The Resource Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)

Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)

Label
Axiomatic Method and Category Theory
Title
Axiomatic Method and Category Theory
Statement of responsibility
by Andrei Rodin
Creator
Contributor
Author
Provider
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Rodin, Andrei
Image bit depth
0
LC call number
BD143-237
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science
Series volume
364
http://library.link/vocab/subjectName
  • Philosophy (General)
  • Genetic epistemology
  • Algebra
  • Logic, Symbolic and mathematical
  • Philosophy
  • Epistemology
  • Category Theory, Homological Algebra
  • Mathematical Logic and Foundations
Label
Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Introduction -- Part I A Brief History of the Axiomatic Method -- Chapter 1. Euclid: Doing and Showing -- Chapter 2. Hilbert: Making It Formal -- Chapter 3. Formal Axiomatic Method and the 20th Century Mathematics -- Chapter. 4 Lawvere: Pursuit of Objectivity -- Conclusion of Part 1 -- Part II. Identity and Categorification -- Chapter 5. Identity in Classical and Constructive Mathematics -- Chapter 6. Identity Through Change, Category Theory and Homotopy Theory -- Conclusion of Part 2 -- Part III. Subjective Intuitions and Objective Structures -- Chapter 7. How Mathematical Concepts Get Their Bodies. Chapter 8. Categories versus Structures -- Chapter 9. New Axiomatic Method (instead of conclusion) -- Bibliography
Dimensions
unknown
Extent
XI, 285 p. 63 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319004044
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-00404-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-00404-4
Label
Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Introduction -- Part I A Brief History of the Axiomatic Method -- Chapter 1. Euclid: Doing and Showing -- Chapter 2. Hilbert: Making It Formal -- Chapter 3. Formal Axiomatic Method and the 20th Century Mathematics -- Chapter. 4 Lawvere: Pursuit of Objectivity -- Conclusion of Part 1 -- Part II. Identity and Categorification -- Chapter 5. Identity in Classical and Constructive Mathematics -- Chapter 6. Identity Through Change, Category Theory and Homotopy Theory -- Conclusion of Part 2 -- Part III. Subjective Intuitions and Objective Structures -- Chapter 7. How Mathematical Concepts Get Their Bodies. Chapter 8. Categories versus Structures -- Chapter 9. New Axiomatic Method (instead of conclusion) -- Bibliography
Dimensions
unknown
Extent
XI, 285 p. 63 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783319004044
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-319-00404-4
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-00404-4

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