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From: Richard Damon <richard@damon-family.org>
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 16:53:50 -0400
Organization: i2pn2 (i2pn.org)
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On 7/4/25 4:43 PM, olcott wrote:
> 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.

And what is the CONTRADICTION?

The result is just some things are not computable.

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

Then so is mathematics, as "numbers" can't be given to Turing Machines, 
only representations of them.

By the exact same idea that we can represent a number by a finite 
string, we can express the algorithm, and input, of a Turing Machine as 
a finite string, and thus can talk about what it will do.

> 
>> 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
> 

Which you just continue to lie to, so proving that you are just a 
pathological liar.