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Groups > sci.math > #644766 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-04-20 11:57 -0500 |
| Last post | 2026-06-30 06:54 +0100 |
| Articles | 20 on this page of 410 — 15 participants |
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Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-27 09:50 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:39 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-28 21:52 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:14 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:18 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:45 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:56 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 22:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:57 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:02 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:17 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 07:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 09:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 13:33 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:40 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:50 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:47 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:11 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:28 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:50 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:52 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 15:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 17:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 17:09 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 19:05 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 18:39 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 20:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 19:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:03 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 00:02 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 08:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:48 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:17 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:12 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:21 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:38 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:46 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 15:22 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:11 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:49 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:13 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 09:36 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:42 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:16 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 10:58 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:21 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:35 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:54 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:09 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:44 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:23 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:31 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:42 -0500
Re: The simple essence of Proof Theoretic Semantics Alan Mackenzie <acm@muc.de> - 2026-07-01 19:18 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:56 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:05 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:53 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:13 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:37 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:50 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 16:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 17:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 18:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 22:36 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:00 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:43 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:59 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 23:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:57 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 09:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 13:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 14:22 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 14:33 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 15:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 16:54 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:12 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:23 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:32 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:47 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 18:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 20:03 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:22 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 10:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 11:50 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:40 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:47 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 17:37 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 21:58 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:05 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:43 -0400
The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-03 22:11 -0500
Re: The truth about the halting problem counter-example input dbush <dbush.mobile@gmail.com> - 2026-07-03 23:23 -0400
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:58 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-04 12:16 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:07 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-06 10:18 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:45 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:58 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:07 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:11 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:27 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:19 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:04 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:46 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:55 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:24 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:30 -0500
Re: The simple essence of Proof Theoretic Semantics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:23 -0700
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 11:57 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:23 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:08 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:10 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:11 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:18 -0400
Re: The simple essence of Proof Theoretic Semantics Brenden Jafarov <rnarnj@rbn.ru> - 2026-07-04 12:47 +0000
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:43 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:04 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:28 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:27 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:45 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:53 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 16:59 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:57 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:01 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:33 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:25 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:10 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 14:08 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 15:12 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:38 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:09 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:28 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:15 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:41 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:38 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:40 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:39 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:14 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:32 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:37 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:06 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:03 +0300
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:25 +0300
Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-06 10:54 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:22 +0300
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-08 22:32 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:25 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:11 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:27 +0300
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: Terms-Of-The-Art are Liars Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 14:59 +0100
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:23 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 10:19 -0400
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:29 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 12:39 -0400
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 13:09 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:46 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 12:39 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:38 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-08 22:40 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:42 +0300
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 14:07 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:38 +0300
Re: Terms-Of-The-Art are Liars dart200 <user7160@newsgrouper.org.invalid> - 2026-07-06 14:53 -0700
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 17:01 -0500
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-07 15:36 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:17 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 10:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 10:07 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:27 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:56 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 13:12 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 12:54 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 14:03 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 14:08 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 15:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 15:13 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:00 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:53 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 17:39 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:52 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:47 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:45 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:44 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 10:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 11:01 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:35 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:54 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 13:14 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 19:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 07:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:56 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:22 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 06:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 12:04 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 22:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 17:22 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:10 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:30 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:11 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:35 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-29 14:27 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-12 16:23 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-13 10:50 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-27 15:35 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-01 21:17 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:34 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 16:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 15:52 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 17:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 11:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 12:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 15:25 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 14:30 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 16:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 15:15 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 17:55 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:16 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:58 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 12:00 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-06 14:19 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100
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| From | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-06-30 23:17 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11220ru$1iatd$4@dont-email.me> |
| In reply to | #645908 |
On 6/30/2026 11:10 PM, olcott wrote: > On 6/30/2026 10:02 PM, dbush wrote: >> On 6/30/2026 10:57 PM, olcott wrote: >>> On 6/30/2026 9:34 PM, dbush wrote: >>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>> >>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>> >>>>>>>>>> No, they are not. No author writing in the framework of proof- >>>>>>>>>> theoretic semantics has ever offered those examples or >>>>>>>>>> comparable examples or made any claims about 'rejecting >>>>>>>>>> expressions as proof theoretic semantically incoherent'. And >>>>>>>>>> there's nothing incoherent about the statement 'no number is >>>>>>>>>> equal to its successor' which is the example under discussion. >>>>>>>>>> >>>>>>>>>> André >>>>>>>>>> >>>>>>>>> >>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>> exactly correct PTS. >>>>>>>> >>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>> >>>>>>> >>>>>>> Yes. That is why I need to carefully find the exact >>>>>>> text that backs me up. Because PTS has their own >>>>>>> private author by author language it must be a >>>>>>> work written for a general audience like this work. >>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>> >>>>>>> >>>>>>>> Would you agree that there is a difference between a statement >>>>>>>> being false and a statement being meaningless? >>>>>>>> >>>>>>> >>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>> simpler analogy in that English words are meaningless until >>>>>>> they are defined. The PTS connection of an expression in >>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>> English word to its definition. A proof merely looks to >>>>>>> see if a definition exists and if it does not then the >>>>>>> English Word / Expression of Q remains meaningless. >>>>>>> >>>>>>> PTS counts a finite sequence of inference steps between >>>>>>> an expression and a set of axioms as the definition of >>>>>>> this expression. These are the two papers that establish >>>>>>> this Definitional View. >>>>>> >>>>>> None of the above answers my question: >>>>>> >>>>>> Would you agree that there is a difference between a statement >>>>>> being false and a statement being meaningless? >>>>>> >>>>> >>>>> I don't answer dumb questions. >>>> >>>> Translation: >>>> >>>> "I don't answer questions that can prove me wrong" >>>> >>>>> That is why I am not responding to any posts >>>>> besides yours. dbush has become a troll again. >>>> >>>> >>>> Reminding people that you admitted that disjunction intruduction is >>>> truth-preserving by your repeated dishonest dodging of how P can be >>>> true and P ∨ Q can be false is not trolling. >>>> >>> >>> In Robinson Arithmetic (often denoted as Q), >>> the statement "no number is equal to its >>> successor" is not provable. While this statement >>> is true for the standard natural numbers, Robinson >>> Arithmetic is too weak to prove it universally >>> (∀ x, S(x) ≠ x). >>> >>> That you brought this up was a brilliant simplification >>> of the point that I was making proving that you can >>> understand the key ideas. >> >> What is was is a way to show more easily how you're wrong. That you >> claim that "no number is equal to its successor" is semantically >> invalid shows everyone that your ideas are worthless. >> > > This is more accurate: > The truth value of (∀ x, S(x) ≠ x) So you admit that the above statement which exists in Q must be either true or false. > does not exist in Q. > You just contradicted yourself.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 22:49 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11222ng$1jm25$1@dont-email.me> |
| In reply to | #645910 |
On 6/30/2026 10:17 PM, dbush wrote: > On 6/30/2026 11:10 PM, olcott wrote: >> On 6/30/2026 10:02 PM, dbush wrote: >>> On 6/30/2026 10:57 PM, olcott wrote: >>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>> >>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>> >>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>> proof- theoretic semantics has ever offered those examples or >>>>>>>>>>> comparable examples or made any claims about 'rejecting >>>>>>>>>>> expressions as proof theoretic semantically incoherent'. And >>>>>>>>>>> there's nothing incoherent about the statement 'no number is >>>>>>>>>>> equal to its successor' which is the example under discussion. >>>>>>>>>>> >>>>>>>>>>> André >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>> exactly correct PTS. >>>>>>>>> >>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>> >>>>>>>> >>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>> text that backs me up. Because PTS has their own >>>>>>>> private author by author language it must be a >>>>>>>> work written for a general audience like this work. >>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>> >>>>>>>> >>>>>>>>> Would you agree that there is a difference between a statement >>>>>>>>> being false and a statement being meaningless? >>>>>>>>> >>>>>>>> >>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>> English word to its definition. A proof merely looks to >>>>>>>> see if a definition exists and if it does not then the >>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>> >>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>> an expression and a set of axioms as the definition of >>>>>>>> this expression. These are the two papers that establish >>>>>>>> this Definitional View. >>>>>>> >>>>>>> None of the above answers my question: >>>>>>> >>>>>>> Would you agree that there is a difference between a statement >>>>>>> being false and a statement being meaningless? >>>>>>> >>>>>> >>>>>> I don't answer dumb questions. >>>>> >>>>> Translation: >>>>> >>>>> "I don't answer questions that can prove me wrong" >>>>> >>>>>> That is why I am not responding to any posts >>>>>> besides yours. dbush has become a troll again. >>>>> >>>>> >>>>> Reminding people that you admitted that disjunction intruduction is >>>>> truth-preserving by your repeated dishonest dodging of how P can be >>>>> true and P ∨ Q can be false is not trolling. >>>>> >>>> >>>> In Robinson Arithmetic (often denoted as Q), >>>> the statement "no number is equal to its >>>> successor" is not provable. While this statement >>>> is true for the standard natural numbers, Robinson >>>> Arithmetic is too weak to prove it universally >>>> (∀ x, S(x) ≠ x). >>>> >>>> That you brought this up was a brilliant simplification >>>> of the point that I was making proving that you can >>>> understand the key ideas. >>> >>> What is was is a way to show more easily how you're wrong. That you >>> claim that "no number is equal to its successor" is semantically >>> invalid shows everyone that your ideas are worthless. >>> >> >> This is more accurate: >> The truth value of (∀ x, S(x) ≠ x) > > So you admit that the above statement which exists in Q must be either > true or false. > >> does not exist in Q. >> > Unlike PA it cannot possibly have any finite sequence of inference steps in Q that resolve to a truth value in Q. > You just contradicted yourself. > > -- 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).
[toc] | [prev] | [next] | [standalone]
| From | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-07-01 00:01 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11223ec$1iatd$5@dont-email.me> |
| In reply to | #645912 |
On 6/30/2026 11:49 PM, olcott wrote: > On 6/30/2026 10:17 PM, dbush wrote: >> On 6/30/2026 11:10 PM, olcott wrote: >>> On 6/30/2026 10:02 PM, dbush wrote: >>>> On 6/30/2026 10:57 PM, olcott wrote: >>>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>>> >>>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>>> >>>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>>> proof- theoretic semantics has ever offered those examples >>>>>>>>>>>> or comparable examples or made any claims about 'rejecting >>>>>>>>>>>> expressions as proof theoretic semantically incoherent'. And >>>>>>>>>>>> there's nothing incoherent about the statement 'no number is >>>>>>>>>>>> equal to its successor' which is the example under discussion. >>>>>>>>>>>> >>>>>>>>>>>> André >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>>> exactly correct PTS. >>>>>>>>>> >>>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>>> >>>>>>>>> >>>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>>> text that backs me up. Because PTS has their own >>>>>>>>> private author by author language it must be a >>>>>>>>> work written for a general audience like this work. >>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>> >>>>>>>>> >>>>>>>>>> Would you agree that there is a difference between a statement >>>>>>>>>> being false and a statement being meaningless? >>>>>>>>>> >>>>>>>>> >>>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>>> English word to its definition. A proof merely looks to >>>>>>>>> see if a definition exists and if it does not then the >>>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>>> >>>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>>> an expression and a set of axioms as the definition of >>>>>>>>> this expression. These are the two papers that establish >>>>>>>>> this Definitional View. >>>>>>>> >>>>>>>> None of the above answers my question: >>>>>>>> >>>>>>>> Would you agree that there is a difference between a statement >>>>>>>> being false and a statement being meaningless? >>>>>>>> >>>>>>> >>>>>>> I don't answer dumb questions. >>>>>> >>>>>> Translation: >>>>>> >>>>>> "I don't answer questions that can prove me wrong" >>>>>> >>>>>>> That is why I am not responding to any posts >>>>>>> besides yours. dbush has become a troll again. >>>>>> >>>>>> >>>>>> Reminding people that you admitted that disjunction intruduction >>>>>> is truth-preserving by your repeated dishonest dodging of how P >>>>>> can be true and P ∨ Q can be false is not trolling. >>>>>> >>>>> >>>>> In Robinson Arithmetic (often denoted as Q), >>>>> the statement "no number is equal to its >>>>> successor" is not provable. While this statement >>>>> is true for the standard natural numbers, Robinson >>>>> Arithmetic is too weak to prove it universally >>>>> (∀ x, S(x) ≠ x). >>>>> >>>>> That you brought this up was a brilliant simplification >>>>> of the point that I was making proving that you can >>>>> understand the key ideas. >>>> >>>> What is was is a way to show more easily how you're wrong. That you >>>> claim that "no number is equal to its successor" is semantically >>>> invalid shows everyone that your ideas are worthless. >>>> >>> >>> This is more accurate: >>> The truth value of (∀ x, S(x) ≠ x) >> >> So you admit that the above statement which exists in Q must be either >> true or false. >> Your lack of reply confirms your above admission. >>> does not exist in Q. >>> >> > > Unlike PA it cannot possibly have any finite sequence > of inference steps in Q that resolve to a truth value in Q. Which means, by definition, you agree that Q is incomplete. > >> You just contradicted yourself. >> >> > >
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 23:20 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11224il$1k40s$2@dont-email.me> |
| In reply to | #645913 |
On 6/30/2026 11:01 PM, dbush wrote: > On 6/30/2026 11:49 PM, olcott wrote: >> On 6/30/2026 10:17 PM, dbush wrote: >>> On 6/30/2026 11:10 PM, olcott wrote: >>>> On 6/30/2026 10:02 PM, dbush wrote: >>>>> On 6/30/2026 10:57 PM, olcott wrote: >>>>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>>>> >>>>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>>>> >>>>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>>>> proof- theoretic semantics has ever offered those examples >>>>>>>>>>>>> or comparable examples or made any claims about 'rejecting >>>>>>>>>>>>> expressions as proof theoretic semantically incoherent'. >>>>>>>>>>>>> And there's nothing incoherent about the statement 'no >>>>>>>>>>>>> number is equal to its successor' which is the example >>>>>>>>>>>>> under discussion. >>>>>>>>>>>>> >>>>>>>>>>>>> André >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>>>> exactly correct PTS. >>>>>>>>>>> >>>>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>>>> text that backs me up. Because PTS has their own >>>>>>>>>> private author by author language it must be a >>>>>>>>>> work written for a general audience like this work. >>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>> >>>>>>>>>> >>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>>>> English word to its definition. A proof merely looks to >>>>>>>>>> see if a definition exists and if it does not then the >>>>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>>>> >>>>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>>>> an expression and a set of axioms as the definition of >>>>>>>>>> this expression. These are the two papers that establish >>>>>>>>>> this Definitional View. >>>>>>>>> >>>>>>>>> None of the above answers my question: >>>>>>>>> >>>>>>>>> Would you agree that there is a difference between a statement >>>>>>>>> being false and a statement being meaningless? >>>>>>>>> >>>>>>>> >>>>>>>> I don't answer dumb questions. >>>>>>> >>>>>>> Translation: >>>>>>> >>>>>>> "I don't answer questions that can prove me wrong" >>>>>>> >>>>>>>> That is why I am not responding to any posts >>>>>>>> besides yours. dbush has become a troll again. >>>>>>> >>>>>>> >>>>>>> Reminding people that you admitted that disjunction intruduction >>>>>>> is truth-preserving by your repeated dishonest dodging of how P >>>>>>> can be true and P ∨ Q can be false is not trolling. >>>>>>> >>>>>> >>>>>> In Robinson Arithmetic (often denoted as Q), >>>>>> the statement "no number is equal to its >>>>>> successor" is not provable. While this statement >>>>>> is true for the standard natural numbers, Robinson >>>>>> Arithmetic is too weak to prove it universally >>>>>> (∀ x, S(x) ≠ x). >>>>>> >>>>>> That you brought this up was a brilliant simplification >>>>>> of the point that I was making proving that you can >>>>>> understand the key ideas. >>>>> >>>>> What is was is a way to show more easily how you're wrong. That >>>>> you claim that "no number is equal to its successor" is >>>>> semantically invalid shows everyone that your ideas are worthless. >>>>> >>>> >>>> This is more accurate: >>>> The truth value of (∀ x, S(x) ≠ x) >>> >>> So you admit that the above statement which exists in Q must be >>> either true or false. >>> > > Your lack of reply confirms your above admission. > I make a very specific statement. You mangle it and ask if I agree. The truth value of (∀ x, S(x) ≠ x) does not exist in Q. If you change that in any way you can assume that I do not agree. >>>> does not exist in Q. >>>> >>> >> >> Unlike PA it cannot possibly have any finite sequence >> of inference steps in Q that resolve to a truth value in Q. > > Which means, by definition, you agree that Q is incomplete. > >> >>> You just contradicted yourself. >>> >>> >> >> > -- 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).
[toc] | [prev] | [next] | [standalone]
| From | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-07-01 07:55 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1122v7q$1r49e$1@dont-email.me> |
| In reply to | #645915 |
On 7/1/2026 12:20 AM, olcott wrote: > On 6/30/2026 11:01 PM, dbush wrote: >> On 6/30/2026 11:49 PM, olcott wrote: >>> On 6/30/2026 10:17 PM, dbush wrote: >>>> On 6/30/2026 11:10 PM, olcott wrote: >>>>> On 6/30/2026 10:02 PM, dbush wrote: >>>>>> On 6/30/2026 10:57 PM, olcott wrote: >>>>>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>>>>> >>>>>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>>>>> >>>>>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>>>>> proof- theoretic semantics has ever offered those examples >>>>>>>>>>>>>> or comparable examples or made any claims about 'rejecting >>>>>>>>>>>>>> expressions as proof theoretic semantically incoherent'. >>>>>>>>>>>>>> And there's nothing incoherent about the statement 'no >>>>>>>>>>>>>> number is equal to its successor' which is the example >>>>>>>>>>>>>> under discussion. >>>>>>>>>>>>>> >>>>>>>>>>>>>> André >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>>>>> exactly correct PTS. >>>>>>>>>>>> >>>>>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>>>>> text that backs me up. Because PTS has their own >>>>>>>>>>> private author by author language it must be a >>>>>>>>>>> work written for a general audience like this work. >>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>>>>> English word to its definition. A proof merely looks to >>>>>>>>>>> see if a definition exists and if it does not then the >>>>>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>>>>> >>>>>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>>>>> an expression and a set of axioms as the definition of >>>>>>>>>>> this expression. These are the two papers that establish >>>>>>>>>>> this Definitional View. >>>>>>>>>> >>>>>>>>>> None of the above answers my question: >>>>>>>>>> >>>>>>>>>> Would you agree that there is a difference between a statement >>>>>>>>>> being false and a statement being meaningless? >>>>>>>>>> >>>>>>>>> >>>>>>>>> I don't answer dumb questions. >>>>>>>> >>>>>>>> Translation: >>>>>>>> >>>>>>>> "I don't answer questions that can prove me wrong" >>>>>>>> >>>>>>>>> That is why I am not responding to any posts >>>>>>>>> besides yours. dbush has become a troll again. >>>>>>>> >>>>>>>> >>>>>>>> Reminding people that you admitted that disjunction intruduction >>>>>>>> is truth-preserving by your repeated dishonest dodging of how P >>>>>>>> can be true and P ∨ Q can be false is not trolling. >>>>>>>> >>>>>>> >>>>>>> In Robinson Arithmetic (often denoted as Q), >>>>>>> the statement "no number is equal to its >>>>>>> successor" is not provable. While this statement >>>>>>> is true for the standard natural numbers, Robinson >>>>>>> Arithmetic is too weak to prove it universally >>>>>>> (∀ x, S(x) ≠ x). >>>>>>> >>>>>>> That you brought this up was a brilliant simplification >>>>>>> of the point that I was making proving that you can >>>>>>> understand the key ideas. >>>>>> >>>>>> What is was is a way to show more easily how you're wrong. That >>>>>> you claim that "no number is equal to its successor" is >>>>>> semantically invalid shows everyone that your ideas are worthless. >>>>>> >>>>> >>>>> This is more accurate: >>>>> The truth value of (∀ x, S(x) ≠ x) >>>> >>>> So you admit that the above statement which exists in Q must be >>>> either true or false. >>>> >> >> Your lack of reply confirms your above admission. >> > > I make a very specific statement. > You mangle it and ask if I agree. There was no mangling. That is the meaning of the words you used. > > The truth value of (∀ x, S(x) ≠ x) In order for it to have a truth value, it must be either true or false. That you say it has a truth value is your admission that it is in fact either true or false. Only a statement that is semantically valid / correct can be true or false, as it is it semantics (in this case the semantics of Q and the English language sentence it translates to) that determines truth values. This therefore constitutes your admission that the above statement is semantically valid / correct, and that by extension PTS is incorrect about this and therefore useless. > does not exist in Q. > If you change that in any way you can assume that I do not agree. > >>>>> does not exist in Q. >>>>> >>>> >>> >>> Unlike PA it cannot possibly have any finite sequence >>> of inference steps in Q that resolve to a truth value in Q. >> >> Which means, by definition, you agree that Q is incomplete. >> >>> >>>> You just contradicted yourself. >>>> >>>> >>> >>> >> > >
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 09:40 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11238s9$1u2jt$1@dont-email.me> |
| In reply to | #645923 |
On 7/1/2026 6:55 AM, dbush wrote: > On 7/1/2026 12:20 AM, olcott wrote: >> On 6/30/2026 11:01 PM, dbush wrote: >>> On 6/30/2026 11:49 PM, olcott wrote: >>>> On 6/30/2026 10:17 PM, dbush wrote: >>>>> On 6/30/2026 11:10 PM, olcott wrote: >>>>>> On 6/30/2026 10:02 PM, dbush wrote: >>>>>>> On 6/30/2026 10:57 PM, olcott wrote: >>>>>>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>>>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>>>>>> proof- theoretic semantics has ever offered those >>>>>>>>>>>>>>> examples or comparable examples or made any claims about >>>>>>>>>>>>>>> 'rejecting expressions as proof theoretic semantically >>>>>>>>>>>>>>> incoherent'. And there's nothing incoherent about the >>>>>>>>>>>>>>> statement 'no number is equal to its successor' which is >>>>>>>>>>>>>>> the example under discussion. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> André >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>>>>>> exactly correct PTS. >>>>>>>>>>>>> >>>>>>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>>>>>> text that backs me up. Because PTS has their own >>>>>>>>>>>> private author by author language it must be a >>>>>>>>>>>> work written for a general audience like this work. >>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>>>>>> English word to its definition. A proof merely looks to >>>>>>>>>>>> see if a definition exists and if it does not then the >>>>>>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>>>>>> >>>>>>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>>>>>> an expression and a set of axioms as the definition of >>>>>>>>>>>> this expression. These are the two papers that establish >>>>>>>>>>>> this Definitional View. >>>>>>>>>>> >>>>>>>>>>> None of the above answers my question: >>>>>>>>>>> >>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> I don't answer dumb questions. >>>>>>>>> >>>>>>>>> Translation: >>>>>>>>> >>>>>>>>> "I don't answer questions that can prove me wrong" >>>>>>>>> >>>>>>>>>> That is why I am not responding to any posts >>>>>>>>>> besides yours. dbush has become a troll again. >>>>>>>>> >>>>>>>>> >>>>>>>>> Reminding people that you admitted that disjunction >>>>>>>>> intruduction is truth-preserving by your repeated dishonest >>>>>>>>> dodging of how P can be true and P ∨ Q can be false is not >>>>>>>>> trolling. >>>>>>>>> >>>>>>>> >>>>>>>> In Robinson Arithmetic (often denoted as Q), >>>>>>>> the statement "no number is equal to its >>>>>>>> successor" is not provable. While this statement >>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>> (∀ x, S(x) ≠ x). >>>>>>>> >>>>>>>> That you brought this up was a brilliant simplification >>>>>>>> of the point that I was making proving that you can >>>>>>>> understand the key ideas. >>>>>>> >>>>>>> What is was is a way to show more easily how you're wrong. That >>>>>>> you claim that "no number is equal to its successor" is >>>>>>> semantically invalid shows everyone that your ideas are worthless. >>>>>>> >>>>>> >>>>>> This is more accurate: >>>>>> The truth value of (∀ x, S(x) ≠ x) >>>>> >>>>> So you admit that the above statement which exists in Q must be >>>>> either true or false. >>>>> >>> >>> Your lack of reply confirms your above admission. >>> >> >> I make a very specific statement. >> You mangle it and ask if I agree. > > There was no mangling. That is the meaning of the words you used. > >> >> The truth value of (∀ x, S(x) ≠ x) > You already mangled it. The truth value of (∀ x, S(x) ≠ x) does not exist in Q. > In order for it to have a truth value, it must be either true or false. > That you say it has a truth value is your admission that it is in fact > either true or false. > > Only a statement that is semantically valid / correct can be true or > false, as it is it semantics (in this case the semantics of Q and the > English language sentence it translates to) that determines truth values. > > This therefore constitutes your admission that the above statement is > semantically valid / correct, and that by extension PTS is incorrect > about this and therefore useless. > > >> does not exist in Q. >> If you change that in any way you can assume that I do not agree. >> > > > >>>>>> does not exist in Q. >>>>>> >>>>> >>>> >>>> Unlike PA it cannot possibly have any finite sequence >>>> of inference steps in Q that resolve to a truth value in Q. >>> >>> Which means, by definition, you agree that Q is incomplete. >>> >>>> >>>>> You just contradicted yourself. >>>>> >>>>> >>>> >>>> >>> >> >> > -- 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 | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-07-01 13:33 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123j1v$21e16$1@dont-email.me> |
| In reply to | #645925 |
On 7/1/2026 10:40 AM, olcott wrote: > On 7/1/2026 6:55 AM, dbush wrote: >> On 7/1/2026 12:20 AM, olcott wrote: >>> On 6/30/2026 11:01 PM, dbush wrote: >>>> On 6/30/2026 11:49 PM, olcott wrote: >>>>> On 6/30/2026 10:17 PM, dbush wrote: >>>>>> On 6/30/2026 11:10 PM, olcott wrote: >>>>>>> On 6/30/2026 10:02 PM, dbush wrote: >>>>>>>> On 6/30/2026 10:57 PM, olcott wrote: >>>>>>>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>>>>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>>>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>>>>>>> proof- theoretic semantics has ever offered those >>>>>>>>>>>>>>>> examples or comparable examples or made any claims about >>>>>>>>>>>>>>>> 'rejecting expressions as proof theoretic semantically >>>>>>>>>>>>>>>> incoherent'. And there's nothing incoherent about the >>>>>>>>>>>>>>>> statement 'no number is equal to its successor' which is >>>>>>>>>>>>>>>> the example under discussion. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>>>>>>> exactly correct PTS. >>>>>>>>>>>>>> >>>>>>>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>>>>>>> text that backs me up. Because PTS has their own >>>>>>>>>>>>> private author by author language it must be a >>>>>>>>>>>>> work written for a general audience like this work. >>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>>>>>>> English word to its definition. A proof merely looks to >>>>>>>>>>>>> see if a definition exists and if it does not then the >>>>>>>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>>>>>>> >>>>>>>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>>>>>>> an expression and a set of axioms as the definition of >>>>>>>>>>>>> this expression. These are the two papers that establish >>>>>>>>>>>>> this Definitional View. >>>>>>>>>>>> >>>>>>>>>>>> None of the above answers my question: >>>>>>>>>>>> >>>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> I don't answer dumb questions. >>>>>>>>>> >>>>>>>>>> Translation: >>>>>>>>>> >>>>>>>>>> "I don't answer questions that can prove me wrong" >>>>>>>>>> >>>>>>>>>>> That is why I am not responding to any posts >>>>>>>>>>> besides yours. dbush has become a troll again. >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> Reminding people that you admitted that disjunction >>>>>>>>>> intruduction is truth-preserving by your repeated dishonest >>>>>>>>>> dodging of how P can be true and P ∨ Q can be false is not >>>>>>>>>> trolling. >>>>>>>>>> >>>>>>>>> >>>>>>>>> In Robinson Arithmetic (often denoted as Q), >>>>>>>>> the statement "no number is equal to its >>>>>>>>> successor" is not provable. While this statement >>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>> (∀ x, S(x) ≠ x). >>>>>>>>> >>>>>>>>> That you brought this up was a brilliant simplification >>>>>>>>> of the point that I was making proving that you can >>>>>>>>> understand the key ideas. >>>>>>>> >>>>>>>> What is was is a way to show more easily how you're wrong. That >>>>>>>> you claim that "no number is equal to its successor" is >>>>>>>> semantically invalid shows everyone that your ideas are worthless. >>>>>>>> >>>>>>> >>>>>>> This is more accurate: >>>>>>> The truth value of (∀ x, S(x) ≠ x) >>>>>> >>>>>> So you admit that the above statement which exists in Q must be >>>>>> either true or false. >>>>>> >>>> >>>> Your lack of reply confirms your above admission. >>>> >>> >>> I make a very specific statement. >>> You mangle it and ask if I agree. >> >> There was no mangling. That is the meaning of the words you used. >> >>> >>> The truth value of (∀ x, S(x) ≠ x) >> > > You already mangled it. > 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? > >> In order for it to have a truth value, it must be either true or >> false. That you say it has a truth value is your admission that it is >> in fact either true or false. >> >> Only a statement that is semantically valid / correct can be true or >> false, as it is it semantics (in this case the semantics of Q and the >> English language sentence it translates to) that determines truth values. >> >> This therefore constitutes your admission that the above statement is >> semantically valid / correct, and that by extension PTS is incorrect >> about this and therefore useless. >> >> >>> does not exist in Q. >>> If you change that in any way you can assume that I do not agree. >>> >> >> >> >>>>>>> does not exist in Q. >>>>>>> >>>>>> >>>>> >>>>> Unlike PA it cannot possibly have any finite sequence >>>>> of inference steps in Q that resolve to a truth value in Q. >>>> >>>> Which means, by definition, you agree that Q is incomplete. >>>> >>>>> >>>>>> You just contradicted yourself. >>>>>> >>>>>> >>>>> >>>>> >>>> >>> >>> >> > >
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 13:01 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123klh$21vqp$1@dont-email.me> |
| In reply to | #645935 |
On 7/1/2026 12:33 PM, dbush wrote: > On 7/1/2026 10:40 AM, olcott wrote: >> On 7/1/2026 6:55 AM, dbush wrote: >>> On 7/1/2026 12:20 AM, olcott wrote: >>>> On 6/30/2026 11:01 PM, dbush wrote: >>>>> On 6/30/2026 11:49 PM, olcott wrote: >>>>>> On 6/30/2026 10:17 PM, dbush wrote: >>>>>>> On 6/30/2026 11:10 PM, olcott wrote: >>>>>>>> On 6/30/2026 10:02 PM, dbush wrote: >>>>>>>>> On 6/30/2026 10:57 PM, olcott wrote: >>>>>>>>>> On 6/30/2026 9:34 PM, dbush wrote: >>>>>>>>>>> On 6/30/2026 6:04 PM, olcott wrote: >>>>>>>>>>>> On 6/30/2026 4:56 PM, André G. Isaak wrote: >>>>>>>>>>>>> On 2026-06-30 15:45, olcott wrote: >>>>>>>>>>>>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>>>>>>>>>>>> On 2026-06-29 21:06, olcott wrote: >>>>>>>>>>>>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Those are specific concrete examples of how >>>>>>>>>>>>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>>>>>>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> No, they are not. No author writing in the framework of >>>>>>>>>>>>>>>>> proof- theoretic semantics has ever offered those >>>>>>>>>>>>>>>>> examples or comparable examples or made any claims >>>>>>>>>>>>>>>>> about 'rejecting expressions as proof theoretic >>>>>>>>>>>>>>>>> semantically incoherent'. And there's nothing >>>>>>>>>>>>>>>>> incoherent about the statement 'no number is equal to >>>>>>>>>>>>>>>>> its successor' which is the example under discussion. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> André >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> None-the-less what I have said remains completely true. >>>>>>>>>>>>>>>> What I have spent 28 years reverse-engineering from first >>>>>>>>>>>>>>>> principles is exactly that. That no one applied PTS >>>>>>>>>>>>>>>> exactly that way before does not mean that it is not >>>>>>>>>>>>>>>> exactly correct PTS. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Unfortunately, your say so carries very little weight. >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Yes. That is why I need to carefully find the exact >>>>>>>>>>>>>> text that backs me up. Because PTS has their own >>>>>>>>>>>>>> private author by author language it must be a >>>>>>>>>>>>>> work written for a general audience like this work. >>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic-semantics/ >>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> PTS is the way that meaning actually works. We can make a >>>>>>>>>>>>>> simpler analogy in that English words are meaningless until >>>>>>>>>>>>>> they are defined. The PTS connection of an expression in >>>>>>>>>>>>>> Q to its axioms Q is analogous to the connection of an >>>>>>>>>>>>>> English word to its definition. A proof merely looks to >>>>>>>>>>>>>> see if a definition exists and if it does not then the >>>>>>>>>>>>>> English Word / Expression of Q remains meaningless. >>>>>>>>>>>>>> >>>>>>>>>>>>>> PTS counts a finite sequence of inference steps between >>>>>>>>>>>>>> an expression and a set of axioms as the definition of >>>>>>>>>>>>>> this expression. These are the two papers that establish >>>>>>>>>>>>>> this Definitional View. >>>>>>>>>>>>> >>>>>>>>>>>>> None of the above answers my question: >>>>>>>>>>>>> >>>>>>>>>>>>> Would you agree that there is a difference between a >>>>>>>>>>>>> statement being false and a statement being meaningless? >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> I don't answer dumb questions. >>>>>>>>>>> >>>>>>>>>>> Translation: >>>>>>>>>>> >>>>>>>>>>> "I don't answer questions that can prove me wrong" >>>>>>>>>>> >>>>>>>>>>>> That is why I am not responding to any posts >>>>>>>>>>>> besides yours. dbush has become a troll again. >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Reminding people that you admitted that disjunction >>>>>>>>>>> intruduction is truth-preserving by your repeated dishonest >>>>>>>>>>> dodging of how P can be true and P ∨ Q can be false is not >>>>>>>>>>> trolling. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> In Robinson Arithmetic (often denoted as Q), >>>>>>>>>> the statement "no number is equal to its >>>>>>>>>> successor" is not provable. While this statement >>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>> (∀ x, S(x) ≠ x). >>>>>>>>>> >>>>>>>>>> That you brought this up was a brilliant simplification >>>>>>>>>> of the point that I was making proving that you can >>>>>>>>>> understand the key ideas. >>>>>>>>> >>>>>>>>> What is was is a way to show more easily how you're wrong. >>>>>>>>> That you claim that "no number is equal to its successor" is >>>>>>>>> semantically invalid shows everyone that your ideas are worthless. >>>>>>>>> >>>>>>>> >>>>>>>> This is more accurate: >>>>>>>> The truth value of (∀ x, S(x) ≠ x) >>>>>>> >>>>>>> So you admit that the above statement which exists in Q must be >>>>>>> either true or false. >>>>>>> >>>>> >>>>> Your lack of reply confirms your above admission. >>>>> >>>> >>>> I make a very specific statement. >>>> You mangle it and ask if I agree. >>> >>> There was no mangling. That is the meaning of the words you used. >>> >>>> >>>> The truth value of (∀ x, S(x) ≠ x) >>> >> >> You already mangled it. >> 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. -- 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 12:10 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123l6r$220jk$1@dont-email.me> |
| In reply to | #645939 |
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 -- 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 13:20 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123lq6$22bse$1@dont-email.me> |
| In reply to | #645941 |
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. -- 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 | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-07-01 14:34 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123mj0$22791$3@dont-email.me> |
| In reply to | #645944 |
On 7/1/2026 2:20 PM, 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. > In other words, (∀x, S(x) ≠ x) is not provable in Q. So once again, you're saying the same thing as everyone else but using different words.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 13:53 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123nmh$22sqa$3@dont-email.me> |
| In reply to | #645946 |
On 7/1/2026 1:34 PM, dbush wrote: > On 7/1/2026 2:20 PM, 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. >> > > In other words, (∀x, S(x) ≠ x) is not provable in Q. > In PTS that means the expression is undefined. It does not mean that Q has undecidable sentences in PTS. > So once again, you're saying the same thing as everyone else but using > different words. -- 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 | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-07-01 14:57 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123nv9$22791$6@dont-email.me> |
| In reply to | #645952 |
On 7/1/2026 2:53 PM, olcott wrote: > On 7/1/2026 1:34 PM, dbush wrote: >> On 7/1/2026 2:20 PM, 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. >>> >> >> In other words, (∀x, S(x) ≠ x) is not provable in Q. >> > > In PTS that means the expression is undefined. > It does not mean that Q has undecidable sentences in PTS. In your own words, what do you think it means for an expression to be undefined, and what do you think it means for a formal system to have undecidable sentences? > >> So once again, you're saying the same thing as everyone else but using >> different words. > >
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 14:06 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123ofi$2364m$1@dont-email.me> |
| In reply to | #645955 |
On 7/1/2026 1:57 PM, dbush wrote: > On 7/1/2026 2:53 PM, olcott wrote: >> On 7/1/2026 1:34 PM, dbush wrote: >>> On 7/1/2026 2:20 PM, 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. >>>> >>> >>> In other words, (∀x, S(x) ≠ x) is not provable in Q. >>> >> >> In PTS that means the expression is undefined. >> It does not mean that Q has undecidable sentences in PTS. > > In your own words, what do you think it means for an expression to be > undefined, and what do you think it means for a formal system to have > undecidable sentences? > I am trying to bridge my work to the work of proof theoretic semantics. I have exactly agreed with Wittgenstein's view about five years before I ever heard of him. What I (and Wittgenstein) call ~True(L,x) PTS mostly calls ~Defined(L,x). >> >>> So once again, you're saying the same thing as everyone else but >>> using different words. >> >> > -- 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 12:40 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123muv$220jk$2@dont-email.me> |
| In reply to | #645944 |
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 simply means it is unprovable in Q. And being ungrounded in the atomic base of Q means that it cannot achieve the PTS meaning of provable but rather remains unprovable. There's no way you can get from any of those things to 'random gibberish'. 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 13:50 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123nh1$22sqa$1@dont-email.me> |
| In reply to | #645948 |
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. > It simply > means it is unprovable in Q. Which means something entirely different in PTS than it means in TCS. > And being ungrounded in the atomic base of > Q means that it cannot achieve the PTS meaning of provable but rather > remains unprovable. What does Boxcar meaning in Chinese? It has no meaning in Chinese. When Boxcar is translated into Chinese: 棚车 then is has a Chinese meaning in Chinese. > There's no way you can get from any of those things > to 'random gibberish'. > The main unprovable that I have been working on for 27 years is cases of pathological self-reference that have incoherent meaning like this famous sentence: Colorless green ideas sleep furiously was composed by Noam Chomsky in his 1957 book Syntactic Structures as an example of a sentence that is grammatically well-formed, but semantically nonsensical. It has no coherent compositional meaning even though each word has meaning. > 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 13:23 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123pf4$220jk$4@dont-email.me> |
| In reply to | #645950 |
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. >> And being ungrounded in the atomic base of Q means that it cannot >> achieve the PTS meaning of provable but rather remains unprovable. > > What does Boxcar meaning in Chinese? > It has no meaning in Chinese. > > When Boxcar is translated into Chinese: 棚车 > then is has a Chinese meaning in Chinese. > >> There's no way you can get from any of those things to 'random >> gibberish'. >> > > The main unprovable that I have been working on > for 27 years is cases of pathological self-reference > that have incoherent meaning like this famous sentence: > > Colorless green ideas sleep furiously was composed by > Noam Chomsky in his 1957 book Syntactic Structures as > an example of a sentence that is grammatically well-formed, > but semantically nonsensical. Chomsky was making a point about *natural* languages, not Q. And I don't think you understand what the purpose of this example was. And, I should note that the example isn't nonsensical as it can have a poetic meaning (something which doesn't exist in formal languages). Chomsky's sole point with this example was to stress that you couldn't appeal to semantic ill-formedness to explain ungrammaticality in natural languages. Rather, syntactic rules had to stand on their own. -- 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 14:47 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123qtg$23ttc$1@dont-email.me> |
| In reply to | #645963 |
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 Does not mean that G is undecidable in PA. -- 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 14:11 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123s93$220jk$6@dont-email.me> |
| In reply to | #645968 |
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 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 -- 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 15:28 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1123t8r$24k8k$1@dont-email.me> |
| In reply to | #645972 |
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. > 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. -- 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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