Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic

By Philip Hugly; Charles Sayward et al. | Go to book overview

Arithmetic and Ontology
A Non-Realist Philosophy of Arithmetic

POZNAŃ STUDIES IN THE PHILOSOPHY OF THE SCIENCES AND THE HUMANITIES, VOLUME 90
MONOGRAPHS-IN-DEBATE

Philip Hugly and Charles Sayward

Edited by
Pieranna Garavaso

Amsterdam - New York, NY 2006

-5-

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Arithmetic and Ontology: A Non-Realist Philosophy of Arithmetic
Table of contents

Table of contents

  • Title Page 5
  • Contents 7
  • Acknowledgments 9
  • Editor’s Introduction 11
  • Preface 27
  • Analytical Table of Contents 31
  • Chapter 1 - Introduction 35
  • Part I - Beginning with Frege 43
  • Chapter 2 - Notes to Grundlagen 45
  • Chapter 3 - Objectivism and Realism in Frege’s Philosophy of Arithmetic 73
  • Part II - Arithmetic and Non-Realism 103
  • Chapter 4 - The Peano Axioms 105
  • Chapter 5 - Existence, Number, and Realism 129
  • Part III - Necessity and Rules 157
  • Chapter 6 - Arithmetic and Necessity 159
  • Chapter 7 - Arithmetic and Rules 183
  • Part IV - The Three Theses 213
  • Chapter 8 - Thesis One 215
  • Chapter 9 - Thesis Two 241
  • Chapter 10 - Thesis Three 254
  • References 285
  • Commentaries 289
  • Numbers, Reference, and Abstraction 291
  • What Is Non-Realism about Arithmetic? 317
  • Non-Realism, Nominalism and Strict Finitism the Sheer Complexity of It All 342
  • Replies to Commentaries 366
  • Replies to Commentaries 368
  • About the Contributors 386
  • Index 388
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