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Groups > sci.logic > #345584 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-04-20 11:57 -0500 |
| Last post | 2026-06-30 06:54 +0100 |
| Articles | 20 on this page of 340 — 15 participants |
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Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-20 11:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:41 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-21 08:33 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 02:48 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-22 11:19 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 08:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-23 10:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-23 08:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:33 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-22 17:06 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-22 20:21 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-04-24 00:19 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:12 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-04-24 21:14 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:25 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-22 18:29 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-20 17:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-20 12:32 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-27 07:53 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-27 09:50 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:39 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-28 21:52 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:14 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 08:29 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 11:05 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 13:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 12:29 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 13:33 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 14:47 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:02 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 15:06 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 14:58 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 15:18 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 16:39 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 16:25 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 17:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:03 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 18:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 17:45 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-29 19:37 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:01 -0600
The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 20:19 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 19:54 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:17 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-29 20:49 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 22:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:18 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:45 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 15:56 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:04 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 22:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:57 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:02 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:10 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:17 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:49 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 00:01 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 07:55 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 09:40 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 13:33 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:20 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:34 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:53 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-07-01 14:57 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:06 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 12:40 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 13:50 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 13:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 14:47 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:11 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:28 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 14:50 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 15:52 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 15:10 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 17:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 17:09 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 19:05 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 18:39 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 20:01 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-01 19:23 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-01 21:03 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 00:02 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 08:45 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 11:48 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:17 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:12 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:21 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 13:38 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:46 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 15:43 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-07-03 15:22 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-03 20:11 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:49 +0300
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-07-04 12:13 -0500
Re: The simple essence of Proof Theoretic Semantics Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:59 +0300
Re: The simple essence of Proof Theoretic Semantics 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 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 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 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> - 2026-07-03 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 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 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 cross@spitfire.i.gajendra.net (Dan Cross) - 2026-07-03 17:27 +0000
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 21:31 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 23:17 -0500
Re: The simple essence of Proof Theoretic Semantics dbush <dbush.mobile@gmail.com> - 2026-06-30 23:04 -0400
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 22:11 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 16:56 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:06 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:08 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 17:42 -0500
Re: The simple essence of Proof Theoretic Semantics André G. Isaak <agisaak@gm.invalid> - 2026-06-30 16:51 -0600
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-30 21:07 -0500
Re: The simple essence of Proof Theoretic Semantics olcott <polcott333@gmail.com> - 2026-06-29 21:26 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:18 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-06-30 08:58 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-01 10:16 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-02 09:49 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:28 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 10:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 11:35 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 13:20 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 12:37 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 15:13 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA André G. Isaak <agisaak@gm.invalid> - 2026-07-03 14:32 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-03 20:08 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:06 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 12:07 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dbush <dbush.mobile@gmail.com> - 2026-07-04 13:11 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-07-04 16:01 -0500
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 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 "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: 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 Mikko <mikko.levanto@iki.fi> - 2026-07-04 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-29 10:50 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA polcott <polcott333@gmail.com> - 2026-06-29 08:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-26 20:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-26 15:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:16 -0400
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:30 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 09:53 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 19:15 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 15:10 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-27 21:03 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 16:57 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:34 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:18 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:37 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-29 09:17 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-30 10:55 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-30 07:01 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-01 11:24 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 10:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 11:01 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:35 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:54 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 13:14 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 15:41 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 19:47 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-02 11:04 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 07:36 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:56 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:22 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 06:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 12:04 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:14 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-27 22:01 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-27 17:22 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-28 11:10 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-04-28 07:30 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Mikko <mikko.levanto@iki.fi> - 2026-04-29 10:11 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Alan Mackenzie <acm@muc.de> - 2026-04-28 10:35 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-04-29 14:27 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-01 21:17 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-01 12:34 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-01 14:38 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-01 22:10 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-02 16:26 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA olcott <polcott333@gmail.com> - 2026-05-02 09:54 -0500
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-02 18:47 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 12:06 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Julio Di Egidio <julio@diegidio.name> - 2026-05-06 21:37 +0200
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA phoenix <j63840576@gmail.com> - 2026-05-06 13:48 -0600
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-06 12:59 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 16:10 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Scott Hoge <nospam@nospam.com> - 2026-05-07 01:12 +0000
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 16:31 +0100
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA 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 Mikko <mikko.levanto@iki.fi> - 2026-07-06 12:58 +0300
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-02 20:56 -0700
Re: Within Proof Theoretic Semantics Gödel's G has no meaning in PA Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-06-30 06:54 +0100
Page 17 of 17 — ← Prev page 1 … 15 16 [17]
| From | Scott Hoge <nospam@nospam.com> |
|---|---|
| Date | 2026-05-02 18:47 +0000 |
| Message-ID | <cFrJR.53508$qu9.44050@fx08.ams4> |
| In reply to | #345788 |
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 | #345793 |
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 | #345793 |
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 | #345839 |
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 | #345840 |
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 | #345840 |
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 | #345839 |
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 | #345839 |
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 | #347496 |
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 | #347541 |
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 | #347541 |
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 | #347545 |
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 | #347547 |
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 | #347549 |
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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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 16:45 -0500 |
| Message-ID | <112eja2$1f8cu$1@dont-email.me> |
| In reply to | #347553 |
On 7/5/2026 4:30 PM, Ross Finlayson wrote: > On 07/05/2026 01:25 PM, olcott wrote: >> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>> On 07/05/2026 09:33 AM, olcott wrote: >>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>> >>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>> non-element. >>>>>>> >>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>> just the resident trolls won't get it. >>>>>>> >>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>> cannot be in the list is quite constructive. >>>>>> >>>>>> "quite" but not "completely". >>>>>> >>>>>> A constructive operation is defined, but a diagonal number is >>>>>> constructed just when that constructive operation is applied to a >>>>>> constructible list. >>>>> >>>>> I should note for the less knowledgable readers of course it's less >>>>> often than that, it is only that often for systems such as the one >>>>> Julio >>>>> and Phoenix are using which allows dequantification of universally >>>>> quantified statements into the system proper which then have derivable >>>>> statements containing actual constructions of the constructible >>>>> objects >>>>> they apply to by virtue of their original quantification. Of course, >>>>> dequantification of fantastically quantified statements doesn't make a >>>>> statement about nonconstructible objects because there aren't any >>>>> outside of the fantastical quantification. >>>>> >>>>> By which I don't mean to argue the countability of the set of reals as >>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>> Reals to include objects quantified over by fantatstical >>>>> quantification >>>>> but not by universal quantification, but it does make some meaning >>>>> clearer. >>>>> >>>>> While some of the sets might have objects in the system proper, >>>>> some of >>>>> the members of some of the sets clearly do not. >>>>> >>>> >>>> % This sentence is not true. >>>> ?- LP = not(true(LP)). >>>> LP = not(true(LP)). >>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>> false. >>>> >>>> Olcott's Minimal Type Theory >>>> G ↔ ¬Prov_PA(⌜G⌝) >>>> Directed Graph of evaluation sequence >>>> 00 ↔ 01 02 >>>> 01 G >>>> 02 ¬ 03 >>>> 03 Prov_PA 04 >>>> 04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>>> tree exists. >>>> >>>> The absence of >>>> (a) finite sequence of inference steps to an atomic base, >>>> (b) canonical proof >>>> (c) well-founded justification tree >>>> makes the above to PTS invalid. >>>> >>> >>> Yeah, come up with something new, or stuff a sock in it. >>> >>> >> >> The above proves that the notion of undecidable >> is incorrect if you understood rather than ignored >> what it says. >> >> It also is the final resolution to the Liar Paradox >> and you would know this if you understood it. >> > > Like I said, > "understanding" is for suckers, > "comprehension" is for knowledge. > Gemini agrees with me and I only gave it the Prolog. https://share.gemini.google/1dJnMwOZ2k5F > > Your axiomatization otherwise is false. > > > It's like they say, > "It just don't mean a thing." > > > WM <- retro-finitist crankety-troll > JG <- retro-finitist crankety-troll > PO <- retro-finitist crankety-troll > "Polluter(s) of sci.math" > > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-07-05 15:15 -0700 |
| Message-ID | <FNucnf8g9Nv-Stf3nZ2dnZfqn_GdnZ2d@giganews.com> |
| In reply to | #347554 |
On 07/05/2026 02:45 PM, olcott wrote: > On 7/5/2026 4:30 PM, Ross Finlayson wrote: >> On 07/05/2026 01:25 PM, olcott wrote: >>> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>>> On 07/05/2026 09:33 AM, olcott wrote: >>>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>>> >>>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>> non-element. >>>>>>>> >>>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>>> just the resident trolls won't get it. >>>>>>>> >>>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>> cannot be in the list is quite constructive. >>>>>>> >>>>>>> "quite" but not "completely". >>>>>>> >>>>>>> A constructive operation is defined, but a diagonal number is >>>>>>> constructed just when that constructive operation is applied to a >>>>>>> constructible list. >>>>>> >>>>>> I should note for the less knowledgable readers of course it's less >>>>>> often than that, it is only that often for systems such as the one >>>>>> Julio >>>>>> and Phoenix are using which allows dequantification of universally >>>>>> quantified statements into the system proper which then have >>>>>> derivable >>>>>> statements containing actual constructions of the constructible >>>>>> objects >>>>>> they apply to by virtue of their original quantification. Of course, >>>>>> dequantification of fantastically quantified statements doesn't >>>>>> make a >>>>>> statement about nonconstructible objects because there aren't any >>>>>> outside of the fantastical quantification. >>>>>> >>>>>> By which I don't mean to argue the countability of the set of >>>>>> reals as >>>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>>> Reals to include objects quantified over by fantatstical >>>>>> quantification >>>>>> but not by universal quantification, but it does make some meaning >>>>>> clearer. >>>>>> >>>>>> While some of the sets might have objects in the system proper, >>>>>> some of >>>>>> the members of some of the sets clearly do not. >>>>>> >>>>> >>>>> % This sentence is not true. >>>>> ?- LP = not(true(LP)). >>>>> LP = not(true(LP)). >>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>> false. >>>>> >>>>> Olcott's Minimal Type Theory >>>>> G ↔ ¬Prov_PA(⌜G⌝) >>>>> Directed Graph of evaluation sequence >>>>> 00 ↔ 01 02 >>>>> 01 G >>>>> 02 ¬ 03 >>>>> 03 Prov_PA 04 >>>>> 04 Gödel_Number_of 01 // cycle indicates no well-founded >>>>> justification >>>>> tree exists. >>>>> >>>>> The absence of >>>>> (a) finite sequence of inference steps to an atomic base, >>>>> (b) canonical proof >>>>> (c) well-founded justification tree >>>>> makes the above to PTS invalid. >>>>> >>>> >>>> Yeah, come up with something new, or stuff a sock in it. >>>> >>>> >>> >>> The above proves that the notion of undecidable >>> is incorrect if you understood rather than ignored >>> what it says. >>> >>> It also is the final resolution to the Liar Paradox >>> and you would know this if you understood it. >>> >> >> Like I said, >> "understanding" is for suckers, >> "comprehension" is for knowledge. >> > > Gemini agrees with me and I only gave it the Prolog. > https://share.gemini.google/1dJnMwOZ2k5F > >> >> Your axiomatization otherwise is false. >> >> >> It's like they say, >> "It just don't mean a thing." >> >> >> WM <- retro-finitist crankety-troll >> JG <- retro-finitist crankety-troll >> PO <- retro-finitist crankety-troll >> "Polluter(s) of sci.math" >> >> > > Gemini agrees with not-you.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-05 17:55 -0500 |
| Message-ID | <112encn$1gkie$1@dont-email.me> |
| In reply to | #347555 |
On 7/5/2026 5:15 PM, Ross Finlayson wrote: > On 07/05/2026 02:45 PM, olcott wrote: >> On 7/5/2026 4:30 PM, Ross Finlayson wrote: >>> On 07/05/2026 01:25 PM, olcott wrote: >>>> On 7/5/2026 2:56 PM, Ross Finlayson wrote: >>>>> On 07/05/2026 09:33 AM, olcott wrote: >>>>>> On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >>>>>>> On 04/07/2026 16:31, Tristan Wibberley wrote: >>>>>>>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>>>>>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>>>>>>> >>>>>>>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>>>>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>>>>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>>>>>>> non-element. >>>>>>>>> >>>>>>>>> Nope, as explained and re-explained ad nauseam around here: >>>>>>>>> just the resident trolls won't get it. >>>>>>>>> >>>>>>>>> Cantor's diagonal argument, the one with the binary sequences, >>>>>>>>> is indeed constructive: a definition of anti-diagonal of *any* >>>>>>>>> (infinite) list is provided, and the proof that the anti-diagonal >>>>>>>>> cannot be in the list is quite constructive. >>>>>>>> >>>>>>>> "quite" but not "completely". >>>>>>>> >>>>>>>> A constructive operation is defined, but a diagonal number is >>>>>>>> constructed just when that constructive operation is applied to a >>>>>>>> constructible list. >>>>>>> >>>>>>> I should note for the less knowledgable readers of course it's less >>>>>>> often than that, it is only that often for systems such as the one >>>>>>> Julio >>>>>>> and Phoenix are using which allows dequantification of universally >>>>>>> quantified statements into the system proper which then have >>>>>>> derivable >>>>>>> statements containing actual constructions of the constructible >>>>>>> objects >>>>>>> they apply to by virtue of their original quantification. Of course, >>>>>>> dequantification of fantastically quantified statements doesn't >>>>>>> make a >>>>>>> statement about nonconstructible objects because there aren't any >>>>>>> outside of the fantastical quantification. >>>>>>> >>>>>>> By which I don't mean to argue the countability of the set of >>>>>>> reals as >>>>>>> defined in what we call Cantor's Proof of the Uncountability of the >>>>>>> Reals to include objects quantified over by fantatstical >>>>>>> quantification >>>>>>> but not by universal quantification, but it does make some meaning >>>>>>> clearer. >>>>>>> >>>>>>> While some of the sets might have objects in the system proper, >>>>>>> some of >>>>>>> the members of some of the sets clearly do not. >>>>>>> >>>>>> >>>>>> % This sentence is not true. >>>>>> ?- LP = not(true(LP)). >>>>>> LP = not(true(LP)). >>>>>> ?- unify_with_occurs_check(LP, not(true(LP))). >>>>>> false. >>>>>> > > Gemini agrees with not-you. > > OK then the point that I was trying to make is exactly what Gemini said right here: https://share.gemini.google/1dJnMwOZ2k5F -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-07-06 12:58 +0300 |
| Message-ID | <112fu8e$1r99u$1@dont-email.me> |
| In reply to | #347545 |
On 05/07/2026 19:33, olcott wrote: > On 7/5/2026 9:52 AM, Tristan Wibberley wrote: >> On 04/07/2026 16:31, Tristan Wibberley wrote: >>> On 06/05/2026 20:37, Julio Di Egidio wrote: >>>> On 02/05/2026 20:47, Scott Hoge wrote: >>>> >>>>> In Cantor's theorem, we do not actually construct a diagonal. >>>>> Rather, we presuppose that we can enumerate a set, and then, >>>>> /purely on the grounds of possibility/, conceive a diagonalized >>>>> non-element. >>>> >>>> Nope, as explained and re-explained ad nauseam around here: >>>> just the resident trolls won't get it. >>>> >>>> Cantor's diagonal argument, the one with the binary sequences, >>>> is indeed constructive: a definition of anti-diagonal of *any* >>>> (infinite) list is provided, and the proof that the anti-diagonal >>>> cannot be in the list is quite constructive. >>> >>> "quite" but not "completely". >>> >>> A constructive operation is defined, but a diagonal number is >>> constructed just when that constructive operation is applied to a >>> constructible list. >> >> I should note for the less knowledgable readers of course it's less >> often than that, it is only that often for systems such as the one Julio >> and Phoenix are using which allows dequantification of universally >> quantified statements into the system proper which then have derivable >> statements containing actual constructions of the constructible objects >> they apply to by virtue of their original quantification. Of course, >> dequantification of fantastically quantified statements doesn't make a >> statement about nonconstructible objects because there aren't any >> outside of the fantastical quantification. >> >> By which I don't mean to argue the countability of the set of reals as >> defined in what we call Cantor's Proof of the Uncountability of the >> Reals to include objects quantified over by fantatstical quantification >> but not by universal quantification, but it does make some meaning >> clearer. >> >> While some of the sets might have objects in the system proper, some of >> the members of some of the sets clearly do not. >> > > % This sentence is not true. > ?- LP = not(true(LP)). > LP = not(true(LP)). > ?- unify_with_occurs_check(LP, not(true(LP))). > false. > > Olcott's Minimal Type Theory > G ↔ ¬Prov_PA(⌜G⌝) > Directed Graph of evaluation sequence > 00 ↔ 01 02 > 01 G > 02 ¬ 03 > 03 Prov_PA 04 > 04 Gödel_Number_of 01 // cycle indicates no well-founded justification > tree exists. That is false. There is no evaluation of G in the determination of the Gödel number of anything. Therefore the claim of a loop is false. That error has already been pointed out but Olcott still hopes that someone might bite the bait and the hook. -- Mikko
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| From | Ross Finlayson <ross.a.finlayson@gmail.com> |
|---|---|
| Date | 2026-05-02 20:56 -0700 |
| Message-ID | <dg2dncMyTZXKWmv0nZ2dnZfqnPudnZ2d@giganews.com> |
| In reply to | #345788 |
On 05/02/2026 07:26 AM, Julio Di Egidio wrote: > On 02/05/2026 00:10, Scott Hoge wrote: > >> Yet nothing prevents us from /expanding/ the semantics given by >> Gödel. What I call the /formally abstracted Gödel sentence/ is >> not the same sentence that he proved undecidable. > <snip> > > Everything prevents us from doing that. Besides that > interesting would a minimal such semantics, you should > rather consider what GIT is actually about: it is not a > logical investigation into some kind of extra-ordinary > statements, it is a mathematical investigation into the > limits of recursively axiomatised systems of arithmetic > (the systems we can run on a concrete computer, or those > that are needed in foundations), up to proving the > incompleteness of any such systems if they are consistent. > Indeed, Gödel's argument rather generalises as a form of > diagonalisation. > > That said, I do find interesting that the argument has a > semantic component to it (contra widespread belief that > it is "purely syntactic"), and what that entails, e.g. as > to the validity(?) of any models in which the G-sentence > is false... Still, as said, you'd have to keep in mind > what the argument is actually about. > > Julio > Schopenhauer would be so proud, yet it's a "qualitas occultas". The extra-ordinary of Mirimanoff models Goedel's incompleteness and vice-versa, it's a most simple sort of consideration since Russell's paradox that expansion-of-comprehension gives it. The idea that Russell's paradox or Cantor's powerset theorem basically gives Peano's successor instead of it being defined, for example as a schema in axiomatics, for that order type is powerset is successor among ubiquitous ordinals, is for the setting where successor resolves Cantor's paradox, and gives an account of an inductive set and counting along the way. Not everybody has the resources to keep a separate mind.
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| From | Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> |
|---|---|
| Date | 2026-06-30 06:54 +0100 |
| Message-ID | <111vlm5$rq8g$1@dont-email.me> |
| In reply to | #345688 |
On 26/04/2026 21:01, Scott Hoge wrote:
...
> The correct interpretation was, I argued, not "This sentence is
> unprovable," but rather:
>
> The following is unprovable (1):
> The following is unprovable (2):
> The following is unprovable (3):
> ...
>
> As regards semantics, I could call statement (1) the "unencoded
> sentence," ...
> 1. The /unencoded sentence/ is /true and meaningful/. It's a
> statement about numbers.
No, it's unbounded in its expression and therefore cannot be assigned
meaning or it contains the ellipsis which is no better defined than
"This sentence is unprovable". At best "..." is there (implicitly, hence
the forever mistake) defined to be identical to "This sentence is
unprovable".
much like (pseudo formality):
Let "..." := "This sentence is unprovable" in
This following is unprovable (1):
...
And you've made no progress by expanding it, in fact you've regressed.
See the Y combinator in combinatory logic which applies quite directly
since you've made no treatment of the (possibly real) distinction
between sentences and propositonal thought objects.
--
Tristan Wibberley
The message body is Copyright (C) 2026 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.
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