Sunday, November 25, 2007

Bracket This

Time to blog about something, but what? (I could brag that my doubts last month, about the dangers of being fat, were justified last week; or I could nit-pick pedantically, or both:) What our curly brackets (e.g. “}”) are for, in this (meta-)language, is a question that cropped up elsewhere recently. I doubt that the reason why they are on our keyboards is to help us to denote sets because many other, more convenient scientific symbols are not there; so:
......Why do we philosophers use them almost exclusively to denote sets? In our pre-keyboard days, we might have used a big “}” to the right of a vertical list (of 2 or more lines) in order to comment upon all of its elements with whatever was written to the left of the central nipple. So their basic use may well be to group things together; but that could give us a set of things (singularly referred to), an atomic fusion (in the mereological sense), a number of things (plurally referred to), and so forth.
......There are lots of examples of collections, and they aren’t all obviously sets. A brace of pheasants is just those 2 pheasants; e.g. if I said “that brace is ready to eat,” there would not be anything over and above the 2 pheasants there, not something edible anyway. Similarly, for a stamp collection that at first contained only one stamp, that stamp would be the collection (there might not even be an album yet), and if I lost it I would not have an empty stamp collection (although I might have an empty album), I would have no stamp collection.
......Conversely, mathematicians use standard sets to be collections and numbers and everything else (as much as possible), a use that is formalistically rather than philosophically motivated. Collections are pretty fundamental things, but they don't seem to be sets (what is the empty set? and what of all the sets?), so why do we seem to use the curly brackets only for sets? Mathematicians use them that way, but don’t philosophers need a better reason than that? What notation are we supposed to use for collections in general, if not our curly brackets?

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