On 2024-02-21 15:14:27 +0000, olcott said:

On 2/21/2024 4:31 AM, Mikko wrote:

On 2024-02-20 14:24:19 +0000, olcott said:

On 2/20/2024 7:57 AM, Mikko wrote:

On 2024-02-20 01:02:42 +0000, polcot2 said:

// Linz Turing machine H --- M applied to w
// --- Does M halt on w?
H.q0 ⟨M⟩ w ⊢* H.qy // M applied to w halts
H.q0 ⟨M⟩ w ⊢* Hqn // M applied to w does not halt

// Linz Turing machine H --- H applied to ⟨H⟩
// --- Do you halt on your own Turing Machine description ?
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qy   // H applied to ⟨H⟩ halts
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qn   // H applied to ⟨H⟩ does not halt >>>>> *Correctly transitions to H.qy*

When we simply append an infinite loop to the above H.qy
then this transforms the above H applied to ⟨H⟩ ⟨H⟩ into
a self-contradictory question.

That you can think that you can convert something to
a sellf-contradictory quesstion proves that it is not
self-contradictory.

WRONG !!!

Nothing wrong at all, on the contrary, a good example to demonstrate
what "conversion to aself contradictory questiion" really means:

"This sentence is true." Is not self-contradictory.
"This sentence is NOT true." Is self-contradictory.

Is this sentence true or false: "This sentence is NOT true." ?
*Both TRUE and FALSE are the wrong answer*

// Linz Turing machine H --- H applied to ⟨H⟩
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qy // H applied to ⟨H⟩ halts
H.q0 ⟨H⟩ ⟨H⟩ ⊢* H.qn // H applied to ⟨H⟩ does not halt
Do you halt on your own Turing Machine description ?
*YES*

When we append an infinite loop to the H.qy state we derive Ȟ

Ȟ.q0 ⟨Ȟ⟩ ⟨Ȟ⟩ ⊢* Ȟ.qy ∞ // Ȟ applied to ⟨Ȟ⟩ halts
H.q0 ⟨Ȟ⟩ ⟨Ȟ⟩ ⊢* Ȟ.qn // Ȟ applied to ⟨Ȟ⟩ does not halt Do you halt on your own Turing Machine description ?
*Both YES and NO are the wrong answer*

Nice to see that you don't disagree.

--
Mikko

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