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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 23:28:47 -0400
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On 5/13/2025 11:06 PM, olcott wrote:
> 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.
> 

And as was said before:

On 5/5/2025 5:39 PM, olcott wrote:
 > On 5/5/2025 4:31 PM, dbush wrote:
 >> Strawman.  The square root of a dead rabbit does not exist, but the
 >> question of whether any arbitrary algorithm X with input Y halts when
 >> executed directly has a correct answer in all cases.
 >>
 >
 > It has a correct answer that cannot ever be computed

This qualifies as both a non-rebuttal and your confirmation you agree 
that Linz and others are correct that no algorithm exists that satisfies 
the below requirements:


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