11 March 2025, Philosophy of Mathematics (Φ-Math) Reading Group

For this session, we will answer the title’s question with the short and sweet: John P. Burgess’s Why I Am Not a Nominalist, a broad overview against various forms of nominalism.

Burgess responds to nominalist attempts to dispense with abstract objects in mathematical and scientific discourse, challenging both instrumentalist and reconstructionist forms of nominalism, among others; arguing that they fail to provide a viable alternative to the standard use of mathematics in science. He maintans that nominalism, rather than Platonism, bears the real “burden of proof”. His critique adresses Goodman, Quine, and Field, among others.