From owner-cse575-fa08-list@LISTSERV.BUFFALO.EDU Thu Oct 30 12:57:39 2008 Date: Thu, 30 Oct 2008 12:57:26 -0400 From: "William J. Rapaport" Subject: 575: Philosophy & Cog Sci of Math To: CSE575-FA08-LIST@LISTSERV.BUFFALO.EDU ------------------------------------------------------------------------ Subject: Philosophy & Cog Sci of Math ------------------------------------------------------------------------ In response to the question about mathematics, here are some pointers to the literature on both the philosophy of math and the cognitive science of math. Philosophy of Mathematics ------------------------------------------------------------------------ A good, encyclopedic overview is: Horsten, Leon (2008), "Philosophy of Mathematics", Stanford Encyclopedia of Philosophy http://plato.stanford.edu/entries/philosophy-mathematics/ The classic anthology of readings is: Benacerraf, P. & Putnam, H. (eds.), 1983. Philosophy of Mathematics: Selected Readings, Cambridge: Cambridge University Press, 2nd edition. (although I personally prefer the first edition, which has some items omitted from the 2nd edition). Cognitive Science of Mathematics ------------------------------------------------------------------------ A useful bibliography is: Goldfain, Albert, "Mathematical Cognition Bibliography" http://www.cse.buffalo.edu/~ag33/MathCognitionBib.html This lists "essential" readings in red. Of those, I would consider the following to be "essentially essential": Gelman, R. and Gallistel, C.R. (1978), The Child's Understanding of Number (Cambridge: Harvard University Press). Dehaene, Stanislas (1997), The Number Sense (Oxford: Oxford University Press). Lakoff, George and Nunez, Rafael E. (2000), Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being (New York: Basic Books). Finally, there's also the doctoral dissertation I mentioned, Ch.2 of which is a literature review of the cognitive science of math: Goldfain, Albert (2008), A Computational Theory of Early Mathematical Cognition, PhD Dissertation, Department of Computer Science and Engineering, State University of New York at Buffalo http://www.cse.buffalo.edu/sneps/Bibliography/GoldfainDissFinal.pdf