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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: This is how I overturn the Tarski Undefinability theorem
Date: Tue, 3 Sep 2024 13:38:04 +0300
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On 2024-09-02 13:01:23 +0000, olcott said:

> 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:
>>>> 
>>>>> *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.
>>>>> 
>>>>> 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.
>>>>> 
>>>>> 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
>>>>> 
>>>>> 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
>>>>> 
>>>>> *Formalized as Prolog*
>>>>> ?- LP = not(true(LP)).
>>>>> LP = not(true(LP)).
>>>> 
>>>> According to Prolog semantics "false" would also be a correct
>>>> response.
>>>> 
>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).
>>>>> false.
>>>> 
>>>> To the extend Prolog formalizes anything, that only formalizes
>>>> the condept of self-reference. I does not say anything about
>>>> int.
>>>> 
>>>>> 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.
>>>> 
>>>> Prolog does not say anything about truth-bearers.
>>>> 
>>> 
>>> 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.

A Prolog impementation applies Prolog operations. For some cases
Prolog offers several operations letting the implementation to
choose which one to apply. Consequently some goals may evaluate
to true in some implementations and false in others, for example

  L = [L].

-- 
Mikko