From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3468 Path: news.gmane.org!not-for-mail From: John Baez Newsgroups: gmane.science.mathematics.categories Subject: Re: cartesian closed categories and holodeck games Date: Mon, 23 Oct 2006 23:24:23 -0700 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241019324 8889 80.91.229.2 (29 Apr 2009 15:35:24 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:35:24 +0000 (UTC) To: categories Original-X-From: rrosebru@mta.ca Tue Oct 24 09:35:08 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 24 Oct 2006 09:35:08 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1GcLMO-00026c-QL for categories-list@mta.ca; Tue, 24 Oct 2006 09:26:24 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 31 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:3468 Archived-At: On Mon, Oct 23, 2006 at 11:15:04PM -0700, Vaughan Pratt wrote: > In your Week 240 post to categories, you said > > > The moral of this game is that all systematic methods for picking > > an element of (X^X)^(X^X) for an unknown set X can be written > > using the lambda calculus. > What is unsystematic about the contagious-fixpoint functional? This is the > functional that maps those functions that have any fixpoints to the identity > function (the function that makes every element a fixpoint) and functions > without fixpoints to themselves (thus preserving the absence of fixpoints). Whoops. I got carried away there. Later I admitted that by "systematic method" I just meant "definable using the lambda calculus". I'll have to fix this. Thanks! Best, jb