Axiomatic Method and Category Theory / by Andrei Rodin
(Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science. ISSN:25428292 ; 364)
Publisher  (Cham : Springer International Publishing : Imprint: Springer) 

Year  2014 
Edition  1st ed. 2014. 
Authors  *Rodin, Andrei author SpringerLink (Online service) 
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OB00168707  Springer Humanities, Social Sciences and Law eBooks (電子ブック)  9783319004044 


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Media type  機械可読データファイル 
Size  XI, 285 p. 63 illus : online resource 
Notes  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 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:URL=https://doi.org/10.1007/9783319004044 
Subjects  LCSH:Knowledge, Theory of LCSH:Algebra, Homological LCSH:Mathematical logic FREE:Epistemology FREE:Category Theory, Homological Algebra FREE:Mathematical Logic and Foundations 
Classification  LCC:BD143237 DC23:120 
ID  8000011234 
ISBN  9783319004044 
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