9783319004037-3319004034-Axiomatic Method and Category Theory (Synthese Library (364))

Axiomatic Method and Category Theory (Synthese Library (364))

ISBN-13: 9783319004037
ISBN-10: 3319004034
Edition: 2014
Author: Rodin, Andrei
Publication date: 2013
Publisher: Springer
Format: Hardcover 296 pages
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Book details

ISBN-13: 9783319004037
ISBN-10: 3319004034
Edition: 2014
Author: Rodin, Andrei
Publication date: 2013
Publisher: Springer
Format: Hardcover 296 pages

Summary

Acknowledged authors Rodin, Andrei wrote Axiomatic Method and Category Theory (Synthese Library (364)) comprising 296 pages back in 2013. Textbook and eTextbook are published under ISBN 3319004034 and 9783319004037. Since then Axiomatic Method and Category Theory (Synthese Library (364)) textbook was available to sell back to BooksRun online for the top buyback price or rent at the marketplace.

Description

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,Rodinpresents 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.

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