Sunday, July 19, 2009

Two New Drafts: Surveys on "Philosophy of Mathematics" and "The Applicability of Mathematics"

I have posted preliminary drafts of two survey articles that are hopefully of interest to readers of this blog. The first is for the Continuum Companion to the Philosophy of Science, edited by French and Saatsi, on "Philosophy of Mathematics":
In this introductory survey I aim to equip the interested philosopher of science with a roadmap that can guide her through the often intimidating terrain of contemporary philosophy of mathematics. I hope that such a survey will make clear how fruitful a more sustained interaction between philosophy of science and philosophy of mathematics could be.
The second is for the Internet Encyclopedia of Philosophy on "The Applicability of Mathematics":
In section 1 I consider one version of the problem of applicability tied to what is often called "Frege's Constraint". This is the view that an adequate account of a mathematical domain must explain the applicability of this domain outside of mathematics. Then, in section 2, I turn to the role of mathematics in the formulation and discovery of new theories. This leaves out several different potential contributions that mathematics might make to science such as unification, explanation and confirmation. These are discussed in section 3 where I suggest that a piecemeal approach to understanding the applicability of mathematics is the most promising strategy for philosophers to pursue.
In line with the aims of the IEP, my article is more introductory, but hopefully points students to the best current literature.

Both surveys are of course somewhat selective, but comments and suggestions are more than welcome!


Kenny said...

The philosophy of math one looks nice, despite leaving out some views like Maddy's Realism in Mathematics view, and Balaguer's view (which is understandable, given that you don't want this to go on too long). I sort of got lost around p. 13 when you moved from the mathematical explanation debate to the semantic view of models by means of Cartwright. Much of this last discussion doesn't really seem to be about the philosophy of mathematics, but maybe that's right here - philosophers of science who don't do phil math will perhaps be more interested in this stuff, and I think I can see how this relates to issues about realism, explanation, and epistemology in mathematics.

Chris Pincock said...

Kenny, thanks for your comments. My own view is that these issues about modeling and representation are an opportunity for philosophers of mathematics to help out philosophers of science. So, I wanted to add some references to that material in to make the connection explicit. But I think I can make the transition more clear, and I also need to see how much overlap there is with other contributions. Gabriele has put his draft online as well here.