# 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

Wright, The Philosophical Significance of Frege’s Theorem in *The Reason’s Proper Study *(OUP 2001)

(*) Studd, Abstraction Reconceived, BJPS (2016)

Weir, An Embarassment of Riches, NDJFL (2003)

## 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)

## Week 7: eliminative structuralism

Benacerraf, What Numbers could not be

Hellman, Mathematics without Numbers: Towards a Modal-Structural interpretation, chapter 1

(*) Hellman, Three Varieties of Mathematical Structuralism

## Week 8: easy road nominalism

Yablo, Does Ontology Rest on a Mistake, PAS Sup. 72 (1998)

(*) Colyvan, There is No Easy Road to Nominalism, Mind 119 (2010)

Azzouni, Taking the Easy Road out of Dodge, Mind 121 (2012)