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Index
Cover Page
Title Page
Copyright Page
Table of Contents
Preface to the 2005 Edition
Preface to the Paperback Edition
Preface
Chapter One: Infinity
A Short History of Infinity
Physical Infinities
Temporal Infinities
Spatial Infinities
Infinities in the Small
Conclusion
Infinities in the Mindscape
The Absolute Infinite
Connections
Puzzles and Paradoxes
Chapter Two: All the Numbers
From Pythagoreanism to Cantorism
Transfinite Numbers
From Omega to Epsilon-Zero
The Alefs
Infinitesimals and Surreal Numbers
Higher Physical Infinities
Puzzles and Paradoxes
Chapter Three: The Unnameable
The Berry Paradox
Naming Numbers
Understanding Names
Random Reals
Constructing Reals
The Library of Babel
Richard’s Paradox
Coding the World
What is Truth?
Conclusion
Puzzles and Paradoxes
Chapter Four: Robots and Souls
Gödel’s Incompleteness Theorem
Conversations with Gödel
Towards Robot Consciousness
Formal Systems and Machines
The Liar Paradox and the Non-Mechanizability of Mathematics
Artificial Intelligence via Evolutionary Processes
Robot Consciousness
Beyond Mechanism?
Puzzles and Paradoxes
Chapter Five: The One and the Many
The Classical One/Many Problem
What is a Set?
The Universe of Set Theory
Pure Sets and the Physical Universe
Proper Classes and Metaphysical Absolutes
Interface Enlightenment
One/Many in Logic and Set Theory
Mysticism and Rationality
Satori
Puzzles and Paradoxes
Excursion One: The Transfinite Cardinals
On and Alef-One
Cardinality
The Continuum
Large Cardinals
Excursion Two: Gödel’s Incompleteness Theorems
Formal Systems
Self-Reference
Gödel’s Proof
A Technical Note on Man-Machine Equivalence
Answers to the Puzzles and Paradoxes
Notes
Bibliography
Index
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