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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 13:01:00 -0500
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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


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