Axiomatic Method and Category Theory

Publisher : Springer Science & Business Media

ISBN-13 : 3319004042

Page : 285 pages

Rating : 4.5/5 from 042 voters

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.

More Books:

Axiomatic Method and Category Theory
Language: en
Pages: 285
Authors: Andrei Rodin
Categories: Philosophy
Type: BOOK - Published: 2013-10-14 - Publisher: Springer Science & Business Media

This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how
Intuition and the Axiomatic Method
Language: en
Pages: 324
Authors: Emily Carson
Categories: Philosophy
Type: BOOK - Published: 2006-07-02 - Publisher: Springer Science & Business Media

Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be o
Relational and Algebraic Methods in Computer Science
Language: en
Pages: 335
Authors: Uli Fahrenberg
Categories: Mathematics
Type: BOOK - Published: 2020-04-01 - Publisher: Springer Nature

This book constitutes the proceedings of the 18th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2020, which was due t
From a Geometrical Point of View
Language: en
Pages: 310
Authors: Jean-Pierre Marquis
Categories: Science
Type: BOOK - Published: 2008-11-20 - Publisher: Springer Science & Business Media

From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematic
Model Theory and the Philosophy of Mathematical Practice
Language: en
Pages: 384
Authors: John Baldwin
Categories: Mathematics
Type: BOOK - Published: 2018-01-31 - Publisher: Cambridge University Press

Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.
Iconicity and Abduction
Language: en
Pages: 180
Authors: Gianluca Caterina
Categories: Philosophy
Type: BOOK - Published: 2016-09-13 - Publisher: Springer

This book consolidates and extends the authors’ work on the connection between iconicity and abductive inference. It emphasizes a pragmatic, experimental and
Categories for the Working Philosopher
Language: en
Pages: 528
Authors: Elaine Landry
Categories: Mathematics
Type: BOOK - Published: 2017-10-19 - Publisher: Oxford University Press

This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a
Functional Analysis and Related Fields
Language: en
Pages: 242
Authors: F. E. Browder
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

On May 20-24. 1968, a Conference on Functional Analysis and Related Fields was held at the Center for Continuing Education of the University cl Chicago in honor
Category Theory 1991: Proceedings of the 1991 Summer Category Theory Meeting, Montreal, Canada
Language: en
Pages: 447
Authors: Robert Andrew George Seely
Categories: Mathematics
Type: BOOK - Published: 1992 - Publisher: American Mathematical Soc.

As category theory approaches its first half-century, it continues to grow, finding new applications in areas that would have seemed inconceivable a generation
Logic and Metalogic
Language: en
Pages:
Authors:
Categories:
Type: BOOK - Published: - Publisher: PediaPress