Truth, Fiction, and Stipulation

Abstract

For the past few years, I have been fortunate enough to teach, annually, a third year undergraduate module in the philosophy of mathematics. It is a testimony to Paul Benacerraf’s great influence on the discipline that the module is structured very naturally in two halves, which could quite easily be subtitled “Before Benacerraf” (BB) and “After Benacerraf” (AB). The story I tell starts at the end of the 19th century, with Cantor’s development of the new infinitary set theory, and mathematicians’ and philosophers’ concerns about how (or whether) we can make sense of this new mathematics that is not grounded in Kantian intuition of space and time.