Jos Laycock asked (icw TOPOS) April 19th: Am I experiencing "cleveland harbour" rit large?
Ant McWatt comments: I don't know, Jos. There's a lot of technical terms etc. in the four physics papers (by Doering & Isham) about TOPOS that you refer to at: http://math.ucr.edu/home/baez/topos_physics/ Starting off with the phrase "topos" itself e.g. "A topos is a categorical model of constructive set theory. In particular, the effective topos is the categorical 'universe' of recursive mathematics. Among its objects are the modest sets, which form a set-theoretic model for polymorphism. More precisely, there is a fibration of modest sets which satisfies suitable categorical completeness properties, that make it a model for various polymorphic type theories." http://www.lfcs.inf.ed.ac.uk/reports/92/ECS-LFCS-92-208 I understand the TOPOS models are analogous to the "paintings in the TRUTHS gallery" illustration found in LILA but is there any chance of you summarising in layman's language of what TOPOS theory (and its principle components) are all about? Best wishes, Anthony >From: "Laycock, Jos (OSPT)" <[EMAIL PROTECTED]> >Reply-To: [email protected] >To: <[email protected]> >Subject: Re: [MD] TOPOS - OY THIS IS IMPORTANT >Date: Thu, 19 Apr 2007 14:22:40 +0100 > > >Ant, Horse, Ian, EVERYONE please go read this, its like our cousins over in >physics are the belatedly arriving cavalry. > >Some further quotes from the NS article: > >"A set is just a collection of objects, anything from the infinite set of >prime numbers to the set of all mammals" > >"TOPOI share one key feature; each gives rise to its own variety of logic" > >"Now they could see boolean algebra for what it was, merely the most >familiar of many possible types of algebra" > >"Does this mean we must acept a universe that is real but about which any >question will recieve myriad answers all of them true" > >Am I experiencing "cleveland harbour" rit large? > _________________________________________________________________ Get Hotmail, News, Sport and Entertainment from MSN on your mobile. http://www.msn.txt4content.com/ moq_discuss mailing list Listinfo, Unsubscribing etc. http://lists.moqtalk.org/listinfo.cgi/moq_discuss-moqtalk.org Archives: http://lists.moqtalk.org/pipermail/moq_discuss-moqtalk.org/ http://moq.org.uk/pipermail/moq_discuss_archive/
