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Bfm:978-3-319-65430-0/1.Pdf Studies in Universal Logic Series Editor Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council, Rio de Janeiro, Brazil) Editorial Board Members Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary) Mark Burgin (University of California, Los Angeles, USA) Razvan˘ Diaconescu (Romanian Academy, Bucharest, Romania) Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France) Arnold Koslow (City University of New York, USA) Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan) Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia) Grzegorz Malinowski (University of Łód´z, Poland) Francesco Paoli (University of Cagliari, Italy) Darko Sarenac (Colorado State University, Fort Collins, USA) Peter Schröder-Heister (University Tübingen, Germany) Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia) This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discussions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers. More information about this series at http://www.springer.com/series/7391 Ángel Garrido • Urszula Wybraniec-Skardowska Editors The Lvov-Warsaw School. Past and Present Editors Ángel Garrido Urszula Wybraniec-Skardowska UNED Cardinal Stefan Wyszynski´ University Department of Fundamental Mathematics in Warsaw Madrid, Spain Warsaw, Poland ISSN 2297-0282 ISSN 2297-0290 (electronic) Studies in Universal Logic ISBN 978-3-319-65429-4 ISBN 978-3-319-65430-0 (eBook) https://doi.org/10.1007/978-3-319-65430-0 Library of Congress Control Number: 2018943846 Mathematics Subject Classification (2010): 01A72, 03-03 © Springer International Publishing AG, part of Springer Nature 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This book is published under the trade name Birkhäuser, www.birkhauser-science.com by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland Preface This book is about the Lvov-Warsaw School. I did not “order” this book, but I am very glad to have received this proposal and the book to be published in a book series I have created inspired by this school. The Lvov-Warsaw School is one of the most important schools in the history of logic but is still not very well known outside of Poland and a circle of aficionados. This book with contributions about the main members of this school and their works will certainly help to fill the gap, reinforcing the already existing attraction and promoting new interests for this school. I would like to thank the editors of this book, Urszula and Angel, for their considerable efforts to gather all the papers included in this big volume, as well as all the contributors of this book and Birkhäuser staff in Basel. Editor-in-Chief Jean-Yves Beziau Studies in Universal Logic Rio de Janeiro, Brazil December 19, 2017 v Contents Part I Twardowski’s School: The Period of Crystallization of LWS Introduction. The School: Its Genesis, Development and Significance ..... 3 Urszula Wybraniec-Skardowska 1 A Short History and Influence of the School . 4 2 On the Structure and Contents of the Anthology . 13 References......................................... 13 Kazimierz Twardowski: A Great Teacher of Great Philosophers ........ 15 Anna Bro˙zek 1 Life.......................................... 15 2 Personality . 16 3 Writings........................................ 17 4 Views......................................... 17 5 Philosophical School . 30 6 Conclusions..................................... 31 KazimierzTwardowski’sWorksMentionedinthePaper............... 32 Jan Łukasiewicz: A Creator of New Ideas in Logic and a Reinterpreter of Its History ....................................... 33 Jacek Jadacki 1 Personality . 33 2 Life.......................................... 34 3 Works......................................... 35 4 Metaphysics . 35 5 Logic......................................... 37 6 Methodology . 42 7 Teacher . 44 JanŁukasiewicz’sWorksMentionedinthePaper................... 45 vii viii Contents Kazimierz Ajdukiewicz: The Cognitive Role of Language ............ 47 Anna Jedynak 1 Life.......................................... 47 2 MainPublications.................................. 48 3 ScientificActivity.................................. 48 4 DisciplesandContinuators............................. 60 References......................................... 60 On Ajdukiewicz’s Project of the Semantic Theory of Knowledge ........ 65 Adam Olech 1 Introduction . 66 2 Presentation of the Meta-Epistemological Project of the Semantic TheoryofKnowledgeandAnalysisThereof................... 70 3 Conclusion...................................... 87 References......................................... 88 Categorial Grammars and Their Logics ....................... 91 Wojciech Buszkowski 1 Introduction . 91 2 BasicCategorialGrammars............................. 93 3 LambekCalculus................................... 98 References......................................... 112 Material Implication and Conversational Implicature in Lvov-Warsaw School ........................................... 117 Rafal Urbaniak and Michał Tomasz Godziszewski 1 Ajdukiewicz’s Equivalence Argument . 117 2 Jackson’sArgument................................. 118 3 Ajdukiewicz on Disjunction . 119 4 Ajdukiewicz vs. Quine on Assertibility . 121 5 Expressingvs.Stating................................ 123 6 Ajdukiewicz on the Diagnostics of Improper Use . 124 7 Generalization, Weakening, Moore’s Paradox . 125 8 ApparentConnectionBetweenDisjuncts..................... 125 9 Ajdukiewicz’s Diagnostics and Grice’s Cancellability . 127 10 Goła¸bonIndicativeConditionals.......................... 130 11 Słupecki’s Reply to Goła¸b............................. 131 12 Ajdukiewicz’s Solution and Goła¸b’sProblem................... 131 References......................................... 132 Tadeusz Cze˙zowski .................................... 133 Dariusz Łukasiewicz 1 Life.......................................... 133 2 MainPapers..................................... 135 3 Views......................................... 135 4 Resonance...................................... 135 5 Pupils......................................... 135 6 Summary....................................... 136 Bibliography........................................ 136 Contents ix Tadeusz Cze˙zowski’s Theory of Knowledge and Beliefs .............. 137 Dariusz Łukasiewicz 1 Introduction . 137 2 Modern Epistemological Individualism: Faith and Testimony inEpistemologicalFramework........................... 138 3 Methodism, Particularism and Belief-Formation Process . 141 4 What Can Justify Beliefs: Basic Beliefs, Internalism and Externalism . 142 5Cze˙zowski’s Theory of Knowledge and Epistemological Individualism . 143 6Cze˙zowski’s Internalism and Fallibilism . 147 7Cze˙zowski and Some Views on Belief-Formation Processes . 149 References......................................... 151 What Is Reasoning? ................................... 153 Robert Kublikowski 1 Introduction . 153 2 The Definition of Reasoning . 155 3 The Conditions of Correctness of Reasoning . 157 4 Conclusions..................................... 162 References......................................... 162 Tadeusz Kotarbinski:´ Socrates of Warsaw ...................... 165 Jacek Jadacki 1 Life.......................................... 165 2 Writings........................................ 166 3 Views......................................... 166 4 Resonance...................................... 170 5 Pupils......................................... 173 6 Summary....................................... 173 Tadeusz Kotarbinski’sWorksMentionedinthePaper.................´ 173 Agency in a Praxiological Approach ......................... 175 Wojciech W. Gasparski 1 Introduction
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