From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8668 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: Current Issues in the Philosophy of Practice of Mathematics & Informatics Date: Fri, 31 Jul 2015 12:35:57 +0200 Message-ID: <20150731103557.GB28214@mathematik.tu-darmstadt.de> References: Reply-To: Thomas Streicher NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1438522589 24073 80.91.229.3 (2 Aug 2015 13:36:29 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 2 Aug 2015 13:36:29 +0000 (UTC) Cc: Categories To: Patrik Eklund Original-X-From: majordomo@mlist.mta.ca Sun Aug 02 15:36:22 2015 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.7.19]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1ZLtR7-0004Cj-QZ for gsmc-categories@m.gmane.org; Sun, 02 Aug 2015 15:36:22 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60426) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ZLtQg-0006G1-JA; Sun, 02 Aug 2015 10:35:54 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ZLtQh-0007vj-0n for categories-list@mlist.mta.ca; Sun, 02 Aug 2015 10:35:55 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8668 Archived-At: > Yet, G??del uses "provability" to create new sentences, and > simply opens up that bag of sentences, and throws in these new ones. It > has always been accepted, but this in fact breaches the lativity > principle, which indeed is not respected in logic. The point is that the provability predicate doesn't require new syntax but can be formulated already with a modicum of arithmetic (that's what has become known as "Goedelization"). It would be a different issue with a "truth" predicate which cannot be expressed in the language (known as Tarski's theorem). Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]