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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: This is how I overturn the Tarski Undefinability theorem
Date: Sat, 7 Sep 2024 08:06:52 -0500
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On 9/7/2024 3:35 AM, Mikko wrote:
> On 2024-09-06 12:22:04 +0000, olcott said:
> 
>> 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.
> 
> The details are permitted to differ.
> 

Instead of using any single order of logic we simultaneously
represent an arbitrary number of orders of logic in a type
hierarchy knowledge ontology.

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