New directions for nominalist philosophers of mathematics

Synthese 176 (2):153 - 175 (2010)
  Copy   BIBTEX


The present paper will argue that, for too long, many nominalists have concentrated their researches on the question of whether one could make sense of applications of mathematics (especially in science) without presupposing the existence of mathematical objects. This was, no doubt, due to the enormous influence of Quine's "Indispensability Argument", which challenged the nominalist to come up with an explanation of how science could be done without referring to, or quantifying over, mathematical objects. I shall admonish nominalists to enlarge the target of their investigations to include the many uses mathematicians make of concepts such as structures and models to advance pure mathematics. I shall illustrate my reasons for admonishing nominalists to strike out in these new directions by using Hartry Field's nominalistic view of mathematics as a model of a philosophy of mathematics that was developed in just the sort of way I argue one should guard against. I shall support my reasons by providing grounds for rejecting both Field's fictionalism and also his deflationist account of mathematical knowledge—doctrines that were formed largely in response to the Indispensability Argument. I shall then give a refutation of Mark Balaguer's argument for his thesis that fictionalism is "the best version of anti-realistic anti-platonism"



    Upload a copy of this work     Papers currently archived: 83,948

External links

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

Through your library


Added to PP

198 (#76,693)

6 months
1 (#505,949)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Fictionalism in the philosophy of mathematics.Mark Balaguer - 2008 - Stanford Encyclopedia of Philosophy.

Add more citations

References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Platonism and anti-Platonism in mathematics.Mark Balaguer - 1998 - New York: Oxford University Press.
Non-standard Analysis.Gert Heinz Müller - 1966 - Princeton University Press.
Constructibility and mathematical existence.Charles S. Chihara - 1990 - New York: Oxford University Press.
Platonism and Anti-Platonism in Mathematics.Mark Balaguer - 1998 - Bulletin of Symbolic Logic 8 (4):516-518.

View all 27 references / Add more references