Quantifier Variance, Mathematicians’ Freedom and the Revenge of Quinean Indispensability Worries

Erkenntnis 87 (5):2201-2218 (2022)
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Abstract

Invoking a form of quantifier variance promises to let us explain mathematicians’ freedom to introduce new kinds of mathematical objects in a way that avoids some problems for standard platonist and nominalist views. In this paper I’ll note that, despite traditional associations between quantifier variance and Carnapian rejection of metaphysics, Siderian realists about metaphysics can naturally be quantifier variantists. Unfortunately a variant on the Quinean indispensability argument concerning grounding seems to pose a problem for philosophers who accept this hybrid. However I will charitably reconstruct this problem and then argue for optimism about solving it.

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Sharon Berry
Indiana University, Bloomington

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References found in this work

Writing the Book of the World.Theodore Sider - 2011 - Oxford, England: Oxford University Press.
Metaphysical grounding.Ricki Bliss & Kelly Trogdon - 2021 - Stanford Encyclopedia of Philosophy.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Ontology Made Easy.Amie Lynn Thomasson - 2014 - New York: Oup Usa.

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