Re: Why Tarski is wrong

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:
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On 3/17/2025 3:57 AM, Mikko wrote:

On 2025-03-17 01:50:24 +0000, olcott said:
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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.
>

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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
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>
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But if x is what you are saying is

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A True(X) predicate can be defined and Tarski never
showed that it cannot.
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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.

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By this criterion True("There is no truth predicate") is TRUE.
>

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The True(X) predicate only takes formalized Natural Language so that
would  be rejected as false.

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No, if we interprete "There is no truth predicate" to represent the
formalized natural language expression that means that there is no
turth predicate.
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>
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