Re: My reviewers think that halt deciders must report on the behavior of their caller

On 7/15/2025 4:15 AM, Mikko wrote:

On 2025-07-14 13:19:15 +0000, olcott said:
 

On 7/14/2025 3:54 AM, Mikko wrote:

On 2025-07-13 15:18:01 +0000, olcott said:
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On 7/13/2025 2:09 AM, Mikko wrote:

On 2025-07-12 14:26:09 +0000, olcott said:
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On 7/12/2025 3:00 AM, Mikko wrote:

On 2025-07-11 15:25:29 +0000, olcott said:
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On 7/11/2025 3:40 AM, Mikko wrote:

On 2025-07-10 14:35:11 +0000, olcott said:
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On 7/10/2025 5:54 AM, Fred. Zwarts wrote:

Op 09.jul.2025 om 15:02 schreef olcott:>

All Turing machine deciders only compute the mapping
from their actual inputs. This entails that they never
compute any mapping from non-inputs.

>
At least one thing you understand.
>

>
*From the bottom of page 319 has been adapted to this*
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
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*The Linz proof does not understand this*

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Proofs don't understand. They prove.

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It fails to prove undecidability when the decider
correctly excludes directly executed Turing machines
from its domain.

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That does not change the last sentence of the proof. Therefore the
proof proves what it would prove anyway.

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It completely invalidates the proof.

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No, it does not. The proof reamins as it was. A proof is valid if there
is no error in the proof. Nothing else is relevant.

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There are errors that you do not understand.

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For the purpose of these discussion it is not neessary to understand
your errors beyond that they are errors.

>
int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
>
*There are errors with the proof*

 You make errors with proofs. But the uncomputability of halting can be
(and has been) proven without errors.

That the errors have never been noticed before
IS NOT THE SAME AS THERE ARE NO ERRORS.

If there were an error in some
proof you would quote the first sentence of the proof that is false or
does not follow from earlier senteces.
 

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}
The official "received view" answer for HHH(DD) is
no one has any idea what value HHH can correctly
return. *This is the first error in the proof*
The second error is that the proofs require a
Turing machine decider to report on the behavior
of the direct execution of another Turing machine
even though directly executed Turing machines
cannot possibly be inputs to any TM decider.
*Here is the adapted and corrected Linz proof*
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
     ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H reaches
     its simulated final halt state of ⟨Ĥ.qn⟩, and
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
     ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H cannot possibly
     reach its simulated final halt state of ⟨Ĥ.qn⟩.
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
With my notational conventions it is easy to distinguish
the machine specification (states beginning with Ĥ.) from
the finite string inputs ⟨Ĥ⟩ ⟨Ĥ⟩.
Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly transitions to Ĥ.qn
because ⟨Ĥ⟩ ⟨Ĥ⟩ simulated by Ĥ.embedded_H cannot
possibly reach its own ⟨Ĥ.qn⟩
The original proof has Ĥ.embedded_H reporting on
its own behavior instead of the behavior that its
input specifies.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer