How should we think about the meaning of the words that make up our language? How does reference of these terms work, and what is their referent when these are connected to abstract objects rather than to concrete ones? Can logic help to address these questions? This collection of papers aims to unify the questions of syntax and semantics of language, which span across the fields of logic, philosophy and ontology of language. The leading motif of the presented selection is the differentiation between linguistic tokens (material, concrete objects) on the one hand and linguistic types (ideal, abstract objects) on the other. Through a promenade among articles that span over all of the Author’s career, this book addresses the complex philosophical question of the ontology of language by following the crystalline conceptual tools offered by logic. At the core of Wybraniec-Skardowska’s scholarship is the idea that language is an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. The application throughout the book of tools of classical logic and set theory results fosters the emergence of a general formal logical theory of syntax, semantics and of the pragmatics of language, which takes into account the duality token-type in the understanding of linguistic expressions. Via a functional approach to language itself, logic appears as ontologically neutral with respect to existential assumptions relating to the nature of linguistic expressions and their extra-linguistic counterparts.
The book is addressed to readers both at the graduate and undergraduate level, but also to a more general audience interested in getting a firmer grip on the interplay between reality and the language we use to describe and understand it.
Author(s): Urszula B. Wybraniec-Skardowska
Series: Studies in Universal Logic
Publisher: Birkhäuser
Year: 2022
Language: English
Pages: 304
City: Cham
Preface
Acknowledgements
Contents
Part I Introduction
Chapter 1 The Dual Ontological Nature of Language Signs and the Problem of Their Mutual Relations
1 Preliminaries
2 The Functional Approach Towards Language as a System of Signs. Two Ways of Using Signs
3 Ch. S. Pierce’s Distinction: Type-token of a Sign
4 Controversies Over the Ontological Status of Language Signs and Relations Between Them
5 Solving the Problems Under Analysis
5.1 The Instantiation View vs the Representation View
6 Theoretical Approach to the Problem of Mutual Relations Between Tokens and Types of Signs
6.1 Syntax
6.2 Semantics
6.3 Signs in Language Communication
7 Conclusions
References
Chapter 2 On the Structure and Contents of the Monograph
Part II Selected Works
Chapter 1 On the Type-Token Relationships
References
Chapter 2 On the Axiomatic Systems of Syntactically-Categorial Languages
1 Introduction
2 The Theories TLTk and TETk
3 Systems TSCL and TSCω-L
4 Systems DTSCL and DTSCω-L
References
Chapter 3 The Logical Foundations of Language Syntax Ontology
Introduction
1 Intuitive Understanding of Categorial Language
1.1 Initial Syntactic Characteristic of Language
1.2 Preliminaries to the Theory of Categorial Languages
2 The Formal Theory Tlk – a Concretistic Approach
2.1 The Level of Concretes; Theory T1k
2.2 The Level of Types; Theory T2k
3 The Formal Theory Tlp – the Platonizing Approach
3.1 The Level of Types; Theory T2p
3.2 The Level of Concretes; Theory T1p
4 Metalogical and Philosophical Consequences
References
Chapter 4 On the Eliminatibility of Ideal Linguistic Entities
1 Non-uniform Semiotic Characterization of Language
2 Preliminary Conventions Concerning Language
3 Dual Theories Concepts and Expressions
4 Theory T1
4.1 Formalization of T1 at the Token Level; Theory T1(tk)
4.1.1 Axioms and Definitions of T1(tk)
4.1.2 Major Theorems of the Theory T1(tk)
4.2 Formalization of T1 at the Type Level; Theory T1(tp)
5 Theory T2
5.1 Formalization of T2 at the Type Level; Theory T2(tp)
5.2 Formalization of T2 at the Token Level; Theory T2(tk)
6 The Equivalence of the Theories T1 and T2
7 Final Conclusions and Remarks
References
Chapter 5 Meaning and Interpretation. Part I
Introduction
1 Preliminaries
1.1 The Problem of the Meaning of ‘Meaning’
1.2 What is a General Theory of Meaning and Interpretation?
1.3 The Aim and Assumptions of the Work
2 Syntax for Language; the Theory T
2.1 Two Kinds of Syntax: a token-syntax and a type-syntax
2.2 Some Basis of the Theory T
3 The General Theory of Meaning: the Theory TM
3.1 Meaning
3.2 Denotation
3.3 Meaning and Denotation
References
Chapter 6 Meaning and Interpretation. Part II
4 The Theory of Meaning and Interpretation: the Theory
4.1 Interpretation and Language Communication
4.2 Meaning and Interpretation
5 Final Remarks
References
Chapter 7 Three Principles of Compositionality
1 Introduction
2 The Theory TC – a Non-formal Characterisation
2.1 Ideas
2.2 Main Assumptions of the Theory of Syntax
2.3 Main Assumptions of the Theory of Semantics and Some Metatheoretical Issues
3 The Theory TC– a Formal Approach
3.1 Some Formal Foundations of the Theory of Syntax
3.2 Formal Foundations of the Theory of Semantics and Some Metatheoretical Issues
3.3 Fundamental Theorems of TC
4 The Role of the Formal Theory TC in Philosophy
References
Chapter 8 On Meta-knowledge and Truth
Introduction
1 Ideas
2 Main Assumptions of the Theory of Syntax and Semantics
2.1 Categorial Syntax and Categorial Semantics
2.2 Three Referential Relationships of Wfes
2.3 Categorial Indices
2.4 Syntactic Operations
2.5 Semantic Operations
2.6 Knowledge and Cognitive Objects
2.7 The Principles of Categorial Agreement
2.8 Algebraic Structures of Categorial Language and its Correlates
2.9 Compositionality
2.10 Concord Between Syntactic Forms and Their Correlates
3 Three Notions of Truthfulness
3.1 Three Kinds of Models of Language and the Notion of Truth
3.2 Three Notions of Truthfulness
3.3 Reliability of Cognition of Reality
3.4 Operations of Replacement
3.5 The Most Important Theorems
4 Final Remarks
References
Chapter 9 On Language Adequacy
1 Introduction
2 The Problem Area of Language Adequacy
3 An Outline of the Theory of Categorial Language
3.1 Categorial Syntax – Theory T
3.1.1 General Characteristics of the Categorial Language
3.1.2 Two Levels of Formalization of Categorial Syntax
3.1.3 The Foundations of the Formal Theory T – the Level of Tokens
3.1.4 Foundations of the Formal Theory T – the Level of Types
3.2 Categorial Semantics – the Theory ST
3.2.1 Intensional Semantics
3.2.2 Extensional semantics
4 Language Adequacy and its Aspects
5 Summary
References
Chapter 10 What Is the Sense in Logic and Philosophy of Language?
1 Introduction
2 Main Ideas of the Formalisation of Categorial Language L
3 General Assumption Concerning the Logical Sense of Expressions of Language L
3.1 Syntactic and Semantic Unambiguity
3.2 Categorial Compatibility
3.2.1 Postulate of Categorial Compatibility
3.2.2 Type-unifying Logical Senses
3.2.3 Semantic Compatibility
3.3 Structural Compatibility
3.3.1 On the Structure of Expressions and Their Semantic Counterparts
3.3.2 Principles of Compositionality
3.3.3 Main Properties of Functions h(f )
3.3.4 Generalisation of Ajdukiewicz’s Cancellation Principles
3.3.5 Models of L and the Notion of Truth
3.3.6 Some Remarks Concerning the Problem of Categories of First-Order Quantifiers
4 Final Remarks
References
Chapter 11 Categories of First-Order Quantifiers
1 Introduction
2 Problem of Quantifiers
3 Some Intuitive Foundations of the Theory of Categorial Languages
3.1 Main Ideas of Formalization of Categorial Language
3.2 Categorial Syntax
3.2.1 An Algebraic Structure of Categorial Language
3.3 Categorial Semantics
3.3.1 An aAlgebraic Ontological Structure Corresponding to the Partial Algebra L
4 The Solution of the Problem of Quantifiers of 1st-Order
4.1 Different Types of the 1st-Order Quantifiers and Their Syntactic Categories
4.2 Denotations of 1st-Order Quantifiers and Their Ontological Categories
4.2.1 Fregean Semantics
4.2.2 Situational Semantics
4.3 The Syntactic and Semantic Compatibility of Quantifiers
5 Conclusions
References
Chapter 12 Logic and the Ontology of Language
1 Introduction
1.1 Knowledge-Language-Reality
1.2 The Logical Conception of Language
1.3 The Dual Ontological Status of Linguistic Expressions
1.4 Categories of Linguistic Expression and Ontic Categories of Object
2 Outline of a Formal-Logical Theory of Language
2.1 On the Logical Theory of Linguistic Syntax
2.2 The Foundations of the Formal-Logical Theory of the Semantics and Pragmatics of Language
3 On the Ontological Neutrality of Logic
Appendix
References
Chapter 13 A Logical Conceptualization of Knowledge on the Notion of Language Communication
1 Introduction
2 Three Aspects in Formalization of the TLC Theory
2.1 The Cognitive-communicative Function of Natural Language According to its Genesis
2.2 The Functional Approach to Natural Language Analysis
2.3 Two Understandings of manner of use and manner of interpreting Language Expressions in Communication
3 Language Syntax; Theory
3.1 Two Levels of Formalization of Syntax of Language
3.2 Identifiability of linguistic tokens
3.2.1 Concatenations
3.2.2 Well-formed Expressions
4 A Theory of Language Communication – Theory TLC
4.1 Token-level
4.1.1 Primitive notions of TLC
4.1.2 Act of Communication
4.1.3 Adequacy of Communication Acts
4.1.4 Miscommunication: Misunderstanding
4.1.5 Miscommunication: Non-understanding
4.2 Type-level
4.2.1 Communication by Means of Expression-types
4.2.2 Using types and Interpreting types
4.2.3 Problem of Adequacy of Language Communication
4.2.4 Notions Relating to Language Communication
4.2.5 Dual Conceptual Counterparts
4.2.6 Adequacy of Language Communication
5 Summary
References
