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

John P. Burgess and Gideon Rosen

Abstract

Numbers and other mathematical objects are exceptional in having no locations in space and time and no causes or effects in the physical world. This makes it difficult to account for the possibility of mathematical knowledge, leading many philosophers to embrace nominalism, the doctrine that there are no abstract entities. It has also led some of them to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects, eliminating so‐called ontological commitment to numbers, sets, and the like. These projects differ considerably in the appar ... More

Keywords: abstract entities, Burgess, mathematical knowledge, mathematical objects, modal logic, nominalism, ontological commitment, philosophy, philosophy of mathematics, Rosen, synthetic geometry

Bibliographic Information

Print publication date: 1999 Print ISBN-13: 9780198250128
Published to Oxford Scholarship Online: November 2003 DOI:10.1093/0198250126.001.0001

Authors

Affiliations are at time of print publication.

John P. Burgess, author
Princeton University
Author Webpage

Gideon Rosen, author
Princeton University
Author Webpage

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Contents

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Part I Philosophical and Technical Background

Part II Three Major Strategies

Part III Further Strategies and a Provisional Assessment