Comments on: Is philosophy of religion taken seriously?

By: Craig on the moral argument : The Uncredible Hallq

Craig on the moral argument : The Uncredible Hallq — Sun, 04 Apr 2010 17:50:28 +0000

[...] fictionalists account for our common-sense views on morality. This is an example of how I realize I should know more about philosophy of mathematics than I [...]

By: Chris Hallquist

Chris Hallquist — Sun, 14 Feb 2010 19:17:28 +0000

Mathematical objects and mathematical knowledge are generally taken as paradigmatic examples of abstract objects and deductive knowledge, respectively, and will get casually mentioned in discussions of those things, but philosophers generally talk as if there’s nothing much to be gained from looking at the specific philosophy of math issues. That seems like a really bad idea.

A point of clarification, though: when I said “mathematical questions” in the original post, I didn’t mean the kind of questions mathematicians answer, I just meant questions about math, and in context philosophical questions about math. I thought that would be clear from context, but now I see it wasn’t. I don’t think we need more philosophers with masters degrees in math, I just think philosophers who cite mathematical examples in their work should know something about how mathematicians think about what they do beyond the crude picture given in high school geometry, and actually do some philosophy of math themselves.

By: mag487

mag487 — Sun, 14 Feb 2010 18:00:59 +0000

I can’t really imagine how it’s not taken seriously. Some of the best-respected philosophers in the country specialize in it (e.g., Hartry Field and Kit Fine at NYU, Hilary Putnam at Harvard), philosophy of mathematics papers are published in some of the best philosophical journals, two philosophy of math books have won the Lakatos Award, etc. You seem to be saying that philosophers don’t take it seriously insofar as they “are willing to use mathematically-derived ideas without considering the issue carefully qua issue about math,” but I don’t understand what this means. Philosophy of math is primarily about the nature of mathematical objects, mathematical knowledge, mathematical objectivity and mathematical explanation. What “mathematically-derived ideas” in common philosophical usage depend on these issues? And what kind of math do you think these issues involve, if you feel philosophers aren’t mathematically literate enough to tackle them seriously?

By: Chris Hallquist

Chris Hallquist — Sun, 14 Feb 2010 17:12:08 +0000

You talk as if it’s just obvious that philosophy of math is taken seriously, but in what sense? Obviously, yes, in that it’s not dismissed as thoroughgoing rubbish. But insofar as many philosophers are willing to use mathematically-derived ideas without considering the issue carefully qua issue about math, it seems fair to say they aren’t taking the subfield seriously.

Also, the “so specialized” charge is subjective. It has a lot to do with how you divide up sub-specialties. It seems to be part of the correct explanation for why there are so few philosophy of action people, but a slight tweak in lists of the big philosophical questions would make that explanation look silly: just imagine if every list of important philosophical specialties gave free will top billing, the way many Phil 101 textbooks do. If we thinking in those terms, maybe more graduate students would be encouraged to develop the skills needed to do philosophy of math.

By: mag487

mag487 — Sun, 14 Feb 2010 00:34:01 +0000

Uh, philosophy of mathematics is taken quite seriously as its own subfield. I’m not sure what high-level math you think it involves beyond a decent amount of mathematical logic and set theory, which I imagine virtually all philosophers of mathematics possess. It’s probably poorly represented because it’s so specialized (compare it to “philosophy of emotion” or something like that), and because many, if not most, philosophers lack some of the technical knowledge they’d need to understand or participate in it.