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Acknowledgments vii INTRODUCTION: Turning on the Light 1 SECTION I: THE LIGHT OF AMBIGUITY 21 CHAPTER 1: Ambiguity in Mathematics 25 CHAPTER 2: The Contradictory in Mathematics 80 CHAPTER 3: Paradoxes and Mathematics: Infinity and the Real Numbers 110 CHAPTER 4: More Paradoxes of Infinity: Geometry, Cardinality, and Beyond 146 SECTION II: THE LIGHT AS IDEA 189 CHAPTER 5: The Idea as an Organizing Principle 193 CHAPTER 6: Ideas, Logic, and Paradox 253 CHAPTER 7: Great Ideas 284 SECTION III: THE LIGHT AND THE EYE OF THE BEHOLDER 323 CHAPTER 8: The Truth of Mathematics 327 CHAPTER 9: Conclusion: Is Mathematics Algorithmic or Creative? 368 Notes 389 Bibliography 399 Index 407
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