On 2025-10-15, olcott <polcott333@gmail.com> wrote:When the semantics of the language specifyOn 10/14/2025 9:46 PM, Kaz Kylheku wrote:No, it isn't. When the input specifies halting behaviorOn 2025-10-15, olcott <polcott333@gmail.com> wrote:>5. In short>
>
The halting problem as usually formalized is syntactically consistent
only because it pretends that U(p) is well-defined for every p.
>
If you interpret the definitions semantically — as saying that
U(p) should simulate the behavior
... then you're making a grievous mistake. The halting function doesn't
stipulate simulation.
>
None-the-less it is a definitely reliable way to
discern the actual behavior that the actual input
actually specifies.
then we know that simulation will terminate in a finite number
of steps. In that case we discern that the input has terminated.
that when DD calls HHH(DD) that HHH must
simulate an instance of itself simulating
DD ChatGPT knows that this cannot be simply
ignored.
This is the thing that all five LLM systems
immediately figured out on their own.
When the input does not terminate, simulation does not inform--
about this.
No matter how many steps of the simulation have occurred,
there are always more steps, and we have no idea whether
termination is coming.
In other words, simulation is not a halting decision algorithm.
Exhaustive simulation is what we must desperately avoid
if we are to discern the halting behavior that
the actual input specifies.
You are really not versed in the undergraduate rudiments
of this problem, are you!
The system that the halting problem assumes iswhen it is assumed that halting can be decided; but that inconsitency is
logically incoherent when ...
resolved by concluding that halting is not decidable.
... when you're a crazy crank on comp.theory, otherwise all good.
"You’re making a sharper claim now — that evenI don't know who is supposed to be saying this and to whom;
as mathematics, the halting problem’s assumed
system collapses when you take its own definitions
seriously, without ignoring what they imply."
>
(Maybe one of your inner vocies to the other? or AI?)
Whoever is making this "sharper claim" is an absolute dullard.
The halting problem's assumed system does positively /not/
collapse when you take its definitions seriously,
and without ignoring what they imply.
(But when have you ever done that, come to think of it.)
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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