Philosophy of Mathematics
This class will take up some recent work in the philosophy of mathematics (but won’t presuppose any prior knowledge in this field). We’ll begin with some much-discussed epistemological problems:
Week 1: epistemological challenges
Benacerraf, Mathematical Truth, Journal of Philosophy 70 (1973), 403–20.
(*) Linnebo, Epistemological Challenges to Mathematical Platonism, Philosophical Studies 129 (2006), 545–574.
Potter, What is the Problem of Mathematical Knowledge, in Leng et al (eds) Mathematical Knowledge (OUP, 2007), 16–32
If you only have time for one article, read the one marked (*).
In weeks 2–8, we’ll focus primarily on two ostensibly very different approaches to the ontology and epistemology of mathematics: (i) the neo-logicist programme developed especially by Hale and Wright and (ii) fictionalist approaches to mathematics, variously advocated by Field, Azzouni, and others.
Week 2: abstraction and the bad company problem
Week 3: the Julius Caesar problem
Week 4: rejectionist responses to neo-logicism
Week 5: indispensability
Week 6: Field’s programme
Field, Realism and Anti-Realism about Mathematics, Philosophical Topics, 13 (1982)
(*) Macbride, Listening to Fictions: a Study of Fieldian Nominalism, BJPS 50 (1999)