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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,comp.ai.philosophy,sci.logic
Subject: Re: Halting Problem Proof ERROR
Date: Sat, 19 Jul 2025 14:59:43 -0500
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On 7/19/2025 12:23 PM, Richard Damon wrote:
> On 7/19/25 10:23 AM, olcott wrote:>>
>> When you change my words and use those words as the basis
>> of your rebuttal you know that you cheat.
>>
>> The infinite simulation of ⟨Ĥ⟩ ⟨Ĥ⟩ by embedded_H
>> cannot possibly reach its own simulated final
>> halt state of ⟨Ĥ.qn⟩ you fucking moron.
> 
> Which is just a strawman, as the definition of non-halting behavior of 
> the input, is that when the machine the input describes, 
If you only learn by rote memorization it may seem that way.
When you have a depth of understanding then you see that
what you said is merely an incorrect paraphrase of this:

Turing machine (at least partial) halt deciders only compute
the mapping from their finite string inputs to the actual
behavior that this input finite string actually specifies.

Conventional notation of a Turing Machine: Ĥ
Conventional notation of a TM description: ⟨Ĥ⟩

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

*Is corrected to this*

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⟩.

*Original proof*
https://www.liarparadox.org/Peter_Linz_HP_317-320.pdf

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