Axiomatic Method and Category Theory (Record no. 92475)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 03835nam a22004815i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-319-00404-4 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220082506.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 131014s2014 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783319004044 |
| -- | 978-3-319-00404-4 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-319-00404-4 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | BD143-237 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | HPK |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PHI004000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 120 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Rodin, Andrei. |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Axiomatic Method and Category Theory |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Andrei Rodin. |
| 264 #1 - | |
| -- | Cham : |
| -- | Springer International Publishing : |
| -- | Imprint: Springer, |
| -- | 2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XI, 285 p. 63 illus. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; |
| Volume number/sequential designation | 364 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Philosophy (General). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Genetic epistemology. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Algebra. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Logic, Symbolic and mathematical. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Philosophy. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Epistemology. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Category Theory, Homological Algebra. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematical Logic and Foundations. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783319004037 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ; |
| Volume number/sequential designation | 364 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-319-00404-4 |
| 912 ## - | |
| -- | ZDB-2-SHU |
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