Path: csiph.com!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: polcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic,sci.math
Subject: Re: Final Resolution of the Liar Paradox
Date: Fri, 28 Nov 2025 08:03:52 -0600
Message-ID: <10gca48$of6n$2@solani.org>
References: <10g9nlr$1fv38$1@dont-email.me> <10g9u87$1iors$1@dont-email.me> <10gbl74$26had$1@dont-email.me>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Fri, 28 Nov 2025 14:03:52 -0000 (UTC)
Injection-Info: solani.org; logging-data="802007"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla Thunderbird
Cancel-Lock: sha1:n6SAZeFbs7aNM5ZflrAaUxTOSq4=
X-Antivirus-Status: Clean
In-Reply-To: <10gbl74$26had$1@dont-email.me>
X-User-ID: eJwFwYEBwCAIA7CXKNDizhmi/59gwhC0K0UlL2/C49NISNtgwz3n+Fj/ZsM8FXf3Kgy4RvYAABgQVg==
X-Antivirus: Norton (VPS 251128-4, 11/28/2025), Outbound message
Content-Language: en-US
Xref: csiph.com comp.theory:136720 sci.logic:342531 sci.math:641341

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.