MARC details
| 000 -LEADER |
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| fixed length control field |
02792cam a22002655i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
136667 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
ISI Library, Kolkata |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20160324134346.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
130917s2013 nyu 000 0 eng |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319004037 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
ISI Library |
| Language of cataloging |
eng |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
511.322 |
| Edition number |
23 |
| Item number |
R692 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Rodin, Andrei. |
| 245 10 - TITLE STATEMENT |
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| Title |
Axiomatic method and category theory / |
| Statement of responsibility, etc |
Andrei Rodin. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication, distribution, etc |
Switzerland : |
| Name of publisher, distributor, etc |
Springer, |
| Date of publication, distribution, etc |
2014. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
xi, 285 p. : |
| Other physical details |
illustrations ; |
| Dimensions |
24 cm. |
| 490 0# - SERIES STATEMENT |
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| Series statement |
Synthese library ; |
| Volume number/sequential designation |
v 364. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc |
Includes bibliographical references and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
1. Introduction.-<br/>Part I A Brief History of the Axiomatic Method.- <br/>2. Euclid: Doing and Showing.- <br/>3. Hilbert: Making It Formal.- <br/>4. Formal Axiomatic Method and the 20th Century Mathematics.- <br/>5 Lawvere: Pursuit of Objectivity.- <br/><br/>Part II. Identity and Categorification.- <br/>6. Identity in Classical and Constructive Mathematics.-<br/>7. Identity Through Change, Category Theory and Homotopy Theory.- <br/><br/>Part III. Subjective Intuitions and Objective Structures.- <br/>8. How Mathematical Concepts Get Their Bodies. <br/>9. Categories versus Structures.- <br/>10. New Axiomatic Method (instead of conclusion).- Bibliography.-<br/>Index. |
| 520 ## - SUMMARY, ETC. |
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| 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 |
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| Topical term or geographic name as entry element |
Axiomatic set theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Categories (Mathematics) |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Philosophy. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
