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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: =?utf-8?Q?Re:_Analysis_of_Richard_Damon=E2=80=99s_Responses_to_Flibble?=
Date: Mon, 19 May 2025 11:57:43 +0300
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On 2025-05-18 17:07:36 +0000, Mr Flibble said:

> Analysis of Richard Damon’s Responses to Flibble
> =================================================
> 
> Overview:
> ---------
> Richard Damon's critiques of Flibble's arguments regarding the Halting
> Problem and pathological inputs are based on a classical Turing model.
> However, his rebuttals fundamentally misunderstand or misrepresent the
> core of Flibble’s alternative framework. Below is a breakdown of the key
> errors in Damon’s reasoning.
> 
> 1. Misconstruing the Category Error
> -----------------------------------
> Damon claims:
>> "No, they are not [category errors]."
> 
> Flibble’s argument is not that the input is syntactically invalid, but
> that it is semantically ill-formed due to conflating two distinct roles:
> - The decider
> - The program being analyzed
> 
> This is a semantic collapse, akin to Russell’s paradox or typing errors in
> logical frameworks. Damon's rebuttal fails to address the **semantic**
> level, focusing only on syntactic permissibility.
> 
> 2. Ignoring the Model Shift
> ----------------------------
> Damon critiques Flibble’s ideas *from within the classical Turing
> framework*, missing the fact that:
> - Flibble is proposing a **different semantic foundation**.
> - In this new foundation, certain forms of self-reference are *disallowed*
> as a matter of type safety.
> 
> Damon’s refusal to recognize the change in assumptions renders his
> critique logically misaligned.
> 
> 3. Misreading Flibble’s Law
> ----------------------------
> Damon dismisses Flibble’s Law:
>> "Which just isn't true..."
> 
> But Flibble’s Law isn’t about infinite computation—it’s about *recognizing
> the structure* of potentially infinite behavior. It’s a meta-level
> principle, not an operational mandate.
> 
> Damon misinterprets it as a proposal for unbounded simulation time, rather
> than an assertion about the necessity of structural analysis.
> 
> 4. Stack Overflow as a Semantic Signal
> --------------------------------------
> Damon argues that stack overflow represents a failed computation:
>> "...it just got the wrong answer."
> 
> Flibble’s view is different:
> - A stack overflow (or crash) isn’t failure.
> - It is the **semantic manifestation** of an ill-formed input—an expected
> behavior when the category boundaries are violated.
> 
> This is a reinterpretation of what “failure” means, not a bug.
> 
> 5. Misidentifying Recursion Criticism
> -------------------------------------
> Damon says:
>> "Just the presence of recursion isn't the problem."
> 
> This is a straw man. Flibble does *not* claim recursion is inherently
> invalid—only that **self-referential decider/input recursion** creates
> type-theoretic inconsistency. Damon’s rebuttal avoids the specific case
> Flibble addresses.
> 
> 6. Downplaying the Role of SHDs
> -------------------------------
> Damon concedes:
>> "Yes, partial deciders have some uses..."
> 
> But Flibble’s point is stronger:
> - SHDs are useful not as general solvers, but as **structural recognizers
> of malformed input**.
> - Their “failure” (e.g., crashing on pathological input) is
> **informative**, not defective.
> 
> Damon reduces SHDs to weak approximators, missing Flibble’s proposed
> semantic role.
> 
> 7. Failing to Address Reframing
> -------------------------------
> Damon says:
>> "The halting problem isn't malformed..."
> 
> In Turing’s model, it isn’t. But Flibble isn’t working in Turing’s model—
> he is reframing the domain entirely to exclude semantically ill-formed
> constructs. Damon critiques within one framework while Flibble builds
> another.
> 
> Conclusion:
> -----------
> Richard Damon's responses fail not because of flawed logic, but due to a
> **category error of interpretation**: he assumes Flibble is arguing within
> the classical Turing framework when Flibble is explicitly rejecting it in
> favor of a type- and semantics-based system.
> 
> Damon's responses miss the mark because they measure Flibble’s ideas by
> the wrong metric. The disagreement isn’t about whether the Halting Problem
> is undecidable—it’s about *how the problem should be framed* in the first
> place.

The question "how the problem should be framed" is a category error:
there is no "should" in mathematical questions.

-- 
Mikko