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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 22:44:00 -0400
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On 5/13/2025 10:41 PM, olcott wrote:
> 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.
> 

They have the *assumption* that the requirements can be met, and via 
proof by contradiction show the assumption to be false.

And the fact that the requirements can't be met is fine, just like the 
the fact that these requirements can't be met is fine:

A mythic number is a number N such that N > 5 and N < 2.