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Showing content from https://link.springer.com/book/10.1007/978-3-7643-8350-3 below:

Labyrinth of Thought: A History of Set Theory and Its Role in Modern Mathematics

Authors:

1. José Ferreirós

   1. Dpto. De Filosofía y Lógica, Universidad de Sevilla Camilo J.Cela, Sevilla, Spain
      

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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.

2. The Emergence of Sets within Mathematics
3. Entering the Labyrinth-Toward Abstract Set Theory
   1. Front Matter

      Pages 169-169
4. In Search of an Axiom System
   1. Front Matter

      Pages 297-298
5. Back Matter

   Pages 393-466

From the book reviews:

“The book is a thorough, deep, fascinating work. It is not only recommended, it is compulsory for anyone interested in the history of mathematical ideas.” (László I. Szabó, Acta Scientiarum Mathematicarum (Szeged), Vol. 75 (1-2), 2009)

• Dpto. De Filosofía y Lógica, Universidad de Sevilla Camilo J.Cela, Sevilla, Spain

  José Ferreirós

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• Book Title: Labyrinth of Thought

• Book Subtitle: A History of Set Theory and Its Role in Modern Mathematics

• Authors: José Ferreirós

• DOI: https://doi.org/10.1007/978-3-7643-8350-3

• Publisher: Birkhäuser Basel

• eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

• Copyright Information: Birkh�user Basel 2007

• Softcover ISBN: 978-3-7643-8349-7Published: 16 August 2007

• eBook ISBN: 978-3-7643-8350-3Published: 04 October 2008

• Edition Number: 2

• Number of Pages: XXVI, 466

• Number of Illustrations: 7 b/w illustrations

• Additional Information: Originally published as volume 23 in the series: Science Networks. Historical Studies

• Topics: History of Mathematical Sciences, Mathematical Physics

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