A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics by John P. BurgessA Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics by John P. Burgess

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

byJohn P. Burgess, Gideon Rosen

Paperback | August 1, 1999

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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 areno abstract entities, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts, with minimal prerequisites, of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluateeach 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.
John Burgess is Professor of Philosophy and Gideon Rosen is Assistant Professor of Philosophy at Princeton University.
Title:A Subject With No Object: Strategies for Nominalistic Interpretation of MathematicsFormat:PaperbackDimensions:272 pages, 8.5 × 5.43 × 0.63 inPublished:August 1, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198250126

ISBN - 13:9780198250128

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Table of Contents

PrefacePart I: Philosophical and Technical BackgroundA. Introduction;B. A Common Framework for StrategiesPart II: Three Major StrategiesA. A Geometric StrategyB. A Purely Modal StrategyC. A Mixed Modal StrategyPart III: Further Strategies and a Provisional AssessmentA. Miscellaneous StrategiesB. Strategies in the LiteratureC. ConclusionBibliographyIndex

Editorial Reviews

`This book has many virtues. It is concentrated on fundamental questions in the philosophy of mathematics, which it explores with an open mind - or even two open minds; it is richly informed and informative in its clear exposition of the details of nominalistic reconstruction programs ... Noattempt will be made here even to summarize the rich and extensive content of this part, except to say that a great service has been performed for both students The formessexxence of the programs is clearly laid out in each case, with just enough detail to give the reader a real sense of how theprogram in question works but not so much as to obscure the broader picture ... it should be clear that this book is of great value and interest and that, on the whole, it exemplifies philosophy practice'Geoffrey Hellman, Philosophia Mathematica