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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: ChatGPT totally understands exactly how I refuted the
 conventional halting problem proof technique
Date: Tue, 24 Jun 2025 16:41:37 -0500
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On 6/24/2025 4:07 PM, joes wrote:
> Am Tue, 24 Jun 2025 13:06:22 -0500 schrieb olcott:
>> On 6/24/2025 12:57 PM, joes wrote:
>>> Am Tue, 24 Jun 2025 12:46:01 -0500 schrieb olcott:
>>>
>>>> It is an easily verified fact that no *input* to any partial halt
>>>> decider (PHD) can possibly do the opposite of what its corresponding
>>>> PHD decides. In all of the years of all of these proofs no such
>>>> *input* was ever presented.
>>>
>>> You should clarify that you don't even think programs can be passed as
>>> input.
>>>
>> It is common knowledge the no Turing Machine can take another directly
>> executed Turing Machine as an input.
> So common that nobody would suggest such. You are the king of strawmen.
> 

*From the bottom of page 319 has been adapted to this*
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

When Ĥ is applied to ⟨Ĥ⟩
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞
   if Ĥ applied to ⟨Ĥ⟩ halts
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
   if Ĥ applied to ⟨Ĥ⟩ does not halt

Ĥ applied to ⟨Ĥ⟩ does not have embedded_H reporting on
the behavior specified by its input ⟨Ĥ⟩ ⟨Ĥ⟩ it has embedded_H
reporting on its own behavior.

Since Turing Machines cannot take directly executing
Turing Machines as inputs this means that the directly
executed Ĥ applied to ⟨Ĥ⟩ is not in the domain of
Ĥ.embedded_H, *thus no contradiction is ever formed*


-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer