Re: This is how I overturn the Tarski Undefinability theorem

On 9/3/24 8:44 AM, olcott wrote:

On 9/3/2024 5:38 AM, Mikko wrote:

On 2024-09-02 13:01:23 +0000, olcott said:
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On 9/2/2024 2:54 AM, Mikko wrote:

On 2024-09-01 13:47:00 +0000, olcott said:
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On 9/1/2024 7:52 AM, Mikko wrote:

On 2024-08-31 18:48:18 +0000, olcott said:
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*This is how I overturn the Tarski Undefinability theorem*
An analytic expression of language is any expression of formal or natural language that can be proven true or false entirely on the basis of a connection to its semantic meaning in this same language.
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This connection must be through a sequence of truth preserving operations from expression x of language L to meaning M in L. A lack of such connection from x or ~x in L is construed as x is not a truth bearer in L.
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Tarski's Liar Paradox from page 248
    It would then be possible to reconstruct the antinomy of the liar
    in the metalanguage, by forming in the language itself a sentence
    x such that the sentence of the metalanguage which is correlated
    with x asserts that x is not a true sentence.
    https://liarparadox.org/Tarski_247_248.pdf
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Formalized as:
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf
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*Formalized as Prolog*
?- LP = not(true(LP)).
LP = not(true(LP)).

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According to Prolog semantics "false" would also be a correct
response.
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?- unify_with_occurs_check(LP, not(true(LP))).
false.

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To the extend Prolog formalizes anything, that only formalizes
the condept of self-reference. I does not say anything about
int.
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When formalized as Prolog unify_with_occurs_check()
detects a cycle in the directed graph of the evaluation
sequence proving the LP is not a truth bearer.

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Prolog does not say anything about truth-bearers.
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It may seem that way if you have no idea what
(a) a directed is
(b) what cycles in a directed graph are
(c) What an evaluation sequence is

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More relevanto would be what a "truth-maker" is.
Anyway, it seems that Prolog does not say anything about
truth-bearers because Prolog does not say anything about
truth-bearers.
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When Prolog derives expression x from Facts and Rules
by applying the truth preserving operations of Rules to
Facts is the truthmaker for truth-bearer x.

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A Prolog impementation applies Prolog operations.

 Which are (like logic) for the most part truth preserving.
If (A & B) then A

But Prolog can not express ALL logical statement.

 

For some cases
Prolog offers several operations letting the implementation to
choose which one to apply.

 I don't thing so. Once the Facts and Rules are specified
Prolog chooses whatever Facts and Rules to prove x or not.
It is back-chained inference.

But the set of Prolog operations are limited compared to logic.

 

Consequently some goals may evaluate
to true in some implementations and false in others, for example
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  L = [L].
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