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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: sci.logic
Subject: Re: Why Tarski is wrong
Date: Wed, 19 Mar 2025 16:09:08 +0200
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On 2025-03-18 15:28:31 +0000, olcott said:

> On 3/18/2025 9:34 AM, Mikko wrote:
>> On 2025-03-17 12:54:53 +0000, olcott said:
>> 
>>> On 3/17/2025 3:57 AM, Mikko wrote:
>>>> On 2025-03-17 01:50:24 +0000, olcott said:
>>>> 
>>>>> On 3/16/2025 5:50 PM, Richard Damon wrote:
>>>>>> On 3/16/25 11:12 AM, olcott wrote:
>>>>>>> On 3/16/2025 7:36 AM, joes wrote:
>>>>>>>> Am Sat, 15 Mar 2025 20:43:11 -0500 schrieb olcott:
>>>>>>>>> 
>>>>>>>>> We can define a correct True(X) predicate that always succeeds except
>>>>>>>>> for unknowns and untruths, Tarski WAS WRONG !!!
>>>>>>>> That does not disprove Tarski.
>>>>>>>> 
>>>>>>> 
>>>>>>> He said that this is impossible and no
>>>>>>> counter-examples exists that shows that I am wrong.
>>>>>>> True(GC) == FALSE Cannot be proven true AKA unknown
>>>>>>> True(LP) == FALSE Not a truth-bearer
>>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> But if x is what you are saying is
>>>>> 
>>>>> A True(X) predicate can be defined and Tarski never
>>>>> showed that it cannot.
>>>>> 
>>>>> True(X) only returns TRUE when a a sequence of truth
>>>>> preserving operations can derive X from the set of basic
>>>>> facts and returns false otherwise.
>>>> 
>>>> By this criterion True("There is no truth predicate") is TRUE.
>>>> 
>>> 
>>> The True(X) predicate only takes formalized Natural Language so that
>>> would  be rejected as false.
>> 
>> No, if we interprete "There is no truth predicate" to represent the
>> formalized natural language expression that means that there is no
>> turth predicate.
>> 
> 
> That is already accounted for by the Liar Paradox.
> Every self-contradictory expression cannot be derived
> from the set of basic facts by applying ONLY truth
> preserving operations.

That depends on "the set of basic facts". OK if they really are facts
but otherwise anything is possible.

>>> LP := ~True(LP) would also be rejected
>>> as ~TRUE. The Principle of explosion does not apply truth preserving
>>> operations.
>> 
>> The expression LP := ~True(LP) should be rejected as a syntax error.
> 
> Formalized natural language must be able to directly
> encode the self-reference of the Liar Paradox
> "This sentence is not true" or it is insufficiently
> expressive.

Depends on your definition of "sufficiently". The truth of a sentence
depends on interpretation, so it is not determined by the real world.

-- 
Mikko