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

On 5/12/25 10:32 AM, olcott wrote:

On 5/12/2025 2:32 AM, Mikko wrote:

On 2025-05-11 11:52:05 +0000, Mr Flibble said:
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On Sun, 11 May 2025 11:49:50 +0000, joes wrote:
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Am Sat, 10 May 2025 23:56:36 +0000 schrieb Mr Flibble:

On Sat, 10 May 2025 18:40:53 -0400, Richard Damon wrote:

On 5/10/25 4:38 PM, Mr Flibble wrote:

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How my refutation differs to Peter's:
* 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.
These two refutations are related but not exactly the same.

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And the problem is that you use incorrect categories.
The decider needs to be of the category "Program".
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.

>
Those two categories you have identified are different hence the
category error.

No. HHH has a string representation, like every program.

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No. Conflating a program with a string representation of the same program
in the manner of a self-referential dependency is a category (type) error.

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There are several meanings for the word "program" but a common one is a
string that specifies what shall happen when the program is executed.
One possible string representation of that string is the string itself.
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 A better name is computational unit.
 

And all of them mean a complete and finite description of the algorithm that is to be used.
If your HHH is one, then DD is also, as it is built by a simple, allowed, and fully described transformation, and it turns out that HHH just can not give the correct answer about DD, which is DEFINED as what DD does when run, despite you frantical (and idiodic) claims that it can't be that, when it is the definition.
The fact that it allows things that can't be computed does not make it wrong, as it can be proven by other means that there MUST be uncomputable functions.