## PHILOSOPHY OF MATHEMATICS

Course Aims:

The course provides an overview of selected topics in contemporary philosophy of mathematics, focusing on metaphysical and epistemological questions such as: Are some mathematical claims true and, if so, what makes them true? Are mathematical truths necessary and independent of the mind? How do we have knowledge of mathematical truths? Is this knowledge a priori, and if so, how do we have epistemic access to mathematical facts? The course explores several attempts to answer these questions, including mathematical realism, intuitionism, naturalism, modalism, (neo-)Logicism, and structuralism. We will examine these positions critically, and look at the relationships between them.

Course Texts:

Philosophy of Mathematics: Selected Readings, second edition, edited by Benacerraf and Putnam

Thinking About Mathematics, by Stewart Shapiro

Additional readings will be made available.

Assessment:

One mid term paper and one final paper.

Course Schedule:

Week 1: Introduction

Week 2: Platonism/Realism

Week 3: Intuitionism

Week 4: Naturalism

Week 5: Logicism

Week 6: Neo-Logicism

Week 7: Thin objects (abstraction and existence)

Week 8: Structuralism overview

Week 9: Non-eliminative structuralism

Week 10: Modalism

Week 11: Identity of indiscernibles

Week 12: Structural abstraction

Week 13: General discussion