**rapaport@cs.Buffalo.EDU (William J. Rapaport)** (09/29/88)

STATE UNIVERSITY OF NEW YORK AT BUFFALO BUFFALO LOGIC COLLOQUIUM 1988-1989 Second Meeting Joint meeting with the Philosophy Colloquium NICOLAS GOODMAN Department of Mathematics SUNY Buffalo "IN DEFENSE OF AN INFINITISTIC MATHEMATICS OF NATURE" Wednesday, October 12, 1988 4:00 P.M. 684 Baldy Hall, Amherst Campus There is a skeptical tradition in the philosophy of mathematics that goes back at least to Hilbert in the 1920s and that is well represented in a recent paper by Stephen Simpson in _J. Symbolic Logic_ 53 (1988) 349-363. This tradition holds that mathematical analysis, even as applied to the description of nature, is so abstract and infinitary that it is implausible, even meaningless, as it stands. To remedy this, the tradition proposes to reduce analysis to some more secure finitistic theory. In the present paper, I defend applied analysis by appealing to ideas from the recent philosophy of the empirical sciences. Specifi- cally, I deny that there is a clear distinction between mathematics and physics, and conclude that mathematical analysis is our best established theory of nature. For further information, contact John Corcoran, (716) 636-2438.