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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.theory
Subject: Re: How do we know that H(P,P)==0 is correct? (V4) [ pathological self-reference(Olcott 2004) ]
Date: Thu, 15 Jul 2021 21:04:28 +0100
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olcott <NoOne@NoWhere.com> writes:

> On 7/15/2021 3:44 AM, Malcolm McLean wrote:
>> On Thursday, 15 July 2021 at 04:12:32 UTC+1, olcott wrote:
>>> On 7/14/2021 9:57 PM, Richard Damon wrote:
>>>
>>> When you provide the context of a TM/input pair then the brand new idea
>>> that I created "incorrect question" is formed:
>>>
>>> When-so-ever a yes/no question has no correct answer from the set of
>>> yes/no or a decision problem TM/input pair has has no final state
>>> indicting a correct Boolean value then it is an error.
>>>
>>> Undecidability has always only been an error.
>>> It is not that the correct true/false value cannot be chosen by the TM.
>>> It is that both true/false values are the wrong answer.
>>>
>> H_Hat is constructed after H.

>>  There's always a right answer -
>
> When the question is what Boolean value can H correctly return to an
> input that does the opposite of what H decides it is as obvious as
> Hell that there is no correct answer to this specific question.

That's your question.  It's not the halting problem "question".  You
gave us the correct answer to that question for your H^ (now called P)
when you posted a trace showing that it halts.  (And you'd also said so,
using rather timid language, before that as well.)

> When you change the question to: Does H P halt on its input you are
> not answering the actual question with its full context.

You are, instead, asking the halting problem "question".  This is a
question that always has a correct yes/no answer, thought algorithm can
determine which in every case.

-- 
Ben.