A Metasemantic Challenge for Mathematical Determinacy

Synthese 197 (2):477-495 (2020)
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Abstract

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic.

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Author Profiles

Daniel Waxman
National University of Singapore
Jared Warren
Stanford University

Citations of this work

Categoricity by convention.Julien Murzi & Brett Topey - 2021 - Philosophical Studies 178 (10):3391-3420.
Infinite Reasoning.Jared Warren - 2020 - Philosophy and Phenomenological Research 103 (2):385-407.
Arithmetic is Determinate.Zachary Goodsell - 2021 - Journal of Philosophical Logic 51 (1):127-150.
Is Mathematics Unreasonably Effective?Daniel Waxman - 2021 - Australasian Journal of Philosophy 99 (1):83-99.

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References found in this work

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
Vagueness.Timothy Williamson - 1996 - New York: Routledge.
The emperor’s new mind.Roger Penrose - 1989 - Oxford University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

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