Grounding and the indispensability argument

Synthese 193 (2):531-548 (2016)
David Liggins
University of Manchester
There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses.
Keywords indispensability argument  grounding  fictionalism  hard road nominalism
Categories (categorize this paper)
DOI 10.1007/s11229-014-0478-2
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 35,496
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Metaphysical Dependence: Grounding and Reduction.Gideon Rosen - 2010 - In Bob Hale & Aviv Hoffmann (eds.), Modality: Metaphysics, Logic, and Epistemology. Oxford University Press. pp. 109-36.
The Things We Mean.Stephen Schiffer - 2003 - Oxford University Press.
There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.

View all 53 references / Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Isn't the Indispensability Argument Necessarily Analogical?Woosuk Park - 2008 - Proceedings of the Xxii World Congress of Philosophy 41:13-18.
How Not to Enhance the Indispensability Argument.Russell Marcus - 2014 - Philosophia Mathematica 22 (3):345-360.
On Frege's Alleged Indispensability Argument.Pieranna Garavaso - 2005 - Philosophia Mathematica 13 (2):160-173.
Quine's Weak and Strong Indispensability Argument.Lieven Decock - 2002 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 33 (2):231-250.
A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
Pythagorean Powers or a Challenge to Platonism.Colin Cheyne & Charles R. Pigden - 1996 - Australasian Journal of Philosophy 74 (4):639 – 645.
In Defence of Indispensability.Mark Colyvan - 1998 - Philosophia Mathematica 6 (1):39-62.


Added to PP index

Total downloads
150 ( #39,725 of 2,287,505 )

Recent downloads (6 months)
7 ( #66,571 of 2,287,505 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature