On the Indispensability of the Distinctively Mathematical

Indispensability arguments purport to show that empirical data provide evidence for the existence of mathematical entities. In this paper we argue that indispensability arguments fail to show that empirical data bears on the mathematical. In order to show this we attempt to clarify what it is to be mathematical, and separate the question whether abstracta in general exist from whether distinctively mathematical abstracta exist. We introduce the notion of an ‘agnostified’ empirical theory as a heuristic device for clarifying the role of mathematical terminology in empirical theories. The special case of spaces is then briefly considered.