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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Tom Donaldson
Simon Fraser University

Citations of this work

Indiscernibility and the Grounds of Identity.Samuel Z. Elgin - forthcoming - Philosophical Studies:1-23.
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.
On what grounds what.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
Ethics without principles.Jonathan Dancy - 2004 - New York: Oxford University Press.
Monism: The Priority of the Whole.Jonathan Schaffer - 2010 - Philosophical Review 119 (1):31-76.
No Work for a Theory of Grounding.Jessica M. Wilson - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535-579.

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