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From: olcott <polcott333@gmail.com>
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Subject: =?UTF-8?Q?Re=3A_Analysis_of_Flibble=E2=80=99s_Latest=3A_Detecting_v?=
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Date: Wed, 21 May 2025 10:54:51 -0500
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On 5/21/2025 12:56 AM, Richard Heathfield wrote:
> On 21/05/2025 06:23, olcott wrote:
>> On 5/20/2025 9:15 PM, Richard Damon wrote:
>>> On 5/20/25 3:10 PM, Mr Flibble wrote:
> 
> <snip>
> 
>>>> Conclusion: ----------- Flibble sharpens his argument by
>>>> clarifying that SHDs are not required to simulate infinite
>>>> execution. They are expected to *detect* infinite behavior
>>>> structurally and respond in finite time. This keeps them
>>>> within the bounds of what a decider must be and
>>>> strengthens the philosophical coherence of his
>>>> redefinition of the Halting Problem.
>>>
>>> But you can't "redefine" the Halting Problem and then say you have 
>>> answered the Halting Problem.
>>
>> Do you mean like how ZFC resolved Russell's
>> Paradox thus converting "set theory" into "naive set theory"?
> 
> No, because there is no paradox in the Halting Problem. A proof by 
> contradiction is not a paradox.
> 

A self-contradictory input and a proof by contradiction
are not the same thing. A proof by contradiction would
conclude that "this sentence is not true" is true because
it cannot be proved false.

ZFC shows how a whole way of examining a problem can be
tossed out as incorrect and replaced with a whole new way.

The HP proofs are based on defining a D that can
actually do the opposite of whatever value that H returns.
No such D can actually exist.

> A better parallel would be Cantor's proof that there are uncountably 
> many real numbers, or Euclid's proof that there is no largest prime. 
> Both of these proofs make a single assumption and then derive a 
> contradiction, thus showing that the assumption must be false. No 
> paradoxes need apply.
> 
> In the Halting Problem's case, the assumption is that a UNIVERSAL 
> algorithm exists for determining whether any arbitrary program halts 
> when applied to given arbitrary input. The argument derives a 
> contradiction showing the assumption to be false.
> 

Likewise with Russell's Paradox it is assumed that there
can be a set of all sets that do not contain themselves as
members. This is "resolved" as nonsense.

> Whatever you think your HHH determines, we know from Turing that it 
> doesn't determine it for arbitrary programs with arbitrary input. It 
> therefore has no bearing whatsoever on the Halting Problem.
> 

void DDD()
{
   HHH(DDD);
   return;
}

DDD correctly simulated by HHH DOES NOT HALT.

-- 
Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer