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Re: Final Resolution of the Liar Paradox

From polcott <polcott333@gmail.com>
Newsgroups comp.theory, sci.logic, sci.math
Subject Re: Final Resolution of the Liar Paradox
Date 2025-11-28 08:03 -0600
Message-ID <10gca48$of6n$2@solani.org> (permalink)
References <10g9nlr$1fv38$1@dont-email.me> <10g9u87$1iors$1@dont-email.me> <10gbl74$26had$1@dont-email.me>

Cross-posted to 3 groups.

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On 11/28/2025 2:06 AM, Mikko wrote:
> olcott kirjoitti 27.11.2025 klo 18.28:
>> On 11/27/2025 8:36 AM, olcott wrote:
>>> This sentence is not true.
>>> It is not true about what?
>>> It is not true about being not true.
>>> It is not true about being not true about what?
>>> It is not true about being not true about being not true.
>>> Oh I see you are stuck in a loop!
>>>
>>> The simple English shows that the Liar Paradox never
>>> gets to the point.
>>>
>>> This is formalized in the Prolog programming language
>>> ?- LP = not(true(LP)).
>>> LP = not(true(LP)).
>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>> False.
>>>
>>> Failing an occurs check seems to mean that the
>>> resolution of an expression remains stuck in
>>> infinite recursion. This is more clearly seen below.
>>>
>>> In Olcott's Minimal Type Theory
>>> LP := ~True(LP)    // LP {is defined as} ~True(LP)
>>> that expands to ~True(~True(~True(~True(~True(~True(...))))))
>>> https://philarchive.org/archive/PETMTT-4v2
>>>
>>> The above seems to prove that the Liar Paradox
>>> has merely been semantically unsound all these years.
>>>
>>
>> *Final Resolution of the Liar Paradox*
>> https://philpapers.org/archive/OLCFRO.pdf
> 
> Nothing is final in philosophy.
> 
> For the most common forms of formal logic this paradox is not possible
> because there is no syntax for definitions.
> 

Lookup Olcott's Minimal Type Theory
I created Olcott's Minimal Type Theory
for the sole purpose of formalizing
Pathological-self-reference(Olcott 2004)

LP := ~True(LP)    // LP {is defined as} ~True(LP)
that expands to ~True(~True(~True(~True(~True(~True(...))))))

G := (F ⊬ G)  // G is defined as unprovable in F
...We are therefore confronted with a proposition which
asserts its own unprovability. 15 … (Gödel 1931:40-41)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia
Mathematica And Related Systems



-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

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Thread

Final Resolution of the Liar Paradox olcott <polcott333@gmail.com> - 2025-11-27 08:36 -0600
  Re: Final Resolution of the Liar Paradox olcott <polcott333@gmail.com> - 2025-11-27 10:28 -0600
    Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-28 10:06 +0200
      Re: Final Resolution of the Liar Paradox polcott <polcott333@gmail.com> - 2025-11-28 08:03 -0600
        Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-29 10:48 +0200
          Re: Final Resolution of the Liar Paradox olcott <polcott333@gmail.com> - 2025-11-29 10:04 -0600
            Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:10 +0200
      Re: Final Resolution of the Liar Paradox dart200 <user7160@newsgrouper.org.invalid> - 2025-11-28 09:29 -0800
        Re: Final Resolution of the Liar Paradox olcott <polcott333@gmail.com> - 2025-11-28 12:10 -0600
        Re: Final Resolution of the Liar Paradox "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 16:42 -0800
          Re: Final Resolution of the Liar Paradox FromTheRafters <FTR@nomail.afraid.org> - 2025-11-28 19:49 -0500
            Re: Final Resolution of the Liar Paradox "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 16:57 -0800
            Re: Final Resolution of the Liar Paradox "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 17:06 -0800
        Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-29 10:55 +0200
          Re: Final Resolution of the Liar Paradox olcott <polcott333@gmail.com> - 2025-11-29 10:10 -0600
            Re: Final Resolution of the Liar Paradox dart200 <user7160@newsgrouper.org.invalid> - 2025-11-29 11:00 -0800
              Re: Final Resolution of the Liar Paradox olcott <polcott333@gmail.com> - 2025-11-29 13:16 -0600
            Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:12 +0200
          on "Nothing is final" dart200 <user7160@newsgrouper.org.invalid> - 2025-11-29 10:53 -0800
            Re: on "Nothing is final" olcott <polcott333@gmail.com> - 2025-11-29 13:00 -0600
  Re: Final Resolution of the Liar Paradox Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-27 18:07 +0000
    Re: Final Resolution of the Liar Paradox "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 16:43 -0800
      Re: Final Resolution of the Liar Paradox Kaz Kylheku <643-408-1753@kylheku.com> - 2025-11-29 01:20 +0000
        Re: Final Resolution of the Liar Paradox "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-28 17:28 -0800
      Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-29 11:06 +0200
        Re: Final Resolution of the Liar Paradox "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2025-11-29 14:37 -0800
          Re: Final Resolution of the Liar Paradox Mikko <mikko.levanto@iki.fi> - 2025-11-30 11:16 +0200

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