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

On 2025-05-11 03:11:43 +0000, Mr Flibble said:

On Sat, 10 May 2025 22:00:26 -0500, olcott wrote:
 

On 5/10/2025 9:51 PM, Mr Flibble wrote:

On Sat, 10 May 2025 21:49:41 -0400, Richard Damon wrote:
 

On 5/10/25 9:18 PM, Mr Flibble wrote:

On Sat, 10 May 2025 21:07:34 -0400, Richard Damon wrote:
 

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:
 

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

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.
 /Flibble

 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.
 

That is correct. A running program and an input finite string ARE
NOT THE SAME.

 But there is a direct relationship between the two.
  

The "Pathological Input" *IS* a Program, built by the simple
rules of composition that are allowed in the system.

 Such composition is invalid.
 

Richard is trying to get away with saying that a finite string THAT
IS NOT A RUNNING PROGRAM <IS> A RUNNING PROGRAM
 

But they are related to each other,

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

 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.
 

Why relationship doesn’t rescue the mistake:
 * 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.

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

 A program and a finite string representing a program are different
categories ergo we have a category error.
 /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.
 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.
 Everyone here takes this false assumption as the infallible word of God.
A textbook says it therefore it must be infallible.

 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.

That is contradicto in adiecto: a refertial dependncy between two entities
of different categories cannot be self-referential. An entity can have a
self-referential dependncy only to itself and it is always of the same
category as it is itself.
--
Mikko