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

From paul wallich <pw@panix.com>
Newsgroups comp.lang.prolog, comp.lang.lisp
Subject Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this)
Date 2019-04-26 13:40 -0400
Organization PANIX Public Access Internet and UNIX, NYC
Message-ID <q9vfpm$qqa$1@reader2.panix.com> (permalink)
References <2_ydnT3SYPULgV7BnZ2dnUU7-cnNnZ2d@giganews.com> <chine.bleu-7C0B92.08201326042019@reader.eternal-september.org> <DKCdnb4BVabItV7BnZ2dnUU7-VvNnZ2d@giganews.com>

Cross-posted to 2 groups.

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On 4/26/19 11:48 AM, peteolcott wrote:
> On 4/26/2019 10:20 AM, Siri Cruise wrote:
>> In article <2_ydnT3SYPULgV7BnZ2dnUU7-cnNnZ2d@giganews.com>,
>>   peteolcott <Here@Home> wrote:
>>
>>> If a the query of the negation of a Prolog goal returns Yes then the 
>>> query is
>>> False: Provable(F, ~X)
>>
>> No. A successful negated goal is that it is unproveable with the 
>> resources
>> provided. The problem is Prolog cannot always implement the excluded 
>> middle.
>>
> 
> That is not a problem at all. That is simply sound deductive inference
> working correctly. In this case the resources provided (Facts and Rules)
> are the formal system of symbolic logic. Not provable or refutable in
> the formal system is UNSOUND in this formal system.
> 
> The formal proofs of symbolic logic are not discerning enough to see that
> every closed WFF that is neither True nor False is semantically unsound.

What you've done is to define the cases that give you trouble out of 
existence. By doing so, you've gotten rid of incompleteness for your 
system, but that says more about your system than about Goedel. (I'd 
argue that you've provided a meta-proof of Goedel, but the margin of 
this point is too small to contain it.)

paul

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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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