- 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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- About this book
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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)
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Introduction
Pages 1-12
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Euclid: Doing and Showing
Pages 15-37
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Hilbert: Making It Formal
Pages 39-72
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Formal Axiomatic Method and the Twentieth Century Mathematics
Pages 73-97
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Lawvere: Pursuit of Objectivity
Pages 99-143
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Axiomatic Method and Category Theory
- Authors
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- Andrei Rodin
- 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
- 63 b/w illustrations
- Topics
