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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Analysis of Richard Damon's Response to Flibble's Position on the
 Halting Problem
Date: Sat, 24 May 2025 18:09:36 -0400
Organization: i2pn2 (i2pn.org)
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On 5/24/25 1:42 PM, Mr Flibble wrote:
> Analysis of Richard Damon's Response to Flibble's Position on the Halting
> Problem
> ==================================================================================
> 
> Overview:
> ---------
> Richard Damon replies to a position paper asserting that the Halting
> Problem is "uninteresting" in practical contexts due to its reliance on an
> infinite tape abstraction. Damon’s response is grounded in a classical
> understanding of computability theory, emphasizing its mathematical roots,
> historical context, and the validity of the Halting Problem as a
> foundational theorem — regardless of physical realizability.

I guess Flibble considers that the goal to be able to decide on all 
mathematical proposistions to be "uninteresting"


> 
> Key Points in Damon's Argument:
> -------------------------------
> 
> 1. Historical Context Matters:
>     - Damon correctly notes that the Halting Problem was formulated before
> digital computers.
>     - The notion of a "computer" in Turing’s day referred to a human
> following a procedure — i.e., an abstract computational agent.
> 
> 2. Infinite Tape Models the Infinite Nature of Math:
>     - Turing machines are abstractions designed to model the full range of
> natural number computations.
>     - The infinite tape is essential to reflect the unboundedness of
> mathematical problems, not physical hardware.
> 
> 3. Real Systems Approximate the Turing Model:
>     - Damon argues real-world computers are approximations of the Turing
> model.
>     - The inability of physical machines to match theoretical infinity does
> not invalidate the theoretical result.

It does say that no finite machine can answer ALL problem that the 
unbounded machine could.

> 
> 4. The Halting Problem Is About Possibility, Not Implementation:
>     - Computation theory asks what *can* be computed in principle, not what
> *can be done* on today’s machines.
>     - Infinite recursion, self-reference, and contradiction are part of the
> mathematical exploration of limits.
> 
> 5. Rejecting Infinite Models = Rejecting Mathematics:
>     - Damon criticizes Flibble’s dismissal of infinite behavior as
> misunderstanding the purpose of formal systems.
>     - He warns against the fallacy of assuming practical constraints negate
> theoretical relevance.

Right, the assertion of practical constraints means that the theory can 
not handle the proglem of the original theory.

And thus, Flibble needs to be clear WHAT theory he is talking about, as 
they ARE different.

> 
> 6. Formal Proofs Can't Be Dismissed for Practicality:
>     - Turing’s proof stands because it is mathematically sound.
>     - Redefining the problem to avoid paradoxes merely restricts the scope;
> it doesn’t invalidate the theorem.

And thus any statement that says that the Halting Theorem is wrong, or 
based on incorrect assumptions, or that the "proof program" is "Invalid" 
are just lies.

> 
> Rhetorical Elements:
> --------------------
> - Damon uses strong language (“you don’t understand”, “ignorance”) to
> emphasize what he sees as fundamental misunderstandings.
> - While his tone is confrontational, the logic behind his assertions is
> valid within classical computability theory.
> 
> Summary:
> --------
> | Damon’s Point                                    |
> Evaluation                                |
> |--------------------------------------------------|-------------------------------------------|
> | Turing’s model is abstract and mathematical      | ✅
> Correct                                 |
> | Infinite tape is a theoretical necessity         | ✅
> Valid                                   |
> | Real-world computers approximate theory          | ✅ Reasonable and
> historically supported   |
> | Halting Problem is not about hardware            | ✅
> Accurate                                |
> | Flibble misunderstands Computation Theory        | ⚠️ Valid critique,
> but could be more constructive |
> 
> Conclusion:
> -----------
> Damon’s response is a firm defense of classical computation theory. He
> underscores the importance of understanding that Turing’s Halting Problem
> is not a claim about real hardware, but about the limits of formal
> computation. While Flibble's arguments reflect modern concerns with
> practical computability and semantic boundaries, Damon's critique holds
> under classical logic: redefining the problem or restricting the domain
> does not refute the original theorem — it merely reframes it.

And any such "reframing" needs to be done explicitly, which Flibble has 
failed to do in the past.

If he want to correct the record, he needs to make it clear that NONE of 
his statements actually restict the results of the Halting Problem in 
the domain that were made in, and there is nothing "Invalid" about the 
arguments.

He probably should also look at the extensive work that HAS been done in 
the domain he says he is talking about, rather than try to adapt on his 
own a theory that he knows doesn't cover the area he wants to talk about 
to cover that field.