Re: Undecidability based on epistemological antinomies V2 --correct reasoning--

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