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| Preface | |
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| Thank Yous | |
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| Editorial Notes | |
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| Acknowledgements | |
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| Introduction | |
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| The Genesis of Grundgesetze | |
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| The Fall and Rise of Grundgesetze | |
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| Frege on the Reals | |
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| Logic in Grundgesetze | |
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| The Centrality of Grundgesetze | |
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| Goals for the Book | |
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| The Logic Behind Frege's Logicism | |
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| Frege and Semantics | |
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| Frege and the Justification of Logical Laws | |
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| Formalism and the Significance of Interpretation | |
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| The Regress Argument | |
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| Grundgesetze I ��29-32 (I) | |
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| The Character of the Induction | |
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| Frege on Free Variables | |
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| The Induction Step | |
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| The Basis Case: The Logical Expressions | |
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| The Basis Case: The Smooth Breathing (I) | |
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| Grundgesetze I �10 | |
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| Philosophical Aspects | |
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| Technical Aspects | |
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| Is Caesar a Value-Range? | |
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| The Second Problem, and Frege's Response | |
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| Are the Arguments in �10 Syntactic or Semantic? | |
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| Grundgesetze I ��29-32 (II) | |
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| The Basis Case: The Smooth Breathing (II) | |
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| Linnebo's Alternative | |
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| Final Remarks on ��29-32 | |
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| The Cost of Frege's Response to the Caesar Problem | |
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| The Mathematics Behind Frege's Logicism | |
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| The Development of Arithmetic | |
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| Frege's Use of Basic Law V | |
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| Frege's Formulations of HP | |
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| Frege's Proofs of Axioms for Arithmetic | |
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| The Concept of Natural Number | |
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| The Basic Facts about the Ancestral | |
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| An Elegant Proof that Every Number has a Successor | |
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| The Strategy of the Proof | |
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| Theorem 154 | |
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| An Important Lemma | |
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| Another Important Lemma | |
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| Completion of the Proof | |
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| Frege's Proofs of the Existence of Successor | |
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| HP in Grundgesetze | |
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| Definition by Recursion | |
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| Frege's Proof of Theorem 263 | |
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| Frege's Use of Ordered Pairs | |
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| Definition by Recursion | |
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| The Definition of Relations by Recursion | |
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| Functionality and the n-Ancestral | |
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| Theorem 207 | |
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| The Adequacy of Frege's Definition of the Ancestral | |
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| Theorem 263 in the Context of Frege's Development of Arithmetic | |
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| Frege on Finitude | |
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| Frege's Characterization of Finitude | |
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| Frege's Proof of Theorem 321 | |
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| The Proof of Theorem 288 | |
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| The Significance of Theorems 327 and 348 | |
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| Finitude, the Least Number Principle, and Well-ordering | |
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| The Finite and the Infinite | |
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| Remarks on Volume II | |
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| Chapter Mu: There is No Cardinal Between the Finite Cardinals and Endlos | |
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| A Generalized Least Number Principle | |
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| Remarks on Frege's Proof of Theorem 359 | |
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| The Proof of Theorem 428 | |
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| The Significance of Theorem 428 | |
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| Chapter Nu | |
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| The Definition of Addition | |
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| A Strengthened Version of HP | |
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| The Proof of Theorem 469 | |
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| The Proof of Theorem 468 | |
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| The Proof of Theorem 463 | |
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| Remarks on Theorem 469 | |
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| Cardinal Multiplication | |
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| Further unto the Infinite | |
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| The Theorems in Chapter Omicron | |
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| The Infinite and the Dedekind Infinite | |
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| Frege and the Axiom of Choice | |
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| Formalization and Frege's Conception of Logical Truth | |
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| Appendices | |
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| Outline of a Fregean Theory of Truth | |
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| Frege's Definitions | |
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| Theorems Concerning the Ancestral | |
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| Trees of Dependencies | |
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| Bibliography | |
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| Index | |