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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: What it would take... People to address my points with reasoning
 instead of rhetoric -- RP
Date: Tue, 13 May 2025 21:41:09 -0500
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On 5/13/2025 8:56 PM, dbush wrote:
> On 5/13/2025 9:52 PM, olcott wrote:
>> On 5/13/2025 8:38 PM, dbush wrote:
>>> On 5/13/2025 9:35 PM, olcott wrote:
>>>> On 5/13/2025 8:26 PM, dbush wrote:
>>>>> On 5/13/2025 9:16 PM, olcott wrote:
>>>>>> On 5/13/2025 8:03 PM, dbush wrote:
>>>>>>> Nope.  Russell's Paradox was derived from the base axioms of 
>>>>>>> naive set theory, proving the whole system was inconsistent.
>>>>>>>
>>>>>>> In contrast, there is nothing in existing computation theory that 
>>>>>>> requires that a halt decider exists.
>>>>>
>>>>> I see you made no attempt to refute the above statement.  Unless 
>>>>> you can show from the axioms of computation theory that the 
>>>>> following requirements can be met, your argument has no basis:
>>>>>
>>>>>
>>>>> 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
>>>>>
>>>>>
>>>>>>>
>>>>>>>> A halt decider doesn't exist
>>>>>>>> for the same reason that the set of all sets
>>>>>>>> that do not contain themselves does not exist.
>>>>>>>> *As defined both were simply wrong-headed ideas*
>>>>>>>
>>>>>>> There's nothing wrong-headed about wanting to know if any 
>>>>>>> arbitrary algorithm X with input Y will halt when executed directly. 
>>>>>>
>>>>>> Yes there is. I have proven this countless times.
>>>>>
>>>>> That requirements are impossible to satisfy doesn't make them 
>>>>> wrong. It just makes them impossible to satisfy, which is a 
>>>>> perfectly reasonable conclusion.
>>>>>
>>>>>
>>>>
>>>> It did with Russell's Paradox.
>>>> ZFC rejected the whole foundation upon which
>>>> RP was built.
>>>>
>>>> ZFC did not solve some other Russell's Paradox
>>>> it rejected the whole idea of RP as nonsense.
>>>>
>>>
>>> Unless you can show from the axioms of computation theory that the 
>>> following requirements can be met, your argument has no basis:
>>>
>>
>> Alternatively I can do what ZFC did and over-rule
>> the whole foundation upon which the HP proofs are build.
> 
> You mean the assumption that the following requirements (which are *not* 
> part of the axioms of computation theory) can be satisfied?  The 
> assumption that Linz and other proved was false and that you 
> *explicitly* agreed with?
> 

The conventional halting problem proofs have your
requirements as its foundation.

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