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A Subject With No ObjectStrategies for Nominalistic Interpretation of Mathematics$
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John P. Burgess and Gideon Rosen

Print publication date: 1999

Print ISBN-13: 9780198250128

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198250126.001.0001

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A Geometric Strategy

A Geometric Strategy

(p.97) A A Geometric Strategy
A Subject With No Object

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Oxford University Press

Develops in some detail a strategy of nominalistic interpretation that assumes that points of spacetime are legitimate, concrete, physical entities. What makes the strategy possible is the fact that analytic geometry in the style of Descartes can be interpreted in synthetic geometry in the style of Euclid, using triples of points to represent real numbers (namely, as ratios of pairs of line segments connecting each of a pair of points with a third). This strategy can handle classical theories based on Euclidean space and special‐relativistic theories based on Minkowski space. The extension of the strategy to general relativity and quantum mechanics remains to be worked out, as does the treatment of the higher branch of geometry known as descriptive set theory.

Keywords:   analytic geometry, Descartes, descriptive set theory, Euclid, general relativity, Minkowski, quantum mechanics, spacetime, special relativity, synthetic geometry

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