Carnegie Mellon University, Department of Philosophy,
80-101 Freshman Seminar, Fall 1998

Mathematics in Scientific Context

Prof. Wilfried Sieg

Course description

The historical, scientific, and philosophical context is given by the development of classical mechanics beginning in the 17th century and that of cognitive science in the 20th century; the parts of mathematics for which this context is provided are the theory of manifolds and the theory of computability. The leading questions are "What is the structure of the universe?" and "What is the structure of the human mind?" The course is consequently divided into two main parts. The first part introduces, against the background of Euclid's geometry, non-Euclidean geometries, Riemann's theory of manifolds, and analysis; it discusses their use in physics to obtain models of the world. The second part develops the theory of computability and discusses its use in psychology to obtain models of human cognition. The goal of the course is to help students recognize the central role mathematics plays in obtaining precise descriptions of parts of human experience. The course is a beginning class and does not presuppose extended knowledge of mathematics or computer science; but it does take for granted a willingness to look at arguments in quite abstract ways.