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Groups > sci.logic > #345584 > 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 309 — 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 dbush <dbush.mobile@gmail.com> - 2026-07-01 14:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:21 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:35 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:54 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:09 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:44 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:23 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:31 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:42 -0500
Re: The simple essence of Proof Theoretic Semantics Alan Mackenzie <acm@muc.de> - 2026-07-01 19:18 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:56 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:05 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:53 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:13 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:37 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:50 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 16:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 17:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 18:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 22:36 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:00 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:43 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:59 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 23:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:57 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 09:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 13:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 14:22 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 14:33 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 15:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 16:54 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:12 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:23 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:32 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:47 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 18:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 20:03 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:22 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 10:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 11:50 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:40 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:47 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 17:37 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 21:58 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:05 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:43 -0400
The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-03 22:11 -0500
Re: The truth about the halting problem counter-example input dbush <dbush.mobile@gmail.com> - 2026-07-03 23:23 -0400
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:58 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-04 12:16 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:58 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:07 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:46 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:55 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:10 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:11 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:18 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:43 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:04 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:27 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:45 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:53 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 16:59 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:57 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:01 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 14:08 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 15:12 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:41 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:38 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:40 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:32 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:37 -0400
Re: The simple essence of Proof Theoretic Semantics cross@spitfire.i.gajendra.net (Dan Cross) - 2026-07-03 17:27 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-30 07:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA 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 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 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
Page 3 of 16 — ← Prev page 1 2 [3] 4 5 … 16 Next page →
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-06-29 17:03 -0600 |
| Message-ID | <111utja$l815$2@dont-email.me> |
| In reply to | #347202 |
On 2026-06-29 16:38, olcott wrote: > On 6/29/2026 5:25 PM, André G. Isaak wrote: >> On 2026-06-29 15:39, olcott wrote: >>> On 6/29/2026 4:18 PM, André G. Isaak wrote: >>>> On 2026-06-29 15:10, olcott wrote: >>>>> On 6/29/2026 3:58 PM, André G. Isaak wrote: >>>>>> On 2026-06-29 14:06, olcott wrote: >>>>>>> On 6/29/2026 3:02 PM, André G. Isaak wrote: >>>>>>>> On 2026-06-29 13:47, olcott wrote: >>>>>>>>> On 6/29/2026 2:33 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-06-29 13:08, olcott wrote: >>>>>>>>>>> On 6/29/2026 1:29 PM, André G. Isaak wrote: >>>>>>>>>> >>>>>>>>>>>> Is "has a box of clowns" in the language of Q? No. I didn't >>>>>>>>>>>> think so, so your example is completely irrelevant. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> It is an idiom stipulated to mean: >>>>>>>>>>> sentences in the language of Q which can neither >>>>>>>>>>> be proven nor disproven by Q >>>>>>>>>> >>>>>>>>>> Q doesn't have idioms. That's a natural language concept alien >>>>>>>>>> to theories of arithmetic. >>>>>>>>>> >>>>>>>>>>>>> So we can say that the halting problem "has a box >>>>>>>>>>>>> of clowns" instead of saying that computation is >>>>>>>>>>>>> in any way limited. >>>>>>>>>>>>> >>>>>>>>>>>>>> When mathematicians talk about rings, do you object based >>>>>>>>>>>>>> on the fact that you can't put them on your finger? >>>>>>>>>>>> >>>>>>>>>>>> No answer? >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> Off topic, irrelevant. >>>>>>>>>>> >>>>>>>>>>>>>> When mathematicians talk about fields, do you object based >>>>>>>>>>>>>> on the fact that nothing can graze on them? >>>>>>>>>>>> >>>>>>>>>>>> No answer? >>>>>>>>>> >>>>>>>>>> These questions are Irrelevant because >>>>>>>>> In Proof Theoretic Semantics >>>>>>>>> statements in the language of that system >>>>>>>>> which can neither be proven nor disproven >>>>>>>>> >>>>>>>>> have not established that they have semantic >>>>>>>>> meaning because semantic meaning is ONLY >>>>>>>>> established in PTS by canonical proofs. >>>>>>>> >>>>>>>> This is a misrepresentation on your part. Whereas truth >>>>>>>> functional semantics takes true and false to be the semantic >>>>>>>> primatives, PTS uses either (depending on which author you >>>>>>>> follow) proven and not proven or provable and not provable as >>>>>>>> its primitives without dealing with truth or falsity. >>>>>>> >>>>>>> Yes that is an accurate paraphrase. >>>>>>> >>>>>>>> Thus, they would treat a statement like 'no number is greater >>>>>>>> than its successor' as being unprovable in Robinson Arithmetic, >>>>>>>> not as being meaningless as you seem to think. >>>>>>>> >>>>>>> >>>>>>> You are not being consistent with you own paraphrase. >>>>>>> I still don't have all of the exact nuances exactly >>>>>>> correct because unlike every other field each author >>>>>>> has their own terms-of-the-art. >>>>>> >>>>>> Of course I am being consistent. Within PTD, unproven/unprovable >>>>>> *is* a semantic value, >>>>> >>>>> Impossibly provable in Q means cannot possibly >>>>> derive a semantic meaning Q. >>>> >>>> 'impossibly' in English is an intensifier, i.e. 'he was impossibly >>>> strong' means 'he was exceedingly strong'. I have no idea what >>>> 'impossibly provable' might mean, but if you intended to say >>>> 'unprovable' then you are misinterpreting PTS. Unprovable is one of >>>> the two semantic primitives used by PTS (the other being provable). >>>> >>> >>> This exactly and perfectly what it precisely means. >> >> If it means 'unprovable' then say 'unprovable' or 'impossible to >> prove'. Don't use a nonsensical expression like 'impossibly provable'. >> > > Impossibly provable because remains stuck > in an infinite loop. You're abusing English. As I said, 'impossibly' is an intensifier. If I say someone is impossibly strong it doesn't mean it is impossible for them to be strong, it means they are stronger than I would have thought possible, i.e. that they are extraordinarily strong. Saying something is 'impossibly provable' would mean it is extraordinarily provable which isn't coherent since provability isn't a gradient concept. What is wrong with simply using the term 'unprovable' which is actually coherent English? >>> % This sentence is not true. >>> ?- LP = not(true(LP)). >>> LP = not(true(LP)). >>> ?- unify_with_occurs_check(LP, not(true(LP))). >>> false. >> >> That's an example, not a definition. Examples don't take the place of >> definitions. >> > > It is the only perfect example of an idea from > Proof Theoretic Semantics that seems to stay a > little bit nebulous because each author uses their > own author specific terminology. It has absolutely nothing to do with Robinson Arithmetic or incompleteness which were the topics under discussion. It's your feeble attempt at trying to formalize the liar paradox in Prolog and it fails at that because the Liar Paradox rests on the interpretation of the deictic expression 'this', and your formulation does not contain anything corresponding to 'this'. It is simply a circular definition. >>>>>> i.e. a meaning; so you can't claim that the expression 'no number >>>>>> is greater than its successor' isn't meaningful in Q. >>>>>> >>>>>> Can you provide a single example of someone working within PTS who >>>>>> has taken issue with incompleteness? Incompleteness exists in PTS >>>>>> just as much as it exists in any other framework. >>>> >>>> I would really like you to answer the above question. >>> >>> If you understand PTS you will understand that their >>> reasoning cannot possibly get to incompleteness. >> >> Then you should be able to produce an actual citation to this effect. > > Each author uses their own author specific terminology > and the meanings slightly change across authors. How does this prevent you from offering a citation? >> As it stands, this is simply a baseless assertion on your part, and >> since your grasp of PTS doesn't seem particularly strong, it carries >> very little weight. >> >> You keep offering PTS as an alternative to truth-functional semantics, >> but incompleteness has absolutely nothing to do with truth-functional >> semantics as the definition of incompleteness doesn't even mention truth > > Truth as an Epistemic Notion --- Dag Prawitz > What is the appropriate notion of truth for > sentences whose meanings are understood in > epistemic terms such as proof or ground for > an assertion? It seems that the truth of such > sentences has to be identified with the existence > of proofs or grounds... > https://link.springer.com/article/10.1007/s11245-011-9107-6 That quotation has nothing to do with anything I said and it certainly makes no claims about incompleteness. >> or falsity (or semantics). If anything, it is more aligned with PTS >> than with TFS since it pertains to theoremhood i.e. provability, the >> semantic primitive used by PTS. >> >> A system is incomplete if there is an expression in the language of >> that system, P such that neither P nor ¬P can be derived as a theorem. > > That is simply not the way that it works in Proof Theoretic Semantics. Then provide a citation which explains how incompleteness is treated by PTS. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 18:36 -0500 |
| Message-ID | <111uvhj$n34q$1@dont-email.me> |
| In reply to | #347203 |
On 6/29/2026 6:03 PM, André G. Isaak wrote: > On 2026-06-29 16:38, olcott wrote: >> On 6/29/2026 5:25 PM, André G. Isaak wrote: >>> On 2026-06-29 15:39, olcott wrote: >>>> On 6/29/2026 4:18 PM, André G. Isaak wrote: >>>>> On 2026-06-29 15:10, olcott wrote: >>>>>> On 6/29/2026 3:58 PM, André G. Isaak wrote: >>>>>>> On 2026-06-29 14:06, olcott wrote: >>>>>>>> On 6/29/2026 3:02 PM, André G. Isaak wrote: >>>>>>>>> On 2026-06-29 13:47, olcott wrote: >>>>>>>>>> On 6/29/2026 2:33 PM, André G. Isaak wrote: >>>>>>>>>>> On 2026-06-29 13:08, olcott wrote: >>>>>>>>>>>> On 6/29/2026 1:29 PM, André G. Isaak wrote: >>>>>>>>>>> >>>>>>>>>>>>> Is "has a box of clowns" in the language of Q? No. I didn't >>>>>>>>>>>>> think so, so your example is completely irrelevant. >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> It is an idiom stipulated to mean: >>>>>>>>>>>> sentences in the language of Q which can neither >>>>>>>>>>>> be proven nor disproven by Q >>>>>>>>>>> >>>>>>>>>>> Q doesn't have idioms. That's a natural language concept >>>>>>>>>>> alien to theories of arithmetic. >>>>>>>>>>> >>>>>>>>>>>>>> So we can say that the halting problem "has a box >>>>>>>>>>>>>> of clowns" instead of saying that computation is >>>>>>>>>>>>>> in any way limited. >>>>>>>>>>>>>> >>>>>>>>>>>>>>> When mathematicians talk about rings, do you object based >>>>>>>>>>>>>>> on the fact that you can't put them on your finger? >>>>>>>>>>>>> >>>>>>>>>>>>> No answer? >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Off topic, irrelevant. >>>>>>>>>>>> >>>>>>>>>>>>>>> When mathematicians talk about fields, do you object >>>>>>>>>>>>>>> based on the fact that nothing can graze on them? >>>>>>>>>>>>> >>>>>>>>>>>>> No answer? >>>>>>>>>>> >>>>>>>>>>> These questions are Irrelevant because >>>>>>>>>> In Proof Theoretic Semantics >>>>>>>>>> statements in the language of that system >>>>>>>>>> which can neither be proven nor disproven >>>>>>>>>> >>>>>>>>>> have not established that they have semantic >>>>>>>>>> meaning because semantic meaning is ONLY >>>>>>>>>> established in PTS by canonical proofs. >>>>>>>>> >>>>>>>>> This is a misrepresentation on your part. Whereas truth >>>>>>>>> functional semantics takes true and false to be the semantic >>>>>>>>> primatives, PTS uses either (depending on which author you >>>>>>>>> follow) proven and not proven or provable and not provable as >>>>>>>>> its primitives without dealing with truth or falsity. >>>>>>>> >>>>>>>> Yes that is an accurate paraphrase. >>>>>>>> >>>>>>>>> Thus, they would treat a statement like 'no number is greater >>>>>>>>> than its successor' as being unprovable in Robinson Arithmetic, >>>>>>>>> not as being meaningless as you seem to think. >>>>>>>>> >>>>>>>> >>>>>>>> You are not being consistent with you own paraphrase. >>>>>>>> I still don't have all of the exact nuances exactly >>>>>>>> correct because unlike every other field each author >>>>>>>> has their own terms-of-the-art. >>>>>>> >>>>>>> Of course I am being consistent. Within PTD, unproven/unprovable >>>>>>> *is* a semantic value, >>>>>> >>>>>> Impossibly provable in Q means cannot possibly >>>>>> derive a semantic meaning Q. >>>>> >>>>> 'impossibly' in English is an intensifier, i.e. 'he was impossibly >>>>> strong' means 'he was exceedingly strong'. I have no idea what >>>>> 'impossibly provable' might mean, but if you intended to say >>>>> 'unprovable' then you are misinterpreting PTS. Unprovable is one of >>>>> the two semantic primitives used by PTS (the other being provable). >>>>> >>>> >>>> This exactly and perfectly what it precisely means. >>> >>> If it means 'unprovable' then say 'unprovable' or 'impossible to >>> prove'. Don't use a nonsensical expression like 'impossibly provable'. >>> >> >> Impossibly provable because remains stuck >> in an infinite loop. > > You're abusing English. As I said, 'impossibly' is an intensifier. If I > say someone is impossibly strong it doesn't mean it is impossible for > them to be strong, it means they are stronger than I would have thought > possible, i.e. that they are extraordinarily strong. Saying something is > 'impossibly provable' would mean it is extraordinarily provable which > isn't coherent since provability isn't a gradient concept. What is wrong > with simply using the term 'unprovable' which is actually coherent English? > 3 is impossibly numerically greater than 5. >>>> % This sentence is not true. >>>> ?- LP = not(true(LP)). >>>> LP = not(true(LP)). >>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>> false. >>> >>> That's an example, not a definition. Examples don't take the place of >>> definitions. >>> >> >> It is the only perfect example of an idea from >> Proof Theoretic Semantics that seems to stay a >> little bit nebulous because each author uses their >> own author specific terminology. > > It has absolutely nothing to do with Robinson Arithmetic or > incompleteness which were the topics under discussion. It perfectly establishes that impossibly provable means has no proof theoretic semantic meaning. There is a key difference between we did not yet find a proof of X and a proof of X cannot possibly exist. > It's your feeble > attempt at trying to formalize the liar paradox in Prolog and it fails > at that because the Liar Paradox rests on the interpretation of the > deictic expression 'this', and your formulation does not contain > anything corresponding to 'this'. It is simply a circular definition. > "this" literally means := when formalized LP := ~True(LP) expands to ~True(~True(~True(~True(~True(~True(~True(...))))))) >>>>>>> i.e. a meaning; so you can't claim that the expression 'no number >>>>>>> is greater than its successor' isn't meaningful in Q. >>>>>>> >>>>>>> Can you provide a single example of someone working within PTS >>>>>>> who has taken issue with incompleteness? Incompleteness exists in >>>>>>> PTS just as much as it exists in any other framework. >>>>> >>>>> I would really like you to answer the above question. >>>> >>>> If you understand PTS you will understand that their >>>> reasoning cannot possibly get to incompleteness. >>> >>> Then you should be able to produce an actual citation to this effect. >> >> Each author uses their own author specific terminology >> and the meanings slightly change across authors. > > How does this prevent you from offering a citation? > It does seem that they do agree that no proof of G can possibly exist in PA does means that G has no semantic meaning in PA. "Failure of Normalization" "Lack of a Canonical Form" "Disharmony" are some of the ways that they describe this. I have to spend a very long time carefully analyzing two papers before I can even use one author's terms regarding one aspect of PTS limited to that author's terms. "anti-realism" seems like it means a psychotic break for reality yet seems to merely specify valid deductive inference in the terms-of-the-art of PTS. -- 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 | 2026-06-29 17:45 -0600 |
| Message-ID | <111v02k$l815$3@dont-email.me> |
| In reply to | #347204 |
On 2026-06-29 17:36, olcott wrote: > On 6/29/2026 6:03 PM, André G. Isaak wrote: >> On 2026-06-29 16:38, olcott wrote: >>> On 6/29/2026 5:25 PM, André G. Isaak wrote: >>>> On 2026-06-29 15:39, olcott wrote: >>>>> On 6/29/2026 4:18 PM, André G. Isaak wrote: >>>>>> On 2026-06-29 15:10, olcott wrote: >>>>>>> On 6/29/2026 3:58 PM, André G. Isaak wrote: >>>>>>>> On 2026-06-29 14:06, olcott wrote: >>>>>>>>> On 6/29/2026 3:02 PM, André G. Isaak wrote: >>>>>>>>>> On 2026-06-29 13:47, olcott wrote: >>>>>>>>>>> On 6/29/2026 2:33 PM, André G. Isaak wrote: >>>>>>>>>>>> On 2026-06-29 13:08, olcott wrote: >>>>>>>>>>>>> On 6/29/2026 1:29 PM, André G. Isaak wrote: >>>>>>>>>>>> >>>>>>>>>>>>>> Is "has a box of clowns" in the language of Q? No. I >>>>>>>>>>>>>> didn't think so, so your example is completely irrelevant. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> It is an idiom stipulated to mean: >>>>>>>>>>>>> sentences in the language of Q which can neither >>>>>>>>>>>>> be proven nor disproven by Q >>>>>>>>>>>> >>>>>>>>>>>> Q doesn't have idioms. That's a natural language concept >>>>>>>>>>>> alien to theories of arithmetic. >>>>>>>>>>>> >>>>>>>>>>>>>>> So we can say that the halting problem "has a box >>>>>>>>>>>>>>> of clowns" instead of saying that computation is >>>>>>>>>>>>>>> in any way limited. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> When mathematicians talk about rings, do you object >>>>>>>>>>>>>>>> based on the fact that you can't put them on your finger? >>>>>>>>>>>>>> >>>>>>>>>>>>>> No answer? >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> Off topic, irrelevant. >>>>>>>>>>>>> >>>>>>>>>>>>>>>> When mathematicians talk about fields, do you object >>>>>>>>>>>>>>>> based on the fact that nothing can graze on them? >>>>>>>>>>>>>> >>>>>>>>>>>>>> No answer? >>>>>>>>>>>> >>>>>>>>>>>> These questions are Irrelevant because >>>>>>>>>>> In Proof Theoretic Semantics >>>>>>>>>>> statements in the language of that system >>>>>>>>>>> which can neither be proven nor disproven >>>>>>>>>>> >>>>>>>>>>> have not established that they have semantic >>>>>>>>>>> meaning because semantic meaning is ONLY >>>>>>>>>>> established in PTS by canonical proofs. >>>>>>>>>> >>>>>>>>>> This is a misrepresentation on your part. Whereas truth >>>>>>>>>> functional semantics takes true and false to be the semantic >>>>>>>>>> primatives, PTS uses either (depending on which author you >>>>>>>>>> follow) proven and not proven or provable and not provable as >>>>>>>>>> its primitives without dealing with truth or falsity. >>>>>>>>> >>>>>>>>> Yes that is an accurate paraphrase. >>>>>>>>> >>>>>>>>>> Thus, they would treat a statement like 'no number is greater >>>>>>>>>> than its successor' as being unprovable in Robinson >>>>>>>>>> Arithmetic, not as being meaningless as you seem to think. >>>>>>>>>> >>>>>>>>> >>>>>>>>> You are not being consistent with you own paraphrase. >>>>>>>>> I still don't have all of the exact nuances exactly >>>>>>>>> correct because unlike every other field each author >>>>>>>>> has their own terms-of-the-art. >>>>>>>> >>>>>>>> Of course I am being consistent. Within PTD, unproven/unprovable >>>>>>>> *is* a semantic value, >>>>>>> >>>>>>> Impossibly provable in Q means cannot possibly >>>>>>> derive a semantic meaning Q. >>>>>> >>>>>> 'impossibly' in English is an intensifier, i.e. 'he was impossibly >>>>>> strong' means 'he was exceedingly strong'. I have no idea what >>>>>> 'impossibly provable' might mean, but if you intended to say >>>>>> 'unprovable' then you are misinterpreting PTS. Unprovable is one >>>>>> of the two semantic primitives used by PTS (the other being >>>>>> provable). >>>>>> >>>>> >>>>> This exactly and perfectly what it precisely means. >>>> >>>> If it means 'unprovable' then say 'unprovable' or 'impossible to >>>> prove'. Don't use a nonsensical expression like 'impossibly provable'. >>>> >>> >>> Impossibly provable because remains stuck >>> in an infinite loop. >> >> You're abusing English. As I said, 'impossibly' is an intensifier. If >> I say someone is impossibly strong it doesn't mean it is impossible >> for them to be strong, it means they are stronger than I would have >> thought possible, i.e. that they are extraordinarily strong. Saying >> something is 'impossibly provable' would mean it is extraordinarily >> provable which isn't coherent since provability isn't a gradient >> concept. What is wrong with simply using the term 'unprovable' which >> is actually coherent English? >> > > 3 is impossibly numerically greater than 5. Not if you're speaking English. >>>>> % This sentence is not true. >>>>> ?- LP = not(true(LP)). >>>>> LP = not(true(LP)). >>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>> false. >>>> >>>> That's an example, not a definition. Examples don't take the place >>>> of definitions. >>>> >>> >>> It is the only perfect example of an idea from >>> Proof Theoretic Semantics that seems to stay a >>> little bit nebulous because each author uses their >>> own author specific terminology. >> >> It has absolutely nothing to do with Robinson Arithmetic or >> incompleteness which were the topics under discussion. > > It perfectly establishes that impossibly provable > means has no proof theoretic semantic meaning. It shows no such thing. > There is a key difference between we did not yet > find a proof of X and a proof of X cannot possibly > exist. Yes. And the two English terms in use for these are 'unproven' and 'unprovable'. Not 'impossibly provable'. >> It's your feeble attempt at trying to formalize the liar paradox in >> Prolog and it fails at that because the Liar Paradox rests on the >> interpretation of the deictic expression 'this', and your formulation >> does not contain anything corresponding to 'this'. It is simply a >> circular definition. >> > > "this" literally means := when formalized > LP := ~True(LP) expands to > ~True(~True(~True(~True(~True(~True(~True(...))))))) No. := means defined as, not 'this'. If you think otherwise, explain how you would formalize a sentence involving what you would call non-pathological self reference using :=. For example, 'this sentence contains five words'. >>>>>>>> i.e. a meaning; so you can't claim that the expression 'no >>>>>>>> number is greater than its successor' isn't meaningful in Q. >>>>>>>> >>>>>>>> Can you provide a single example of someone working within PTS >>>>>>>> who has taken issue with incompleteness? Incompleteness exists >>>>>>>> in PTS just as much as it exists in any other framework. >>>>>> >>>>>> I would really like you to answer the above question. >>>>> >>>>> If you understand PTS you will understand that their >>>>> reasoning cannot possibly get to incompleteness. >>>> >>>> Then you should be able to produce an actual citation to this effect. >>> >>> Each author uses their own author specific terminology >>> and the meanings slightly change across authors. >> >> How does this prevent you from offering a citation? >> > > It does seem that they do agree that no proof > of G can possibly exist in PA does means that > G has no semantic meaning in PA. I've not seen anyone operating in PTS who says anything remotely like that. They do not agree with this; rather, you are projecting your own peculiar views onto their theory. André > "Failure of Normalization" > "Lack of a Canonical Form" > "Disharmony" > are some of the ways that they describe this. > > I have to spend a very long time carefully > analyzing two papers before I can even use > one author's terms regarding one aspect of PTS > limited to that author's terms. > > "anti-realism" seems like it means a psychotic > break for reality yet seems to merely specify > valid deductive inference in the terms-of-the-art > of PTS. > > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 19:37 -0500 |
| Message-ID | <111v358$nv7c$1@dont-email.me> |
| In reply to | #347205 |
On 6/29/2026 6:45 PM, André G. Isaak wrote: > On 2026-06-29 17:36, olcott wrote: >> On 6/29/2026 6:03 PM, André G. Isaak wrote: >>> On 2026-06-29 16:38, olcott wrote: >>>> On 6/29/2026 5:25 PM, André G. Isaak wrote: >>>>> On 2026-06-29 15:39, olcott wrote: >>>>>> On 6/29/2026 4:18 PM, André G. Isaak wrote: >>>>>>> On 2026-06-29 15:10, olcott wrote: >>>>>>>> On 6/29/2026 3:58 PM, André G. Isaak wrote: >>>>>>>>> On 2026-06-29 14:06, olcott wrote: >>>>>>>>>> On 6/29/2026 3:02 PM, André G. Isaak wrote: >>>>>>>>>>> On 2026-06-29 13:47, olcott wrote: >>>>>>>>>>>> On 6/29/2026 2:33 PM, André G. Isaak wrote: >>>>>>>>>>>>> On 2026-06-29 13:08, olcott wrote: >>>>>>>>>>>>>> On 6/29/2026 1:29 PM, André G. Isaak wrote: >>>>>>>>>>>>> >>>>>>>>>>>>>>> Is "has a box of clowns" in the language of Q? No. I >>>>>>>>>>>>>>> didn't think so, so your example is completely irrelevant. >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> It is an idiom stipulated to mean: >>>>>>>>>>>>>> sentences in the language of Q which can neither >>>>>>>>>>>>>> be proven nor disproven by Q >>>>>>>>>>>>> >>>>>>>>>>>>> Q doesn't have idioms. That's a natural language concept >>>>>>>>>>>>> alien to theories of arithmetic. >>>>>>>>>>>>> >>>>>>>>>>>>>>>> So we can say that the halting problem "has a box >>>>>>>>>>>>>>>> of clowns" instead of saying that computation is >>>>>>>>>>>>>>>> in any way limited. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> When mathematicians talk about rings, do you object >>>>>>>>>>>>>>>>> based on the fact that you can't put them on your finger? >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> No answer? >>>>>>>>>>>>>>> >>>>>>>>>>>>>> >>>>>>>>>>>>>> Off topic, irrelevant. >>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> When mathematicians talk about fields, do you object >>>>>>>>>>>>>>>>> based on the fact that nothing can graze on them? >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> No answer? >>>>>>>>>>>>> >>>>>>>>>>>>> These questions are Irrelevant because >>>>>>>>>>>> In Proof Theoretic Semantics >>>>>>>>>>>> statements in the language of that system >>>>>>>>>>>> which can neither be proven nor disproven >>>>>>>>>>>> >>>>>>>>>>>> have not established that they have semantic >>>>>>>>>>>> meaning because semantic meaning is ONLY >>>>>>>>>>>> established in PTS by canonical proofs. >>>>>>>>>>> >>>>>>>>>>> This is a misrepresentation on your part. Whereas truth >>>>>>>>>>> functional semantics takes true and false to be the semantic >>>>>>>>>>> primatives, PTS uses either (depending on which author you >>>>>>>>>>> follow) proven and not proven or provable and not provable as >>>>>>>>>>> its primitives without dealing with truth or falsity. >>>>>>>>>> >>>>>>>>>> Yes that is an accurate paraphrase. >>>>>>>>>> >>>>>>>>>>> Thus, they would treat a statement like 'no number is greater >>>>>>>>>>> than its successor' as being unprovable in Robinson >>>>>>>>>>> Arithmetic, not as being meaningless as you seem to think. >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> You are not being consistent with you own paraphrase. >>>>>>>>>> I still don't have all of the exact nuances exactly >>>>>>>>>> correct because unlike every other field each author >>>>>>>>>> has their own terms-of-the-art. >>>>>>>>> >>>>>>>>> Of course I am being consistent. Within PTD, unproven/ >>>>>>>>> unprovable *is* a semantic value, >>>>>>>> >>>>>>>> Impossibly provable in Q means cannot possibly >>>>>>>> derive a semantic meaning Q. >>>>>>> >>>>>>> 'impossibly' in English is an intensifier, i.e. 'he was >>>>>>> impossibly strong' means 'he was exceedingly strong'. I have no >>>>>>> idea what 'impossibly provable' might mean, but if you intended >>>>>>> to say 'unprovable' then you are misinterpreting PTS. Unprovable >>>>>>> is one of the two semantic primitives used by PTS (the other >>>>>>> being provable). >>>>>>> >>>>>> >>>>>> This exactly and perfectly what it precisely means. >>>>> >>>>> If it means 'unprovable' then say 'unprovable' or 'impossible to >>>>> prove'. Don't use a nonsensical expression like 'impossibly provable'. >>>>> >>>> >>>> Impossibly provable because remains stuck >>>> in an infinite loop. >>> >>> You're abusing English. As I said, 'impossibly' is an intensifier. If >>> I say someone is impossibly strong it doesn't mean it is impossible >>> for them to be strong, it means they are stronger than I would have >>> thought possible, i.e. that they are extraordinarily strong. Saying >>> something is 'impossibly provable' would mean it is extraordinarily >>> provable which isn't coherent since provability isn't a gradient >>> concept. What is wrong with simply using the term 'unprovable' which >>> is actually coherent English? >>> >> >> 3 is impossibly numerically greater than 5. > > Not if you're speaking English. > >>>>>> % This sentence is not true. >>>>>> ?- LP = not(true(LP)). >>>>>> LP = not(true(LP)). >>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>> false. >>>>> >>>>> That's an example, not a definition. Examples don't take the place >>>>> of definitions. >>>>> >>>> >>>> It is the only perfect example of an idea from >>>> Proof Theoretic Semantics that seems to stay a >>>> little bit nebulous because each author uses their >>>> own author specific terminology. >>> >>> It has absolutely nothing to do with Robinson Arithmetic or >>> incompleteness which were the topics under discussion. >> >> It perfectly establishes that impossibly provable >> means has no proof theoretic semantic meaning. > > It shows no such thing. > >> There is a key difference between we did not yet >> find a proof of X and a proof of X cannot possibly >> exist. > > Yes. And the two English terms in use for these are 'unproven' and > 'unprovable'. Not 'impossibly provable'. > >>> It's your feeble attempt at trying to formalize the liar paradox in >>> Prolog and it fails at that because the Liar Paradox rests on the >>> interpretation of the deictic expression 'this', and your formulation >>> does not contain anything corresponding to 'this'. It is simply a >>> circular definition. >>> >> >> "this" literally means := when formalized >> LP := ~True(LP) expands to >> ~True(~True(~True(~True(~True(~True(~True(...))))))) > > No. := means defined as, not 'this'. > It only means that: when formalized. > If you think otherwise, explain how you would formalize a sentence > involving what you would call non-pathological self reference using :=. > For example, 'this sentence contains five words'. > >>>>>>>>> i.e. a meaning; so you can't claim that the expression 'no >>>>>>>>> number is greater than its successor' isn't meaningful in Q. >>>>>>>>> >>>>>>>>> Can you provide a single example of someone working within PTS >>>>>>>>> who has taken issue with incompleteness? Incompleteness exists >>>>>>>>> in PTS just as much as it exists in any other framework. >>>>>>> >>>>>>> I would really like you to answer the above question. >>>>>> >>>>>> If you understand PTS you will understand that their >>>>>> reasoning cannot possibly get to incompleteness. >>>>> >>>>> Then you should be able to produce an actual citation to this effect. >>>> >>>> Each author uses their own author specific terminology >>>> and the meanings slightly change across authors. >>> >>> How does this prevent you from offering a citation? >>> >> >> It does seem that they do agree that no proof >> of G can possibly exist in PA does means that >> G has no semantic meaning in PA. > > I've not seen anyone operating in PTS who says anything remotely like > that. They do not agree with this; rather, you are projecting your own > peculiar views onto their theory. > > André > Because they beat around the bush about that using terminology that varies across every author. >> "Failure of Normalization" >> "Lack of a Canonical Form" >> "Disharmony" >> are some of the ways that they describe this. >> >> I have to spend a very long time carefully >> analyzing two papers before I can even use >> one author's terms regarding one aspect of PTS >> limited to that author's terms. >> >> "anti-realism" seems like it means a psychotic >> break for reality yet seems to merely specify >> valid deductive inference in the terms-of-the-art >> of PTS. >> >> > -- 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 | 2026-06-29 19:01 -0600 |
| Message-ID | <111v4hh$l815$4@dont-email.me> |
| In reply to | #347206 |
On 2026-06-29 18:37, olcott wrote: > On 6/29/2026 6:45 PM, André G. Isaak wrote: >> On 2026-06-29 17:36, olcott wrote: >>> It does seem that they do agree that no proof >>> of G can possibly exist in PA does means that >>> G has no semantic meaning in PA. >> >> I've not seen anyone operating in PTS who says anything remotely like >> that. They do not agree with this; rather, you are projecting your own >> peculiar views onto their theory. >> >> André >> > > Because they beat around the bush about that using > terminology that varies across every author. It's not that they are beating around the bush; it's that they aren't actually saying what you want them to say. Face it, you really don't understand the PTS literature as it is above your head. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 20:19 -0500 |
| Subject | The simple essence of Proof Theoretic Semantics |
| Message-ID | <111v5ih$oh5p$1@dont-email.me> |
| In reply to | #347207 |
On 6/29/2026 8:01 PM, André G. Isaak wrote: > On 2026-06-29 18:37, olcott wrote: >> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>> On 2026-06-29 17:36, olcott wrote: > >>>> It does seem that they do agree that no proof >>>> of G can possibly exist in PA does means that >>>> G has no semantic meaning in PA. >>> >>> I've not seen anyone operating in PTS who says anything remotely like >>> that. They do not agree with this; rather, you are projecting your >>> own peculiar views onto their theory. >>> >>> André >>> >> >> Because they beat around the bush about that using >> terminology that varies across every author. > > It's not that they are beating around the bush; it's that they aren't > actually saying what you want them to say. Face it, you really don't > understand the PTS literature as it is above your head. > > André > 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. -- 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 | 2026-06-29 19:54 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111v7ku$l815$5@dont-email.me> |
| In reply to | #347208 |
On 2026-06-29 19:19, olcott wrote: > On 6/29/2026 8:01 PM, André G. Isaak wrote: >> On 2026-06-29 18:37, olcott wrote: >>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>> On 2026-06-29 17:36, olcott wrote: >> >>>>> It does seem that they do agree that no proof >>>>> of G can possibly exist in PA does means that >>>>> G has no semantic meaning in PA. >>>> >>>> I've not seen anyone operating in PTS who says anything remotely >>>> like that. They do not agree with this; rather, you are projecting >>>> your own peculiar views onto their theory. >>>> >>>> André >>>> >>> >>> Because they beat around the bush about that using >>> terminology that varies across every author. >> >> It's not that they are beating around the bush; it's that they aren't >> actually saying what you want them to say. Face it, you really don't >> understand the PTS literature as it is above your head. >> >> André >> > > 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. That's not what PTS says; that's simply you. There is a difference between meaningless and wrong. ''Twas brillig, and the slithey toves did did gyre and gimble in the wabe.' is meaningless. 'five plus six equals seven' is wrong but meaningful. Neither are provable. If an expression P is provable in PTS, then its negation ¬P is unprovable, but to say that it is meaningless is simply wrong. We often discuss statements which are false and need to do so. If they were truly meaningless we would have no reason to do so. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 21:17 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111v8ve$p8i6$1@dont-email.me> |
| In reply to | #347209 |
On 6/29/2026 8:54 PM, André G. Isaak wrote: > On 2026-06-29 19:19, olcott wrote: >> On 6/29/2026 8:01 PM, André G. Isaak wrote: >>> On 2026-06-29 18:37, olcott wrote: >>>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>>> On 2026-06-29 17:36, olcott wrote: >>> >>>>>> It does seem that they do agree that no proof >>>>>> of G can possibly exist in PA does means that >>>>>> G has no semantic meaning in PA. >>>>> >>>>> I've not seen anyone operating in PTS who says anything remotely >>>>> like that. They do not agree with this; rather, you are projecting >>>>> your own peculiar views onto their theory. >>>>> >>>>> André >>>>> >>>> >>>> Because they beat around the bush about that using >>>> terminology that varies across every author. >>> >>> It's not that they are beating around the bush; it's that they aren't >>> actually saying what you want them to say. Face it, you really don't >>> understand the PTS literature as it is above your head. >>> >>> André >>> >> >> 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. > > That's not what PTS says; that's simply you. > > There is a difference between meaningless and wrong. > % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. Olcott's Minimal Type Theory G ↔ ¬Prov_PA(⌜G⌝) Directed Graph of evaluation sequence 00 ↔ 01 02 01 G 02 ¬ 03 03 Prov_PA 04 04 Gödel_Number_of 01 // cycle indicates no well-founded justification tree exists. -- 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 | 2026-06-29 20:31 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111v9qs$l815$6@dont-email.me> |
| In reply to | #347210 |
On 2026-06-29 20:17, olcott wrote: > On 6/29/2026 8:54 PM, André G. Isaak wrote: >> On 2026-06-29 19:19, olcott wrote: >>> On 6/29/2026 8:01 PM, André G. Isaak wrote: >>>> On 2026-06-29 18:37, olcott wrote: >>>>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>>>> On 2026-06-29 17:36, olcott wrote: >>>> >>>>>>> It does seem that they do agree that no proof >>>>>>> of G can possibly exist in PA does means that >>>>>>> G has no semantic meaning in PA. >>>>>> >>>>>> I've not seen anyone operating in PTS who says anything remotely >>>>>> like that. They do not agree with this; rather, you are projecting >>>>>> your own peculiar views onto their theory. >>>>>> >>>>>> André >>>>>> >>>>> >>>>> Because they beat around the bush about that using >>>>> terminology that varies across every author. >>>> >>>> It's not that they are beating around the bush; it's that they >>>> aren't actually saying what you want them to say. Face it, you >>>> really don't understand the PTS literature as it is above your head. >>>> >>>> André >>>> >>> >>> 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. >> >> That's not what PTS says; that's simply you. >> >> There is a difference between meaningless and wrong. >> > % This sentence is not true. > ?- LP = not(true(LP)). > LP = not(true(LP)). > ?- unify_with_occurs_check(LP, not(true(LP))). > false. > > Olcott's Minimal Type Theory > G ↔ ¬Prov_PA(⌜G⌝) > Directed Graph of evaluation sequence > 00 ↔ 01 02 > 01 G > 02 ¬ 03 > 03 Prov_PA 04 > 04 Gödel_Number_of 01 // cycle indicates no well-founded justification > tree exists. That's completely nonresponsive. You're simply copying and pasting text from previous posts without any explanation of how you think it relates to the point I made (which you disingenuously snipped). The Liar's Paradox isn't what I am discussing. I am discussing the fact that 'no number is equal to its successor' can't be proven in Q. That statement has absolutely no similarities to the Liar's Paradox. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 21:42 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111vads$phuu$1@dont-email.me> |
| In reply to | #347212 |
On 6/29/2026 9:31 PM, André G. Isaak wrote: > On 2026-06-29 20:17, olcott wrote: >> On 6/29/2026 8:54 PM, André G. Isaak wrote: >>> On 2026-06-29 19:19, olcott wrote: >>>> On 6/29/2026 8:01 PM, André G. Isaak wrote: >>>>> On 2026-06-29 18:37, olcott wrote: >>>>>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>>>>> On 2026-06-29 17:36, olcott wrote: >>>>> >>>>>>>> It does seem that they do agree that no proof >>>>>>>> of G can possibly exist in PA does means that >>>>>>>> G has no semantic meaning in PA. >>>>>>> >>>>>>> I've not seen anyone operating in PTS who says anything remotely >>>>>>> like that. They do not agree with this; rather, you are >>>>>>> projecting your own peculiar views onto their theory. >>>>>>> >>>>>>> André >>>>>>> >>>>>> >>>>>> Because they beat around the bush about that using >>>>>> terminology that varies across every author. >>>>> >>>>> It's not that they are beating around the bush; it's that they >>>>> aren't actually saying what you want them to say. Face it, you >>>>> really don't understand the PTS literature as it is above your head. >>>>> >>>>> André >>>>> >>>> >>>> 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. >>> >>> That's not what PTS says; that's simply you. >>> >>> There is a difference between meaningless and wrong. >>> >> % This sentence is not true. >> ?- LP = not(true(LP)). >> LP = not(true(LP)). >> ?- unify_with_occurs_check(LP, not(true(LP))). >> false. >> >> Olcott's Minimal Type Theory >> G ↔ ¬Prov_PA(⌜G⌝) >> Directed Graph of evaluation sequence >> 00 ↔ 01 02 >> 01 G >> 02 ¬ 03 >> 03 Prov_PA 04 >> 04 Gödel_Number_of 01 // cycle indicates no well-founded >> justification tree exists. > > That's completely nonresponsive. You're simply copying and pasting text > from previous posts without any explanation of how you think it relates > to the point I made (which you disingenuously snipped). > > The Liar's Paradox isn't what I am discussing. I am discussing the fact > that 'no number is equal to its successor' can't be proven in Q. That > statement has absolutely no similarities to the Liar's Paradox. > > André > Those are specific concrete examples of how Proof Theoretic Semantics rejects expressions as Proof Theoretic Semantically incoherent. -- 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 | 2026-06-29 20:49 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111var4$l815$7@dont-email.me> |
| In reply to | #347213 |
On 2026-06-29 20:42, olcott wrote: > On 6/29/2026 9:31 PM, André G. Isaak wrote: >> On 2026-06-29 20:17, olcott wrote: >>> On 6/29/2026 8:54 PM, André G. Isaak wrote: >>>> On 2026-06-29 19:19, olcott wrote: >>>>> On 6/29/2026 8:01 PM, André G. Isaak wrote: >>>>>> On 2026-06-29 18:37, olcott wrote: >>>>>>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>>>>>> On 2026-06-29 17:36, olcott wrote: >>>>>> >>>>>>>>> It does seem that they do agree that no proof >>>>>>>>> of G can possibly exist in PA does means that >>>>>>>>> G has no semantic meaning in PA. >>>>>>>> >>>>>>>> I've not seen anyone operating in PTS who says anything remotely >>>>>>>> like that. They do not agree with this; rather, you are >>>>>>>> projecting your own peculiar views onto their theory. >>>>>>>> >>>>>>>> André >>>>>>>> >>>>>>> >>>>>>> Because they beat around the bush about that using >>>>>>> terminology that varies across every author. >>>>>> >>>>>> It's not that they are beating around the bush; it's that they >>>>>> aren't actually saying what you want them to say. Face it, you >>>>>> really don't understand the PTS literature as it is above your head. >>>>>> >>>>>> André >>>>>> >>>>> >>>>> 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. >>>> >>>> That's not what PTS says; that's simply you. >>>> >>>> There is a difference between meaningless and wrong. >>>> >>> % This sentence is not true. >>> ?- LP = not(true(LP)). >>> LP = not(true(LP)). >>> ?- unify_with_occurs_check(LP, not(true(LP))). >>> false. >>> >>> Olcott's Minimal Type Theory >>> G ↔ ¬Prov_PA(⌜G⌝) >>> Directed Graph of evaluation sequence >>> 00 ↔ 01 02 >>> 01 G >>> 02 ¬ 03 >>> 03 Prov_PA 04 >>> 04 Gödel_Number_of 01 // cycle indicates no well-founded >>> justification tree exists. >> >> That's completely nonresponsive. You're simply copying and pasting >> text from previous posts without any explanation of how you think it >> relates to the point I made (which you disingenuously snipped). >> >> The Liar's Paradox isn't what I am discussing. I am discussing the >> fact that 'no number is equal to its successor' can't be proven in Q. >> That statement has absolutely no similarities to the Liar's Paradox. >> >> André >> > > 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 -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 22:06 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111vbrb$prr1$1@dont-email.me> |
| In reply to | #347214 |
On 6/29/2026 9:49 PM, André G. Isaak wrote: > On 2026-06-29 20:42, olcott wrote: >> On 6/29/2026 9:31 PM, André G. Isaak wrote: >>> On 2026-06-29 20:17, olcott wrote: >>>> On 6/29/2026 8:54 PM, André G. Isaak wrote: >>>>> On 2026-06-29 19:19, olcott wrote: >>>>>> On 6/29/2026 8:01 PM, André G. Isaak wrote: >>>>>>> On 2026-06-29 18:37, olcott wrote: >>>>>>>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>>>>>>> On 2026-06-29 17:36, olcott wrote: >>>>>>> >>>>>>>>>> It does seem that they do agree that no proof >>>>>>>>>> of G can possibly exist in PA does means that >>>>>>>>>> G has no semantic meaning in PA. >>>>>>>>> >>>>>>>>> I've not seen anyone operating in PTS who says anything >>>>>>>>> remotely like that. They do not agree with this; rather, you >>>>>>>>> are projecting your own peculiar views onto their theory. >>>>>>>>> >>>>>>>>> André >>>>>>>>> >>>>>>>> >>>>>>>> Because they beat around the bush about that using >>>>>>>> terminology that varies across every author. >>>>>>> >>>>>>> It's not that they are beating around the bush; it's that they >>>>>>> aren't actually saying what you want them to say. Face it, you >>>>>>> really don't understand the PTS literature as it is above your head. >>>>>>> >>>>>>> André >>>>>>> >>>>>> >>>>>> 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. >>>>> >>>>> That's not what PTS says; that's simply you. >>>>> >>>>> There is a difference between meaningless and wrong. >>>>> >>>> % This sentence is not true. >>>> ?- LP = not(true(LP)). >>>> LP = not(true(LP)). >>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>> false. >>>> >>>> Olcott's Minimal Type Theory >>>> G ↔ ¬Prov_PA(⌜G⌝) >>>> Directed Graph of evaluation sequence >>>> 00 ↔ 01 02 >>>> 01 G >>>> 02 ¬ 03 >>>> 03 Prov_PA 04 >>>> 04 Gödel_Number_of 01 // cycle indicates no well-founded >>>> justification tree exists. >>> >>> That's completely nonresponsive. You're simply copying and pasting >>> text from previous posts without any explanation of how you think it >>> relates to the point I made (which you disingenuously snipped). >>> >>> The Liar's Paradox isn't what I am discussing. I am discussing the >>> fact that 'no number is equal to its successor' can't be proven in Q. >>> That statement has absolutely no similarities to the Liar's Paradox. >>> >>> André >>> >> >> 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. The biggest mistake that humanity makes that is killing the whole planet is treating unbelievable as exactly one-and-the-same-thing as untrue. -- 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 | 2026-06-30 15:18 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121br6$1e51b$1@dont-email.me> |
| In reply to | #347215 |
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. Would you agree that there is a difference between a statement being false and a statement being meaningless? > The biggest mistake that humanity makes that is killing > the whole planet is treating unbelievable as exactly > one-and-the-same-thing as untrue. I have no idea what you're getting at here. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 16:45 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121ddj$1elir$1@dont-email.me> |
| In reply to | #347235 |
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. The Definitional View of Atomic Systems in Proof-Theoretic Semantics Thomas Piecha and Peter Schroeder-Heister Atomic Systems in Proof-Theoretic Semantics: Two Approaches Thomas Piecha & Peter Schroeder-Heister >> The biggest mistake that humanity makes that is killing >> the whole planet is treating unbelievable as exactly >> one-and-the-same-thing as untrue. > > I have no idea what you're getting at here. > Climate change is killing the planet and too many people do not believe this because of the well funded hired liars. > 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 | 2026-06-30 15:56 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121e21$1epkc$1@dont-email.me> |
| In reply to | #347236 |
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? That's a simple yes/no question. If you want to append an explanation that's fine, but please start your answer with either yes or no. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 17:04 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121ehs$1evpl$1@dont-email.me> |
| In reply to | #347237 |
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. That is why I am not responding to any posts besides yours. dbush has become a troll again. Here is meaningless: Iz droopingstin pathorm mopygird Here is false: bovine cows are a kind of race car. Please go back and carefully study my careful response. I very carefully composed exactly what constitutes meaning. Failing to meet that spec entails meaningless. > That's a simple yes/no question. If you want to append an explanation > that's fine, but please start your answer with either yes or no. > > 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 | dbush <dbush.mobile@gmail.com> |
|---|---|
| Date | 2026-06-30 22:34 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121ub2$1iatd$1@dont-email.me> |
| In reply to | #347239 |
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.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 21:57 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121vmo$1ivpi$1@dont-email.me> |
| In reply to | #347245 |
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. -- 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 | 2026-06-30 23:02 -0400 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121vvh$1iatd$2@dont-email.me> |
| In reply to | #347247 |
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.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 22:10 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <11220ea$1j77n$1@dont-email.me> |
| In reply to | #347249 |
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) does not exist in Q. -- 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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