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Groups > comp.theory > #140926 > 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 306 — 16 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 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 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> - 2026-07-04 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 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 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 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 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> - 2026-07-04 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> - 2026-07-04 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 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
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: 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> - 2026-04-30 07:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:24 +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 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 Andy Walker <anw@cuboid.co.uk> - 2026-04-28 16:21 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 19:48 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Andy Walker <anw@cuboid.co.uk> - 2026-04-29 16:34 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA wij <wyniijj5@gmail.com> - 2026-04-30 09:19 +0800
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Andy Walker <anw@cuboid.co.uk> - 2026-04-30 17:16 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-05-01 15:10 -0700
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 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 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 | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-01 14:50 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123uir$220jk$8@dont-email.me> |
| In reply to | #142266 |
On 2026-07-01 14:28, olcott wrote: > On 7/1/2026 3:11 PM, André G. Isaak wrote: >> On 2026-07-01 13:47, olcott wrote: >>> On 7/1/2026 2:23 PM, André G. Isaak wrote: >>>> On 2026-07-01 12:50, olcott wrote: >>>>> On 7/1/2026 1:40 PM, André G. Isaak wrote: >>>>>> On 2026-07-01 12:20, olcott wrote: >>>>>>> On 7/1/2026 1:10 PM, André G. Isaak wrote: >>>>>>>> On 2026-07-01 12:01, olcott wrote: >>>>>>>>> On 7/1/2026 12:33 PM, dbush wrote: >>>>>>>>>> On 7/1/2026 10:40 AM, olcott wrote: >>>>>>>> >>>>>>>>>>> The truth value of (∀ x, S(x) ≠ x) does not exist in Q. >>>>>>>>>> >>>>>>>>>> In your own words, what does it mean for the truth value of >>>>>>>>>> statement to not exist in a formal system? >>>>>>>>>> >>>>>>>>> >>>>>>>>> The same thing as: "cats are animals" expressed in >>>>>>>>> English has no English meaning in Chinese. >>>>>>>>> >>>>>>>>> Until "cats are animals" is translated into Chinese >>>>>>>>> it is just random gibberish that has no meaning or >>>>>>>>> truth value in Chinese. >>>>>>>> >>>>>>>> But ∀ x, S(x) ≠ x *isn't* random gibberish in Q. It is a well- >>>>>>>> formed expression of Q that has a well-defined meaning. It just >>>>>>>> happens to be unprovable. If it were random gibberish no one >>>>>>>> would have entertained the question of whether it could or could >>>>>>>> not be proven in Q. >>>>>>>> >>>>>>>> André >>>>>>>> >>>>>>> >>>>>>> It has no finite sequence of inference steps between >>>>>>> the expression and the axioms of Q. This seems to >>>>>>> mean that (∀x, S(x) ≠ x) is ungrounded in the atomic >>>>>>> base of Q in many of the different ways that this >>>>>>> can be expressed by different PTS authors. >>>>>> >>>>>> Having no finite sequence of inference steps between the >>>>>> expression and the axioms of Q is *not* the same thing as random >>>>>> gibberish. >>>>> >>>>> It is closer to an English word such as "cat" that is >>>>> defined in English us undefined in Chinese. >>>> >>>> That's a completely spurious analogy. 'cat' isn't an expression of >>>> the Chinese language. ∀ x, S(x) ≠ x *is* an expression of the >>>> language of Q. >>>> >>>>>> It simply means it is unprovable in Q. >>>> >>>> Then you're either using a completely idiosyncratic definition of >>>> 'gibberish' or a completely idiosyncratic definition of 'provable' >>>> (or both). That's why people keep asking you to provide *your* >>>> definitions, but you only respond with examples or analogies which >>>> fail to clarify what you might mean. >>>> >>>>> Which means something entirely different in PTS than >>>>> it means in TCS. >>>> >>>> unprovable means the same thing in both. >>>> >>> >>> Wittgenstein (1937) >>> 'True in Russell's system' means, as was said: >>> proved in Russell's system; and 'false in Russell's >>> system' means: the opposite has been proved >>> in Russell's system >> >> You keep quoting this particular bit despite the fact that its been >> pointed out on numerous occasions that Wittgenstein wrote the above in >> his private notes *before* he had actually read Gödel's paper, and he > > What matters is the it is the way that true on the > basis of meaning expressed in language has always > worked. Also what matters is that I came up with > this exact same thing years before I ever heard > of him. If that's what you believe then make your case. But don't cite Wittgenstein as supporting your position when it's unlikely he actually stood by those remarks >> never went on to publish anything to this effect suggesting he didn't >> subscribe to this position after he'd actually read Gödel. >> >>> Does not mean that G is undecidable in PA. >> >> It doesn't say anything at all about whether G is decidable in PA. >> >> André >> > > Any expression X that is unprovable in any formal > system F is untrue in that formal system F > > Any expression X that is irrefutable in any formal > system F is unfalse in that formal system F. So now you have a four-valued logic? (true, false, untrue, unfalse). If so, you'll need to define what all of these values actually mean, and you'll need to completely redefine all of the basic logical operators so that they account for these four values. 5 = 5 is irrefutable in Q. According to what you say above that makes it 'unfalse'. How is that different from being 'true'? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 15:52 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123um8$250rk$2@dont-email.me> |
| In reply to | #142272 |
On 7/1/2026 3:50 PM, André G. Isaak wrote: > On 2026-07-01 14:28, olcott wrote: >> On 7/1/2026 3:11 PM, André G. Isaak wrote: >>> On 2026-07-01 13:47, olcott wrote: >>>> On 7/1/2026 2:23 PM, André G. Isaak wrote: >>>>> On 2026-07-01 12:50, olcott wrote: >>>>>> On 7/1/2026 1:40 PM, André G. Isaak wrote: >>>>>>> On 2026-07-01 12:20, olcott wrote: >>>>>>>> On 7/1/2026 1:10 PM, André G. Isaak wrote: >>>>>>>>> On 2026-07-01 12:01, olcott wrote: >>>>>>>>>> On 7/1/2026 12:33 PM, dbush wrote: >>>>>>>>>>> On 7/1/2026 10:40 AM, olcott wrote: >>>>>>>>> >>>>>>>>>>>> The truth value of (∀ x, S(x) ≠ x) does not exist in Q. >>>>>>>>>>> >>>>>>>>>>> In your own words, what does it mean for the truth value of >>>>>>>>>>> statement to not exist in a formal system? >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> The same thing as: "cats are animals" expressed in >>>>>>>>>> English has no English meaning in Chinese. >>>>>>>>>> >>>>>>>>>> Until "cats are animals" is translated into Chinese >>>>>>>>>> it is just random gibberish that has no meaning or >>>>>>>>>> truth value in Chinese. >>>>>>>>> >>>>>>>>> But ∀ x, S(x) ≠ x *isn't* random gibberish in Q. It is a well- >>>>>>>>> formed expression of Q that has a well-defined meaning. It just >>>>>>>>> happens to be unprovable. If it were random gibberish no one >>>>>>>>> would have entertained the question of whether it could or >>>>>>>>> could not be proven in Q. >>>>>>>>> >>>>>>>>> André >>>>>>>>> >>>>>>>> >>>>>>>> It has no finite sequence of inference steps between >>>>>>>> the expression and the axioms of Q. This seems to >>>>>>>> mean that (∀x, S(x) ≠ x) is ungrounded in the atomic >>>>>>>> base of Q in many of the different ways that this >>>>>>>> can be expressed by different PTS authors. >>>>>>> >>>>>>> Having no finite sequence of inference steps between the >>>>>>> expression and the axioms of Q is *not* the same thing as random >>>>>>> gibberish. >>>>>> >>>>>> It is closer to an English word such as "cat" that is >>>>>> defined in English us undefined in Chinese. >>>>> >>>>> That's a completely spurious analogy. 'cat' isn't an expression of >>>>> the Chinese language. ∀ x, S(x) ≠ x *is* an expression of the >>>>> language of Q. >>>>> >>>>>>> It simply means it is unprovable in Q. >>>>> >>>>> Then you're either using a completely idiosyncratic definition of >>>>> 'gibberish' or a completely idiosyncratic definition of 'provable' >>>>> (or both). That's why people keep asking you to provide *your* >>>>> definitions, but you only respond with examples or analogies which >>>>> fail to clarify what you might mean. >>>>> >>>>>> Which means something entirely different in PTS than >>>>>> it means in TCS. >>>>> >>>>> unprovable means the same thing in both. >>>>> >>>> >>>> Wittgenstein (1937) >>>> 'True in Russell's system' means, as was said: >>>> proved in Russell's system; and 'false in Russell's >>>> system' means: the opposite has been proved >>>> in Russell's system >>> >>> You keep quoting this particular bit despite the fact that its been >>> pointed out on numerous occasions that Wittgenstein wrote the above >>> in his private notes *before* he had actually read Gödel's paper, and he >> >> What matters is the it is the way that true on the >> basis of meaning expressed in language has always >> worked. Also what matters is that I came up with >> this exact same thing years before I ever heard >> of him. > > If that's what you believe then make your case. But don't cite > Wittgenstein as supporting your position when it's unlikely he actually > stood by those remarks > >>> never went on to publish anything to this effect suggesting he didn't >>> subscribe to this position after he'd actually read Gödel. >>> >>>> Does not mean that G is undecidable in PA. >>> >>> It doesn't say anything at all about whether G is decidable in PA. >>> >>> André >>> >> >> Any expression X that is unprovable in any formal >> system F is untrue in that formal system F >> >> Any expression X that is irrefutable in any formal >> system F is unfalse in that formal system F. > > So now you have a four-valued logic? (true, false, untrue, unfalse). > Like the expression: "What time is it?" we have true, false, not truth apt. > If so, you'll need to define what all of these values actually mean, and > you'll need to completely redefine all of the basic logical operators so > that they account for these four values. > > 5 = 5 is irrefutable in Q. According to what you say above that makes it > 'unfalse'. How is that different from being 'true'? > > André > -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-01 15:10 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123vo7$220jk$9@dont-email.me> |
| In reply to | #142273 |
On 2026-07-01 14:52, olcott wrote: > On 7/1/2026 3:50 PM, André G. Isaak wrote: >>> Any expression X that is unprovable in any formal >>> system F is untrue in that formal system F >>> >>> Any expression X that is irrefutable in any formal >>> system F is unfalse in that formal system F. >> >> So now you have a four-valued logic? (true, false, untrue, unfalse). >> > > Like the expression: "What time is it?" > we have true, false, not truth apt. So a three-valued system. Then the same remarks apply. You need to actually define your three-valued system and show how the basic logical operators actually work in that system. And your natural language example is entirely unrevealing. Natural language distinguishes between interrogative and declarative sentences. Q has only declarative sentences and declarative sentences, by definition, are sentences which evaluate to a truth value. And in standard logic there is this thing called the law of the excluded middle which states that every declarative sentence is either true or false. You can't just introduce some concept like "not truth apt" without completely redefining logic from the ground up. You haven't made even the feeblest attempt at doing this. You simply introduce concepts as if they will magically fit into an existing system rather than exploring what the consequences of introducing such concepts would actually have >> If so, you'll need to define what all of these values actually mean, >> and you'll need to completely redefine all of the basic logical >> operators so that they account for these four values. >> >> 5 = 5 is irrefutable in Q. According to what you say above that makes >> it 'unfalse'. How is that different from being 'true'? No answer? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 17:43 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1124569$26qjr$1@dont-email.me> |
| In reply to | #142276 |
On 7/1/2026 4:10 PM, André G. Isaak wrote: > On 2026-07-01 14:52, olcott wrote: >> On 7/1/2026 3:50 PM, André G. Isaak wrote: > >>>> Any expression X that is unprovable in any formal >>>> system F is untrue in that formal system F >>>> >>>> Any expression X that is irrefutable in any formal >>>> system F is unfalse in that formal system F. >>> >>> So now you have a four-valued logic? (true, false, untrue, unfalse). >>> >> >> Like the expression: "What time is it?" >> we have true, false, not truth apt. > > So a three-valued system. Then the same remarks apply. You need to > actually define your three-valued system and show how the basic logical > operators actually work in that system. > It is not a three-valued system as these are commonly understood. When we go with the expressiveness of natural language then construing all sentences as true or false is directly seen to be as stupid as it has always been. > And your natural language example is entirely unrevealing. Natural > language distinguishes between interrogative and declarative sentences. > Q has only declarative sentences and declarative sentences, by > definition, are sentences which evaluate to a truth value. > Because logic only has propositions that it incorrectly assumed must be true or false it stupidly ignores the third possibility of semantically ill-formed. > And in standard logic there is this thing called the law of the excluded > middle which states that every declarative sentence is either true or > false. You can't just introduce some concept like "not truth apt" > without completely redefining logic from the ground up. Not truth apt and not a truth bearer already has established well-defined meanings that logic stupidly ignores. The law of the excluded middle forces logicians to stupidly classify semantic nonsense as true or false. > You haven't made > even the feeblest attempt at doing this. You simply introduce concepts > as if they will magically fit into an existing system rather than > exploring what the consequences of introducing such concepts would > actually have > >>> If so, you'll need to define what all of these values actually mean, >>> and you'll need to completely redefine all of the basic logical >>> operators so that they account for these four values. >>> >>> 5 = 5 is irrefutable in Q. According to what you say above that makes >>> it 'unfalse'. How is that different from being 'true'? > > No answer? > > André > Wittgenstein (1937) 'True in Russell's system' means, as was said: proved in Russell's system; and 'false in Russell's system' means: the opposite has been proved in Russell's system Has been inherently the way that true on the basis of meaning expressed in language HAS ALWAYS WORKED. Expressions of language are ONLY true, or false on the basis of their connections to other Expressions of language. -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-01 17:09 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11246nj$26qlv$1@dont-email.me> |
| In reply to | #142278 |
On 2026-07-01 16:43, olcott wrote: > On 7/1/2026 4:10 PM, André G. Isaak wrote: >> On 2026-07-01 14:52, olcott wrote: >>> On 7/1/2026 3:50 PM, André G. Isaak wrote: >> >>>>> Any expression X that is unprovable in any formal >>>>> system F is untrue in that formal system F >>>>> >>>>> Any expression X that is irrefutable in any formal >>>>> system F is unfalse in that formal system F. >>>> >>>> So now you have a four-valued logic? (true, false, untrue, unfalse). >>>> >>> >>> Like the expression: "What time is it?" >>> we have true, false, not truth apt. >> >> So a three-valued system. Then the same remarks apply. You need to >> actually define your three-valued system and show how the basic >> logical operators actually work in that system. >> > > It is not a three-valued system as these are commonly > understood. If it divides sentences into anything other than true and false then it is a three-valued system. > When we go with the expressiveness of > natural language then construing all sentences as > true or false is directly seen to be as stupid as it > has always been. Natural language tells us nothing about Q. >> And your natural language example is entirely unrevealing. Natural >> language distinguishes between interrogative and declarative >> sentences. Q has only declarative sentences and declarative sentences, >> by definition, are sentences which evaluate to a truth value. >> > Because logic only has propositions that it incorrectly assumed > must be true or false it stupidly ignores the third possibility > of semantically ill-formed. > >> And in standard logic there is this thing called the law of the >> excluded middle which states that every declarative sentence is either >> true or false. You can't just introduce some concept like "not truth >> apt" without completely redefining logic from the ground up. > > Not truth apt and not a truth bearer already has established > well-defined meanings that logic stupidly ignores. AFAICT, 'truth bearer' is simply a synonym for 'declarative sentence'. And declarative sentences are the only kind of sentence found in Q. Whatever meaning you intended is not an 'established well-defined meaning'. It is your own private meaning. And ∀ x, S(x) ≠ x is most definitely a truth bearer. > The law of the excluded middle forces logicians to stupidly > classify semantic nonsense as true or false. Which is exactly what we want in Boolean logic. >> You haven't made even the feeblest attempt at doing this. You simply >> introduce concepts as if they will magically fit into an existing >> system rather than exploring what the consequences of introducing such >> concepts would actually have >> >>>> If so, you'll need to define what all of these values actually mean, >>>> and you'll need to completely redefine all of the basic logical >>>> operators so that they account for these four values. >>>> >>>> 5 = 5 is irrefutable in Q. According to what you say above that >>>> makes it 'unfalse'. How is that different from being 'true'? >> >> No answer? >> >> André >> > > Wittgenstein (1937) > 'True in Russell's system' means, as was said: > proved in Russell's system; and 'false in Russell's > system' means: the opposite has been proved > in Russell's system I explained to you not two hours ago why this particular quote carries absolutely no weight with me, so there's really no point in bringing it up again. If true and provable were equivalent, we wouldn't have two different words for them. 'true' is an ontological category; 'provable' is an epistemic category. They don't map onto one another. André > Has been inherently the way that true on the basis > of meaning expressed in language HAS ALWAYS WORKED. > > Expressions of language are ONLY true, or false on > the basis of their connections to other Expressions > of language. > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 19:05 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11249vm$281db$1@dont-email.me> |
| In reply to | #142279 |
On 7/1/2026 6:09 PM, André G. Isaak wrote: > On 2026-07-01 16:43, olcott wrote: >> On 7/1/2026 4:10 PM, André G. Isaak wrote: >>> On 2026-07-01 14:52, olcott wrote: >>>> On 7/1/2026 3:50 PM, André G. Isaak wrote: >>> >>>>>> Any expression X that is unprovable in any formal >>>>>> system F is untrue in that formal system F >>>>>> >>>>>> Any expression X that is irrefutable in any formal >>>>>> system F is unfalse in that formal system F. >>>>> >>>>> So now you have a four-valued logic? (true, false, untrue, unfalse). >>>>> >>>> >>>> Like the expression: "What time is it?" >>>> we have true, false, not truth apt. >>> >>> So a three-valued system. Then the same remarks apply. You need to >>> actually define your three-valued system and show how the basic >>> logical operators actually work in that system. >>> >> >> It is not a three-valued system as these are commonly >> understood. > > If it divides sentences into anything other than true and false then it > is a three-valued system. > >> When we go with the expressiveness of >> natural language then construing all sentences as >> true or false is directly seen to be as stupid as it >> has always been. > > Natural language tells us nothing about Q. > >>> And your natural language example is entirely unrevealing. Natural >>> language distinguishes between interrogative and declarative >>> sentences. Q has only declarative sentences and declarative >>> sentences, by definition, are sentences which evaluate to a truth value. >>> >> Because logic only has propositions that it incorrectly assumed >> must be true or false it stupidly ignores the third possibility >> of semantically ill-formed. >> >>> And in standard logic there is this thing called the law of the >>> excluded middle which states that every declarative sentence is >>> either true or false. You can't just introduce some concept like "not >>> truth apt" without completely redefining logic from the ground up. >> >> Not truth apt and not a truth bearer already has established >> well-defined meanings that logic stupidly ignores. > > AFAICT, 'truth bearer' is simply a synonym for 'declarative sentence'. > And declarative sentences are the only kind of sentence found in Q. > Whatever meaning you intended is not an 'established well-defined > meaning'. It is your own private meaning. > Not exactly because most every human has been too stupid to understand that "This sentence is not true" is a semantically incoherent declarative sentence. Even the great Saul Kripke (did better than everyone else) yet did not quite get there. > And ∀ x, S(x) ≠ x is most definitely a truth bearer. > If is it not provable in Q then it is not a truth bearer in Q. Because we can see that it is provable in PA this causes us to screw up and think that this means that it is true in Q. >> The law of the excluded middle forces logicians to stupidly >> classify semantic nonsense as true or false. > > Which is exactly what we want in Boolean logic. > >>> You haven't made even the feeblest attempt at doing this. You simply >>> introduce concepts as if they will magically fit into an existing >>> system rather than exploring what the consequences of introducing >>> such concepts would actually have >>> >>>>> If so, you'll need to define what all of these values actually >>>>> mean, and you'll need to completely redefine all of the basic >>>>> logical operators so that they account for these four values. >>>>> >>>>> 5 = 5 is irrefutable in Q. According to what you say above that >>>>> makes it 'unfalse'. How is that different from being 'true'? >>> >>> No answer? >>> >>> André >>> >> >> Wittgenstein (1937) >> 'True in Russell's system' means, as was said: >> proved in Russell's system; and 'false in Russell's >> system' means: the opposite has been proved >> in Russell's system > > I explained to you not two hours ago why this particular quote carries > absolutely no weight with me, so there's really no point in bringing it > up again. > Of course woefully fallible humans never give a rat's ass for infallible truth. They only care if they believe something. You don't believe Wittgenstein thus can't be bothered to see that he is inherently correct. > If true and provable were equivalent, we wouldn't have two different > words for them. 'true' is an ontological category; 'provable' is an > epistemic category. They don't map onto one another. > Truth as an Epistemic Notion Truth as an Epistemic Notion Truth as an Epistemic Notion https://link.springer.com/article/10.1007/s11245-011-9107-6 For all expressions that are true on the basis of their meaning expressed in language IT IS ONLY THIS MEANING EXPRESSED IN LANGUAGE THAT MAKES THEM TRUE. > André > >> Has been inherently the way that true on the basis >> of meaning expressed in language HAS ALWAYS WORKED. >> >> Expressions of language are ONLY true, or false on >> the basis of their connections to other Expressions >> of language. >> > -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-01 18:39 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1124bv7$27ngr$1@dont-email.me> |
| In reply to | #142281 |
On 2026-07-01 18:05, olcott wrote: > On 7/1/2026 6:09 PM, André G. Isaak wrote: > Not exactly because most every human has been too stupid > to understand that "This sentence is not true" is a semantically > incoherent declarative sentence. Even the great Saul Kripke > (did better than everyone else) yet did not quite get there. Claiming that it is semantically incoherent is *your* view. It is hardly universally accepted and therefore you are required to actually defend this view rather than simply assert it. Also, that isn't the sentence we are considering. We are considering ∀ x, S(x) ≠ x in Q. There is no reason to think that any claim you might make about the LP is also applicable to this sentence. >> And ∀ x, S(x) ≠ x is most definitely a truth bearer. >> > > If is it not provable in Q then it is not a truth > bearer in Q. Because we can see that it is provable > in PA this causes us to screw up and think that this > means that it is true in Q. I never claimed that it was true, nor did I claim that it was false. I simply claimed that it was a truth-bearer without committing to its actual truth value. Do you actually understand *why* ∀ x, S(x) ≠ x is not provable in Q? Until you understand this you really don't have a good grasp of what it means for Q to be incomplete. The reason why we cannot prove that ∀ x, S(x) ≠ x in Q is because it is possible in Q to construct a model in which that statement is *false*. Such a model would not correspond to the natural numbers as commonly understood, but it would be a consistent model. In a model corresponding to the natural numbers as commonly understood, this statement would be *true*. For any given model of Q, ∀ x, S(x) ≠ x is either true or it is false. It is never some indeterminate value. But the truth value of this statement cannot be proven solely by considering the axioms of Q. We need to look at the actual model. Thus, Q is incomplete because its axioms don't lead to a single, unique model. And that will hold true for all but the simplest systems. >>> The law of the excluded middle forces logicians to stupidly >>> classify semantic nonsense as true or false. >> >> Which is exactly what we want in Boolean logic. >> >>>> You haven't made even the feeblest attempt at doing this. You simply >>>> introduce concepts as if they will magically fit into an existing >>>> system rather than exploring what the consequences of introducing >>>> such concepts would actually have >>>> >>>>>> If so, you'll need to define what all of these values actually >>>>>> mean, and you'll need to completely redefine all of the basic >>>>>> logical operators so that they account for these four values. >>>>>> >>>>>> 5 = 5 is irrefutable in Q. According to what you say above that >>>>>> makes it 'unfalse'. How is that different from being 'true'? >>>> >>>> No answer? >>>> >>>> André >>>> >>> >>> Wittgenstein (1937) >>> 'True in Russell's system' means, as was said: >>> proved in Russell's system; and 'false in Russell's >>> system' means: the opposite has been proved >>> in Russell's system >> >> I explained to you not two hours ago why this particular quote carries >> absolutely no weight with me, so there's really no point in bringing >> it up again > > Of course woefully fallible humans never give a rat's ass for infallible > truth. You don't have any special ability to identify 'infallible truth'. > They only care if they believe something. You don't believe > Wittgenstein thus can't be bothered to see that he is inherently > correct. That wasn't my point. I claimed that it wasn't clear that *Wittgenstein* actually believed this once he had actually reflected on the problem, and that therefore this quote really cannot be legitimately used to support any particular position. >> If true and provable were equivalent, we wouldn't have two different >> words for them. 'true' is an ontological category; 'provable' is an >> epistemic category. They don't map onto one another. >> > > Truth as an Epistemic Notion > Truth as an Epistemic Notion > Truth as an Epistemic Notion Saying it three times doesn't achieve anything. And I would argue that Prawitz is confused here. Citing a single article that makes a claim doesn't validate that claim. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 20:01 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1124d98$28p1n$1@dont-email.me> |
| In reply to | #142282 |
On 7/1/2026 7:39 PM, André G. Isaak wrote: > On 2026-07-01 18:05, olcott wrote: >> On 7/1/2026 6:09 PM, André G. Isaak wrote: > >> Not exactly because most every human has been too stupid >> to understand that "This sentence is not true" is a semantically >> incoherent declarative sentence. Even the great Saul Kripke >> (did better than everyone else) yet did not quite get there. > > Claiming that it is semantically incoherent is *your* view. It <is> semantically incoherent in such a way that anyone disagreeing is ABSOLUTELY INCORRECT. > It is hardly > universally accepted and therefore you are required to actually defend > this view rather than simply assert it. > It used to be universally agree that the Earth is flat. > Also, that isn't the sentence we are considering. We are considering ∀ > x, S(x) ≠ x in Q. There is no reason to think that any claim you might > make about the LP is also applicable to this sentence. > We are also considering that sentence. >>> And ∀ x, S(x) ≠ x is most definitely a truth bearer. >>> >> >> If is it not provable in Q then it is not a truth >> bearer in Q. Because we can see that it is provable >> in PA this causes us to screw up and think that this >> means that it is true in Q. > > I never claimed that it was true, nor did I claim that it was false. I > simply claimed that it was a truth-bearer without committing to its > actual truth value. > Yes that that is the vagueness that prevents much of what is semantically incoherent to be undecidable. Q was intentionally defined to be weaker than PA. > Do you actually understand *why* ∀ x, S(x) ≠ x is not provable in Q? > Until you understand this you really don't have a good grasp of what it > means for Q to be incomplete. > it lacks the mathematical induction axiom schema required to generalize this rule to all elements in a domain > The reason why we cannot prove that ∀ x, S(x) ≠ x in Q is because it is > possible in Q to construct a model in which that statement is *false*. Not when you make sure to completely and totally toss model theory out on its ass and replace it with proof theoretic semantics instead. > Such a model would not correspond to the natural numbers as commonly > understood, but it would be a consistent model. In a model corresponding > to the natural numbers as commonly understood, this statement would be > *true*. > > For any given model of Q, ∀ x, S(x) ≠ x is either true or it is false. > It is never some indeterminate value. But the truth value of this > statement cannot be proven solely by considering the axioms of Q. We > need to look at the actual model. Thus, Q is incomplete because its > axioms don't lead to a single, unique model. And that will hold true for > all but the simplest systems. > > >>>> The law of the excluded middle forces logicians to stupidly >>>> classify semantic nonsense as true or false. >>> >>> Which is exactly what we want in Boolean logic. >>> >>>>> You haven't made even the feeblest attempt at doing this. You >>>>> simply introduce concepts as if they will magically fit into an >>>>> existing system rather than exploring what the consequences of >>>>> introducing such concepts would actually have >>>>> >>>>>>> If so, you'll need to define what all of these values actually >>>>>>> mean, and you'll need to completely redefine all of the basic >>>>>>> logical operators so that they account for these four values. >>>>>>> >>>>>>> 5 = 5 is irrefutable in Q. According to what you say above that >>>>>>> makes it 'unfalse'. How is that different from being 'true'? >>>>> >>>>> No answer? >>>>> >>>>> André >>>>> >>>> >>>> Wittgenstein (1937) >>>> 'True in Russell's system' means, as was said: >>>> proved in Russell's system; and 'false in Russell's >>>> system' means: the opposite has been proved >>>> in Russell's system >>> >>> I explained to you not two hours ago why this particular quote >>> carries absolutely no weight with me, so there's really no point in >>> bringing it up again > >> Of course woefully fallible humans never give a rat's ass for infallible >> truth. > > You don't have any special ability to identify 'infallible truth'. > >> They only care if they believe something. You don't believe >> Wittgenstein thus can't be bothered to see that he is inherently >> correct. > > That wasn't my point. I claimed that it wasn't clear that *Wittgenstein* > actually believed this once he had actually reflected on the problem, > and that therefore this quote really cannot be legitimately used to > support any particular position. > >>> If true and provable were equivalent, we wouldn't have two different >>> words for them. 'true' is an ontological category; 'provable' is an >>> epistemic category. They don't map onto one another. >>> >> >> Truth as an Epistemic Notion >> Truth as an Epistemic Notion >> Truth as an Epistemic Notion > > Saying it three times doesn't achieve anything. And I would argue that > Prawitz is confused here. Citing a single article that makes a claim > doesn't validate that claim. > You were sure that provable is epistemic and thus truth is not. Truth as an Epistemic Notion is the core of Wittgenstein. > André > > -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-01 19:23 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1124ei5$27ngr$2@dont-email.me> |
| In reply to | #142283 |
On 2026-07-01 19:01, olcott wrote: > On 7/1/2026 7:39 PM, André G. Isaak wrote: >> On 2026-07-01 18:05, olcott wrote: >>> On 7/1/2026 6:09 PM, André G. Isaak wrote: >> >>> Not exactly because most every human has been too stupid >>> to understand that "This sentence is not true" is a semantically >>> incoherent declarative sentence. Even the great Saul Kripke >>> (did better than everyone else) yet did not quite get there. >> >> Claiming that it is semantically incoherent is *your* view. > > It <is> semantically incoherent in such a way that > anyone disagreeing is ABSOLUTELY INCORRECT. > >> It is hardly universally accepted and therefore you are required to >> actually defend this view rather than simply assert it. >> > > It used to be universally agree that the Earth is flat. Actually, there's no evidence to support this claim. Can you name a single work on the topic of geography or astronomy which actually asserted that the world was flat? There are religious texts which *can* be interpreted as consistent with a flat earth, but those texts weren't dealing with geography; they were dealing with allegory. >> Also, that isn't the sentence we are considering. We are considering ∀ >> x, S(x) ≠ x in Q. There is no reason to think that any claim you might >> make about the LP is also applicable to this sentence. >> > > We are also considering that sentence. You may be. I am not. I'm discussing Q and the Liar Paradox isn't stateable in Q. >>>> And ∀ x, S(x) ≠ x is most definitely a truth bearer. >>>> >>> >>> If is it not provable in Q then it is not a truth >>> bearer in Q. Because we can see that it is provable >>> in PA this causes us to screw up and think that this >>> means that it is true in Q. >> >> I never claimed that it was true, nor did I claim that it was false. I >> simply claimed that it was a truth-bearer without committing to its >> actual truth value. >> > > Yes that that is the vagueness that prevents much > of what is semantically incoherent to be undecidable. > Q was intentionally defined to be weaker than PA. > >> Do you actually understand *why* ∀ x, S(x) ≠ x is not provable in Q? >> Until you understand this you really don't have a good grasp of what >> it means for Q to be incomplete. >> > > it lacks the mathematical induction axiom schema > required to generalize this rule to all elements in a domain That's something that distinguishes Q from PA. By itself, it's not an explanation of why ∀ x, S(x) ≠ x isn't provable in Q. I'm trying to see whether you really even understand this. >> The reason why we cannot prove that ∀ x, S(x) ≠ x in Q is because it >> is possible in Q to construct a model in which that statement is *false*. > > Not when you make sure to completely and totally toss > model theory out on its ass and replace it with proof > theoretic semantics instead. PTS doesn't rely on model theoretic semantics because it is interested in epistemic rather than ontological questions. That's not the same thing as discarding models altogether or throwing model theory 'out on its ass'. Q isn't particularly useful in absence of a model. I don't think you really understand what models actually are. >>> Truth as an Epistemic Notion >> >> Saying it three times doesn't achieve anything. And I would argue that >> Prawitz is confused here. Citing a single article that makes a claim >> doesn't validate that claim. >> > > You were sure that provable is epistemic and thus > truth is not. Truth as an Epistemic Notion is the > core of Wittgenstein. And I am still sure of this. Prawitz is simply misguided. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 21:03 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1124gsp$29gpj$1@dont-email.me> |
| In reply to | #142284 |
On 7/1/2026 8:23 PM, André G. Isaak wrote: > On 2026-07-01 19:01, olcott wrote: >> On 7/1/2026 7:39 PM, André G. Isaak wrote: >>> On 2026-07-01 18:05, olcott wrote: >>>> On 7/1/2026 6:09 PM, André G. Isaak wrote: >>> >>>> Not exactly because most every human has been too stupid >>>> to understand that "This sentence is not true" is a semantically >>>> incoherent declarative sentence. Even the great Saul Kripke >>>> (did better than everyone else) yet did not quite get there. >>> >>> Claiming that it is semantically incoherent is *your* view. >> >> It <is> semantically incoherent in such a way that >> anyone disagreeing is ABSOLUTELY INCORRECT. >> >>> It is hardly universally accepted and therefore you are required to >>> actually defend this view rather than simply assert it. >>> >> >> It used to be universally agree that the Earth is flat. > > Actually, there's no evidence to support this claim. Can you name a > single work on the topic of geography or astronomy which actually > asserted that the world was flat? There are religious texts which *can* > be interpreted as consistent with a flat earth, but those texts weren't > dealing with geography; they were dealing with allegory. > >>> Also, that isn't the sentence we are considering. We are considering >>> ∀ x, S(x) ≠ x in Q. There is no reason to think that any claim you >>> might make about the LP is also applicable to this sentence. >>> >> >> We are also considering that sentence. > > You may be. I am not. I'm discussing Q and the Liar Paradox isn't > stateable in Q. > >>>>> And ∀ x, S(x) ≠ x is most definitely a truth bearer. >>>>> >>>> >>>> If is it not provable in Q then it is not a truth >>>> bearer in Q. Because we can see that it is provable >>>> in PA this causes us to screw up and think that this >>>> means that it is true in Q. >>> >>> I never claimed that it was true, nor did I claim that it was false. >>> I simply claimed that it was a truth-bearer without committing to its >>> actual truth value. >>> >> >> Yes that that is the vagueness that prevents much >> of what is semantically incoherent to be undecidable. >> Q was intentionally defined to be weaker than PA. >> >>> Do you actually understand *why* ∀ x, S(x) ≠ x is not provable in Q? >>> Until you understand this you really don't have a good grasp of what >>> it means for Q to be incomplete. >>> >> >> it lacks the mathematical induction axiom schema >> required to generalize this rule to all elements in a domain > > That's something that distinguishes Q from PA. By itself, it's not an > explanation of why ∀ x, S(x) ≠ x isn't provable in Q. I'm trying to see > whether you really even understand this. > It seems to me that I do understand that by itself is the one and only reason why (∀x, S(x) ≠ x) is unprovable in Q. That would entail that you would be flat out lying. Q cannot do the ∀x without an infinite sequence of steps. Since you know that why do you lie about that? -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 00:02 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1127fov$35nf4$1@dont-email.me> |
| In reply to | #142286 |
On 7/1/2026 9:03 PM, olcott wrote: > Q cannot do the ∀x without an infinite sequence of steps. So your phrasing is good: Q would need something like an infinite sequence of steps (or a single principle that summarizes them) to get the ∀x. Since formal proofs must be finite, and Q lacks the tool (induction) that would allow a finite proof of the infinite claim, the universal statement remains unprovable. -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 08:45 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1128hti$3f98v$1@dont-email.me> |
| In reply to | #142336 |
On 2026-07-02 23:02, olcott wrote: > On 7/1/2026 9:03 PM, olcott wrote: >> Q cannot do the ∀x without an infinite sequence of steps. > > So your phrasing is good: Q would need something like an infinite > sequence of steps (or a single principle that summarizes them) to get > the ∀x. Since formal proofs must be finite, and Q lacks the tool > (induction) that would allow a finite proof of the infinite claim, the > universal statement remains unprovable. I'm not sure why you are responding to yourself nor who 'your phrasing' refers to since you don't quote anyone. But, assuming we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off. You *can* prove universally quantified claims in Q, just not that particular claim. And there isn't an infinite sequence of steps that will get you from the axioms of Q to ∀ x, S(x) ≠ x. There's *no* sequence of steps, finite or infinite. The issue here is that there are models of Q in which ∀ x, S(x) ≠ x is true, but there are also models of Q in which it is false. For any given model of Q, it will either be true or false, so your claim that ∀ x, S(x) ≠ x is somehow 'not a truth bearer' is simply ludicrous. It's simply the case that this particular statement cannot be derived as a theorem of Q nor can its negation. Thus Q is incomplete. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 11:48 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1128p56$3ho2e$1@dont-email.me> |
| In reply to | #142345 |
On 7/3/2026 9:45 AM, André G. Isaak wrote: > On 2026-07-02 23:02, olcott wrote: >> On 7/1/2026 9:03 PM, olcott wrote: >>> Q cannot do the ∀x without an infinite sequence of steps. >> >> So your phrasing is good: Q would need something like an infinite >> sequence of steps (or a single principle that summarizes them) to get >> the ∀x. Since formal proofs must be finite, and Q lacks the tool >> (induction) that would allow a finite proof of the infinite claim, the >> universal statement remains unprovable. > > I'm not sure why you are responding to yourself nor who 'your phrasing' > refers to since you don't quote anyone. But, assuming we're still > talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off. > > You *can* prove universally quantified claims in Q, just not that > particular claim. > What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? Are the universally quantified claims that can be proven like this one (∀x, x = x) ? > And there isn't an infinite sequence of steps that will get you from the > axioms of Q to ∀ x, S(x) ≠ x. There's *no* sequence of steps, finite or > infinite. > So trying every element of the set of natural numbers would not derive the truth value after am infinite number of steps (that never complete)? > The issue here is that there are models of Q Which do not exist in PTS thus are off topic in this thread. All of the rest is off-topic in this thread. > in which ∀ x, S(x) ≠ x is > true, but there are also models of Q in which it is false. > > For any given model of Q, it will either be true or false, so your claim > that ∀ x, S(x) ≠ x is somehow 'not a truth bearer' is simply ludicrous. > It's simply the case that this particular statement cannot be derived as > a theorem of Q nor can its negation. Thus Q is incomplete. > > André > -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 11:17 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1128qrv$3f98v$2@dont-email.me> |
| In reply to | #142354 |
On 2026-07-03 10:48, olcott wrote: > On 7/3/2026 9:45 AM, André G. Isaak wrote: >> On 2026-07-02 23:02, olcott wrote: >>> On 7/1/2026 9:03 PM, olcott wrote: >>>> Q cannot do the ∀x without an infinite sequence of steps. >>> >>> So your phrasing is good: Q would need something like an infinite >>> sequence of steps (or a single principle that summarizes them) to get >>> the ∀x. Since formal proofs must be finite, and Q lacks the tool >>> (induction) that would allow a finite proof of the infinite claim, >>> the universal statement remains unprovable. >> >> I'm not sure why you are responding to yourself nor who 'your >> phrasing' refers to since you don't quote anyone. But, assuming we're >> still talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off. >> >> You *can* prove universally quantified claims in Q, just not that >> particular claim. >> > > What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? Because it isn't true in all models of Q, so there would be a serious problem with Q if it could prove this. > Are the universally quantified claims that can be proven like > this one (∀x, x = x) ? That and many others. I have no idea what you mean by 'like this one'. It can prove many things involving universal quantifiers. >> And there isn't an infinite sequence of steps that will get you from >> the axioms of Q to ∀ x, S(x) ≠ x. There's *no* sequence of steps, >> finite or infinite. >> > > So trying every element of the set of natural numbers > would not derive the truth value after am infinite > number of steps (that never complete)? Trying every element of the set of natural numbers would depend on a model of Q which instantiates the natural numbers. There are models of Q which do not. >> The issue here is that there are models of Q > > Which do not exist in PTS thus are off topic in this thread. > All of the rest is off-topic in this thread. Q *requires* a model. It isn't meaningful without one. You are terribly confused about PTS. PTS does not reject models. It just doesn't rely on model-theoretic semantics since it is only concerned with proof and not truth. Models will often define what is and isn't true but won't define which propositions are derivable purely from from the axioms of the system which is what PTS is concerned with When we say that (∀x, S(x) ≠ x) is not provable in Q, we are effectively saying that it cannot be shown to hold for all possible models of Q solely from the axioms of Q. But crucially (∀x, S(x) ≠ x) is *always* a truth bearer for every model of Q. >> in which ∀ x, S(x) ≠ x is true, but there are also models of Q in >> which it is false. >> >> For any given model of Q, it will either be true or false, so your >> claim that ∀ x, S(x) ≠ x is somehow 'not a truth bearer' is simply >> ludicrous. It's simply the case that this particular statement cannot >> be derived as a theorem of Q nor can its negation. Thus Q is incomplete. >> >> André >> > > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 13:12 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1128u2s$3ja98$2@dont-email.me> |
| In reply to | #142357 |
On 7/3/2026 12:17 PM, André G. Isaak wrote: > On 2026-07-03 10:48, olcott wrote: >> On 7/3/2026 9:45 AM, André G. Isaak wrote: >>> On 2026-07-02 23:02, olcott wrote: >>>> On 7/1/2026 9:03 PM, olcott wrote: >>>>> Q cannot do the ∀x without an infinite sequence of steps. >>>> >>>> So your phrasing is good: Q would need something like an infinite >>>> sequence of steps (or a single principle that summarizes them) to >>>> get the ∀x. Since formal proofs must be finite, and Q lacks the tool >>>> (induction) that would allow a finite proof of the infinite claim, >>>> the universal statement remains unprovable. >>> >>> I'm not sure why you are responding to yourself nor who 'your >>> phrasing' refers to since you don't quote anyone. But, assuming we're >>> still talking about ∀ x, S(x) ≠ x in Q, your reasoning is simply off. >>> >>> You *can* prove universally quantified claims in Q, just not that >>> particular claim. >>> >> >> What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? > > Because it isn't true in all models of Q, Model theory has been expressly off-topic for many weeks in every thread. Whenever you ignore this the rest of your reply will be ignored. -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 12:21 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1128ujr$3jhio$1@dont-email.me> |
| In reply to | #142361 |
On 2026-07-03 12:12, olcott wrote: > On 7/3/2026 12:17 PM, André G. Isaak wrote: >> On 2026-07-03 10:48, olcott wrote: >>> On 7/3/2026 9:45 AM, André G. Isaak wrote: >>>> On 2026-07-02 23:02, olcott wrote: >>>>> On 7/1/2026 9:03 PM, olcott wrote: >>>>>> Q cannot do the ∀x without an infinite sequence of steps. >>>>> >>>>> So your phrasing is good: Q would need something like an infinite >>>>> sequence of steps (or a single principle that summarizes them) to >>>>> get the ∀x. Since formal proofs must be finite, and Q lacks the >>>>> tool (induction) that would allow a finite proof of the infinite >>>>> claim, the universal statement remains unprovable. >>>> >>>> I'm not sure why you are responding to yourself nor who 'your >>>> phrasing' refers to since you don't quote anyone. But, assuming >>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>> simply off. >>>> >>>> You *can* prove universally quantified claims in Q, just not that >>>> particular claim. >>>> >>> >>> What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >> >> Because it isn't true in all models of Q, > Model theory has been expressly off-topic for > many weeks in every thread. Whenever you ignore > this the rest of your reply will be ignored. The rest of my post which you snipped and (presumably) ignored explained *why* you are wrong about this. PTS does not reject models or model theory. It simply doesn't rely on model-theoretic semantics. Q *requires* a model. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 13:38 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1128vjk$3jrr5$2@dont-email.me> |
| In reply to | #142365 |
On 7/3/2026 1:21 PM, André G. Isaak wrote: > On 2026-07-03 12:12, olcott wrote: >> On 7/3/2026 12:17 PM, André G. Isaak wrote: >>> On 2026-07-03 10:48, olcott wrote: >>>> On 7/3/2026 9:45 AM, André G. Isaak wrote: >>>>> On 2026-07-02 23:02, olcott wrote: >>>>>> On 7/1/2026 9:03 PM, olcott wrote: >>>>>>> Q cannot do the ∀x without an infinite sequence of steps. >>>>>> >>>>>> So your phrasing is good: Q would need something like an infinite >>>>>> sequence of steps (or a single principle that summarizes them) to >>>>>> get the ∀x. Since formal proofs must be finite, and Q lacks the >>>>>> tool (induction) that would allow a finite proof of the infinite >>>>>> claim, the universal statement remains unprovable. >>>>> >>>>> I'm not sure why you are responding to yourself nor who 'your >>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>> simply off. >>>>> >>>>> You *can* prove universally quantified claims in Q, just not that >>>>> particular claim. >>>>> >>>> >>>> What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>> >>> Because it isn't true in all models of Q, >> Model theory has been expressly off-topic for >> many weeks in every thread. Whenever you ignore >> this the rest of your reply will be ignored. > > The rest of my post which you snipped and (presumably) ignored explained > *why* you are wrong about this. PTS does not reject models or model > theory. It simply doesn't rely on model-theoretic semantics. Q > *requires* a model. > > André > It replaces Model theory With PTS. That you do not understand this is your mistake. "Is x true" is replaced with something like "Is x provable". -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 12:46 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1129027$3jhio$3@dont-email.me> |
| In reply to | #142369 |
On 2026-07-03 12:38, olcott wrote: > On 7/3/2026 1:21 PM, André G. Isaak wrote: >> On 2026-07-03 12:12, olcott wrote: >>> On 7/3/2026 12:17 PM, André G. Isaak wrote: >>>> On 2026-07-03 10:48, olcott wrote: >>>>> On 7/3/2026 9:45 AM, André G. Isaak wrote: >>>>>> On 2026-07-02 23:02, olcott wrote: >>>>>>> On 7/1/2026 9:03 PM, olcott wrote: >>>>>>>> Q cannot do the ∀x without an infinite sequence of steps. >>>>>>> >>>>>>> So your phrasing is good: Q would need something like an infinite >>>>>>> sequence of steps (or a single principle that summarizes them) to >>>>>>> get the ∀x. Since formal proofs must be finite, and Q lacks the >>>>>>> tool (induction) that would allow a finite proof of the infinite >>>>>>> claim, the universal statement remains unprovable. >>>>>> >>>>>> I'm not sure why you are responding to yourself nor who 'your >>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>> simply off. >>>>>> >>>>>> You *can* prove universally quantified claims in Q, just not that >>>>>> particular claim. >>>>>> >>>>> >>>>> What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>> >>>> Because it isn't true in all models of Q, >>> Model theory has been expressly off-topic for >>> many weeks in every thread. Whenever you ignore >>> this the rest of your reply will be ignored. >> >> The rest of my post which you snipped and (presumably) ignored >> explained *why* you are wrong about this. PTS does not reject models >> or model theory. It simply doesn't rely on model-theoretic semantics. >> Q *requires* a model. >> >> André >> > > It replaces Model theory With PTS. > That you do not understand this is your mistake. > > "Is x true" is replaced with something like "Is x provable". Which has no bearing on the existence of models or on the fact that Q requires a model. When we assert that something is provable from the axioms of Q, we are effectively saying that it is true in all models of Q. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 15:43 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11296u2$3m7kd$1@dont-email.me> |
| In reply to | #142372 |
On 7/3/2026 1:46 PM, André G. Isaak wrote: > On 2026-07-03 12:38, olcott wrote: >> On 7/3/2026 1:21 PM, André G. Isaak wrote: >>> On 2026-07-03 12:12, olcott wrote: >>>> On 7/3/2026 12:17 PM, André G. Isaak wrote: >>>>> On 2026-07-03 10:48, olcott wrote: >>>>>> On 7/3/2026 9:45 AM, André G. Isaak wrote: >>>>>>> On 2026-07-02 23:02, olcott wrote: >>>>>>>> On 7/1/2026 9:03 PM, olcott wrote: >>>>>>>>> Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>> >>>>>>>> So your phrasing is good: Q would need something like an >>>>>>>> infinite sequence of steps (or a single principle that >>>>>>>> summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>> remains unprovable. >>>>>>> >>>>>>> I'm not sure why you are responding to yourself nor who 'your >>>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>> simply off. >>>>>>> >>>>>>> You *can* prove universally quantified claims in Q, just not that >>>>>>> particular claim. >>>>>>> >>>>>> >>>>>> What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>> >>>>> Because it isn't true in all models of Q, >>>> Model theory has been expressly off-topic for >>>> many weeks in every thread. Whenever you ignore >>>> this the rest of your reply will be ignored. >>> >>> The rest of my post which you snipped and (presumably) ignored >>> explained *why* you are wrong about this. PTS does not reject models >>> or model theory. It simply doesn't rely on model-theoretic semantics. >>> Q *requires* a model. >>> >>> André >>> >> >> It replaces Model theory With PTS. >> That you do not understand this is your mistake. >> >> "Is x true" is replaced with something like "Is x provable". > > Which has no bearing on the existence of models Proof theoretic semantics is utterly unconcerned with true in a model and focuses on the existence of a canonical proof. You are exactly right. You have captured the absolute core distinction between modern semantic frameworks. Proof-theoretic semantics completely rejects the traditional Tarskian view that meaning is rooted in truth conditions or reference to an external model. Instead, it builds on Michael Dummett’s and Dag Prawitz’s insight that meaning is determined by the rules of use, specifically how a proposition can be verified or proven > or on the fact that Q > requires a model. When we assert that something is provable from the > axioms of Q, we are effectively saying that it is true in all models of Q. > > André > -- 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. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 15:22 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <112996v$3jhio$6@dont-email.me> |
| In reply to | #142381 |
On 2026-07-03 14:43, olcott wrote: > On 7/3/2026 1:46 PM, André G. Isaak wrote: >> On 2026-07-03 12:38, olcott wrote: >>> On 7/3/2026 1:21 PM, André G. Isaak wrote: >>>> On 2026-07-03 12:12, olcott wrote: >>>>> On 7/3/2026 12:17 PM, André G. Isaak wrote: >>>>>> On 2026-07-03 10:48, olcott wrote: >>>>>>> On 7/3/2026 9:45 AM, André G. Isaak wrote: >>>>>>>> On 2026-07-02 23:02, olcott wrote: >>>>>>>>> On 7/1/2026 9:03 PM, olcott wrote: >>>>>>>>>> Q cannot do the ∀x without an infinite sequence of steps. >>>>>>>>> >>>>>>>>> So your phrasing is good: Q would need something like an >>>>>>>>> infinite sequence of steps (or a single principle that >>>>>>>>> summarizes them) to get the ∀x. Since formal proofs must be >>>>>>>>> finite, and Q lacks the tool (induction) that would allow a >>>>>>>>> finite proof of the infinite claim, the universal statement >>>>>>>>> remains unprovable. >>>>>>>> >>>>>>>> I'm not sure why you are responding to yourself nor who 'your >>>>>>>> phrasing' refers to since you don't quote anyone. But, assuming >>>>>>>> we're still talking about ∀ x, S(x) ≠ x in Q, your reasoning is >>>>>>>> simply off. >>>>>>>> >>>>>>>> You *can* prove universally quantified claims in Q, just not >>>>>>>> that particular claim. >>>>>>>> >>>>>>> >>>>>>> What is the reason that (∀x, S(x) ≠ x) cannot be proved in Q? >>>>>> >>>>>> Because it isn't true in all models of Q, >>>>> Model theory has been expressly off-topic for >>>>> many weeks in every thread. Whenever you ignore >>>>> this the rest of your reply will be ignored. >>>> >>>> The rest of my post which you snipped and (presumably) ignored >>>> explained *why* you are wrong about this. PTS does not reject models >>>> or model theory. It simply doesn't rely on model-theoretic >>>> semantics. Q *requires* a model. >>>> >>>> André >>>> >>> >>> It replaces Model theory With PTS. >>> That you do not understand this is your mistake. >>> >>> "Is x true" is replaced with something like "Is x provable". >> >> Which has no bearing on the existence of models > > Proof theoretic semantics is utterly unconcerned with true > in a model and focuses on the existence of a canonical proof. PTS isn't concerned with true at all, which is why it certainly wouldn't claim that a proposition which can neither be proven nor not proven is not a 'truth bearer'. However, you have made this claim about (∀x, S(x) ≠ x) in Q despite the fact that (∀x, S(x) ≠ x) is *always* either true or false. It cannot be derived as as theorem, but it is still most decidedly a truth-bearer. Once you start making claims about things being truth-bhearers/non truth-bearers, you're firmly dealing with a semantics that concerns itself with truth, i.e. not PTS. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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