Abstract

Mathematical apriorism holds that mathematical truths must be established using a priori processes. Against this, it has been argued that apparently a priori mathematical processes can, under certain circumstances, fail to warrant the beliefs they produce; this shows that these warrants depend on contingent features of the contexts in which they are used. They thus cannot be a priori. In this paper I develop a position that combines a reliabilist version of mathematical apriorism with a platonistic view of mathematical ontology. I argue that this view both withstands the above objection and explains the reliability of a priori mathematical warrant.