Mathematical Science, Naturalism, and Normativity

Michael Friedman (Stanford) gives a talk at the MCMP Colloquium titled "Mathematical Science, Naturalism, and Normativity". Abstract: I address concerns in contemporary philosophy about the place of mathematics andmoral (and other) norms in a naturalistic world picture. I think that these worriesare largely misplaced, and I address them with an historical narrative from Platoto Kant, beginning from the fact that Plato's original "platonism" (in the theoryof forms) tried to give a kind of unified account of both mathematics and moralnorms. I contend that this was not mysterious or "spooky" but a perfectlyreasonable and intelligible response to the state of mathematical science of thetime—especially concerned with the relationship between ideal mathematicalstructures and the physical world. I then explore how this last relationship wasfundamentally transformed in the early modern period, beginning with Galileo, andcontinuing from Descartes, through Leibniz and Newton, and finally to Kant—where aradically new kind of relationship between mathematics (especially appliedmathematics) and moral normativity (still in the spirit of Plato) then emerged.