Re: Refutation of Turing’s 1936 Halting Problem Proof Based on Self-Referential Conflation as a Category (Type) Error

On 4/21/2025 5:08 PM, Keith Thompson wrote:

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]
>

 Computer Science Professor Eric Hehner PhD
and I all seem to agree that the same view
that Flibble has is the correct view.