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From: olcott <polcott333@gmail.com>
Newsgroups: sci.logic
Subject: Re: Why Tarski is wrong
Date: Wed, 19 Mar 2025 18:36:52 -0500
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In-Reply-To: <vrej64$116jv$1@dont-email.me>

On 3/19/2025 9:09 AM, Mikko wrote:
> 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.
> 

Yes they really are facts thus actual elements of the
set of human general knowledge that can be expressed
using language.

>>>> 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.
> 

The ONLY formal language that I know that can directly
express self-reference is the Minimal Type Theory that
I created for the purpose of directly expressing
self-reference.

Tarski's Liar Paradox
x ∉ True if and only if p
where the symbol 'p' represents the whole sentence x
https://liarparadox.org/Tarski_275_276.pdf

Expressed the self-reference in the English and
never formalized it in any formal language.

LP := ~True(LP) directly encodes
~True(~True(~True(~True(~True(~True(~True(...)))))))

Clocksin and Mellish saying the same thing.
   ?- equal(foo(Y), Y).

Y will stand for foo(Y), which is foo(foo(Y)) (because of what Y stands 
for), which is foo(foo(foo(Y))), and soon. So Y ends up standing for 
some kind of infinite structure.

thus directly encodes foo(foo(foo(foo(foo(foo(...))))))

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