ABSTRACT
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. For the narrow focus of the ‘internal’ questions concerning the philosophy of mathematics fails to locate mathematics within the broader context of human thought and history. Without such a context, according to Lakatos, the philosophy of mathematics loses its content. In contrast, fallibilist views of the nature of mathematics, by acknowledging the role of error in mathematics cannot escape from considering theory replacement and tie growth of knowledge. Beyond this, such views must be concerned with the human contexts of knowledge creation and the historical genesis of mathematics, if they are to account adequately for mathematics, in all its fullness.
