ABSTRACT
Quasi-empiricism is less a philosophical theory about mathematics than it is an approach to the philosophy of mathematics, an approach that stresses both mathematical practice and the natural connection between mathematics and natural science (see Tymoczko, 1986, for discussions of quasi-empiricism). This chapter describes a particular variant of quasi-empiricism called ‘structuralism’ and explains how structuralism solves the main problems of traditional philosophy of mathematics. Nevertheless, structuralism does not end the philosophy of mathematics—far from it. Instead it leaves us with a profound challenge to our understanding of mathematics.
