Logic, Language, and Meaning

by Gamut, L. T. F.

• ISBN13: 9780226280851
• ISBN10: 0226280853
• Format: Paperback
• Copyright: 1990-12-15
• Publisher: Univ of Chicago Pr

Summary

Although the two volumes ofLogic, Language, and Meaningcan be used independently of one another, together they provide a comprehensive overview of modern logic as it is used as a tool in the analysis of natural language. Both volumes provide exercises and their solutions. Volume 1,Introduction to Logic, begins with a historical overview and then offers a thorough introduction to standard propositional and first-order predicate logic. It provides both a syntactic and a semantic approach to inference and validity, and discusses their relationship. Although language and meaning receive special attention, this introduction is also accessible to those with a more general interest in logic. In addition, the volume contains a survey of such topics as definite descriptions, restricted quantification, second-order logic, and many-valued logic. The pragmatic approach to non-truthconditional and conventional implicatures are also discussed. Finally, the relation between logic and formal syntax is treated, and the notions of rewrite rule, automation, grammatical complexity, and language hierarchy are explained.

Author Biography

L. T. F. Gamut is a collective pseudonym for J. F. A. K. van Benthem, professor of mathematical logic; J. A. G. Groenendijk, associate professor of philosophy and computational linguistics; D. H. J. de Jongh, associate professor of mathematics and philosophy; M. J. B. Stokhof, associate professor of philosophy and computational linguistics, all at the University of Amsterdam, and H. J. Verkuyl, professor of linguistics at the University of Utrecht.

Table of Contents

Foreword

Preface

Introduction

Arguments, Valid Arguments, and Argument Schemata

Logic and Meaning

Logical Constants and Logical Systems

Logic and Linguistics before the Twentieth Century

The Twentieth Century

Logical Form versus Grammatical Form

Ordinary Language Philosophy

Linguistics and Philosophy

Formal Languages

Propositional Logic

Truth-Functional Connectives

Connectives and Truth Tables

Formulas

Functions

The Semantics of Propositional Logic

Truth Functions

Coordinating and Subordinating Connectives

Predicate Logic

Atomic Setences

Quantifying Expressions: Quantifiers

Formulas

Some More Quantifying Expressions and Their Translations

Sets

The Semantics of Predicate Logic

Interpretation Functions

Interpretation by Substitution

Interpretation by Means of Assignments

Universal Validity

Rules

Identity

Some Properties of Relations

Function Symbols

Arguments and Inferences

Arguments and Argument Schemata

Semantic Inference Relations

Semantic Validity

The Principle of Extensionality

Natural Deduction: A Syntactic Approach to Inference

Introduction and Elimination Rules

Conjunction

Implication

Disjunction

Negation

Quantifiers

Rules

Soundness and Completeness

Beyond Standard Logic

Introduction

Definite Descriptions

Restricted Quantification: Many-Sorted Predicate Logic

Second-Order Logic

Many-Valued Logic

Introduction

Three-Valued Logical Systems

Three-Valued Logics and the Semantic Notion of Presupposition

Logical Systems with More than Three Values

Four-Valued Logics and the Semantic Notion of Presupposition

The Limits of Many-Valued Logics in the Analysis of Presupposition

Elimination of Variables

Pragmatics: Meaning and Usage

Non-Truth-Conditional Aspects of Meaning

Logical Conjunction and Word Order

Usage and the Cooperation Principle

Inclusive and Exclusive Disjunction

Disjunctions and Informativeness

Conversational Maxims and Conversational Implicatures

The Controversial Implicatures of Disjunctions

Implication and Informativeness

Presuppositions and Conversational Implicatures

Conventional Implicatures, Presuppositions, and Implications

Formal Syntax

The Hierarchy of Rewrite Rules

Grammars and Automata

The Theory of Formal Languages

Grammatical Complexity of Natural Languages

Grammars, Automata, and Logic Solutions to Exercises

Bibliographical

Notes

References

Index

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