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