Logic & Natural Language: On Plural Reference and Its Semantic and Logical Significance

✍ Scribed by Hanoch Ben-Yami

• Publisher: Routledge
• Year: 2004
• Tongue: English
• Leaves: 169
• Edition: 1°
• Category: Library

✦ Synopsis

Frege's invention of the predicate calculus has been the most influential event in the history of modern logic. The calculus’ place in logic is so central that many philosophers think, in fact, of it when they think of logic. This book challenges the position in contemporary logic and philosophy of language of the predicate calculus claiming that it is based on mistaken assumptions. Ben-Yami shows that the predicate calculus is different from natural language in its fundamental semantic characteristics, primarily in its treatment of reference and quantification, and that as a result the calculus is inadequate for the analysis of the semantics and logic of natural language. Ben-Yami develops both an alternative analysis of the semantics of natural language and an alternative deductive system comparable in its deductive power to first order predicate calculus but more adequate than it for the representation of the logic of natural language. Ben-Yami's book is a revolutionary challenge to classical first order predicate calculus, casting doubt on many of the central claims of modern logic.

✦ Table of Contents

Cover
Half Title
Title
Copyright
Contents
Preface
1. Introduction
PART I: PLURAL REFERRING EXPRESSIONS
2 Plural Referring Expressions in Natural Language
2.1 The Common View on Reference
2.2 Plural Reference
2.3 The Implausibility of Reductive Analyses of Plural Referring Expressions
3 Common Nouns as Plural Referring Expressions
3.1 The Functioning of Common Nouns
3.2 On an Alleged Ambiguity of the Copula
3.3 Attributive and Predicative Adjectives
3.4 Natural Kind Terms
3.5 Empty Names
4 The Sources of the Analysis of Referring Nouns as Predicates
4.1 Frege
4.2 Russell and Bradley
5 Reference
PART II: QUANTIFICATION
6 Quantification: Natural Language versus the Predicate Calculus
6.1 The Nature of Quantification, and the Differences between Its Implementations
6.2 Definite and Indefinite Noun Phrases
6.3 Geach and Strawson on Plural Reference and Quantification
6.4 Binary and Restricted Quantification, and Comparative Quantifiers
6.5 Is 'Existence' a Quantifier?
7 Multiple Quantification
7.1 On Ambiguity and Formalization
7.2 Iterative Reading of Multiply Quantified Sentences
7.3 Additional Readings of Quantified Sentences
7.4 On the Passive, Converse Relation-Names, and the Copula
8 Pronouns, Variables, and Bound Anaphors
8.1 Pronouns and other Definitive Noun Phrases as Alleged Variables
8.2 Variables versus Bound Anaphors
8.3 Rules for the Choice of Anaphors
8.4 Conditional Donkey Anaphora
8.5 Predicate Connectives, and Bound Anaphora across Sentential Connectives
8.6 The Relation between the Truth-Value of a Quantified Sentence and those of Its Instances
PART III: A DEDUCTIVE SYSTEM FOR NATURAL LANGUAGE
9 Derivation Rules and Consistency
9.1 Some General Considerations
9.2 Basic Characteristics of the System
9.3 Transposition
9.4 Universal Elimination
9.5 Universal Introduction
9.6 Particular Introduction
9.7 Particular Elimination
9.8 Referential Import
10 Applications I: Aristotelian Logic
10.1 The Square of Opposition
10.2 Immediate Inferences
10.3 Syllogisms
11 Application II: Beyond Aristotelian Logic
11.1 Generalization of Transposition
11.2 Multiply Quantified Sentences
11.3 Predicate-and Sentence-Connectives
11.4 The Logic of Relations
11.5 Identity
12 Conclusions
Bibliography
Index