Mathematical knowledge, the analytic method, and naturalism

This article aims to suggest that a promising step towards the elaboration of an adequate naturalist account of mathematics and mathematical knowledge may be to take the method of mathematics to be the analytic method rather than the axiomatic method. Indeed, it seems impossible to naturalize mathematics without challenging at least some crucial aspects of the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method. Nor does it seem possible to keep maintaining that the method of mathematics is the axiomatic method and mathematical knowledge is certain, if we dismiss that view. The analytic view of the method of mathematics, which has been mainly advocated by Carlo Cellucci in recent years (Cellucci forthcoming, 2017, 2013), will be illustrated in some detail; then, I will argue that this view could contribute to develop a naturalist account of mathematics and mathematical knowledge. I will also take Cellucci’s insight further and point out that the analytic view of method can do that at a cost: it forces us to rethink the ‘traditional image’ of mathematics. Indeed, if we take the method of mathematics to be the analytic method, mathematical knowledge cannot be said to be certain, and the only kind of mathematical knowledge that we can have is plausible knowledge.