On Realism in Set Theory

Abstract

In her recent book, "Realism in mathematics", Penelope Maddy attempts to reconcile a naturalistic epistemology with realism about set theory. The key to this reconciliation is an analogy between mathematics and the physical sciences based on the claim that we perceive the objects of set theory. In this paper I try to show that neither this claim nor the analogy can be sustained. But even if the claim that we perceive some sets is granted, I argue that Maddy's account fails to explain the key issue faced by an epistemology for mathematics, namely the step from knowledge of the finite to knowledge of the infinite.