- New
-
Topics
- All Categories
- Metaphysics and Epistemology
- Value Theory
- Science, Logic, and Mathematics
- Science, Logic, and Mathematics
- Logic and Philosophy of Logic
- Philosophy of Biology
- Philosophy of Cognitive Science
- Philosophy of Computing and Information
- Philosophy of Mathematics
- Philosophy of Physical Science
- Philosophy of Social Science
- Philosophy of Probability
- General Philosophy of Science
- Philosophy of Science, Misc
- History of Western Philosophy
- Philosophical Traditions
- Philosophy, Misc
- Other Academic Areas
- Journals
- Submit material
- More
The (Metaphysical) Foundations of Arithmetic?
Noûs 51 (4):775-801 (2017)
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.Author's Profile
DOI
10.1111/nous.12147
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 - 2013 - 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.
Frege, Dedekind, and Peano on the Foundations of Arithmetic (Routledge Revivals).J. P. Mayberry - 2011 - Assen, Netherlands: Routledge.
The foundations of arithmetic: a logico-mathematical enquiry into the concept of number.Gottlob Frege - 1953 - Evanston, Ill.: Northwestern University Press. Edited by J. L. Austin.
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.
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
508 (#22,747)
6 months
84 (#16,781)
2016-05-19
Downloads
508 (#22,747)
6 months
84 (#16,781)
Historical graph of downloads
Author's Profile
Citations of this work
Explaining identity and distinctness.Erica Shumener - 2020 - Philosophical Studies 177 (7):2073-2096.
Grounding nonexistence.Daniel Muñoz - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (2):209-229.
The Metaphysics of Identity: Is Identity Fundamental?Erica Shumener - 2017 - Philosophy Compass 12 (1):1-13.
References found in this work
Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109-135.
Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical Grounding. Cambridge University Press. pp. 37--80.
PhilPapers logo by Andrea Andrews and Meghan Driscoll.
This site uses cookies and Google Analytics (see our terms & conditions for details regarding the privacy implications). Use of this site is subject to terms & conditions.
All rights reserved by The PhilPapers Foundation
Server: philpapers-web-5b5888c749-7q792 N