The indispensability argument and the nature of mathematical objects

Abstract

I will contrast two conceptions of the nature of mathematical objects: the conception of mathematical objects as preconceived objects (Yablo 2010), and heavy duty platonism (Knowles 2015). I will argue that friends of the indispensability argument are committed to some metaphysical theses and that one promising way to motivate such theses is to adopt heavy duty platonism. On the other hand, combining the indispensability argument with the conception of mathematical objects as preconceived objects yields an unstable position. The conclusion is that the metaphysical commitments of the indispensability argument should be carefully scrutinized.