Thu Sep 20, 2012
Howison Library, 4:10–6 PM
Michael Friedman (Stanford University)
Mathematical Science, Naturalism, and Normativity
The three lectures as a whole develop and illustrate a kind of neo-Kantian philosophical approach to the history and philosophy of the mathematical exact sciences in which the development of the relevant sciences is closely integrated with the contemporaneous development of philosophical reflection upon these sciences. The first lecture begins with a philosophical response to Kuhn’s theory of scientific revolutions in which Kuhn’s central example of such a revolution–the transition from Newton to Einstein–is considered in light of contemporaneous developments in scientific philosophy from Kant through Helmholtz, Mach, and Poincaré to early logical empiricism. It argues, on this basis, that a relativized and historicized version of Kant’s original conception of scientific rationality and objectivity can still be maintained. It thereby embraces, at least partially, both Kuhn’s conception of “incommensurability” and his later commitment to a “Kantianism with movable categories”. The second lecture extends the resulting historical narrative (which I call “the dynamics of reason”) to include elements of cultural and political history as well–by focussing, in particular, on the ways in which the scientific and philosophical contributions of Newton and Leibniz were entangled with the radically new configuration of science, society, religion, and philosophy emerging from the aftermath of the Reformation and the scientific revolution. Here I appeal to John Heilbron’s well-known discussion of the relationship between astronomy and the Church during this period, and I connect these developments with Kant’s radical break from the seventeenth-century project of providing a theological foundation for the new science. The third lecture, finally, applies my version of a “Kantianism with movable categories” to contemporary philosophical qualms about the place of both mathematics–with its “platonic” realm of abstract objects–and the realm of (moral) normativity within the world-picture of modern natural science. It attempts to undermine such qualms by constructing an appropriate historical narrative depicting the mutual interactions between the development of the mathematical sciences themselves and the closely related development of philosophical reflection upon these science–a development, this time, that begins with Plato and ends, once again, with Kant.