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Synthese Library

Axiomatic Method and Category Theory

Authors: Rodin, Andrei

  • Offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method
  • Provides a deep textual analysis of Euclid, Hilbert, and Lawvere that describes how their ideas are different and how their ideas progressed over time 
  • Presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics
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eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-00404-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-00403-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 13, 2016
  • ISBN 978-3-319-37551-9
  • Free shipping for individuals worldwide
About this book

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia.

The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics.

Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences.

This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.

Table of contents (10 chapters)

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-319-00404-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-319-00403-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: October 13, 2016
  • ISBN 978-3-319-37551-9
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Axiomatic Method and Category Theory
Authors
Series Title
Synthese Library
Series Volume
364
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-00404-4
DOI
10.1007/978-3-319-00404-4
Hardcover ISBN
978-3-319-00403-7
Softcover ISBN
978-3-319-37551-9
Edition Number
1
Number of Pages
XI, 285
Number of Illustrations and Tables
63 b/w illustrations
Topics