Frege, Indispensability, and the Compatibilist Heresy

Philosophia Mathematica 23 (1):11-30 (2015)
  Copy   BIBTEX

Abstract

In Grundgesetze, Vol. II, §91, Frege argues that ‘it is applicability alone which elevates arithmetic from a game to the rank of a science’. Many view this as an in nuce statement of the indispensability argument later championed by Quine. Garavaso has questioned this attribution. I argue that even though Frege's applicability argument is not a version of ia, it facilitates acceptance of suitable formulations of ia. The prospects for making the empiricist ia compatible with a rationalist Fregean framework appear thus much less dim than expected. Nonetheless, those arguing for such compatibility eventually face an hardly surmountable dilemma

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 102,190

External links

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

Through your library

Similar books and articles

On Frege's Alleged Indispensability Argument.Pieranna Garavaso - 2005 - Philosophia Mathematica 13 (2):160-173.
The Indispensability Argument for Mathematical Realism and Scientific Realism.Jacob Busch - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (1):3-9.
Indispensability and Holism.Jacob Busch - 2011 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 42 (1):47-59.
In defence of indispensability.Mark Colyvan - 1998 - Philosophia Mathematica 6 (1):39-62.
Grundgesetze der arithmetic I §10.Richard Heck - 1999 - Philosophia Mathematica 7 (3):258-292.

Analytics

Added to PP
2014-02-02

Downloads
87 (#244,522)

6 months
5 (#1,066,262)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Andrea Sereni
Scuola Universitaria Superiore IUSS Pavia

Citations of this work

On the Philosophical Significance of Frege’s Constraint.Andrea Sereni - 2019 - Philosophia Mathematica 27 (2):244–275.
Mathematical platonism meets ontological pluralism?Matteo Plebani - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):655-673.
A Quinean Reformulation of Fregean Arguments.Nathaniel Gan - 2023 - Acta Analytica 38 (3):481-494.

Add more citations

References found in this work

Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.
The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
Frege.Michael Dummett - 1981 - Cambridge: Harvard University Press.
On What There Is.W. V. O. Quine - 2011 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 221-233.

View all 37 references / Add more references