Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!weretis.net!feeder8.news.weretis.net!news.szaf.org!news.karotte.org!news.space.net!news.muc.de!.POSTED.news.muc.de!not-for-mail From: Alan Mackenzie 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. Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Injection-Date: Tue, 6 May 2025 15:38:36 -0000 (UTC) Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2"; logging-data="36652"; mail-complaints-to="news-admin@muc.de" User-Agent: tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64)) olcott wrote: > On 5/6/2025 3:17 AM, Alan Mackenzie wrote: >> [ Followup-To: set ] >> In comp.theory olcott 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).