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Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this)

From "Pascal J. Bourguignon" <pjb@informatimago.com>
Newsgroups comp.lang.prolog, comp.lang.lisp
Subject Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this)
Date 2019-04-30 07:08 +0200
Organization Informatimago
Message-ID <m2k1fcxepj.fsf@despina.home> (permalink)
References (13 earlier) <87ef5mkia5.fsf@nightsong.com> <j46dnWVt_8qrj1jBnZ2dnUU7-LPNnZ2d@giganews.com> <d855c8d9-b346-4909-b2d8-4d975c40721a@googlegroups.com> <c3461c97-d07c-4261-8505-17c1e5704edf@googlegroups.com> <TOydnSJT068oJVrBnZ2dnUU7-dPNnZ2d@giganews.com>

Cross-posted to 2 groups.

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peteolcott <Here@Home> writes:

> On 4/28/2019 6:36 AM, j4n bur53 wrote:
>> Pure Prolog is not able to enumerate a model M,
>> because it uses depth first. negation of failure
>> subsequently also does cannot enumerate a model M.
>>
>
> I am not talking about every aspect of Prolog.
> I am only talking about the aspect of Prolog that "understands"
> that Provable(X) is True(X), Provable (¬X) is False(X).
>
> From this much we can build:
> (¬Provable(X) ∧ ¬Provable(¬X)) ↔ Unsound(X)
> Which means that a sentence must be true or false.

The problem is that it's not interesting to have no unsound sentences.
What's interesting is to have no inconsistency.
That is that you have not True(X) ∧ False(X),
ie that you don't have (Provable(X) ∧ Provable(¬X)) for any X.

And what Gödel proved, is that if you have a non-trivial formal system
that is not unsound, then it is inconsistent.

So, bravo, you've built a useless formal system!

-- 
__Pascal J. Bourguignon__
http://www.informatimago.com

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Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 09:58 -0500
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Siri Cruise <chine.bleu@yahoo.com> - 2019-04-26 08:20 -0700
    Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 10:48 -0500
      Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) paul wallich <pw@panix.com> - 2019-04-26 13:40 -0400
        Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:10 -0500
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 10:51 -0500
    Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) j4n bur53 <bursejan@gmail.com> - 2019-04-26 10:38 -0700
    Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-26 17:48 +0000
      Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-26 17:22 -0500
        Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-27 01:13 +0000
          Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 11:23 -0500
            Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-27 18:26 +0000
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) j4n bur53 <bursejan@gmail.com> - 2019-04-27 14:33 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:49 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 16:58 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:13 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:28 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 17:44 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 18:59 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 19:44 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 19:48 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) j4n bur53 <bursejan@gmail.com> - 2019-04-27 18:10 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 20:27 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 21:38 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) j4n bur53 <bursejan@gmail.com> - 2019-04-28 03:37 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) j4n bur53 <bursejan@gmail.com> - 2019-04-28 04:36 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 21:53 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-04-30 07:08 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-30 00:41 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-30 11:55 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-30 12:02 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 07:50 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-05-01 14:53 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 09:29 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-05-01 18:37 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 13:53 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 13:56 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Keith Thompson <kst-u@mib.org> - 2019-05-01 10:48 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Bonita Montero <Bonita.Montero@gmail.com> - 2019-05-01 20:25 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (HP Proof refutation) peteolcott <Here@Home> - 2019-05-01 15:01 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 14:01 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) David Brown <david.brown@hesbynett.no> - 2019-05-01 23:28 +0200
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:14 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 18:43 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 22:06 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:10 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:12 -0500
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-01 15:12 -0500
            Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Richard Damon <Richard@Damon-Family.org> - 2019-05-04 15:05 -0400
              Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-04 15:07 -0500
        Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) j4n bur53 <bursejan@gmail.com> - 2019-04-27 03:17 -0700
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Keith Thompson <kst-u@mib.org> - 2019-04-26 19:43 -0700
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Bonita Montero <Bonita.Montero@gmail.com> - 2019-05-01 17:56 +0200

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