Philosophy of Mathematics

Catalog description

This course examines a variety of issues in the metaphysics and epistemology of mathematics. Mathematics poses interesting questions for philosophers. Mathematical statements appear to state objective truths, but it is difficult to see what the grounds of that truth are. Does mathematics somehow depend on us and our practices? Is it grounded in logic? Does it instead depend on the arrangement of some pre-existing objects, "the numbers"? These numbers appear not to be located in space-time. If they are not, how do we come to know about them? What explains the tremendous success of mathematics in providing useful applications in other disciplines? What does it take for something to count as a mathematical "proof"? We consider some surprising mathematical results, including Godel's incompleteness theorems, multiple sizes of infinity, and the status of the continuum hypothesis, and examine their philosophical significance. This is a course in the philosophy, not the practice, of mathematics. No specific mathematical knowledge or skills will be assumed. Students will, however, be asked to cope with sometimes difficult and abstract mathematical concepts.