Re: The halting problem as defined is a category error

On 7/23/2025 8:31 AM, joes wrote:

Am Wed, 23 Jul 2025 07:22:55 -0500 schrieb olcott:

On 7/23/2025 2:34 AM, Mikko wrote:

On 2025-07-22 13:56:36 +0000, olcott said:

On 7/22/2025 5:51 AM, Mikko wrote:

On 2025-07-21 14:07:27 +0000, olcott said:

 

The category error is a type mismatch error where a Turing Machine
decider is required to report on the behavior of a directly executed
machine yet cannot take a directly executed machine as an input.

>
That is not a category error. A category error is a word or phrase of
some category in a context that requires a word or phrase of a
different category.

>
The category error is the mistake of assuming that a directly
executing Turing machine is in the category of input to a Turing
machine halt decider.

>
That error is not present in the halting problem. It is also not
present in https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf
which is the prototype of proofs that you falsely claim to have
refuted.
>

I am either going to go by the Linz proof or my own code

Your decision. Anyway the hypothetical halting decider obviously
only takes descriptions of TMs as input, with the OUTput required
to be what the universal simulation or direct execution *of that
input* (namely, DDD *not* calling a UTM) does.
 

That is incorrect in the case where DD calls its
own simulating termination analyzer or the Linz Ĥ
contains its own simulating halt decider.
The actual behavior that is actually specified must
include that in both of these cases recursive simulation
is specified. We can't just close our eyes and pretend
otherwise.
--
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer