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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: How a True(X) predicate can be defined for the set of analytic knowledge
Date: Sun, 6 Apr 2025 14:37:05 +0300
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On 2025-04-05 18:01:00 +0000, olcott said:

> 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.

No, you haven't. Which sentence is false?

> <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

-- 
Mikko