I should probably not have felt the desire to move into the philosophy of mathematics had it not been for my encounter with two philosophical works. The first of these was Imre Lakatos's Proofs and Refutations (1976), a copy of which was thrust into my hands by a good friend Darian Leader, who happens to be the godson of Lakatos. The second was an article entitled ‘The Uses and Abuses of the History of Topos Theory’ by Colin McLarty (1990), a philosopher then unknown to me. What these works share is the simple idea that what mathematicians think and do should be important for philosophy, and both express a certain annoyance that anyone could think otherwise.

Finding a post today as a philosopher of mathematics is no easy task. Finding a post as a philosopher of mathematics promoting change is even harder. When a discipline is in decline, conservatism usually sets in. I am, therefore, grateful beyond words to my PhD supervisor, Donald Gillies, both for his support over the last decade and for going to the enormous trouble of applying for the funding of two research projects, succeeding in both, and offering one to me. The remit of the project led me in directions I would not myself have chosen to go, especially the work reported in chapters 2 and 3, and I rather think chapters 5 and 6 as well, but this is often no bad thing.