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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic
 knowledge
Date: Sat, 5 Apr 2025 16:08:20 -0500
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On 4/5/2025 3:20 PM, Richard Damon wrote:
> On 4/5/25 2:01 PM, olcott wrote:
>> On 4/5/2025 2:48 AM, Mikko wrote:
>>> On 2025-04-02 16:05:28 +0000, olcott said:
>>>
>>>> On 4/2/2025 4:43 AM, Mikko wrote:
>>>>> On 2025-04-01 18:00:56 +0000, olcott said:
>>>>>
>>>>>> On 4/1/2025 1:36 AM, Mikko wrote:
>>>>>>> On 2025-03-31 18:29:32 +0000, olcott said:
>>>>>>>
>>>>>>>> On 3/31/2025 4:04 AM, Mikko wrote:
>>>>>>>>> On 2025-03-30 11:20:05 +0000, olcott said:
>>>>>>>>>
>>>>>>>>> You have never expressed any disagreement with the starting 
>>>>>>>>> points of
>>>>>>>>> Tarski's proof. You have ever claimed that any of Tarski's 
>>>>>>>>> inferences
>>>>>>>>> were not truth preserving. But you have claimed that the last 
>>>>>>>>> one of
>>>>>>>>> these truth preservin transformation has produced a false 
>>>>>>>>> conclusion.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It is ALWAYS IMPOSSIBLE to specify True(X) ∧ ~Provable(X)
>>>>>>>> (what Tarski proved) when-so-ever True(X) ≡ Provable(X).
>>>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>>>
>>>>>>> Tarski's proof was not about provability. Gödel had already proved
>>>>>>> that there are unprovable true sentences. Tarski's work is about
>>>>>>> definability.
>>>>>>
>>>>>> https://liarparadox.org/Tarski_275_276.pdf
>>>>>> Step (3) is self-contradictory, thus his whole proof fails.
>>>>>
>>>>> Irrelevant. As Traski clearly points out, (3) can be derived from 
>>>>> (1) and
>>>>> (2) with a truth preserving transformation.
>>>>
>>>> (3) is false, thus his whole proof is dead.
>>>
>>> So you reject the principle that a truth preserving transfromation from
>>> true sentences always produces a true sentence.
>>>
>>
>> Tarski started with a false sentence, as I have shown.
>>
>> <DIRECT QUOTE>
>> THEOREM I. (α) In whatever way the symbol 'Tr', denoting a
>> class of expressions, is defined in the metatheory, it will be possible
>> to derive from it the negation of one of the sentences which were
>> described in the condition (α) of the convention T;
>>
>> (β) assuming that the class of all provable sentences of the metatheory
>> is consistent, it is impossible to construct an adequate
>> definition of truth in the sense of convention T on the basis of the
>> metatheory. ...
>>
>> Should we succeed in constructing in the metalanguage
>> a correct definition of truth, then ...
>>
>> 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.
>> </DIRECT QUOTE>
>>
>> https://liarparadox.org/Tarski_247_248.pdf
>>
>>
> 
> But that Theorem has been proven, and isn't just a "false assumption", 
> and thus it is YOUR claim that is based on lies.
> 

(1) x ∉ Provable if and only if p
I have just shown that Step (1) of the proof is a false assumption.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer