Abstract

LAVERS, Gregory. Frege and numbers as self-subsistent objects. discus.filos [online]. 2010, vol.11, n.17, pp.97-118. ISSN 0124-6127.

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.

Keywords : Dummett; Frege; Grundlagen; independence of Mathematics; metaphysical platonism.

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