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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic,comp.ai.philosophy
Subject: Re: The error of the standard proof of the halting problem
Date: Tue, 22 Jul 2025 11:22:10 -0500
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On 7/22/2025 6:39 AM, Richard Damon wrote:
> On 7/22/25 12:17 AM, olcott wrote:
>> On 7/21/2025 9:20 PM, Richard Damon wrote:
>>> On 7/21/25 9:45 AM, olcott wrote:
>>>> On 7/21/2025 4:06 AM, Mikko wrote:
>>>>> On 2025-07-20 11:48:37 +0000, Mr Flibble said:
>>>>>
>>>>>> On Sun, 20 Jul 2025 07:13:43 -0400, Richard Damon wrote:
>>>>>>
>>>>>>> On 7/20/25 12:58 AM, olcott wrote:
>>>>>>>> Title: A Structural Analysis of the Standard Halting Problem Proof
>>>>>>>>
>>>>>>>> Author: PL Olcott
>>>>>>>>
>>>>>>>> Abstract:
>>>>>>>> This paper presents a formal critique of the standard proof of the
>>>>>>>> undecidability of the Halting Problem. While we do not dispute the
>>>>>>>> conclusion that the Halting Problem is undecidable, we argue 
>>>>>>>> that the
>>>>>>>> conventional proof fails to establish this conclusion due to a
>>>>>>>> fundamental misapplication of Turing machine semantics. 
>>>>>>>> Specifically,
>>>>>>>> we show that the contradiction used in the proof arises from 
>>>>>>>> conflating
>>>>>>>> the behavior of encoded simulations with direct execution, and from
>>>>>>>> making assumptions about a decider's domain that do not hold 
>>>>>>>> under a
>>>>>>>> rigorous model of computation.
>>>>>>>>
>>>>>>> Your problem is you don't understand the meaning of the words you 
>>>>>>> are
>>>>>>> using.
>>>>>>
>>>>>> This is an ad hominem attack, not argumentation.
>>>>>
>>>>> It is also honest and truthful, which is not as common as it should.
>>>>>
>>>>
>>>> It is also honest and truthful that people
>>>> that deny verified facts are either liars
>>>> or lack sufficient technical competence.
>>>>
>>>
>>> Right, so YOU are the liar.
>>>
>>> It is a verified fact that the PROGRAM DDD halts since your HHH(DDD) 
>>> returns 0.
>>>
>>
>> It is a self-evident truth that the halting problem proof
>> has always been incorrect when it requires a halt decider
>> to report on the behavior of the direct execution of any
>> Turing machine because no Turing machine decider can ever
>> take another directly executed Turing machine as its input.
> 
> If it seems "self-evident" to you, that just shows how warped you ideas 
> are of what the field means.
> 

In this field it is common knowledge that no Turing machine
decider ever takes another directly executed Turing machine
as its input.

This means that Linz is wrong that machine M
should report on the behavior of its own direct
execution as his words state below.

WM is the machine description of M

q0 WM ⊢* Ĥq0 WM WM ⊢* Ĥ∞,
    if M applied to WM halts, and
q0 WM ⊢* Ĥq0 Wm WM ⊢* Ĥ y1 qn y2,
    if M applied to WM does not halt.

TM's can only compute the mapping from inputs and M
is not an input.
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