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Groups > comp.lang.lisp > #32774

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

From Kaz Kylheku <847-115-0292@kylheku.com>
Newsgroups comp.lang.lisp, comp.lang.prolog, comp.lang.c++, comp.lang.c
Subject Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this)
Followup-To comp.lang.lisp
Date 2019-04-27 01:13 +0000
Organization Aioe.org NNTP Server
Message-ID <20190426174714.286@kylheku.com> (permalink)
References <2_ydnT3SYPULgV7BnZ2dnUU7-cnNnZ2d@giganews.com> <q9v7qv$ga5$1@gioia.aioe.org> <DKCdnbkBVaZCtV7BnZ2dnUU7-VudnZ2d@giganews.com> <20190426104732.755@kylheku.com> <rsqdnaWxiMopGV7BnZ2dnUU7-KvNnZ2d@giganews.com>

Cross-posted to 4 groups.

Followups directed to: comp.lang.lisp

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["Followup-To:" header set to comp.lang.lisp.]
On 2019-04-26, peteolcott <Here@Home> wrote:
> On 4/26/2019 12:48 PM, Kaz Kylheku wrote:
>> ["Followup-To:" header set to comp.lang.lisp.]
>> On 2019-04-26, peteolcott <Here@Home> wrote:
>>> The only way to know for sure is to find at least one valid
>>> counter-example to my assertion.
>> 
>> Warning: numerous past debates with Peter Olcott have convinced me that
>> he doesn't know what a counter-example is, and such.
>> 
>
> I have come a very long way since the last time that we talked four
> years ago.

If you aren't doing this in some kind of Lisp, though, it's off topic in
comp.lang.lisp.

> Converting formal proofs of symbolic logic to conform to the sound
> deductive inference model:
>
> Then True(X) means Provable(X) and False(X) mean Provable(¬X) Leaving
> everything else as Unsound(X).

If all truths are provable, and anything not provable is false, then the
system has been weakened; it is incomplete.

Gödel's work is not restricted to examining the properties of
a system which conforms to these constraints; it speaks about a more
general system in which a truth can be unprovable.

(You can wish that that system didn't exist, but that doesn't make
it go away.)

Similarly, in computing, we could restrict ourselves to a programming
language that has only bounded loops and no recursion. Then claim,
look, everything halts!

Everything surely halts in that language which conforms to those
restrictions, but not in a model of computation that doesn't have those
restrictions.

That's all I'm going to say on the subject, except for this:

If True(X) means Provable(X), and only *only* True(X) means that, then
that means your system has no axioms; how can it exist and do anything
useful?

Formal systems require axioms: the basic propositions that are painted
as true rather than proven, from which other things follow. "Provable"
is synonymous with "derivable from axioms". How could you have
forgotten these?

Gödel's work informs us, essentially, that the syntax of formal systems is
capable of expressing new axioms.  These are well-formed statements
which do not conflict with any of the existing axioms, yet which we are
not able to derive from those axioms either: they relate to the existing
axioms in the same way that those axioms to each other.  (Just like
Euclid's Fifth Postulate can't be proven from the other four. It either
has to be accepted, rejected (resulting in a weaker form of geometry) or
replaced with different versions (leading to alternative geometries).

Contrary to your past claims, you have not found a devastating mistake
in Gödel's work; nobody has. It stands.

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Thread

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) Siebe de Vos <siebe@de-vos.de> - 2019-04-26 17:24 +0200
    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) 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 17:10 -0500
        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) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 14:44 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-28 03:40 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 16:48 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 14:52 -0700
                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) Jeff Barnett <jbb@notatt.com> - 2019-04-27 17:12 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 18:41 -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) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 17:10 -0700
                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) Jeff Barnett <jbb@notatt.com> - 2019-04-27 19:26 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-27 18:52 -0700
                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) 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) taruss@google.com - 2019-04-30 09:23 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) "Pascal J. Bourguignon" <pjb@informatimago.com> - 2019-04-30 18:47 +0200
                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> - 2019-04-30 11:55 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-27 21:28 -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) Spiros Bousbouras <spibou@gmail.com> - 2019-04-28 00:16 +0000
                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) paul wallich <pw@panix.com> - 2019-04-29 17:53 -0400
                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) luserdroog <mijoryx@yahoo.com> - 2019-04-29 17:22 -0700
                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) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-04-30 00:18 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Paul Rubin <no.email@nospam.invalid> - 2019-04-29 18:11 -0700
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-04-29 21:58 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Stefan Monnier <monnier@iro.umontreal.ca> - 2019-05-02 15:11 -0400
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Jeff Barnett <jbb@notatt.com> - 2019-05-02 16:46 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Kaz Kylheku <847-115-0292@kylheku.com> - 2019-05-02 23:21 +0000
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-02 22:04 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Jeff Barnett <jbb@notatt.com> - 2019-05-02 21:13 -0600
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) peteolcott <Here@Home> - 2019-05-02 22:42 -0500
                Re: Eliminating Undecidability and Incompleteness in Formal Systems (Halting Problem) peteolcott <Here@Home> - 2019-05-02 22:46 -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 17:49 -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) 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) 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
  Re: Eliminating Undecidability and Incompleteness in Formal Systems (Prolog already does this) Rabican <gavinschuette@gmail.com> - 2019-05-06 05:51 -0700

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