From Newsgroup: comp.ai.philosophy

On 10/14/2022 7:44 PM, Ben Bacarisse wrote:

Python <python@invalid.org> writes:

Olcott (annotated):

If simulating halt decider H correctly simulates its input D until H
correctly determines that its simulated D would never stop running

[comment: as D halts, the simulation is faulty, Pr. Sipser has been
fooled by Olcott shell game confusion "pretending to simulate" and
"correctly simulate"]

unless aborted then H can abort its simulation of D and correctly
report that D specifies a non-halting sequence of configurations.

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.

int DD()
{
int Halt_Status = HHH(DD);
if (Halt_Status)
HERE: goto HERE;
return Halt_Status;
}

*This is Claude AI summarizing my rebuttal of Ben's words*

Summary of the key point:
The halting problem's self-referential construction
creates two distinct computational entities:

Input (DD-as-simulated-by-HHH): Shows non-halting
behavior - recursive pattern that HHH correctly
identifies Non-input (DD-as-directly-executed):
Halts because HHH returns 0

The category error occurs when the halting problem
asks HHH to report on the direct execution behavior,
which:

Depends on HHH's own return value Is therefore not
a property of the input HHH analyzes Represents a
different computational object than what HHH can
examine through simulation

The philosophical point: A Turing machine decider
should only be expected to report on properties
determinable from its input. When the halting
problem construction makes the "actual behavior"
dependent on the decider's output, it's asking
the decider to report on something outside its
input - hence, a category error.

This reframes the "impossibility" of the halting
problem not as a limitation of computation per se,
but as a conflation between what an analyzer observes
about its input versus what happens when that input
is executed with the analyzer's answer embedded in it.

The distinction between input-behavior and
non-input-behavior is the crux of resolving the
apparent paradox.

*The full dialogue is right here* https://claude.ai/share/6e4ccef9-9749-4fb4-b58d-946fe18e7c73
--
Copyright 2025 Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer
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