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Groups > sci.logic > #346714 > unrolled thread
| Started by | olcott <polcott333@gmail.com> |
|---|---|
| First post | 2026-06-17 16:14 -0500 |
| Last post | 2026-06-23 09:55 -0500 |
| Articles | 20 on this page of 368 — 11 participants |
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Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-17 16:14 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-18 14:35 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-19 10:23 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 07:46 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-19 20:28 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 15:50 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-19 21:05 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 16:24 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 15:57 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 18:30 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-19 22:27 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:20 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 21:35 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-19 22:27 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-19 23:04 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:29 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:22 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-19 21:40 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-20 11:05 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 14:02 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 15:17 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 12:30 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 15:45 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 15:03 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 16:17 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 16:03 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 17:17 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 13:02 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 12:57 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 18:51 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-21 20:16 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-22 10:13 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 08:13 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 11:01 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 13:12 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 12:28 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-23 08:39 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-23 09:29 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-24 11:23 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-24 15:19 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:09 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-25 08:43 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-26 09:17 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-26 07:59 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:16 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 12:48 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 13:36 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics phoenix <j63840576@gmail.com> - 2026-06-21 12:54 -0600
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-22 09:23 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 00:18 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 08:50 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-20 15:34 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 10:47 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-20 16:08 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 11:37 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-07-11 22:52 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 13:11 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 18:55 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-22 09:27 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 00:19 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 07:05 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-23 08:43 +0300
Re: Ross A. Finlayson, readings in (some of the) --- One-two punch Destroys Liars olcott <polcott333@gmail.com> - 2026-06-23 09:38 -0500
Re: Ross A. Finlayson, readings in (some of the) --- One-two punch Destroys Liars Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 08:53 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:51 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 14:04 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 16:39 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics phoenix <j63840576@gmail.com> - 2026-06-21 16:36 -0600
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 18:15 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics phoenix <j63840576@gmail.com> - 2026-06-21 18:32 -0600
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 19:44 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-22 10:46 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 10:16 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-23 08:49 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-23 09:40 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-24 12:45 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-24 15:23 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:14 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-25 08:47 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-26 09:23 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-26 08:02 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:19 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics polcott <polcott333@gmail.com> - 2026-06-27 10:34 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-21 21:27 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 00:22 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-21 21:16 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics André G. Isaak <agisaak@gm.invalid> - 2026-06-21 18:05 -0600
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 19:14 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-20 10:50 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:41 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 13:17 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 18:58 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-22 09:41 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 07:09 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-23 08:55 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-23 09:47 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-24 12:52 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-24 15:25 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:18 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-25 08:58 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-26 09:34 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-26 08:05 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:27 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics polcott <polcott333@gmail.com> - 2026-06-27 10:36 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:04 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-19 22:25 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:18 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 10:36 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 09:54 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 10:57 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 10:22 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 11:23 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 10:44 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 11:48 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 09:45 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 16:20 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 09:29 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 11:45 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 09:47 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 11:57 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 13:13 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 10:21 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 10:19 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-20 12:33 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics dbush <dbush.mobile@gmail.com> - 2026-06-20 13:36 -0400
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-20 12:13 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-20 19:48 +0000
Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-20 16:00 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction dbush <dbush.mobile@gmail.com> - 2026-06-20 17:19 -0400
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-20 16:30 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction dbush <dbush.mobile@gmail.com> - 2026-06-20 17:34 -0400
Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-20 17:26 -0500
Re: Disjunction introduction --- new premise from out of no where dbush <dbush.mobile@gmail.com> - 2026-06-20 20:11 -0400
Re: Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-20 19:26 -0500
Re: Disjunction introduction --- new premise from out of no where dbush <dbush.mobile@gmail.com> - 2026-06-20 20:29 -0400
Re: Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-20 20:06 -0500
Re: Disjunction introduction --- new premise from out of no where dbush <dbush.mobile@gmail.com> - 2026-06-20 21:28 -0400
Re: Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-20 20:32 -0500
Re: Disjunction introduction --- new premise from out of no where dbush <dbush.mobile@gmail.com> - 2026-06-20 21:38 -0400
Re: Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-20 20:48 -0500
Re: Disjunction introduction --- new premise from out of no where dbush <dbush.mobile@gmail.com> - 2026-06-20 21:51 -0400
Re: Disjunction introduction --- new premise from out of no where "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-06-25 12:54 -0700
Re: Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-25 16:01 -0500
Re: Disjunction introduction --- new premise from out of no where olcott <polcott333@gmail.com> - 2026-06-25 16:05 -0500
Re: Disjunction introduction --- new premise from out of no where Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2026-07-04 15:11 +0100
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Alan Mackenzie <acm@muc.de> - 2026-06-20 21:43 +0000
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-20 17:47 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Alan Mackenzie <acm@muc.de> - 2026-06-21 11:26 +0000
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-21 13:42 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction phoenix <j63840576@gmail.com> - 2026-06-21 12:53 -0600
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Alan Mackenzie <acm@muc.de> - 2026-06-21 20:04 +0000
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-21 15:42 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction André G. Isaak <agisaak@gm.invalid> - 2026-06-21 15:08 -0600
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-21 18:02 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge André G. Isaak <agisaak@gm.invalid> - 2026-06-21 18:02 -0600
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge -- Kristen Welker olcott <polcott333@gmail.com> - 2026-06-21 19:12 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge -- Kristen Welker dbush <dbush.mobile@gmail.com> - 2026-06-21 20:20 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-22 09:49 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-22 07:10 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-23 09:06 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-23 09:48 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 08:53 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-24 13:00 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-24 15:26 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:21 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-25 11:14 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-26 09:39 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 08:10 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 09:20 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 08:45 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 09:57 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 09:24 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 12:08 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 12:22 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 13:25 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 12:39 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 13:42 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 12:53 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 14:02 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge André G. Isaak <agisaak@gm.invalid> - 2026-06-26 12:14 -0600
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 13:48 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 14:51 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 14:07 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 15:17 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 14:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 15:55 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 17:01 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 18:08 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 17:58 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 19:18 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 19:05 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 20:23 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 19:48 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 21:11 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 20:39 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-26 21:51 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-26 21:00 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge polcott <polcott333@gmail.com> - 2026-06-27 08:34 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-27 11:05 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge polcott <polcott333@gmail.com> - 2026-06-27 10:47 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 15:37 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:47 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 19:24 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 22:21 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 19:25 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:22 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:17 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:48 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge polcott <polcott333@gmail.com> - 2026-06-27 10:45 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:38 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-27 10:35 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge polcott <polcott333@gmail.com> - 2026-06-27 10:43 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 14:01 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 13:27 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 14:29 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 13:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 14:39 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:01 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 15:04 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:16 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 15:23 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:40 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 15:54 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:04 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:11 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:17 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:22 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:27 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:30 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:36 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 15:52 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 16:59 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 16:24 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 17:50 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:11 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:15 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:18 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:21 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:29 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:33 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 17:44 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 18:53 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 18:27 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 19:33 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 18:59 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge dbush <dbush.mobile@gmail.com> - 2026-06-27 21:13 -0400
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 20:33 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 12:38 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 12:31 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-28 22:12 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-29 09:23 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-29 08:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-30 10:48 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-30 08:43 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:01 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-01 10:09 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-30 11:43 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-30 09:22 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-01 10:13 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-01 10:13 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-02 09:44 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-02 09:45 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-02 08:16 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-02 11:47 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:15 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-03 11:41 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-03 10:23 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-03 10:34 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-03 13:17 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-03 13:36 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-03 18:14 -0700
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:02 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-04 09:58 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-04 08:24 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-06 13:13 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-06 12:51 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:29 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-03 12:39 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-03 11:43 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-04 10:22 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-04 08:29 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Alan Mackenzie <acm@muc.de> - 2026-07-04 14:07 +0000
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-04 11:38 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Alan Mackenzie <acm@muc.de> - 2026-07-04 17:42 +0000
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-06 10:10 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-06 08:51 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-08 10:35 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-07-08 22:12 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-07-09 10:51 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:38 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge André G. Isaak <agisaak@gm.invalid> - 2026-06-27 13:40 -0600
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-27 14:46 -0500
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Mikko <mikko.levanto@iki.fi> - 2026-06-28 11:32 +0300
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge Alan Mackenzie <acm@muc.de> - 2026-06-22 12:47 +0000
Re: Readings in (some of the) foundations of mathematics --- tree of knowledge olcott <polcott333@gmail.com> - 2026-06-22 09:30 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Mikko <mikko.levanto@iki.fi> - 2026-06-22 10:23 +0300
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-22 09:44 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Alan Mackenzie <acm@muc.de> - 2026-06-22 15:22 +0000
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-22 10:36 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 12:07 -0700
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-22 14:21 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Mikko <mikko.levanto@iki.fi> - 2026-06-23 09:15 +0300
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-23 09:52 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 08:54 -0700
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 09:06 -0700
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-23 11:56 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Mikko <mikko.levanto@iki.fi> - 2026-06-24 13:06 +0300
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction olcott <polcott333@gmail.com> - 2026-06-24 16:31 -0500
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:49 +0300
Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction Mikko <mikko.levanto@iki.fi> - 2026-07-09 10:55 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 13:26 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-21 13:23 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-21 19:00 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-22 10:40 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 10:12 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-22 15:48 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 11:23 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-22 18:42 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 13:59 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-22 19:50 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 15:06 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Alan Mackenzie <acm@muc.de> - 2026-06-22 20:38 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 16:01 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 16:55 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 21:00 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 23:14 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 21:31 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-23 09:22 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 08:51 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-23 11:54 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 10:32 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-23 10:58 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-23 13:24 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:26 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-23 13:20 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Mikko <mikko.levanto@iki.fi> - 2026-06-24 13:13 +0300
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-24 16:33 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs phoenix <j63840576@gmail.com> - 2026-06-24 18:28 -0600
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Mikko <mikko.levanto@iki.fi> - 2026-06-25 10:29 +0300
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-25 11:16 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Mikko <mikko.levanto@iki.fi> - 2026-06-26 09:45 +0300
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-26 08:15 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Mikko <mikko.levanto@iki.fi> - 2026-06-27 11:13 +0300
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:25 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs polcott <polcott333@gmail.com> - 2026-06-27 10:53 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Mikko <mikko.levanto@iki.fi> - 2026-06-28 12:51 +0300
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-30 06:23 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-30 09:53 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-30 10:36 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-30 19:47 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-06-30 22:01 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-01 05:13 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs olcott <polcott333@gmail.com> - 2026-07-01 09:59 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-01 10:00 -0700
DAG of all general knowledge that can be expressed in Language olcott <polcott333@gmail.com> - 2026-07-01 12:57 -0500
Re: DAG of all general knowledge that can be expressed in Language Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-01 12:31 -0700
Re: DAG of all general knowledge that can be expressed in Language "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-01 12:37 -0700
Re: DAG of all general knowledge that can be expressed in Language Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-07-01 13:16 -0700
Re: DAG of all general knowledge that can be expressed in Language "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-07-01 18:59 -0700
Re: DAG of all general knowledge that can be expressed in Language olcott <polcott333@gmail.com> - 2026-07-01 14:51 -0500
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-27 07:19 -0700
Re: Ross A. Finlayson, readings in (some of the) --- cycles in directed graphs Python <python@cccp.invalid> - 2026-06-23 21:04 +0000
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 21:16 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-06-22 21:28 -0700
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-22 15:08 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-23 09:17 -0500
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics Mikko <mikko.levanto@iki.fi> - 2026-06-23 09:26 +0300
Re: Ross A. Finlayson, readings in (some of the) foundations of mathematics olcott <polcott333@gmail.com> - 2026-06-23 09:55 -0500
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-04 08:29 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112b1rf$5ie3$1@dont-email.me> |
| In reply to | #347469 |
On 7/4/2026 2:22 AM, Mikko wrote: > On 03/07/2026 19:43, olcott wrote: >> On 7/3/2026 4:39 AM, Mikko wrote: >>> On 02/07/2026 17:45, olcott wrote: >>>> >>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>> Cats are animals, if you disagree then you are necessarily incorrect. >>> >>> You may use "cats are animals" as a part of the defintion of "cat" >>> or of the definition of "animal" but not both. However, above you >>> have done neither, so you haven't excluded the possibility that >>> "cats are animals" is a statement about the real world. >> >> cats ⊂ animals >> animals ⊃ cats >> They prove each other, thus only one of them is >> an atomic fact. Atomic facts are facts that cannot >> be derived from other facts. >> >> In my actual system cats would inherit from animals >> in the knowledge ontology / simple type hierarchy. > > In that case the sentence "cats are animals" does not tell anyting > about the real world. > It tells us exactly one thing. A complete finite list of "atomic facts" of general knowledge tells us everything that can be expressed in language. This finite list also has all of the kinds of relations between these facts. -- 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 | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2026-07-04 14:07 +0000 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112b42o$1s60$1@news.muc.de> |
| In reply to | #347488 |
[ Followup-To: set ] In sci.math olcott <polcott333@gmail.com> wrote: [ .... ] > A complete finite list of "atomic facts" of general > knowledge tells us everything that can be expressed > in language. This finite list also has all of the > kinds of relations between these facts. Seems doubtful. Falsehoods can also be expressed in language, together with that vast trove of expressions which are neither true nor false. In fact, when it comes to "everything that can be expressed in language", a list of "atomic facts" would appear to be unhelpful, just as much as a list of "atomic falsehoods" would be, whatever that might mean. > -- > Copyright 2026 Olcott -- Alan Mackenzie (Nuremberg, Germany).
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-04 11:38 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112bcu8$9hna$1@dont-email.me> |
| In reply to | #347493 |
On 7/4/2026 9:07 AM, Alan Mackenzie wrote: > [ Followup-To: set ] > > In sci.math olcott <polcott333@gmail.com> wrote: > > [ .... ] > >> A complete finite list of "atomic facts" of general >> knowledge tells us everything that can be expressed >> in language. This finite list also has all of the >> kinds of relations between these facts. > > Seems doubtful. Falsehoods can also be expressed in language, together > with that vast trove of expressions which are neither true nor false. In > fact, when it comes to "everything that can be expressed in language", a > list of "atomic facts" would appear to be unhelpful, just as much as a > list of "atomic falsehoods" would be, whatever that might mean. > A complete finite list of "atomic facts" of general knowledge only includes true truth bearers and only facts that cannot be derived from anything else. This excludes falsehoods and expressions that are neither true nor false. It is the axiomatic basis of knowledge of the world. >> -- >> Copyright 2026 Olcott > -- 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 | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2026-07-04 17:42 +0000 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112bgmf$1s60$2@news.muc.de> |
| In reply to | #347497 |
[ Followup-To: set ] In comp.theory olcott <polcott333@gmail.com> wrote: > On 7/4/2026 9:07 AM, Alan Mackenzie wrote: > > In sci.math olcott <polcott333@gmail.com> wrote: > > [ .... ] > >> A complete finite list of "atomic facts" of general > >> knowledge tells us everything that can be expressed > >> in language. This finite list also has all of the > >> kinds of relations between these facts. > > Seems doubtful. Falsehoods can also be expressed in language, together > > with that vast trove of expressions which are neither true nor false. In > > fact, when it comes to "everything that can be expressed in language", a > > list of "atomic facts" would appear to be unhelpful, just as much as a > > list of "atomic falsehoods" would be, whatever that might mean. > A complete finite list of "atomic facts" of general knowledge > only includes true truth bearers and only facts that cannot > be derived from anything else. This excludes falsehoods and > expressions that are neither true nor false. It is the axiomatic > basis of knowledge of the world. WHOOOOSHHH! (The loud noise of you completely missing the point of my post.) Let's start again. A complete list of "atomic facts", were such possible, would tell you NOTHING about what can be expressed in language. Your favourite nonsense quote about green thoughts sleeping furiously is just as expressible as "Olcott is intelligent" or "the halting problem is solvable". Expressibility has no connection with truth or falsehood or provability. > -- > Copyright 2026 Olcott -- Alan Mackenzie (Nuremberg, Germany).
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-07-06 10:10 +0300 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112fkde$1oe0m$1@dont-email.me> |
| In reply to | #347488 |
On 04/07/2026 16:29, olcott wrote: > On 7/4/2026 2:22 AM, Mikko wrote: >> On 03/07/2026 19:43, olcott wrote: >>> On 7/3/2026 4:39 AM, Mikko wrote: >>>> On 02/07/2026 17:45, olcott wrote: >>>>> >>>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>>> Cats are animals, if you disagree then you are necessarily incorrect. >>>> >>>> You may use "cats are animals" as a part of the defintion of "cat" >>>> or of the definition of "animal" but not both. However, above you >>>> have done neither, so you haven't excluded the possibility that >>>> "cats are animals" is a statement about the real world. >>> >>> cats ⊂ animals >>> animals ⊃ cats >>> They prove each other, thus only one of them is >>> an atomic fact. Atomic facts are facts that cannot >>> be derived from other facts. >>> >>> In my actual system cats would inherit from animals >>> in the knowledge ontology / simple type hierarchy. >> >> In that case the sentence "cats are animals" does not tell anyting >> about the real world. > > It tells us exactly one thing. Which thing? If the meanings of the words are already known it does not tell anything that is not obvious from those meanings. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-06 08:51 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112gbt4$217j2$1@dont-email.me> |
| In reply to | #347557 |
On 7/6/2026 2:10 AM, Mikko wrote: > On 04/07/2026 16:29, olcott wrote: >> On 7/4/2026 2:22 AM, Mikko wrote: >>> On 03/07/2026 19:43, olcott wrote: >>>> On 7/3/2026 4:39 AM, Mikko wrote: >>>>> On 02/07/2026 17:45, olcott wrote: >>>>>> >>>>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>>>> Cats are animals, if you disagree then you are necessarily incorrect. >>>>> >>>>> You may use "cats are animals" as a part of the defintion of "cat" >>>>> or of the definition of "animal" but not both. However, above you >>>>> have done neither, so you haven't excluded the possibility that >>>>> "cats are animals" is a statement about the real world. >>>> >>>> cats ⊂ animals >>>> animals ⊃ cats >>>> They prove each other, thus only one of them is >>>> an atomic fact. Atomic facts are facts that cannot >>>> be derived from other facts. >>>> >>>> In my actual system cats would inherit from animals >>>> in the knowledge ontology / simple type hierarchy. >>> >>> In that case the sentence "cats are animals" does not tell anyting >>> about the real world. >> >> It tells us exactly one thing. > > Which thing? If the meanings of the words are already known it does > not tell anything that is not obvious from those meanings. > "cats" ⊂ "animals" "animals" ⊃ "cats" Is to be construed as the first time that anyone has every seen those finite strings. We are defining the English meaning of words to a computer program that starts as a completely blank slate. The end result of defining every "atomic fact" of empirical general knowledge is that the computer has complete general knowledge of the world. -- 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 | 2026-07-08 10:35 +0300 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112kuj9$3e7um$1@dont-email.me> |
| In reply to | #347584 |
On 06/07/2026 16:51, olcott wrote: > On 7/6/2026 2:10 AM, Mikko wrote: >> On 04/07/2026 16:29, olcott wrote: >>> On 7/4/2026 2:22 AM, Mikko wrote: >>>> On 03/07/2026 19:43, olcott wrote: >>>>> On 7/3/2026 4:39 AM, Mikko wrote: >>>>>> On 02/07/2026 17:45, olcott wrote: >>>>>>> >>>>>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>>>>> Cats are animals, if you disagree then you are necessarily >>>>>>> incorrect. >>>>>> >>>>>> You may use "cats are animals" as a part of the defintion of "cat" >>>>>> or of the definition of "animal" but not both. However, above you >>>>>> have done neither, so you haven't excluded the possibility that >>>>>> "cats are animals" is a statement about the real world. >>>>> >>>>> cats ⊂ animals >>>>> animals ⊃ cats >>>>> They prove each other, thus only one of them is >>>>> an atomic fact. Atomic facts are facts that cannot >>>>> be derived from other facts. >>>>> >>>>> In my actual system cats would inherit from animals >>>>> in the knowledge ontology / simple type hierarchy. >>>> >>>> In that case the sentence "cats are animals" does not tell anyting >>>> about the real world. >>> >>> It tells us exactly one thing. >> >> Which thing? If the meanings of the words are already known it does >> not tell anything that is not obvious from those meanings. > > "cats" ⊂ "animals" > "animals" ⊃ "cats" > Is to be construed as the first time that anyone > has every seen those finite strings. > > We are defining the English meaning of words > to a computer program that starts as a completely > blank slate. > > The end result of defining every "atomic fact" > of empirical general knowledge is that the computer > has complete general knowledge of the world. The computer does not know that there is a real world. It just does wbat it is made to do. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-07-08 22:12 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112n3iv$3j7p$1@dont-email.me> |
| In reply to | #347683 |
On 7/8/2026 2:35 AM, Mikko wrote: > On 06/07/2026 16:51, olcott wrote: >> On 7/6/2026 2:10 AM, Mikko wrote: >>> On 04/07/2026 16:29, olcott wrote: >>>> On 7/4/2026 2:22 AM, Mikko wrote: >>>>> On 03/07/2026 19:43, olcott wrote: >>>>>> On 7/3/2026 4:39 AM, Mikko wrote: >>>>>>> On 02/07/2026 17:45, olcott wrote: >>>>>>>> >>>>>>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>>>>>> Cats are animals, if you disagree then you are necessarily >>>>>>>> incorrect. >>>>>>> >>>>>>> You may use "cats are animals" as a part of the defintion of "cat" >>>>>>> or of the definition of "animal" but not both. However, above you >>>>>>> have done neither, so you haven't excluded the possibility that >>>>>>> "cats are animals" is a statement about the real world. >>>>>> >>>>>> cats ⊂ animals >>>>>> animals ⊃ cats >>>>>> They prove each other, thus only one of them is >>>>>> an atomic fact. Atomic facts are facts that cannot >>>>>> be derived from other facts. >>>>>> >>>>>> In my actual system cats would inherit from animals >>>>>> in the knowledge ontology / simple type hierarchy. >>>>> >>>>> In that case the sentence "cats are animals" does not tell anyting >>>>> about the real world. >>>> >>>> It tells us exactly one thing. >>> >>> Which thing? If the meanings of the words are already known it does >>> not tell anything that is not obvious from those meanings. >> >> "cats" ⊂ "animals" >> "animals" ⊃ "cats" >> Is to be construed as the first time that anyone >> has every seen those finite strings. >> >> We are defining the English meaning of words >> to a computer program that starts as a completely >> blank slate. >> >> The end result of defining every "atomic fact" >> of empirical general knowledge is that the computer >> has complete general knowledge of the world. > The computer does not know that there is a real world. > It just does wbat it is made to do. > As I have said many many dozens of times we encode all of the "basic facts" of general knowledge both empirical (the facts of the actual world) and analytical knowledge into a finite set of axioms. -- 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 | 2026-07-09 10:51 +0300 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <112njud$7ndt$2@dont-email.me> |
| In reply to | #347708 |
On 09/07/2026 06:12, olcott wrote: > On 7/8/2026 2:35 AM, Mikko wrote: >> On 06/07/2026 16:51, olcott wrote: >>> On 7/6/2026 2:10 AM, Mikko wrote: >>>> On 04/07/2026 16:29, olcott wrote: >>>>> On 7/4/2026 2:22 AM, Mikko wrote: >>>>>> On 03/07/2026 19:43, olcott wrote: >>>>>>> On 7/3/2026 4:39 AM, Mikko wrote: >>>>>>>> On 02/07/2026 17:45, olcott wrote: >>>>>>>>> >>>>>>>>> https://en.wikipedia.org/wiki/Stipulative_definition >>>>>>>>> Cats are animals, if you disagree then you are necessarily >>>>>>>>> incorrect. >>>>>>>> >>>>>>>> You may use "cats are animals" as a part of the defintion of "cat" >>>>>>>> or of the definition of "animal" but not both. However, above you >>>>>>>> have done neither, so you haven't excluded the possibility that >>>>>>>> "cats are animals" is a statement about the real world. >>>>>>> >>>>>>> cats ⊂ animals >>>>>>> animals ⊃ cats >>>>>>> They prove each other, thus only one of them is >>>>>>> an atomic fact. Atomic facts are facts that cannot >>>>>>> be derived from other facts. >>>>>>> >>>>>>> In my actual system cats would inherit from animals >>>>>>> in the knowledge ontology / simple type hierarchy. >>>>>> >>>>>> In that case the sentence "cats are animals" does not tell anyting >>>>>> about the real world. >>>>> >>>>> It tells us exactly one thing. >>>> >>>> Which thing? If the meanings of the words are already known it does >>>> not tell anything that is not obvious from those meanings. >>> >>> "cats" ⊂ "animals" >>> "animals" ⊃ "cats" >>> Is to be construed as the first time that anyone >>> has every seen those finite strings. >>> >>> We are defining the English meaning of words >>> to a computer program that starts as a completely >>> blank slate. >>> >>> The end result of defining every "atomic fact" >>> of empirical general knowledge is that the computer >>> has complete general knowledge of the world. >> The computer does not know that there is a real world. >> It just does wbat it is made to do. > > As I have said many many dozens of times we encode > all of the "basic facts" of general knowledge both > empirical (the facts of the actual world) and analytical > knowledge into a finite set of axioms. A computer can process those axioms as programmed but it cannot relate them to the real world because it is not aware of the real world. -- Mikko
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-28 11:38 +0300 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <111qmhs$3gd0r$1@dont-email.me> |
| In reply to | #347099 |
On 27/06/2026 21:38, olcott wrote: > On 6/27/2026 1:29 PM, dbush wrote: >> On 6/27/2026 2:27 PM, olcott wrote: >>> On 6/27/2026 1:01 PM, dbush wrote: >>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>> You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness >>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have >>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't >>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of >>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> "grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as >>>>>>>>>>>>>>>> a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> The CycL language and the Cyc Project. >>>>>>>>>>>>>> >>>>>>>>>>>>>> They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to >>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>> >>>>>>>>>>>>> It must at least be a directed acyclic graph or >>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>> completes. >>>>>>>>>>>> >>>>>>>>>>>> How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop >>>>>>>>>>>> when looking for a proof? >>>>>>>>>>> >>>>>>>>>>> By looking upward in a type hierarchy. >>>>>>>>>> >>>>>>>>>> If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof. >>>>>>>>> >>>>>>>>> Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>> expressed in language together into one coherent body >>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>> or mathematical incompleteness. >>>>>>>> >>>>>>>> Looking for a proof does not need any semantics so it is not >>>>>>>> obvious >>>>>>>> how switching to another semantics could improve it. >>>>>>> >>>>>>> In proof theoretic semantics an expression only gains >>>>>>> semantic meaning by finding a proof. >>>>>> >>>>>> It should be obvious that finding a proof does not happen before >>>>>> looking for a proof. >>>>>> >>>>> >>>>> If there is no sequence of inference steps in Q from >>>>> ~∃x x=S(x) to the axioms of Q >>>> >>>> There are, but that sequence is infinite >>>> >>> >>> If there is no FINITE sequence of inference steps >>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>> is ungrounded in the PTS atomic base of Q. >> >> i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >> > Is it commonly known that ~∃x x=S(x) is > semantic nonsense in Q? All of logic took > a psychotic break from reality when they > took semantics out of logic and put it in > a separate model. All of mathematics and logic is disconnected from reality. Proof theoretic semantics is just a way to emphasize the disconnection. The connection is made when one wants to apply logic or mathematics to description of the real world or to solving real world problems. -- Mikko
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2026-06-27 13:40 -0600 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <111p8vt$35hi1$1@dont-email.me> |
| In reply to | #347095 |
On 2026-06-27 12:27, olcott wrote: > On 6/27/2026 1:01 PM, dbush wrote: >> On 6/27/2026 11:43 AM, polcott wrote: >>> On 6/27/2026 2:35 AM, Mikko wrote: >>>> On 26/06/2026 16:10, olcott wrote: >>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>> truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have >>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't >>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> "grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean. >>>>>>>>>>>>>> >>>>>>>>>>>>>>> All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>> >>>>>>>>>>>>>> What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as >>>>>>>>>>>>>> a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>> some language? >>>>>>>>>>>>> >>>>>>>>>>>>> The CycL language and the Cyc Project. >>>>>>>>>>>> >>>>>>>>>>>> They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to >>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>> >>>>>>>>>>> It must at least be a directed acyclic graph or >>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>> completes. >>>>>>>>>> >>>>>>>>>> How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof? >>>>>>>>> >>>>>>>>> By looking upward in a type hierarchy. >>>>>>>> >>>>>>>> If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof. >>>>>>> >>>>>>> Truth Conditional Semantics (TCS) <is> incoherent >>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>> PTS just coherently connects the semantic meanings >>>>>>> expressed in language together into one coherent body >>>>>>> of general knowledge. It does this without undecidability >>>>>>> or mathematical incompleteness. >>>>>> >>>>>> Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it. >>>>> >>>>> In proof theoretic semantics an expression only gains >>>>> semantic meaning by finding a proof. >>>> >>>> It should be obvious that finding a proof does not happen before >>>> looking for a proof. >>>> >>> >>> If there is no sequence of inference steps in Q from >>> ~∃x x=S(x) to the axioms of Q >> >> There are, but that sequence is infinite >> > > If there is no FINITE sequence of inference steps > in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) > is ungrounded in the PTS atomic base of Q. > > PTS also says FINITE sequence. > I cannot use the convoluted way that PTS says it in > all of their different author-by-author terms-of-the-art > and still be understood. If PTS is so convoluted, why should we take your word for it that you are actually interpreting it correctly? > The above version is very close to the way that one > PTS author would say it and does convey the same > gist of meanings that other PTS authors accept. very close to doesn't mean the same as. Why don't you actually quote the author in question so we can see for ourselves exactly how close to it your formulation is? André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-27 14:46 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <111p9bc$366u4$1@dont-email.me> |
| In reply to | #347105 |
On 6/27/2026 2:40 PM, André G. Isaak wrote: > On 2026-06-27 12:27, olcott wrote: >> On 6/27/2026 1:01 PM, dbush wrote: >>> On 6/27/2026 11:43 AM, polcott wrote: >>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>> On 26/06/2026 16:10, olcott wrote: >>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>> truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have >>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't >>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of >>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> "grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as >>>>>>>>>>>>>>> a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>> >>>>>>>>>>>>>> The CycL language and the Cyc Project. >>>>>>>>>>>>> >>>>>>>>>>>>> They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to >>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>> >>>>>>>>>>>> It must at least be a directed acyclic graph or >>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>> completes. >>>>>>>>>>> >>>>>>>>>>> How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop >>>>>>>>>>> when looking for a proof? >>>>>>>>>> >>>>>>>>>> By looking upward in a type hierarchy. >>>>>>>>> >>>>>>>>> If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof. >>>>>>>> >>>>>>>> Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>> expressed in language together into one coherent body >>>>>>>> of general knowledge. It does this without undecidability >>>>>>>> or mathematical incompleteness. >>>>>>> >>>>>>> Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it. >>>>>> >>>>>> In proof theoretic semantics an expression only gains >>>>>> semantic meaning by finding a proof. >>>>> >>>>> It should be obvious that finding a proof does not happen before >>>>> looking for a proof. >>>>> >>>> >>>> If there is no sequence of inference steps in Q from >>>> ~∃x x=S(x) to the axioms of Q >>> >>> There are, but that sequence is infinite >>> >> >> If there is no FINITE sequence of inference steps >> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >> is ungrounded in the PTS atomic base of Q. >> >> PTS also says FINITE sequence. >> I cannot use the convoluted way that PTS says it in >> all of their different author-by-author terms-of-the-art >> and still be understood. > > If PTS is so convoluted, why should we take your word for it that you > are actually interpreting it correctly? > >> The above version is very close to the way that one >> PTS author would say it and does convey the same >> gist of meanings that other PTS authors accept. > > very close to doesn't mean the same as. Why don't you actually quote the > author in question so we can see for ourselves exactly how close to it > your formulation is? > > André > All of the author's use their own terms of the art that define things differently than the other authors. This may be the closest paper to my views. The Definitional View of Atomic Systems in Proof-Theoretic Semantics THOMAS PIECHA AND PETER SCHROEDER-HEISTER https://bibliographie.uni-tuebingen.de/xmlui/bitstream/handle/10900/129466/Piecha_Schroeder-Heister_Logica-Yearbook-2016.pdf?sequence=1 -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-28 11:32 +0300 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <111qm76$3g61e$2@dont-email.me> |
| In reply to | #347083 |
On 27/06/2026 18:43, polcott wrote: > On 6/27/2026 2:35 AM, Mikko wrote: >> On 26/06/2026 16:10, olcott wrote: >>> On 6/26/2026 1:39 AM, Mikko wrote: >>>> On 25/06/2026 19:14, olcott wrote: >>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> I don't believe you. You have no respect for or >>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>> truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have >>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>> >>>>>>>>>>>>>> "grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>> >>>>>>>>>>>>> All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings. >>>>>>>>>>>> >>>>>>>>>>>> What makes you believe semantic relations that can be >>>>>>>>>>>> structured as >>>>>>>>>>>> a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in >>>>>>>>>>>> some language? >>>>>>>>>>> >>>>>>>>>>> The CycL language and the Cyc Project. >>>>>>>>>> >>>>>>>>>> They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure? >>>>>>>>> >>>>>>>>> It must at least be a directed acyclic graph or >>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>> completes. >>>>>>>> >>>>>>>> How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof? >>>>>>> >>>>>>> By looking upward in a type hierarchy. >>>>>> >>>>>> If you mean not looking elsewhere that may indeed prevent loops. >>>>>> In most cases that also prevents finding the proof. >>>>> >>>>> Truth Conditional Semantics (TCS) <is> incoherent >>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>> PTS just coherently connects the semantic meanings >>>>> expressed in language together into one coherent body >>>>> of general knowledge. It does this without undecidability >>>>> or mathematical incompleteness. >>>> >>>> Looking for a proof does not need any semantics so it is not obvious >>>> how switching to another semantics could improve it. >>> >>> In proof theoretic semantics an expression only gains >>> semantic meaning by finding a proof. >> >> It should be obvious that finding a proof does not happen before >> looking for a proof. >> > > If there is no sequence of inference steps in Q from > ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is > ungrounded in the PTS atomic base of Q. > This does not mean undecidable or incomplete > it means that ~∃x x=S(x) is out-of-scope for Q. > >>> This is the same sort of thing as finding the defined >>> meaning of a word. If you cannot find its recursively >>> defined meaning then it never gains any meaning. > >> That does not follow. Words have meanings even without definitions. >> You can't present the first definition unless you already have >> meaningful words. >> > > A particular new word can only be defined in terms > of other existing words that already have definitions. > PTS works in a similar way. If ~∃x x=S(x) cannot connect > to its meanings in Q the it remains undefined in Q. > >> Typically the presentation of a formal theory begins with the >> introduction of undefined symbols. But the symbols are not >> fully meaningless. They get some amount of meaning from being >> introduces as symbols of a particular syntactic category and >> more from being used in the postulates of the theory. > > The body of knowledge expressed in language starts > with an atomic basis of expressions of language that > are stipulated to be true. You cannot have any expressions in a language before you have a language. -- Mikko
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| From | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2026-06-22 12:47 +0000 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <111bash$f9p$1@news.muc.de> |
| In reply to | #346857 |
[ Followup-To: set ] In comp.theory olcott <polcott333@gmail.com> wrote: > On 6/21/2026 4:08 PM, André G. Isaak wrote: > > On 2026-06-21 14:42, olcott wrote: > >> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: > >> It is a verified fact that Gödel's G is ungrounded > >> in the atomic base of PA. That you do not understand > >> what: "grounded in the atomic base" means is less > >> than no rebuttal at all. > > "grounded in the atomic base of PA" is an expression used only by you, > > and it is one which you have never explicitly defined, so the fault here > > certainly doesn't lie with Alan. It's certainly not a 'verified fact' > > when you haven't even adequately explained what it is that you mean. > > André > All of knowledge expressed in language is structured as a tree of > semantic relations specified syntactically between finite strings. That is vanishingly unlikely to be true. Look at any half decent English dictionary, and it will contain lots of cycles. Any non-empty finite tree contains leaf nodes. Either your "tree of semantic relations" is infinite (hence useless) or it contains leaf nodes. Feel free to give an example of a leaf node in your purported tree. > I am working in anchoring all of the relevant details > of "grounded in the atomic base" in quotes from > published papers. As remarked already "grounded in the atomic base" is undefined and meaningless. > -- > Copyright 2026 Olcott -- Alan Mackenzie (Nuremberg, Germany).
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-22 09:30 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- tree of knowledge |
| Message-ID | <111bgv4$1j7cv$1@dont-email.me> |
| In reply to | #346901 |
On 6/22/2026 7:47 AM, Alan Mackenzie wrote: > [ Followup-To: set ] > > In comp.theory olcott <polcott333@gmail.com> wrote: >> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>> On 2026-06-21 14:42, olcott wrote: >>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>> It is a verified fact that Gödel's G is ungrounded >>>> in the atomic base of PA. That you do not understand >>>> what: "grounded in the atomic base" means is less >>>> than no rebuttal at all. > >>> "grounded in the atomic base of PA" is an expression used only by you, >>> and it is one which you have never explicitly defined, so the fault here >>> certainly doesn't lie with Alan. It's certainly not a 'verified fact' >>> when you haven't even adequately explained what it is that you mean. > >>> André > >> All of [general] knowledge expressed in language is structured >> as a tree of semantic relations specified syntactically between >> finite strings. >> > That is vanishingly unlikely to be true. Look at any half decent English > dictionary, and it will contain lots of cycles. Any non-empty finite > tree contains leaf nodes. Either your "tree of semantic relations" is > infinite (hence useless) or it contains leaf nodes. Feel free to give an > example of a leaf node in your purported tree. > It may be a directed acyclic graph instead of a tree. Viral Pneumonia may requires multiple inheritance. >> I am working in anchoring all of the relevant details >> of "grounded in the atomic base" in quotes from >> published papers. > > As remarked already "grounded in the atomic base" is undefined and > meaningless. > When you make sure to not know the terms of the art of proof theoretic semantics it may seem that way. Atomic Systems in Proof-Theoretic Semantics: Two Approaches https://link.springer.com/chapter/10.1007/978-3-319-26506-3_2 Also an issue with PTS is that each author seems to use their own terms-of-the-art that are equivalent to the different terms that other PTS authors use. I am working through this. It is tedious and time consuming. It will probably best be presented as the different ways that each author says the same thing. >> -- >> Copyright 2026 Olcott > -- Copyright 2026 Olcott My 28 year goal has been to make "true on the basis of meaning expressed in language" reliably computable for the entire body of knowledge. The complete structure of this system is now defined. The entire body of knowledge expressed in language is comprised of two types of relations between finite strings: (a) *Axioms* Expressions of language that are stipulated to be true. My system bridges the analytic/synthetic distinction by expressly encoding all empirical "atomic facts" in a formal language such as CycL of the Cyc project. (b) *Inference Rules* Expressions of language that are semantically entailed syntactically from (a) and/or (b).
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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Date | 2026-06-22 10:23 +0300 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction |
| Message-ID | <111anug$1bi0u$1@dont-email.me> |
| In reply to | #346850 |
On 21/06/2026 23:42, olcott wrote: > On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >> [ Followup-To: set ] >> >> In comp.theory olcott <polcott333@gmail.com> wrote: >>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>> I just found the term: >>>>> "grounding in a proof theoretic atomic base" yesterday. >> >>>> You can find any number of terms. That doesn't mean you're capable of >>>> understanding them. >> >> >>> The above is the key reason why under PTS Gödel 1931 incompleteness >>> fails. >> >> I don't believe you. You have no respect for or understanding of the >> truth. If you really want to persuade anybody that PTS somehow causes >> Gödel's theorem not to hold, then cite an academic expert who'll have >> some credibility. >> >>> If they are mere gibberish words to you then you will not understand. >> >> You don't understand Proof-theoritic Semantics, and you certainly don't >> understand Gödel's Theorem, neither the theorem itself nor any proof of >> it. >> > It is a verified fact that Gödel's G is ungrounded > in the atomic base of PA. It is a verified fact that Gödel's completeness and incompleteness theorems are inevitable consequences of Peano arithmetic. -- Mikko
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-22 09:44 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction |
| Message-ID | <111bhoh$1jf8n$1@dont-email.me> |
| In reply to | #346894 |
On 6/22/2026 2:23 AM, Mikko wrote: > On 21/06/2026 23:42, olcott wrote: >> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>> [ Followup-To: set ] >>> >>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>> I just found the term: >>>>>> "grounding in a proof theoretic atomic base" yesterday. >>> >>>>> You can find any number of terms. That doesn't mean you're capable of >>>>> understanding them. >>> >>> >>>> The above is the key reason why under PTS Gödel 1931 incompleteness >>>> fails. >>> >>> I don't believe you. You have no respect for or understanding of the >>> truth. If you really want to persuade anybody that PTS somehow causes >>> Gödel's theorem not to hold, then cite an academic expert who'll have >>> some credibility. >>> >>>> If they are mere gibberish words to you then you will not understand. >>> >>> You don't understand Proof-theoritic Semantics, and you certainly don't >>> understand Gödel's Theorem, neither the theorem itself nor any proof of >>> it. >>> >> It is a verified fact that Gödel's G is ungrounded >> in the atomic base of PA. > > It is a verified fact that Gödel's completeness and incompleteness > theorems are inevitable consequences of Peano arithmetic. > Within the foundation of Truth Conditional Semantics this is true. Within the foundation of strict Proof Theoretic Semantics this is false. Some PTS called base-extension semantics seem to think that they can extend PA so that it is different and not clearly acknowledge that they converted PA into PA+. They would then say that G is grounded in PA when they actually mean that G becomes grounded in the modified PA+. -- 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 | Alan Mackenzie <acm@muc.de> |
|---|---|
| Date | 2026-06-22 15:22 +0000 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction |
| Message-ID | <111bk01$f9p$2@news.muc.de> |
| In reply to | #346907 |
[ Followup-To: set ] In comp.theory olcott <polcott333@gmail.com> wrote: > On 6/22/2026 2:23 AM, Mikko wrote: > > It is a verified fact that Gödel's completeness and incompleteness > > theorems are inevitable consequences of Peano arithmetic. > Within the foundation of Truth Conditional Semantics > this is true. Within the foundation of strict Proof > Theoretic Semantics this is false. You have not understood Mikko's statement. It is a VERIFIED FACT that Gödel's completeness and incompleteness theorems are inevitable consequences of Peano arithmetic. You are clueless about Gödel's theorems therefore are unqualified to make definitive comments about them. If you wish to demonstrate the highly unlikely proposition that PTS somehow renders Gödel's theorems inapplicable, you must prove that. Since you yourself are incapable of a mathematical proof, you must cite some expert, somebody who understands both Gödel's therems and PTS, who can explain these things. You understand neither of them. > Some PTS called base-extension semantics seem to think > that they can extend PA so that it is different and > not clearly acknowledge that they converted PA into PA+. > They would then say that G is grounded in PA when > they actually mean that G becomes grounded in the > modified PA+. What is the nature of this alleged extension? PA is a set of axioms from which, amongst other things, Gödel's theorems can be proven. You seem to be asserting that for this to work, some additional axioms are needed. What is the nature of these extra axioms? Can you give an example of one? > -- > Copyright 2026 Olcott -- Alan Mackenzie (Nuremberg, Germany).
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| From | olcott <polcott333@gmail.com> |
|---|---|
| Date | 2026-06-22 10:36 -0500 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction |
| Message-ID | <111bkq5$1kfo9$1@dont-email.me> |
| In reply to | #346912 |
On 6/22/2026 10:22 AM, Alan Mackenzie wrote: > [ Followup-To: set ] > > In comp.theory olcott <polcott333@gmail.com> wrote: >> On 6/22/2026 2:23 AM, Mikko wrote: > >>> It is a verified fact that Gödel's completeness and incompleteness >>> theorems are inevitable consequences of Peano arithmetic. > >> Within the foundation of Truth Conditional Semantics >> this is true. Within the foundation of strict Proof >> Theoretic Semantics this is false. > > You have not understood Mikko's statement. It is a VERIFIED FACT that > Gödel's completeness and incompleteness theorems are inevitable > consequences of Peano arithmetic. Within the foundation of Truth Conditional Semantics (TCS) and not Within the foundation of strict Proof Theoretic (PTS) Semantics. When G is unprovable in PA then in strict PTS G is ungrounded in PA. There is a sub field of PTS called Base-Extension Semantics (B-eS) that is not strict PTS. (B-eS) extends PA to become PA+ then G becomes grounded in PA+. This is the same thing as saying that G is provable in meta-math thus making it true in PA. -- 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 | 2026-06-22 12:07 -0700 |
| Subject | Re: Readings in (some of the) foundations of mathematics --- analytic/synthetic distinction |
| Message-ID | <5tycndslC-eVFaT3nZ2dnZfqnPqdnZ2d@giganews.com> |
| In reply to | #346913 |
On 06/22/2026 08:36 AM, olcott wrote: > On 6/22/2026 10:22 AM, Alan Mackenzie wrote: >> [ Followup-To: set ] >> >> In comp.theory olcott <polcott333@gmail.com> wrote: >>> On 6/22/2026 2:23 AM, Mikko wrote: >> >>>> It is a verified fact that Gödel's completeness and incompleteness >>>> theorems are inevitable consequences of Peano arithmetic. >> >>> Within the foundation of Truth Conditional Semantics >>> this is true. Within the foundation of strict Proof >>> Theoretic Semantics this is false. >> >> You have not understood Mikko's statement. It is a VERIFIED FACT that >> Gödel's completeness and incompleteness theorems are inevitable >> consequences of Peano arithmetic. > Within the foundation of Truth Conditional Semantics (TCS) > and not Within the foundation of strict Proof Theoretic (PTS) > Semantics. When G is unprovable in PA then in strict PTS > G is ungrounded in PA. > > There is a sub field of PTS called Base-Extension Semantics > (B-eS) that is not strict PTS. (B-eS) extends PA to become > PA+ then G becomes grounded in PA+. This is the same thing > as saying that G is provable in meta-math thus making it > true in PA. > "Meta" math? Is that the one where you hire a kid off the street to promote a venue and he takes the fliers and dumps them in the first trash-bin and walks off with the money? Sort of "Instant Audience" instead of "Artificial Intelligence"?
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