Path: news.eternal-september.org!eternal-september.org!.POSTED!not-for-mail
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 23:35:13 -0500
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On 5/13/2025 10:48 PM, dbush wrote:
> On 5/13/2025 11:38 PM, olcott wrote:
>> On 5/13/2025 10:28 PM, dbush wrote:
>>> 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
>>>
>>
>> It is true that a TM either halts or does not halt.
>>
>> None-the-less the above requirements simply ignore
>> that some inputs specify behavior that differs
>> from the behavior of their direct execution.
> 
> What you think the input specifies is irrelevant. 

What it actually specifies rules the computation.

> What's relevant is 
> that the input is a description of an algorithm, 

The term "description" is too vague. The behavior
that an encoded sequence of steps specifies is most relevant.

> and it's the halt 
> status of that algorithm when executed directly that we want to know about.
> 
> That the above requirements can't be satisfied doesn't change that.
> 

It is like you are insisting on resolving
Russell's Paradox in naive set theory.


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