Boccuni, F and Woods, J (2020) Structuralist Neologicism. Philosophia Mathematica, 28 (3). pp. 296-316. ISSN 0031-8019
Abstract
Neofregeanism and structuralism are among the most promising recent approaches to the philosophy of mathematics. Yet both have serious costs. We develop a view, structuralist neologicism, which retains the central advantages of each while avoiding their more serious costs. The key to our approach is using arbitrary reference to explicate how mathematical terms, introduced by abstraction principles, refer. Focusing on numerical terms, this allows us to treat abstraction principles as implicit definitions determining all (known) properties of the numbers, achieving a key neofregean advantage, while preserving the key structuralist advantage, which objects play the number role does not matter.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018, The Authors. Published by Oxford University Press. This is an author produced version of a paper published in Philosophia Mathematica. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Structuralism; Neologicism; Reference |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Arts, Humanities and Cultures (Leeds) > School of Philosophy, Religion and History of Science (Leeds) > School of Philosophy (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Sep 2018 13:10 |
Last Modified: | 14 Dec 2020 15:14 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/philmat/nky017 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:135303 |