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

Op 08.jul.2025 om 17:17 schreef olcott:

On 7/8/2025 6:18 AM, Richard Damon wrote:

On 7/7/25 10:52 PM, olcott wrote:

On 7/7/2025 9:24 PM, Richard Damon wrote:

On 7/7/25 7:47 PM, olcott wrote:>>

That Turing machines cannot take directly executing Turing
Machines as inputs entails that these directly executed
machines are outside of the domain of every Turing machine
based halt decider.

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But they can take the finite-stringt encoding of those machines.
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Yes.
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I guess you idea of Turing Machine is so limited that you think they can't do arithmatic, as you can't actually put a "Number" as the input, only the finite-string encoding of a number, which puts it outside the domain of them.
>

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No one here has any understanding of the philosophy of
computation. They can only memorize the rules and have
no idea about the reasoning behind these rules.
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That you cannot understand that is a truism is only your
own lack of understanding.

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But it isn't a truism, it is just a stupid lie that ignores that almost everything done with programs is via an "encoding" for the input.
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Gross ignorance about the reasoning behind the rules
of computation would tell you that.
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https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
*Here is the Linz proof corrected to account for that*
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*adapted from bottom of page 319*
When Ĥ is applied to ⟨Ĥ⟩
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⟩
>
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⟩
>
>

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Which is just an admission of your lying strawman, as the question is NOT about the (partial) simulation done by your H / embedded_H, but about the direct execution of the input H^ (H^) as that is what the input to H is encoding.
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Because no Turing machine can take a directly executed
Turing machine as an input, directly executed Turing
machines have always been outside of the domain of every
Turing machine based decider.

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Then evdrything in reality is outside the domain of Turing Machines.
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"the direct execution of the input H^ (H^)" has always been
out-of-scope for every Turing machine based halt decider.
That no one bothered to notice this ever before
*DOES NOT MAKE ME WRONG*

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But it hasn't been, and thus you are just wrong.
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An actual rebuttal requires proving that Turing machines
can take directly executing Turing machines (that are not
finite string encodings) as inputs.

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But the Turing Machine that is directly executed CAN be represented by a finite string,.
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 In the case of pathological self-reference the
representation has different behavior than the
directly executed machine and halt deciders only
report on the actual behavior actually specified
by their inputs.
 

As usual a false claim, without evidence.
The evidence is that the input includes the code to abort and halt, but HHH is unable to reach that part. This failure of HHH does not make the specification any different. It only shows that this simulating decider is not the right tool for this input.
HHH should report on the behaviour specified, not on the behaviour it can see. If HHH has bugs, so that it does not see the full specification, the specification does not change.
Closing your eyes and pretend that what you do not see does not exists, is childish.