A Critical Introduction to the Philosophy of

Gottlob Frege is one of the greatest logicians ever and also a philosopher of great significance. In this book Rosado Haddock offers a critical presentation of the main topics of Frege's philosophy, including, among others, his philosophy of arithmetic, his sense-referent distinction, his distinction between function and object, and his criticisms of formalism and psychologism.More than just an introduction to Frege's philosophy this book is also a highly critical and mature assessment of it as a whole in which the limitations, confusions and other weaknesses of Frege's thought are closely examined. The author is also a Husserlian scholar and this book contains valuable discussions of Husserl's neglected views and comparisons between the two great philosophers.

Preface

vii

Chapter 1 Philosophy in Begriffsschrift

§ 1 An Epistemological Distinction

1

(1)

§ 2 On the Nature of Arithmetical Statements

2

(1)

§ 3 Concept-Script versus Natural Language

3

(1)

§ 4 Judgeable Content

4

(1)

§ 5 Conceptual Content

5

(1)

§ 6 The Universal Predicate of all Statements

6

(1)

§ 7 Abandonment of some Traditional Distinctions

7

(2)

§ 8 Identity Statements in Begriffsschrift

9

(2)

§ 9 Functions in Begriffsschrift

11

(4)

§ 10 Axiom Systems

15

(2)

Chapter 2 Die Grundlagen der Arithmetik: First Part (§§1-45)

§ 1 The Need for a Clarification of the Nature of Mathematics

17

(2)

§ 2 The Methodological Principles

19

(3)

§ 3 The Classification of Statements

22

(1)

§ 4 The Naturalist Conception of Mathematics

23

(2)

§ 5 The Nature of Geometry

25

(3)

§ 6 Numbers and Properties of Objects

28

(2)

§ 7 Psychologism in Mathematics

30

(3)

§ 8 Numbers and the Process of Abstraction

33

(2)

Chapter 3 Die Grundlagen der Arithmetik: Second Part (§§46-109)

§ 1 Predications about Concepts

35

(2)

§ 2 Concept and Object in Die Grundlagen der Arithmetik

37

(2)

§ 3 First Attempt at a Definition of Number

39

(3)

§ 4 Second Attempt at a Definition of Number

42

(7)

§ 5 Third Attempt at a Definition of Number

49

(8)

§ 6 A Brief Sketch of the System

57

(5)

§ 7 Frege's Summary and his Assessment of Kant's Views

62

(5)

Chapter 4 The Basic Distinctions I: Sense and Referent

§ 1 Sense and Referent

67

(5)

§ 2 The Context Principle and Frege's Semantics of Sense and Referent

72

(3)

§ 3 Critical Remarks I

75

(1)

§ 4 Critical Remarks II

76

(5)

§ 5 Critical Remarks III

81

(2)

§ 6 Critical Remarks IV

83

(3)

§ 7 Identity Statements

86

(5)

Chapter 5 The Basic Distinctions II: Function and Object

§ 1 The Nature of Functions

91

(3)

§ 2 The Predicative Nature of Concepts

94

(5)

§ 3 Value Ranges

99

(3)

§ 4 Some Difficulties

102

(3)

§ 5 Value Ranges and Extensions

105

(4)

Chapter 6 Fundamental Philosophical Issues in Grundgesetze

§ 1 Introduction

109

(1)

§ 2 Frege's Criticism of Psychologism in Logic

110

(4)

§ 3 Logicism in Grundgesetze der Arithmetik

114

(1)

§ 4 Frege's Platonism

115

(2)

§ 5 Frege's Criticism of Formalism in Mathematics

117

(2)

§ 6 On the Nature of Definitions

119

(4)

§ 7 Some Critical Remarks

123

(6)

Chapter 7 Some Remaining Philosophical Issues

§ 1 The Zermelo-Russell Paradox and Frege's Reaction to Russell's Letter

129

(4)

§ 2 The Controversy on the Foundations of Geometry

133

(4)

§ 3 Frege's Abandonment of Logicism

137

(6)

Bibliography

143

(8)

Name Index

151

(4)

Subject Index

155

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A Critical Introduction to the Philosophy of Gottlob Frege

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