Overview
- 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
Part of the book series: Synthese Library (SYLI, volume 364)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (10 chapters)
-
Front Matter
-
A Brief History of the Axiomatic Method
-
Front Matter
-
-
Back Matter
-
Identity and Categorification
-
Front Matter
-
-
Back Matter
-
Subjective Intuitions and Objective Structures
-
Front Matter
-
-
Back Matter
Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Axiomatic Method and Category Theory
Authors: Andrei Rodin
Series Title: Synthese Library
DOI: https://doi.org/10.1007/978-3-319-00404-4
Publisher: Springer Cham
eBook Packages: Humanities, Social Sciences and Law, Philosophy and Religion (R0)
Copyright Information: Springer International Publishing Switzerland 2014
Hardcover ISBN: 978-3-319-00403-7Published: 24 October 2013
Softcover ISBN: 978-3-319-37551-9Published: 27 August 2016
eBook ISBN: 978-3-319-00404-4Published: 14 October 2013
Series ISSN: 0166-6991
Series E-ISSN: 2542-8292
Edition Number: 1
Number of Pages: XI, 285
Number of Illustrations: 63 b/w illustrations
Topics: Epistemology, Category Theory, Homological Algebra, Mathematical Logic and Foundations