Re: This is how I overturn the Tarski Undefinability theorem

On 9/6/2024 6:55 AM, Mikko wrote:

On 2024-09-03 12:44:00 +0000, olcott said:
 

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.

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

 Logic where the infoerence rules are for the most part truth prserving
is not useful. They all must be.
 

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

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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.

 Standard Prolog is what the Prolog standard says. Conforming implementations
may vary if the standard allows. If you think otherwise you are wrong.
There are also non-starndard Prlongs that vary even more.
 

The fundamental architectural overview of all Prolog implementations
is the same True(x) means X is derived by applying Rules (AKA truth preserving operations) to Facts.
That is the way that all expressions X of language L are determined
to be true in L on the basis of the connection from X in L by truth preserving operations to the semantic meaning of X in L.
{Linguistic truth} is the philosophical foundation of truth
in math and logic, AKA relations between finite strings.

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

 No matter what you think this is an example. It is outside of the intended
application area but not prohibited.
 

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