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

On 5/11/25 7:14 PM, olcott wrote:

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

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

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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.

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Can this exclusion be performed reliably and consistently?
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 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.
 

So, try to do it.
Note, if your system *IS* the equivalent of a Turing Machine, then if yours can do it so can a Turing Machine.
The problem is that you system is NOT the equivalent of the pair of Turing Machines, and you have even made stipulations that prove that your system is less than Turing Complete.
The key problem is that you have inforced a restriction that the function HHH can not be "cloned" as can be done in a real Turing System. If I can make an equvalent copy of the code of HHH (and perhaps make some cosmetic but not functional changing) then HHH can not detect that operation.
This is of course, beyond your comprehension.