Mathematical Thought An Introduction to the Philosophy of Mathematic
In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it
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SYNTHESE LIBRARY A SERIES OF MONOGRAPHS ON THE RECENT DEVELOPMENT OF SYMBOLIC LOGIC, SIGNIFICS, SOCIOLOGY OF LANGUAGE, SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE, STATISTICS OF LANGUAGE AND RELATED FIELDS
Editors: B. H. KAZEMIER
I D. VUYSJE
EVERT W. BETH
MATH EMAT ICAL THOU GHT AN INTRODUCTI ON TO THE PHILOSOPHY OF MATHEMATIC S
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Part oi this work has been translated irom the Dutch by Horace S. Glover
ISBN 978-90-481-8327-2 ISBN 978-94-017-2207-0 (eBook) DOI 10.1007/978-94-017-2207-0 1965
AlI rights reserved No part ofthis book may be reproduced in any form, by print, photoprint, microfilm, or any other means without permission from the publisher
Softcover reprint ofthe hardcover lst edition 1965
TO MY WIFE
FOREWORD
In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A., for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR
VII
PREFACE
A few years ago Mr. Horace S. Glover, who had been my student in the University of Amsterdam, expressed his willingness to prepare an English translation of my Inleiding tot de Wijsbegeerte der Wiskunde which, he felt, would provide a suitable textbook for graduate students in philosophy whose lack of "technical" knowledge in the fields of logic and foundations might prevent them from reading texts primarily adapted to the needs of a mathematician. But, although I highly appreciated this kind suggestion, I realized that, if the resulting book were to fulfil its specific purpose, the execution of Mr. Glover's project would unavoidably meet with certain serious difficulties. In point of fact, my Inleiding had been based on work done between 1932 and 1935 while I still was an advanced student of mathematics, physics, and philosophy in Utrecht, Leyden, and Brussels. The book was written between 1936 and 1939 and it was published in 1940; a second edition, identical to the first except for a few minor corrections, appeared in 1942. It hardly needs saying that, although I have no reason to disavow the ideas propounded in the philosophical part of the book, the chapters devoted to the more "technical" subjects could not now be reprinted in their original form. However, rewriting the "technical" chapters w
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