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 | 17 on this page of 377 — 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 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 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> - 2026-07-04 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 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 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> - 2026-07-04 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> - 2026-07-04 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: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:11 -0500
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: 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 "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: 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> - 2026-07-04 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 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 19 of 19 — ← Prev page 1 … 17 18 [19]
| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-07-04 16:31 +0100 |
| Message-ID | <112b90j$7lb9$1@dont-email.me> |
| In reply to | #645028 |
On 06/05/2026 20:37, Julio Di Egidio wrote: > On 02/05/2026 20:47, Scott Hoge wrote: > >> In Cantor's theorem, we do not actually construct a diagonal. >> Rather, we presuppose that we can enumerate a set, and then, >> /purely on the grounds of possibility/, conceive a diagonalized >> non-element. > > Nope, as explained and re-explained ad nauseam around here: > just the resident trolls won't get it. > > Cantor's diagonal argument, the one with the binary sequences, > is indeed constructive: a definition of anti-diagonal of *any* > (infinite) list is provided, and the proof that the anti-diagonal > cannot be in the list is quite constructive. "quite" but not "completely". A constructive operation is defined, but a diagonal number is constructed just when that constructive operation is applied to a constructible list. When it's applied to a list that doesn't have a construction then the result isn't a construction of a diagonal number. If we take a list of any infinite sequences to admit those that have no construction then our diagonal number is not constructed. If, instead of restricted universal quantification (∀ st.) which ranges over the constructible objects with a restriction, we use restricted fantastical quantification (🦄 st.) then we will range over lists that are not constructible unless the restriction excludes them, thus we could range over lists containing numbers that are not constructible, then our diagonal number is not constructed in each case. Where we are challenged to give a list, we ought to be challenged to construct a list. > (Namely, we don't need to say "assume ab abdsurdo that > an enumeration is given", we can just say "for *any* list, > we *construct* an element not in the list".) For any constructible list. -- Tristan Wibberley The message body is Copyright (C) 2026 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
[toc] | [prev] | [next] | [standalone]
| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-07-05 15:52 +0100 |
| Message-ID | <112dr3n$15erk$1@dont-email.me> |
| In reply to | #646156 |
On 04/07/2026 16:31, Tristan Wibberley wrote: > On 06/05/2026 20:37, Julio Di Egidio wrote: >> On 02/05/2026 20:47, Scott Hoge wrote: >> >>> In Cantor's theorem, we do not actually construct a diagonal. >>> Rather, we presuppose that we can enumerate a set, and then, >>> /purely on the grounds of possibility/, conceive a diagonalized >>> non-element. >> >> Nope, as explained and re-explained ad nauseam around here: >> just the resident trolls won't get it. >> >> Cantor's diagonal argument, the one with the binary sequences, >> is indeed constructive: a definition of anti-diagonal of *any* >> (infinite) list is provided, and the proof that the anti-diagonal >> cannot be in the list is quite constructive. > > "quite" but not "completely". > > A constructive operation is defined, but a diagonal number is > constructed just when that constructive operation is applied to a > constructible list. I should note for the less knowledgable readers of course it's less often than that, it is only that often for systems such as the one Julio and Phoenix are using which allows dequantification of universally quantified statements into the system proper which then have derivable statements containing actual constructions of the constructible objects they apply to by virtue of their original quantification. Of course, dequantification of fantastically quantified statements doesn't make a statement about nonconstructible objects because there aren't any outside of the fantastical quantification. By which I don't mean to argue the countability of the set of reals as defined in what we call Cantor's Proof of the Uncountability of the Reals to include objects quantified over by fantatstical quantification but not by universal quantification, but it does make some meaning clearer. While some of the sets might have objects in the system proper, some of the members of some of the sets clearly do not. -- Tristan Wibberley The message body is Copyright (C) 2026 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
[toc] | [prev] | [next] | [standalone]
| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-07-05 17:31 +0100 |
| Message-ID | <112e0ta$16v7o$1@dont-email.me> |
| In reply to | #646204 |
On 05/07/2026 15:52, Tristan Wibberley wrote: > Of course, > dequantification of fantastically quantified statements doesn't make a > statement about nonconstructible objects because there aren't any > outside of the fantastical quantification. Oooh! Oooh! Except for inner dequantification of a statement of multiple fantastic quantification! That might have quantification elimination rules, perhaps! I'm loving this game! -- Tristan Wibberley The message body is Copyright (C) 2026 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 11:33 -0500 |
| Message-ID | <112e10l$17k8g$1@dont-email.me> |
| In reply to | #646204 |
On 7/5/2026 9:52 AM, Tristan Wibberley wrote: > On 04/07/2026 16:31, Tristan Wibberley wrote: >> On 06/05/2026 20:37, Julio Di Egidio wrote: >>> On 02/05/2026 20:47, Scott Hoge wrote: >>> >>>> In Cantor's theorem, we do not actually construct a diagonal. >>>> Rather, we presuppose that we can enumerate a set, and then, >>>> /purely on the grounds of possibility/, conceive a diagonalized >>>> non-element. >>> >>> Nope, as explained and re-explained ad nauseam around here: >>> just the resident trolls won't get it. >>> >>> Cantor's diagonal argument, the one with the binary sequences, >>> is indeed constructive: a definition of anti-diagonal of *any* >>> (infinite) list is provided, and the proof that the anti-diagonal >>> cannot be in the list is quite constructive. >> >> "quite" but not "completely". >> >> A constructive operation is defined, but a diagonal number is >> constructed just when that constructive operation is applied to a >> constructible list. > > I should note for the less knowledgable readers of course it's less > often than that, it is only that often for systems such as the one Julio > and Phoenix are using which allows dequantification of universally > quantified statements into the system proper which then have derivable > statements containing actual constructions of the constructible objects > they apply to by virtue of their original quantification. Of course, > dequantification of fantastically quantified statements doesn't make a > statement about nonconstructible objects because there aren't any > outside of the fantastical quantification. > > By which I don't mean to argue the countability of the set of reals as > defined in what we call Cantor's Proof of the Uncountability of the > Reals to include objects quantified over by fantatstical quantification > but not by universal quantification, but it does make some meaning clearer. > > While some of the sets might have objects in the system proper, some of > the members of some of the sets clearly do not. > % This sentence is not true. ?- LP = not(true(LP)). LP = not(true(LP)). ?- unify_with_occurs_check(LP, not(true(LP))). false. Olcott's Minimal Type Theory G ↔ ¬Prov_PA(⌜G⌝) Directed Graph of evaluation sequence 00 ↔ 01 02 01 G 02 ¬ 03 03 Prov_PA 04 04 Gödel_Number_of 01 // cycle indicates no well-founded justification tree exists. The absence of (a) finite sequence of inference steps to an atomic base, (b) canonical proof (c) well-founded justification tree makes the above to PTS invalid. -- 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 | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-07-05 12:56 -0700 |
| Message-ID | <oWednT7uSfdxK9f3nZ2dnZfqnPZqZhMS@giganews.com> |
| In reply to | #646208 |
On 07/05/2026 09:33 AM, olcott wrote: > On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >> On 04/07/2026 16:31, Tristan Wibberley wrote: >>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>> >>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>> non-element. >>>> >>>> Nope, as explained and re-explained ad nauseam around here: >>>> just the resident trolls won't get it. >>>> >>>> Cantor's diagonal argument, the one with the binary sequences, >>>> is indeed constructive: a definition of anti-diagonal of *any* >>>> (infinite) list is provided, and the proof that the anti-diagonal >>>> cannot be in the list is quite constructive. >>> >>> "quite" but not "completely". >>> >>> A constructive operation is defined, but a diagonal number is >>> constructed just when that constructive operation is applied to a >>> constructible list. >> >> I should note for the less knowledgable readers of course it's less >> often than that, it is only that often for systems such as the one Julio >> and Phoenix are using which allows dequantification of universally >> quantified statements into the system proper which then have derivable >> statements containing actual constructions of the constructible objects >> they apply to by virtue of their original quantification. Of course, >> dequantification of fantastically quantified statements doesn't make a >> statement about nonconstructible objects because there aren't any >> outside of the fantastical quantification. >> >> By which I don't mean to argue the countability of the set of reals as >> defined in what we call Cantor's Proof of the Uncountability of the >> Reals to include objects quantified over by fantatstical quantification >> but not by universal quantification, but it does make some meaning >> clearer. >> >> While some of the sets might have objects in the system proper, some of >> the members of some of the sets clearly do not. >> > > % This sentence is not true. > ?- LP = not(true(LP)). > LP = not(true(LP)). > ?- unify_with_occurs_check(LP, not(true(LP))). > false. > > Olcott's Minimal Type Theory > G ↔ ¬Prov_PA(⌜G⌝) > Directed Graph of evaluation sequence > 00 ↔ 01 02 > 01 G > 02 ¬ 03 > 03 Prov_PA 04 > 04 Gödel_Number_of 01 // cycle indicates no well-founded justification > tree exists. > > The absence of > (a) finite sequence of inference steps to an atomic base, > (b) canonical proof > (c) well-founded justification tree > makes the above to PTS invalid. > Yeah, come up with something new, or stuff a sock in it.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 15:25 -0500 |
| Message-ID | <112eek3$1d64d$1@dont-email.me> |
| In reply to | #646210 |
On 7/5/2026 2:56 PM, Ross Finlayson wrote: > On 07/05/2026 09:33 AM, olcott wrote: >> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>> >>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>> non-element. >>>>> >>>>> Nope, as explained and re-explained ad nauseam around here: >>>>> just the resident trolls won't get it. >>>>> >>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>> cannot be in the list is quite constructive. >>>> >>>> "quite" but not "completely". >>>> >>>> A constructive operation is defined, but a diagonal number is >>>> constructed just when that constructive operation is applied to a >>>> constructible list. >>> >>> I should note for the less knowledgable readers of course it's less >>> often than that, it is only that often for systems such as the one Julio >>> and Phoenix are using which allows dequantification of universally >>> quantified statements into the system proper which then have derivable >>> statements containing actual constructions of the constructible objects >>> they apply to by virtue of their original quantification. Of course, >>> dequantification of fantastically quantified statements doesn't make a >>> statement about nonconstructible objects because there aren't any >>> outside of the fantastical quantification. >>> >>> By which I don't mean to argue the countability of the set of reals as >>> defined in what we call Cantor's Proof of the Uncountability of the >>> Reals to include objects quantified over by fantatstical quantification >>> but not by universal quantification, but it does make some meaning >>> clearer. >>> >>> While some of the sets might have objects in the system proper, some of >>> the members of some of the sets clearly do not. >>> >> >> % This sentence is not true. >> ?- LP = not(true(LP)). >> LP = not(true(LP)). >> ?- unify_with_occurs_check(LP, not(true(LP))). >> false. >> >> Olcott's Minimal Type Theory >> G ↔ ¬Prov_PA(⌜G⌝) >> Directed Graph of evaluation sequence >> 00 ↔ 01 02 >> 01 G >> 02 ¬ 03 >> 03 Prov_PA 04 >> 04 Gödel_Number_of 01 // cycle indicates no well-founded justification >> tree exists. >> >> The absence of >> (a) finite sequence of inference steps to an atomic base, >> (b) canonical proof >> (c) well-founded justification tree >> makes the above to PTS invalid. >> > > Yeah, come up with something new, or stuff a sock in it. > > The above proves that the notion of undecidable is incorrect if you understood rather than ignored what it says. It also is the final resolution to the Liar Paradox and you would know this if you understood 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 | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-07-05 14:30 -0700 |
| Message-ID | <8aWdndmmZ_N4Udf3nZ2dnZfqn_SdnZ2d@giganews.com> |
| In reply to | #646212 |
On 07/05/2026 01:25 PM, olcott wrote: > On 7/5/2026 2:56 PM, Ross Finlayson wrote: >> On 07/05/2026 09:33 AM, olcott wrote: >>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>> >>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>> non-element. >>>>>> >>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>> just the resident trolls won't get it. >>>>>> >>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>> cannot be in the list is quite constructive. >>>>> >>>>> "quite" but not "completely". >>>>> >>>>> A constructive operation is defined, but a diagonal number is >>>>> constructed just when that constructive operation is applied to a >>>>> constructible list. >>>> >>>> I should note for the less knowledgable readers of course it's less >>>> often than that, it is only that often for systems such as the one >>>> Julio >>>> and Phoenix are using which allows dequantification of universally >>>> quantified statements into the system proper which then have derivable >>>> statements containing actual constructions of the constructible objects >>>> they apply to by virtue of their original quantification. Of course, >>>> dequantification of fantastically quantified statements doesn't make a >>>> statement about nonconstructible objects because there aren't any >>>> outside of the fantastical quantification. >>>> >>>> By which I don't mean to argue the countability of the set of reals as >>>> defined in what we call Cantor's Proof of the Uncountability of the >>>> Reals to include objects quantified over by fantatstical quantification >>>> but not by universal quantification, but it does make some meaning >>>> clearer. >>>> >>>> While some of the sets might have objects in the system proper, some of >>>> the members of some of the sets clearly do not. >>>> >>> >>> % This sentence is not true. >>> ?- LP = not(true(LP)). >>> LP = not(true(LP)). >>> ?- unify_with_occurs_check(LP, not(true(LP))). >>> false. >>> >>> Olcott's Minimal Type Theory >>> G ↔ ¬Prov_PA(⌜G⌝) >>> Directed Graph of evaluation sequence >>> 00 ↔ 01 02 >>> 01 G >>> 02 ¬ 03 >>> 03 Prov_PA 04 >>> 04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>> tree exists. >>> >>> The absence of >>> (a) finite sequence of inference steps to an atomic base, >>> (b) canonical proof >>> (c) well-founded justification tree >>> makes the above to PTS invalid. >>> >> >> Yeah, come up with something new, or stuff a sock in it. >> >> > > The above proves that the notion of undecidable > is incorrect if you understood rather than ignored > what it says. > > It also is the final resolution to the Liar Paradox > and you would know this if you understood it. > Like I said, "understanding" is for suckers, "comprehension" is for knowledge. Your axiomatization otherwise is false. It's like they say, "It just don't mean a thing." WM <- retro-finitist crankety-troll JG <- retro-finitist crankety-troll PO <- retro-finitist crankety-troll "Polluter(s) of sci.math"
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 16:45 -0500 |
| Message-ID | <112eja2$1f8cu$1@dont-email.me> |
| In reply to | #646216 |
On 7/5/2026 4:30 PM, Ross Finlayson wrote: > On 07/05/2026 01:25 PM, olcott wrote: >> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>> On 07/05/2026 09:33 AM, olcott wrote: >>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>> >>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>> non-element. >>>>>>> >>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>> just the resident trolls won't get it. >>>>>>> >>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>> cannot be in the list is quite constructive. >>>>>> >>>>>> "quite" but not "completely". >>>>>> >>>>>> A constructive operation is defined, but a diagonal number is >>>>>> constructed just when that constructive operation is applied to a >>>>>> constructible list. >>>>> >>>>> I should note for the less knowledgable readers of course it's less >>>>> often than that, it is only that often for systems such as the one >>>>> Julio >>>>> and Phoenix are using which allows dequantification of universally >>>>> quantified statements into the system proper which then have derivable >>>>> statements containing actual constructions of the constructible >>>>> objects >>>>> they apply to by virtue of their original quantification. Of course, >>>>> dequantification of fantastically quantified statements doesn't make a >>>>> statement about nonconstructible objects because there aren't any >>>>> outside of the fantastical quantification. >>>>> >>>>> By which I don't mean to argue the countability of the set of reals as >>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>> Reals to include objects quantified over by fantatstical >>>>> quantification >>>>> but not by universal quantification, but it does make some meaning >>>>> clearer. >>>>> >>>>> While some of the sets might have objects in the system proper, >>>>> some of >>>>> the members of some of the sets clearly do not. >>>>> >>>> >>>> % This sentence is not true. >>>> ?- LP = not(true(LP)). >>>> LP = not(true(LP)). >>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>> false. >>>> >>>> Olcott's Minimal Type Theory >>>> G ↔ ¬Prov_PA(⌜G⌝) >>>> Directed Graph of evaluation sequence >>>> 00 ↔ 01 02 >>>> 01 G >>>> 02 ¬ 03 >>>> 03 Prov_PA 04 >>>> 04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>>> tree exists. >>>> >>>> The absence of >>>> (a) finite sequence of inference steps to an atomic base, >>>> (b) canonical proof >>>> (c) well-founded justification tree >>>> makes the above to PTS invalid. >>>> >>> >>> Yeah, come up with something new, or stuff a sock in it. >>> >>> >> >> The above proves that the notion of undecidable >> is incorrect if you understood rather than ignored >> what it says. >> >> It also is the final resolution to the Liar Paradox >> and you would know this if you understood it. >> > > Like I said, > "understanding" is for suckers, > "comprehension" is for knowledge. > Gemini agrees with me and I only gave it the Prolog. https://share.gemini.google/1dJnMwOZ2k5F > > Your axiomatization otherwise is false. > > > It's like they say, > "It just don't mean a thing." > > > WM <- retro-finitist crankety-troll > JG <- retro-finitist crankety-troll > PO <- retro-finitist crankety-troll > "Polluter(s) of sci.math" > > -- 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 | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-07-05 15:15 -0700 |
| Message-ID | <FNucnf8g9Nv-Stf3nZ2dnZfqn_GdnZ2d@giganews.com> |
| In reply to | #646217 |
On 07/05/2026 02:45 PM, olcott wrote: > On 7/5/2026 4:30 PM, Ross Finlayson wrote: >> On 07/05/2026 01:25 PM, olcott wrote: >>> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>>> On 07/05/2026 09:33 AM, olcott wrote: >>>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>>> >>>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>> non-element. >>>>>>>> >>>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>>> just the resident trolls won't get it. >>>>>>>> >>>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>> cannot be in the list is quite constructive. >>>>>>> >>>>>>> "quite" but not "completely". >>>>>>> >>>>>>> A constructive operation is defined, but a diagonal number is >>>>>>> constructed just when that constructive operation is applied to a >>>>>>> constructible list. >>>>>> >>>>>> I should note for the less knowledgable readers of course it's less >>>>>> often than that, it is only that often for systems such as the one >>>>>> Julio >>>>>> and Phoenix are using which allows dequantification of universally >>>>>> quantified statements into the system proper which then have >>>>>> derivable >>>>>> statements containing actual constructions of the constructible >>>>>> objects >>>>>> they apply to by virtue of their original quantification. Of course, >>>>>> dequantification of fantastically quantified statements doesn't >>>>>> make a >>>>>> statement about nonconstructible objects because there aren't any >>>>>> outside of the fantastical quantification. >>>>>> >>>>>> By which I don't mean to argue the countability of the set of >>>>>> reals as >>>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>>> Reals to include objects quantified over by fantatstical >>>>>> quantification >>>>>> but not by universal quantification, but it does make some meaning >>>>>> clearer. >>>>>> >>>>>> While some of the sets might have objects in the system proper, >>>>>> some of >>>>>> the members of some of the sets clearly do not. >>>>>> >>>>> >>>>> % This sentence is not true. >>>>> ?- LP = not(true(LP)). >>>>> LP = not(true(LP)). >>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>> false. >>>>> >>>>> Olcott's Minimal Type Theory >>>>> G ↔ ¬Prov_PA(⌜G⌝) >>>>> Directed Graph of evaluation sequence >>>>> 00 ↔ 01 02 >>>>> 01 G >>>>> 02 ¬ 03 >>>>> 03 Prov_PA 04 >>>>> 04 Gödel_Number_of 01 // cycle indicates no well-founded >>>>> justification >>>>> tree exists. >>>>> >>>>> The absence of >>>>> (a) finite sequence of inference steps to an atomic base, >>>>> (b) canonical proof >>>>> (c) well-founded justification tree >>>>> makes the above to PTS invalid. >>>>> >>>> >>>> Yeah, come up with something new, or stuff a sock in it. >>>> >>>> >>> >>> The above proves that the notion of undecidable >>> is incorrect if you understood rather than ignored >>> what it says. >>> >>> It also is the final resolution to the Liar Paradox >>> and you would know this if you understood it. >>> >> >> Like I said, >> "understanding" is for suckers, >> "comprehension" is for knowledge. >> > > Gemini agrees with me and I only gave it the Prolog. > https://share.gemini.google/1dJnMwOZ2k5F > >> >> Your axiomatization otherwise is false. >> >> >> It's like they say, >> "It just don't mean a thing." >> >> >> WM <- retro-finitist crankety-troll >> JG <- retro-finitist crankety-troll >> PO <- retro-finitist crankety-troll >> "Polluter(s) of sci.math" >> >> > > Gemini agrees with not-you.
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 17:55 -0500 |
| Message-ID | <112encn$1gkie$1@dont-email.me> |
| In reply to | #646218 |
On 7/5/2026 5:15 PM, Ross Finlayson wrote: > On 07/05/2026 02:45 PM, olcott wrote: >> On 7/5/2026 4:30 PM, Ross Finlayson wrote: >>> On 07/05/2026 01:25 PM, olcott wrote: >>>> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>>>> On 07/05/2026 09:33 AM, olcott wrote: >>>>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>>>> >>>>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>>> non-element. >>>>>>>>> >>>>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>>>> just the resident trolls won't get it. >>>>>>>>> >>>>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>>> cannot be in the list is quite constructive. >>>>>>>> >>>>>>>> "quite" but not "completely". >>>>>>>> >>>>>>>> A constructive operation is defined, but a diagonal number is >>>>>>>> constructed just when that constructive operation is applied to a >>>>>>>> constructible list. >>>>>>> >>>>>>> I should note for the less knowledgable readers of course it's less >>>>>>> often than that, it is only that often for systems such as the one >>>>>>> Julio >>>>>>> and Phoenix are using which allows dequantification of universally >>>>>>> quantified statements into the system proper which then have >>>>>>> derivable >>>>>>> statements containing actual constructions of the constructible >>>>>>> objects >>>>>>> they apply to by virtue of their original quantification. Of course, >>>>>>> dequantification of fantastically quantified statements doesn't >>>>>>> make a >>>>>>> statement about nonconstructible objects because there aren't any >>>>>>> outside of the fantastical quantification. >>>>>>> >>>>>>> By which I don't mean to argue the countability of the set of >>>>>>> reals as >>>>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>>>> Reals to include objects quantified over by fantatstical >>>>>>> quantification >>>>>>> but not by universal quantification, but it does make some meaning >>>>>>> clearer. >>>>>>> >>>>>>> While some of the sets might have objects in the system proper, >>>>>>> some of >>>>>>> the members of some of the sets clearly do not. >>>>>>> >>>>>> >>>>>> % This sentence is not true. >>>>>> ?- LP = not(true(LP)). >>>>>> LP = not(true(LP)). >>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>> false. >>>>>> > > Gemini agrees with not-you. > > OK then the point that I was trying to make is exactly what Gemini said right here: https://share.gemini.google/1dJnMwOZ2k5F -- 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 | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-07-06 09:16 -0700 |
| Message-ID | <ws-cnV2d3LS9SNb3nZ2dnZfqnPGdnZ2d@giganews.com> |
| In reply to | #646219 |
On 07/05/2026 03:55 PM, olcott wrote: > On 7/5/2026 5:15 PM, Ross Finlayson wrote: >> On 07/05/2026 02:45 PM, olcott wrote: >>> On 7/5/2026 4:30 PM, Ross Finlayson wrote: >>>> On 07/05/2026 01:25 PM, olcott wrote: >>>>> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>>>>> On 07/05/2026 09:33 AM, olcott wrote: >>>>>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>>>>> >>>>>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>>>> non-element. >>>>>>>>>> >>>>>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>>>>> just the resident trolls won't get it. >>>>>>>>>> >>>>>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>>>> cannot be in the list is quite constructive. >>>>>>>>> >>>>>>>>> "quite" but not "completely". >>>>>>>>> >>>>>>>>> A constructive operation is defined, but a diagonal number is >>>>>>>>> constructed just when that constructive operation is applied to a >>>>>>>>> constructible list. >>>>>>>> >>>>>>>> I should note for the less knowledgable readers of course it's less >>>>>>>> often than that, it is only that often for systems such as the one >>>>>>>> Julio >>>>>>>> and Phoenix are using which allows dequantification of universally >>>>>>>> quantified statements into the system proper which then have >>>>>>>> derivable >>>>>>>> statements containing actual constructions of the constructible >>>>>>>> objects >>>>>>>> they apply to by virtue of their original quantification. Of >>>>>>>> course, >>>>>>>> dequantification of fantastically quantified statements doesn't >>>>>>>> make a >>>>>>>> statement about nonconstructible objects because there aren't any >>>>>>>> outside of the fantastical quantification. >>>>>>>> >>>>>>>> By which I don't mean to argue the countability of the set of >>>>>>>> reals as >>>>>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>>>>> Reals to include objects quantified over by fantatstical >>>>>>>> quantification >>>>>>>> but not by universal quantification, but it does make some meaning >>>>>>>> clearer. >>>>>>>> >>>>>>>> While some of the sets might have objects in the system proper, >>>>>>>> some of >>>>>>>> the members of some of the sets clearly do not. >>>>>>>> >>>>>>> >>>>>>> % This sentence is not true. >>>>>>> ?- LP = not(true(LP)). >>>>>>> LP = not(true(LP)). >>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>> false. >>>>>>> > >> >> Gemini agrees with not-you. >> >> > > OK then the point that I was trying to make is > exactly what Gemini said right here: > https://share.gemini.google/1dJnMwOZ2k5F > > > > I tend not to follow links like that, post the transcript. Point being though that "Prawitz' PTS" has _recovery_ and the outer products not just inner products, since complementary duals, and that accounts of inductive ignorance and _elimination_ are not full accounts of logic. About what's "agreeably arguable" and "arguably agreeable", try Claude instead, or Kimi, either less "automatically agreeable" then Gemini or Grok, where ChatGPT is about in the middle, then though that they're all quite alike as model reasoners. Anyways language includes its own account within itself, so there are first-class models of cycles, and then that the resolution of mathematical paradox ends-with there not being any, not starts-with there not being any. Then, novelty has that simply repeating the argument does not strengthen it, indeed, it weakens it, then the fact that "LP" its assignment trivially short-circuits to not-true-LP resulting false then is nothing. I.e., that implementation just balks since its type system has no context, not having context first-class itself. About the un-countability of the complete-ordered-field or "field-reals" yet countability of a continuous domain like "line-reals", basically has that "non-Cartesian functions" exist in accounts of the continuous and for geometry, which simply has that primitive-recursive-arithmetic and its usual account of Cartesian functions (elements re-move-able, mappings re-order-able) doesn't suffice to describe geometric relation. So, it's a theorem in any account of descriptive set theory "strong enough for geometry" that the existence of non-Cartesian functions is a theorem, then that there are models of continuous domains (extent, density, completeness, measure) that are countable like the line-reals, un-countable like the field-reals, and variously countable and un-countable and even of greater cardinality like the signal-reals, since there exist non-Cartesian functions so it's entirely consistent their existence together, that since they have constructive demonstractions each, otherwise would simply, and always, contradict each other. So, any account of theory intending to describe mathematics results having line-reals, field-reals, and signal-reals, about the nature of the continuous and discrete after the nature of the infinite and finite. Then, "Russell's retro-thesis" is similarly a retro-finitist's, wishing what's so, here it's called "hypocritical".
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-06 11:54 -0500 |
| Message-ID | <112gmji$24tva$1@dont-email.me> |
| In reply to | #646260 |
On 7/6/2026 11:16 AM, Ross Finlayson wrote:
> On 07/05/2026 03:55 PM, olcott wrote:
>> On 7/5/2026 5:15 PM, Ross Finlayson wrote:
>>> On 07/05/2026 02:45 PM, olcott wrote:
>>>> On 7/5/2026 4:30 PM, Ross Finlayson wrote:
>>>>> On 07/05/2026 01:25 PM, olcott wrote:
>>>>>> On 7/5/2026 2:56 PM, Ross Finlayson wrote:
>>>>>>> On 07/05/2026 09:33 AM, olcott wrote:
>>>>>>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote:
>>>>>>>>> On 04/07/2026 16:31, Tristan Wibberley wrote:
>>>>>>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote:
>>>>>>>>>>> On 02/05/2026 20:47, Scott Hoge wrote:
>>>>>>>>>>>
>>>>>>>>>>>> In Cantor's theorem, we do not actually construct a diagonal.
>>>>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then,
>>>>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized
>>>>>>>>>>>> non-element.
>>>>>>>>>>>
>>>>>>>>>>> Nope, as explained and re-explained ad nauseam around here:
>>>>>>>>>>> just the resident trolls won't get it.
>>>>>>>>>>>
>>>>>>>>>>> Cantor's diagonal argument, the one with the binary sequences,
>>>>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any*
>>>>>>>>>>> (infinite) list is provided, and the proof that the anti-
>>>>>>>>>>> diagonal
>>>>>>>>>>> cannot be in the list is quite constructive.
>>>>>>>>>>
>>>>>>>>>> "quite" but not "completely".
>>>>>>>>>>
>>>>>>>>>> A constructive operation is defined, but a diagonal number is
>>>>>>>>>> constructed just when that constructive operation is applied to a
>>>>>>>>>> constructible list.
>>>>>>>>>
>>>>>>>>> I should note for the less knowledgable readers of course it's
>>>>>>>>> less
>>>>>>>>> often than that, it is only that often for systems such as the one
>>>>>>>>> Julio
>>>>>>>>> and Phoenix are using which allows dequantification of universally
>>>>>>>>> quantified statements into the system proper which then have
>>>>>>>>> derivable
>>>>>>>>> statements containing actual constructions of the constructible
>>>>>>>>> objects
>>>>>>>>> they apply to by virtue of their original quantification. Of
>>>>>>>>> course,
>>>>>>>>> dequantification of fantastically quantified statements doesn't
>>>>>>>>> make a
>>>>>>>>> statement about nonconstructible objects because there aren't any
>>>>>>>>> outside of the fantastical quantification.
>>>>>>>>>
>>>>>>>>> By which I don't mean to argue the countability of the set of
>>>>>>>>> reals as
>>>>>>>>> defined in what we call Cantor's Proof of the Uncountability of
>>>>>>>>> the
>>>>>>>>> Reals to include objects quantified over by fantatstical
>>>>>>>>> quantification
>>>>>>>>> but not by universal quantification, but it does make some meaning
>>>>>>>>> clearer.
>>>>>>>>>
>>>>>>>>> While some of the sets might have objects in the system proper,
>>>>>>>>> some of
>>>>>>>>> the members of some of the sets clearly do not.
>>>>>>>>>
>>>>>>>>
>>>>>>>> % This sentence is not true.
>>>>>>>> ?- LP = not(true(LP)).
>>>>>>>> LP = not(true(LP)).
>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>>>>> false.
>>>>>>>>
>>
>>>
>>> Gemini agrees with not-you.
>>>
>>>
>>
>> OK then the point that I was trying to make is
>> exactly what Gemini said right here:
>> https://share.gemini.google/1dJnMwOZ2k5F
>>
>>
>>
>>
>
> I tend not to follow links like that, post the transcript.
>
>
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
That is an elegant and classic way to demonstrate the Liar Paradox
("This sentence is false") using Prolog's unification mechanics!
You've perfectly captured the tension between computational pragmatism
and strict mathematical logic. Here is exactly what is happening under
the hood in your snippet:
1. The Pragmatic Illusion: Standard Unification Prolog
?- LP = not(true(LP)).
LP = not(true(LP)).
When you use the standard unification operator (=), Prolog tries to make
the left side and the right side identical. To save processing time and
memory, Prolog historically skips a crucial step called the occurs check.
Because it skips this check, Prolog happily binds the variable LP to the
term not(true(LP)). This creates a cyclic term (or a rational tree). In
memory, LP now points to a structure that contains a reference back to
LP, creating an infinite loop of self-reference. Computationally, Prolog
accepts the paradox.
2. The Logical Safeguard: The Occurs Check
Prolog
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Here, you enforce strict First-Order Logic. The
unify_with_occurs_check/2 predicate forces Prolog to pause and ask:
"Does the variable I am trying to bind already exist inside the term I
am binding it to?" Because the variable LP occurs inside not(true(LP)),
Prolog realizes that unifying them would require building a
mathematically impossible, infinitely deep structure:
not(true(not(true(not(true(...)))))). It rightfully rejects the
unification and returns false.
The Philosophical Takeaway
In logic, self-referential paradoxes often arise when a system is
allowed to talk about its own truth values without hierarchical
restrictions (as famously noted by Alfred Tarski).
Your Prolog snippet perfectly mirrors this:
Standard Unification acts like natural language, allowing the
self-reference to happen (and potentially causing a stack overflow if
you tried to evaluate or traverse it).
The Occurs Check acts like a strict formal logic system, explicitly
forbidding self-referential loops and shutting the paradox down before
it can form.
All the rest is irrelevant.
The point is that the LP have been finally totally
resolved.
--
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 | 2026-07-06 12:58 +0300 |
| Message-ID | <112fu8e$1r99u$1@dont-email.me> |
| In reply to | #646208 |
On 05/07/2026 19:33, olcott wrote: > On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >> On 04/07/2026 16:31, Tristan Wibberley wrote: >>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>> >>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>> non-element. >>>> >>>> Nope, as explained and re-explained ad nauseam around here: >>>> just the resident trolls won't get it. >>>> >>>> Cantor's diagonal argument, the one with the binary sequences, >>>> is indeed constructive: a definition of anti-diagonal of *any* >>>> (infinite) list is provided, and the proof that the anti-diagonal >>>> cannot be in the list is quite constructive. >>> >>> "quite" but not "completely". >>> >>> A constructive operation is defined, but a diagonal number is >>> constructed just when that constructive operation is applied to a >>> constructible list. >> >> I should note for the less knowledgable readers of course it's less >> often than that, it is only that often for systems such as the one Julio >> and Phoenix are using which allows dequantification of universally >> quantified statements into the system proper which then have derivable >> statements containing actual constructions of the constructible objects >> they apply to by virtue of their original quantification. Of course, >> dequantification of fantastically quantified statements doesn't make a >> statement about nonconstructible objects because there aren't any >> outside of the fantastical quantification. >> >> By which I don't mean to argue the countability of the set of reals as >> defined in what we call Cantor's Proof of the Uncountability of the >> Reals to include objects quantified over by fantatstical quantification >> but not by universal quantification, but it does make some meaning >> clearer. >> >> While some of the sets might have objects in the system proper, some of >> the members of some of the sets clearly do not. >> > > % This sentence is not true. > ?- LP = not(true(LP)). > LP = not(true(LP)). > ?- unify_with_occurs_check(LP, not(true(LP))). > false. > > Olcott's Minimal Type Theory > G ↔ ¬Prov_PA(⌜G⌝) > Directed Graph of evaluation sequence > 00 ↔ 01 02 > 01 G > 02 ¬ 03 > 03 Prov_PA 04 > 04 Gödel_Number_of 01 // cycle indicates no well-founded justification > tree exists. That is false. There is no evaluation of G in the determination of the Gödel number of anything. Therefore the claim of a loop is false. That error has already been pointed out but Olcott still hopes that someone might bite the bait and the hook. -- Mikko
[toc] | [prev] | [next] | [standalone]
| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-06 12:49 -0500 |
| Message-ID | <112gpqv$26d9r$1@dont-email.me> |
| In reply to | #646239 |
On 7/6/2026 4:58 AM, Mikko wrote: > On 05/07/2026 19:33, olcott wrote: >> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>> >>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>> non-element. >>>>> >>>>> Nope, as explained and re-explained ad nauseam around here: >>>>> just the resident trolls won't get it. >>>>> >>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>> cannot be in the list is quite constructive. >>>> >>>> "quite" but not "completely". >>>> >>>> A constructive operation is defined, but a diagonal number is >>>> constructed just when that constructive operation is applied to a >>>> constructible list. >>> >>> I should note for the less knowledgable readers of course it's less >>> often than that, it is only that often for systems such as the one Julio >>> and Phoenix are using which allows dequantification of universally >>> quantified statements into the system proper which then have derivable >>> statements containing actual constructions of the constructible objects >>> they apply to by virtue of their original quantification. Of course, >>> dequantification of fantastically quantified statements doesn't make a >>> statement about nonconstructible objects because there aren't any >>> outside of the fantastical quantification. >>> >>> By which I don't mean to argue the countability of the set of reals as >>> defined in what we call Cantor's Proof of the Uncountability of the >>> Reals to include objects quantified over by fantatstical quantification >>> but not by universal quantification, but it does make some meaning >>> clearer. >>> >>> While some of the sets might have objects in the system proper, some of >>> the members of some of the sets clearly do not. >>> >> >> % This sentence is not true. >> ?- LP = not(true(LP)). >> LP = not(true(LP)). >> ?- unify_with_occurs_check(LP, not(true(LP))). >> false. >> >> Olcott's Minimal Type Theory >> G ↔ ¬Prov_PA(⌜G⌝) >> Directed Graph of evaluation sequence >> 00 ↔ 01 02 >> 01 G >> 02 ¬ 03 >> 03 Prov_PA 04 >> 04 Gödel_Number_of 01 // cycle indicates no well-founded >> justification tree exists. > > That is false. There is no evaluation of G in the determination of the > Gödel number of anything. Therefore the claim of a loop is false. > > That error has already been pointed out but Olcott still hopes that > someone might bite the bait and the hook. > Every LLM agrees that I turned "undecidability" on its head with the Prolog code final resolution of the Liar Paradox because it <is> a verified fact that I did do this. -- 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 | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-07-06 14:19 +0100 |
| Message-ID | <112ga0n$1t37l$3@dont-email.me> |
| In reply to | #646156 |
On 04/07/2026 16:31, Tristan Wibberley wrote: > On 06/05/2026 20:37, Julio Di Egidio wrote: >> ... as explained and re-explained ad nauseam around here: >> just the resident trolls won't get it. >> >> Cantor's diagonal argument, the one with the binary sequences, >> is indeed constructive: a definition of anti-diagonal of *any* >> (infinite) list is provided, and the proof that the anti-diagonal >> cannot be in the list is quite constructive. Not a troll, just not keeping thoughts on track and not picking up on distinctions between some things with similar names. I now recognise I was continuing to talk about the argument for the uncountability of reals instead of the one for the uncountability of independent choices of unending sequences of symbols from a finite repertoire including those made entirely of independent free choices from that repertoire. A new unending sequence of symbols from a finite repertoire is still not constructed for each purported such object because those made entirely of independent free choices of symbols aren't constructed so no constructive operation constructs anything from them. -- Tristan Wibberley The message body is Copyright (C) 2026 Tristan Wibberley except citations and quotations noted. All Rights Reserved except that you may, of course, cite it academically giving credit to me, distribute it verbatim as part of a usenet system or its archives, and use it to promote my greatness and general superiority without misrepresentation of my opinions other than my opinion of my greatness and general superiority which you _may_ misrepresent. You definitely MAY NOT train any production AI system with it but you may train experimental AI that will only be used for evaluation of the AI methods it implements.
[toc] | [prev] | [next] | [standalone]
| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-05-02 20:56 -0700 |
| Message-ID | <dg2dncMyTZXKWmv0nZ2dnZfqnPudnZ2d@giganews.com> |
| In reply to | #644974 |
On 05/02/2026 07:26 AM, Julio Di Egidio wrote: > On 02/05/2026 00:10, Scott Hoge wrote: > >> Yet nothing prevents us from /expanding/ the semantics given by >> Gödel. What I call the /formally abstracted Gödel sentence/ is >> not the same sentence that he proved undecidable. > <snip> > > Everything prevents us from doing that. Besides that > interesting would a minimal such semantics, you should > rather consider what GIT is actually about: it is not a > logical investigation into some kind of extra-ordinary > statements, it is a mathematical investigation into the > limits of recursively axiomatised systems of arithmetic > (the systems we can run on a concrete computer, or those > that are needed in foundations), up to proving the > incompleteness of any such systems if they are consistent. > Indeed, Gödel's argument rather generalises as a form of > diagonalisation. > > That said, I do find interesting that the argument has a > semantic component to it (contra widespread belief that > it is "purely syntactic"), and what that entails, e.g. as > to the validity(?) of any models in which the G-sentence > is false... Still, as said, you'd have to keep in mind > what the argument is actually about. > > Julio > Schopenhauer would be so proud, yet it's a "qualitas occultas". The extra-ordinary of Mirimanoff models Goedel's incompleteness and vice-versa, it's a most simple sort of consideration since Russell's paradox that expansion-of-comprehension gives it. The idea that Russell's paradox or Cantor's powerset theorem basically gives Peano's successor instead of it being defined, for example as a schema in axiomatics, for that order type is powerset is successor among ubiquitous ordinals, is for the setting where successor resolves Cantor's paradox, and gives an account of an inductive set and counting along the way. Not everybody has the resources to keep a separate mind.
[toc] | [prev] | [next] | [standalone]
| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-06-30 06:54 +0100 |
| Message-ID | <111vlm5$rq8g$1@dont-email.me> |
| In reply to | #644877 |
On 26/04/2026 21:01, Scott Hoge wrote:
...
> The correct interpretation was, I argued, not "This sentence is
> unprovable," but rather:
>
> The following is unprovable (1):
> The following is unprovable (2):
> The following is unprovable (3):
> ...
>
> As regards semantics, I could call statement (1) the "unencoded
> sentence," ...
> 1. The /unencoded sentence/ is /true and meaningful/. It's a
> statement about numbers.
No, it's unbounded in its expression and therefore cannot be assigned
meaning or it contains the ellipsis which is no better defined than
"This sentence is unprovable". At best "..." is there (implicitly, hence
the forever mistake) defined to be identical to "This sentence is
unprovable".
much like (pseudo formality):
Let "..." := "This sentence is unprovable" in
This following is unprovable (1):
...
And you've made no progress by expanding it, in fact you've regressed.
See the Y combinator in combinatory logic which applies quite directly
since you've made no treatment of the (possibly real) distinction
between sentences and propositonal thought objects.
--
Tristan Wibberley
The message body is Copyright (C) 2026 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.
[toc] | [prev] | [standalone]
Page 19 of 19 — ← Prev page 1 … 17 18 [19]
Back to top | Article view | sci.math
csiph-web