A Nominalist’s Dilemma and its Solution∗

Current versions of nominalism in the philosophy of mathematics have the benefit of avoiding commitment to the existence of mathematical objects. But this comes with a cost: to avoid commitment to mathematical entities, nominalists cannot take mathematical theories literally, and so, they seem unable to accommodate mathematical practice. In a recent work, Jody Azzouni has challenged this conclusion, by formulating a nominalist view that doesn’t have this cost (Azzouni 2004). In this paper, we argue that, as it stands, Azzouni’s proposal doesn’t yet succeed. It faces a dilemma to the effect that either the view isn’t nominalist or it fails to take mathematics literally. So, in the end, it still doesn’t do justice to mathematical practice. After presenting the dilemma, we suggest a solution which the nominalist should be able to accept.