06 September 2008

A lexicographical copout

Definitions of "set" (as a noun) in the OXford English Dictionary include:

Math. Used variously, as defined by the individual author. Obs.

(This is set, n.2, definition 10b. Definition 10c is "An assemblage of distinct entities, either individually specified or which satisfy certain specified conditions", which is what mathematicians usually mean by "set". set, n.2 basically is the definitions of "set" that mean "bunch of things", while set, n.1 has to do with things hardening, hanging, etc.

I was led to this definition by a talk about the modern dictionary from the TED conference, in which Erin McKean, an editor for the OED, talks about how in the future dictionaries won't be like they are now. (A transcript of the talk is here.) She mentions that set has many definitions, one of which is "miscellaneous technical senses". I was actually hoping that this would include the mathematical sense, and I could write a post about how the compilers of the OED hate mathematicians. The numbered definition she was talking about, set, n.1 definition #30, has various lettered sub-definitions; usually the sub-definitions under a number are related, but this one isn't. McKean's theory is that it was Friday afternoon and the people writing it wanted to go down to the pub, and she called it a lexicographical copout.

But McKean also makes a more substantial point in the talk; it's not her job to enforce rules about the language, but rather to describe it. And nowhere is this more true in mathematics, where we basically just define words, in our papers, to mean whatever we want them to mean. The definition I gave above may be obsolete -- we've pretty much converged on a meaning for set -- but the spirit there lives on.

No comments: