Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!2.eu.feeder.erje.net!3.eu.feeder.erje.net!feeder.erje.net!news2.arglkargh.de!news.karotte.org!news.space.net!news.muc.de!.POSTED.news.muc.de!not-for-mail From: Alan Mackenzie Newsgroups: sci.logic,comp.theory Subject: Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable Followup-To: comp.theory Date: Mon, 5 May 2025 10:47:54 -0000 (UTC) Organization: muc.de e.V. Message-ID: References: Injection-Date: Mon, 5 May 2025 10:47:54 -0000 (UTC) Injection-Info: news.muc.de; posting-host="news.muc.de:2001:608:1000::2"; logging-data="70651"; mail-complaints-to="news-admin@muc.de" User-Agent: tin/2.6.4-20241224 ("Helmsdale") (FreeBSD/14.2-RELEASE-p1 (amd64)) [ Followup-To: set ] In comp.theory olcott wrote: > When we define formal systems as a finite list of basic facts and allow > semantic logical entailment as the only rule of inference we have > systems that can express any truth that can be expressed in language. > Also with such systems Undecidability is impossible. The only > incompleteness are things that are unknown or unknowable. Do you believe in the tooth fairy, too? [ .... ] > -- > Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius > hits a target no one else can see." Arthur Schopenhauer -- Alan Mackenzie (Nuremberg, Germany).