Jump to ContentJump to Main Navigation
A Subject With No ObjectStrategies for Nominalistic Interpretation of Mathematics$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 19 October 2019

A Geometric Strategy

A Geometric Strategy

Chapter:
(p.97) A A Geometric Strategy
Source:
A Subject With No Object
Author(s):

John P. Burgess (Contributor Webpage)

Gideon Rosen (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198250126.003.0003

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

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .