From Newsgroup: comp.theory
On 10/14/2022 7:44 PM, Ben Bacarisse wrote:
I don't think that is the shell game.
PO really /has/ an H (it's trivial to
do for this one case) that correctly
determines that P(P) *would* never stop
running *unless* aborted.
He knows and accepts that P(P) actually does stop.
The wrong answer is justified by what would
happen if H (and hence a different P) where not
what they actually are.
When the halting problem requires a halt decider
to report on the behavior of a Turing machine this
is always a category error.
The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.
This analysis is in the C programming language so
that it is 100% concrete without any key details
being abstracted away.
int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}
(a) HHH(DD) does report on the behavior that its
input finite string specifies as measured by DD
simulated by HHH according to the semantics of
the C programming language.
(b) Reporting on anything else is outside of the
scope of Turing Machine Computable functions.
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.
This required establishing a new foundation
for correct reasoning.
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