Patterns of Change Linguistic Innovations in the Development of Clas
This book offers a reconstruction of linguistic innovations in the history of mathematics; innovations which changed the ways in which mathematics was done, understood and philosophically interpreted. It argues that there are at least three ways in which
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Editorial Board: K. Andersen, Aarhus D. Buchwald, 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, München P. Galison, Cambridge, Mass. I. Grattan-Guinness, London J. Gray, Milton Keynes
R. Halleux, Liège S. Hildebrandt, Bonn Ch. Meinel, Regensburg J. Peiffer, Paris W. Purkert, Bonn D. Rowe, Mainz A.I. Sabra, Cambridge, Mass. Ch. Sasaki, Tokyo R.H. Stuewer, Minneapolis H. Wußing, Leipzig V.P. Vizgin, Moskva
Ladislav Kvasz
Patterns of Change Linguistic Innovations in the Development of Classical Mathematics
Birkhäuser Basel · Boston · Berlin
Ladislav Kvasz Comenius University Faculty of Mathematics, Physics and Informatics Mlynska dolina 842 48 Bratislava Slovakia and Charles University Faculty of Education M. D. Rettigove 4 116 39 Praha Czech Republic e-mail: [email protected]
2000 Mathematical Subject Classification: 01-02, 00A30, 00A35, 97C30, 97D20
Library of Congress Control Number: 2008926677 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
ISBN 978-3-7643-8839-3 Birkhäuser Verlag AG, Basel - Boston - Berlin 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. © 2008 Birkhäuser Verlag AG Basel · Boston · Berlin P.O. Box 133, CH-4010 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TCF∞ Cover illustration: Ambrogio Lorenzetti, Annunciation, see page 116. Printed in Germany ISBN 978-3-7643-8839-3
e-ISBN 978-3-7643-8840-9
987654321
www.birkhauser.ch
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Acknowledgements
The present book is the result of my research in the field of history and philosophy of mathematics that spanned more than twenty-five years. During this time I was helped by contacts with many experts in the field in my home country, Slovakia, as well as abroad. I would like to express my appreciation and gratitude to all of them – my teachers, colleagues, students or simply friends – who during this rather long period of time encouraged and supported my work. In Slovakia these were my teachers, friends and later colleagues: Peter Cvik, Vladim´ır Burjan, Milan Hejn´y, Egon G´al, Pavol Zlatoˇs, and Peter Bug´ar. With many of them I met at different private seminars during the communist era. Some became university professors, others never entered academia, but they all were part of an unforgettable atmosphere of parallel culture in the 1980s. I feel a special debt to Professor Dimitri D. Sokoloff, whom I met during my stays at the Moscow State University in 1989–1991. Thanks t
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