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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This is how I overturn the Tarski Undefinability theorem
Date: Fri, 6 Sep 2024 07:22:04 -0500
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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:
>>>
>>>> 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.
>>
>> 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.
>>
>> 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
>>>
>>>  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