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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: Undecidability based on epistemological antinomies V2 --correct
 reasoning--
Date: Thu, 25 Apr 2024 12:04:50 -0500
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On 4/25/2024 6:32 AM, Richard Damon wrote:
> On 4/25/24 12:33 AM, olcott wrote:
>> On 4/24/2024 10:59 PM, Ross Finlayson wrote:
>> The only thing that I have ever been talking about is True(L,x)
>> specified as relations between finite strings such that a
>> correct and consistent True(L,x) can be defined for every
>> element of human knowledge that can be expressed using language.
>>
>> As far as Eastern religion goes Zen/Tao & Advaita.
>>
> 
> 
> Then what is the value of True(L,x) where x is defined as to be the 
> stagtement: "Not True(L,x)"?
> 
> If it is TRUE, the x is the equivalent of NOT TRUE, or FALSE and thus 
> your True(L,x) has said a false statement was true.
> 
> If it is FALSE, then x is the equivalent of NOT FALSE, or TRUE, and thus 
> your True(L,x) has said that a TRUE statement was FALSE.
> 
> If it refuses to answer, then you have lied that it can be defined for 
> ANY finite string.
> 
> That, our your logic system just can't handle the basics of the problem.

∃L ∈ Formal_Systems, ∃x ∈ L (True(L, x)  ≡ (L ⊢ x))
∃L ∈ Formal_Systems, ∃x ∈ L (False(L, x) ≡ (L ⊢ ~x))
∃L ∈ Formal_Systems, ∃x ∈ L (Truth_Bearer(L, x) ≡ (True(L, x) ∨ False(L, 
x)))

https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF 


I created Minimal Type Theory so that I could concisely encode
actual self-reference. In all the literature it is conventional
to encode self-reference incorrectly.

LP := ~True(LP)

Prolog rejects expressions having the same structure as LP
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.

Truth_Bearer(L, LP) == FALSE


-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer