Numbers without Science

Dissertation, The Graduate School and University Center of the City University of New York (2007)
  Copy   BIBTEX

Abstract

Numbers without Science opposes the Quine-Putnam indispensability argument, seeking to undermine the argument and reduce its profound influence. Philosophers rely on indispensability to justify mathematical knowledge using only empiricist epistemology. I argue that we need an independent account of our knowledge of mathematics. The indispensability argument, in broad form, consists of two premises. The major premise alleges that we are committed to mathematical objects if science requires them. The minor premise alleges that science in fact requires mathematical objects. The most common rejection of the argument denies its minor premise by introducing scientific theories which do not refer to mathematical objects. Hartry Field has shown how we can reformulate some physical theories without mathematical commitments. I argue that Field’s preference for intrinsic explanation, which underlies his reformulation, is ill-motivated, and that his resultant fictionalism suffers unacceptable consequences. I attack the major premise instead. I argue that Quine provides a mistaken criterion for ontic commitment. Our uses of mathematics in scientific theory are instrumental and do not commit us to mathematical objects. Furthermore, even if we accept Quine’s criterion for ontic commitment, the indispensability argument justifies only an anemic version of mathematics, and does not yield traditional mathematical objects. The first two chapters of the dissertation develop these results for Quine’s indispensability argument. In the third chapter, I apply my findings to other contemporary indispensabilists, specifically the structuralists Michael Resnik and Stewart Shapiro. In the fourth chapter, I show that indispensability arguments which do not rely on Quine’s holism, like that of Putnam, are even less successful. Also in Chapter 4, I show how Putnam’s work in the philosophy of mathematics is unified around the indispensability argument. In the last chapter of the dissertation, I conclude that we need an account of mathematical knowledge which does not appeal to empirical science and which does not succumb to mysticism and speculation. Briefly, my strategy is to argue that any defensible solution to the demarcation problem of separating good scientific theories from bad ones will find mathematics to be good, if not empirical, science.

Links

PhilArchive

External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Intrinsic Explanation and Field’s Dispensabilist Strategy.Russell Marcus - 2013 - International Journal of Philosophical Studies 21 (2):163-183.
Indispensability arguments and instrumental nominalism.Richard Pettigrew - 2012 - Review of Symbolic Logic 5 (4):687-709.
On field's nominalization of physical theories.Mate Szabo - 2010 - Magyar Filozofiai Szemle 54 (4):231-239.
Indispensability Without Platonism.Anne Newstead & James Franklin - 2012 - In Alexander Bird, Brian Ellis & Howard Sankey (eds.), Properties, Powers, and Structures: Issues in the Metaphysics of Realism. New York, USA: Routledge. pp. 81-97.
In defence of indispensability.Mark Colyvan - 1998 - Philosophia Mathematica 6 (1):39-62.
Scientific realism and mathematical nominalism: A marriage made in hell.Mark Colyvan - 2006 - In Colin Cheyne (ed.), Rationality and Reality. Conversations with Alan Musgrave. Netherlands: Springer. pp. 225-237. Translated by John Worrall.
A Truthmaker Indispensability Argument.Sam Baron - 2013 - Synthese 190 (12):2413-2427.
Contrastive empiricism and indispensability.Mark Colyvan - 1999 - Erkenntnis 51 (2-3):323-332.

Analytics

Added to PP
2013-01-14

Downloads
479 (#35,883)

6 months
81 (#46,778)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Russell Marcus
Hamilton College

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references