Re: Halting Problem: How my refutation differs to Peter Olcott's

On 5/11/25 7:39 AM, Mr Flibble wrote:

On Sun, 11 May 2025 06:58:42 -0400, Richard Damon wrote:
 

On 5/10/25 11:11 PM, Mr Flibble wrote:

On Sat, 10 May 2025 22:00:26 -0500, olcott wrote:
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On 5/10/2025 9:51 PM, Mr Flibble wrote:

On Sat, 10 May 2025 21:49:41 -0400, Richard Damon wrote:
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On 5/10/25 9:18 PM, Mr Flibble wrote:

On Sat, 10 May 2025 21:07:34 -0400, Richard Damon wrote:
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On 5/10/25 9:00 PM, olcott wrote:

On 5/10/2025 6:56 PM, Mr Flibble wrote:

On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:
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On 5/10/25 4:38 PM, Mr Flibble wrote:

How my refutation differs to Peter's:
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* Peter refutes the halting problem based on pathological
input manifesting in a simulating halt decider as infinite
recursion, this being treated as non-halting.
* Flibble refutes the halting problem based on patholgical
input manifesting as decider/input self-referencial
conflation, resulting in the contradiction at the heart of the
halting problem being a category (type) error, i.e.
ill-formed.
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These two refutations are related but not exactly the same.
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/Flibble

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And the problem is that you use incorrect categories.
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The decider needs to be of the category "Program".
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The input also needs to be of the category "Program", but
provided via a representation. The act of representation lets
us convert items of category Program to the category of Finite
String which can be an input.

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Those two categories you have identified are different hence the
category error.
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That is correct. A running program and an input finite string ARE
NOT THE SAME.

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But there is a direct relationship between the two.
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The "Pathological Input" *IS* a Program, built by the simple
rules of composition that are allowed in the system.

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Such composition is invalid.
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Richard is trying to get away with saying that a finite string
THAT IS NOT A RUNNING PROGRAM <IS> A RUNNING PROGRAM
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But they are related to each other,

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Even if there is some perceived relationship between the two
different categories it doesn't mean there still isn't a category
error.

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So, what is the error, since the input *IS* the finite string that
was built by the program representation operation, and thus *IS*
what an input needs to be.
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Why relationship doesn’t rescue the mistake:
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* Shared context ≠ shared type.
– A pupil and a teacher are clearly related (one teaches, one
learns), but the question “Who is taller, the lesson?” commits a
category error because a lesson isn’t the kind of thing that has
height, regardless of its pedagogical ties to people.

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Which doesn't apply here, and you are just indicationg you don't
understand what a representation is.
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The input is a finite string that represents a program.

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A program and a finite string representing a program are different
categories ergo we have a category error.
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/Flibble

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This made no difference difference until my simulating termination
analyzer discovered they they don't always have the same behavior as
was merely presumed for 90 years.
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A halt decider was "defined" to report on the behavior of the direct
execution of the input ONLY because no one knew that it could possibly
be different behavior than what the input finite string specifies.
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Everyone here takes this false assumption as the infallible word of
God.
A textbook says it therefore it must be infallible.

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Yes, the reason why these two different categories cause a category
error is because of the self-referential dependency between them, which
manifests as infinite recursion in your simulating halt decider case.
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/Flibble

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Which isn't a category error. Your problem is you invoke category errors
in defining your categories.

 You are simply mistaken, just like Turing and all that followed were
mistaken: diagonalization cannot take place because the self-referential
dependency is a category error: this is what was overlooked.
 /Flibble

The Linz proof doesn't use "diagonalizeation".
Note, giving the decider H, an input from a program that was created by the compostion of H with other code is not a category error.
Which "category" that exist in the problem was violated?