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

On 5/11/25 7:05 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?

that is the problem, as the answer is no. It is possible to create a "patholgocial" input that can not be determined to be such, as to make his pathological input, you just need to make a finction that returns the same values as the original, and you can tweak the code in an infinite number of ways to hide the pathology.

 

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?