The (Metaphysical) Foundations of Arithmetic?

Noûs 51 (4):775-801 (2017)
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Abstract

Gideon Rosen and Robert Schwartzkopff have independently suggested (variants of) the following claim, which is a varian of Hume's Principle: When the number of Fs is identical to the number of Gs, this fact is grounded by the fact that there is a one-to-one correspondence between the Fs and Gs. My paper is a detailed critique of the proposal. I don't find any decisive refutation of the proposal. At the same time, it has some consequences which many will find objectionable.

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2016

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10.1111/nous.12147

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Tom Donaldson
Simon Fraser University

Citations of this work

Indiscernibility and the Grounds of Identity.Samuel Z. Elgin - forthcoming - Philosophical Studies:1-23.
Abstraction and grounding.Louis deRosset & Øystein Linnebo - 2023 - Philosophy and Phenomenological Research 109 (1):357-390.
Emptying a Paradox of Ground.Jack Woods - 2018 - Journal of Philosophical Logic 47 (4):631-648.
Platonism in the Philosophy of Mathematics.Øystein Linnebo - forthcoming - Stanford Encyclopedia of Philosophy.
Grounding nonexistence.Daniel Muñoz - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (2):209-229.

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References found in this work

Writing the Book of the World.Theodore Sider - 2011 - Oxford, England: Oxford University Press.
Ethics without principles.Jonathan Dancy - 2004 - New York: Oxford University Press.
Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder, Metaphysical grounding: understanding the structure of reality. Cambridge: Cambridge University Press. pp. 37--80.
Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann, Modality: metaphysics, logic, and epistemology. qnew York: Oxford University Press. pp. 109-135.
On what grounds what.Jonathan Schaffer - 2009 - In Ryan Wasserman, David Manley & David Chalmers, Metametaphysics: New Essays on the Foundations of Ontology. Oxford, England: Oxford University Press. pp. 347-383.

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