## Table of contents for Infinity and the mind : the science and philosophy of the infinite / Rudy Rucker.

Bibliographic record and links to related information available from the Library of Congress catalog

Information from electronic data provided by the publisher. May be incomplete or contain other coding.

Preface to the Paperback Edition ix

Preface xi

Chapter One: Infinity 1

A Short History of Infinity 1

Physical Infinities 9

Temporal Infinities 10

Spatial Infinities 15

Infinities in the Small 24

Conclusion 34

Infinities in the Mindscape 35

The Absolute Infinite 44

Connections 49

Puzzles and Paradoxes 51

Chapter Two: All the Numbers 53

From Pythagoreanism to Cantorism 53

Transfinite Numbers 64

From Omega to Epsilon-Zero 65

The Alefs 73

lnfinitesimals and Surreal Numbers 78

Higher Physical Infinities 87

Puzzles and Paradoxes 91

Chapter Three: The Unnameable 93

The Berry Paradox 93

Naming Numbers 95

Understanding Names 100

Random Reals 107

Constructing Reals 108

The Library of Babel 120

Richard's Paradox 126

Coding the World 130

What is Truth? 143

Conclusion 152

Puzzles and Paradoxes 155

Chapter Four: Robots and Souls 157

Godel's incompleteness Theorem 157

Conversations with Godel 164

Towards Robot Consciousness 171

Formal Systems and Machines 172

The Liar Paradox and the Non-Mechanizability of Mathematics 175

Artificial Intelligence via Evolutionary Processes 180

Robot Consciousness 183

Beyond Mechanism? 185

Puzzles and Paradoxes 187

Chapter Five: The One and the Many 189

The Classical One/Many Problem 189

What is a Set? 191

The Universe of Set Theory 196

Pure Sets and the Physical Universe 196

Proper Classes and Metaphysical Absolutes 202

Interface Enlightenment 206

One/Many in Logic and Set Theory 207

Mysticism and Rationality 209

Satori 214

Puzzles and Paradoxes 219

Excursion One: The Transfinite Cardinals 221

On and Alef-One 221

Cardinality 226

The Continuum 238

Large Cardinals 253

Excursion Two: Godel's Incompleteness Theorems 267

Formal Systems 267

Self-Reference 280

Godel's Proof 285

A Technical Note on Man-Machine Equivalence 292

Answers to the Puzzles and Paradoxes 295

Notes 307

Bibliography 329

Index 339

Library of Congress subject headings for this publication:

Logic, Symbolic and mathematical.

Set theory.

Infinite.