Logical dilemmas : the life and work of Kurt Gödel PDF
Preview Logical dilemmas : the life and work of Kurt Gödel
Logical Dilemmas Kurt Gödelat AmherstCollege, 1967 Logical Dilemmas The Life and Work of Kurt Gödel John W. Dawson, Jr. Department ofMathematics Pennsylvania State University York,Pennsylvania A K Peters Wellesley, Massachusetts Editorial,Sales,andCustomerServiceOffice AKPeters,Ltd. 888WorcesterStreet,Suite230 Wellesley, MA02482 www.akpeters.com Copyright©1997byAKPeters,Ltd. Originallyprinted inhardcover. All rights reserved. No part of the material protected by this copyright notice may be reproduced orutilized inanyform, electronic or mechanical, including photocopying, recording,orbyanyinformationstorageandretrievalsystem,withoutwrittenpermission fromthecopyright owner. Library of Congress Cataloging-in-Publication Data Dawson, JohnW.(JohnWilliam),1944– LogicalDilemmas: thelifeandworkof KurtGödel/ JohnW. Dawson. p. cm. Includesbibliographicalreferences(p. – )andindex. ISBN:1-56881-256-6 1. Gödel, Kurt. 2. Logicians–United States–Biography. 3. Logicians–Austria–Biography. I. Title QA29.058D39 1996 193–dc2 [B] 96-50001 CIP KolomanMoser’s“HomagetotheAmericanDancer,LoïeFuller”reprintedbypermis- sionof Heinrich Moser (for the Moser Estate), and Graphische Sammlung Albertina, Vienna. Excerpt from “Burnt Norton” in FOUR QUARTETS, copyright 1943 by T.S. Eliot and renewed1971 byEsmeValerieEliot, reprinted bypermissionof Harcourt,Inc. PrintedintheUnited StatesofAmerica 0908 0706 05 10987 65432 1 To Cheryl Without whose love, assistance, and forbearance this book could not have been written Contents Preface and Acknowledgments ix I Der Herr Warum 1 (1920-1924) II Intellectual Maturation 21 (1924-29) III Excursus: 37 A Capsule History of the Development of Logic to 1928 IV Moment of Impact 53 (1929-31) V Dozent in absentia 81 (1932-37) VI “Jetzt, Mengenlehre” 115 (1937-39) VII Homecoming and Hegira 139 (1939-40) vii viii Logical Dilemmas VIII Years of Transition 153 (1940-46) IX Philosophy and Cosmology 173 (1946-51) X Recognition and Reclusion 193 (1951-61) XI New Light on the Continuum Problem 215 (1961-68) XII Withdrawal 229 (1969-78) XIII Aftermath 255 XIV Reflections on Gödel’s Life and Legacy 261 Notes 271 Appendix A: Chronology 313 Appendix B: Family Genealogies 317 Appendix C: Biographical Vignettes 321 Bibliography 329 Index 345 Preface and Acknowledgments Every biographer is confronted with certain questions whose answers depend upon the nature of the particular life to be examined: What is it that sets it apart from others and makes it worth writing about? What sources are there to draw upon? To whom should one’s account be addressed? What should its central focus be? In the case of Kurt Gödel the subject was a reclusive genius whose work has generally been considered abstruse and whose life, combining elements of rationality and psychopathology, has been the subject more of rumor than of concrete factual knowledge. There is, however, no doubt that Gödel’s discov- eries have been of the utmost importance within mathematics, and there is growing awareness of the impact they have had on our modern world view. Theproblemistomaketheideasunderlyinghisworkcomprehensibletonon- specialistswithoutlapsingintooversimplificationordistortion,andtoreconcile his personality with his achievements. Sinceabiographyisnotatextbook,onewhosesubjectisatwentieth-century mathematician must of necessity be addressed to persons who possess a mod- icumofmathematicalunderstanding. Ihaveconsequentlypresumedthatread- ersofthisvolumewillhavesomeacquaintancewiththelarge-scalestructureof modern mathematics and at least a passing familiarity with some of its major figures. Those, for example, who are wholly ignorant of nineteenth-century developments in analysis, when the notions of function and of real number were first made precise, cannot be expected to appreciate foundational ques- tions that arose therefrom; and those who have never heard of Hilbert or von Neumann are unlikely to have heard of Gödel either. Ihavenot,however,presumedanyacquaintancewithmodernmathematical logic, since even among mathematicians of the first rank such knowledge is often wanting. In chapter III, I have interrupted the narrative of Gödel’s ix x Logical Dilemmas life to provide a pr´ecis of the development of logic up to the time of his own contributions;inchapterVI,Ihavereviewedinsomewhatmoredetailtheearly history of set theory; and in an appendix I have included brief biographical vignettes of some of the major figures mentioned in the text. Forthosewellversedinlogicthepresentworkisintendedasacomplement to Gödel’s Collected Works. The three volumes of that compilation so far published contain fulltextsof allof Gödel’s publications (with parallelEnglish translations of all German originals), as well as previously unpublished essays and lectures. Incisive commentary on the content, significance, and influence of each item is given in an accompanying introductory note, and there is an extensive bibliography of related literature. The edition is modeled on Jean van Heijenoort’s deservedly lauded From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931, inwhich a selectionof seminaltextsleading up to Gödel’s incompleteness paper is similarly presented. IncitingreferencesIhaveadoptedtheformatemployedinthoseexemplars: Sourcesareindicatedbyacodeconsistingoftheauthor’snameandthedateof publication (or of composition, in the case of unpublished manuscripts), both set in italics – e.g., Gödel 1931a. When the author is clear from context I have sometimes omitted the name, and when more than one work by an author appeared duringthesameyear I haveused letter suffixestodistinguish among them. For the most part, information concerning sources has been put into num- beredendnotes,citedwithinbrackets,thatarecollectedtogetheratthebackof the volume. Explanatory footnotes, on the other hand, appear at the bottom of the page. ♦ ♦ ♦ Because Gödel’s circle of acquaintances was so restricted, accounts of his life must rely primarily on documentary sources rather than interviews. The most important collection of such sources is Gödel’s own Nachlaß (literary remains, designated hereinbythelettersGN),housed attheFirestoneLibrary of Princeton University. It appears that Gödel retained almost every scrap of paper that crossed his desk, including library request slips, luggage tags, crank correspondence, and letters from autograph seekers and mathematical amateurs, so his Nachlaß is perhaps best described as a scholarly midden. Withinit,forthosewillingtosievethroughthemassofaccessorymaterial,lies embedded a rich trove of information.
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