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From: dbush <dbush.mobile@gmail.com>
Newsgroups: comp.theory
Subject: Re: Refutation of the Halting Problem Assuming the Self-Referential
 Paradox is a Category Error --- Linz Proof
Date: Sat, 26 Apr 2025 18:00:38 -0400
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In-Reply-To: <vujkuj$39g88$1@dont-email.me>

On 4/26/2025 5:58 PM, olcott wrote:
> On 4/26/2025 4:39 PM, dbush wrote:
>> On 4/26/2025 5:34 PM, olcott wrote:
>>> On 4/26/2025 4:30 PM, dbush wrote:
>>>> On 4/26/2025 5:26 PM, olcott wrote:
>>>>> On 4/26/2025 3:56 PM, Mr Flibble wrote:
>>>>>> Refutation of the Halting Problem Assuming the Self-Referential 
>>>>>> Paradox is
>>>>>> a Category Error in All Computational Models and the Mathematical 
>>>>>> Universe
>>>>>> Hypothesis is True
>>>>>>
>>>>>
>>>>> Yes and you are one of three people in the world that knows this.
>>>>> You acquired expertise about this in about a year where most
>>>>> people are indoctrinated into "received view" by mindless conformity.
>>>>> Even Christ knew that people are sheep.
>>>>>
>>>>> The other thing about the Halting Problem is that
>>>>> a simulating halt decider proves that the contradictory
>>>>> part has always been unreachable code.
>>>>>
>>>>> When we apply the finite string transformation rules
>>>>> specified by the Turing Machine language to the input
>>>>> to the Linz proof 
>>>>
>>>> Which starts with the assumption that an H exists that computes the 
>>>> following mapping:
>>>>
>>>>
>>>> Given any algorithm (i.e. a fixed immutable sequence of 
>>>> instructions) X described as <X> with input Y:
>>>>
>>>> A solution to the halting problem is an algorithm H that computes 
>>>> the following mapping:
>>>>
>>>> (<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
>>>> (<X>,Y) maps to 0 if and only if X(Y) does not halt when executed 
>>>> directly
>>>>
>>>>
>>>
>>> THAT IS NOT ALLOWED because that cannot possibly be derived
>>> by applying the finite string transformation rules specified
>>> by the x86 language to the input to HHH(DD).
>>>
>>
>> In other words, a contradiction was reached. 
> 
> 
> The error is reached when people stupidly assume
> that HHH 

Meets the following requirements:


Given any algorithm (i.e. a fixed immutable sequence of instructions) X 
described as <X> with input Y:

A solution to the halting problem is an algorithm H that computes the 
following mapping:

(<X>,Y) maps to 1 if and only if X(Y) halts when executed directly
(<X>,Y) maps to 0 if and only if X(Y) does not halt when executed directly



And because a contradiction is reached, the assumption that an H exists 
that meets the above requirements is proven false.