000			02792cam a22002655i 4500
001			136667
003			ISI Library, Kolkata
005			20160324134346.0
008			130917s2013 nyu 000 0 eng
020			_a9783319004037
040			_aISI Library _beng
082	0	4	_a511.322 _223 _bR692
100	1		_aRodin, Andrei.
245	1	0	_aAxiomatic method and category theory / _cAndrei Rodin.
260			_aSwitzerland : _bSpringer, _c2014.
300			_axi, 285 p. : _billustrations ; _c24 cm.
490	0		_aSynthese library ; _vv 364.
504			_aIncludes bibliographical references and index.
505	0		_a1. Introduction.- Part I A Brief History of the Axiomatic Method.- 2. Euclid: Doing and Showing.- 3. Hilbert: Making It Formal.- 4. Formal Axiomatic Method and the 20th Century Mathematics.- 5 Lawvere: Pursuit of Objectivity.- Part II. Identity and Categorification.- 6. Identity in Classical and Constructive Mathematics.- 7. Identity Through Change, Category Theory and Homotopy Theory.- Part III. Subjective Intuitions and Objective Structures.- 8. How Mathematical Concepts Get Their Bodies. 9. Categories versus Structures.- 10. New Axiomatic Method (instead of conclusion).- Bibliography.- Index.
520			_aThis 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	_aAxiomatic set theory.
650		0	_aCategories (Mathematics)
650		0	_aPhilosophy.
942			_2ddc _cBK
999			_c420221 _d420221