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From: Keith Thompson <Keith.S.Thompson+u@gmail.com>
Newsgroups: comp.theory
Subject: Re: Refutation of =?utf-8?Q?Turing=E2=80=99s?= 1936 Halting Problem
 Proof Based on Self-Referential Conflation as a Category (Type) Error
Date: Mon, 21 Apr 2025 15:08:34 -0700
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Mr Flibble <flibble@red-dwarf.jmc.corp> writes:
> This document refutes Alan Turing’s 1936 proof of the undecidability of 
> the halting problem, as presented in “On Computable Numbers, with an 
> Application to the Entscheidungsproblem” (Proceedings of the London 
> Mathematical Society, 1936), by leveraging the assumption that self-
> referential conflation of a halt decider and its input constitutes a 
> category (type) error. The refutation argues that Turing’s proof, which 
> relies on a self-referential construction, is invalid in a typed system 
> where such conflation is prohibited.

You're acknowledging that it's an "assumption".

Sure, *if* you **assume** that "self-referential conflation of a
halt decider and its input constitutes a category (type) error",
then Turing's proof is invalid in a system where that assumption
is true (if your terms can be rigorously defined).

Of course Turing's proof wasn't intended to be interpreted in such
a system, and there is no actual self-reference.  If Turing's proof
actually relied on self-reference, you might have a valid claim.
The proposed halt decider does not operate on itself, or on a
reference to itself; it operates on a modified copy of itself.

Are you ever going to answer my questions about Goldbach's
Conjecture?

[SNIP]

-- 
Keith Thompson (The_Other_Keith) Keith.S.Thompson+u@gmail.com
void Void(void) { Void(); } /* The recursive call of the void */