Re: This is how I overturn the Tarski Undefinability theorem

On 9/2/2024 2:54 AM, Mikko wrote:

On 2024-09-01 13:47:00 +0000, olcott said:
 

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

 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.
 

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.

If you do know these things then Prolog proved that LP
has no truth-maker and thus cannot be a truth-bearer.

 Prolog does not prove anythng about truth bearers.

Sure it does and it does this most directly when x is
unprovable in Prolog this proves that x has no truth-maker
in a set of Facts and Rules within the set of Facts and
Rules (AKA formal system).

Certain kind
of Prolog programs can be regarded as proofs in a weak formal
system but that does not include those that end with "false".
Even then the proof is not a proof about anything, just a
formal proof.
 

False in Prolog simply means that ~x is proved by a set of Facts
and Rules. When neither x nor ~x can be proved withing a set
of facts and Rules then x is not a truth-bearer in this formal
system of facts and Rules.

The purpose of this work was to show that algorithmic
undecidability is a misconception providing more details
than Wittgenstein's rebuttal of Gödel.

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Which it didn't show.

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I showed it to everyone knowing (a)(b)(c)

 No, you did not.
 

I just showed that when neither x nor ~x is provable within
a set of Facts and Rules (AKA formal system) that x is simply
not a truth bearer in this formal system.
If the formal system is about lug-nuts then we cannot say that
it is incomplete for not knowing about birthday cakes.
If x is self-contradictory then x is rejected as invalid input
the same way that Prolog rejects the Liar Paradox.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Prolog detects a cycle in the directed graph of the
evaluation sequence of LP meaning that the evaluation
of LP has an infinite loop that would never end.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer