XPost: comp.theory
From: polcott333@gmail.com
On 10/29/2025 1:21 PM, Kaz Kylheku wrote:
> On 2025-10-29, olcott wrote:
>> The halting problem as defined requires something
>> that is outside of the scope of all Turing machines.
>
> That is false. The halting problem simply /asks/ a question whether a
> Turing machine can exist which does something. The answer comes back
> negative in the form of a theorem.
>
When the halting problem asks anything other than
exactly what the input to a decider specifies the
halting problem is asking for something that is
outside the scope of Turing machines.
> The halting problem doesn't require anything of Turing computation
> that it cannot do; it's not a requirements specification.
>
It is a requirements specification for the behavior
that is specified by a finite string that is different
than the behavior that this finite string as an input
specifies.
The halting problem is asking for the behavior of
UTM(D) when the behavior of the input to H(D) is not
the same as the behavior of UTM(D).
> The input cases which are not decided correctly by a given partial
> decider are real, constructable entities which have a definite halting
status.
> They are not paradoxical absurdities that cannot exist; you cannot dismiss
> something which exists.
>
UTM(D) does indeed specify a behavior yet H(D) specifies
a different behavior. The halting problem itself commits
a category error when it requires the behavior of UTM(D)
from H(D).
> It's like "solving" indivisibility by two by banning odd numbers
> as incorrect.
>
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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