Frege and the Logic of Sense and Reference

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ISBN: 9780415937900 | 0415937906
Cover: Hardcover
Copyright: 11/16/2001

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This book aims to develop certain aspects of Gottlob Frege's theory of meaning, especially those relevant to intentional logic. It offers a new interpretation of the nature of senses, and attempts to devise a logical calculus for the theory of sense and reference that captures as closely as possible the views of the historical Frege.

Preface

Abbreviations

xiii

The Need for a Logical Calculus for the Theory of Sinn and Bedeutung

(22)

Introduction

(1)

Frege's Project: Logicism and the Notion of Begriffsschrift

(4)

The Theory of Sinn and Bedeutung

(6)

The Limitations of the Begriffsschrift

(7)

Filling the Gap

(4)

The Logic of the Grundgesetze

(34)

Logical Language and the Content of Logic

(3)

Functionality and Predication

(4)

Quantifiers and Gothic Letters

(6)

Roman Letters: An Alternative Notation for Generality

(4)

Value-Ranges and Extensions of Concepts

(2)

The Syntactic Rules of the Begriffsschrift

(5)

The Axiomatization of Frege's System

(7)

Responses to the Paradox

(3)

Sinne and Gedanken

(36)

The Nature of Sinne Generally

(6)

The Sinne of Incomplete Expressions and the Composition of Gedanken

(11)

Context Principle, Priority Thesis, and Multiple Analyses: Challenges to Compositionality

(13)

The Identity Conditions of Sinne and Gedanken

(6)

Church's Logic of Sense and Denotation

(30)

Overview

(1)

The Method of Transparent Intensional Logic

(5)

Alternatives (0), (1) and (2) and Synonymous Isomorphism

101

(4)

The Formulation of the Systems

105

(6)

Problems in Church's Logic of Sense and Denotation

111

(6)

The UnFregean Elements of Church's Logic of Sense and Denotation

117

(8)

A Logical Calculus for the Theory of Sinn and Bedeutung

125

(46)

Basic Features

125

(2)

Names and Variables for Sinne

127

(4)

The New Constants of the Expanded Language

131

(5)

Syntactic Rules of the Expanded Language

136

(5)

Axioms and Inference Rules of the Expanded Calculi

141

(12)

Inferences Involving Propositional Attitudes and Quantifying In

153

(5)

Difficulties with the Expanded Calculi

158

(13)

Comparison with Russell and Other Thinkers

171

(30)

``Solatium miseris, socios habuisse malorum.''

171

(1)

Russell's Ontology of Propositions

172

(3)

Russell and the Principles of Mathematics Appendix B Paradox

175

(6)

Frege and the Principles of Mathematics Appendix B Paradox

181

(8)

Lessons Learned from Russell

189

(2)

Other Systems of Intensional Logic

191

(10)

Possible Revisions to Frege's Philosophy

201

(30)

Adequate versus Ad Hoc Solutions

201

(1)

A Cantorian Analysis of the Difficulties

202

(4)

Dropping Classes and/or Concepts

206

(7)

Reducing the Number of Sinne and Gedanken

213

(8)

Ramification as a Solution to the Paradoxes

221

(3)

The Justification of Ramification

224

(4)

Conclusion

228

(3)

Appendix: Summary of Definitions, Axioms and Inference Rules

231

(8)

Bibliography

239

(14)

Index

253

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Frege and the Logic of Sense and Reference

Summary

Table of Contents

Supplemental Materials