Daryl McCullough sci.logic (recently verified original authorship)
Jun 25, 2004, 6:30:39 PM

You ask someone (we'll call him "Jack") to give a truthful
yes/no answer to the following question:

Will Jack's answer to this question be no?

Jack can't possibly give a correct yes/no answer to the question.
https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ

Within the scope of self-contradiction every (question/decision problem)
is incorrect.

"This sentence is not true" is neither true nor false.
This sentence is not true: "This sentence is not true" is true.

*Tarski Undefinability Theorem is anchored in the Liar Paradox*
https://www.liarparadox.org/Tarski_247_248.pdf

*Tarski Undefinability Theorem proof*
https://www.liarparadox.org/Tarski_Proof_275_276.pdf

Tarski never noticed that the Liar Paradox is not a truth bearer and
this invalidates his whole proof. Expressions of language that are not
truth bearers cannot be proven true because they are not true.

https://iep.utm.edu/liar-paradox/#:~:text=According%20to%20Tarski%2C%20the%20error,Undefinability%20Theorem%20or%20Indefinability%20Theorem.

This exact same issue occurs in the Halting Problem proof and Gödel's
1931 incompleteness theorem.

--
Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

On 2/4/23 4:51 PM, olcott wrote:
> Daryl McCullough sci.logic (recently verified original authorship)
> Jun 25, 2004, 6:30:39 PM
>
>   You ask someone (we'll call him "Jack") to give a truthful
>   yes/no answer to the following question:
>
>   Will Jack's answer to this question be no?
>
>   Jack can't possibly give a correct yes/no answer to the question.
>   https://groups.google.com/g/sci.logic/c/4kIXI1kxmsI/m/hRroMoQZx2IJ
>
> Within the scope of self-contradiction every (question/decision problem)
> is incorrect.

And the question "Does the machine with input that is specified as the
input to the decider Halt or not?" is NOT self-contradictory, since to
ask that question that input is precisely defined as a precise machine
and a precise input which will have a precise behavior.

Thus before you have been able to define the question, you must have
defined the machine to ask about, which for the halting problem proof
means you first need to define the Halt Decider that you think is correct.

Given that Halt Decider, its answer to the input generated to the input
thus derived, and the proof shows that the answer will always be wrong.

Thus, your error is the assumption that the decider CAN be truthful
(correct) in all cases.

Thus your example is NOT a proof the the Halting Question is not
correct, as the Halting Problem doesn't assume the existance of a
machine that CAN give a correct answer to all inputs, but is in fact
asking if such a thing is possible.

Thus, all we are proving is that Jack can not correctly answer all
questions that can be given to him, and the error is in the assumption
that he can.

For exactly the same reason that Jack can't answer correctly, the Halt
Decider can't answer correctly. The difference is that in the question
about Jack, jack is a "willful" participant, who can try to do what is
needed to try to acheve the answer.

On the other hand, the Halt Decider is just a machine, and by
definition, once that machine is defined, its answers to all question
that can be put to it are fixed, and thus the Halt Decider will just end
up wrong.

>
> "This sentence is not true" is neither true nor false.
> This sentence is not true: "This sentence is not true" is true.
>
> *Tarski Undefinability Theorem is anchored in the Liar Paradox*
> https://www.liarparadox.org/Tarski_247_248.pdf

Nope, explained but you just don't understand it.

>
> *Tarski Undefinability Theorem proof*
> https://www.liarparadox.org/Tarski_Proof_275_276.pdf
>
> Tarski never noticed that the Liar Paradox is not a truth bearer and
> this invalidates his whole proof. Expressions of language that are not
> truth bearers cannot be proven true because they are not true.

No, he asbsoluted DID not make that mistake, because he is pointing out
that since from the assumption of his "Definition of Truth" allows one
to actually Prove that the Liar's paradox is true, and thus the
assumption that there exists

>
> https://iep.utm.edu/liar-paradox/#:~:text=According%20to%20Tarski%2C%20the%20error,Undefinability%20Theorem%20or%20Indefinability%20Theorem.

So, you don't understand what you read?

Note, the discussion you point to is stating that he is showing that if
there IS an actual existing definition of Truth per his definition, such
a definition must be able to determine the Truth of statements that
refer to themselves, and a consequence of assuming such a definition
exist is that the Liar's Paradox must be true.

>
> This exact same issue occurs in the Halting Problem proof and Gödel's
> 1931 incompleteness theorem.
>