On 10/14/2025 9:46 PM, Kaz Kylheku wrote:On 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.
No, it isn't. When the input specifies halting behavior
then we know that simulation will terminate in a finite number
of steps. In that case we discern that the input has terminated.
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 is
logically incoherent when ...
when it is assumed that halting can be decided; but that inconsitency is
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 even
as mathematics, the halting problem’s assumed
system collapses when you take its own definitions
seriously, without ignoring what they imply."
>
I don't know who is supposed to be saying this and to whom;
(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.)
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