Table of Contents
Cats and Tails v
Acknowledgments ix
The Dark Side - Paradoxes 1
Part I Magic 3
An Elusive Crook 5
A Nation Enamored with Paradoxes 8
Zeno and Tortoises 10
Are there Sand Heaps in the World? 13
Crocodiles and Lawyers 15
Epimenides and the Mishtakes 17
A Useful Paradox 20
Smullyan's Island 22
Proving the Existence of the Loch Ness Monster 24
Part II Free Will 27
Newcomb Overturns the Rules of Nature 29
Written in the Stars 32
Nothing to It - Or Perhaps There is Something? 35
The Idle Argument 37
Why Can We Not Change the Past? 40
And Yet It Moves? 43
Cat and Tail: Choosing the Choice 45
The Matrix 47
All is Foreseen (From the Outside) and Permission is Granted (From the Inside) 49
Part III The Mind-Body Problem 51
A Meeting of Non-Meeters 53
The Philosophical Discontent 55
A Therapist of Thought 57
Ryle Visits a University 60
From the Inside or From the Outside? 62
Direct Knowledge 64
Socrates and Lewis Carroll on Direct Knowledge 66
How do People Learn about Their Mental Events? 68
The Cat Sits, Therefore the Cat Is 70
The Red King's Dream 72
The Illuminated Side - Scientific Breakthroughs 75
Part IV Large Infinities and Still Larger Ones 77
You Shall See the Land from Afar 79
What is "Counting" 82
A Surprise 84
Inequality Between Sets 87
Cantor Plays with Mr. Potato Head 90
The Paradoxes of Set Theory 94
Part V Godel's Incompleteness Theorem 97
A Revolution in a Small Town 99
Copernican Revolutions 101
The Cement of Mathematical Thought 104
Meanwhile, Across the Channel 107
A Very Ambitious and Very Wrong Program 109
Gödel's Paradox 112
From Paradox to Proof 114
Surprise Tests 117
The Theorem of the Century? 119
Why it was Imperative to Mummify Lenin 122
Part VI Turing Invents the Computer 125
From Olympus Down to Earth 127
The Halting Problem 129
The Imitation Game 131
Searle's Chinese Room 134
Personality and Genius 136
Can a Machine Know that it is a Machine? 137
Three Families, One Secret 139
The Jail of Personality 147
Part VII For the Experienced Hikers 151
The Diagonal Method 153
Conclusion: The Real Numbers are Not Countable 155
A Methodical but Not Very Efficient Detective 156
Why Godel's Paradox Doesn't Generate a Mathematical Contradiction 158
Why the Incompleteness Theorem Doesn't Contradict the Completeness Theorem 160
Bibliography 163
