Re: Analysis of Richard Damon's Responses to Flibble's Detection Argument

On 5/21/25 2:04 PM, Mr Flibble wrote:

Analysis of Richard Damon's Responses to Flibble's Detection Argument
=====================================================================
 Overview:
---------
Richard Damon's latest response to Flibble's refined position on
Simulating Halt Deciders (SHDs) and infinite recursion continues to apply
classical Turing logic to a fundamentally different model. This leads to
multiple critical misinterpretations and categorical mismatches in
reasoning.

THen you are willing to admit that you system has no impact on the classical Halting Problem, and thus does "solve" that problem?

 1. Misunderstanding Detection vs. Simulation
--------------------------------------------
Damon says:

"Wrong, because you can only detect infinite recursion if it is actually

there."
 Flibble never claims detection occurs without cause. He asserts that
*some* forms of infinite recursion can be detected **structurally**—
without runtime simulation. Damon’s assumption that only simulation can
confirm recursion ignores the entire field of static analysis.

So, if the input program doesn't actually have infinite recursion, your decider would be incorrect to say it is there?

 Flibble's approach mirrors:
- Structural analysis in compilers.
- Termination proofs in dependently typed languages.
 2. Rigid and Misapplied Conception of Decidability
---------------------------------------------------
Damon says:

"Violation of the rules of the system."

 Flibble agrees that deciders must halt in finite time. His law refers to
the *necessity* of reasoning about infinite behavior—not to *performing*
infinite computation.

So you don't understand the objection. To *BE* a decider, it must be a program with fully defined operations and thus fully defined behavor for any input. THus H(D) will ALWAYS give the same result.
That means that the "pathological" program built on it will also be fully defined in operation, and thus fully defined behavior for any input it is given. Thus D() will ALWAYS do the same thing, no matter who/what is looking at it.

 Damon's response assumes that *mentioning* infinity implies unbounded
execution, which misconstrues Flibble’s meta-theoretical intent.

Nope. That comment just says you don't understand what I am talking about.

 3. Incorrect Dismissal of Type Theory and Proof Assistants
-----------------------------------------------------------
Damon says:

"No it doesn't." (on alignment with Coq/Agda)

 This is false. Proof assistants like Agda and Coq use:
- Structural recursion.
- Finite proofs to ensure termination.
 Flibble’s SHD aligns with these practices by seeking **compile-time
recognizability** of non-termination. Damon mischaracterizes these
systems, likely from lack of direct experience with their constraints.

But the fact that DD() does terminate means that it is IMPOSSIBLE for the decider to somehow correctly determined that it doesn't

 4. Misframing Overflow as Error Instead of Signal
--------------------------------------------------
Damon says:

"Overflow... isn't an out for the SHD."

 Flibble argues that stack overflow is a **semantic indicator** of an ill-
posed question, not an execution failure. This is analogous to:
- Type errors in type-safe languages.
- Runtime protection against undefined behavior.

No stack overflow is not allowed in Turing Complete systems, and when using finite approximatios for Turing Complete systems, it indictes a inability of the system to handle the problem.

 Damon views overflow through a hardware lens, while Flibble interprets it
as a meta-semantic signal—again, a mismatch of frameworks.

Ok, so you are just admitting you "framework" is insufficient for the probmme.

 5. False Strawman Accusation
-----------------------------
Damon says:

"You can't redefine the Halting Problem and then say you have answered

it."
 Flibble does **not** claim to solve the Halting Problem. He claims:
- The classical framing is ill-typed or semantically malformed in
pathological cases.
- A meaningful reformulation avoids this by respecting type/category
boundaries.
 Damon misreads Flibble's reframing as a refutation, then attacks that
strawman.
 6. Conceding Without Recognizing It
------------------------------------
Damon says:

"You ADMIT that... no universal Halt Decider exists."

 Yes—Flibble agrees. The disagreement is not about the *result*, but about
the *reason*.

But if you claim to be talking about the REASON that the Halting Problem doesn't work, IN ITS SYSTEM, you have to use ITS SYSTEM.
Sorry, you are just admitting you are starting with a category error.

 | Turing           | Flibble                          |
|------------------|-----------------------------------|
| Contradiction ⇒ undecidability | Contradiction ⇒ ill-formed input |
| Input space includes all valid strings | Input space excludes
semantically ill-formed programs |

The halting problem itself doesn't have a "contradiction"
The proof uses proof by contradiction, but there is no contradiction in the system. (and in fact, it doesn't need to use a proof by contradiction, we can also prove it by exhaustive analysis).
The proof just shows that for *ANY* possible machine that is claimed to be a Halt Decider, we can construct an input that it will get wrong.

 Damon claims inconsistency where Flibble has already clarified agreement—
just via a different reasoning path.

Then you need to stop talking about what the classical Halting Problem is about.
Either you ARE talking about some opther system, in which case that system doesn't say anything about the original system, or
You are talking about the original system, but violating the rules, and thus are incorrect.
There is no other case.

 Conclusion:
-----------
Richard Damon's critique fails because he measures Flibble’s typed,
semantic model using classical Turing assumptions. His rebuttals are
consistent only within a framework Flibble explicitly rejects.
 Thus, Damon’s critiques:
- Are not wrong *in themselves*,
- But are irrelevant when applied to a model that redefines the semantic
rules of the game.

And thus Flibble's model is irrelevant to the classic problem, and can't be used to call it "wrong".

 In trying to defend classical computability, Damon inadvertently **commits
the very category error** that Flibble critiques in the Halting Problem.

And thus Flibble admits to making that same category error when trying to apply is reasoning to the Halting Problem. You can't talk about why it is wrong in its system, when reasoning from another system.
The problem is that, when talking about the classical system, it is YOU who is making the category error, and thus to say my defense of the classical system is wrong, just shows that you are just lying about really being in a different model, or you are just to stupid to understand that different models don't affect each other.