Table Of ContentBy the same author also with Birkhauser Publishing
The Mathematical Philosophy of Bertrand Russell:
Origins and Development (1991)
Kurt
Gădel
U npubl ished
Philosophical Essays
Edited by
Francisco A. Rodriguez-Consuegra
With a historico-philosophicallntroduction
by the Editor
1995 Springer Basel AG
Author's Address: Universidad de Valencia
Departamento de Logica y Filosofia de la Ciencia
Apartado 22.109
E-46071 Valencia/Spain
e-mail: [email protected]
Cover illustration: Cube with magic bands, lithography, 1957, by M.C. Escher
© 1995 M.C. Escher/Cordon Art-Baarn-Holland. Ali rights reserved.
Originally published in 1994 as "Kurt Godel - Ensayos ineditos"
by Mondadori, Barcelona
© 1994 Francisco Rodriguez-Consuegra
© 1994 de la edici6n castellana para Espafia y America: Mondadori
(Grijalbo Comerical, S.A.), Arag6, 385, Barcelona, Espafia
A CIP catalogue record for this book is available from the Library
of Congress, Washington D.C., USA.
Deutsche Bibliothek Cataloging-in-Publication Data
Giidel, Kurt:
Kurt Godel : unpublished philosophical essays ; with a historico-philosophical introduction 1
ed. by Francisco A. Rodriguez-Consuegra.-Basel; Boston; Berlin : Birkhăuser, 1995
[Sammlungl
ISBN 978-3-0348-9961-1 ISBN 978-3-0348-9248-3 (eBook)
DOI 10.1007/978-3-0348-9248-3
NE: Rodriguez-Consuegra, Francisco A. [Hrsg.J
This work is subject to copyright. Ali rights are reserved, whether the whole or part of the
material is concerned, specifically the rights of translation, reprinting, re-u se 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.
© The copyright for the English language of the Godel-texts is held by The Institute for
Advanced Study, Princeton, U.S.A.
© 1995 Springer Base1 AG
Urspriinglich erschienen bei Birkhăuser Verlag 1995
Softcover reprint ofthe hardcover 1s t edition 1995
Printed on acid-free paper produced from chlorine-free pulp. TCF ~
Layout and design: Miriam Bussmann, Basel
987654321
Contents
Foreword by W.V. Quine 7
Acknowledgements 9
Introduction 11
Part I
Kurt Codel and the philosophy of mathematics
1. Realism, metamathematics and the
unpublished essays 17
2. The analytic-synthetic distinction 43
3. The mathematics-physics analogy 71
Bibliography 99
Part II
The unpublished essays
1. The character and origin of the manuscripts in the
present edition 109
2. Some basic theorems on the foundations of
mathematics and their philosophical implications (1951) 129
Codel's footnotes 149
Appendix: Loose fragments and footnotes 159
3. Is mathematics syntax of language?, II (1953-54?) 171
Codel's footnotes 191
4. Is mathematics syntax of language?, VI (1955-56?) 213
Editorial footnotes of comparison with version V 219
Index 223
Foreword
G6del's famous incompleteness theorem shows that no formal
proof procedure can reach every truth of mathematics, not even of
the elementary theory of positive integers. His proof of this theorem,
strictly mathematical of itself, wrought an abrupt turn in the philos
ophy of mathematics. We had supposed that truth, in mathematics,
consisted in provability.
G6del is celebrated in the philosophy of mathematics for this
great discovery and also three other philosophically significant re
sults, all strictly mathematical. Beyond these he published sundry
brief notes in technical logic, many reviews, and some speculations
on his friend Einstein's relativity physics, but of outright philosophy
he published virtually nothing.
It was new for philosophers, therefore, when G6del's Nachlass
was found to contain manuscripts on the philosophy of mathemat
ics, including even a substantial one on the philosophical bearing of
his theorems. This is one of the two that Dr. Rodriguez-Consuegra
has meticulously edited and presented in the present volume. At last
we can glimpse G6del's own philosophical adjustment to his bewil
dering discovery.
His philosophy of mathematics is at odds with the attitudes of
most latter-day philosophers who deal with mathematics and logic.
For him the abstract objects of mathematics are as real as sticks and
stones, and their laws are objective matters of discovery on a par with
those of physics. The other paper, written and repeatedly revised for
a volume of commentaries on Carnap but never submitted, brings
out these divergences very directly, for Carnap was a leading repre
sentative of the more dominant view.
Both manuscripts were tangles of revisions within revisions,
labyrinthine transpositions, cryptic abbreviations, smudged erasures.
These reflect G6del's continuing sense of not having got the philos
ophy quite to his satisfaction.
Clearly the deciphering and linearizing of the manuscripts and
the annotating of successive layers cost Dr. Rodriguez-Consuegra a
lot of drudgery and demanded much scholarly ingenuity and a deep
understanding of the subject. Rodrfguez-Consuegra is a bright new
light in the study of mathematical logic, set theory, and the philos
ophy of mathematics as these developed over the past twelve
decades. His painstaking analysis The Mathematical Philosophy of
Bertrand Russell: Origins and Development has already appeared as a
book in English (Birkhauser, 1991). With the present book he es
tablishes yet another milestone in Spain's impressive latter-day
progress in scientific philosophy.
W.V. Quine
Acknowledgements
In the Spanish edition of these manuscripts (Barcelona: Monda
dori, 1994) I already expressed my gratefulness to the following peo
ple, all of whom helped or encouraged me in connection with the
project: Francine Abeles, Jose Alfredo Amor, Irving Anellis, Ken
Blackwell, Irving Copi, John Corcoran, Mark Darby, John Dawson,
Solomon Feferman, Eugenio Gallego, Alejandro Garciadiego, Ivor
Grattan-Guinness, Nick Griffin, Jesus Hernandez, Ramon Jansana,
Faridah Kassim, Eckehart Kohler, Albert Lewis, Carlos Martin Vide,
Greg Moore, Javier Moreno, Roman Murawski, Javier Ordonez,
Charles Parsons, Klaus Puh!, Elliot Shore, Friedrich Stadler, Carlos
Soifs, Roberto Torretti, Luis Vega, and Zbigniew W. Wolkowski.
Also, special thanks were due to Ignacio Jane, for reading and
criticizing my introductory essay; Jose Manuel Sanchez Ron, who
first gave me the opportunity to write a book like this; Hao Wang,
for having read and approved my reconstruction of the Gibbs lecture,
and for generously having sent me a copy of his Conversations with
Code!, still unpublished; and Willard V. Quine, for his illuminating
remarks in conversation and correspondence, as well as for having
written the Foreword. My final thanks were due to Kurt Godel him
self, for having written such fascinating essays.
Regarding the present edition I am grateful to Juan Climent and
Enrique Trillas, who pointed out to me some errata in the previous
edition and suggested improvements. Also, to George Boolos, Mic
Detlefsen, and Ivor Grattan-Guinness, all of whom read parts - or the
whole - of the introductory essay and sent me remarks useful for im
proving it. Also, I would like to express my thanks to Ms. Baec
Birkhauser's language editor, for improving my English, and very es
pecially to Doris Worner, who approved the project of publishing this
book and was very patient with my delay in the delivery of the man
uscript. Finally, I am grateful to the help provided by the Spanish
grant DGICYT PS93-0220.
Departamento de Logica y Filosofia de la Ciencia
Universidad de Valencia
Introduction
Kurt Gbdel, together with Bertrand Russell, is the most impor
tant name in logic, foundations and philosophy of mathematics of
this century. However, although Russell devoted many pages to ar
ticulating his ideas in these and many other fields, Gbdel published
very little apart from his well-known writings in logic, metamathe
matics and set theory. His introverted personality inclined him away
from philosophical controversy, while his continuous search for de
finitively conclusive arguments in philosophy made it difficult for
him to publish his less conclusive writings. Thus, the sum of his pub
lished philosophical remarks runs to what is found in the papers on
Russell and Cantor and a few scattered remarks elsewhere.
Fortunately, Gbdel the philosopher, who devoted many more
years of his life to philosophy than to technical investigation, wrote
hundreds of pages on philosophy of mathematics, as well as on other
fields of philosophy. However, it seems that not even his closest col
leagues and friends were allowed to read those manuscripts, let alone
to discuss them. Only the opening of his literary estate in Princeton
for scholarly research, following the catalogization made from 1982
to 1984, have made it possible that all these materials may someday
appear in print.
The fundamental goal of this book is to make available to the
scholarly public solid reconstructions and editions of three of the
most important essays which Gbdel wrote on the philosophy of
mathematics. Since in chapter l/part II give details about the char
acter and origin of the manuscripts appearing here, as well as the par
ticulars about their present edition, I shall devote the rest of this in
troduction to a summary of the book as a whole.
I thought that many - perhaps most - of the readers would be
grateful if the Gbdel essays were accompanied by an introductory ap
paratus, devoted not only to the manuscripts themselves but also to
the philosophical context in which they were written. This led me
to divide the book into two parts, the first providing the reader with
that context, the second offering certain pertinent information re-
