Re: Flibble’s Leap: Why Behavioral Divergence Implies a Type Distinction in the Halting Problem

On 5/11/2025 6:05 PM, Keith Thompson wrote:

Mr Flibble <flibble@red-dwarf.jmc.corp> writes:

On Sun, 11 May 2025 18:15:47 +0100, Richard Heathfield wrote:
>

On 11/05/2025 17:59, Mr Flibble wrote:

it is impossible to obtain a halting result

>
>
That sure looks like a concession that it's impossible to devise an
algorithm that will produce a halting result.
>
Well done. We got you there in the end.

>
No. The reason why it is impossible to obtain a halting result for
pathological input is not the reason proposed by Turing (i.e. self-
referential diagonalization), it is impossible to obtain a halting result
for pathological input because the self-referential conflation of decider
and input is a category error that prevents us from performing
diagonalization.

 Is it possible to determine whether a given input is "pathological" or not?
 

To usefully advance research in this area pathological input needs to be
excluded from the set of programs that can be analysed by a decider.

 Can this exclusion be performed reliably and consistently?
 

That is a good question. The answer is definitely
yes. When HHH emulates DDD it only needs to see
that DDD is calling itself with no conditional branch
instructions inbetween.
Whether a function computed by a Turing machine can
do this is a different question.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer