From: Vaughan Pratt <pratt@cs.stanford.edu>
To: categories@mta.ca
Subject: Re: Categories ridiculously abstract
Date: Sun, 03 Dec 2000 21:30:39 -0800 [thread overview]
Message-ID: <200012040530.VAA06421@coraki.Stanford.EDU> (raw)
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 <abstract entity>
1b: difficult to understand: ABSTRUSE <abstract problems>
1c: IDEAL <abstract justice>
1d: insufficiently factual: FORMAL <possessed only an abstract right>
2: expressing a quality apart from an object <the word poem is concrete,
poetry is abstract>
3a: dealing with a subject in its abstract aspects: THEORETICAL <abstract
science>
3b: IMPERSONAL, DETACHED <the abstract compassion of a surgeon --Time>
4: having only intrinsic form with little or no attempt at pictorial
representation or narrative content <abstract painting> -- ab.stract.ly
\ab-'strak-(t)l<e^->, 'ab-,\ adv -- ab.stract.ness \ab-'strak(t)-n<e>s,
'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
next reply other threads:[~2000-12-04 5:30 UTC|newest]
Thread overview: 8+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-12-04 5:30 Vaughan Pratt [this message]
-- strict thread matches above, loose matches on Subject: below --
2000-11-30 17:30 Tom Leinster
2000-12-01 22:19 ` Michael MAKKAI
2000-12-06 19:18 ` DR Mawanda
2000-12-02 13:34 ` Robert J. MacG. Dawson
2000-11-29 13:39 John Duskin
2000-11-29 16:48 ` Michael Barr
2000-11-30 20:52 ` Todd Wilson
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