Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
From: dbush <dbush.mobile@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 21:56:31 -0400
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In-Reply-To: <1000t1a$24sr2$4@dont-email.me>

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?


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