tea.mathoverflow.net - Discussion Feed (MO and the Philosophy of Mathematical Practice)

gilkalai comments on "MO and the Philosophy of Mathematical Practice" (20998)

gilkalai — Mon, 24 Dec 2012 12:22:16 -0800

We did have a few questions (probably 100-300) of philosophical nature, some of them were good and some were not as good, just like in other areas. I think that good and clear questions in philosophy relevant to mathematics or in mathematics relevant to philosophy, or in philosophy of mathematics, are welcome in MO. Relations between mathematics and other academic areas are certainly part of what research mathematicians care about (well not all and certainly not all the time) and the relations with philosophy are quite important.

(But I could not understand what question, if any, was proposed here.)

fedja comments on "MO and the Philosophy of Mathematical Practice" (20994)

fedja — Mon, 24 Dec 2012 06:49:32 -0800

The general problem with "philosophy of mathematics" is that the languages of philosophers and mathematicians are almost entirely disjoint and (let's put it symmetrically) neither side has any idea of what the other one is really doing, so many such discussions tend to degenerate into total nonsense and mutual disdain very quickly. However, if there is some common ground and we agree to speak plain English without using any high-tech mumbo-jumbo on either side, I would be very much interested in such discussions despite, of course, "it is not what MO was originally intended for". So, jonbannon, I suggest you just make a post and see how it works out. The only thing you risk is to get your post closed, which can hardly affect your life in any adverse way :).

jonbannon comments on "MO and the Philosophy of Mathematical Practice" (20888)

jonbannon — Tue, 18 Dec 2012 06:12:51 -0800

Although this is a repeat, I have proposed such a stackexchange site here: http://area51.stackexchange.com/proposals/48664/philosophy-of-mathematics

For those who would find such a site interesting, please participate in populating the site with interesting questions. (This is, sort of, an answer to my above question...since there may be no better way to find out if such a site is useful than to propose one and see what happens.)

jonbannon comments on "MO and the Philosophy of Mathematical Practice" (20887)

jonbannon — Tue, 18 Dec 2012 05:58:50 -0800

It does appear in the body of that thread. Perhaps the comments there are the most I should expect on this. Do you have the power to delete this discussion?

François G. Dorais comments on "MO and the Philosophy of Mathematical Practice" (20886)

François G. Dorais — Tue, 18 Dec 2012 04:28:28 -0800

Jon, this seems to be essentially a repeat of an earlier post: http://tea.mathoverflow.net/discussion/1490/bourbaki-thread/#Item_18

jonbannon comments on "MO and the Philosophy of Mathematical Practice" (20885)

jonbannon — Tue, 18 Dec 2012 03:12:36 -0800

The question below appears (fruitlessly) at math.stackexchange. I moved a modification of it here, as it's too discussion-y for MO, but could use an answer.

Certain philosophers of mathematics are interested in aspects of [the philosophy of mathematical practice.][1] Mathematicians, perhaps, would be interested in philosophy that may affect their day to day work, as is noted near the end of Gowers's article on [whether mathematics needs a philosophy][2].

JDH's curiosity about structuralism on a recent Bourbaki thread makes me wonder:

>**Question:** Is there an appropriate "stack exchange" for questions on the philosophy of mathematical practice? Is MO a good place for such questions? If the answer to the second question is `yes', then what are some guidelines for asking appropriate questions of this nature?

I ask the final subquestion because I really don't think that we want to see an overpopulation of the front page of MO by philosophical language. In fact, I think that would be a disaster.

I think questions about the philosophy of mathematics are inappropriate for MO in general, but may be interesting for mathematicians if handled elsewhere. Unfortunately, philosophy.stackexchange doesn't seem very helpful for the type of question I'm thinking of. I'm also not interested in a site that is dominated by questions targeting old foundational issues more than contemporary practice. I imagine, also, that many naive questions would populate such a forum and so am not necessarily suggesting that one would be a good idea.

[1]: http://www.ams.org/notices/201203/rtx120300424p.pdf
[2]: https://www.dpmms.cam.ac.uk/~wtg10/philosophy.html