Re: On recursion and infinite recursion (reprise #3)

[olcott]

On 5/5/2022 11:50 AM, Mr Flibble wrote:
> This post is mostly for the benefit of Richard Damon who likes to play
> word games.
>
> The primary halting problem theorem proof [Turing, 1936] (upon which
> other currently extant halting problem proofs are derived) is invalid
> due to an invalid "impossible program" [Strachey, 1965] that arises not
> from a function call-like infinite recursion but from a category error
> in the form of an invalid (erroneous) infinite recursion present in the
> proof [Wikipedia, 2022].
>
> The categories involved in the category error are the decider and that
> which is being decided. Currently extant attempts to conflate the
> decider with that which is being decided are infinitely recursive and
> thus invalid.
>
> /Flibble
>

Proof of this is that the halting theorem has the exactly same
self-contradictory pattern as the Liar Paradox.

For any program f that might determine if programs halt, a
"pathological" program g, called with some input, can pass its own
source and its input to f and then specifically do the opposite of what
f predicts g will do.

https://en.wikipedia.org/wiki/Halting_problem

--
Copyright 2022 Pete Olcott "Talent hits a target no one else can hit;
Genius hits a target no one else can see." Arthur Schopenhauer

[olcott]

On 5/5/2022 8:43 PM, Ben wrote:
> olcott <polc...@gmail.com> writes:
>
>> On 5/5/2022 2:56 PM, Ben wrote:

>>> olcott <polc...@gmail.com> writes:
>>>
>>>> Proof of this is that the halting theorem has the exactly same
>>>> self-contradictory pattern as the Liar Paradox.
>>>>
>>>> For any program f that might determine if programs halt, a
>>>> "pathological" program g, called with some input, can pass its own
>>>> source and its input to f and then specifically do the opposite of
>>>> what f predicts g will do.
>>>> https://en.wikipedia.org/wiki/Halting_problem

>>> So finally you agree that no single TM can decide TM halting??? How
>>> long has it taken you to get to this point?
>>
>> H1(P,P)==true is empirically proven to be correct
>> H(P,P)==false is empirically proven to be correct
>>
>> You keep trying to get away with a halt decider that computes the
>> mapping from non-inputs even when you know this is incorrect.
>
> Any conclusion I can form this is unkind. You are either dishonest and
> are intentionally misrepresenting what other people write, or you are so
> lost that even after 18 years you don't know what that halting problem
> is.
>

I am not trying to be unkind. When people happily disagree with verified
facts I construe that as playing head games for sadistic pleasure. Those
people really need a strong (at least metaphorical) slap in the face.

It is a proven fact that H(P,P) and H1(P,P) do correctly compute the
mapping from their input parameters to the halt status specified by
these inputs.