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Essays on Frege's Basic Laws of Arithmetic$
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Philip A. Ebert and Marcus Rossberg

Print publication date: 2019

Print ISBN-13: 9780198712084

Published to Oxford Scholarship Online: November 2019

DOI: 10.1093/oso/9780198712084.001.0001

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Mathematical Creation in Frege’s Grundgesetze

Mathematical Creation in Frege’s Grundgesetze

Chapter:
(p.325) 13 Mathematical Creation in Frege’s Grundgesetze
Source:
Essays on Frege's Basic Laws of Arithmetic
Author(s):

Philip A. Ebert

Marcus Rossberg

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198712084.003.0013

We discuss a passage from Grundgesetze der Arithmetik that raises doubts regarding Frege’s attitude towards platonism. First, we motivate a platonist interpretation of Frege’s mature philosophy of mathematics and outline his conception of the aims of definition. We then present the passage which prima facie raises doubts about a platonist interpretation of his logicism. We then survey and discuss readings of this passage by other interpreters. Finally, we present an interpretation that renders the passage compatible with a platonist interpretation of Frege and offers an explanation of Frege’s rather uncharacteristic concessive attitude in the passage.

Keywords:   Frege, Grundgesetze, Platonism, creative definition, mathematical creation, Dedekind

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