Frege and numbers as self-subsistent Objects

This paper argues that Frege is not the metaphysical platonist about mathematics that he is standardly taken to be. It is shown that Frege’s project has two distinct stages: the identification of what is true of our ordinary notions, and then the provision of a systematic account that shares the identified features. Neither of these stages involves much metaphysics. The paper criticizes in detail Dummett’s interpretation of §§55-61 of Grundlagen. These sections fall under the heading ‘Every number is a self-subsistent object’ and are described by Dummett as containing the worst arguments put forward by Frege. It is argued that essentially all of Dummett’s interpretive points are mistaken. Finally, I show that Frege’s claims about the independence of mathematics from humans and their activities does not commit him to any particularly metaphysical position either.