Philosophy of Mathematics: Five Questions

I’ve mentioned before the now newly published Philosophy of Mathematics: Five Questions, in which some twenty eight philosophers, logicians and mathematicians respond to a bunch of questions related to how they see the current state of the philosophy of mathmatics. My copy arrived today. (Some of the contributions are on the authors’ web-sites: Jeremy Avigad, Mark Colyvan, Solomon Feferman, Edward Zalta. There are other pieces worth reading by e.g. Geoffrey Hellman, Stewart Shapiro, Alan Weir, and Crispin Wright.)

My first impressions are that (i) it is worth ordering for your university’s library (I imagine that some of the pieces would be quite useful and interesting orientation for students), but (ii) it is a very mixed bag (thus, Feferman offers twenty informative pages, while Thomas Jech and Penelope Maddy provide barely three pages between them), and overall (iii) I guess it is rather disappointing, with too many remarks too brisk and allusive to be very useful to anyone. It is no surprise, for example, that Steve Awodey’s answer to the question “What do you consider the most neglected topics and/or contributions in late 2oth century philosophy of mathematics?” is “Category theory”. But he doesn’t tell us why.

Maybe the editors should have been more directive.

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