PHILOSOPHY OF MATHEMATICS
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.
Philosophy of Mathematics: Selected Readings, second edition, edited by Benacerraf and Putnam
Thinking About Mathematics, by Stewart Shapiro
Additional readings will be made available.
One mid term paper and one final paper.
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