Table Of Contentsecond edition
LOGIC, SEMANTICS,
METAMATHEMATICS
PAPERS FROM 1923 TO 1938
BY
ALFRED TARSKI
TRANSLATED BY
J.H. WOODGER
Second edition edited and
introduced by JoHN CoRcORAN
HACKETT PUBLISHING COMPANY
First edition published in 1956 by Oxford University Press
Copyright © 1983 by Hackett Publishing Company,I nc.
All rights reserved
Printed in the United States of America
10 09 08 07 «45678
For further information, please address
Hackett Publishing Company,I nc.
P.O. Box 44937
Indianapolis, Indiana 46244-0937
Library of Congress Cataloging in Publication Data
Tarski, Alfred.
Logic, semantics, metamathematics.
Includes bibliographical references and indexes.
1, Logic, Symbolic and mathematical—Addresses,
essays, lectures. 2. Semantics (Philosophy) —
Address, essays, lectures. 1. Corcoran, John.
II. Title.
BC135.T35 1983 160 83-10850
ISBN 0-915144-75-1
ISBN-13: 978-0-915144-75-4 (cloth)
The paper used in this publication meets the minimum requirements of
American National Standard for Information Sciences—Permanence of
Paper for Printed Library Materials, ANSI Z39.48-1984.
TO THE MEMORY OF
HIS TEACHER
TADEUSZ KOTARBINSKI
THE AUTHOR
EDITOR’S PREFACE
TO THE REVISED EDITION
THE revised edition is intended to supersede the first edition in several
respects. Two considerations which guided the design of the revisions were
(1) the desire to increase the accuracy andc larity of the articles without
altering their usefulness as historical documents and (2) the need to
make Tarski’s early thought more accessible to the current generation
of linguists, logicians, mathematicians, philosophers, and historians. The
Editor’s Introduction and the Analytical Index are new with this edition.
The Editor’s Introduction shows how Tarski’s development of much of
the modern framework of logic and methodology can be traced in the
articles in this volume. The Analytical Index is much more than a guide
to locations of terms; it is as much an indexo f ideas as of terminology, and
it lists, besides terms used by Tarski, not only current synonyms for the
terminology of the articles, but also current terms for ideas used by but
not named by Tarski.
Included in this edition are all seventeen articles collected in the first edi-
tion. All of the front material of the original has been retained unchanged.
Several items have been addedt o the bibliography. Over 150 pages have
been altered in various ways. The fact that Tarski had been unable to
read a considerable part of the original text before publication accounts
for many of the changes. Some changes in wording were neededf or sake of
clarity, uniformity, or precision. Typographical errors, in prose and in
mathematical formulas, have been corrected (although there were fewer
of these than would have been expected given the complexity of the work).
In several places, whole sentences have been rewritten in order to elimi-
nate ambiguity or misleading connotations and in somep laces, where more
extensive rewriting would have been called for, footnotes have been added
indicating the nature of the difficulty.
The bibliographical note attached to the “Wahrheitsbegriff” (article
VIII) has been rewritten as hast he first paragraph oft his article’s his-
torical note. Postscripts have been addedt o articles IV and V. Various
new historical references have been inserted as footnotes.
There was cross-referencing among the original articles which wass ig-
nificantly increased in the translations and increased even more in the
present edition.
All the rewriting was done by Tarski andt he final form of every change
has received Tarski’s explicit approval. Tarski prepared over fifty single-
spaced pages of changes which have been incorporated into the present
text. In addition, with the help of M. Scanlan (Oregon State University),
viii EDITOR’S PREFACE
H. G. Bohnert (Michigan State University) and H. Hiz (University of
Pennsylvania), I prepared hundreds of suggestions to which Tarski re-
spondedi n writing, by phone, or in conversation. S. Givant (Mills College)
assisted Tarski.
Various methods to identify changed passages were considered and
found to be too awkward, too expensive, and too time consuming, espe-
cially in light of the fact that changes in the articles as originally written
had beeni ntroduced already in thef irst edition. For example, it is some-
times difficult to determine whether phrasing, terminology, and restruc-
turing of a sentence to conform to the needso f a different language could
conceal subtle changes in viewpoint. For most scholarly purposes this
edition can be regarded as an authoritative substitute for the first edition.
However, writers involved in delicate historical questions may need to
consult the original papers themselves as event he first edition may prove
insufficient for such purposes.
Je;
IN this printing, the third of the second edition, all errata that had come to
my attention have been corrected. These corrections are added to those
madei n the secondp rinting. Noneo f the errata would have required Tarski’s
attention. Thanks go to S. Nambiar, P. Chen, andK . Herreid (all of the Uni-
versity of Buffalo) as well as to M. Schirn (University of Munich) who
detected a missing fourteen-word (fifteen in the Germano riginal) passage
on p. 172 in the course of comparing the English translation of the
Wahrheitsbegriff with the original German text. Thet ranslation oft he pre-
viously missing passage, which appearsa s a newf ootnote, is by Professor
Schirn.
J. C., 1997
Editorial Note to the Fourth Printing: Shortly following the 1983 first
printing of the second edition, all of the papers translated here were
reprinted in their original untranslated form in the 1986 four-volume
work, Alfred Tarski: Collected Papers, Basel, Birkhauser, edited by S.G i-
vant and R. McKenzie. The entire four volumes were reviewed in 1991 in
Mathematical Reviews [MR 91h: 01101-4]. Of course, the secondaryl itera-
ture on Tarski has continued to grow; especially notable is the 2004 biog-
raphy, Alfred Tarski Life and Logic, by A. Feferman and S. Feferman,
Cambridge University Press.
Several logicians made suggestions for corrections in this printing;
special thanks go to J. Gasser (Lausanne), D. Hitchcock (Hamilton),
A. Koslow (New York), F Nabrasa (Sarasota), J. Sagiiillo (Santiago de
Compostela), R. Santos (Lisbon), and P. Simons (Leeds).
J. C., 2006
TRANSLATOR’S PREFACE
Tue setting free of Poland after the First World War wasf ol-
lowed byi ntensive activity in her Universities. In the depart-
ments of philosophy and mathematics this took the form, in a
number of places, of new and powerful investigations in the
fields of mathematical logic, the foundations of mathematics,
and the methodology of the sciences. Prominent in this, move-
ment was the Warsaw school led by Lukasiewicz, Kotarbinski,
and Lesniewski. Undert heir skilled guidance a younger genera-
tion grew up and among these Alfred Tarski quickly dis-
tinguished himself.
Evers ince I first enjoyed the hospitality of Professor Tarski
in Warsaw in 1936, it has seemed to me that the importance
and scope of the Polish school of logicians were insufficiently
known and appreciated in the English-speaking world. Then
came the Second World War, bringing ruin once moret o Poland,
killing men, destroying laboratories, and burning manuscripts
and libraries. After this war it occurred to me that I should be
performing a public service, as well as acknowledging in some
small measure my debt to my Polish friends, if I prepared a
collected edition of some of Professor Tarski’s publications in
English translation. When hev isited England in 1950 to deliver
the Sherman Lectures at University College, London, I men-
tioned my plan to him and received his approval.
This volume contains Tarski’s major contributions to logic,
semantics, and metamathematics published before the Second
World War; their arrangement here corresponds to the chrono-
logical order in which they first appeared in print. With the
exception of articles II and XI (which are too closely connected
with, and too often referred to in, the other articles to be
omitted), the volume does not include Tarski’s studies in the
foundations of special mathematical disciplines—set theory,
group theory, etc. Neither does it contain his papers of a
pronouncedly mathematical character, dealing with special
topics from the domain of set theory, measure theory, abstract
algebra, elementary geometry, etc. Also excluded are short
notes, abstracts, and preliminary reports which are closely
related to some of the articles included in the volume and the
contents of which are more fully presented in these articles.
x TRANSLATOR’S PREFACE
A longer paper from the domain of logic and methodology
which has been omitted is ‘Sur la méthode déductive’ in Travaux
du IX* Congrés International de Philosophie (Paris 1937); this
paper is a purely expository one, and its ideas have been fully
developed in Chapter VI of Tarski’s book Introduction to logic
(New York, 1941).
In a sense the present work is more than a volumeo f transla-
tions. Naturally an attempt has been made to remove the
misprints and errors which occuri n the originals. Moreover, the
articles have been provided by the author with cross-references
to other articles in the volume and with notes referring to later
developments and recent literature. Occasionally some new
remarks have been added for the purpose of clarifying certain
passages in the original text. Articles II and VI contain more
serious changes, Tarski having inserted in them several passages
which, he hopes, will help toc larify and amplify their contents.
While the work of translation was in progress, the passages
which seemed to me doubtful and difficult were noted down and
sent to Professor Tarski in Berkeley, California. In this way it
was possible to adjust the text of the translations in many
points, so as to meet the author’s wishes. However, in view of
the time limit and the geographical distance between ther esi-
dences of the author and the translator, it was impracticable to
send the whole manuscript to Professor Tarski before it was
set in print. Instead he received galley proofs, on which for
obvious reasons he could not suggest too extensive changes. It
also proved impossible to discuss the suggested changes in
detail, and it was left to my decision which changes were
actually to be carried through. Thus Professor Tarski is not
responsible for the final text or the technical aspect of the book.
Three articles in this volumea re joint publications of Tarski
and other authors: Professor C. Kuratowski (article VII), Dr.
A. Lindenbaum (article XIII), and Professor J. Lukasiewicz
(article IV). We are greatly obliged to Professors Kuratowski
and Lukasiewicz for their permission to include the translations
of the jointly published articles in the volume, Dr. Lindenbaum
fell a victim to the Gestapo during the war.
The papers included in the volume originally appeared in the
following periodicals and collective works: Actes du Congrés
International de Philosophie Scientifique (articles XV and XVI),
Comptes Rendus de la Société des Sciences et des Lettres de Varsovie
TRANSLATOR’S PREFACE xi
(articles III and IV), Ergebnisse eines mathematischen Kol-
loquiums (articles XIII and XIV), E'rkenntnis (article X), Funda-
menta Mathematicae (articles I, VI, VII, XI, XII, and XVII),
Ksiega Pamiqtkowa Pierwszego Polskiego Zjazdu Matematycznego
(article II), Monatshefte fiir Mathematik und Physik (articles V
and IX), Przeglad Filozoficzny (articles I, X, XV, and XVI), and
Travaux de la Société des Sciences et des Lettres de Varsovie
(article VIII). Acknowledgements should be made to the pub-
lishers and editors of these periodicals for their generosity.
I am obliged to Mr. 8. W. P. Steen for kindly reading the
proofs of article VIII and throughout the work I have received
much help from my son, Michael Woodger. Wea re also indebted
to several colleagues and students of Professor Tarski—Dr.
C. C. Chang, Professor A. C. Davis, Professor J. Kalicki, Mr.
R. Montague, Professor J. Myhill, Professor D. Rynin, and Mr.
D. Scott—for their assistance in revising the original text of the
articles and in reading galley proofs.
Finally it is a pleasure to acknowledge the courtesy and help
which we have received from the staff of the Clarendon Press at
all stages in the production of the book.
J. H.W.
