Philosophy of mathematics and philosophy of history

The arguments in this book depend more on the study of history than on the study of logic; logic plays a role, but it is subordinate or subsidiary. Philosophers are now used to the idea that history is central to philosophy of science, but its pertinence to the philosophy of mathematics seems to need renewed defense. Thus I rehearse the helpful argument of the philosopher of history, W. B. Gallie, who shows that there can be no Ideal Chronicle, which in turn helps me to contest Philip Kitcher’s early and influential position in The Nature of Mathematical Knowledge, where he invokes the history of mathematics but in a manner that finally leaves mathematics once again ahistorical. Thus I turn to the French philosopher of mathematics Jean Cavaillès whose sense of history was more refined, make some remarks about reference, and take up briefly Wiles’ strategy in his celebrated proof of Fermat’s Last Theorem, in order to carry out a thought experiment involving the ‘Math Genie’ that shows that proofs are embedded in history, like all human actions.