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Groups > sci.math > #644766 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-04-20 11:57 -0500 |
| Last post | 2026-06-30 06:54 +0100 |
| Articles | 20 on this page of 410 — 15 participants |
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Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-27 09:50 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:39 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-28 21:52 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:14 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:18 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:45 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:56 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 22:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:57 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:02 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:17 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 07:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 09:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 13:33 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:40 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:50 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:47 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:11 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:28 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:50 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:52 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 15:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 17:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 17:09 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 19:05 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 18:39 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 20:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 19:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:03 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 00:02 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 08:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:48 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:17 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:12 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:21 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:38 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:46 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 15:22 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:11 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:49 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:13 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 09:36 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:42 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:16 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 10:58 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:21 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:35 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:54 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:09 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:44 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:23 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:31 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:42 -0500
Re: The simple essence of Proof Theoretic Semantics Alan Mackenzie <acm@muc.de> - 2026-07-01 19:18 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:56 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:05 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:53 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:13 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:37 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:50 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 16:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 17:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 18:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 22:36 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:00 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:43 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:59 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 23:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:57 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 09:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 13:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 14:22 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 14:33 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 15:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 16:54 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:12 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:23 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:32 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:47 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 18:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 20:03 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:22 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 10:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 11:50 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:40 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:47 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 17:37 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 21:58 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:05 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:43 -0400
The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-03 22:11 -0500
Re: The truth about the halting problem counter-example input dbush <dbush.mobile@gmail.com> - 2026-07-03 23:23 -0400
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:58 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-04 12:16 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:07 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-06 10:18 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:45 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:58 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:07 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:11 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:27 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:19 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:04 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:46 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:55 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:24 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:30 -0500
Re: The simple essence of Proof Theoretic Semantics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:23 -0700
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 11:57 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:23 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:08 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:10 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:11 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:18 -0400
Re: The simple essence of Proof Theoretic Semantics Brenden Jafarov <rnarnj@rbn.ru> - 2026-07-04 12:47 +0000
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:43 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:04 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:28 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:27 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:45 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:53 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 16:59 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:57 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:01 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:33 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:25 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:10 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 14:08 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 15:12 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:38 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:09 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:28 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:15 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:41 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:38 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:40 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:39 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:14 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:32 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:37 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:06 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:03 +0300
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:25 +0300
Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-06 10:54 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:22 +0300
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-08 22:32 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:25 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:11 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:27 +0300
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: Terms-Of-The-Art are Liars Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 14:59 +0100
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:23 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 10:19 -0400
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:29 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 12:39 -0400
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 13:09 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:46 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 12:39 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:38 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-08 22:40 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:42 +0300
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 14:07 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:38 +0300
Re: Terms-Of-The-Art are Liars dart200 <user7160@newsgrouper.org.invalid> - 2026-07-06 14:53 -0700
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 17:01 -0500
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-07 15:36 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:17 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 10:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 10:07 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:27 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:56 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 13:12 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 12:54 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 14:03 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 14:08 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 15:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 15:13 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:00 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:53 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 17:39 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:52 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:47 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:45 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:44 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 10:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 11:01 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:35 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:54 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 13:14 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 19:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 07:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:56 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:22 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 06:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 12:04 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 22:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 17:22 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:10 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:30 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:11 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:35 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-29 14:27 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-12 16:23 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-13 10:50 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-27 15:35 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-01 21:17 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:34 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 16:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 15:52 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 17:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 11:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 12:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 15:25 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 14:30 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 16:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 15:15 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 17:55 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:16 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:58 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 12:00 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-06 14:19 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-06-27 07:19 -0700 |
| Message-ID | <WWWdnf3h7PpaRqL3nZ2dnZfqnPudnZ2d@giganews.com> |
| In reply to | #645720 |
On 06/26/2026 11:53 PM, Tristan Wibberley wrote: > On 20/06/2026 18:32, olcott wrote: > >> A proof theoretic expression is known to be true when >> it is fully grounded in its atomic base. Only two >> PTS semantics researchers deal with true Dag Prawitz >> is the one that began this. PTS previously only dealt >> with semantic meaning and never got around to true(L,x). > > > That's surprising, disregard for axioms? > > > It's sadly common these days with "non-classical logics" or "synthetic pluralism", the, "ignoring definition" or where that's defensible inside an axiomatics, "having contradictory definition". Some words have two definitions - a few have it that their definitions are opposites, like "entropy", Aristotle's and Leibnitz'. Mostly though if they're not the same they have different contexts altogether, so today's "pluralistic" accounts are almost always contradictory each other, and "non-classical logics" are quite often having contradictions in them. (Here "classical logic" is a modal, temporal, relevance logic, with axiomless natural deduction, that most people find as most usual the common sense logically about logic.)
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| From | polcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-27 09:50 -0500 |
| Message-ID | <111onv1$sism$2@solani.org> |
| In reply to | #645720 |
On 6/27/2026 1:53 AM, Tristan Wibberley wrote: > On 20/06/2026 18:32, olcott wrote: > >> A proof theoretic expression is known to be true when >> it is fully grounded in its atomic base. Only two >> PTS semantics researchers deal with true Dag Prawitz >> is the one that began this. PTS previously only dealt >> with semantic meaning and never got around to true(L,x). > > > That's surprising, disregard for axioms? > > If there is no sequence of inference steps in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is ungrounded in the PTS atomic base of Q. This does not mean undecidable or incomplete it means that ~∃x x=S(x) is out-of-scope for 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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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-28 11:39 +0300 |
| Message-ID | <111qmjb$3gd0r$3@dont-email.me> |
| In reply to | #645736 |
On 27/06/2026 17:50, polcott wrote: > On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >> On 20/06/2026 18:32, olcott wrote: >> >>> A proof theoretic expression is known to be true when >>> it is fully grounded in its atomic base. Only two >>> PTS semantics researchers deal with true Dag Prawitz >>> is the one that began this. PTS previously only dealt >>> with semantic meaning and never got around to true(L,x). >> >> That's surprising, disregard for axioms? > > If there is no sequence of inference steps in Q from > ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is > ungrounded in the PTS atomic base of Q. > > This does not mean undecidable or incomplete > it means that ~∃x x=S(x) is out-of-scope for Q. It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable and Q is incomplete, bcause that is what the words mean. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-28 21:52 -0500 |
| Message-ID | <111smlc$130j$1@dont-email.me> |
| In reply to | #645817 |
On 6/28/2026 3:39 AM, Mikko wrote: > On 27/06/2026 17:50, polcott wrote: >> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>> On 20/06/2026 18:32, olcott wrote: >>> >>>> A proof theoretic expression is known to be true when >>>> it is fully grounded in its atomic base. Only two >>>> PTS semantics researchers deal with true Dag Prawitz >>>> is the one that began this. PTS previously only dealt >>>> with semantic meaning and never got around to true(L,x). >>> >>> That's surprising, disregard for axioms? >> >> If there is no sequence of inference steps in Q from >> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >> ungrounded in the PTS atomic base of Q. >> >> This does not mean undecidable or incomplete >> it means that ~∃x x=S(x) is out-of-scope for Q. > > It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the > language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable > and Q is incomplete, bcause that is what the words mean. > Q also can't bake a birthday cake, this does not make Q in any way "incomplete" relative to what it was defined to do. Incomplete only counts relative to its intended purpose. A car without an engine is incomplete relative to a mode of transportation. -- 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 | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-29 09:14 +0300 |
| Message-ID | <111t2g8$4r3a$1@dont-email.me> |
| In reply to | #645827 |
On 29/06/2026 05:52, olcott wrote: > On 6/28/2026 3:39 AM, Mikko wrote: >> On 27/06/2026 17:50, polcott wrote: >>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>> On 20/06/2026 18:32, olcott wrote: >>>> >>>>> A proof theoretic expression is known to be true when >>>>> it is fully grounded in its atomic base. Only two >>>>> PTS semantics researchers deal with true Dag Prawitz >>>>> is the one that began this. PTS previously only dealt >>>>> with semantic meaning and never got around to true(L,x). >>>> >>>> That's surprising, disregard for axioms? >>> >>> If there is no sequence of inference steps in Q from >>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>> ungrounded in the PTS atomic base of Q. >>> >>> This does not mean undecidable or incomplete >>> it means that ~∃x x=S(x) is out-of-scope for Q. >> >> It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >> and Q is incomplete, bcause that is what the words mean. > > Q also can't bake a birthday cake, this does not make > Q in any way "incomplete" relative to what it was > defined to do. Incomplete only counts relative to > its intended purpose. A car without an engine is > incomplete relative to a mode of transportation. Irrelevant. The definition of completeness inly refers to the sentences in the language of the theory. To bake a cake is an action, not a sentence, so irrelevant. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 08:29 -0500 |
| Message-ID | <111ts0i$cg0f$1@dont-email.me> |
| In reply to | #645832 |
On 6/29/2026 1:14 AM, Mikko wrote: > On 29/06/2026 05:52, olcott wrote: >> On 6/28/2026 3:39 AM, Mikko wrote: >>> On 27/06/2026 17:50, polcott wrote: >>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>> On 20/06/2026 18:32, olcott wrote: >>>>> >>>>>> A proof theoretic expression is known to be true when >>>>>> it is fully grounded in its atomic base. Only two >>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>> is the one that began this. PTS previously only dealt >>>>>> with semantic meaning and never got around to true(L,x). >>>>> >>>>> That's surprising, disregard for axioms? >>>> >>>> If there is no sequence of inference steps in Q from >>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>> ungrounded in the PTS atomic base of Q. >>>> >>>> This does not mean undecidable or incomplete >>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>> >>> It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>> and Q is incomplete, bcause that is what the words mean. >> >> Q also can't bake a birthday cake, this does not make >> Q in any way "incomplete" relative to what it was >> defined to do. Incomplete only counts relative to >> its intended purpose. A car without an engine is >> incomplete relative to a mode of transportation. > > Irrelevant. The definition of completeness It a misnomer and does not literally mean (as it implies) that something is missing that could be added to make it complete. The way that terms-of-the-art are formed is very misleading and as much as intentionally deceptive. "undecidable" often means input is semantically incoherent. Whenever the input is semantically incoherent it is more accurately called incoherent rather than undecidable. Food is called inedible for many reasons such as spoilage. We could also call a railroad tie inedible ignoring the type mismatch error. A railroad tie is inedible for the same kind of reason that some expressions are undecidable. > inly refers to the > sentences in the language of the theory. To bake a cake is an > action, not a sentence, so irrelevant. > Q intentionally defined to not be able to prove ~∃x x=S(x). A car that had its engine removed to make it undrivable is not incomplete relative to its intended purpose. -- 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 11:05 -0600 |
| Message-ID | <111u8k6$ga34$1@dont-email.me> |
| In reply to | #645840 |
On 2026-06-29 07:29, olcott wrote: > On 6/29/2026 1:14 AM, Mikko wrote: >> On 29/06/2026 05:52, olcott wrote: >>> On 6/28/2026 3:39 AM, Mikko wrote: >>>> On 27/06/2026 17:50, polcott wrote: >>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>> >>>>>>> A proof theoretic expression is known to be true when >>>>>>> it is fully grounded in its atomic base. Only two >>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>> is the one that began this. PTS previously only dealt >>>>>>> with semantic meaning and never got around to true(L,x). >>>>>> >>>>>> That's surprising, disregard for axioms? >>>>> >>>>> If there is no sequence of inference steps in Q from >>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>> ungrounded in the PTS atomic base of Q. >>>>> >>>>> This does not mean undecidable or incomplete >>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>> >>>> It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>> and Q is incomplete, bcause that is what the words mean. >>> >>> Q also can't bake a birthday cake, this does not make >>> Q in any way "incomplete" relative to what it was >>> defined to do. Incomplete only counts relative to >>> its intended purpose. A car without an engine is >>> incomplete relative to a mode of transportation. >> >> Irrelevant. The definition of completeness > > It a misnomer and does not literally mean (as it implies) > that something is missing that could be added to make > it complete. The way that terms-of-the-art are formed > is very misleading and as much as intentionally deceptive. You really need to learn that terms used in a given field have definitions within that field that may or may not correspond to what you want a term to mean, and that you actually need to learn those definitions. In mathematics, a system is incomplete if there are statements in the language of that system which can neither be proven nor disproven. That's *all* incomplete means. No more, no less. It doesn't mean that something is missing that could be added. It makes no reference whatsoever to the purpose for which a system was designed. When mathematicians talk about rings, do you object based on the fact that you can't put them on your finger? When mathematicians talk about fields, do you object based on the fact that nothing can graze on them? To put things in terms of your system, the term 'incomplete' as used by mathematicians has a different GUID than the term 'incomplete' when used colloquially, just as the term 'pen' has different GUIDs depending on whether it is used to store pigs or ink. [note that I do not actually endorse the use of GUIDs; that's just plain silly]. 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 13:16 -0500 |
| Message-ID | <111ucps$hp2k$1@dont-email.me> |
| In reply to | #645846 |
On 6/29/2026 12:05 PM, André G. Isaak wrote: > On 2026-06-29 07:29, olcott wrote: >> On 6/29/2026 1:14 AM, Mikko wrote: >>> On 29/06/2026 05:52, olcott wrote: >>>> On 6/28/2026 3:39 AM, Mikko wrote: >>>>> On 27/06/2026 17:50, polcott wrote: >>>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>> >>>>>>>> A proof theoretic expression is known to be true when >>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>> >>>>>>> That's surprising, disregard for axioms? >>>>>> >>>>>> If there is no sequence of inference steps in Q from >>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>> ungrounded in the PTS atomic base of Q. >>>>>> >>>>>> This does not mean undecidable or incomplete >>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>> >>>>> It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>>> and Q is incomplete, bcause that is what the words mean. >>>> >>>> Q also can't bake a birthday cake, this does not make >>>> Q in any way "incomplete" relative to what it was >>>> defined to do. Incomplete only counts relative to >>>> its intended purpose. A car without an engine is >>>> incomplete relative to a mode of transportation. >>> >>> Irrelevant. The definition of completeness >> >> It a misnomer and does not literally mean (as it implies) >> that something is missing that could be added to make >> it complete. The way that terms-of-the-art are formed >> is very misleading and as much as intentionally deceptive. > > You really need to learn that terms used in a given field have > definitions within that field that may or may not correspond to what you > want a term to mean, and that you actually need to learn those definitions. > That is the way that it usually works. In Proof Theoretic Semantics each author has their own terms-of-the-art that has a very similar yet not exactly the same semantic meaning as entirely different terms-of-the-art used by another author. Also these meanings gradually evolve over time so they change in subtle ways from their original meanings. > In mathematics, a system is incomplete if there are statements in the > language of that system which can neither be proven nor disproven. > Q was intentionally defined to handle less than PA thus is not at all in any way incomplete relative to its defined purpose. > That's *all* incomplete means. No more, no less. It doesn't mean that > something is missing that could be added. It makes no reference > whatsoever to the purpose for which a system was designed. > So they could have defined "has a box of clowns" as the situation where en expression can neither be proven nor refuted in Q. 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? > > When mathematicians talk about fields, do you object based on the fact > that nothing can graze on them? > > To put things in terms of your system, the term 'incomplete' as used by > mathematicians has a different GUID than the term 'incomplete' when used > colloquially, just as the term 'pen' has different GUIDs depending on > whether it is used to store pigs or ink. [note that I do not actually > endorse the use of GUIDs; that's just plain silly]. > > André > And likewise "undecidable" really means that the expression is semantically incoherent. We could equally call this "has a square box of clowns". -- 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 12:29 -0600 |
| Message-ID | <111udj2$hesm$1@dont-email.me> |
| In reply to | #645847 |
On 2026-06-29 12:16, olcott wrote: > On 6/29/2026 12:05 PM, André G. Isaak wrote: >> On 2026-06-29 07:29, olcott wrote: >>> On 6/29/2026 1:14 AM, Mikko wrote: >>>> On 29/06/2026 05:52, olcott wrote: >>>>> On 6/28/2026 3:39 AM, Mikko wrote: >>>>>> On 27/06/2026 17:50, polcott wrote: >>>>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>>> >>>>>>>>> A proof theoretic expression is known to be true when >>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>> >>>>>>>> That's surprising, disregard for axioms? >>>>>>> >>>>>>> If there is no sequence of inference steps in Q from >>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>> >>>>>>> This does not mean undecidable or incomplete >>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>> >>>>>> It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>>>> and Q is incomplete, bcause that is what the words mean. >>>>> >>>>> Q also can't bake a birthday cake, this does not make >>>>> Q in any way "incomplete" relative to what it was >>>>> defined to do. Incomplete only counts relative to >>>>> its intended purpose. A car without an engine is >>>>> incomplete relative to a mode of transportation. >>>> >>>> Irrelevant. The definition of completeness >>> >>> It a misnomer and does not literally mean (as it implies) >>> that something is missing that could be added to make >>> it complete. The way that terms-of-the-art are formed >>> is very misleading and as much as intentionally deceptive. >> >> You really need to learn that terms used in a given field have >> definitions within that field that may or may not correspond to what >> you want a term to mean, and that you actually need to learn those >> definitions. >> > > That is the way that it usually works. In Proof Theoretic > Semantics each author has their own terms-of-the-art that > has a very similar yet not exactly the same semantic meaning > as entirely different terms-of-the-art used by another author. > > Also these meanings gradually evolve over time so they > change in subtle ways from their original meanings. > >> In mathematics, a system is incomplete if there are statements in the >> language of that system which can neither be proven nor disproven. >> > > Q was intentionally defined to handle less than PA > thus is not at all in any way incomplete relative > to its defined purpose. The definition of 'incomplete' makes no reference whatsoever to 'defined purpose'. If there are sentences in the language of Q which can neither be proven nor disproven by Q, then Q is incomplete. And it is. >> That's *all* incomplete means. No more, no less. It doesn't mean that >> something is missing that could be added. It makes no reference >> whatsoever to the purpose for which a system was designed. >> > > So they could have defined "has a box of clowns" as > the situation where en expression can neither be > proven nor refuted in Q. Is "has a box of clowns" in the language of Q? No. I didn't think so, so your example is completely irrelevant. > 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? >> When mathematicians talk about fields, do you object based on the fact >> that nothing can graze on them? No answer? André >> To put things in terms of your system, the term 'incomplete' as used >> by mathematicians has a different GUID than the term 'incomplete' when >> used colloquially, just as the term 'pen' has different GUIDs >> depending on whether it is used to store pigs or ink. [note that I do >> not actually endorse the use of GUIDs; that's just plain silly]. >> >> André >> > > And likewise "undecidable" really means that the > expression is semantically incoherent. We could > equally call this "has a square box of clowns". > > -- 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 14:08 -0500 |
| Message-ID | <111ufqj$iml9$1@dont-email.me> |
| In reply to | #645848 |
On 6/29/2026 1:29 PM, André G. Isaak wrote: > On 2026-06-29 12:16, olcott wrote: >> On 6/29/2026 12:05 PM, André G. Isaak wrote: >>> On 2026-06-29 07:29, olcott wrote: >>>> On 6/29/2026 1:14 AM, Mikko wrote: >>>>> On 29/06/2026 05:52, olcott wrote: >>>>>> On 6/28/2026 3:39 AM, Mikko wrote: >>>>>>> On 27/06/2026 17:50, polcott wrote: >>>>>>>> On 6/27/2026 1:53 AM, Tristan Wibberley wrote: >>>>>>>>> On 20/06/2026 18:32, olcott wrote: >>>>>>>>> >>>>>>>>>> A proof theoretic expression is known to be true when >>>>>>>>>> it is fully grounded in its atomic base. Only two >>>>>>>>>> PTS semantics researchers deal with true Dag Prawitz >>>>>>>>>> is the one that began this. PTS previously only dealt >>>>>>>>>> with semantic meaning and never got around to true(L,x). >>>>>>>>> >>>>>>>>> That's surprising, disregard for axioms? >>>>>>>> >>>>>>>> If there is no sequence of inference steps in Q from >>>>>>>> ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is >>>>>>>> ungrounded in the PTS atomic base of Q. >>>>>>>> >>>>>>>> This does not mean undecidable or incomplete >>>>>>>> it means that ~∃x x=S(x) is out-of-scope for Q. >>>>>>> >>>>>>> It comes close. If ∃x x=S(x) is likewise "ungrounded" but in the >>>>>>> language of Q then ~∃x x=S(x) and ∃x x=S(x) are both undecidable >>>>>>> and Q is incomplete, bcause that is what the words mean. >>>>>> >>>>>> Q also can't bake a birthday cake, this does not make >>>>>> Q in any way "incomplete" relative to what it was >>>>>> defined to do. Incomplete only counts relative to >>>>>> its intended purpose. A car without an engine is >>>>>> incomplete relative to a mode of transportation. >>>>> >>>>> Irrelevant. The definition of completeness >>>> >>>> It a misnomer and does not literally mean (as it implies) >>>> that something is missing that could be added to make >>>> it complete. The way that terms-of-the-art are formed >>>> is very misleading and as much as intentionally deceptive. >>> >>> You really need to learn that terms used in a given field have >>> definitions within that field that may or may not correspond to what >>> you want a term to mean, and that you actually need to learn those >>> definitions. >>> >> >> That is the way that it usually works. In Proof Theoretic >> Semantics each author has their own terms-of-the-art that >> has a very similar yet not exactly the same semantic meaning >> as entirely different terms-of-the-art used by another author. >> >> Also these meanings gradually evolve over time so they >> change in subtle ways from their original meanings. >> >>> In mathematics, a system is incomplete if there are statements in the >>> language of that system which can neither be proven nor disproven. >>> >> >> Q was intentionally defined to handle less than PA >> thus is not at all in any way incomplete relative >> to its defined purpose. > > The definition of 'incomplete' makes no reference whatsoever to 'defined > purpose'. If there are sentences in the language of Q which can neither > be proven nor disproven by Q, then Q is incomplete. And it is. > >>> That's *all* incomplete means. No more, no less. It doesn't mean that >>> something is missing that could be added. It makes no reference >>> whatsoever to the purpose for which a system was designed. >>> >> >> So they could have defined "has a box of clowns" as >> the situation where en expression can neither be >> proven nor refuted in Q. > > 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 >> 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? > Off topic, irrelevant. When Peter Schroeder-Heister talks about The Definitional View of Atomic Systems in Proof-Theoretic Semantics How close is this to Dag Prawitz Theory of Grounds? Same ball park, they never seem to ever talk about exact the same thing, yet it is within PTS just the same. > André > >>> To put things in terms of your system, the term 'incomplete' as used >>> by mathematicians has a different GUID than the term 'incomplete' >>> when used colloquially, just as the term 'pen' has different GUIDs >>> depending on whether it is used to store pigs or ink. [note that I do >>> not actually endorse the use of GUIDs; that's just plain silly]. >>> >>> André >>> >> >> And likewise "undecidable" really means that the >> expression is semantically incoherent. We could >> equally call this "has a square box of clowns". >> >> > -- 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 13:33 -0600 |
| Message-ID | <111uh9d$j1vo$1@dont-email.me> |
| In reply to | #645849 |
On 2026-06-29 13:08, olcott wrote: > On 6/29/2026 1:29 PM, André G. Isaak wrote: >> Is "has a box of clowns" in the language of Q? No. I didn't think so, >> so your example is completely irrelevant. >> > > It is an idiom stipulated to mean: > sentences in the language of Q which can neither > be proven nor disproven by Q Q doesn't have idioms. That's a natural language concept alien to theories of arithmetic. >>> So we can say that the halting problem "has a box >>> of clowns" instead of saying that computation is >>> in any way limited. >>> >>>> When mathematicians talk about rings, do you object based on the >>>> fact that you can't put them on your finger? >> >> No answer? >> > > Off topic, irrelevant. > >>>> When mathematicians talk about fields, do you object based on the >>>> fact that nothing can graze on them? >> >> No answer? These questions are relevant because they get to whether your objection to the term 'incomplete' extends to other terms as well. If Gödel had used the term 'fnord' instead of incomplete, I suspect you wouldn't have the same objection to it. Your objection seems to be entirely based on the fact that you are reading things into the term 'incomplete' which aren't actually there based on your own interpretation of the colloquial term 'incomplete'. But the mathematical term and the colloquial term are different, just as the mathematical term 'ring' differs from the colloquial term. Technical terms often diverge significantly from colloquial ones. For example, to an astronomer, oxygen is classified as a metal despite the fact that this doesn't correspond to everyday usage. This doesn't cause problems for astronomers. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 14:47 -0500 |
| Message-ID | <111ui4p$jd5b$1@dont-email.me> |
| In reply to | #645850 |
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 simply the same way that actual meaning really works. Model theory is merely a strange idea that was adopted because keeping semantics and syntax together as one was too difficult for people to figure out back when model theory was first created. -- 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 14:02 -0600 |
| Message-ID | <111uj0f$j560$1@dont-email.me> |
| In reply to | #645851 |
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. 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. 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 15:06 -0500 |
| Message-ID | <111uj7p$jofl$1@dont-email.me> |
| In reply to | #645852 |
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. > 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 | 2026-06-29 14:58 -0600 |
| Message-ID | <111um90$kkcp$1@dont-email.me> |
| In reply to | #645853 |
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, 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. 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 16:10 -0500 |
| Message-ID | <111umvc$kqhq$1@dont-email.me> |
| In reply to | #645854 |
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. > 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. > > 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 | 2026-06-29 15:18 -0600 |
| Message-ID | <111uner$kkcp$2@dont-email.me> |
| In reply to | #645855 |
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). >> 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. I've never seen any author writing within PTS express any misgivings about the fact that some formal systems are inconsistent. This is something that you are projecting onto that theory based on the fact that you really do not understand it. 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 16:39 -0500 |
| Message-ID | <111uolv$lb85$1@dont-email.me> |
| In reply to | #645856 |
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. % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. >>> 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. I have been trying to get you to understand this reasoning and you are making some progress. > I've never seen > any author writing within PTS express any misgivings about the fact that > some formal systems are inconsistent. This is something that you are > projecting onto that theory based on the fact that you really do not > understand it. > > André > That whole thing is totally out-of-sync with the way that they think. -- 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 16:25 -0600 |
| Message-ID | <111urdj$l815$1@dont-email.me> |
| In reply to | #645857 |
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'. > % 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. >>>> 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. 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 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. 'Theorem' is a notion pertaining to provability, not truth. 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 17:38 -0500 |
| Message-ID | <111us54$m8gu$1@dont-email.me> |
| In reply to | #645858 |
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. >> % 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. >>>>> 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. > 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 > 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. > 'Theorem' is a notion pertaining to provability, not truth. > > 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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