Groups | Search | Server Info | Keyboard shortcuts | Login | Register [http] [https] [nntp] [nntps]
Groups > sci.math > #644766 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-04-20 11:57 -0500 |
| Last post | 2026-06-30 06:54 +0100 |
| Articles | 20 on this page of 408 — 15 participants |
Back to article view | Back to sci.math
Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-27 09:50 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:39 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-28 21:52 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:14 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:18 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:45 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:56 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 22:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:57 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:02 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:17 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 07:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 09:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 13:33 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:40 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:50 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:47 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:11 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:28 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:50 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:52 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 15:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 17:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 17:09 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 19:05 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 18:39 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 20:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 19:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:03 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 00:02 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 08:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:48 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:17 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:12 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:21 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:38 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:46 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 15:22 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:11 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:49 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:13 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 09:36 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:42 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:16 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 10:58 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:21 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:35 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:54 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:09 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:44 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:23 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:31 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:42 -0500
Re: The simple essence of Proof Theoretic Semantics Alan Mackenzie <acm@muc.de> - 2026-07-01 19:18 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:56 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:05 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:53 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:13 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:37 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:50 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 16:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 17:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 18:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 22:36 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:00 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:43 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:59 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 23:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:57 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 09:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 13:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 14:22 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 14:33 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 15:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 16:54 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:12 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:23 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:32 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:47 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 18:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 20:03 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:22 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 10:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 11:50 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:40 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:47 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 17:37 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 21:58 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:05 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:43 -0400
The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-03 22:11 -0500
Re: The truth about the halting problem counter-example input dbush <dbush.mobile@gmail.com> - 2026-07-03 23:23 -0400
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:58 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-04 12:16 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:07 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-06 10:18 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:45 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:58 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:07 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:11 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:27 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:19 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:04 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:46 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:55 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:24 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:30 -0500
Re: The simple essence of Proof Theoretic Semantics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:23 -0700
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 11:57 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:23 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:08 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:10 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:11 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:18 -0400
Re: The simple essence of Proof Theoretic Semantics Brenden Jafarov <rnarnj@rbn.ru> - 2026-07-04 12:47 +0000
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:43 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:04 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:28 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:27 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:45 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:53 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 16:59 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:57 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:01 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:33 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:25 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:10 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 14:08 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 15:12 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:38 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:09 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-08 22:28 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:15 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:41 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:38 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:40 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:39 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:14 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:32 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:37 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:06 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:03 +0300
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:25 +0300
Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-06 10:54 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:22 +0300
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-08 22:32 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:25 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:11 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:27 +0300
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: Terms-Of-The-Art are Liars Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 14:59 +0100
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:23 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 10:19 -0400
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:29 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 12:39 -0400
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 13:09 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:46 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 12:39 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:38 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-08 22:40 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:42 +0300
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 14:07 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:38 +0300
Re: Terms-Of-The-Art are Liars dart200 <user7160@newsgrouper.org.invalid> - 2026-07-06 14:53 -0700
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 17:01 -0500
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-07 15:36 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-09 11:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:17 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 10:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 10:07 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:27 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:56 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 13:12 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 12:54 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 14:03 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 14:08 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 15:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 15:13 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:00 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:53 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 17:39 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:52 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:47 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:45 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:44 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 10:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 11:01 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:35 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:54 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 13:14 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 19:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 07:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:56 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:22 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 06:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 12:04 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 22:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 17:22 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:10 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:30 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:11 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:35 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-29 14:27 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-27 15:35 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-01 21:17 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:34 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 16:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 15:52 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 17:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 11:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 12:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 15:25 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 14:30 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 16:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 15:15 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 17:55 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:16 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:58 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 12:00 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-06 14:19 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100
Page 14 of 21 — ← Prev page 1 … 12 13 [14] 15 16 … 21 Next page →
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 16:56 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121e2r$1eq2q$1@dont-email.me> |
| In reply to | #645892 |
On 6/30/2026 4:18 PM, André G. Isaak wrote: > On 2026-06-29 21:06, olcott wrote: >> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>> On 2026-06-29 20:42, olcott wrote: > >>>> Those are specific concrete examples of how >>>> Proof Theoretic Semantics rejects expressions >>>> as Proof Theoretic Semantically incoherent. >>> >>> No, they are not. No author writing in the framework of proof- >>> theoretic semantics has ever offered those examples or comparable >>> examples or made any claims about 'rejecting expressions as proof >>> theoretic semantically incoherent'. And there's nothing incoherent >>> about the statement 'no number is equal to its successor' which is >>> the example under discussion. >>> >>> André >>> >> >> None-the-less what I have said remains completely true. >> What I have spent 28 years reverse-engineering from first >> principles is exactly that. That no one applied PTS >> exactly that way before does not mean that it is not >> exactly correct PTS. > > Unfortunately, your say so carries very little weight. > > Would you agree that there is a difference between a statement being > false and a statement being meaningless? > Of course and that is such a dumb question that I ignored it. >> The biggest mistake that humanity makes that is killing >> the whole planet is treating unbelievable as exactly >> one-and-the-same-thing as untrue. > > I have no idea what you're getting at here. > > André > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-06-30 16:06 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121elv$1epkc$2@dont-email.me> |
| In reply to | #645895 |
On 2026-06-30 15:56, olcott wrote: > On 6/30/2026 4:18 PM, André G. Isaak wrote: >> On 2026-06-29 21:06, olcott wrote: >>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>> On 2026-06-29 20:42, olcott wrote: >> >>>>> Those are specific concrete examples of how >>>>> Proof Theoretic Semantics rejects expressions >>>>> as Proof Theoretic Semantically incoherent. >>>> >>>> No, they are not. No author writing in the framework of proof- >>>> theoretic semantics has ever offered those examples or comparable >>>> examples or made any claims about 'rejecting expressions as proof >>>> theoretic semantically incoherent'. And there's nothing incoherent >>>> about the statement 'no number is equal to its successor' which is >>>> the example under discussion. >>>> >>>> André >>>> >>> >>> None-the-less what I have said remains completely true. >>> What I have spent 28 years reverse-engineering from first >>> principles is exactly that. That no one applied PTS >>> exactly that way before does not mean that it is not >>> exactly correct PTS. >> >> Unfortunately, your say so carries very little weight. >> >> Would you agree that there is a difference between a statement being >> false and a statement being meaningless? >> > > Of course and that is such a dumb question that I > ignored it. But your interpretation of PTS claims that there is no difference. You claim that unprovable statements are meaningless; but any false statement will be unprovable in a consistent logic. PA can prove that 2 + 3 = 5 PA can't prove that 2 + 3 ≠ 5 But the latter isn't meaningless, it's simply false. You're simply wrong when you assert that PTS claims that unprovable claims are meaningless; that's simply not a coherent view. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 17:08 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121ep9$1evpl$2@dont-email.me> |
| In reply to | #645897 |
On 6/30/2026 5:06 PM, André G. Isaak wrote: > On 2026-06-30 15:56, olcott wrote: >> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>> On 2026-06-29 21:06, olcott wrote: >>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>> On 2026-06-29 20:42, olcott wrote: >>> >>>>>> Those are specific concrete examples of how >>>>>> Proof Theoretic Semantics rejects expressions >>>>>> as Proof Theoretic Semantically incoherent. >>>>> >>>>> No, they are not. No author writing in the framework of proof- >>>>> theoretic semantics has ever offered those examples or comparable >>>>> examples or made any claims about 'rejecting expressions as proof >>>>> theoretic semantically incoherent'. And there's nothing incoherent >>>>> about the statement 'no number is equal to its successor' which is >>>>> the example under discussion. >>>>> >>>>> André >>>>> >>>> >>>> None-the-less what I have said remains completely true. >>>> What I have spent 28 years reverse-engineering from first >>>> principles is exactly that. That no one applied PTS >>>> exactly that way before does not mean that it is not >>>> exactly correct PTS. >>> >>> Unfortunately, your say so carries very little weight. >>> >>> Would you agree that there is a difference between a statement being >>> false and a statement being meaningless? >>> >> >> Of course and that is such a dumb question that I >> ignored it. > > But your interpretation of PTS claims that there is no difference. Spent at least ten minutes carefully studying my first response. > You > claim that unprovable statements are meaningless; but any false > statement will be unprovable in a consistent logic. > > PA can prove that 2 + 3 = 5 > PA can't prove that 2 + 3 ≠ 5 > > But the latter isn't meaningless, it's simply false. > > You're simply wrong when you assert that PTS claims that unprovable > claims are meaningless; that's simply not a coherent view. > > 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).
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 17:42 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121goa$1fi1e$1@dont-email.me> |
| In reply to | #645897 |
On 6/30/2026 5:06 PM, André G. Isaak wrote: > On 2026-06-30 15:56, olcott wrote: >> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>> On 2026-06-29 21:06, olcott wrote: >>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>> On 2026-06-29 20:42, olcott wrote: >>> >>>>>> Those are specific concrete examples of how >>>>>> Proof Theoretic Semantics rejects expressions >>>>>> as Proof Theoretic Semantically incoherent. >>>>> >>>>> No, they are not. No author writing in the framework of proof- >>>>> theoretic semantics has ever offered those examples or comparable >>>>> examples or made any claims about 'rejecting expressions as proof >>>>> theoretic semantically incoherent'. And there's nothing incoherent >>>>> about the statement 'no number is equal to its successor' which is >>>>> the example under discussion. >>>>> >>>>> André >>>>> >>>> >>>> None-the-less what I have said remains completely true. >>>> What I have spent 28 years reverse-engineering from first >>>> principles is exactly that. That no one applied PTS >>>> exactly that way before does not mean that it is not >>>> exactly correct PTS. >>> >>> Unfortunately, your say so carries very little weight. >>> >>> Would you agree that there is a difference between a statement being >>> false and a statement being meaningless? >>> >> >> Of course and that is such a dumb question that I >> ignored it. > > But your interpretation of PTS claims that there is no difference. You > claim that unprovable statements are meaningless; but any false > statement will be unprovable in a consistent logic. > > PA can prove that 2 + 3 = 5 > PA can't prove that 2 + 3 ≠ 5 > > But the latter isn't meaningless, it's simply false. > If no connection exists between an expression E (or its negation ~E) and the axioms of formal system F then E is undefined in F. > You're simply wrong when you assert that PTS claims that unprovable > claims are meaningless; that's simply not a coherent view. > > 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).
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-06-30 16:51 -0600 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121h98$1epkc$3@dont-email.me> |
| In reply to | #645899 |
On 2026-06-30 16:42, olcott wrote: > On 6/30/2026 5:06 PM, André G. Isaak wrote: >> On 2026-06-30 15:56, olcott wrote: >>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>> On 2026-06-29 21:06, olcott wrote: >>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>> On 2026-06-29 20:42, olcott wrote: >>>> >>>>>>> Those are specific concrete examples of how >>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>> as Proof Theoretic Semantically incoherent. >>>>>> >>>>>> No, they are not. No author writing in the framework of proof- >>>>>> theoretic semantics has ever offered those examples or comparable >>>>>> examples or made any claims about 'rejecting expressions as proof >>>>>> theoretic semantically incoherent'. And there's nothing incoherent >>>>>> about the statement 'no number is equal to its successor' which is >>>>>> the example under discussion. >>>>>> >>>>>> André >>>>>> >>>>> >>>>> None-the-less what I have said remains completely true. >>>>> What I have spent 28 years reverse-engineering from first >>>>> principles is exactly that. That no one applied PTS >>>>> exactly that way before does not mean that it is not >>>>> exactly correct PTS. >>>> >>>> Unfortunately, your say so carries very little weight. >>>> >>>> Would you agree that there is a difference between a statement being >>>> false and a statement being meaningless? >>>> >>> >>> Of course and that is such a dumb question that I >>> ignored it. >> >> But your interpretation of PTS claims that there is no difference. You >> claim that unprovable statements are meaningless; but any false >> statement will be unprovable in a consistent logic. >> >> PA can prove that 2 + 3 = 5 >> PA can't prove that 2 + 3 ≠ 5 >> >> But the latter isn't meaningless, it's simply false. >> > > If no connection exists between an expression E > (or its negation ~E) and the axioms of formal > system F then E is undefined in F. So now you are adding 'or its negation' to your position (something not present in your earlier presentations). Can you provide a reference to a single author writing in PTS who makes such a claim? And does 'undefined' differ from your earlier term 'meaningless'? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 21:07 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <1121soh$1icml$1@dont-email.me> |
| In reply to | #645900 |
On 6/30/2026 5:51 PM, André G. Isaak wrote: > On 2026-06-30 16:42, olcott wrote: >> On 6/30/2026 5:06 PM, André G. Isaak wrote: >>> On 2026-06-30 15:56, olcott wrote: >>>> On 6/30/2026 4:18 PM, André G. Isaak wrote: >>>>> On 2026-06-29 21:06, olcott wrote: >>>>>> On 6/29/2026 9:49 PM, André G. Isaak wrote: >>>>>>> On 2026-06-29 20:42, olcott wrote: >>>>> >>>>>>>> Those are specific concrete examples of how >>>>>>>> Proof Theoretic Semantics rejects expressions >>>>>>>> as Proof Theoretic Semantically incoherent. >>>>>>> >>>>>>> No, they are not. No author writing in the framework of proof- >>>>>>> theoretic semantics has ever offered those examples or comparable >>>>>>> examples or made any claims about 'rejecting expressions as proof >>>>>>> theoretic semantically incoherent'. And there's nothing >>>>>>> incoherent about the statement 'no number is equal to its >>>>>>> successor' which is the example under discussion. >>>>>>> >>>>>>> André >>>>>>> >>>>>> >>>>>> None-the-less what I have said remains completely true. >>>>>> What I have spent 28 years reverse-engineering from first >>>>>> principles is exactly that. That no one applied PTS >>>>>> exactly that way before does not mean that it is not >>>>>> exactly correct PTS. >>>>> >>>>> Unfortunately, your say so carries very little weight. >>>>> >>>>> Would you agree that there is a difference between a statement >>>>> being false and a statement being meaningless? >>>>> >>>> >>>> Of course and that is such a dumb question that I >>>> ignored it. >>> >>> But your interpretation of PTS claims that there is no difference. >>> You claim that unprovable statements are meaningless; but any false >>> statement will be unprovable in a consistent logic. >>> >>> PA can prove that 2 + 3 = 5 >>> PA can't prove that 2 + 3 ≠ 5 >>> >>> But the latter isn't meaningless, it's simply false. >>> >> >> If no connection exists between an expression E >> (or its negation ~E) and the axioms of formal >> system F then E is undefined in F. > > So now you are adding 'or its negation' to your position (something not > present in your earlier presentations). Can you provide a reference to a > single author writing in PTS who makes such a claim? > I did not put negation in there because I thought that my words obviously included it. Clearly I was wrong about this. The PTS people themselves mostly talk about canonical proof, normalization and harmony. > And does 'undefined' differ from your earlier term 'meaningless'? > > 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).
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-29 21:26 -0500 |
| Subject | Re: The simple essence of Proof Theoretic Semantics |
| Message-ID | <111v9fu$pbsb$1@dont-email.me> |
| In reply to | #645866 |
On 6/29/2026 8:54 PM, André G. Isaak wrote: > On 2026-06-29 19:19, olcott wrote: >> On 6/29/2026 8:01 PM, André G. Isaak wrote: >>> On 2026-06-29 18:37, olcott wrote: >>>> On 6/29/2026 6:45 PM, André G. Isaak wrote: >>>>> On 2026-06-29 17:36, olcott wrote: >>> >>>>>> It does seem that they do agree that no proof >>>>>> of G can possibly exist in PA does means that >>>>>> G has no semantic meaning in PA. >>>>> >>>>> I've not seen anyone operating in PTS who says anything remotely >>>>> like that. They do not agree with this; rather, you are projecting >>>>> your own peculiar views onto their theory. >>>>> >>>>> André >>>>> >>>> >>>> Because they beat around the bush about that using >>>> terminology that varies across every author. >>> >>> It's not that they are beating around the bush; it's that they aren't >>> actually saying what you want them to say. Face it, you really don't >>> understand the PTS literature as it is above your head. >>> >>> André >>> >> >> PTS is the way that meaning actually works. >> We can make a simpler analogy in that English >> words are meaningless until they are defined. >> >> The PTS connection of an expression in Q to >> its axioms Q is analogous to the connection >> of an English word to its definition. >> >> A proof merely looks to see if a definition >> exists and if it does not then the English >> Word / Expression of Q remains meaningless. > > That's not what PTS says; that's simply you. > That <is> the essence of what PTS says. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-30 11:18 +0300 |
| Message-ID | <111vu4c$ucl0$1@dont-email.me> |
| In reply to | #645840 |
On 29/06/2026 16:29, 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. It does mean that something is missing that could be added to enabe a proof of an unprovable sentence. For example, the theory of a group does not tell whether ∀x∀y (x * y = y * x). It could be true or it could be false. But it is possible to add an axiom to make it provagle, e.g, x∀y (x * y = y * x) itself, giving the theory of an Abelian group, which is still incomplete but can be said to be less incomplete. Therefore the meaning of "complete" is not very different from its common sense meaning, just not as ambiguous. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-30 08:58 -0500 |
| Message-ID | <1120i33$14i37$1@dont-email.me> |
| In reply to | #645877 |
On 6/30/2026 3:18 AM, Mikko wrote: > On 29/06/2026 16:29, 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. > > It does mean that something is missing that could be added to > enabe a proof of an unprovable sentence. Base-Extension Semantics (B-eS) allows that. It never was incomplete. It always did what it was defined to do. When Q is extended to become PA it stops being Q and becomes PA. > For example, the theory > of a group does not tell whether ∀x∀y (x * y = y * x). It could > be true or it could be false. But it is possible to add an > axiom to make it provagle, e.g, x∀y (x * y = y * x) itself, > giving the theory of an Abelian group, which is still incomplete > but can be said to be less incomplete. Therefore the meaning of > "complete" is not very different from its common sense meaning, > just not as ambiguous. > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-07-01 10:24 +0300 |
| Message-ID | <1122fb2$1modk$1@dont-email.me> |
| In reply to | #645885 |
On 30/06/2026 16:58, olcott wrote: > On 6/30/2026 3:18 AM, Mikko wrote: >> On 29/06/2026 16:29, 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. >> >> It does mean that something is missing that could be added to >> enabe a proof of an unprovable sentence. > > Base-Extension Semantics (B-eS) allows that. > It never was incomplete. It always did what it was defined to do. > When Q is extended to become PA it stops being Q and becomes PA. However, there are theories that reamain incomplete even when more postolates are added, as long as there is a way to know which sentences are included in the added postulates. Important examples include Peano arithmetic and ZFC set theory. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-01 10:16 -0500 |
| Message-ID | <1123avq$1unru$2@dont-email.me> |
| In reply to | #645921 |
On 7/1/2026 2:24 AM, Mikko wrote: > On 30/06/2026 16:58, olcott wrote: >> On 6/30/2026 3:18 AM, Mikko wrote: >>> On 29/06/2026 16:29, 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. >>> >>> It does mean that something is missing that could be added to >>> enabe a proof of an unprovable sentence. >> >> Base-Extension Semantics (B-eS) allows that. >> It never was incomplete. It always did what it was defined to do. >> When Q is extended to become PA it stops being Q and becomes PA. > > However, there are theories that reamain incomplete even when > more postolates are added, as long as there is a way to know > which sentences are included in the added postulates. Important > examples include Peano arithmetic and ZFC set theory. > Base-Extension Semantics (B-eS) seems to be essentially a cheat. When we ask what is grounded in an atomic base of Q and we add axioms to Q to become PA we cheated in that we changed the original question rather than answered it. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-07-02 09:55 +0300 |
| Message-ID | <112521j$2dfqp$1@dont-email.me> |
| In reply to | #645932 |
On 01/07/2026 18:16, olcott wrote: > On 7/1/2026 2:24 AM, Mikko wrote: >> On 30/06/2026 16:58, olcott wrote: >>> On 6/30/2026 3:18 AM, Mikko wrote: >>>> On 29/06/2026 16:29, 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. >>>> >>>> It does mean that something is missing that could be added to >>>> enabe a proof of an unprovable sentence. >>> >>> Base-Extension Semantics (B-eS) allows that. >>> It never was incomplete. It always did what it was defined to do. >>> When Q is extended to become PA it stops being Q and becomes PA. >> >> However, there are theories that reamain incomplete even when >> more postolates are added, as long as there is a way to know >> which sentences are included in the added postulates. Important >> examples include Peano arithmetic and ZFC set theory. > > Base-Extension Semantics (B-eS) seems to be essentially a cheat. > When we ask what is grounded in an atomic base of Q and we > add axioms to Q to become PA we cheated in that we changed > the original question rather than answered it. Yes, in a sense. But sometimes it is better to have a partial answer rather than no answer at all. Of course Q with any additional postulate is not Q but if the additional postulates are true about natural numbers then the strengthened theory is still a theory of natural numbers. PA is one such strengthened Q but still incomplete and can be strengthened further. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-02 09:49 -0500 |
| Message-ID | <1125tpb$2lqo1$1@dont-email.me> |
| In reply to | #646014 |
On 7/2/2026 1:55 AM, Mikko wrote: > On 01/07/2026 18:16, olcott wrote: >> On 7/1/2026 2:24 AM, Mikko wrote: >>> On 30/06/2026 16:58, olcott wrote: >>>> On 6/30/2026 3:18 AM, Mikko wrote: >>>>> On 29/06/2026 16:29, 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. >>>>> >>>>> It does mean that something is missing that could be added to >>>>> enabe a proof of an unprovable sentence. >>>> >>>> Base-Extension Semantics (B-eS) allows that. >>>> It never was incomplete. It always did what it was defined to do. >>>> When Q is extended to become PA it stops being Q and becomes PA. >>> >>> However, there are theories that reamain incomplete even when >>> more postolates are added, as long as there is a way to know >>> which sentences are included in the added postulates. Important >>> examples include Peano arithmetic and ZFC set theory. >> >> Base-Extension Semantics (B-eS) seems to be essentially a cheat. >> When we ask what is grounded in an atomic base of Q and we >> add axioms to Q to become PA we cheated in that we changed >> the original question rather than answered it. > > Yes, in a sense. But sometimes it is better to have a partial answer > rather than no answer at all. Of course Q with any additional > postulate is not Q but if the additional postulates are true about > natural numbers then the strengthened theory is still a theory of > natural numbers. PA is one such strengthened Q but still incomplete > and can be strengthened further. > Is (∀ x, S(x) ≠ x) provable or refutable in Q? Yes if you cheat, no if you don't cheat. One cannot properly study math and logic without looking at them through computation because computation requires things that math and logic incorrectly assume away. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-07-03 12:28 +0300 |
| Message-ID | <1127vb4$39pjk$1@dont-email.me> |
| In reply to | #646022 |
On 02/07/2026 17:49, olcott wrote: > On 7/2/2026 1:55 AM, Mikko wrote: >> On 01/07/2026 18:16, olcott wrote: >>> On 7/1/2026 2:24 AM, Mikko wrote: >>>> On 30/06/2026 16:58, olcott wrote: >>>>> On 6/30/2026 3:18 AM, Mikko wrote: >>>>>> On 29/06/2026 16:29, 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. >>>>>> >>>>>> It does mean that something is missing that could be added to >>>>>> enabe a proof of an unprovable sentence. >>>>> >>>>> Base-Extension Semantics (B-eS) allows that. >>>>> It never was incomplete. It always did what it was defined to do. >>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>> >>>> However, there are theories that reamain incomplete even when >>>> more postolates are added, as long as there is a way to know >>>> which sentences are included in the added postulates. Important >>>> examples include Peano arithmetic and ZFC set theory. >>> >>> Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>> When we ask what is grounded in an atomic base of Q and we >>> add axioms to Q to become PA we cheated in that we changed >>> the original question rather than answered it. >> >> Yes, in a sense. But sometimes it is better to have a partial answer >> rather than no answer at all. Of course Q with any additional >> postulate is not Q but if the additional postulates are true about >> natural numbers then the strengthened theory is still a theory of >> natural numbers. PA is one such strengthened Q but still incomplete >> and can be strengthened further. > > Is (∀ x, S(x) ≠ x) provable or refutable in Q? > Yes if you cheat, no if you don't cheat. As I already pointed out in another message, which you apparently missed, it is neither. It is true about natural numbers but there are other models of Rbinsons Q, and it is false in some of them. A simple example is a model that incudes all natural numbers and one additional element that is its own successor. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 10:38 -0500 |
| Message-ID | <1128l23$3gafg$2@dont-email.me> |
| In reply to | #646061 |
On 7/3/2026 4:28 AM, Mikko wrote: > On 02/07/2026 17:49, olcott wrote: >> On 7/2/2026 1:55 AM, Mikko wrote: >>> On 01/07/2026 18:16, olcott wrote: >>>> On 7/1/2026 2:24 AM, Mikko wrote: >>>>> On 30/06/2026 16:58, olcott wrote: >>>>>> On 6/30/2026 3:18 AM, Mikko wrote: >>>>>>> On 29/06/2026 16:29, 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. >>>>>>> >>>>>>> It does mean that something is missing that could be added to >>>>>>> enabe a proof of an unprovable sentence. >>>>>> >>>>>> Base-Extension Semantics (B-eS) allows that. >>>>>> It never was incomplete. It always did what it was defined to do. >>>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>>> >>>>> However, there are theories that reamain incomplete even when >>>>> more postolates are added, as long as there is a way to know >>>>> which sentences are included in the added postulates. Important >>>>> examples include Peano arithmetic and ZFC set theory. >>>> >>>> Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>> When we ask what is grounded in an atomic base of Q and we >>>> add axioms to Q to become PA we cheated in that we changed >>>> the original question rather than answered it. >>> >>> Yes, in a sense. But sometimes it is better to have a partial answer >>> rather than no answer at all. Of course Q with any additional >>> postulate is not Q but if the additional postulates are true about >>> natural numbers then the strengthened theory is still a theory of >>> natural numbers. PA is one such strengthened Q but still incomplete >>> and can be strengthened further. >> >> Is (∀x, S(x) ≠ x) provable or refutable in Q? >> Yes if you cheat, no if you don't cheat. > > As I already pointed out in another message, which you apparently > missed, it is neither. Thus PTS would say that (∀x, S(x) ≠ x) is semantically undefined in Q. > It is true about natural numbers but there > are other models of Rbinsons Q, and it is false in some of them. > A simple example is a model that incudes all natural numbers and > one additional element that is its own successor. > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 11:35 -0600 |
| Message-ID | <1128rsg$3f98v$3@dont-email.me> |
| In reply to | #646068 |
On 2026-07-03 09:38, olcott wrote: > On 7/3/2026 4:28 AM, Mikko wrote: >> On 02/07/2026 17:49, olcott wrote: >>> On 7/2/2026 1:55 AM, Mikko wrote: >>>> On 01/07/2026 18:16, olcott wrote: >>>>> On 7/1/2026 2:24 AM, Mikko wrote: >>>>>> On 30/06/2026 16:58, olcott wrote: >>>>>>> On 6/30/2026 3:18 AM, Mikko wrote: >>>>>>>> On 29/06/2026 16:29, 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. >>>>>>>> >>>>>>>> It does mean that something is missing that could be added to >>>>>>>> enabe a proof of an unprovable sentence. >>>>>>> >>>>>>> Base-Extension Semantics (B-eS) allows that. >>>>>>> It never was incomplete. It always did what it was defined to do. >>>>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>>>> >>>>>> However, there are theories that reamain incomplete even when >>>>>> more postolates are added, as long as there is a way to know >>>>>> which sentences are included in the added postulates. Important >>>>>> examples include Peano arithmetic and ZFC set theory. >>>>> >>>>> Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>> When we ask what is grounded in an atomic base of Q and we >>>>> add axioms to Q to become PA we cheated in that we changed >>>>> the original question rather than answered it. >>>> >>>> Yes, in a sense. But sometimes it is better to have a partial answer >>>> rather than no answer at all. Of course Q with any additional >>>> postulate is not Q but if the additional postulates are true about >>>> natural numbers then the strengthened theory is still a theory of >>>> natural numbers. PA is one such strengthened Q but still incomplete >>>> and can be strengthened further. >>> >>> Is (∀x, S(x) ≠ x) provable or refutable in Q? >>> Yes if you cheat, no if you don't cheat. >> >> As I already pointed out in another message, which you apparently >> missed, it is neither. > > Thus PTS would say that (∀x, S(x) ≠ x) is semantically > undefined in Q. And that differs from claiming that Q is incomplete exactly how...? -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 13:20 -0500 |
| Message-ID | <1128ui8$3jijc$1@dont-email.me> |
| In reply to | #646079 |
On 7/3/2026 12:35 PM, André G. Isaak wrote: > On 2026-07-03 09:38, olcott wrote: >> On 7/3/2026 4:28 AM, Mikko wrote: >>> On 02/07/2026 17:49, olcott wrote: >>>> On 7/2/2026 1:55 AM, Mikko wrote: >>>>> On 01/07/2026 18:16, olcott wrote: >>>>>> On 7/1/2026 2:24 AM, Mikko wrote: >>>>>>> On 30/06/2026 16:58, olcott wrote: >>>>>>>> On 6/30/2026 3:18 AM, Mikko wrote: >>>>>>>>> On 29/06/2026 16:29, 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. >>>>>>>>> >>>>>>>>> It does mean that something is missing that could be added to >>>>>>>>> enabe a proof of an unprovable sentence. >>>>>>>> >>>>>>>> Base-Extension Semantics (B-eS) allows that. >>>>>>>> It never was incomplete. It always did what it was defined to do. >>>>>>>> When Q is extended to become PA it stops being Q and becomes PA. >>>>>>> >>>>>>> However, there are theories that reamain incomplete even when >>>>>>> more postolates are added, as long as there is a way to know >>>>>>> which sentences are included in the added postulates. Important >>>>>>> examples include Peano arithmetic and ZFC set theory. >>>>>> >>>>>> Base-Extension Semantics (B-eS) seems to be essentially a cheat. >>>>>> When we ask what is grounded in an atomic base of Q and we >>>>>> add axioms to Q to become PA we cheated in that we changed >>>>>> the original question rather than answered it. >>>>> >>>>> Yes, in a sense. But sometimes it is better to have a partial answer >>>>> rather than no answer at all. Of course Q with any additional >>>>> postulate is not Q but if the additional postulates are true about >>>>> natural numbers then the strengthened theory is still a theory of >>>>> natural numbers. PA is one such strengthened Q but still incomplete >>>>> and can be strengthened further. >>>> >>>> Is (∀x, S(x) ≠ x) provable or refutable in Q? >>>> Yes if you cheat, no if you don't cheat. >>> >>> As I already pointed out in another message, which you apparently >>> missed, it is neither. >> >> Thus PTS would say that (∀x, S(x) ≠ x) is semantically >> undefined in Q. > > And that differs from claiming that Q is incomplete exactly how...? > The base definition of "incomplete" means that it is not operating according to design spec. terms of the art are often misleading, thus deceptive. When we start with an exhaustively complete list of empirical "atomic facts" of general knowledge (combining the analytic/synthetic distinction into one single system) then any expression x that cannot be derived by semantic entailment expressed syntactically in this system is not an element of the body of general knowledge expressed in language. -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 12:37 -0600 |
| Message-ID | <1128vgk$3jhio$2@dont-email.me> |
| In reply to | #646084 |
On 2026-07-03 12:20, olcott wrote: > On 7/3/2026 12:35 PM, André G. Isaak wrote: >> And that differs from claiming that Q is incomplete exactly how...? >> > > The base definition of "incomplete" means that it is > not operating according to design spec. And where exactly do you get this 'base definition' from? It certainly does not correspond to any definition that I am aware of. > terms of the art > are often misleading, thus deceptive. Terms of the art are what they are. They are precisely defined so there is no doubt about what they mean. So how can they therefore be misleading. It's colloquial terms that have the potential to be misleading since they are often not precisely defined. > When we start with an exhaustively complete list of > empirical "atomic facts" of general knowledge (combining > the analytic/synthetic distinction into one single system) > then any expression x that cannot be derived by semantic > entailment expressed syntactically in this system is > not an element of the body of general knowledge expressed > in language. Q isn't concerned with general knowledge (expressed in language or otherwise). It doesn't contain any notion of 'atomic fact'. So none of this is relevant to the question of whether Q is complete. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-03 15:13 -0500 |
| Message-ID | <112955e$3lm54$1@dont-email.me> |
| In reply to | #646088 |
On 7/3/2026 1:37 PM, André G. Isaak wrote: > On 2026-07-03 12:20, olcott wrote: >> On 7/3/2026 12:35 PM, André G. Isaak wrote: > >>> And that differs from claiming that Q is incomplete exactly how...? >>> >> >> The base definition of "incomplete" means that it is >> not operating according to design spec. > > And where exactly do you get this 'base definition' from? It certainly > does not correspond to any definition that I am aware of. > An motor vehicle that is missing a motor is incomplete. A bicycle that is missing a motor is NOT incomplete. Incomplete is an adjective that describes something missing essential parts, lacking necessary details, or left unfinished. >> terms of the art >> are often misleading, thus deceptive. > > Terms of the art are what they are. They are precisely defined so there > is no doubt about what they mean. So how can they therefore be > misleading. It's colloquial terms that have the potential to be > misleading since they are often not precisely defined. > These TOTA that diverge from their base meanings confuse people into thinking that computation is limited. The inability to correctly compute the numerical square-root of a dead chicken does not make computation incomplete or limited. >> When we start with an exhaustively complete list of >> empirical "atomic facts" of general knowledge (combining >> the analytic/synthetic distinction into one single system) >> then any expression x that cannot be derived by semantic >> entailment expressed syntactically in this system is >> not an element of the body of general knowledge expressed >> in language. > > Q isn't concerned with general knowledge (expressed in language or > otherwise). It doesn't contain any notion of 'atomic fact'. So none of > this is relevant to the question of whether Q is complete. > > André > It has the "atomic facts" of Q. Any expression that cannot reach these "atomic fact" axioms is ungrounded in the atomic base of 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).
[toc] | [prev] | [next] | [standalone]
| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-07-03 14:32 -0600 |
| Message-ID | <112969q$3jhio$5@dont-email.me> |
| In reply to | #646098 |
On 2026-07-03 14:13, olcott wrote: > On 7/3/2026 1:37 PM, André G. Isaak wrote: >> On 2026-07-03 12:20, olcott wrote: >>> On 7/3/2026 12:35 PM, André G. Isaak wrote: >> >>>> And that differs from claiming that Q is incomplete exactly how...? >>>> >>> >>> The base definition of "incomplete" means that it is >>> not operating according to design spec. >> >> And where exactly do you get this 'base definition' from? It certainly >> does not correspond to any definition that I am aware of. >> > > An motor vehicle that is missing a motor is incomplete. > A bicycle that is missing a motor is NOT incomplete. > > Incomplete is an adjective that describes something > missing essential parts, lacking necessary details, > or left unfinished. That's *one* definition of incomplete. It's hardly *the* definition and you have provided no reason to think that it is the 'base definition' whatever that might mean to you. >>> terms of the art >>> are often misleading, thus deceptive. >> >> Terms of the art are what they are. They are precisely defined so >> there is no doubt about what they mean. So how can they therefore be >> misleading. It's colloquial terms that have the potential to be >> misleading since they are often not precisely defined. >> > > These TOTA that diverge from their base meanings confuse > people into thinking that computation is limited. No. It confuses *you*. The vast majority of people are not confused by this. And stating that Q is incomplete has nothing to do with computation. Computation is a separate field. André > The > inability to correctly compute the numerical square-root > of a dead chicken does not make computation incomplete > or limited. > >>> When we start with an exhaustively complete list of >>> empirical "atomic facts" of general knowledge (combining >>> the analytic/synthetic distinction into one single system) >>> then any expression x that cannot be derived by semantic >>> entailment expressed syntactically in this system is >>> not an element of the body of general knowledge expressed >>> in language. >> >> Q isn't concerned with general knowledge (expressed in language or >> otherwise). It doesn't contain any notion of 'atomic fact'. So none of >> this is relevant to the question of whether Q is complete. >> >> André >> > > It has the "atomic facts" of Q. > Any expression that cannot reach these "atomic fact" > axioms is ungrounded in the atomic base of Q. > -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
[toc] | [prev] | [next] | [standalone]
Page 14 of 21 — ← Prev page 1 … 12 13 [14] 15 16 … 21 Next page →
Back to top | Article view | sci.math
csiph-web