Wednesday, September 30, 2009
Tuesday, September 15, 2009
One consideration in favor of his view that Cole emphasizes is the creativity that mathematicians have to posit new entities. Qua mathematician, he notes "the freedom I felt I had to introduce a new mathematical theory whose variables ranged over any mathematical entities I wished, provided it served a legitimate mathematical purpose" (p. 589). Other mathematicians have of course said similar things, from Cantor's claim that "the essence of mathematics lies precisely in its freedom" (noted by Linnebo in his essay in this volume) and Hilbert's conception of axioms in his debate with Frege.
I have two worries with this starting point. First, is it so clear that mathematicians really have this freedom? The history of mathematics seems filled with controversies about new objects or new mathematical techniques that seem to presuppose the existence problematic objects. Second, even if mathematicians have a certain kind of freedom to posit new objects, how do we determine that this freedom is independent of prior metaphysical commitments? One option for the traditional platonist or the ante rem structuralist is to insist that mathematicians are now free to posit new objects only because it is highly likely that these new objects can find a place in their background set theory or theory of structures. This of course would not settle the issue against practice-dependent realism, but it gives the realist a strategy to accommodate the same data.
Wednesday, September 9, 2009
Call for Papers
Mathematical and Scientific Philosophy
with a special session on the Darwin Bicentenary
Indiana Philosophical Association Fall Meeting
Invited Speakers: Colin Allen, Elisabeth Lloyd, Larry Moss
Saturday AND Sunday, 5-6 December 2009
Indiana Memorial Union, IU Bloomington
We invite submissions—from philosophers, logicians, and historians and philosophers of science—on topics that fall under the theme of the meeting. Papers should be 35 minutes reading time, i.e., no more than 17 double-spaced pages. Papers will be blind reviewed; the author’s name and affiliation should therefore appear only on the cover sheet.
Send one copy of your paper and a short, one–paragraph abstract to one of the following.
Department of Philosophy
Esch Hall 044U
University of Indianapolis
Indianapolis, IN 46227
murphyp at uindy.edu
Department of Philosophy
CM 21 026
Fort Wayne, IN 46805
buldtb at ipfw.edu
The Logic Program
Bloomington, IN 47405
dmccarty at indiana.edu
Electronic submissions of papers and abstracts in MSWord or pdf formats are encouraged.
Deadline for Submissions: 15 October 2009
Deadline for Notifications: 9 November 2009
For further information, please email Charles McCarty at dmccarty at indiana.edu
Tuesday, September 8, 2009
My favorite part is where Krugman says "the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth". But he never really follows this up with much discussion of the mathematics or why it might have proven so seductive. Section III attacks "Panglossian Finance", but this is presented as if it assumes "The price of a company's stock, for example, always accurately reflects the company's value given the information available". But, at least as I understand it, this is not the "efficient market hypothesis" which underlies models like Black-Scholes. Instead, this hypothesis makes the much weaker assumption that "successive price changes may be considered as uncorrelated random variables" (Almgren 2002, p. 1). This is the view that prices over time amount to a "random walk". It has serious problems as well, but I wish Krugman had spent an extra paragraph attacking his real target.
Almgren, R. (2002). Financial derivatives and partial differential equations.
American Mathematical Monthly, 109: 1-12, 2002.