Epistemological issues, although controversial, are central to teaching and learning and have long been a theme of PME. A central epistemological issue is that of the philosophy of mathematics. It is argued that the traditional absolutist philosophies need to be replaced by a conceptual change view of mathematics. Building on the principles of radical constructivism together with the assumption of the existence of the physical and social worlds, a social constructivist philosophy of mathematics is proposed. This suggests an explanation of both the apparent objectivity and the utility of mathematics. A consequence is that the criticism that radical constructivism is necessarily solipsistic is overcome.