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S. Leśniewski’s Lecture Notes in Logic PDF

190 Pages·1988·4.364 MB·English
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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. Kluwer Academic Publishers incorporates the publishing programmes of D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. 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

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