Structuralist Neologicism†

Author:

Boccuni Francesca1ORCID,Woods Jack2ORCID

Affiliation:

1. Philosophy Faculty, University Vita-Salute San Raffaele, Milan, Italy

2. School of Philosophy, Religion, and History of Science, University of Leeds, Leeds, U.K

Abstract

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.

Publisher

Oxford University Press (OUP)

Subject

Philosophy,General Mathematics

Reference37 articles.

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