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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 22:06:14 -0500
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On 5/13/2025 9:44 PM, dbush wrote:
> 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.

We can also say that no computation can compute
the square root of a dead rabbit. In none of these
cases is computation actually limited.

We could equally say that no whale can give
birth to a pigeon. This places no actual limit
on the behavior of whales. Whales were never
meant to give birth to pigeons.

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