Mathematical Perception and Religious Epistemology
Kurt Godel, among others, described our acquiring knowledge of mathematical facts as being analogous to sense perception. Just as our sensory faculties provide us with direct knowledge of the natural world, on the basis of which we go on to construct scientific theories, so too does our mathematical intuition provide us with direct knowledge of mathematical facts, on the basis of which we construct the axiom systems we are familiar with. This approach sufferers from a number of problems – how can we perceive acausal objects such as numbers? – and is not the most popular account of mathematical justification. Nonetheless, it holds intuitive appeal and fits closely the actual practices of mathematicians. In my research project I explore analogies between mathematical perception and accounts of religious experience found in Alvin Plantings and William Alston, experience which plausibly gives us knowledge of God. Such accounts, suitably modified, ought to give us insight into mathematical perception; like mathematical objects, God is (perhaps) outside of space and time and therefore difficult to fit into a naturalized epistemology. To the extent that Plantinga and Alston have provided compelling accounts of direct religious perception, we ought then to expect the analogous mathematical account to be similarly compelling. If such an analogy can be made out, it will provide a defence of the Godelian model of mathematical justification and serve as a good case study for justifying intellectual intuition generally.