nothing >>>>>> more than "false". >>>>>> >>>>>>> If you don't give a rat's ass for this truth I am done >>>>>>> talking to you. >>>>>> >>>>>> We already know you don't care about this truth any more than >>>>>> other truths. >>>>> >>>>> I just emphasized that because of the lack of truth >>>>> life on Earth will not survive and you said this was >>>>> off topic. >>>> >>>> It is. >>>> >>> >>> Yu >>>>> Though it does not say why unify_with_occurs_check fails. The >>> result >>>>>>>> is the same for unify_with_occurs_check(5, not(true(LP))). >>>>>>>> >>>>>>> >>>>>>> >>>>>>>>>> It has certain standard predicates >>>>>>>> >>>>>>>> including unify_with_occurs_check >>>>>>>> >>>>>>>> >> that makes such detection simpler than in typical programming >>>>>>>> >> languages(like Fortran) but the same detection is possible in >>>>>>>> >> those, too. >>>>>>>>>> Gödel's sentence is a sentence in the first order Peano >>>>>>>>>> arithmetic. >>>>>>>>>> In that language there is no way to express a reference and in >>>>>>>>>> particular a self-reference. For the undecidability proof >>>>>>>>>> there is >>>>>>>>>> no need to interprete the theorem at all. In the proof of an >>>>>>>>>> Peano- >>>>>>>>>> unprovable arithmetic truth the usual arithmetic >>>>>>>>>> interpretation is >>>>>>>>>> relevant. >>>>>>>> >>>>>>>>> In PTS if directly in PA there are no inference steps >>>>>>>>> that derive G directly in PA then G is ungrounded in >>>>>>>>> PA thus essentially meaningless in PA. >>>>>>>> >>>>>>>> Meaning is not relevant. >>>>>>> >>>>>>> Not being able to prove meaningless gibberish has >>>>>>> never been any actual limitation. The meaningless >>>>>>> gibberish should have always been rejected as bad input. >>>>>> >>>>>> Not to be able to give meaning to an arithmetic statement has >>>>>> never been more than a personal limitation. Every natural number >>>>>> is a natural number number and Gödel numbers are no exception. >>>>> >>>>> 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. >>>> >>>> And not desiderable when discussing arithmetic. >>> >>> The most important thing about arithmetic is to get the >>> correct answer. When a gibberish nonsense expression of >>> PA is construed as meaningful just because its syntax is >>> correct this is a woefully stupid mistake. Because you are >>> a mindless robot utterly bereft of a living soul you will >>> never get this. >>> >>>> Therefore the formal >>>> languages for logic and arithemtic are desigend so that that kind of >>>> nonsense is not expressible. >>>> >>> >>> >> >> >> In my theory of light and color I actually make an account where >> there's "green-shift" and there really is "colorless green" or >> as about "mono-green-shift", since something like Ogden Rood's >> "Modern Chromatics". >> >> One imagines "colorless green" and "sleep furiously" came out >> of an early generative program and since multi-pass parsers >> greatly modify the considerations of usual formal methods and >> right linear automatons perhaps equipped with look-ahead. >> Multi-pass parsers are an entirely different model of computation, >> and natural languages here have Tesniere grammars. >> >> So, maybe he just didn't get it, it's "grue" and "bleen", >> about Nelson Goodman's "Riddle of Induction". Absent a >> modal temporal relevance logic that's quite weak. >> >> Anyways "sleep furiously" simply reflects on that the brain >> works rather continuously on background problems, the digestion >> and the internalization, for usual accounts of problems best >> worked by taking a nap. >> >> >> Chomsky lost a lot of cachet since the whole >> hedonism/corruption/blackmail bit. Anyways >> also the account of one-pass small-stack grammar's >> is not according to the usual account of natural >> language the parsing. >> >> So, natural language grammars in their complexity >> and the flow in the accidence and adjectival force >> are much more about Tesniere and dependency-clause >> grammars as students in English learned to diagram >> sentences about the same time as mathematical "proof" >> was introduced. >> >> > > It seems that you are trying to get away with pretending > that you fail to understand the notion of a type mismatch > error. > > Kurt Gödel in his 1944 Russell's mathematical logic gave the following > definition of the "theory of simple types" in a footnote: > > By the theory of simple types I mean the doctrine which says that the > objects of thought (or, in another interpretation, the symbolic > expressions) are divided into types, namely: individuals, properties of > individuals, relations between individuals, properties of such > relations, etc. (with a similar hierarchy for extensions), and that > sentences of the form: " a has the property φ ", " b bears the relation > R to c ", etc. are meaningless, if a, b, c, R, φ are not of types > fitting together. > > https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 > No, I'm just not ignorant of the lack of class/set distinction. About the transfer principle, and about accounts where something that is so for each apiece is so for all together, there's one where there's a non-standard countable model of integer with a point at infinity naturally simply since quantification also makes it so, like Russell's paradox, that Goedel's first object outside the theory would be. Then, usually "Peirce" or "Pierce" are better sources for type theory, though Russell whipped up ramified and stratified types in set theory. https://iep.utm.edu/peir-log/ https://www.cis.upenn.edu/~bcpierce/tapl/ Russell comes across as an erudite logician and schooled philosopher, yet though plenty of his accounts see him as a self-aggrandizing free-loader. Not that there's anything necessarily wrong with that, .... https://ncatlab.org/nlab/show/set+theory https://en.wikipedia.org/wiki/Class_(set_theory) Anyways Goedel's world of theorems of his arithmetization is the same before and after second arithmetization, maybe you'd be happier instead arguing against his completeness results.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-05-01 15:36 -0500 |
| Message-ID | <10t32sj$1mhk1$1@dont-email.me> |
| In reply to | #644948 |
On 5/1/2026 2:54 PM, Ross Finlayson wrote: > On 05/01/2026 12:35 PM, olcott wrote: >> On 5/1/2026 12:47 PM, Ross Finlayson wrote: >>> On 05/01/2026 07:54 AM, olcott wrote: >>>> On 5/1/2026 3:24 AM, Mikko wrote: >>>>> On 30/04/2026 15:01, olcott wrote: >>>>>> On 4/30/2026 2:55 AM, Mikko wrote: >>>>>>> On 29/04/2026 17:17, olcott wrote: >>>>>>>> On 4/29/2026 1:37 AM, Mikko wrote: >>>>>>>>> On 28/04/2026 15:18, olcott wrote: >>>>>>>>>> On 4/28/2026 2:34 AM, Mikko wrote: >>>>>>>>>>> On 28/04/2026 00:57, olcott wrote: >>>>>>>>>>>> On 4/27/2026 4:03 PM, Alan Mackenzie wrote: >>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>> >>>>>>>>>>>>> In sci.math Scott Hoge <nospam@nospam.com> wrote: >>>>>>>>>>>>>> On 2026-04-27, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>> [...] >>>>>>>>>>>>> >>>>>>>>>>>>>>>>> On 4/26/2026 3:01 PM, Scott Hoge wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> [...] >>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> The correct interpretation was, I argued, not "This >>>>>>>>>>>>>>>>>> sentence >>>>>>>>>>>>>>>>>> is unprovable," but rather: >>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> The following is unprovable (1): >>>>>>>>>>>>>>>>>> The following is unprovable (2): >>>>>>>>>>>>>>>>>> The following is unprovable (3): >>>>>>>>>>>>>>>>>> ... >>>>>>>>>>>>> >>>>>>>>>>>>>>> The directed graph of the evaluation sequence of G >>>>>>>>>>>>>>> has a cycle preventing its evaluation from ever >>>>>>>>>>>>>>> terminating. >>>>>>>>>>>>> >>>>>>>>>>>>>>> If you have no idea what directed graphs are you will >>>>>>>>>>>>>>> never get this. If you always knew what directed graphs >>>>>>>>>>>>>>> of evaluation sequences that contain cycles are then >>>>>>>>>>>>>>> you rebuttal has always been pure dishonesty. >>>>>>>>>>>>> >>>>>>>>>>>>>> I learned what directed graphs were in high school. >>>>>>>>>>>>> >>>>>>>>>>>>>> It seems our views are somewhat in agreement, but my directed >>>>>>>>>>>>>> graph looks like this: >>>>>>>>>>>>> >>>>>>>>>>>>>> (D1) >>>>>>>>>>>>>> · ─→ · ─→ · ─→ · ─→ ... >>>>>>>>>>>>> >>>>>>>>>>>>> I strongly urge you to read and understand an actual proof of >>>>>>>>>>>>> Gödel's >>>>>>>>>>>>> incompleteness theorem[*]. There are no looping or endless >>>>>>>>>>>>> directed >>>>>>>>>>>>> graphs in these. Such notions result from misunderstandings >>>>>>>>>>>>> by those >>>>>>>>>>>>> lacking formal training in mathematics. >>>>>>>>>>>>> >>>>>>>>>>>>> [*] I would suggest finding a second hand copy of "Gödel, >>>>>>>>>>>>> Escher, Bach, >>>>>>>>>>>>> an Eternal Golden Braid" by Douglas Hofstadter, published >>>>>>>>>>>>> around 1978 or >>>>>>>>>>>>> 1979. A proof of the incompleteness theorem is a central >>>>>>>>>>>>> theme of the >>>>>>>>>>>>> book, which is witty and entertaining and well worth reading. >>>>>>>>>>>>> >>>>>>>>>>>>> Peter Olcott has never read and understood such a proof. >>>>>>>>>>>>> Although not >>>>>>>>>>>>> particularly difficult, it is beyond his understanding. >>>>>>>>>>>> >>>>>>>>>>>> After all these years where I have repeatedly proven that Gödel >>>>>>>>>>>> himself says that his proof does have pathological self >>>>>>>>>>>> reference >>>>>>>>>>>> you repeatedly deny this because you and everyone else here >>>>>>>>>>>> only >>>>>>>>>>>> cares about denigration rather than truth. >>>>>>>>>>>> >>>>>>>>>>>> Prolog detects [and rejects] pathological self reference in the >>>>>>>>>>>> Gödel sentence >>>>>>>>>>> >>>>>>>>>>> Prolog alone does not detect pathological self reference. >>>>>>>>>> >>>>>>>>>> Counter-factual. unify_with_occurs_check() <is> Prolog. >>>>>>>>> >>>>>>>>> The predicate unify_with_occurs_check is not the same as Prolog. >>>>>>>>> It is >>>>>>>>> just a small part of the standard language. It is one of those >>>>>>>>> library >>>>>>>>> predicates that can be used as I said below. >>>>>>>>>> % This sentence is not true. >>>>>>>>>> ?- LP = not(true(LP)). >>>>>>>>>> LP = not(true(LP)). >>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>> false. >>>>>>>> >>>>>>>> You can check it every which way and find that it fails >>>>>>>> because LP does not have a finite set of inference steps >>>>>>>> thus would be rejected by proof theoretic semantics as >>>>>>>> semantically ungrounded. >>>>>>> >>>>>>> You can check it ever whixh way and find that it says nothing >>>>>>> more than "false". >>>>>>> >>>>>>>> If you don't give a rat's ass for this truth I am done >>>>>>>> talking to you. >>>>>>> >>>>>>> We already know you don't care about this truth any more than >>>>>>> other truths. >>>>>> >>>>>> I just emphasized that because of the lack of truth >>>>>> life on Earth will not survive and you said this was >>>>>> off topic. >>>>> >>>>> It is. >>>>> >>>> >>>> Yu >>>>> Though it does not say why unify_with_occurs_check fails. The >>>> result >>>>>>>>> is the same for unify_with_occurs_check(5, not(true(LP))). >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>>>>> It has certain standard predicates >>>>>>>>> >>>>>>>>> including unify_with_occurs_check >>>>>>>>> >>>>>>>>> >> that makes such detection simpler than in typical programming >>>>>>>>> >> languages(like Fortran) but the same detection is possible in >>>>>>>>> >> those, too. >>>>>>>>>>> Gödel's sentence is a sentence in the first order Peano >>>>>>>>>>> arithmetic. >>>>>>>>>>> In that language there is no way to express a reference and in >>>>>>>>>>> particular a self-reference. For the undecidability proof >>>>>>>>>>> there is >>>>>>>>>>> no need to interprete the theorem at all. In the proof of an >>>>>>>>>>> Peano- >>>>>>>>>>> unprovable arithmetic truth the usual arithmetic >>>>>>>>>>> interpretation is >>>>>>>>>>> relevant. >>>>>>>>> >>>>>>>>>> In PTS if directly in PA there are no inference steps >>>>>>>>>> that derive G directly in PA then G is ungrounded in >>>>>>>>>> PA thus essentially meaningless in PA. >>>>>>>>> >>>>>>>>> Meaning is not relevant. >>>>>>>> >>>>>>>> Not being able to prove meaningless gibberish has >>>>>>>> never been any actual limitation. The meaningless >>>>>>>> gibberish should have always been rejected as bad input. >>>>>>> >>>>>>> Not to be able to give meaning to an arithmetic statement has >>>>>>> never been more than a personal limitation. Every natural number >>>>>>> is a natural number number and Gödel numbers are no exception. >>>>>> >>>>>> 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. >>>>> >>>>> And not desiderable when discussing arithmetic. >>>> >>>> The most important thing about arithmetic is to get the >>>> correct answer. When a gibberish nonsense expression of >>>> PA is construed as meaningful just because its syntax is >>>> correct this is a woefully stupid mistake. Because you are >>>> a mindless robot utterly bereft of a living soul you will >>>> never get this. >>>> >>>>> Therefore the formal >>>>> languages for logic and arithemtic are desigend so that that kind of >>>>> nonsense is not expressible. >>>>> >>>> >>>> >>> >>> >>> In my theory of light and color I actually make an account where >>> there's "green-shift" and there really is "colorless green" or >>> as about "mono-green-shift", since something like Ogden Rood's >>> "Modern Chromatics". >>> >>> One imagines "colorless green" and "sleep furiously" came out >>> of an early generative program and since multi-pass parsers >>> greatly modify the considerations of usual formal methods and >>> right linear automatons perhaps equipped with look-ahead. >>> Multi-pass parsers are an entirely different model of computation, >>> and natural languages here have Tesniere grammars. >>> >>> So, maybe he just didn't get it, it's "grue" and "bleen", >>> about Nelson Goodman's "Riddle of Induction". Absent a >>> modal temporal relevance logic that's quite weak. >>> >>> Anyways "sleep furiously" simply reflects on that the brain >>> works rather continuously on background problems, the digestion >>> and the internalization, for usual accounts of problems best >>> worked by taking a nap. >>> >>> >>> Chomsky lost a lot of cachet since the whole >>> hedonism/corruption/blackmail bit. Anyways >>> also the account of one-pass small-stack grammar's >>> is not according to the usual account of natural >>> language the parsing. >>> >>> So, natural language grammars in their complexity >>> and the flow in the accidence and adjectival force >>> are much more about Tesniere and dependency-clause >>> grammars as students in English learned to diagram >>> sentences about the same time as mathematical "proof" >>> was introduced. >>> >>> >> >> It seems that you are trying to get away with pretending >> that you fail to understand the notion of a type mismatch >> error. >> >> Kurt Gödel in his 1944 Russell's mathematical logic gave the following >> definition of the "theory of simple types" in a footnote: >> >> By the theory of simple types I mean the doctrine which says that the >> objects of thought (or, in another interpretation, the symbolic >> expressions) are divided into types, namely: individuals, properties of >> individuals, relations between individuals, properties of such >> relations, etc. (with a similar hierarchy for extensions), and that >> sentences of the form: " a has the property φ ", " b bears the relation >> R to c ", etc. are meaningless, if a, b, c, R, φ are not of types >> fitting together. >> >> https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 >> > > No, I'm just not ignorant of the lack of class/set distinction. > > About the transfer principle, and about accounts where > something that is so for each apiece is so for all together, > there's one where there's a non-standard countable model of > integer with a point at infinity naturally simply since > quantification also makes it so, like Russell's paradox, > that Goedel's first object outside the theory would be. > Within completely coherent semantics the notion of undecidability cannot exist. Model Theoretic Semantics is incoherent. Proof Theoretic Semantics is coherent. > Then, usually "Peirce" or "Pierce" are better sources for type theory, > though Russell whipped up ramified and stratified types in set theory. > > https://iep.utm.edu/peir-log/ > https://www.cis.upenn.edu/~bcpierce/tapl/ > > > Russell comes across as an erudite logician and schooled philosopher, > yet though plenty of his accounts see him as a self-aggrandizing > free-loader. > > Not that there's anything necessarily wrong with that, .... > > https://ncatlab.org/nlab/show/set+theory > https://en.wikipedia.org/wiki/Class_(set_theory) > > Anyways Goedel's world of theorems of his arithmetization is > the same before and after second arithmetization, maybe you'd be > happier instead arguing against his completeness results. > > > > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-06-30 13:14 +0100 |
| Message-ID | <1120bv2$12kma$1@dont-email.me> |
| In reply to | #644949 |
On 01/05/2026 21:36, olcott wrote: > Within completely coherent semantics the notion of > undecidability cannot exist. Model Theoretic Semantics > is incoherent. Proof Theoretic Semantics is coherent. Then Proof Theoretic Semantics seems unnecessarily restricted. Is there a Deduction Theoretic Semantics without that limitation and does it subsume (by embedding, for example) the Model Theoretic Semantics and the Proof Theoretic Semantics? -- Tristan Wibberley The message body is Copyright (C) 2026 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
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