S. Leśniewski’s Lecture Notes in Logic

190 Pages·1988·4.364 MB·English

by  Jan T. J. Srzednicki, Zbigniew Stachniak

S. LESNIEWSKI'S LECTURE NOTES IN LOGIC
NIJHOFF INTERNATIONAL PHILOSOPHY SERIES
VOLUME 24
General Editor: Jan T.J. Srzednicki
Editor for volumes on Applying Philosophy: Lynne M. Broughton
Editor for volumes on Logic and Applying Logic: Stanislaw J. Surma
Editor for volumes on Contributions to Philosophy: Jan T.J. Srzednicki
Assistant to the General Editor: David Wood
Editorial Advisory Board:
R.M. Chisholm, Brown University, Rhode Island. Mats Furberg, Goteborg University.
D.A.T. Gasking, University of Melbourne. H.L.A. Hart, University College, Oxford.
S. Korner, University ofB ristol and Yale University. H.J. McCloskey, La Trobe University,
Bundoora, Melbourne . .T. Passmore, Australian National University, Canberra. A. Quinton,
Trinity College, Oxford. Nathan Rotenstreich, The Hebrew University of Jerusalem.
Franco Spisani, Centro Superiore di Logica e Scienze Comparate, Bologna. R. Ziedins,
Waikato University, New Zealand.
s.
Lesniewski's
Lecture Notes in Logic
Edited by
JAN T.J. SRZEDNICKI and ZBIGNIEW STACHNIAK
Kluwer Academic Publishers
DORDRECHT/BOSTON/LONDON
Library of Congress Cataloging in Publication Data
Lesniewski, Stanis~aw, 1886-1939.
S. Lesniewski's lecture notes in logic.
(Logic and applying logic) (Nijhoff international
philosophy series ; v. 24)
"List of seminars and courses delivered by
Lesniewski at Warsaw University between 1919 and 1939"; p.
Bibliography: p.
1. Logic, Symbolic and mathematical. I. Stachniak,
Zbigniew. II. Srzednicki, Jan T. J. Ill. Title.
IV. Title: Logic lecture notes. V. Series. VI. Series:
Nijhoff international philosophy series ; v. 24.
QA92.L4725 1987 511.3 86-23459
ISBN -13:978-94-0 I 0-7730-9 e-ISBN-13:978-94-009-2741-4
DOl: 10 .1007/978-94-009-2741-4
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
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In all other countries, sold and distributed
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All Rights Reserved
© 1988 by Kluwer Academic Publishers
Softcover reprint of the hardcover 1st edition 1988
No part of the material protected by this copyright notice may be reproduced or utilized in any form
or by any means, electronic or mechanical, including photocopying, recording, or by any information
storage and retrieval system, without written permission from the copyright owners.
The Lesniewski Collection
The Ballieu Library and the Philosophy Department of the University of
Melbourne have formed the LeSniewski Collection. This collection com
prises all materials published by Stanislaw Lesniewski during his lifetime,
and some unpublished materials in their original languages.
LeSniewski's works are being published in English translation in the
Nijhoff International Philosophy Series:
S. Lesniewski's Collected Works
Edited by J.T.J. Srzednicki, S.J. Surma and D. Barnett (in
preparation).
S. Lesniewski's Lecture Notes in Logic
Edited by J.T.J. Srzednicki and Z. Stachniak.
Contained in the present volume.
Together with:
S. LeSniewski's Systems
articles by various authors in two volumes:
- Ontology and Mereology
Edited by J.T.J. Srzednicki, V.F. Rickey and J. Czelakowski.
1984 (NIPS 13) ISBN 90-247-2879-7
- Protothetics
(in preparation)
As supporting service for researchers the Ballieu Library will on application, and payment
of a fee for costs, provide micro-fiche copies of the Lesniewski originals in the original
languages. Applications can be made to:
Philosophy Department, University of Melbourne or to:
The Ballieu Library, University of Melbourne,
Parkville 3052, Victoria, Australia.
Contents
Translator's Foreword IX
PART ONE: FOUNDATIONS OF MATHEMATICS
1. From the foundations of Protothetic 3
2. Definitions and theses of Lesniewski's Ontology 29
3. Class theory 59
PART TWO: PEANO ARITHMETIC AND WHITEHEAD'S
THEORY OF EVENTS
4. Primitive terms of arithmetic 129
5. Inductive definitions 153
6. Whitehead's theory of events 171
List of seminars and courses delivered by Lesniewski at Warsaw
University between 1919 and 1939 179
Bibliography 181
VII
Translator's Foreword
Stanislaw Lesniewski (1886-1939) was one of the leading Polish logicians and
founders of the Warsaw School of Logic whose membership included, beside
himself, Jan Lukasiewicz, Tadeusz Kotarbinski, Alfred Tarski, and many others.
In his lifetime LeSniewski published only a few hundred pages. He produced
many important results in many areas of mathematics; these stood in various
relations to each other, and to materials produced by others, and, in time, created
more and more editorial problems. Very many were left unpublished at the time
of his death. Then in 1944 in the fire of Warsaw the whole of this material was
burned and lost - a considerable loss since a great deal of what is important could
have been reconstructed from these notes.
The present publication aims at presenting unique Lesniewski's materials
from alternative sources comprising lecture notes taken during some of
Lesniewski's lectures and seminars delivered at the University of Warsaw be
tween the two world wars. The editors are aware of the limitations of student
notes which cannot compensate for the loss of the original materials. However,
they are unique in reflecting Lesniewski's ideas as he himself presented them.
Already at the time of his death it was realized that these notes would provide a
unique access to Lesniewski's own thought as well as a valuable record of some of
the activities of the Warsaw School of Logic.
At that time there were many sets of notes available, taken, among others, by
Bilich, Choynowski, Hiz, Kreczmer, Lejewski, and Sobocinski. These notes were
carefully edited, checked against each other, added to and copied, but eventually,
in August and September of 1944, most of them shared the fate of the original
materials left by Lesniewski himself. These that, almost miraculously, survived
constitute the present volume.
I saw these notes first in 1981 and was impressed by their precision, depth, and
attention to detail. From the three hundred pages one gathered the impression of
serious and responsible dedication to research and of unwavering dedication to
truth. In late 70's Slupecki entrusted these handwritten notes to the Polish
Academy of Sciences. Kotarbinski, who originally made an attempt to publish
them, handed the notes to Slupecki when that project failed. At that time the
IX
notes were physically present, but it was not known who had taken them, when
they were taken, who collected the notes, and how they came into Kotarbinski's
possession. It also seemed unlikely that these questions would ever be answered.
Sobocinski died in 1980, Kotarbinski in 1981, Slupecki and Tarski were by then
too frail to provide robust help in the search. There were only two clues, the item
From the Foundations of Protothetic was signed Mieczyslaw Choynowski, and
the handwriting matched. Henryk Hiz suggested that Choynowski was the
author and eventually he was proved right.
Choynowski attended Lesniewski's lectures for at least three years, from 1932,
and he took notes from the courses devoted to protothetic, ontology, and
inductive definitions, all of them presented in this book. During early years of the
Second World War, 1940-1942, he carefully copied various notes taken by
Lesniewski's former students (mainly by Sobocinski), putting an enormous
amount of work, knowledge, and responsibility into the project. Throughout the
war years his notes served as a unique source from which the knowledge of
Lesniewski's work and ideas was extensively drawn by others. 'These notes had
played a significant role in my development. For two years, during the War, they
were on my desk, and I was supplementing my knowledge about Lesniewski's
ideas with them.' recalled Hiz. After the War, Choynowski gave the notes to
Kotarbinski, presumably influenced by Kotarbinski's idea to publish the collec
ted works of LeSniewski, but Choynowski does not remember the details. And
this is how the story ends.
Choynowski's notes consist almost entirely of definitions and theorems, and
this can partially be explained by reference to Lesniewski's style of lecturing.
Usually, he began by searching for a sheet of paper with a formal, or rather
symbolic, part of a lecture on it, in his big (always packed to the limit) brief-case.
Then, he checked and orally sketched a proof, or a problem, finishing with 'so, it
goes', and then, with great care, he started writing on the blackboard. Lesniewski
preferred discussion or workshop style of teaching to the formal lecturing
method, and when he 'got onto a problem', as he would say, he spent as much
time on it as its complete analysis required, often leaving the designated course in
ruins. 'He was far from sacrificing research work and invention for his duties as a
teacher. He was convinced that to teach well one had first of all to possess a
thorough knowledge of the subject which one intended to teach. Outside of that
the whole didactic skill was for him stuff and nonsense. Thorough knowledge
implied perfectly clear thinking ... So, whatever he had to say, he crammed it into
his listeners' brains ignoring time and the fact that many students would rather
move forth with the subject-matter at a quicker pace.'!
From Kotarbiilski [1965].
1
x
The present book is divided into two parts, each consisting of three lecture
notes. Part one includes lecture notes presenting Lesniewski's system of the
foundations of mathematics. The lecture notes constituting the second part are
devoted to the system of Peano arithmetic and Whitehead's theory of events. The
joint bibliography, as well as the list of courses and seminars delivered by
Lesniewski at the Warsaw University between 1919 and 1939, is placed at the end
of the book. All lecture notes have been provided by the translator with short
introductions (quotes from Lesniewski's writings) and are followed by editorial
notes. The underlying principle assumed by the editors was to present unab
ridged and complete texts of the notes, preserving their original structures as well
as their content. Some parts of the notes which were visibly incomplete, am
biguous, or accidentally arranged, have either been supplemented with com
ments (enclosed in square brackets), replaced, or included as comments. In search
for a reasonable compromise between the desire for uniformity of notation, and
the desire to conform to all the original sources, only the structure and a
graphical form of theorems and their proofs, as well as some logical and metalog
ical notations have been dovetailed.
The present book does not contain all the lecture notes available to the
editors. The notes entitled Russell's Antinomy, compiled by Choynowski from his
own and Mostowski's notes taken during the seminar in 1935, have proven to be
an incomplete summary of Lesniewski's analysis of Russell's antinomy actually
published by LeSniewski in 0 Podstawach M atematyki. 2 Further, some notes
taken by J. Drewnowski during one of Lesniewski's earliest courses on ontology
are in the possession of the Department of Logic at KUL University, Lublin,
Poland, and will be published by KUL in the near future.
Many people have contributed their efforts to the completion and to the
improvement of this book. I would like to express my deep gratitude to Profes
sors Mieczyslaw Choynowski, Henryk Hiz, Boguslaw Iwanus, Czeslaw Lejewski,
Christopher Reynolds, Jerzy Slupecki, and to my wife Ewa Stachniak for her help
and patience.
ZBIGNIEW STACHNIAK
2 Cf. Lesniewski [1927-31], XXX, vide S. Lesniewski's Collected Works (ed.) Surma,
Srzednicki, Barnett. NIPS forthcoming.
XI
PART ONE
Foundations of Mathematics