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From: Alan Mackenzie <acm@muc.de>
Newsgroups: comp.theory
Subject: Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable
Date: Tue, 6 May 2025 15:38:36 -0000 (UTC)
Organization: muc.de e.V.
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olcott <polcott333@gmail.com> wrote:
> On 5/6/2025 3:17 AM, Alan Mackenzie wrote:
>> [ Followup-To: set ]

>> In comp.theory olcott <polcott333@gmail.com> wrote:

[ .... ]

>>> When we begin with truth and only apply truth preserving
>>> operations then WE NECESSARILY MUST END UP WITH TRUTH.

>> You will necessarily end up with only a subset of truth, no matter how
>> shouty you are in writing it.  You'll also end up with undecidability,
>> no matter how hard you try to pretend it isn't there.

>>> When we ALWAYS end up with TRUTH then we NEVER end up with
>>> UNDECIDABILITY.

>> Shut your eyes, and you won't see it.

> Try to provide one simple concrete example where we begin with truth
> and only apply truth preserving operations and end up with
> undecidability.

There is no need to provide examples for rigorously proven mathematical
theorems, in particular for G=C3=B6del's incompleteness theorem.  I don't=
 go
around providing examples for 2 + 2 =3D 4 either.

Experience shows that if anybody actually did provide such an example,
you wouldn't understand it, and you'd carry on lying about nobody having
produced an example.

> With the Tarski Undefinability theorem Tarski began with a falsehood.

That mis-impression of yours is due to you utterly failing to understand
the concept of proof by contradiction, and even more, utterly failing to
understand the concept of a mathematical proof.

These aren't particularly difficult things to comprehend.  As I keep
saying, you ought to show a lot more respect for people who are
mathematically educated.

[ .... ]

> --=20
> Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
> hits a target no one else can see." Arthur Schopenhauer

--=20
Alan Mackenzie (Nuremberg, Germany).