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From: Richard Heathfield <rjh@cpax.org.uk>
Newsgroups: comp.theory
Subject: =?UTF-8?Q?Re=3A_Analysis_of_Flibble=E2=80=99s_Latest=3A_Detecting_v?=
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Date: Wed, 21 May 2025 17:09:11 +0100
Organization: Fix this later
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On 21/05/2025 16:54, olcott wrote:
> On 5/21/2025 12:56 AM, Richard Heathfield wrote:
>> On 21/05/2025 06:23, olcott wrote:

<snip>

>>> Do you mean like how ZFC resolved Russell's
>>> Paradox thus converting "set theory" into "naive set theory"?
>>
>> No, because there is no paradox in the Halting Problem. A proof 
>> by contradiction is not a paradox.
>>
> 
> A self-contradictory input and a proof by contradiction
> are not the same thing.

Agreed.

> A proof by contradiction would
> conclude that "this sentence is not true" is true because
> it cannot be proved false.

A proof by contradiction would conclude that 'by assuming A was 
possible we have derived a contradiction. We conclude that A is 
not possible'.

There is no self-contradictory input because such an input is 
impossible.

> ZFC shows how a whole way of examining a problem can be
> tossed out as incorrect and replaced with a whole new way.

The Halting Problem shows how there are some problems that cannot 
be computed by a finite algorithm.

> The HP proofs are based on defining a D that can
> actually do the opposite of whatever value that H returns.
> No such D can actually exist.

That an algorithm for ascertaining whether an arbitrary program 
with arbitrary input halts cannot actually exist is precisely 
what the Halting Problem proves.

<snip>

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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