PHIL √-1 Introduction to Philosophy of Mathematics
An "imaginary" and (so far) unapproved course in the philosophy of mathematics.
Lecturer: Josh Smith email: [email protected] Office hours: TBD.
Overview There seems to be something remarkable about mathematics that sets it apart from the natural sciences. While the natural sciences are concerned with real entities, mathematics appears to be concerned with abstract concepts. The methods of mathematics differ, too. We seem to acquire mathematical knowledge through deductive reasoning, quite differently than the inductive methods used in the natural sciences. We are left to wonder how and why mathematics is effective, what mathematical entities are, and how we come to mathematical knowledge at all. Our course will take us on a whirlwind tour of the philosophy of mathematics, beginning with a brief history of some traditional views. We will work through a variety of schools and debates: logicism, formalism, intuitionism, platonism, nominalism, and struc