The (Metaphysical) Foundations of Arithmetic?

Noûs 51 (4):775-801 (2017)
  Copy   BIBTEX

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.

Categories

Keywords

Reprint years

2016

DOI

10.1111/nous.12147

Links

PhilArchive

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.
On the foundations of Greek arithmetic.Holger A. Leuz - 2009 - History of Philosophy & Logical Analysis 12:13-47.
Basic Laws of Arithmetic.Gottlob Frege - 1893 - Oxford, U.K.: Oxford University Press. Edited by Philip A. Ebert, Marcus Rossberg & Crispin Wright.
A philosophical introduction to the foundations of elementary arithmetic.Andrew Boucher - manuscript
Frege, Dedekind, and Peano on the Foundations of Arithmetic. [REVIEW]J. P. Mayberry - 1984 - Philosophical Quarterly 34 (136):424.
Challenges to predicative foundations of arithmetic.Solomon Feferman - manuscript
Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals).J. P. Mayberry - 2013 - Assen, Netherlands: Routledge.
The foundations of arithmetic: a logico-mathematical enquiry into the concept of number.Gottlob Frege - 1959 - Evanston, Ill.: Northwestern University Press. Edited by J. L. Austin.
Elementary arithmetic.B. R. Buckingham - 1947 - Boston,: Ginn.
The foundations of arithmetic in finite bounded Zermelo set theory.Richard Pettigrew - 2010 - Cahiers du Centre de Logique 17:99-118.
Classical arithmetic as part of intuitionistic arithmetic.Michael Potter - 1998 - Grazer Philosophische Studien 55 (1):127-41.
Equivalence of F with a sub-theory of peano arithmetic.Andrew Boucher - manuscript
Arithmetic with Fusions.Jeff Ketland & Thomas Schindler - 2016 - Logique Et Analyse 234:207-226.
Models of arithmetic and upper Bounds for arithmetic sets.Alistair H. Lachlan & Robert I. Soare - 1994 - Journal of Symbolic Logic 59 (3):977-983.
Sobre las posibilidades de Una equivalencia para el fundamento de la aritmética.Carlos Álvarez - 1987 - Theoria 2 (2):345-364.

Analytics

Added to PP
2016-05-19

Downloads
719 (#21,554)

6 months
133 (#24,782)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

View all 32 citations / Add more citations

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.

View all 35 references / Add more references