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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

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

Philip A. Ebert

Marcus Rossberg

Oxford University Press

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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