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

Authors
Daniel Waxman
National University of Singapore
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

Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
Models and Reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
Minds, Machines and Gödel.John R. Lucas - 1961 - Philosophy 36 (137):112-127.
Vagueness.Timothy Williamson - 1995 - British Journal for the Philosophy of Science 46 (4):589-601.

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Citations of this work BETA

Supertasks and Arithmetical Truth.Jared Warren & Daniel Waxman - 2020 - Philosophical Studies 177 (5):1275-1282.
Infinite Reasoning.Jared Warren - forthcoming - Philosophy and Phenomenological Research.
Is Mathematics Unreasonably Effective?Daniel Waxman - 2021 - Australasian Journal of Philosophy 99 (1):83-99.

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