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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: Re: Turing Machine computable functions apply finite string
 transformations to inputs VERIFIED FACT
Date: Wed, 30 Apr 2025 07:05:30 +0100
Organization: Fix this later
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On 30/04/2025 03:45, Richard Damon wrote:
> On 4/29/25 3:57 PM, olcott wrote:
>> On 4/29/2025 10:33 AM, Fred. Zwarts wrote:
>>> Op 29.apr.2025 om 15:11 schreef olcott:

<snip>

>>>> No H can possibly see the behavior of P(D)
>>>> when-so-ever D has defined a pathological
>>>> relationship with H this 
>>>
>>> makes it impossible for H to see the behaviour of P(D).
>>> The behaviour of P(D) does not change, but H does not see it.
>>
>> H MUST REPORT ON THE BEHAVIOR THAT IT DOES SEE
>>
> 
> No, it must report on the behavior that exists.
> 
> It is only ABLE to correctly report on behavior it can "see", but 
> there is no structural restriction that says we can't ask it 
> about something that it can't see.

Nor is there any restriction that says it can't deduce behaviour 
it can't see, simply by reading the tapes.

Mr Olcott seems unable to recognise this possibility. Having 
built his hammer, he is determined to see the Halting Problem as 
a nail that cannot withstand being pounded hard enough.

Unfortunately for him, the problem is more like a 16 puzzle with 
two tiles swapped. If he plays by the rules there is no solution, 
no matter how hard he hits it.

This is why he keeps trying to change the rules, with word salad 
like 'pathological self-reference', when self-reference is the 
whole reason the proof works.

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within