Skip Navigation

Mind 2000 109(435):455-480; doi:10.1093/mind/109.435.455
© 2000 by Mind Association
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Melia, J
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Weaseling away the indispensability argument

J Melia

Department of Philosophy, Derwent College, University of York, York YO10 5DD, UK E-mail: jwm9@york.ac.uk

According to the indispensability argument, the fact that we quantify over numbers, sets and functions in our best scientific theories gives us reason for believing that such objects exist. I examine a strategy to dispense with such quantification by simply replacing any given platonistic theory by the set of sentences in the nominalist vocabulary it logically entails. I argue that, as a strategy, this response fails: for there is no guarantee that the nominalist world that go beyond the set of sentences in the nominalist language such theories entail. However, I argue that what such theories show is that mathematics can enable us to express possibilities about the concrete world that may not be expressible in nominalistically acceptable language. While I grant that this may make quantification over abstracta indispensable, I deny that such indispensability is a reason for accepting them into our ontology. I urge that the nominalist should be allowed to quantify over abstracta whilst denying their existence and I explain how this apparently contradictory practice (a practice I call 'weaseling') is in fact coherent, unproblematic and rational. Finally, I examine the view that platonistic theories are simpler or more attractive than their nominalistic reformulations, and thus that abstract ought to be accepted into our ontology for the same sorts of reasons as other theoretical objects. I argue that, at least in the case of numbers, functions and sets, such arguments misunderstand the kind of simplicity and attractiveness we seek.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?


This article has been cited by other articles:


Home page
 AnalysisHome page
J. Tallant
Ontological cheats might just prosper
Analysis, July 1, 2009; 69(3): 422 - 430.
[Full Text] [PDF]

Home page
 Br J Philos SciHome page
R. W. Batterman
On the Explanatory Role of Mathematics in Empirical Science
Brit J Philos Sci, June 17, 2009; (2009) axp018v1.
[Abstract] [Full Text] [PDF]

Home page
 Philosophia MathematicaHome page
M. Balaguer
Fictionalism, Theft, and the Story of Mathematics
Philosophia Mathematica, June 1, 2009; 17(2): 131 - 162.
[Abstract] [Full Text] [PDF]


Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.