Re: Title: A Structural Analysis of the Standard Halting Problem Proof

On 7/20/2025 11:13 AM, Alan Mackenzie wrote:

[ Followup-To: set ]
 In comp.theory olcott <polcott333@gmail.com> wrote:

On 7/20/2025 8:05 AM, Alan Mackenzie wrote:

[ Followup-To: set ]

 

In comp.theory Mr Flibble <flibble@red-dwarf.jmc.corp> wrote:

On Sun, 20 Jul 2025 07:13:43 -0400, Richard Damon wrote:

 

On 7/20/25 12:58 AM, olcott wrote:

Title: A Structural Analysis of the Standard Halting Problem Proof

 

Author: PL Olcott

 

Abstract:
This paper presents a formal critique of the standard proof of the
undecidability of the Halting Problem. While we do not dispute the
conclusion that the Halting Problem is undecidable, we argue that the
conventional proof fails to establish this conclusion due to a
fundamental misapplication of Turing machine semantics. Specifically,
we show that the contradiction used in the proof arises from conflating
the behavior of encoded simulations with direct execution, and from
making assumptions about a decider's domain that do not hold under a
rigorous model of computation.

  

Your problem is you don't understand the meaning of the words you are
using.

 

This is an ad hominem attack, not argumentation.

 

Maybe it was you wanting to create that impression by dishonestly
snipping the substance of Richard's post, where he illustrated some of
the words whose meaning PO fails to understand.

 

It never has been that I do not understand
the definitions of words it is that I have
proven that some of these definitions are incorrect.

 You do not understand these words.  You clearly don't understand what
"prove" means in mathematics, and you have been known to have a less than
scrupulous regard for the truth.  Your notion that you have "proven" some
incorrectness is nothing more than a spurious delusion of grandeur.
 

*The definition of the halting problem is provably incorrect*

 Garbage.  It is perfectly OK.  Do you really think that for such a simple
problem, known and understood by millions over nearly a century, any flaw
would not have already been found long ago?  You are intellectually not
up to the task; a typical student will understand the halting problem and
its resolution in at most a few hours.  You have spent 20 years and still
haven't got it.
 

<ChatGPT>

[ Snip further garbage ]

</ChatGPT>

 [ .... ]
 

I have proven its key mistake.
I only did this very recently.
Below we have one half of this
proof of its mistake.
*Despicable lying scumbag bastards snip my proof*
The proof is not that ChatGPT agrees. The proof
is that this reasoning is provably sound.
<ChatGPT>
Misrepresentation of Input:
The standard proof assumes a decider
H(M,x) that determines whether machine
M halts on input x.
But this formulation is flawed, because:
Turing machines can only process finite
encodings (e.g. ⟨M⟩), not executable entities
like M.
So the valid formulation must be
H(⟨M⟩,x), where ⟨M⟩ is a string.
</ChatGPT>

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

 

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