From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8666 Path: news.gmane.org!not-for-mail From: Andreas Blass Newsgroups: gmane.science.mathematics.categories Subject: Current Issues in the Philosophy and Practice of Mathematics & Informatics Date: Thu, 30 Jul 2015 08:28:03 -0700 Message-ID: Reply-To: Andreas Blass NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1438522435 21942 80.91.229.3 (2 Aug 2015 13:33:55 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sun, 2 Aug 2015 13:33:55 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sun Aug 02 15:33:47 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 1ZLtOd-0003Jk-Cu for gsmc-categories@m.gmane.org; Sun, 02 Aug 2015 15:33:47 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:60416) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1ZLtO5-0005qw-MR; Sun, 02 Aug 2015 10:33:13 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1ZLtO6-0007sk-8T for categories-list@mlist.mta.ca; Sun, 02 Aug 2015 10:33:14 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8666 Archived-At: I just received Patrik Eklund's message containing the statement "Yet, G=C3=B6del uses "provability" to create new sentences, and simply opens up = that bag of sentences, and throws in these new ones." Presumably others have already responded to this in messages that haven't yet reached me, but, just in case they haven't: Much of the work in G=C3=B6del's paper on the incompleteness theorems is devoted to making sure that what Eklund wrote here is not the case. G=C3=B6del shows how statements about provability ca= n be encoded as arithmetical statements, which are not at all new but were available (in what Eklund calls "that bag") all along. Andreas Blass [For admin and other information see: http://www.mta.ca/~cat-dist/ ]