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Frege and numbers as self-subsistent objects

Keywords: dummett, frege, grundlagen, independence of mathematics, metaphysical platonism.

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Abstract:

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.

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