A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics

Oxford, England: Oxford University Press (1997)
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Abstract

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed.

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Author Profiles

John Burgess
Princeton University
Gideon Rosen
Princeton University

Citations of this work

On what grounds what.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
The Intellectual Given.John Bengson - 2015 - Mind 124 (495):707-760.
There is No Easy Road to Nominalism.M. Colyvan - 2010 - Mind 119 (474):285-306.
Individuals: an essay in revisionary metaphysics.Shamik Dasgupta - 2009 - Philosophical Studies 145 (1):35-67.
Conceptual Ethics II.Alexis Burgess & David Plunkett - 2013 - Philosophy Compass 8 (12):1102-1110.

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