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Groups > comp.theory > #140926 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-04-20 11:57 -0500 |
| Last post | 2026-06-30 06:54 +0100 |
| Articles | 20 on this page of 391 — 16 participants |
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Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-27 09:50 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:39 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-28 21:52 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:14 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:18 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:45 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:56 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 22:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:57 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:02 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:17 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 07:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 09:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 13:33 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:40 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:50 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:47 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:11 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:28 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:50 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:52 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 15:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 17:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 17:09 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 19:05 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 18:39 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 20:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 19:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:03 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 00:02 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 08:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:48 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:17 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:12 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:21 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:38 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:46 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 15:22 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:11 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:49 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:13 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 09:36 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:42 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:21 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:35 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:54 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:09 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:44 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:23 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:31 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:42 -0500
Re: The simple essence of Proof Theoretic Semantics Alan Mackenzie <acm@muc.de> - 2026-07-01 19:18 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:56 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 15:05 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:53 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:13 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:37 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:50 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 16:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 16:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 17:15 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 18:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 22:36 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:00 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:29 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 23:43 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 22:59 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 23:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:57 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 09:51 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 12:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 13:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 14:22 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 14:33 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 15:52 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 15:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 16:54 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:12 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:23 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 16:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 17:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:13 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:32 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:47 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 17:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 18:59 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-02 18:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-02 20:03 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:22 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 10:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 11:50 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:18 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:36 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:40 -0400
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:47 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 17:37 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 21:58 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:05 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:19 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:37 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:43 -0400
The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-03 22:11 -0500
Re: The truth about the halting problem counter-example input dbush <dbush.mobile@gmail.com> - 2026-07-03 23:23 -0400
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:58 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-04 12:16 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:07 +0300
Re: The truth about the halting problem counter-example input olcott <polcott333@gmail.com> - 2026-07-06 10:18 -0500
Re: The truth about the halting problem counter-example input Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:45 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:58 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:07 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:11 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:27 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:48 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:46 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:55 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:24 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:30 -0500
Re: The simple essence of Proof Theoretic Semantics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:23 -0700
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 11:57 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:10 -0400
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 20:11 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 21:02 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 22:18 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:43 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 11:52 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:04 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:28 +0300
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:27 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:45 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 14:53 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:35 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 16:59 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:57 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:01 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 13:10 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:33 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 14:08 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-03 15:12 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:03 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 11:55 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:38 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:09 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:41 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:38 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:40 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:00 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-06 10:39 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:14 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:37 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 08:32 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-04 09:37 -0400
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:06 +0300
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:03 +0300
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:25 +0300
Terms-of-the-art are Liars that violate the preexisting order of knowledge olcott <polcott333@gmail.com> - 2026-07-06 10:54 -0500
Re: Terms-of-the-art are Liars that violate the preexisting order of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:22 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:11 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:27 +0300
Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-04 16:12 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-04 17:30 -0400
Re: Terms-Of-The-Art are Liars Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 14:59 +0100
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:23 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 10:19 -0400
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-05 11:29 -0500
Re: Terms-Of-The-Art are Liars dbush <dbush.mobile@gmail.com> - 2026-07-05 12:39 -0400
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 13:09 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:46 +0300
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 12:39 -0500
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:38 +0300
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-05 14:07 -0700
Re: Terms-Of-The-Art are Liars Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:38 +0300
Re: Terms-Of-The-Art are Liars dart200 <user7160@newsgrouper.org.invalid> - 2026-07-06 14:53 -0700
Re: Terms-Of-The-Art are Liars olcott <polcott333@gmail.com> - 2026-07-06 17:01 -0500
Re: Terms-Of-The-Art are Liars "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-07 15:36 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:17 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 10:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 10:07 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:27 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 11:56 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 13:12 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 12:54 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 14:03 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 14:08 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 15:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 15:13 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:00 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 16:53 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 17:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-06 17:39 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 19:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:52 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:47 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:45 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 11:44 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-30 07:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA 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 Andy Walker <anw@cuboid.co.uk> - 2026-04-28 16:21 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 19:48 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Andy Walker <anw@cuboid.co.uk> - 2026-04-29 16:34 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA wij <wyniijj5@gmail.com> - 2026-04-30 09:19 +0800
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Andy Walker <anw@cuboid.co.uk> - 2026-04-30 17:16 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-05-01 15:10 -0700
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 olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 16:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 15:52 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-05 17:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 11:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 12:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 15:25 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 14:30 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 16:45 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-05 15:15 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-05 17:55 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-06 09:16 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 11:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:58 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-06 12:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-08 12:00 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-06 14:19 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-04-27 15:35 -0700 |
| Message-ID | <AXOdnbEGCOJdeXL0nZ2dnZfqnPWdnZ2d@giganews.com> |
| In reply to | #141030 |
On 04/27/2026 02:03 PM, Alan Mackenzie wrote: > [ Followup-To: set ] > > In sci.math Scott Hoge <nospam@nospam.com> wrote: >> On 2026-04-27, olcott <polcott333@gmail.com> wrote: > >> [...] > >>>>> On 4/26/2026 3:01 PM, 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): >>>>>> ... > >>> The directed graph of the evaluation sequence of G >>> has a cycle preventing its evaluation from ever >>> terminating. > >>> If you have no idea what directed graphs are you will >>> never get this. If you always knew what directed graphs >>> of evaluation sequences that contain cycles are then >>> you rebuttal has always been pure dishonesty. > >> I learned what directed graphs were in high school. > >> It seems our views are somewhat in agreement, but my directed >> graph looks like this: > >> (D1) >> · ─→ · ─→ · ─→ · ─→ ... > > I strongly urge you to read and understand an actual proof of Gödel's > incompleteness theorem[*]. There are no looping or endless directed > graphs in these. Such notions result from misunderstandings by those > lacking formal training in mathematics. > > [*] I would suggest finding a second hand copy of "Gödel, Escher, Bach, > an Eternal Golden Braid" by Douglas Hofstadter, published around 1978 or > 1979. A proof of the incompleteness theorem is a central theme of the > book, which is witty and entertaining and well worth reading. > > Peter Olcott has never read and understood such a proof. Although not > particularly difficult, it is beyond his understanding. > > And please note, this theorem is _TRUE_. It has been proven rigorously > and verified by millions of students and academics over a very long time > period. > > Peter Olcott doesn't like it any more than he doesn't understand it, so > he pours scorn on the distinguished mathematicians of the past, falsely > claiming it to be false. I would urge you to be sceptical of _any_ so > called "result" emanating from him. > > [ .... ] > >> -- Scott Hoge > https://en.wikipedia.org/wiki/Zeno_machine
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| From | Julio Di Egidio <julio@diegidio.name> |
|---|---|
| Date | 2026-05-01 21:17 +0200 |
| Message-ID | <10t2u7p$1hf24$1@dont-email.me> |
| In reply to | #141028 |
On 27/04/2026 21:15, Scott Hoge wrote: > The formally abstracted sentence is closer in concept to "This > sentence is unprovable." The rendition "I am not provable" is informal, the very self-reference is informal (so your diagrams). OTOH, its arithmetization cannot be circular (or even divergent) or it's not arithmetic. Try and read the whole parer: Gödel does give a semantics (an interpretation), based on relations, and that semantics is essential to reaching the conclusion he reaches, and without circularity. Have fun, Julio
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-05-01 14:38 -0500 |
| Message-ID | <10t2vf4$1lhef$1@dont-email.me> |
| In reply to | #141066 |
On 5/1/2026 2:17 PM, Julio Di Egidio wrote: > On 27/04/2026 21:15, Scott Hoge wrote: > >> The formally abstracted sentence is closer in concept to "This >> sentence is unprovable." > The rendition "I am not provable" is informal, the very > self-reference is informal (so your diagrams). OTOH, its > arithmetization cannot be circular (or even divergent) or > it's not arithmetic. > > Try and read the whole parer: Gödel does give a semantics > (an interpretation), based on relations, and that semantics > is essential to reaching the conclusion he reaches, and > without circularity. > > Have fun, > > Julio > F ⊢ GF ↔ ¬ProvF(⌜GF⌝) https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom The above <is> an accepted simplification of Gödel's G. The below <is> a correct Directed Graph of evaluation sequence of this G. Do you know what a cycle is? Olcott's Minimal Type Theory G ↔ ¬Prov_PA(⌜G⌝) Directed Graph of evaluation sequence 00 ↔ 01 02 01 G 02 ¬ 03 03 Prov_PA 04 04 Gödel_Number_of 01 // cycle -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. This required establishing a new foundation
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| From | Scott Hoge <nospam@nospam.com> |
|---|---|
| Date | 2026-05-01 22:10 +0000 |
| Message-ID | <_w9JR.81647$kT.59546@fx16.ams4> |
| In reply to | #141066 |
On 2026-05-01, Julio Di Egidio <julio@diegidio.name> wrote: > On 27/04/2026 21:15, Scott Hoge wrote: >> The formally abstracted sentence is closer in concept to "This >> sentence is unprovable." > > The rendition "I am not provable" is informal, the very > self-reference is informal (so your diagrams). OTOH, its > arithmetization cannot be circular (or even divergent) or it's > not arithmetic. > > Try and read the whole [paper]: Gödel does give a semantics (an > interpretation), based on relations, and that semantics is > essential to reaching the conclusion he reaches, and without > circularity. Admittedly, I haven't thoroughly perused (let alone memorized) the entire paper. Committing it that well to memory would be an ongoing project. 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. Rather than a statement about its own Gödel encoding (which, as you correctly note, /does/ avoid circularity), it is an abstraction from all levels of encoding of all nestedly-encoded Gödel sentences. As for whether such an abstracted sentence is /informal/, I suppose this depends on how we classify an "informal sentence" in the foundations of mathematics. -- Scott Hoge
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| From | Julio Di Egidio <julio@diegidio.name> |
|---|---|
| Date | 2026-05-02 16:26 +0200 |
| Message-ID | <10t51ji$26cn4$1@dont-email.me> |
| In reply to | #141072 |
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
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-05-02 09:54 -0500 |
| Message-ID | <10t536d$282p2$1@dont-email.me> |
| In reply to | #141092 |
On 5/2/2026 9:26 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. Model Theoretic Semantics has never been the way that semantics actually works in reality. Proof Theoretic Semantics accurately captures the inherent truth that the entire body of knowledge expressed as finite strings has always only been expressed as relations between finite strings. By the theory of simple types I mean the doctrine which says that the objects of thought [expressed as finite strings] ... are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations, ... and that sentences of the form: " a has the property φ ", " b bears the relation R to c ", etc. are meaningless, if a, b, c, R, φ are not of types fitting together. https://en.wikipedia.org/wiki/History_of_type_theory#G%C3%B6del_1944 > 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 > -- 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. This required establishing a new foundation
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| From | Scott Hoge <nospam@nospam.com> |
|---|---|
| Date | 2026-05-02 18:47 +0000 |
| Message-ID | <cFrJR.53508$qu9.44050@fx08.ams4> |
| In reply to | #141092 |
On 2026-05-02, Julio Di Egidio <julio@diegidio.name> 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. >> >> [...] > > 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 [...] Theoretical physicist Roger Penrose has speculated that Gödel's Incompleteness Theorem relates to both quantum mechanics and consciousness. Based on the premise that consciousness depends on grasping undecidable and uncomputable truths, his theory is called Orchestrated Objective Reduction, or Orch-OR. Orch-OR proposes that consciousness arises from wave function collapse, and that it does so through attributes of the brain and of its biological constitution. These attributes allow the brain to transcend the limits of what a computer can do, which is where Gödel's incompleteness enters into the theory. > Indeed, Gödel's argument rather generalises as a form of > diagonalisation. > > [...] My view is that consciousness may require some kind of subjective indeterminism, whether in the form of "freedom," "choice," or "uncertainty," that permits the following characteristics: 1. Presence in the here-and-now. 2. Synthesis of a manifold of perception. 3. Undecidability of certain problems on the basis of "antinomy." 4. Thought regarding what /possibly/ may happen. By "synthesis of a manifold," I mean the binding and putting-together of multiple items of consciousness. I may see a desk, a chair, a computer, and some flash drives all drawn together in my field of vision. These presentations, or items of consciousness, carry signification insofar as it is logically possible for me to apprehend any one of them selectively. I may nudge the chair, insert one of the flash drives, or turn on the computer; freedom or uncertainty therefore seems tied to manifoldness of presentation. By "antinomy," I mean unsolvable questions about what happens beyond the limits of sensibility, such as at the infinite. 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. This links diagonalization to criterion (4) of consciousness. On the foregoing basis, we may conjecture that Penrose was in some sense right about Orch-OR. Gödel's theorem provides us with knowledge about the unknowability of what happens "at infinity" in the nested sequence of Gödel sentences. How this relates to what happens in the brain is another question that Penrose attempted to answer on the basis of microtubules. On the other hand, I think that /any/ physical phenomenon resulting from amplification from the microscopic world via self-reinforcing feedback loops may provide the link between Gödel sentences and human consciousness. -- Scott Hoge
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| From | dart200 <user7160@newsgrouper.org.invalid> |
|---|---|
| Date | 2026-05-02 12:06 -0700 |
| Message-ID | <10t5hvt$2c8h3$1@dont-email.me> |
| In reply to | #141097 |
On 5/2/26 11:47 AM, Scott Hoge wrote: > On 2026-05-02, Julio Di Egidio <julio@diegidio.name> 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. >>> >>> [...] >> >> 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 [...] > > Theoretical physicist Roger Penrose has speculated that Gödel's > Incompleteness Theorem relates to both quantum mechanics and > consciousness. Based on the premise that consciousness depends on > grasping undecidable and uncomputable truths, his theory is nah they aren't related we're subject to the halting problem as much any computer is and this can be demonstrated by placing a conscious entity in place of the decider. penrose is misinformed there unfortunately. > called Orchestrated Objective Reduction, or Orch-OR. i really like his and hameroff's work on consciousnesses otherwise, i don't think tying it to incompleteness is necessary > > Orch-OR proposes that consciousness arises from wave function > collapse, and that it does so through attributes of the brain and > of its biological constitution. These attributes allow the brain > to transcend the limits of what a computer can do, which is where > Gödel's incompleteness enters into the theory. > >> Indeed, Gödel's argument rather generalises as a form of >> diagonalisation. >> >> [...] > > My view is that consciousness may require some kind of subjective > indeterminism, whether in the form of "freedom," "choice," or > "uncertainty," that permits the following characteristics: > > 1. Presence in the here-and-now. > 2. Synthesis of a manifold of perception. > 3. Undecidability of certain problems on the basis of "antinomy." > 4. Thought regarding what /possibly/ may happen. > > By "synthesis of a manifold," I mean the binding and > putting-together of multiple items of consciousness. I may see a > desk, a chair, a computer, and some flash drives all drawn > together in my field of vision. These presentations, or items of > consciousness, carry signification insofar as it is logically > possible for me to apprehend any one of them selectively. I may > nudge the chair, insert one of the flash drives, or turn on the > computer; freedom or uncertainty therefore seems tied to > manifoldness of presentation. > > By "antinomy," I mean unsolvable questions about what happens > beyond the limits of sensibility, such as at the infinite. > > 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. This links diagonalization to criterion (4) of > consciousness. > > On the foregoing basis, we may conjecture that Penrose was in > some sense right about Orch-OR. Gödel's theorem provides us with > knowledge about the unknowability of what happens "at infinity" > in the nested sequence of Gödel sentences. > > How this relates to what happens in the brain is another question > that Penrose attempted to answer on the basis of microtubules. > On the other hand, I think that /any/ physical phenomenon > resulting from amplification from the microscopic world via > self-reinforcing feedback loops may provide the link between > Gödel sentences and human consciousness. > > -- Scott Hoge -- arising us out of the computing dark ages, please excuse my pseudo-pyscript, ~ the lil crank that could
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| From | Julio Di Egidio <julio@diegidio.name> |
|---|---|
| Date | 2026-05-06 21:37 +0200 |
| Message-ID | <10tg5ah$1dvta$1@dont-email.me> |
| In reply to | #141097 |
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. (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".) Just look it up. Here is my own rendition in Rocq: <https://gist.github.com/jp-diegidio/eb05f6265c38b35c85853514ed46ab47> > This links diagonalization to criterion (4) of consciousness. Rather, and to sum up, it links diagonalisation to the limits of physicalism... HTH, Julio
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| From | phoenix <j63840576@gmail.com> |
|---|---|
| Date | 2026-05-06 13:48 -0600 |
| Message-ID | <n61k90Fh012U1@mid.individual.net> |
| In reply to | #141152 |
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. > > (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".) > > Just look it up. Here is my own rendition in Rocq: > <https://gist.github.com/jp-diegidio/eb05f6265c38b35c85853514ed46ab47> > >> This links diagonalization to criterion (4) of consciousness. > > Rather, and to sum up, it links diagonalisation to the limits > of physicalism... > > HTH, > > Julio > I guess my question is this: If the diagonal sequence is inadequate, just what exactly is Cantor attempting to represent with the diagonal sequence at all? -- War in the east War in the west War up north War down south War War
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-05-06 12:59 -0700 |
| Message-ID | <Jm2dneEl3K0CAGb0nZ2dnZfqnPidnZ2d@giganews.com> |
| In reply to | #141154 |
On 05/06/2026 12:48 PM, phoenix wrote: > 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. >> >> (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".) >> >> Just look it up. Here is my own rendition in Rocq: >> <https://gist.github.com/jp-diegidio/eb05f6265c38b35c85853514ed46ab47> >> >>> This links diagonalization to criterion (4) of consciousness. >> >> Rather, and to sum up, it links diagonalisation to the limits >> of physicalism... >> >> HTH, >> >> Julio >> > > I guess my question is this: If the diagonal sequence is inadequate, > just what exactly is Cantor attempting to represent with the diagonal > sequence at all? > Maybe you should ask duBois-Reymond who Cantor cribbed it from, though accounts of the anti-diagonal are as old as making tables, then the nested-intervals idea is since the Pythagoreans who though made an account that the same would go for the rationals, then Cantor is acribed an "m-w" proof, though that would probably enough be Dirichlet's, for pigeonhole-principle. Saying that usually the account of anti-diagonalization is a proof by contradiction so it's non-constructive, is pretty usual. Then, getting into accounts otherwise of "quantifying over the universe" or the usual notions of "equivalence classes" themselves gets into class/set distinction, is about the domain of discourse of the universe of mathematical objects, this was a bit too much for Cantor to bear, though, his paradox or Cantor's paradox is the usual idea that theories with universes (or rather, "a" universe, which by definition makes sense only that way) make counter-examples. Then the powerset-theorem ends up just looking like grounds for increment itself and why Peano's integers follow from that instead of being "axiomatized", in what's a "constructive" account.
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| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-06-30 16:10 +0100 |
| Message-ID | <1120ma1$160pq$1@dont-email.me> |
| In reply to | #141154 |
On 06/05/2026 20:48, phoenix wrote: > I guess my question is this: If the diagonal sequence is inadequate, > just what exactly is Cantor attempting to represent with the diagonal > sequence at all? The outline is that the argument involves showing that /each/ and /every/ sequence of /all/ the reals in [0,1) (should there be any) can be mapped by a function to a real in [0,1) - perhaps a different one for each sequence - that could not have been in the sequence it was generated from. Thereby one shows that there is no sequence of /all/ the reals in [0,1) - a solution and the only solution. It is usually taught as "write a list of all the reals and then..." which is useless. It is usually also taught with steps missing since the formalisation of reals and limits that we trust today wasn't available to Cantor so his proof doesn't involve them. If someone were to bother making what would be a valid proof today instead of what would have been called a proof back /then/ they would use theorems about limits and either a constructive definition of the reals or a constructive definition of a constraint on constructions to those that define the reals (as they are conceived rather than later constructively explicated). -- 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.
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| From | Scott Hoge <nospam@nospam.com> |
|---|---|
| Date | 2026-05-07 01:12 +0000 |
| Message-ID | <8GRKR.193217$wA9.119953@fx06.ams4> |
| In reply to | #141152 |
On 2026-05-06, Julio Di Egidio <julio@diegidio.name> 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. An AI query seems to agree with you that constructiv-/ist/ mathematics permits Cantor's diagonal argument. I hadn't thought about that in detail. What I rather suggested was that Penrose's Orch-OR theory relates to our ability to cognize through the mode of /possibility/ (where a computer might be confined to /existence/ or /actuality/). That's why I said we do not /actually/ construct a diagonal -- we merely think it possible as we enumerate. Now compare a neuron to a computer chip. The computer chip is deterministic. The same, macroscopic input invariably yields the same, macroscopic output. Actuality gives way to actuality. In contrast, a neuron generates an impulse through an influx of ions across a voltage-gated ion channel. This behaves like a "butterfly effect" or "avalanche": the flow of ions provides a /self-reinforcing feedback loop/ on the basis of which infinitely small differences in the microscopic world may affect the neuron's "decision." A neuron thus conceives /possibility/ where a computer is restricted to what is actual. Then we just relate the infinitely small for the neuron to the infinitely distant for Gödel's theorem and diagonalization. That provides us with at least some basis for understanding the Orch-OR theory. -- Scott Hoge
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| 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 | #141152 |
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.
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| 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 | #142431 |
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.
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| 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 | #142476 |
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.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 11:33 -0500 |
| Message-ID | <112e10l$17k8g$1@dont-email.me> |
| In reply to | #142476 |
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).
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-07-05 12:56 -0700 |
| Message-ID | <oWednT7uSfdxK9f3nZ2dnZfqnPZqZhMS@giganews.com> |
| In reply to | #142480 |
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.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 15:25 -0500 |
| Message-ID | <112eek3$1d64d$1@dont-email.me> |
| In reply to | #142482 |
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).
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| 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 | #142484 |
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"
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