This thesis attempts to provide a response to the Access Problem by developing a naturalist account of our access to mathematical knowledge. On the basis of recent empirical research into the nature of mathematical cognition, it is argued that our most basic access to arithmetical content is mediated by perceptual processes. Moreover, in line with the theory of embodied cognition, arithmetical cognition is grounded in the perceptual systems responsible for these processes, as well as other perceptual and motor systems that are involved with our everyday interaction with the world. This motivates a response to the Access Problem according to which access to some mathematical content is on a par with our access to everyday objects of perception. Whilst the picture that emerges on the basis of this response is ontologically neutral, in the sense of being compatible with either a realist or anti-realist approach to mathematics, it places significant constraints on a naturalistically acceptable approach to the ontology of mathematics.