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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 17:39:23 -0400
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In-Reply-To: <vujjh5$35hcg$8@dont-email.me>

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