Studies in Universal Logic

Transcription

1

2 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) Răzvan 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 Łódź, 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

3 Ángel Garrido Urszula Wybraniec-Skardowska Editors The Lvov-Warsaw School. Past and Present

4 Editors Ángel Garrido UNED Department of Fundamental Mathematics Madrid, Spain Urszula Wybraniec-Skardowska Cardinal Stefan Wyszyński University in Warsaw Warsaw, Poland ISSN ISSN (electronic) Studies in Universal Logic ISBN ISBN (ebook) Library of Congress Control Number: Mathematics Subject Classification (2010): 01A72, 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, by the registered company Springer International Publishing AG part of Springer Nature. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

5 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 Studies in Universal Logic Rio de Janeiro, Brazil December 19, 2017 Jean-Yves Beziau v

6 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 On the Structure and of the Anthology References Kazimierz Twardowski: A Great Teacher of Great Philosophers Anna Brożek 1 Life Personality Writings Views Philosophical School Conclusions KazimierzTwardowski sworksmentionedinthepaper Jan Łukasiewicz: A Creator of New Ideas in Logic and a Reinterpreter of Its History Jacek Jadacki 1 Personality Life Works Metaphysics Logic Methodology Teacher JanŁukasiewicz sworksmentionedinthepaper vii

7 viii Kazimierz Ajdukiewicz: The Cognitive Role of Language Anna Jedynak 1 Life MainPublications ScientificActivity DisciplesandContinuators References On Ajdukiewicz s Project of the Semantic Theory of Knowledge Adam Olech 1 Introduction Presentation of the Meta-Epistemological Project of the Semantic TheoryofKnowledgeandAnalysisThereof Conclusion References Categorial Grammars and Their Logics Wojciech Buszkowski 1 Introduction BasicCategorialGrammars LambekCalculus References Material Implication and Conversational Implicature in Lvov-Warsaw School Rafal Urbaniak and Michał Tomasz Godziszewski 1 Ajdukiewicz s Equivalence Argument Jackson sargument Ajdukiewicz on Disjunction Ajdukiewicz vs. Quine on Assertibility Expressingvs.Stating Ajdukiewicz on the Diagnostics of Improper Use Generalization, Weakening, Moore s Paradox ApparentConnectionBetweenDisjuncts Ajdukiewicz s Diagnostics and Grice s Cancellability Goła bonindicativeconditionals Słupecki s Reply to Goła b Ajdukiewicz s Solution and Goła b sproblem References Tadeusz Czeżowski Dariusz Łukasiewicz 1 Life MainPapers Views Resonance Pupils Summary Bibliography

8 ix Tadeusz Czeżowski s Theory of Knowledge and Beliefs Dariusz Łukasiewicz 1 Introduction Modern Epistemological Individualism: Faith and Testimony inepistemologicalframework Methodism, Particularism and Belief-Formation Process What Can Justify Beliefs: Basic Beliefs, Internalism and Externalism Czeżowski s Theory of Knowledge and Epistemological Individualism Czeżowski s Internalism and Fallibilism Czeżowski and Some Views on Belief-Formation Processes References What Is Reasoning? Robert Kublikowski 1 Introduction The Definition of Reasoning The Conditions of Correctness of Reasoning Conclusions References Tadeusz Kotarbiński: Socrates of Warsaw Jacek Jadacki 1 Life Writings Views Resonance Pupils Summary Tadeusz Kotarbiński sworksmentionedinthepaper Agency in a Praxiological Approach Wojciech W. Gasparski 1 Introduction Agency in Tadeusz Kotarbiński sapproach OtherApproaches Conclusion References Zygmunt Zawirski: A Creator of New Ideas in Methodology of Science and Scientific Metaphysics Krzysztof Śleziński 1 Life Writings Views Resonance Pupils Summary ZygmuntZawirski sworksmentionedinthepaper

9 x Zygmunt Zawirski s Concept of Scientific Metaphysics Krzysztof Śleziński 1 Introduction Relation Between Science and Metaphysics Synthesis of Human Knowledge and Metaphysics References Stanisław Leśniewski: Original and Uncompromising Logical Genius Peter Simons 1 Life PhasesofActivity EarlyWritings Antinomies,Classes,Parts Formalization ConsolidationandPublication FinalYears Metalogic Teaching and Students Colleagues and Personality Legacy Stanisław Leśniewski sworksmentionedinthepaper Izydora Dambska: The First Lady of the Twentieth-Century Polish Philosophy Anna Brożek and Jacek Jadacki 1 Personality Life Work The Lvov-Warsaw School Versus Neopositivism and Linguistic Philosophy Metaphysics Semiotics Methodology Axiology Significance Izydora Dąmbska sworksmentionedinthepaper Maria Kokoszyńska-Lutmanowa: The Great Polemist Filip Kawczyński 1 Life MainPapers Views Pupils Summary References

10 xi Seweryna Łuszczewska-Romahnowa Roman Murawski and Jerzy Pogonowski 1 Life MainWorks Views Resonance Pupils Summary References On Existential Dependence and Independence in the World of Thoughts and States of Affairs (with Reference to Eugenia Ginsberg-Blaustein s and Roman Ingarden s Analyses) Urszula M. Żegleń 1 Introduction Ingarden sdefinitionsandtheorems Dependence in the Mental Sphere of Thoughts ConcludingRemarks References Józef I.M. Bocheński Korneliusz Policki 1 Life MainResearchInterests Bocheński sviews Reactions Criticism Summary J.M. Bocheński s Theory of Signs Korneliusz Policki 1 Introduction OntologicalAssumptions PsychologicalAssumptions TheConceptoftheSign TheTheoryofSignsandAuthority The Theory of Signs and Philosophical Superstitions Conclusion References Jan Salamucha ( ) Kordula Świętorzecka 1 Beginnings Education Didactics Priesthood Death

11 xii 6 IntellectualFormation SelectedPublications Struve and Biegański: Towards Modern Approach to Logic Roman Murawski 1 HenrykStruve Władysław Biegański Conclusion References Part II Warsaw School of Logic, Its Main Figures and Ideas: The Period of Prosperity Łukasiewicz and His Followers in Many-Valued Logic Grzegorz Malinowski 1 Łukasiewicz swaytomany-valuedness MatrixSemanticsforn-ValuedLogics Post Logics and Słupecki s Functional Completeness Programme AlgebraicInterpretationsofŁukasiewiczLogics InSearchforInterpretationofŁukasiewiczLogics On Applications and Influence of Łukasiewicz Work References Tomorrow s Sea-Battle and the Beginning of Temporal Logic Kazimierz Trzęsicki 1 Introduction Language and Semantics BranchingTimeLogic TemporalLogicofPossibleWorlds Conclusion References Leśniewski and Mereology Peter Simons 1 HowLeśniewskiCametoMereology Leśniewski sunderstandingofsetsorclasses Terminology TheEarlySystem Remarks About This System SymbolicReconstruction LaterImprovements Whitehead salternativemereology ThePolishContinuation TheHarvardVariant SubsequentDevelopments Prospects References

12 xiii Alfred Tarski ( ) Jan Woleński Bibliography Some Philosophical Aspects of Semantic Theory of Truth Jan Woleński References Tarski s Influence on Computer Science Solomon Feferman References The Absence of Multiple Universes of Discourse in the 1936 Tarski Consequence-Definition Paper John Corcoran and José Miguel Sagüillo 1 Introduction Corcoran s Awareness of the Issue in the 1960s and 1970s The Place of the Monistic-Pluralistic Distinction The Origin of the Modern form of the Monistic Framework ConcludingRemarks References Alfred Tarski: Auxiliary Notes on His Legacy Jan Zygmunt 1 Life SetTheory GeometryandMeasureTheory DecidableandUndecidableTheories SelectedWorksofTarski Stanisław Jaśkowski: Life and Work Andrzej Indrzejczak 1 Life Works Influence References Stanisław Jaśkowski and Natural Deduction Systems Andrzej Indrzejczak 1 Introduction NaturalDeductioninGeneral Jaśkowski sresearchonnd OtherApproachestoND References

13 xiv Variations on Jaśkowski s Discursive Logic Barbara Dunin-Kęplicz, Alina Powała, and Andrzej Szałas 1 Prelude Theme:Jaśkowski s Discursive Logic D Movement:BeliefBasesandBeliefStructures Variations Part I: D 4 A New Framework for Discursive Logics Variations Part II: Relation to Dialogue Variations Part III: Relation to Argumentation Coda References Czesław Lejewski: Propagator of Lvov-Warsaw Ideas Abroad Peter Simons 1 Life MainWorks Views Influence, Teaching, Personality WorksbyCzesławLejewskiMentionedinthePaper Adolf Lindenbaum, Metric Spaces and Decompositions Robert Purdy and Jan Zygmunt 1 Introduction AShortLife Metric Spaces Decomposition of Point Sets, and Their Equivalence by Decomposition Decompositions and Equivalence of Polygons in Elementary Geometry Bibliography Acknowledgments Andrzej Mostowski: A Biographical Note Marcin Mostowski 1 Life MainWorks MainScientificAchievements InfluenceofHisWorks Students LastWords References Foundations and Philosophy of Mathematics in Warsaw, the School of Andrzej Mostowski and Philosophy Marcin Mostowski 1 Introduction Some Mathematical Works in the Foundations Old School and Old Ideas The Old School and New Ideas: Computations What for Philosophy? WhoIsYourMaster? References

14 xv Jerzy Słupecki ( ) Jan Woleński ReferencesandBibliography Rejection in Łukasiewicz s and Słupecki s Sense Urszula Wybraniec-Skardowska 1 Introduction Reconstruction of Concepts of Rejection and Decidability: The Notions IntroducedandUsedbyŁukasiewicz The Problem of Decidability of Aristotle s Syllogistics, Set by Łukasiewicz,andItsSolutionGivenbySłupecki Notions of Rejection in a Deductive System and Notions of Ł-Decidability More Important Findings Concerning Ł-Decidability of Deductive Systems RejectionOperation RejectionOperationasaPrimitiveNotion References Bolesław Sobociński: The Ace of the Second Generation of the LWS Kordula Świętorzecka 1 Life NationalService AcademicCareer InterestsandAchievements Sobociński Personality Selected Publications by Bolesław Sobociński References Bolesław Sobociński on Universals Kordula Świętorzecka and Marek Porwolik 1 Leśniewski s Nominalist Argumentation in Sobociński s Version Sobociński smetaconceptualism References Many-Valued Logics in the Iberian Peninsula Angel Garrido 1 Introduction Many-Valued Logics and the Lvov-Warsaw School Reception of Many-valued Logics and Fuzzy Logic in the Iberian Peninsula FinalNote References Ontology of Logic and Mathematics in Lvov-Warsaw School Roman Murawski 1 JanŁukasiewicz:(Neo)Platonism Stanisław Leśniewski:Nominalism AlfredTarski:Nominalism

15 xvi 4 Tadeusz Kotarbiński:Reism LeonChwistek:Nominalism Kazimierz Ajdukiewicz and Ontology of Mathematics Andrzej Mostowski: Nominalism, Reism, Constructivism Conclusion References Part III The War and Post-War Period A View of Revival of Mathematical Logic in Warsaw, Victor W. Marek 1 Introduction TheBeginnings AndrzejMostowskiandHisStudents HelenaRasiowaandHerGroup AndrzejGrzegorczyk Conclusions References Andrzej Mostowski and the Notion of a Model Wilfrid Hodges 1 TheEmergenceofaNewDiscipline Mostowski swritingsinmodeltheory Background and Notation Some of Tarski s Proposals Theories Models Thirty Years of Foundational Studies Robinson scomplaint Mostowski sattributionsingeneral Conclusion References All Quantifiers Versus the Quantifier All Stanisław Krajewski 1 TheUniversalQuantifierandItsDual A Digression on the Range of the Familiar Quantifiers ThePowerof and GeneralizedQuantifiersinLogic Characterizing Context-Independent Quantifiers Formalism-Free Definition of -DefinableQuantifiers? References Helena Rasiowa ( ) Andrzej Jankowski and Andrzej Skowron References

16 xvii Post Algebras in the Work of Helena Rasiowa Ewa Orłowska 1 PlainSemi-PostAlgebras PostAlgebrasofOrderm Post Algebras of Order ω Post Algebras of Order ω + ω References Andrzej Grzegorczyk, a Logician Par Excellence Stanisław Krajewski 1 Life LogicalAccomplishments Views Influence References A Mystery of Grzegorczyk s Logic of Descriptions Joanna Golińska-Pilarek and Taneli Huuskonen 1 Introduction The Logic of Descriptions LD Properties of LD Extensions and Modifications of LD Conclusions References Roman Suszko: Logician and Philosopher Mieczysław Omyła 1 Life MainPapers Views Influences Summary From Formal Theory of Knowledge to Non-Fregean Logic Mieczysław Omyła 1 DiachronicLogic Non-FregeanLogic References Categories of First-Order Quantifiers Urszula Wybraniec-Skardowska 1 Introduction ProblemofQuantifiers Some Intuitive Foundations of the Theory of Categorial Languages TheSolutionoftheProblemofQuantifiersof1st-Order Conclusions References

17 xviii The Lvov-Warsaw School: A True Mythology Jean-Yves Beziau 1 FromBahíaBlancatoWrocław The Atopicity of the Lvov-Warsaw School The Future of the Lvov-Warsaw School References