Table of contents
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.
- Book Title Axiomatic Method and Category Theory
- Series Title Synthese Library
- Series Abbreviated Title Synthese Library
- DOI https://doi.org/10.1007/978-3-319-00404-4
- Copyright Information Springer International Publishing Switzerland 2014
- Publisher Name Springer, Cham
- eBook Packages Humanities, Social Sciences and Law Philosophy and Religion (R0)
- Hardcover ISBN 978-3-319-00403-7
- Softcover ISBN 978-3-319-37551-9
- eBook ISBN 978-3-319-00404-4
- Edition Number 1
- Number of Pages XI, 285
- Number of Illustrations 63 b/w illustrations, 0 illustrations in colour
Category Theory, Homological Algebra
Mathematical Logic and Foundations
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