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Groups > comp.theory > #21465 > unrolled thread
| Started by | olcott <NoOne@NoWhere.com> |
|---|---|
| First post | 2020-07-05 22:52 -0500 |
| Last post | 2020-07-08 19:04 -0500 |
| Articles | 20 on this page of 335 — 10 participants |
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Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-05 22:52 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) André G. Isaak <agisaak@gm.invalid> - 2020-07-05 22:06 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-05 23:33 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) André G. Isaak <agisaak@gm.invalid> - 2020-07-05 22:58 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-06 00:41 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) André G. Isaak <agisaak@gm.invalid> - 2020-07-05 23:59 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-06 11:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 11:18 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (axiomatic basis of truth) olcott <NoOne@NoWhere.com> - 2020-07-07 13:13 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 15:00 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) André G. Isaak <agisaak@gm.invalid> - 2020-07-07 14:17 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 15:25 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) André G. Isaak <agisaak@gm.invalid> - 2020-07-07 14:50 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 17:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) André G. Isaak <agisaak@gm.invalid> - 2020-07-07 18:27 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 19:43 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) Jeff Barnett <jbb@notatt.com> - 2020-07-07 19:28 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 21:31 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) Jeff Barnett <jbb@notatt.com> - 2020-07-07 21:29 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 22:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) Jeff Barnett <jbb@notatt.com> - 2020-07-08 12:27 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-08 14:19 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-10 10:39 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-10 08:41 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 08:03 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-10 09:17 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-10 12:41 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-10 09:26 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) André G. Isaak <agisaak@gm.invalid> - 2020-07-07 21:52 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) olcott <NoOne@NoWhere.com> - 2020-07-07 23:00 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 ∃φ (φ ↔ T ⊬ φ) André G. Isaak <agisaak@gm.invalid> - 2020-07-07 22:43 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 00:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-07 23:39 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 00:54 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-08 00:14 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 10:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-08 09:50 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 11:09 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 11:29 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 11:49 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-09 06:56 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 11:02 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-09 11:33 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 23:23 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-10 12:13 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 23:50 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 12:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-09 07:40 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 11:14 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-09 12:14 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 23:28 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-10 11:54 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-10 14:46 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 16:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-10 17:20 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 16:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 09:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 09:29 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 09:42 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 10:54 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 10:55 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 11:02 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 12:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 11:27 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 13:04 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 12:12 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 15:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 14:27 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 15:42 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-10 15:00 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 16:36 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 20:19 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-11 04:20 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-11 19:24 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-11 18:57 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (TRUTH BEARER DEFINED) olcott <NoOne@NoWhere.com> - 2020-07-11 22:58 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (TRUTH BEARER DEFINED) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 00:37 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 11:43 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 12:07 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 13:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 13:36 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 15:31 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 16:24 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 15:37 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 18:04 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 17:21 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 18:53 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 18:07 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 19:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 18:58 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 23:06 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-13 07:01 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-13 09:32 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) André G. Isaak <agisaak@gm.invalid> - 2020-07-13 08:47 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-13 19:52 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-13 09:07 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) David Kleinecke <dkleinecke@gmail.com> - 2020-07-12 17:28 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (NATURE OF TRUTH ITSELF) olcott <NoOne@NoWhere.com> - 2020-07-12 19:47 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-10 19:21 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 13:35 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-11 12:25 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-11 19:05 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-12 14:10 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-12 13:24 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-12 14:04 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-12 18:48 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-12 17:22 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-12 19:52 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-12 19:32 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-12 22:47 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-13 08:05 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 19:49 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 19:11 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 09:43 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-14 08:57 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 10:22 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-14 09:30 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 10:38 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-15 11:24 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 19:18 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-15 20:38 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 16:16 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-16 16:01 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 19:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-16 18:40 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-13 23:48 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 10:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-14 09:20 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 10:26 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-14 09:36 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 10:41 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-14 11:25 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 10:52 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-15 11:04 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 19:07 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-15 18:42 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 12:10 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 11:46 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 16:35 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 15:19 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 23:19 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-16 22:49 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 00:34 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-17 01:04 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 17:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-17 16:16 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 18:59 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-18 03:13 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 22:01 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-18 17:17 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-18 12:43 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-18 15:08 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-18 20:28 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-19 03:45 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-19 11:46 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-19 11:05 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-19 12:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-19 11:30 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-19 12:36 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-19 20:51 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-19 15:28 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-20 02:44 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-20 12:40 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-21 01:52 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-20 21:35 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-20 19:59 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-21 10:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-21 10:00 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-21 19:50 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-21 17:57 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-22 09:07 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-22 02:03 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-22 09:03 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-23 00:30 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-22 09:06 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-19 22:23 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-20 10:33 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-20 10:50 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-17 12:16 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 17:04 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 17:09 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-18 00:22 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-13 13:05 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 10:07 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-13 20:01 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 12:24 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 [--Obvious Yet?--] olcott <NoOne@NoWhere.com> - 2020-07-13 14:58 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 18:33 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 17:46 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 09:36 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-14 09:53 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 10:49 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-13 23:42 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 18:45 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-14 01:26 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 22:06 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-14 17:00 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 18:15 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-15 02:56 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 21:55 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) David Kleinecke <dkleinecke@gmail.com> - 2020-07-14 20:30 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 23:13 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Mapping to Boolean) olcott <NoOne@NoWhere.com> - 2020-07-15 09:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-15 16:48 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 11:46 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-15 11:32 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 19:13 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-16 01:37 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 22:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-16 16:05 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-16 14:18 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 13:32 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-16 22:39 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 21:00 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-17 02:17 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-16 21:01 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-17 03:54 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-16 23:27 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-17 11:36 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 11:10 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) David Kleinecke <dkleinecke@gmail.com> - 2020-07-17 11:11 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 14:24 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-17 20:28 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 16:47 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Kaz Kylheku <793-849-0957@kylheku.com> - 2020-07-17 20:26 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 17:39 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-17 16:06 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 18:40 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 17:47 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-17 18:01 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 22:24 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 21:34 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 22:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 22:01 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-18 13:34 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-17 21:09 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-18 10:14 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-18 15:05 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 17:23 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 18:52 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 18:01 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 22:35 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 21:55 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-18 13:49 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) David Kleinecke <dkleinecke@gmail.com> - 2020-07-17 22:12 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 14:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-18 02:17 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Membership algorithm) olcott <NoOne@NoWhere.com> - 2020-07-17 21:53 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-15 18:23 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 11:51 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 11:21 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 13:41 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 13:10 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 22:36 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 21:04 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-17 12:10 +0100
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) R Kym Horsell <kym@kymhorsell.com> - 2020-07-17 11:50 +0000
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 17:00 -0500
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 17:40 -0600
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-17 17:46 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 17:07 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-18 00:30 +0100
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) R Kym Horsell <kym@kymhorsell.com> - 2020-07-18 02:21 +0000
Re: Simply defining G"odel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-18 16:19 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-17 22:03 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-18 16:12 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-18 11:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-15 20:25 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 16:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 14:31 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 22:45 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 21:10 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-16 15:58 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 22:47 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 21:18 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-16 22:38 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-16 00:35 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 18:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-16 01:16 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 19:28 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) David Kleinecke <dkleinecke@gmail.com> - 2020-07-15 17:44 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 20:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-16 02:19 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 22:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-16 16:08 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 14:20 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-16 13:12 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-16 22:37 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 17:52 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 21:12 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 20:11 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 22:48 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) David Kleinecke <dkleinecke@gmail.com> - 2020-07-13 21:38 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 00:03 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) David Kleinecke <dkleinecke@gmail.com> - 2020-07-13 22:26 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 00:32 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-14 14:41 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 10:14 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Chris Buckley <alan@sabir.com> - 2020-07-14 18:24 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-14 17:44 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Chris Buckley <alan@sabir.com> - 2020-07-15 18:08 +0000
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-15 18:47 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) David Kleinecke <dkleinecke@gmail.com> - 2020-07-12 17:30 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-12 19:50 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-12 18:53 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-12 23:48 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 00:58 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-13 13:07 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 14:12 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-13 15:32 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 15:06 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-14 00:56 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-07-13 23:26 +0100
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-13 16:10 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-13 09:57 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-13 13:12 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-10 12:53 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 16:25 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-10 15:06 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 17:21 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) David Kleinecke <dkleinecke@gmail.com> - 2020-07-10 15:58 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-10 18:01 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-11 04:10 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-11 19:13 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-08 12:39 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 23:37 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Jeff Barnett <jbb@notatt.com> - 2020-07-09 00:40 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 09:38 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 09:18 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-09 12:15 -0700
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 15:10 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V27 (Simple enough yet?) olcott <NoOne@NoWhere.com> - 2020-07-08 16:25 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V27 (Simple enough yet?) André G. Isaak <agisaak@gm.invalid> - 2020-07-09 07:02 -0600
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V27 (Simple enough yet?) olcott <NoOne@NoWhere.com> - 2020-07-09 11:11 -0500
Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Shell game) olcott <NoOne@NoWhere.com> - 2020-07-08 19:04 -0500
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| From | André G. Isaak <agisaak@gm.invalid> |
|---|---|
| Date | 2020-07-17 17:09 -0600 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <retb36$g5r$1@dont-email.me> |
| In reply to | #21751 |
On 2020-07-17 16:04, olcott wrote: > On 7/17/2020 6:16 AM, Alan Smaill wrote: >> olcott <NoOne@NoWhere.com> writes: >> >>> On 7/16/2020 1:46 PM, Keith Thompson wrote: >>>> olcott <NoOne@NoWhere.com> writes: >>>>> On 7/15/2020 8:42 PM, Keith Thompson wrote: >>>>>> olcott <NoOne@NoWhere.com> writes: >>>>>>> On 7/15/2020 1:04 PM, Keith Thompson wrote: >>>>>>>> olcott <NoOne@NoWhere.com> writes: >>>>>>>>> On 7/14/2020 1:25 PM, Keith Thompson wrote: >>>>>>>>>> olcott <NoOne@NoWhere.com> writes: >>>>>>>>>> [...] >>>>>>>>>>> Since everyone here is indoctrinated into believing that Gödel >>>>>>>>>>> is correct I have to use different terms for provability so >>>>>>>>>>> that people will carefully analyze my reasoning and not simply >>>>>>>>>>> dismiss it out-of-hand on the basis of their indoctrination. >>>>>>>>>> >>>>>>>>>> It seems to me that the best way to demonstrate that Gödel is >>>>>>>>>> incorrect would be to demonstrate a flaw in what he actually >>>>>>>>>> wrote. I haven't read everything you've written here, but I >>>>>>>>>> don't recall you ever directly quoting Gödel's proof. >>>>>>>>> >>>>>>>>> Not really. When we refute the enormously simplified key result >>>>>>>>> of his claim: true and unprovable can possibly coexist, then the >>>>>>>>> steps that he used to get to this key result are moot. >>>>>>>> >>>>>>>> You've been asserting that for years, and nobody believes you >>>>>>> https://scholar.google.com/scholar?hl=en&as_sdt=0%2C28&q=%22true+and+unprovable%22+godel&btnG=&oq=%22true+and+unprovable%22 >>>>>>> >>>>>> >>>>>> 125 results. No, I'm not going to read them. >>>>> >>>>> 125 different people that all believe that Gödel showed that true and >>>>> unprovable formulas exists, and 125 > 0, thus "nobody believes you" is >>>>> proven to be false. >>>> >>>> Wait, what? Is that really what you meant to say? Gödel *did* show >>>> that true and unprovable formulas exist. Did you omit a "not"? >>> >>> OK that is even better. I thought that he only concluded that some >>> formulas are neither provable nor disprovable. >> >> The conclusion of his original proof (as opposed to comments elsewhere) >> is that in the system he looked at, a particular arithmetical statement >> is neither provable nor refutable (ie its negation is not >> provable). >> >> You are disputing that claim, of course, even though it does not >> refer to truth, but only to provability in a given formal system. >> > > Apparently 126 references on Google Scholar seem to think that he proved > more than that: That would be compared to the 19,800 results one gets when searching for Gödel's Incompleteness Theorem or less than 1% of all results. Are these numbers meaningful? Not really, since things found through Google Scholar are hardly a representative sampling of work in this area. If you want an actual answer to the question what did Gödel prove, the obvious way to get this would be to simply read Gödel's paper. Gödel's paper does not include the word "truth" period. If you want to understand the position of those 126 references or other interpretations of Gödel which does make use of 'truth', you simply need to consider the law of the excluded middle. Given some formula φ, either φ must be true or ¬φ must be true. Since Gödel showed that, in the type of system he was concerned with, there must always exists formulas φ such that neither φ nor ¬φ are derivable as theorems, that entails that, if we were to consider the semantics of the system (i.e. to introduce the notion of 'truth'), then there would be true propositions which are not provable. But Gödel was concerned with formal proofs, not with truth, so he does not mention this. André -- To email remove 'invalid' & replace 'gm' with well known Google mail service.
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2020-07-18 00:22 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <fwemu3xg20j.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #21751 |
olcott <NoOne@NoWhere.com> writes: > On 7/17/2020 6:16 AM, Alan Smaill wrote: >> olcott <NoOne@NoWhere.com> writes: >> [..] >>> >>> OK that is even better. I thought that he only concluded that some >>> formulas are neither provable nor disprovable. >> >> The conclusion of his original proof (as opposed to comments elsewhere) >> is that in the system he looked at, a particular arithmetical statement >> is neither provable nor refutable (ie its negation is not >> provable). >> >> You are disputing that claim, of course, even though it does not >> refer to truth, but only to provability in a given formal system. > > Apparently 126 references on Google Scholar seem to think that he > proved more than that: What is this, Olcott agreeing with some straw poll, rather than thinking for himself?? Appeal to authority?? If looking at the conclusion (Proposition VI) is too hard for you, try the title: (English version): On formally undecidable propositions of Principia Mathematica And shortly after: "We now define an undecidable proposition of the system PM, i.e. a proposition A such that neither A nor not-A are provable ... " -- which he goes on to do. We all know you reject the conclusion that (in PM) there is an arithmetical statement which is neither provable nor refutable. So I'm not asking about that here. Here is a much simpler question. Do you agree that Goedel did at least make that claim? Please give a yes/no answer before anything else you want to add. thanks -- AS
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2020-07-13 13:05 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <fwezh83boxw.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #21605 |
olcott <NoOne@NoWhere.com> writes: > On 7/12/2020 7:22 PM, Keith Thompson wrote: >> olcott <NoOne@NoWhere.com> writes: >>> On 7/12/2020 4:04 PM, Keith Thompson wrote: >>>> olcott <NoOne@NoWhere.com> writes: [..] >>>> Robinson Arithmetic cannot prove or disprove commutativity >>>> of addition. We can construct a consistent system based on >>>> Robinson Arithmetic in which addition is provably commutative. >>> >>> Sure just add an axiom: ∀x ∈ ℕ ∃y ∈ ℕ (x + y = y + x) No. You want ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) -- don't you? >>>> Can we construct a consistent system based on Robinson Arithmetic >>>> in which addition is provably *not* commutative? >>> >>> Not within the conventional semantics of the meaning of those terms. The question is not about semantics, it's about provability. it's about the existence of a formal system which is both syntactically consistent (ie cannot prove S and also not S, for some statement), extends Q, and can prove non-commutativity. That's a different question. >> OK. Can you prove that? > > Nothing can possibly be disproved that is true by definition. But the sound deductive model for Q does not *prove* that commutativity is true, so does not prove it "true by definition". You have acceoted that upthread. -- AS
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-13 10:07 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <kZ-dnXdGw7oC5ZHCnZ2dnUU7-f_NnZ2d@giganews.com> |
| In reply to | #21613 |
On 7/13/2020 7:05 AM, Alan Smaill wrote: > olcott <NoOne@NoWhere.com> writes: > >> On 7/12/2020 7:22 PM, Keith Thompson wrote: >>> olcott <NoOne@NoWhere.com> writes: >>>> On 7/12/2020 4:04 PM, Keith Thompson wrote: >>>>> olcott <NoOne@NoWhere.com> writes: > [..] >>>>> Robinson Arithmetic cannot prove or disprove commutativity >>>>> of addition. We can construct a consistent system based on >>>>> Robinson Arithmetic in which addition is provably commutative. >>>> >>>> Sure just add an axiom: ∀x ∈ ℕ ∃y ∈ ℕ (x + y = y + x) > > No. > You want ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) -- > don't you? Yes, typo. > >>>>> Can we construct a consistent system based on Robinson Arithmetic >>>>> in which addition is provably *not* commutative? >>>> >>>> Not within the conventional semantics of the meaning of those terms. > > The question is not about semantics, it's about provability. > > it's about the existence of a formal system which is both syntactically > consistent (ie cannot prove S and also not S, for some statement), > extends Q, and can prove non-commutativity. For the same reason that "cats are animals" is true in biology and not true in mathematics there cannot be any expression of the language of any formal system that is true in this formal system yet lacks a mapping in this formal system from this expression to a Boolean value. > > That's a different question. > >>> OK. Can you prove that? >> >> Nothing can possibly be disproved that is true by definition. > > But the sound deductive model for Q does not *prove* that > commutativity is true, so does not prove it "true by definition". > You have acceoted that upthread. > φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) φ is not true or false in Q because Q lacks a mapping in Q from φ to a Boolean value. -- Copyright 2020 Pete Olcott
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| From | Alan Smaill <smaill@SPAMinf.ed.ac.uk> |
|---|---|
| Date | 2020-07-13 20:01 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <fweh7ubck7y.fsf@foxtrot.inf.ed.ac.uk> |
| In reply to | #21620 |
olcott <NoOne@NoWhere.com> writes: > On 7/13/2020 7:05 AM, Alan Smaill wrote: >> olcott <NoOne@NoWhere.com> writes: >> >>> On 7/12/2020 7:22 PM, Keith Thompson wrote: >>>> olcott <NoOne@NoWhere.com> writes: >>>>> On 7/12/2020 4:04 PM, Keith Thompson wrote: >>>>>> olcott <NoOne@NoWhere.com> writes: >> [..] >>>>>> Robinson Arithmetic cannot prove or disprove commutativity >>>>>> of addition. We can construct a consistent system based on >>>>>> Robinson Arithmetic in which addition is provably commutative. >>>>> >>>>> Sure just add an axiom: ∀x ∈ ℕ ∃y ∈ ℕ (x + y = y + x) >> >> No. >> You want ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) -- >> don't you? > > Yes, typo. > >>>>>> Can we construct a consistent system based on Robinson Arithmetic >>>>>> in which addition is provably *not* commutative? >>>>> >>>>> Not within the conventional semantics of the meaning of those terms. >> >> The question is not about semantics, it's about provability. >> >> it's about the existence of a formal system which is both syntactically >> consistent (ie cannot prove S and also not S, for some statement), >> extends Q, and can prove non-commutativity. > > For the same reason that "cats are animals" is true in biology and not > true in mathematics there cannot be any expression of the language of > any formal system that is true in this formal system yet lacks a > mapping in this formal system from this expression to a Boolean value. Let's stick with the example at hand, which you said you wanted to sort out 100% before moving on. >> That's a different question. >> >>>> OK. Can you prove that? >>> >>> Nothing can possibly be disproved that is true by definition. >> >> But the sound deductive model for Q does not *prove* that >> commutativity is true, so does not prove it "true by definition". >> You have acceoted that upthread. > > φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) > > φ is not true or false in Q because Q lacks a mapping in Q from φ to a > Boolean value. That's not what I was asking about. >> But the sound deductive model for Q does not *prove* that >> commutativity is true, so does not prove it "true by definition". >> You have accepted that upthread. In other words, I am asking you about what is *provable* or not in Q, not about whether commutativity is "true or false". You have accepted that Q does not prove commutativity. If you want to change your mind on that, let us know. -- Alan Smaill
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2020-07-13 12:24 -0700 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <87pn8z43ru.fsf@nosuchdomain.example.com> |
| In reply to | #21621 |
Alan Smaill <smaill@SPAMinf.ed.ac.uk> writes:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 7/13/2020 7:05 AM, Alan Smaill wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 7/12/2020 7:22 PM, Keith Thompson wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>> On 7/12/2020 4:04 PM, Keith Thompson wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>> [..]
>>>>>>> Robinson Arithmetic cannot prove or disprove commutativity
>>>>>>> of addition. We can construct a consistent system based on
>>>>>>> Robinson Arithmetic in which addition is provably commutative.
>>>>>>
>>>>>> Sure just add an axiom: ∀x ∈ ℕ ∃y ∈ ℕ (x + y = y + x)
>>>
>>> No.
>>> You want ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) --
>>> don't you?
>>
>> Yes, typo.
>>
>>>>>>> Can we construct a consistent system based on Robinson Arithmetic
>>>>>>> in which addition is provably *not* commutative?
>>>>>>
>>>>>> Not within the conventional semantics of the meaning of those terms.
>>>
>>> The question is not about semantics, it's about provability.
>>>
>>> it's about the existence of a formal system which is both syntactically
>>> consistent (ie cannot prove S and also not S, for some statement),
>>> extends Q, and can prove non-commutativity.
>>
>> For the same reason that "cats are animals" is true in biology and not
>> true in mathematics there cannot be any expression of the language of
>> any formal system that is true in this formal system yet lacks a
>> mapping in this formal system from this expression to a Boolean value.
>
> Let's stick with the example at hand, which you said you wanted to
> sort out 100% before moving on.
>
>>> That's a different question.
>>>
>>>>> OK. Can you prove that?
>>>>
>>>> Nothing can possibly be disproved that is true by definition.
>>>
>>> But the sound deductive model for Q does not *prove* that
>>> commutativity is true, so does not prove it "true by definition".
>>> You have acceoted that upthread.
>>
>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x)
>>
>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a
>> Boolean value.
>
> That's not what I was asking about.
>
>>> But the sound deductive model for Q does not *prove* that
>>> commutativity is true, so does not prove it "true by definition".
>>> You have accepted that upthread.
>
> In other words, I am asking you about what is *provable* or not in Q,
> not about whether commutativity is "true or false".
>
> You have accepted that Q does not prove commutativity.
> If you want to change your mind on that, let us know.
He believes that provability and truth are the same thing. He also
seems to believe that it's so obvious that they're the same thing
that anyone who says otherwise (like Gödel, for example) is being
deliberately disingenuous. (That last part is my interpretation
and may not be an entirely accurate summary of his belief.)
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips Healthcare
void Void(void) { Void(); } /* The recursive call of the void */
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-13 14:58 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 [--Obvious Yet?--] |
| Message-ID | <je6dnf5tiMlUIZHCnZ2dnUU7-a_NnZ2d@giganews.com> |
| In reply to | #21624 |
On 7/13/2020 2:24 PM, Keith Thompson wrote: > Alan Smaill <smaill@SPAMinf.ed.ac.uk> writes: >> olcott <NoOne@NoWhere.com> writes: >> >>> On 7/13/2020 7:05 AM, Alan Smaill wrote: >>>> olcott <NoOne@NoWhere.com> writes: >>>> >>>>> On 7/12/2020 7:22 PM, Keith Thompson wrote: >>>>>> olcott <NoOne@NoWhere.com> writes: >>>>>>> On 7/12/2020 4:04 PM, Keith Thompson wrote: >>>>>>>> olcott <NoOne@NoWhere.com> writes: >>>> [..] >>>>>>>> Robinson Arithmetic cannot prove or disprove commutativity >>>>>>>> of addition. We can construct a consistent system based on >>>>>>>> Robinson Arithmetic in which addition is provably commutative. >>>>>>> >>>>>>> Sure just add an axiom: ∀x ∈ ℕ ∃y ∈ ℕ (x + y = y + x) >>>> >>>> No. >>>> You want ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) -- >>>> don't you? >>> >>> Yes, typo. >>> >>>>>>>> Can we construct a consistent system based on Robinson Arithmetic >>>>>>>> in which addition is provably *not* commutative? >>>>>>> >>>>>>> Not within the conventional semantics of the meaning of those terms. >>>> >>>> The question is not about semantics, it's about provability. >>>> >>>> it's about the existence of a formal system which is both syntactically >>>> consistent (ie cannot prove S and also not S, for some statement), >>>> extends Q, and can prove non-commutativity. >>> >>> For the same reason that "cats are animals" is true in biology and not >>> true in mathematics there cannot be any expression of the language of >>> any formal system that is true in this formal system yet lacks a >>> mapping in this formal system from this expression to a Boolean value. >> >> Let's stick with the example at hand, which you said you wanted to >> sort out 100% before moving on. >> >>>> That's a different question. >>>> >>>>>> OK. Can you prove that? >>>>> >>>>> Nothing can possibly be disproved that is true by definition. >>>> >>>> But the sound deductive model for Q does not *prove* that >>>> commutativity is true, so does not prove it "true by definition". >>>> You have acceoted that upthread. >>> >>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>> >>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>> Boolean value. >> >> That's not what I was asking about. >> >>>> But the sound deductive model for Q does not *prove* that >>>> commutativity is true, so does not prove it "true by definition". >>>> You have accepted that upthread. >> >> In other words, I am asking you about what is *provable* or not in Q, >> not about whether commutativity is "true or false". >> >> You have accepted that Q does not prove commutativity. >> If you want to change your mind on that, let us know. > > He believes that provability and truth are the same thing. He also > seems to believe that it's so obvious that they're the same thing > that anyone who says otherwise (like Gödel, for example) is being > deliberately disingenuous. (That last part is my interpretation > and may not be an entirely accurate summary of his belief.) > Try and show that an expression of formal or natural language that does not have any mapping to Boolean values can still be true or false. Try and show how an expression of the language of a formal system that has no mapping in this formal system to Boolean values is still true or false IN THIS SYSTEM. Try and show that zebras and elephants are a kind of office building made entirely out of nonexistent baby kittens that are completely colorless and red with pink stripes. -- Copyright 2020 Pete Olcott
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-13 18:33 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <h9qdnV2508rMcpHCnZ2dnUU7-bfNnZ2d@giganews.com> |
| In reply to | #21621 |
On 7/13/2020 2:01 PM, Alan Smaill wrote: > olcott <NoOne@NoWhere.com> writes: > >> On 7/13/2020 7:05 AM, Alan Smaill wrote: >>> olcott <NoOne@NoWhere.com> writes: >>> >>>> On 7/12/2020 7:22 PM, Keith Thompson wrote: >>>>> olcott <NoOne@NoWhere.com> writes: >>>>>> On 7/12/2020 4:04 PM, Keith Thompson wrote: >>>>>>> olcott <NoOne@NoWhere.com> writes: >>> [..] >>>>>>> Robinson Arithmetic cannot prove or disprove commutativity >>>>>>> of addition. We can construct a consistent system based on >>>>>>> Robinson Arithmetic in which addition is provably commutative. >>>>>> >>>>>> Sure just add an axiom: ∀x ∈ ℕ ∃y ∈ ℕ (x + y = y + x) >>> >>> No. >>> You want ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) -- >>> don't you? >> >> Yes, typo. >> >>>>>>> Can we construct a consistent system based on Robinson Arithmetic >>>>>>> in which addition is provably *not* commutative? >>>>>> >>>>>> Not within the conventional semantics of the meaning of those terms. >>> >>> The question is not about semantics, it's about provability. >>> >>> it's about the existence of a formal system which is both syntactically >>> consistent (ie cannot prove S and also not S, for some statement), >>> extends Q, and can prove non-commutativity. >> >> For the same reason that "cats are animals" is true in biology and not >> true in mathematics there cannot be any expression of the language of >> any formal system that is true in this formal system yet lacks a >> mapping in this formal system from this expression to a Boolean value. > > Let's stick with the example at hand, which you said you wanted to > sort out 100% before moving on. > >>> That's a different question. >>> >>>>> OK. Can you prove that? >>>> >>>> Nothing can possibly be disproved that is true by definition. >>> >>> But the sound deductive model for Q does not *prove* that >>> commutativity is true, so does not prove it "true by definition". >>> You have acceoted that upthread. >> >> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >> >> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >> Boolean value. > > That's not what I was asking about. > >>> But the sound deductive model for Q does not *prove* that >>> commutativity is true, so does not prove it "true by definition". >>> You have accepted that upthread. > > In other words, I am asking you about what is *provable* or not in Q, > not about whether commutativity is "true or false". > > You have accepted that Q does not prove commutativity. > If you want to change your mind on that, let us know. > The single-minded focus of all of these last ten or more threads is how there can be a sentence that is true in a formal system and not provable in this same a formal system. I know it is impossible because: an expression of the language of a formal system that has no mapping in this formal system to Boolean values has no possible way to be true or false IN THIS SYSTEM. It is like this simpler question: How do you get from point "A" to point "B" when no path from point "A" to point "B" exists? https://scholar.google.com/scholar?start=10&q=%22true+and+unprovable%22&hl=en&as_sdt=0,28 -- Copyright 2020 Pete Olcott
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2020-07-13 17:46 -0700 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <871rle53ff.fsf@nosuchdomain.example.com> |
| In reply to | #21632 |
olcott <NoOne@NoWhere.com> writes:
[...]
> The single-minded focus of all of these last ten or more threads is
> how there can be a sentence that is true in a formal system and not
> provable in this same a formal system.
>
> I know it is impossible because: an expression of the language of a
> formal system that has no mapping in this formal system to Boolean
> values has no possible way to be true or false IN THIS SYSTEM.
Gödel proved otherwise. Redefining terms doesn't change that.
[...]
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips Healthcare
void Void(void) { Void(); } /* The recursive call of the void */
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-14 09:36 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <cpydnUOtwvl7X5DCnZ2dnUU7-bednZ2d@giganews.com> |
| In reply to | #21635 |
On 7/13/2020 7:46 PM, Keith Thompson wrote: > olcott <NoOne@NoWhere.com> writes: > [...] >> The single-minded focus of all of these last ten or more threads is >> how there can be a sentence that is true in a formal system and not >> provable in this same a formal system. >> >> I know it is impossible because: an expression of the language of a >> formal system that has no mapping in this formal system to Boolean >> values has no possible way to be true or false IN THIS SYSTEM. > > Gödel proved otherwise. Redefining terms doesn't change that. > > [...] > In other words you are claiming that an undecidable sentence has been decided to be true. -- Copyright 2020 Pete Olcott
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| From | Keith Thompson <Keith.S.Thompson+u@gmail.com> |
|---|---|
| Date | 2020-07-14 09:53 -0700 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <874kqa2g36.fsf@nosuchdomain.example.com> |
| In reply to | #21651 |
olcott <NoOne@NoWhere.com> writes:
> On 7/13/2020 7:46 PM, Keith Thompson wrote:
>> olcott <NoOne@NoWhere.com> writes:
>> [...]
>>> The single-minded focus of all of these last ten or more threads is
>>> how there can be a sentence that is true in a formal system and not
>>> provable in this same a formal system.
>>>
>>> I know it is impossible because: an expression of the language of a
>>> formal system that has no mapping in this formal system to Boolean
>>> values has no possible way to be true or false IN THIS SYSTEM.
>>
>> Gödel proved otherwise. Redefining terms doesn't change that.
>>
>> [...]
>
> In other words you are claiming that an undecidable sentence has been
> decided to be true.
No.
--
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
Working, but not speaking, for Philips Healthcare
void Void(void) { Void(); } /* The recursive call of the void */
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-15 10:49 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <VLWdneTp55AMuJLCnZ2dnUU7-KnNnZ2d@giganews.com> |
| In reply to | #21662 |
On 7/14/2020 11:53 AM, Keith Thompson wrote:
> olcott <NoOne@NoWhere.com> writes:
>> On 7/13/2020 7:46 PM, Keith Thompson wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>> [...]
>>>> The single-minded focus of all of these last ten or more threads is
>>>> how there can be a sentence that is true in a formal system and not
>>>> provable in this same a formal system.
>>>>
>>>> I know it is impossible because: an expression of the language of a
>>>> formal system that has no mapping in this formal system to Boolean
>>>> values has no possible way to be true or false IN THIS SYSTEM.
>>>
>>> Gödel proved otherwise. Redefining terms doesn't change that.
>>>
>>> [...]
>>
>> In other words you are claiming that an undecidable sentence has been
>> decided to be true.
>
> No.
>
A map is a way of associating unique objects to every element in a given
set. So a map f : A ↦ B from A to B is a function f such that for every
a ∈ A, there is a unique object f(a) ∈ B. The terms function and mapping
are synonymous for map. https://mathworld.wolfram.com/Map.html
∀φ (TruthBearer(T,φ) ↔ f(T,φ) ∈ {true, false})
For all φ of theory T φ is a truth bearer in T if and only if there is a
function in T from φ to exactly one element of the set of {true, false}.
The only way to show the above mapping in T is through the axioms and
rules-of-inferences of T and then adding an interpretation.
Satisfiability
A formula is satisfiable if it is possible to find an interpretation
(model) that makes the formula true.
https://en.wikipedia.org/wiki/Satisfiability
Interpretation (logic)
An interpretation is an assignment of meaning to the
[non-logical] symbols of a formal language.
https://en.wikipedia.org/wiki/Interpretation_(logic)
Model theory
A model of a theory is a structure (e.g. an interpretation)
that satisfies the sentences of that theory.
https://en.wikipedia.org/wiki/Model_theory
In other provability is a required aspect of the above mathematical
mapping thus proving that true and unprovable cannot possibly co-exist.
--
Copyright 2020 Pete Olcott
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2020-07-13 23:42 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <87365vnik3.fsf@bsb.me.uk> |
| In reply to | #21620 |
olcott <NoOne@NoWhere.com> writes: > φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) > > φ is not true or false in Q because Q lacks a mapping in Q from φ to a > Boolean value. Would you like to learn why that's wrong, or would you rather just keep repeating it? If you'd like to learn, you have to be a student. I'd ask a student to consider an instance of x + y = y + x in Q, for example this one: S0 + SS0 = SS0 + S0. and I'd ask them: what can you say about this formula in Q? -- Ben.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-13 18:45 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <TJidnbVhNKGAb5HCnZ2dnUU7-WfNnZ2d@giganews.com> |
| In reply to | #21630 |
On 7/13/2020 5:42 PM, Ben Bacarisse wrote: > olcott <NoOne@NoWhere.com> writes: > >> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >> >> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >> Boolean value. > > Would you like to learn why that's wrong, or would you rather just keep > repeating it? > > If you'd like to learn, you have to be a student. I'd ask a student to > consider an instance of x + y = y + x in Q, for example this one: > > S0 + SS0 = SS0 + S0. > > and I'd ask them: what can you say about this formula in Q? > How do you get from point "A" to point "B" when no path from point "A" to point "B" exists? YOU DON'T !!! How do you show that an expression of language is true when there is no mapping from this expression to Boolean values? YOU DON'T !!! How do you show that an expression of language of a formal system is true in this formal system when there is no mapping in this formal system from this expression to Boolean values? YOU DON'T !!! -- Copyright 2020 Pete Olcott
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2020-07-14 01:26 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <87a703lz5c.fsf@bsb.me.uk> |
| In reply to | #21633 |
olcott <NoOne@NoWhere.com> writes: > On 7/13/2020 5:42 PM, Ben Bacarisse wrote: >> olcott <NoOne@NoWhere.com> writes: >> >>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>> >>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>> Boolean value. >> >> Would you like to learn why that's wrong, or would you rather just keep >> repeating it? >> >> If you'd like to learn, you have to be a student. I'd ask a student to >> consider an instance of x + y = y + x in Q, for example this one: >> >> S0 + SS0 = SS0 + S0. >> >> and I'd ask them: what can you say about this formula in Q? >> > > How do you get from point "A" to point "B" when no path from point "A" > to point "B" exists? YOU DON'T !!! This does not appear to answer my question. Are you implying that nothing can be said about S0 + SS0 = SS0 + S0 in Q? Because that is not the case. Here's a hint: apply the axioms for + to the LRS and to the RHS. -- Ben.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-13 22:06 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <avadnRPjFtHdvJDCnZ2dnUU7-dfNnZ2d@giganews.com> |
| In reply to | #21634 |
On 7/13/2020 7:26 PM, Ben Bacarisse wrote: > olcott <NoOne@NoWhere.com> writes: > >> On 7/13/2020 5:42 PM, Ben Bacarisse wrote: >>> olcott <NoOne@NoWhere.com> writes: >>> >>>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>>> >>>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>>> Boolean value. >>> >>> Would you like to learn why that's wrong, or would you rather just keep >>> repeating it? >>> >>> If you'd like to learn, you have to be a student. I'd ask a student to >>> consider an instance of x + y = y + x in Q, for example this one: >>> >>> S0 + SS0 = SS0 + S0. >>> >>> and I'd ask them: what can you say about this formula in Q? >>> >> >> How do you get from point "A" to point "B" when no path from point "A" >> to point "B" exists? YOU DON'T !!! > > This does not appear to answer my question. Are you implying that > nothing can be said about S0 + SS0 = SS0 + S0 in Q? Because that is not > the case. Here's a hint: apply the axioms for + to the LRS and to the > RHS. > That you can prove that 1 + 2 = 2 + 1 in Q merely diverts attention away from the fact that this expression ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) cannot be proved in Q. The only way that any expression of language can be shown to be true is to show a mathematical mapping from the expression to a Boolean value. When anyone tries to show that an expression of the formal language of a formal system is true and unprovable they are saying that an undecidable sentence has been decided to be true, thus contradicting themselves. -- Copyright 2020 Pete Olcott
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2020-07-14 17:00 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <87pn8ykrwq.fsf@bsb.me.uk> |
| In reply to | #21641 |
olcott <NoOne@NoWhere.com> writes: > On 7/13/2020 7:26 PM, Ben Bacarisse wrote: >> olcott <NoOne@NoWhere.com> writes: >> >>> On 7/13/2020 5:42 PM, Ben Bacarisse wrote: >>>> olcott <NoOne@NoWhere.com> writes: >>>> >>>>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>>>> >>>>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>>>> Boolean value. >>>> >>>> Would you like to learn why that's wrong, or would you rather just keep >>>> repeating it? >>>> >>>> If you'd like to learn, you have to be a student. I'd ask a student to >>>> consider an instance of x + y = y + x in Q, for example this one: >>>> >>>> S0 + SS0 = SS0 + S0. >>>> >>>> and I'd ask them: what can you say about this formula in Q? >>>> >>> >>> How do you get from point "A" to point "B" when no path from point "A" >>> to point "B" exists? YOU DON'T !!! >> >> This does not appear to answer my question. Are you implying that >> nothing can be said about S0 + SS0 = SS0 + S0 in Q? Because that is not >> the case. Here's a hint: apply the axioms for + to the LRS and to the >> RHS. > > That you can prove that 1 + 2 = 2 + 1 in Q merely diverts attention > away from the fact that this expression ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) > cannot be proved in Q. Your rant about paths made me think you did not know that S0 + SS0 = SS0 + S0 is a theorem of Q. I will assume you accept that every formula of the form S^n0 + S^m0 = S^m0 + S^n0 is also a theorem of Q. (Do say if you dispute this.) My next questions (I continue to assume you want to learn) would be: do you know what a model of Q is? Could you give an example of a model of Q? This is crucial. I need you to understand a bit about models of Q so I can explain why ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) is, in fact, a rather confusing formula. It has two meanings and they are subtly different. -- Ben.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-14 18:15 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <7e-dnQpoj9jkoZPCnZ2dnUU7-UHNnZ2d@giganews.com> |
| In reply to | #21661 |
On 7/14/2020 11:00 AM, Ben Bacarisse wrote: > olcott <NoOne@NoWhere.com> writes: > >> On 7/13/2020 7:26 PM, Ben Bacarisse wrote: >>> olcott <NoOne@NoWhere.com> writes: >>> >>>> On 7/13/2020 5:42 PM, Ben Bacarisse wrote: >>>>> olcott <NoOne@NoWhere.com> writes: >>>>> >>>>>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>>>>> >>>>>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>>>>> Boolean value. >>>>> >>>>> Would you like to learn why that's wrong, or would you rather just keep >>>>> repeating it? >>>>> >>>>> If you'd like to learn, you have to be a student. I'd ask a student to >>>>> consider an instance of x + y = y + x in Q, for example this one: >>>>> >>>>> S0 + SS0 = SS0 + S0. >>>>> >>>>> and I'd ask them: what can you say about this formula in Q? >>>>> >>>> >>>> How do you get from point "A" to point "B" when no path from point "A" >>>> to point "B" exists? YOU DON'T !!! >>> >>> This does not appear to answer my question. Are you implying that >>> nothing can be said about S0 + SS0 = SS0 + S0 in Q? Because that is not >>> the case. Here's a hint: apply the axioms for + to the LRS and to the >>> RHS. >> >> That you can prove that 1 + 2 = 2 + 1 in Q merely diverts attention >> away from the fact that this expression ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >> cannot be proved in Q. > > Your rant about paths made me think you did not know that S0 + SS0 = SS0 > + S0 is a theorem of Q. I will assume you accept that every formula of > the form S^n0 + S^m0 = S^m0 + S^n0 is also a theorem of Q. (Do say if > you dispute this.) > > My next questions (I continue to assume you want to learn) would be: do > you know what a model of Q is? Could you give an example of a model of > Q? This is crucial. I need you to understand a bit about models of Q > so I can explain why ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) is, in fact, a rather > confusing formula. It has two meanings and they are subtly different. > This is the subject of the last few threads: https://scholar.google.com/scholar?hl=en&as_sdt=0%2C28&q=%22true+and+unprovable%22+godel&btnG=&oq= Ultimately True(T, φ) is a mathematical mapping in T from φ to a Boolean value. What I just said is correct and true and a proper use of all the terms that I used. It is not, however the usual way that these sort of things are typically described. If provable(T, φ) is a required element of the only way that φ can be mathematically mapped in T to true, then True(T, φ) and Uprovable(T, φ) are impossble. -- Copyright 2020 Pete Olcott
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| From | Ben Bacarisse <ben.usenet@bsb.me.uk> |
|---|---|
| Date | 2020-07-15 02:56 +0100 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <875zapk0bb.fsf@bsb.me.uk> |
| In reply to | #21666 |
olcott <NoOne@NoWhere.com> writes: > On 7/14/2020 11:00 AM, Ben Bacarisse wrote: >> olcott <NoOne@NoWhere.com> writes: >> >>> On 7/13/2020 7:26 PM, Ben Bacarisse wrote: >>>> olcott <NoOne@NoWhere.com> writes: >>>> >>>>> On 7/13/2020 5:42 PM, Ben Bacarisse wrote: >>>>>> olcott <NoOne@NoWhere.com> writes: >>>>>> >>>>>>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>>>>>> >>>>>>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a >>>>>>> Boolean value. >>>>>> >>>>>> Would you like to learn why that's wrong, or would you rather just keep >>>>>> repeating it? >>>>>> >>>>>> If you'd like to learn, you have to be a student. I'd ask a student to >>>>>> consider an instance of x + y = y + x in Q, for example this one: >>>>>> >>>>>> S0 + SS0 = SS0 + S0. >>>>>> >>>>>> and I'd ask them: what can you say about this formula in Q? >>>>>> >>>>> >>>>> How do you get from point "A" to point "B" when no path from point "A" >>>>> to point "B" exists? YOU DON'T !!! >>>> >>>> This does not appear to answer my question. Are you implying that >>>> nothing can be said about S0 + SS0 = SS0 + S0 in Q? Because that is not >>>> the case. Here's a hint: apply the axioms for + to the LRS and to the >>>> RHS. >>> >>> That you can prove that 1 + 2 = 2 + 1 in Q merely diverts attention >>> away from the fact that this expression ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) >>> cannot be proved in Q. >> >> Your rant about paths made me think you did not know that S0 + SS0 = SS0 >> + S0 is a theorem of Q. I will assume you accept that every formula of >> the form S^n0 + S^m0 = S^m0 + S^n0 is also a theorem of Q. (Do say if >> you dispute this.) >> >> My next questions (I continue to assume you want to learn) would be: do >> you know what a model of Q is? Could you give an example of a model of >> Q? This is crucial. I need you to understand a bit about models of Q >> so I can explain why ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) is, in fact, a rather >> confusing formula. It has two meanings and they are subtly different. > > This is the subject of the last few threads: > > https://scholar.google.com/scholar?hl=en&as_sdt=0%2C28&q=%22true+and+unprovable%22+godel&btnG=&oq= > > Ultimately True(T, φ) is a mathematical mapping in T from φ to a > Boolean value. I had hoped you wanted to learn what logicians mean by "true". The example of Robinson arithmetic is an enlightening one (that's why it was devised) but if you'd rather just re-state you opinions (as it anyone should care about them), go ahead. My offer to explain still stands. Just say if you know what a model is, and we can take it from there. > What I just said is correct and true and a proper use of all the terms > that I used. That is not an opinion that is widely shared. > It is not, however the usual way that these sort of > things are typically described. Indeed. It makes it impossible for you to talk about these theorems, because you simply insert your meanings without alerting anyone. I've advised before that you put a PO- prefix onto words you've made up, but that would make it clear that you have nothing to say about any of the actual theorems. > If provable(T, φ) is a required element of the only way that φ can be > mathematically mapped in T to true, then True(T, φ) and Uprovable(T, > φ) are impossble. What you mean is that if PO-provable(T, φ) is a PO-required PO-element of the only way that φ can be mathematically PO-mapped in T to PO-true, then PO-True(T, φ) and PO-Unprovable(T, φ) are PO-impossible. But if you actually said that, no one would care. -- Ben.
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| From | olcott <NoOne@NoWhere.com> |
|---|---|
| Date | 2020-07-14 21:55 -0500 |
| Subject | Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V24 (Are we there yet?) |
| Message-ID | <zsCdncdz36GK7ZPCnZ2dnUU7-S_NnZ2d@giganews.com> |
| In reply to | #21667 |
On 7/14/2020 8:56 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
>
>> On 7/14/2020 11:00 AM, Ben Bacarisse wrote:
>>> olcott <NoOne@NoWhere.com> writes:
>>>
>>>> On 7/13/2020 7:26 PM, Ben Bacarisse wrote:
>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>
>>>>>> On 7/13/2020 5:42 PM, Ben Bacarisse wrote:
>>>>>>> olcott <NoOne@NoWhere.com> writes:
>>>>>>>
>>>>>>>> φ = ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x)
>>>>>>>>
>>>>>>>> φ is not true or false in Q because Q lacks a mapping in Q from φ to a
>>>>>>>> Boolean value.
>>>>>>>
>>>>>>> Would you like to learn why that's wrong, or would you rather just keep
>>>>>>> repeating it?
>>>>>>>
>>>>>>> If you'd like to learn, you have to be a student. I'd ask a student to
>>>>>>> consider an instance of x + y = y + x in Q, for example this one:
>>>>>>>
>>>>>>> S0 + SS0 = SS0 + S0.
>>>>>>>
>>>>>>> and I'd ask them: what can you say about this formula in Q?
>>>>>>>
>>>>>>
>>>>>> How do you get from point "A" to point "B" when no path from point "A"
>>>>>> to point "B" exists? YOU DON'T !!!
>>>>>
>>>>> This does not appear to answer my question. Are you implying that
>>>>> nothing can be said about S0 + SS0 = SS0 + S0 in Q? Because that is not
>>>>> the case. Here's a hint: apply the axioms for + to the LRS and to the
>>>>> RHS.
>>>>
>>>> That you can prove that 1 + 2 = 2 + 1 in Q merely diverts attention
>>>> away from the fact that this expression ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x)
>>>> cannot be proved in Q.
>>>
>>> Your rant about paths made me think you did not know that S0 + SS0 = SS0
>>> + S0 is a theorem of Q. I will assume you accept that every formula of
>>> the form S^n0 + S^m0 = S^m0 + S^n0 is also a theorem of Q. (Do say if
>>> you dispute this.)
>>>
>>> My next questions (I continue to assume you want to learn) would be: do
>>> you know what a model of Q is? Could you give an example of a model of
>>> Q? This is crucial. I need you to understand a bit about models of Q
>>> so I can explain why ∀x ∈ ℕ ∀y ∈ ℕ (x + y = y + x) is, in fact, a rather
>>> confusing formula. It has two meanings and they are subtly different.
>>
>> This is the subject of the last few threads:
>>
>> https://scholar.google.com/scholar?hl=en&as_sdt=0%2C28&q=%22true+and+unprovable%22+godel&btnG=&oq=
>>
>> Ultimately True(T, φ) is a mathematical mapping in T from φ to a
>> Boolean value.
>
> I had hoped you wanted to learn what logicians mean by "true".
Do you understand that the only thing that it can possibly mean is what
I just said using more steps and more complex language?
> The
> example of Robinson arithmetic is an enlightening one (that's why it was
> devised) but if you'd rather just re-state you opinions (as it anyone
> should care about them), go ahead. My offer to explain still stands.
> Just say if you know what a model is, and we can take it from there.
>
Here is what I know of model theory:
Satisfiability
A formula is satisfiable if it is possible to find an interpretation
(model) that makes the formula true.
https://en.wikipedia.org/wiki/Satisfiability
Interpretation (logic)
An interpretation is an assignment of meaning to the
[non-logical] symbols of a formal language.
https://en.wikipedia.org/wiki/Interpretation_(logic)
Model theory
A model of a theory is a structure (e.g. an interpretation)
that satisfies the sentences of that theory.
https://en.wikipedia.org/wiki/Model_theory
Here is a key additional insight explaining which formulas are truth
bearers and which are not.
In classical logic a sentence in a language is true or false under
(and only under) an interpretation and is therefore a truth-bearer.
https://en.wikipedia.org/wiki/Truth-bearer#Sentences_in_languages_of_classical_logic
>> What I just said is correct and true and a proper use of all the terms
>> that I used.
>
> That is not an opinion that is widely shared.
Anyone fully understanding mathematical mapping knows that I am correct
about this.
>
>> It is not, however the usual way that these sort of
>> things are typically described.
>
> Indeed. It makes it impossible for you to talk about these theorems,
Not for anyone that sufficiently understands mathematical mapping.
> because you simply insert your meanings without alerting anyone. I've
> advised before that you put a PO- prefix onto words you've made up, but
> that would make it clear that you have nothing to say about any of the
> actual theorems.
-- Ultimately True(T, φ) is a mathematical mapping in T from φ to a
-- Boolean value.
These terms were used perfectly according to their standard meaning:
>>>mathematical mapping in T from φ to a Boolean value<<<
>> If provable(T, φ) is a required element of the only way that φ can be
>> mathematically mapped in T to true, then True(T, φ) and Uprovable(T,
>> φ) are impossble.
>
> What you mean is that if PO-provable(T, φ) is a PO-required PO-element
> of the only way that φ can be mathematically PO-mapped in T to PO-true,
> then PO-True(T, φ) and PO-Unprovable(T, φ) are PO-impossible. But if you
> actually said that, no one would care.
>
--
Copyright 2020 Pete Olcott
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