From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6782 Path: news.gmane.org!not-for-mail From: Patrik Eklund Newsgroups: gmane.science.mathematics.categories Subject: Re: Re: Timelines for category theory: a response to comments Date: Wed, 13 Jul 2011 09:43:04 +0200 (MEST) Message-ID: References: Reply-To: Patrik Eklund NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1310580115 3927 80.91.229.12 (13 Jul 2011 18:01:55 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 13 Jul 2011 18:01:55 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Jul 13 20:01:50 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qh3ks-0000hd-Bh for gsmc-categories@m.gmane.org; Wed, 13 Jul 2011 20:01:50 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41785) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1Qh3iE-0003dW-BY; Wed, 13 Jul 2011 14:59:06 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qh3iD-0005wg-N3 for categories-list@mlist.mta.ca; Wed, 13 Jul 2011 14:59:05 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6782 Archived-At: Can we do history of category theory without considering history leading=20 to category theory? Is history an attachment of subhistories, or are=20 there paths that can be followed, and how do we teach these things to=20 young researchers? What I say is I like the '... and foundations of=20 mathematics'. I always wondered if the term 'categorical this-and-that' every once=20 in a while should be considered with its counterpart 'this-and-thatical=20 category theory'. It's also about meta and object languages, I believe. And sometimes categorists 'internalize', so that the roles of meta and=20 object ar blurred. Isn't a topos basically a 'logical category', where=20 'categorical logic' is something else? 'Topological category' is not the=20 same as 'categorical topology', and so on. Also, 'categories in computer science' is too general. Still, most of=20 categories, used in recognized areas in computer science, relate to logic= =20 in one way or the other, and to logic in a broad sense. Sometimes we also= =20 say computer science has given many interesting problems for category=20 theory. I don't think this is really true in such a phrasing. What has=20 happened is that computer scientist in their work to formalize computable= =20 logic and computability has been forced to go back to foundations of=20 mathematics in order to understand what is really going on. Computer=20 scientists, however, usually don't bother to formalize something they=20 already 'understand' (type theory is a good example), where a mathematicians refuses to understand before it's formalized (that's why=20 there isn't any mathematical type theory). Yes, we can. We can do history of category theory without considering=20 history leading to category theory. But why should we? And how does it=20 help to bring out all flavours of things we are still working on? Will=20 this history writing provide me with those utensils I need for things I=20 need to do. Or do I have to go elsewhere to look for it? History writing is also a bit dangerous as it almost says this is now the= =20 state-of-the-art, and if you don't play your etudes properly you are not=20 allowed to play structure and provide interpration. Talent is=20 thereby often surpressed, and mostly by teachers who really never=20 understood counterpoint anyway. So what I really say is I like the '... and foundations of mathematics'.=20 Keeping meta and object apart, and category theory taught me how to=20 do that, is important for logic and foundations, as we know e.g. from=20 G=F6del numbering and creating sentences about it. To which logic these=20 sentences belong, nobody ever told me, so please do. Best regards, Patrik On Tue, 12 Jul 2011, Graham White wrote: > I think, judging by comments so far, that there are basically two > goals concealed within "this project". One is to write an outline of > category theory as it seems to us now; the other is to write a history > of category theory, and, specifically, a history of who influenced whom= . > Both of these are very worth doing, but the second is much more > difficult. > > It's difficult mainly because it entails recovering a consistent histor= y > from people's reminiscences, and these will not be consistent with > each other: they will be inconsistent not just because people's memorie= s > are not accurate, but because everyone has remained active in the field > and they alter their memories according to what they think now. This is > probably especially true of mathematicians, because mathematicians > always rephrase other people's stuff in their own terms: it's how they > come to understand it. (Remember Goethe's remark, "Mathematicians are > like Frenchmen: if you tell them something, they rephrase it in their > own language, and you cannot understand it any more"? Well, > mathematicians do that to each other as well as to non-mathematicians). > > The history is hard to do, but also potentially very valuable: it would > show how a revolution in mathematics took place. Hard work, though. > > And *not* in the form of a Wiki, because Wikis deal with contradictions > between documents by erasing one document in favour of the other. (I > know, you can always look back in edit history, but it still relegates > one of the testimonies to the sidelines: you might well be in a > situation where you just have more than one testimony, and where it > would not be sensible to prefer one to the other). > > Graham > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]