From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1734 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Categories ridiculously abstract Date: Sun, 03 Dec 2000 21:30:39 -0800 Message-ID: <200012040530.VAA06421@coraki.Stanford.EDU> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241018054 32655 80.91.229.2 (29 Apr 2009 15:14:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:14:14 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Dec 4 11:55:59 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eB4FKIE08739 for categories-list; Mon, 4 Dec 2000 11:20:18 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 7 Original-Lines: 62 Xref: news.gmane.org gmane.science.mathematics.categories:1734 Archived-At: 1 ab.stract \ab-'strakt, 'ab-,\ adj (15c) [ML abstractus, fr. L, pp. of abstrahere to draw away, fr. abs-, ab- + trahere to draw -- more at DRAW] 1a: disassociated from any specific instance 1b: difficult to understand: ABSTRUSE 1c: IDEAL 1d: insufficiently factual: FORMAL 2: expressing a quality apart from an object 3a: dealing with a subject in its abstract aspects: THEORETICAL 3b: IMPERSONAL, DETACHED 4: having only intrinsic form with little or no attempt at pictorial representation or narrative content -- ab.stract.ly \ab-'strak-(t)l, 'ab-,\ adv -- ab.stract.ness \ab-'strak(t)-ns, 'ab-,\ n 1a: Sets and categories as mathematical abstractions are equally disassociated from specific instances. 1b: For almost every interesting known theorem of category theory there is a harder interesting known theorem of set theory, and vice versa. It is plausible that the exceptions from set theory outnumber those from category theory, but it is equally plausible that a majority of mathematical literates judge category theory harder than set theory. No clear winner here. 1c: Sets and categories are both ideal entities. 1d: Set theory and category theory are equally factual, and equally formal. 2: In this sense set theory and category theory are both abstract while sets and categories are objects and so not abstract. 3a: Set theory and category theory deal equally with the abstract aspects of their respective subjects. 3b: The FOM mailing list tends to get worked up much more often and rather more heatedly about the set-vs-category debate than does the categories mailing list. 4. Categories lend themselves better to diagrams than do sets. Conclusions (organized by dictionary meaning of "abstract"): 1 to 3a: No difference. 3b: Category theorists are more abstract than set theorists. 4: Sets are more abstract than categories. -- Vaughan Pratt O res ridicula! immensa stultitia. --Chorus of Old Men, Catulli Carmina