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

On 4/25/24 1:04 PM, olcott wrote:

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.
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As far as Eastern religion goes Zen/Tao & Advaita.
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Then what is the value of True(L,x) where x is defined as to be the stagtement: "Not True(L,x)"?
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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.
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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.
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If it refuses to answer, then you have lied that it can be defined for ANY finite string.
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That, our your logic system just can't handle the basics of the problem.

 ∃L ∈ Formal_Systems, ∃x ∈ L (True(L, x)  ≡ (L ⊢ x))

So, that True give ONE correct answer doesn't make it correct.

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

And, again ONE correct answer doesn't make it correct.

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

And that fact that there exists at least one statement that is either true or false doesn't mean a lot.
You seem to have a VERY weak concept of what a Truth Predicate needs to do, or don't understand what the logic statement you are using mean.

 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
 

In other words, you are admitting that your "True" predicate, can't handle ALL statements.
Glad you admit it, or is it that you just don't understand what you are talkling about