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

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
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.
Constructing the World.David J. Chalmers - 2012 - Oxford University Press.
Truth.Paul Horwich - 1998 - Clarendon Press.

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Citations of this work BETA

Is Mathematics Unreasonably Effective?Daniel Waxman - 2021 - Australasian Journal of Philosophy 99 (1):83-99.
Physical Possibility and Determinate Number Theory.Sharon Berry - forthcoming - Philosophia Mathematica:nkab013.
Supertasks and Arithmetical Truth.Jared Warren & Daniel Waxman - 2020 - Philosophical Studies 177 (5):1275-1282.
Arithmetic is Determinate.Zachary Goodsell - 2022 - Journal of Philosophical Logic 51 (1):127-150.
Infinite Reasoning.Jared Warren - 2021 - Philosophy and Phenomenological Research 103 (2):385-407.

View all 7 citations / Add more citations

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