Abstract

My thesis is devoted to an attempt to offer, on behalf of mathematical Platonism, a reply to what may seem to be a powerful objection to it. The objection is this: If there is, as the Platonist supposes, mathematical knowledge of abstract objects, then there is a correlation between our beliefs and the mathematical facts. However, how is such a correlation to be explained given that mathematical objects are a-causal? The worry is that no explanation is possible and that this is a considerable mark against mathematical Platonism. The source of the difficulty here is obvious: standard models for explaining such correlations proceed via the idea that facts cause beliefs, or that beliefs cause facts, or that there was a common cause. But these possibilities are not available to the Platonist given the a-causality of mathematical objects. ;I claim that such a correlation is explicable in a way which neither, contra expectation, renders abstract objects causal nor assigns to us capacities the exercise of which allows to us to explain the correlation on some implausible extension of a perceptual model. The thought is this: that explaining the correlation requires explaining conjunctions of facts and beliefs. But the conjunctions in question are, at least for the Platonism here considered, conjunctions of a brute fact and an explicable fact . However I argue, and this is the core of the thesis, that such conjunctions can always be explained by reiterating the brute fact and citing whatever explains the explicable fact. If this thesis about explanation is accepted, then such correlations are readily explicable. ;The rest of the thesis is devoted to examining various objections to this reply and to the thesis concerning explanation. I argue that they are not fatal