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Index
Preface
Editorial Notes
Origin of the Chapters xii
Frege's Theorem: An Overview
1.1 Frege on Frege's Theorem 9
1.2 The Caesar Problem 13
1.3 What Does HP Have To Do With Arithmetic? 27
1.4 Logicism and Neo-Logicism 37
2 The Development of Arithmetic in Frege's Grundgesetze der Arithmetik
2.1 Basic Law V in Grundgesetze 41
2.2 HP and Fregean Arithmetic
2.3 Frege's Derivation of the Axioms of Arithmetic 47
2.4 Frege's Derivation of the Axioms of Arithmetic, continued 51
2.5 An Elegant Proof that Every Number has a Successor
2.6 Frege's Axiomatization of Arithmetic
2.7 Closing 64
Postscript 66
3 Die Grundlagen der Arithmetik ยงยง82-83
Appendix: Counterparts in Grundgesetze of Some Propositions of Die Grundlagen 86
Postscript
4 Frege's Principle
4.1 Numbers as Extensions of Concepts 92
4.2 The Importance of HP in Frege's Philosophy of Arithmetic
4.3 The Role of Basic Law V in Frege's Derivation of Arithmetic 97
4.4 Frege's Derivations of HP 99
4.5 HP versus Frege's Principle
4.6 Frege's Principle and the Explicit Definition 104
4.7 The Caesar Problem Revisited 105
4.8 Closing 107
Postscript 108
5 Julius Caesar and Basic Law V
5.1 The Caesar Problem 113
5.2 The Caesar Problem in Grundgesetze 115
5.3 The Caesar Problem and the Apprehension of Logical Objects 118
5.4 Closing 125
6 The Julius Caesar Objection
6.1 Why the Caesar Objection Has To Be Taken Seriously 131
6.2 The Caesar Objection and the Feasibility of the Logicist Project 136
6.3 Avoiding the Caesar Objection 147
6.4 Closing 152
7 Cardinality, Counting, and Equinumerosity
7.1 Technical Preliminaries
7.2 Frege and Husserl 163
7.3 Counting and Cardinality 168
7.4 Counting and Ascriptions of Number 172
7.5 Closing 176
8 Syntactic Reductionism
8.1 Motivating Nominalism 182
8.2 Taking Reductionism Seriously
8.3 The Ineliminability of Names of Abstract Objects 193
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