Borrow it
 African Studies Library
 Alumni Medical Library
 Astronomy Library
 Fineman and Pappas Law Libraries
 Frederick S. Pardee Management Library
 Howard Gotlieb Archival Research Center
 Mugar Memorial Library
 Music Library
 Pikering Educational Resources Library
 School of Theology Library
 Science & Engineering Library
 Stone Science Library
The Resource Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)
Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)
Resource Information
The item Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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 wellknown 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 Hilbertstyle 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
 Language
 eng
 Extent
 XI, 285 p. 63 illus.
 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
 Isbn
 9783319004044
 Label
 Axiomatic Method and Category Theory
 Title
 Axiomatic Method and Category Theory
 Statement of responsibility
 by Andrei Rodin
 Subject

 Algebra
 Algebra
 Genetic epistemology
 Genetic epistemology
 Mathematical Logic and Foundations
 Epistemology
 Logic, Symbolic and mathematical
 Algebra
 Logic, Symbolic and mathematical
 Philosophy
 Electronic resources
 Category Theory, Homological Algebra
 Logic, Symbolic and mathematical
 Philosophy (General)
 Genetic epistemology
 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 wellknown 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 Hilbertstyle 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
 http://library.link/vocab/creatorName
 Rodin, Andrei
 Image bit depth
 0
 LC call number
 BD143237
 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)
 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
 10.1007/9783319004044
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319004044
 Label
 Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)
 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
 10.1007/9783319004044
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319004044
Subject
 Algebra
 Algebra
 Algebra
 Category Theory, Homological Algebra
 Electronic resources
 Epistemology
 Genetic epistemology
 Genetic epistemology
 Genetic epistemology
 Logic, Symbolic and mathematical
 Logic, Symbolic and mathematical
 Logic, Symbolic and mathematical
 Mathematical Logic and Foundations
 Philosophy
 Philosophy (General)
Member of
Library Locations

African Studies LibraryBorrow it771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US42.350723 71.108227


Astronomy LibraryBorrow it725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US42.350259 71.105717

Fineman and Pappas Law LibrariesBorrow it765 Commonwealth Avenue, Boston, MA, 02215, US42.350979 71.107023

Frederick S. Pardee Management LibraryBorrow it595 Commonwealth Avenue, Boston, MA, 02215, US42.349626 71.099547

Howard Gotlieb Archival Research CenterBorrow it771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US42.350723 71.108227


Music LibraryBorrow it771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US42.350723 71.108227

Pikering Educational Resources LibraryBorrow it2 Silber Way, Boston, MA, 02215, US42.349804 71.101425

School of Theology LibraryBorrow it745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US42.350494 71.107235

Science & Engineering LibraryBorrow it38 Cummington Mall, Boston, MA, 02215, US42.348472 71.102257

Embed (Experimental)
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/AxiomaticMethodandCategoryTheorybyAndrei/XlymWVbmm0c/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/AxiomaticMethodandCategoryTheorybyAndrei/XlymWVbmm0c/">Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/AxiomaticMethodandCategoryTheorybyAndrei/XlymWVbmm0c/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/AxiomaticMethodandCategoryTheorybyAndrei/XlymWVbmm0c/">Axiomatic Method and Category Theory, by Andrei Rodin, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>