From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9079 Path: news.gmane.org!.POSTED!not-for-mail From: Patrik Eklund Newsgroups: gmane.science.mathematics.categories Subject: Re: Theorem or Paradox Date: Fri, 13 Jan 2017 09:22:15 +0200 Message-ID: References: Reply-To: Patrik Eklund NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: blaine.gmane.org 1484512533 4307 195.159.176.226 (15 Jan 2017 20:35:33 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Sun, 15 Jan 2017 20:35:33 +0000 (UTC) Cc: P.B.Levy@cs.bham.ac.uk, graham.white@qmul.ac.uk To: Categories Original-X-From: majordomo@mlist.mta.ca Sun Jan 15 21:35:27 2017 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1cSrWH-00089C-6M for gsmc-categories@m.gmane.org; Sun, 15 Jan 2017 21:35:17 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:38118) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1cSrNP-0004Av-1C; Sun, 15 Jan 2017 16:26:07 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1cSrN0-00030z-N1 for categories-list@mlist.mta.ca; Sun, 15 Jan 2017 16:25:42 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9079 Archived-At: > What else could he have done, having read the proof? > > Paul Dear Paul, Your question may turn out to be one of the most important questions in the history of mathematics, when looking back at it in 2103 (= 2017 + (2017 - 1931)). A sibling question, therefore, and for me a more important one, is "What else could we (= The Category Theory Community) do, having read the proof?". I have no interest to deeply analyze WHY G??del did what he did, even if I may be a bit curious about that as well. It relates to theatre and stage, or drama and logic. As far as I can tell, even Shakespeare did both. No, indeed not why, as I am more interested in how, and in showing that we need types, not just to distinguish terms, but also to distinguish sentences, and further to distinguish proofs from sentences, and so on. Category theory embraces tools to do that. We have already provided some first results in that direction. G??del didn't possess any of those tools. Neither did Kleene. Nor did any of the two contribute to creating those tools, I believe. I raised the seemingly harmless and philosophical question about theorem or paradox under this mailing list because I believe we [= The Category Theory Community) can settle this thesis by means of mathematics and category theory, and without philosophy, I would like to add, even if philosophers are welcome to learn more about mathematics and category theory in order to enrich their philosophical questions e.g. by the use of enriched categories. As you may have seen, I tend to believe that the thesis [G??del is wrong, so Hilbert's question remains open] is _right_, and indeed that "[G??del is wrong, so Hilbert's question remains open] is _right_" is well decidable. The thesis is still an open question, i.e., the thesis in the form presented here. I wouldn't interpret non-reply to the sibling question "What else could we do, having read the proof?" as a _good_ proof that "[G??del is wrong, so Hilbert's question remains open] is _wrong_". If it turns out that "[G??del is wrong, so Hilbert's question remains open] is _right_", also in the sense that there is a majority in a most important, well recognized and large mathematical community that agrees upon that, then I will be happy to refer to you, Paul, and to your question as having been the de facto starting point for the process leading to this dramatic and logical solution. On Friday the 13th, January, 2017, Patrik [For admin and other information see: http://www.mta.ca/~cat-dist/ ]