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Cover: 9783764383497 | Labyrinth of Thought | José Ferreirós | Taschenbuch | Paperback | xxvi
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Labyrinth of Thought
A History of Set Theory and Its Role in Modern Mathematics
Taschenbuch von José Ferreirós
Sprache: Englisch

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Beschreibung
Labyrinth of Thought discusses the emergence and development of set theory and the set-theoretic approach to mathematics during the period 1850-1940. Rather than focusing on the pivotal figure of Georg Cantor, it analyzes his work and the emergence of transfinite set theory within the broader context of the rise of modern mathematics. The text has a tripartite structure. Part 1, The Emergence of Sets within Mathematics, surveys the initial motivations for a mathematical notion of a set within several branches of the discipline (geometry, algebra, algebraic number theory, real and complex analysis), emphasizing the role played by Riemann in fostering acceptance of the set-theoretic approach. In Part 2, Entering the Labyrinth, attention turns to the earliest theories of sets, their evolution, and their reception by the mathematical community; prominent are the epoch-making contributions of Cantor and Dedekind, and the complex interactions between them. Part 3, In Search of an Axiom System, studies the four-decade period from the discovery of set-theoretic paradoxes to Gödel¿s independence results, an era during which set theory gradually became assimilated into mainstream mathematics; particular attention is given to the interactions between axiomatic set theory and modern systems of formal logic, especially the interplay between set theory and type theory. A new Epilogue for this second edition offers further reflections on the foundations of set theory, including the "dichotomy conception" and the well-known iterative conception.
Labyrinth of Thought discusses the emergence and development of set theory and the set-theoretic approach to mathematics during the period 1850-1940. Rather than focusing on the pivotal figure of Georg Cantor, it analyzes his work and the emergence of transfinite set theory within the broader context of the rise of modern mathematics. The text has a tripartite structure. Part 1, The Emergence of Sets within Mathematics, surveys the initial motivations for a mathematical notion of a set within several branches of the discipline (geometry, algebra, algebraic number theory, real and complex analysis), emphasizing the role played by Riemann in fostering acceptance of the set-theoretic approach. In Part 2, Entering the Labyrinth, attention turns to the earliest theories of sets, their evolution, and their reception by the mathematical community; prominent are the epoch-making contributions of Cantor and Dedekind, and the complex interactions between them. Part 3, In Search of an Axiom System, studies the four-decade period from the discovery of set-theoretic paradoxes to Gödel¿s independence results, an era during which set theory gradually became assimilated into mainstream mathematics; particular attention is given to the interactions between axiomatic set theory and modern systems of formal logic, especially the interplay between set theory and type theory. A new Epilogue for this second edition offers further reflections on the foundations of set theory, including the "dichotomy conception" and the well-known iterative conception.
Inhaltsverzeichnis
The Emergence of Sets within Mathematics.- Institutional and Intellectual Contexts in German Mathematics, 1800-1870.- A New Fundamental Notion: Riemann's Manifolds.- Dedekind and the Set-theoretical Approach to Algebra.- The Real Number System.- Origins of the Theory of Point-Sets.- Entering the Labyrinth-Toward Abstract Set Theory.- The Notion of Cardinality and the Continuum Hypothesis.- Sets and Maps as a Foundation for Mathematics.- The Transfinite Ordinals and Cantor's Mature Theory.- In Search of an Axiom System.- Diffusion, Crisis, and Bifurcation: 1890 to 1914.- Logic and Type Theory in the Interwar Period.- Consolidation of Axiomatic Set Theory.
Details
Erscheinungsjahr: 2007
Fachbereich: Populäre Darstellungen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 496
Inhalt: xxvi
466 S.
7 s/w Illustr.
466 p. 7 illus.
ISBN-13: 9783764383497
ISBN-10: 3764383496
Sprache: Englisch
Herstellernummer: 12020058
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Ferreirós, José
Auflage: 2nd ed. 2007
Hersteller: Birkhäuser Basel
Springer Basel AG
Maße: 242 x 170 x 27 mm
Von/Mit: José Ferreirós
Erscheinungsdatum: 16.08.2007
Gewicht: 0,841 kg
preigu-id: 102081141
Inhaltsverzeichnis
The Emergence of Sets within Mathematics.- Institutional and Intellectual Contexts in German Mathematics, 1800-1870.- A New Fundamental Notion: Riemann's Manifolds.- Dedekind and the Set-theoretical Approach to Algebra.- The Real Number System.- Origins of the Theory of Point-Sets.- Entering the Labyrinth-Toward Abstract Set Theory.- The Notion of Cardinality and the Continuum Hypothesis.- Sets and Maps as a Foundation for Mathematics.- The Transfinite Ordinals and Cantor's Mature Theory.- In Search of an Axiom System.- Diffusion, Crisis, and Bifurcation: 1890 to 1914.- Logic and Type Theory in the Interwar Period.- Consolidation of Axiomatic Set Theory.
Details
Erscheinungsjahr: 2007
Fachbereich: Populäre Darstellungen
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 496
Inhalt: xxvi
466 S.
7 s/w Illustr.
466 p. 7 illus.
ISBN-13: 9783764383497
ISBN-10: 3764383496
Sprache: Englisch
Herstellernummer: 12020058
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Ferreirós, José
Auflage: 2nd ed. 2007
Hersteller: Birkhäuser Basel
Springer Basel AG
Maße: 242 x 170 x 27 mm
Von/Mit: José Ferreirós
Erscheinungsdatum: 16.08.2007
Gewicht: 0,841 kg
preigu-id: 102081141
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