Philosophy of Mathematics

(3 Credit Hours) · Undergraduate

Philosophical conundrums pervade mathematics, from fundamental questions of mathematical ontology to deep questions of epistemology. What are numbers? What is the nature of infinity? How do or can we come to mathematical knowledge? What are the relations between truth, proof, and meaning? Does every mathematical truth admit of proof? What role do figures play in geometric argument? Do mathematical objects exist that we cannot construct? Can every mathematical question be solved in principle by computation? By what criteria are we to accept or reject mathematical axioms? These are merely a few of the questions we shall consider while exploring various philosophical positions, including platonism, realism, logicism, structuralism, formalism, constructivism, and many others. No specific mathematical knowledge is required for study in this subject, but a stronger mathematical background may enable a deeper understanding. The course is part of the philosophy major, but interested students from mathematics and computer science are welcome and indeed encouraged to participate. Main text: Joel David Hamkins, Lectures on the Philosophy of Mathematics, MIT Press 2021. There will be supplemental readings from the philosophical literature.