Table Of ContentStudies in Universal Logic
Urszula B. Wybraniec-Skardowska
Logic -
Language -
Ontology
Selected Works
Studies in Universal Logic
Series Editor
Jean-Yves Béziau, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil
Editorial Board Members
Hajnal Andréka, Hungarian Academy of Sciences, Budapest, Hungary
Mark Burgin, UCLA, Los Angeles, California, USA
Răzvan Diaconescu, Romanian Academy, Bucharest, Romania
Raffaela Giovagnoli, Pontifical Lateran University, Vatican
Andreas Herzig, University Paul Sabatier, Toulouse, France
Arnold Koslow, City University of New York, New York, NY, USA
Jui-Lin Lee, National Formosa University, Huwei Township, Taiwan
Larissa Maksimova, Russian Academy of Sciences, Novosibirsk, Russia
Grzegorz Malinowski, University of Lódz, Lódz, Poland
Francesco Paoli, University of Cagliari, Cagliari, Italy
Peter Schröder-Heister, University of Tübingen, Tübingen, Germany
Vladimir Vasyukov, Russian Academy of Sciences, Moscow, Russia
Anna Zamansky, University of Haifa, Haifa, Israel
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. All works are peer-reviewed to meet the
highest standards of scientific literature.
Urszula B. Wybraniec-Skardowska
Logic - Language - Ontology
Selected Works
Urszula B. Wybraniec-Skardowska
Department of Philosophy
Cardinal Stefan Wyszyński University in Warsaw
Warsaw, Poland
ISSN 2297-0282 ISSN 2297-0290 (electronic)
Studies in Universal Logic
ISBN 978-3-031-22329-7 ISBN 978-3-031-22330-3 (eBook)
https://doi.org/10.1007/978-3-031-22330-3
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland
AG 2022
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Preface
Thismonographbelongsinthedomainofuniversallogicandthereforepertainsto
the broadly-understood logic which has its application in a variety of disciplines
of science and knowledge. It spans these formalized aspects of classical logic, set
theoryandlogicalsemiotics,whicharemadeuseofincontemporaryphilosophyof
languageandontology.Becauseataskofontologyistodescribethestructureofa
beingorreality,andbecauseitislanguagethatservesthispurpose,languageshould
reflectthestructureofrealityincompliancewithitsownsystem.Itsstructure,which
preserves this compliance, is dealt with by the logical theory of language syntax
andsemantics.Accordingly,inthebook,thistheoryisformalizedintheindividual
chapters with the aid of means of classical formal logic and set theory. Thus, in
ordertounderstandit,itsufficestoholdelementarylogicalknowledgeandsimple
knowledgeofissuesrelatingtoaxiomatizationoftheories.
This book is intended for undergraduate and graduate students, as well as re-
searcherswhoareinterestedinareaswhereformallogicandlogicoflanguageare
appliedtolearnmoreaboutontology,cognitivescience,symbolicsystems,informa-
tionscienceandlinguistics.Basically,theworkscollectedinthisbookcanberead
separately, although they are for the most part connected thematically in the order
they follow one another. I hope that studying the chapters of the monograph will
offer the reader a solid and up-to-date view that will enable comprehending many
problemswhicharestillencounteredincurrentlyconductedresearch.
Warsaw,June2021 UrszulaWybraniec-Skardowska
v
Acknowledgements
I would like to pay my debt of gratitude. First, for being given the opportunity to
havemyselectedworkspublishedbyBirkhäuserinStudiesinUniversalLogic(SUL)
serieseditedbyJean-YvesBeziau.Second,ImustexpressmygratitudetothePolish
Academy of Sciences, Białystok Publishing House, Adam Marszałek Publishing
House, De Gruyter and Springer for their permissions to republish these selected
worksinSUL.
ItwanttoacknowledgetheassistancethatIhad.Iwouldliketoexpressmygrat-
itudetoalltherefereesofmyoriginallypublishedworks.ToZbigniewBonikowski
Iownsincerethanksforhispainstakingeffortstoreformattheworksincompliance
withthestyleacceptedbySUL.
Severalpartsofthisbookgobacktodiscussionswithmyteacher,JerzySłupecki,
concerningcategorialsyntaxandthencategorialsemanticsinscientificmeetingsat
Tilburg University and Amsterdam University during my stays there (a grant from
The Netherlands Organization for Scientific Research). Many people from these
universities helped me in many different ways, rendering their works available or
facilitating access to necessary literature. Here, I would like in particular to thank
JohanvanBenthem,FilipBuekens,JanvanEijck,TheoJanssenandHarriedeSwart.
I received valuable comments and suggestions from my colleagues or co-
workers,includingTadeuszBatóg,AndrzejBiłat,ZbigniewBonikowski,Wojciech
Buszkowski,JaakkoHintikka,WilfridHodges,AndrzejIndrzejczak,JacekJędrze-
jowski, Jacek Malinowski, Jerrold Jacob Katz, Arnold Koslow, Marek Magdziak,
Witold Marciszewski, Alex Orenstein, Jerzy Perzanowski, Bartłomiej Skowron,
Mieszko Tałasiewicz and Heinrich Wansing. I want to thank them all for their
support.
I am also greatly indebted to my husband, Adam Skardowski, who created the
best possible conditions for me to continue my research work and to work on this
monograph.
vii
Contents
PartI Introduction
1 TheDualOntologicalNatureofLanguageSignsandtheProblemof
TheirMutualRelations ......................................... 3
1 Preliminaries .............................................. 4
2 TheFunctionalApproachTowardsLanguageasaSystemofSigns.
TwoWaysofUsingSigns.................................... 5
3 Ch.S.Pierce’sDistinction:Type-tokenofaSign ................ 5
4 ControversiesOvertheOntologicalStatusofLanguageSignsand
RelationsBetweenThem .................................... 6
5 SolvingtheProblemsUnderAnalysis.......................... 9
5.1 TheInstantiationViewvstheRepresentationView ........ 10
6 TheoreticalApproachtotheProblemofMutualRelationsBetween
TokensandTypesofSigns................................... 11
6.1 Syntax ............................................. 11
6.2 Semantics .......................................... 12
6.3 SignsinLanguageCommunication ..................... 13
7 Conclusions ............................................... 14
References ..................................................... 15
2 OntheStructureandContentsoftheMonograph ................. 17
PartII SelectedWorks
1 OntheType-TokenRelationships ................................ 21
References ..................................................... 24
2 OntheAxiomaticSystemsofSyntactically-CategorialLanguages.... 27
1 Introduction ............................................... 27
2 TheTheoriesTLTkandTETk ................................ 28
3 SystemsTSCLandTSC𝜔-L .................................. 30
ix
x Contents
4 SystemsDTSCLandDTSC𝜔-L ............................... 32
References ..................................................... 33
3 TheLogicalFoundationsofLanguageSyntaxOntology ............ 35
1 IntuitiveUnderstandingofCategorialLanguage ................. 37
1.1 InitialSyntacticCharacteristicofLanguage .............. 37
1.2 PreliminariestotheTheoryofCategorialLanguages ...... 40
2 TheFormalTheory𝑇𝑙 –aConcretisticApproach................ 46
𝑘
2.1 TheLevelofConcretes;Theory𝑇1 ..................... 46
𝑘
2.2 TheLevelofTypes;Theory𝑇2......................... 52
𝑘
3 TheFormalTheory𝑇𝑙 –thePlatonizingApproach .............. 54
𝑝
3.1 TheLevelofTypes;Theory𝑇2......................... 55
𝑝
3.2 TheLevelofConcretes;Theory𝑇1 ..................... 55
𝑝
4 MetalogicalandPhilosophicalConsequences ................... 57
References ..................................................... 59
4 OntheEliminatibilityofIdealLinguisticEntities.................. 61
1 Non-uniformSemioticCharacterizationofLanguage............. 62
2 PreliminaryConventionsConcerningLanguage ................. 63
3 DualTheoriesConceptsandExpressions....................... 64
4 TheoryT1 ................................................ 67
4.1 FormalizationofT1attheTokenLevel;TheoryT1(tk)..... 67
4.2 FormalizationofT1attheTypeLevel;TheoryT1(tp)...... 79
5 TheoryT2 ................................................ 81
5.1 FormalizationofT2attheTypeLevel;TheoryT2(tp)...... 81
5.2 FormalizationofT2attheTokenLevel;TheoryT2(tk)..... 82
6 TheEquivalenceoftheTheoriesT1andT2..................... 84
7 FinalConclusionsandRemarks............................... 86
References ..................................................... 87
5 MeaningandInterpretation.PartI............................... 91
1 Preliminaries .............................................. 92
1.1 TheProblemoftheMeaningof‘Meaning’............... 92
1.2 WhatisaGeneralTheoryofMeaningandInterpretation? .. 94
1.3 TheAimandAssumptionsoftheWork.................. 95
2 SyntaxforLanguage;theTheoryT............................ 98
2.1 TwoKindsofSyntax:atoken-syntaxandatype-syntax .... 98
2.2 SomeBasisoftheTheoryT ........................... 99
3 TheGeneralTheoryofMeaning:theTheoryTM ...............102
3.1 Meaning............................................102
3.2 Denotation..........................................107
3.3 MeaningandDenotation ..............................110
References .....................................................112
Contents xi
6 MeaningandInterpretation.PartII..............................117
4 TheTheoryofMeaningandInterpretation:theTheoryTMI.......117
4.1 InterpretationandLanguageCommunication.............117
4.2 MeaningandInterpretation............................121
5 FinalRemarks .............................................126
References .....................................................127
7 ThreePrinciplesofCompositionality .............................131
1 Introduction ...............................................132
2 TheTheoryTC –aNon-formalCharacterisation ................134
2.1 Ideas...............................................134
2.2 MainAssumptionsoftheTheoryofSyntax ..............134
2.3 MainAssumptionsoftheTheoryofSemanticsandSome
MetatheoreticalIssues ................................137
3 TheTheoryTC –aFormalApproach .........................143
3.1 SomeFormalFoundationsoftheTheoryofSyntax........143
3.2 FormalFoundationsoftheTheoryofSemanticsandSome
MetatheoreticalIssues ................................148
3.3 FundamentalTheoremsofTC .........................154
4 TheRoleoftheFormalTheoryTCinPhilosophy................158
References .....................................................160
8 OnMeta-knowledgeandTruth ..................................163
1 Ideas .....................................................164
2 MainAssumptionsoftheTheoryofSyntaxandSemantics........166
2.1 CategorialSyntaxandCategorialSemantics..............166
2.2 ThreeReferentialRelationshipsofWfes .................167
2.3 CategorialIndices....................................168
2.4 SyntacticOperations .................................168
2.5 SemanticOperations .................................169
2.6 KnowledgeandCognitiveObjects ......................170
2.7 ThePrinciplesofCategorialAgreement .................170
2.8 Algebraic Structures of Categorial Language and its
Correlates ..........................................171
2.9 Compositionality ....................................173
2.10 ConcordBetweenSyntacticFormsandTheirCorrelates....173
3 ThreeNotionsofTruthfulness ................................177
3.1 ThreeKindsofModelsofLanguageandtheNotionofTruth177
3.2 ThreeNotionsofTruthfulness .........................178
3.3 ReliabilityofCognitionofReality ......................179
3.4 OperationsofReplacement ............................180
3.5 TheMostImportantTheorems .........................180
4 FinalRemarks .............................................182
References .....................................................183
