From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5028 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Can you spot a flaw in this argument? Date: Fri, 26 Jun 2009 09:32:47 +0100 (BST) Message-ID: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1246089057 13309 80.91.229.12 (27 Jun 2009 07:50:57 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 27 Jun 2009 07:50:57 +0000 (UTC) To: Meredith Gregory , Original-X-From: categories@mta.ca Sat Jun 27 09:50:50 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1MKSgS-0003wD-In for gsmc-categories@m.gmane.org; Sat, 27 Jun 2009 09:50:48 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MKS86-0001ue-Jz for categories-list@mta.ca; Sat, 27 Jun 2009 04:15:18 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5028 Archived-At: Dear Gregory, I think the problem resides in what you mean by "no internal structure". If by this you mean that the *set* of names has no internal structure, then it's obviously impossible -- to require the set to have decidable equality is to impose internal structure on it. But it's still possible for the names themselves to be atomic: you can identify the set of names with the set of natural numbers (which has lots of internal structure, including decidable equality) without identifying the individual names with von Neumann-style natural numbers (or Russell-style cardinals, or ...) Peter Johnstone On Thu, 25 Jun 2009, Meredith Gregory wrote: > All, > > This is an argument about effective theories and so i would love to hear > from the topos-theory crowd. i'll state the argument in lowly computational > terms, using two distinct proposals for foundational models of computing: > the lambda calculus and the ?-calculus. Both the lambda calculus and the > ?-calculus suffer a dependence on a theory of names (aka variables). Both > require two things of whatever theory of names is provided to them: > > - at least countably infinitely many names > - an effective equality on names > > Now, to this recent proposals[1] add a third constraint, namely > > - names are atomic -- they have no internal structure ... [For admin and other information see: http://www.mta.ca/~cat-dist/ ]