Philosophia Mathematica 28 (3):296-316 (2020)

Authors
Francesca Boccuni
University Vita-Salute San Raffaele
Jack Woods
University of Leeds
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 properties of the numbers, achieving a key neofregean advantage, while preserving the key structuralist advantage, which objects play the number role does not matter.
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DOI 10.1093/philmat/nky017
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References found in this work BETA

Naming and Necessity.Saul Kripke - 1980 - Harvard University Press.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Naming and Necessity.Saul Kripke - 1981 - Philosophy 56 (217):431-433.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.

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