A metasemantic challenge for mathematical determinacy

Synthese:1-19 (forthcoming)
Authors
Daniel Waxman
Lingnan University
Jared Warren
Stanford University
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.
Keywords determinacy  metasemantics  indeterminacy  incompleteness
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DOI 10.1007/s11229-016-1266-y
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References found in this work BETA

Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Models and Reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.

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