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Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak)

From André G. Isaak <agisaak@gm.invalid>
Newsgroups comp.theory, comp.ai.philosophy, comp.ai.nat-lang, sci.lang.semantics
Subject Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak)
Date 2020-07-06 13:55 -0600
Organization Christians and Atheists United Against Creeping Agnosticism
Message-ID <rdvvj3$pop$1@dont-email.me> (permalink)
References (19 earlier) <87zh8dbkev.fsf@nosuchdomain.example.com> <3I-dnWs52teNM5_CnZ2dnUU7-Y3NnZ2d@giganews.com> <87o8otaxka.fsf@nosuchdomain.example.com> <CJqdnaJVqJmD3Z7CnZ2dnUU7-TPNnZ2d@giganews.com> <rdvkkb$flj$1@dont-email.me>

Cross-posted to 4 groups.

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On 2020-07-06 10:48, André G. Isaak wrote:

> A self-contradictory sentence such as "this sentence is false" can 
> easily be proven to be true just as it can easily be shown to be
> false (just apply a reductio ad absurdum). It is inconsistent. It
> isn't, therefore, evidence of incompleteness. But neither Tarski nor
> Gödel make use of such sentences as I explain above.
> 
> Incompleteness: There exist expressions which can neither be derived
> as theorems nor can their negations be derived as theorems.
> 
> Inconsistency: There exist expressions which can be derived as
> theorems and whose negations can also be derived as theorems.

Just a brief addition to the above. If you want to think about 
incompleteness in English (as opposed to formal systems) it isn't the 
liar's paradox you want, but rather the following self-referential sentence:

"This sentence is true".

That is an actual example of an undecidable proposition. It is perfectly 
consistent with being either true or false.

We could create a system in which the above is included as an axiom, and 
it would be perfectly consistent.

We could create a system in which its negation is included as an axiom, 
and that system would also be perfectly consistent.

If neither is included as an axiom, then we have an undecidable 
proposition, meaning such a system would be incomplete.

So "This sentence is false" leads to inconsistency.

whereas

"This sentence is true" leads to incompleteness (provided neither it nor 
its negation are axioms).

André

-- 
To email remove 'invalid' & replace 'gm' with well known Google mail
service.

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Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-26 20:03 -0500
  Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-26 20:53 -0700
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-26 23:46 -0500
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-26 22:54 -0700
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 11:04 -0500
    Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-06-27 10:24 +0100
      Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 11:14 -0500
        Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-27 09:38 -0700
          Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 11:58 -0500
            Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-27 11:54 -0700
              Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 15:26 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-27 14:52 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 17:09 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-27 17:43 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 19:46 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-27 20:15 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-27 22:11 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-28 16:32 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 David Kleinecke <dkleinecke@gmail.com> - 2020-06-28 14:43 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 olcott <NoOne@NoWhere.com> - 2020-06-28 16:59 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 André G. Isaak <agisaak@gm.invalid> - 2020-06-28 20:18 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-28 21:45 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-28 21:27 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-28 21:59 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 00:48 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-28 23:57 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 13:28 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 12:33 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 14:33 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 13:52 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 15:02 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 14:14 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 15:39 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 15:13 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-29 17:09 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-29 21:21 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 01:09 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 00:24 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 16:46 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 16:46 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 18:24 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 18:15 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 19:33 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 19:18 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 20:34 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 20:06 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 21:31 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-06-30 20:54 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-01 11:03 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-01 10:35 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-01 17:35 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-01 22:47 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 07:01 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 10:51 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 10:46 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 13:59 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 13:37 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-07-02 08:53 +0100
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 09:52 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-02 15:06 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 10:56 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-02 22:52 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 18:35 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Chris Buckley <alan@sabir.com> - 2020-07-02 23:48 +0000
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 18:57 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) David Kleinecke <dkleinecke@gmail.com> - 2020-07-02 19:22 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-02 22:03 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 23:13 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 00:36 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-02 23:43 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 12:50 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 12:19 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 13:21 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 12:33 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 13:48 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 13:55 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 13:06 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 13:07 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 12:56 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 14:14 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 13:38 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-03 15:59 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-03 22:54 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-04 08:56 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-04 08:12 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-07-04 10:06 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) André G. Isaak <agisaak@gm.invalid> - 2020-07-04 09:31 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V20 (Text Analysis) olcott <NoOne@NoWhere.com> - 2020-07-04 14:31 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V20 (Text Analysis) André G. Isaak <agisaak@gm.invalid> - 2020-07-04 15:17 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V20 (Text Analysis) olcott <NoOne@NoWhere.com> - 2020-07-04 17:29 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-05 13:01 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-05 16:40 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-05 23:52 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) Keith Thompson <Keith.S.Thompson+u@gmail.com> - 2020-07-06 00:53 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-06 10:15 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) David Kleinecke <dkleinecke@gmail.com> - 2020-07-06 08:33 -0700
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-06 11:49 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 11:27 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-07 22:22 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 10:48 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) André G. Isaak <agisaak@gm.invalid> - 2020-07-06 13:55 -0600
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-07 22:13 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V23 (Newspeak) olcott <NoOne@NoWhere.com> - 2020-07-07 22:44 -0500
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) Alan Smaill <smaill@SPAMinf.ed.ac.uk> - 2020-06-30 11:17 +0100
                Re: Simply defining Gödel Incompleteness and Tarski Undefinability away V13 (Isomorphism) olcott <NoOne@NoWhere.com> - 2020-06-30 08:44 -0500

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