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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory,sci.logic
Subject: Re: My reviewers think that halt deciders must report on the behavior
 of their caller
Date: Fri, 4 Jul 2025 15:43:38 -0500
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On 6/3/2025 10:02 PM, dbush wrote:
> On 6/3/2025 10:58 PM, olcott wrote:
>> On 6/3/2025 9:46 PM, dbush wrote:
>>> On 6/3/2025 10:34 PM, olcott wrote:
>>>> On 6/3/2025 9:12 PM, dbush wrote:
>>>>>
>>>>> 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
>>>>>
>>>>
>>>> Yes there is no algorithm that does that 
>>>
>>> Excellent!
>>>
>>> Let The Record Show
>>>
>>> That Peter Olcott
>>>
>>> Has *EXPLICITLY* admitted
>>>
>>> That no algorithm H exists that meets the above requirements, which 
>>> is precisely the theorem that the halting problem proofs prove.
>>
>> In the exact same way that there is no set of all set
>> that contain themselves. ZFC did not solve Russell's
>> Paradox as much as it showed that Russell's Paradox
>> was anchored in an incoherent foundation, now called
>> naive set theory.
> 
> Which arose because the axioms of naive set theory created a contradiction.
> 

Likewise with halt deciders that are required to report
on the behavior of directly executed Turing machines.

Directly executed Turing machines are outside of the
domain of every Turing machine decider.

> In contrast, the axioms of computation theory do *not* create a 
> contradiction.  It simply follows from those axioms that no H exists the 
> meets the above requirements, which is a completely valid conclusion.

*Claude.ai seems to be the smartest bot about computation*
https://claude.ai/share/48aab578-aec3-44a5-8bb3-6851e0f8b02e

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