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

On 5/10/25 11:00 PM, olcott wrote:

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

 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.

Sure they do.
The problem is you don't understand the definition of the "Behavior of the Input" and how it is defined.

 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.

Nope, because BY THE DEFINITION the finite string is a representation of a program and the behavior specified is of that program it represents.

 Everyone here takes this false assumption as the
infallible word of God. A textbook says it therefore
it must be infallible.
 

But it isn't FALSE, it is defined.
Your problem is you beleive your own lies about what things are, including the lie that you are allowed to change the definitions that you don't like, because you don't understand that two different things are different, and you can't just change the existing system and have it still be the existing system.