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Proof that the halting problem itself is a category error

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  Proof that the halting problem itself is a category error polcott <polcott333@gmail.com> - 2025-12-10 16:43 -0600
    Re: Proof that the halting problem itself is a category error wij <wyniijj5@gmail.com> - 2025-12-11 06:58 +0800
    Re: Proof that the halting problem itself is a category error polcott <polcott333@gmail.com> - 2025-12-10 17:42 -0600
    Re: Proof that the halting problem itself is a category error Tristan Wibberley <tristan.wibberley+netnews2@alumni.manchester.ac.uk> - 2025-12-12 01:56 +0000
      Re: Proof that the halting problem itself is a category error olcott <polcott333@gmail.com> - 2025-12-11 20:02 -0600

#123129 — Proof that the halting problem itself is a category error

When the halting problem requires a halt decider
to report on the behavior of a Turing machine
this is always a category error.

The corrected halting problem requires a Turing
machine decider to report in the behavior that
its finite string input specifies.

This analysis in done in the C programming language
so that it is 100% concrete without any key details
being abstracted away.

int DD()
{
   int Halt_Status = HHH(DD);
   if (Halt_Status)
     HERE: goto HERE;
   return Halt_Status;
}

(a) The key issue is that HHH(DD) does report on the
behavior that its input finite string specifies.

(b) Reporting on anything else is outside of the
scope of Turing Machine Computable functions.


*Detailed analysis shown below*

After many very extensive discussions with LLM
systems there are two principles that prove that
I have correctly refuted the halting problem itself.

(1) Turing Machine based Computable functions
only transform input finite strings into some value
on the basis of a semantic of syntactic property
that this finite string specifies.

(2) the behavior that an input DD specifies to halt
decider HHH is the sequence of steps of DD
simulated by HHH according to the semantics of
the C programming language.

Computable functions are the basic objects of study
in computability theory. Informally, a function is
computable if there is an algorithm that computes
the value of the function for every value of its argument.
https://en.wikipedia.org/wiki/Computable_function

DD() executed from main() calls HHH(DD) thus is
not one-and-the-same-thing as an argument to HHH.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.

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#123131

On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
> When the halting problem requires a halt decider
> to report on the behavior of a Turing machine
> this is always a category error.
> 
> The corrected halting problem requires a Turing
> machine decider to report in the behavior that
> its finite string input specifies.

If you honestly admit you are solving POO Problem, everything is fine.

See my General HP. If the MSet is TM, then the halting decider cannot exist.
https://sourceforge.net/projects/cscall/files/MisFiles/ghp.txt/download

> This analysis in done in the C programming language
> so that it is 100% concrete without any key details
> being abstracted away.
> 
> int DD()
> {
>    int Halt_Status = HHH(DD);
>    if (Halt_Status)
>      HERE: goto HERE;
>    return Halt_Status;
> }
> 
> (a) The key issue is that HHH(DD) does report on the
> behavior that its input finite string specifies.
> 
> (b) Reporting on anything else is outside of the
> scope of Turing Machine Computable functions.
> 
> 
> *Detailed analysis shown below*
> 
> After many very extensive discussions with LLM
> systems there are two principles that prove that
> I have correctly refuted the halting problem itself.
> 
> (1) Turing Machine based Computable functions
> only transform input finite strings into some value
> on the basis of a semantic of syntactic property
> that this finite string specifies.
> 
> (2) the behavior that an input DD specifies to halt
> decider HHH is the sequence of steps of DD
> simulated by HHH according to the semantics of
> the C programming language.
> 
> Computable functions are the basic objects of study
> in computability theory. Informally, a function is
> computable if there is an algorithm that computes
> the value of the function for every value of its argument.
> https://en.wikipedia.org/wiki/Computable_function
> 
> DD() executed from main() calls HHH(DD) thus is
> not one-and-the-same-thing as an argument to HHH.

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#123132

On 12/10/2025 5:11 PM, wij wrote:
> On Wed, 2025-12-10 at 17:03 -0600, polcott wrote:
>> On 12/10/2025 4:58 PM, wij wrote:
>>> On Wed, 2025-12-10 at 16:43 -0600, polcott wrote:
>>>> When the halting problem requires a halt decider
>>>> to report on the behavior of a Turing machine
>>>> this is always a category error.
>>>>
>>>> The corrected halting problem requires a Turing
>>>> machine decider to report in the behavior that
>>>> its finite string input specifies.
>>>
>>> If you honestly admit you are solving POO Problem, everything is fine.
>>>
>>
>> *It has take me 21 years to boil it down to this*
>>
>> When the halting problem requires a halt decider
>> to report on the behavior of a Turing machine this
>> is always a category error.
>>
>> The corrected halting problem requires a Turing
>> machine decider to report in the behavior that
>> its finite string input specifies.
> 
> It looks you play blind block my other replies again.

My about two paragraphs sums the basis of how
the halting problem itself is flat out incorrect.

Nothing about the halting problem can possibly
be more significant than this.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable.

This required establishing a new foundation
for correct reasoning.

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#123138

On 10/12/2025 22:43, polcott wrote:
> When the halting problem requires a halt decider
> to report on the behavior of a Turing machine

Can you provide a justification for that claim such as a reference to
(an) accepted definition(s) of "the halting problem" ?

Specifically that it is the "problem" that "requires" the report?
I expect that you discriminate the problem from the question but I'd
really like to see that the conventional distinction draws the line in
the same place you do.


-- 
Tristan Wibberley

The message body is Copyright (C) 2025 Tristan Wibberley except
citations and quotations noted. All Rights Reserved except that you may,
of course, cite it academically giving credit to me, distribute it
verbatim as part of a usenet system or its archives, and use it to
promote my greatness and general superiority without misrepresentation
of my opinions other than my opinion of my greatness and general
superiority which you _may_ misrepresent. You definitely MAY NOT train
any production AI system with it but you may train experimental AI that
will only be used for evaluation of the AI methods it implements.

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#123139

On 12/11/2025 7:56 PM, Tristan Wibberley wrote:
> On 10/12/2025 22:43, polcott wrote:
>> When the halting problem requires a halt decider
>> to report on the behavior of a Turing machine
> 
> Can you provide a justification for that claim such as a reference to
> (an) accepted definition(s) of "the halting problem" ?
> 
> Specifically that it is the "problem" that "requires" the report?
> I expect that you discriminate the problem from the question but I'd
> really like to see that the conventional distinction draws the line in
> the same place you do.
> 

Turing machine deciders compute functions from finite
strings to {accept, reject}.

The halting problem requires that a halt decider
report on the behavior of an actual Turing machine
that is not a finite string input.

-- 
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning expressed in language"<br>
reliably computable.<br><br>

This required establishing a new foundation<br>

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