Truth in Mathematics

Abstract

This chapter discusses four questions concerning the nature and role of the concept of truth in mathematics. First, the question as to whether the concept of truth is needed in a philosophical account of mathematics is answered affirmatively: a formalist approach to the language of mathematics is inadequate. Next, following Frege, a classical conception of mathematical truth is defended, involving the existence of mathematical objects. The third question concerns the relation between the existence of mathematical objects and the objectivity of mathematical truth. A traditional platonist seeks to explain the latter in terms of the former, while Frege reverses this order of explanation. Finally, the question regarding the extent to which mathematical statements have objective truth-values is discussed.