ABSTRACT
In the previous chapter we entertained the hypothesis that mathematical knowledge is a set of truths, in the form of a set of propositions with proofs, and that the function of the philosophy of mathematics is to establish the certainty of this knowledge. Having found that this hypothesis is untenable we are forced to reconsider the nature of the philosophy of mathematics. What is the function and scope of the philosophy of mathematics?
As the philosophy of law does not legislate, or the philosophy of science devise or test scientific hypotheses — the philosophy of mathematics does not add to the number of mathematical theorems and theories. It is not mathematics. It is reflection upon mathematics, giving rise to its own particular questions and answers.
(Korner, 1960, page 9)The philosophy of mathematics begins when we ask for a general account of mathematics, a synoptic vision of the discipline that reveals its essential features and explains just how it is that human beings are able to do mathematics.
(Tymoczko, 1986, page viii)