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From: "Fred. Zwarts" <F.Zwarts@HetNet.nl>
Newsgroups: comp.theory,sci.logic
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Tue, 8 Jul 2025 09:55:46 +0200
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Op 08.jul.2025 om 04:52 schreef olcott:
> 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.
>>
>> But they can take the finite-stringt encoding of those machines.
>>
> 
> Yes.
> 
>> 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.
>>
> 
> 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.
> 
>>>
>>> That you cannot understand that is a truism is only your
>>> own lack of understanding.
>>
>> 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.
>>
> 
> Gross ignorance about the reasoning behind the rules
> of computation would tell you that.
> 
>>>
>>> https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf
>>> *Here is the Linz proof corrected to account for that*
>>>
>>> *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⟩
>>>
>>>
>>
>> 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.
>>
> 
> 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.
> 
> "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*
That is your misconception. No one ever asked to take the direct 
execution as input. You are fighting windmills again, which is not a 
rebuttal.

A decider must report on its input.
If exactly this same input is proven to specify a halting program, then 
the decider must report that it halts.
Whether this proof is by direct execution, by a correct simulation, or 
by other means, is irrelevant, although the proof by direct execution is 
of course the easiest to understand.
In this case the input of HHH has been proven to specify a halting 
program by direct execution. HHH does not need to know that, but when it 
does a correct analysis it must come to the same conclusion. If not, 
then HHH is wrong as a self-evident fact.