Labyrinth of Thought A History of Set Theory and Its Role in Modern
"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major in
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Edited by Erwin Hiebert, Eberhard Knobloch and Erhard Scholz Editorial Board: K. Andersen, Aarhus D. Barkan, Pasadena H.J.M. Bos, Utrecht U. Bottazzini, Roma J.Z. Buchwald, Cambridge, Mass. K. Chemla, Paris S.S. Demidov, Moskva E.A. Fellmann, Basel M. Folkerts, Munchen P. Galison, Cambridge, Mass. I. Grattan-Guinness, London J. Gray, Milton Keynes
R. Halleux, Liege S. Hildebrandt, Bonn D. Laugwitz, Muhltal Ch. Meinel, Regensburg J. Peiffer, Paris w. Purkert, Leipzig D. Rowe, Mainz A.1. Sabra, Cambridge, Mass. R.H. Stuewer, Minneapolis H. WuBing, Leipzig V.P. Vizgin, Moskva
Jose Ferreir6s
Labyrinth of Thought A History of Set Theory and Its Role in Modern Mathematics
Springer Basel AG
Author: Jose Ferreiros Dpto. de Filosofia y Logica Universidad de Sevilla Avda. San Francisco Javier, sin E-41005 Sevilla e-mail: [email protected]
Library of Congress Cataloging-in-Publication Data Ferreiros Dominguez, Jose. Labyrinth of thought: a history of set theory and its role in modern mathematics I Jose Ferreiros. p. cm. -- (Science networks historical studies; v. 23) Includes bibliographical references and index. ISBN 978-3-0348-5051-3 ISBN 978-3-0348-5049-0 (eBook) DOI 10.1007/978-3-0348-5049-0
1. Set theory--H istory. QA248.F4671999 511.3'22'09 - dc21
I. Title.
II. Series.
Deutsche Bibliothek Cataloging-in-Publication Data Ferreir6s Dominguez, Jose: Labyrinth of thought: a history of set theory and its role in modern mathematics I Jose Ferreiros. (Science networks; Vol. 23)
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use, permission of the copyright owner must be obtained. ©1999 Springer Basel AG Originally published by Birkhauser Verlag Basel - Boston - Berlin in 1999 Softcover reprint of the hardcover 1st edition 1999 Camera-ready copy prepared by the author. Printed on acid-free paper produced from chlorine-free pulp. TCF 00 Cover design: Micha Lotrovsky, Therwil, Switzerland Cover illustration: Riemann and Dedekind (left), Cantor (center), Zermelo and Russell (right) 3-7643-5749-5 98765432
A Dolores, por todos estos afios.
Contents
Introduction ........................................................................................................
Xl
1. Aims and Scope ........................................................................................ xiii 2. General Historiographical Remarks ......................................................... xvii
Part One: The Emergence of Sets within Mathematics ............... . I
Institutional and Intellectual Contexts in German Mathematics, 1800-1870 ............................................................
3
1. Mathematics at the Reformed German Universities ..... ...........................
4
2. Traditional and 'Modem' Foundational Viewpoints ................................
10
3. T
