Read Labyrinths of Reason Online
Authors: William Poundstone
To William Hilliard, Jr.
1.
Paradox
Brains in Vats
•
Dreams and Evil Geniuses
•
Ambiguity
•
Is Anything Certain?
•
Deduction and Induction
•
Confirmation Theory
•
Paradox
•
Science as a Map
•
Paradox and SATISFIABILITY
•
The Universal Problem
Confirmation
•
Matter and Antimatter
•
Absolute and Incremental Confirmation
•
Counterexamples
•
Crank Theories
•
Contrapositives
•
Never Say Never
•
Stream of Consciousness
•
Infinitesimal Confirmation
•
The Paradox of the 99-Foot Man
•
Ravens and Total Evidence
3.
Categories: The Grue-Bleen Paradox
Grue Emeralds
•
Gerrymander Categories
•
Counterfactuals
•
The Rotating Color Wheel
•
The Inverted Spectrum
•
Demon Theory No. 16
•
Anything Confirms Anything
•
Ockam’s Razor
•
The Day of Judgment
•
Projectability
•
Are Quark Colors Grue-ish?
4.
The Unknowable: Nocturnal Doubling
Antirealism
•
Physics Goes Haywire
•
Demons and Doubling
•
Variations
•
Did Time Begin Five Minutes Ago?
•
Perils of Antirealism
•
Black-Hole Probes
•
Other Minds
•
Nocturnal Doubling of Pleasure/Pain
•
Is Reality Unique?
Interlude: The Puzzles of John H. Watson, M.D
.
A Test of Ingenuity
•
Gas, Water, and Electricity
•
The Company Grapevine
•
The Graveyard Riddle
•
A Surveyor’s Quandary
•
Solutions
5.
Deduction: The Paradox of the Heap
Theseus’ Ship
•
Sorites
•
Complexity
•
Liars and Truth Tellers
•
Who Is Lying?
•
SATISFIABILITY
•
The Pork-Chop Problem
•
The Elevator Problem
•
Science and Puzzles
6.
Belief: The Unexpected Hanging
Pop Quizzes and Hidden Eggs
•
Hollis’s Paradox
•
A Minimal Paradox
•
A Time-Travel Paradox
•
What Is Knowledge?
•
Science and the Tripartite Account
•
Buridan Sentences
•
Gettier Counterexamples
•
A Fourth Condition
•
The Prisoner and Gettier
7.
The Impossible: The Expectancy Paradox
Catch-22
•
Can Such Things Be?
•
Possible Worlds
•
How Many Worlds Are Possible?
•
Paradox and Possible Worlds
•
The Paradox of the Preface
•
Must Justified Beliefs Be Compatible?
•
Pollock’s Gas Chamber
The Pi Machine
•
Zeno’s Paradoxes
•
Building a Thomson Lamp
•
Geometric Progressions
•
The Malthusian Catastrophe
•
Olbers’s Paradox
•
Against Plurality
•
Olbers’s Paradox Resolved
•
The Paradox of Tristram Shandy
9.
NP-Completeness: The Labyrinth of Ts’ui Pên
NP-Complete
•
Maze Algorithms
•
The Right-Hand Rule
•
The Trémaux Algorithm
•
An Infinite Labyrinth
•
The Ore Algorithm
•
NP-Completeness of the Maze
•
The Oracle of the Maze
•
P and NP
•
The Hardest Problem
•
A Catalogue of Experience
•
A Computer as Big as the Universe
Roger Bacon
•
False Decodings
•
Sense and Gibberish
•
The Parable of the Cave
•
The Electronic Cave
•
The Binary Cave
•
Can a Brain in a Vat Know It?
•
Twin Earth
•
Twin Earth Chemistry
•
The Libraries of Atlantis
•
Poe’s iiiii … Cipher
•
Brute Force
•
Justifying a Decipherment
•
Where Is Meaning?
11.
Mind: Searle’s Chinese Room
The Thinking Machine
•
The Paradox of Functionalism
•
The Turing Test
•
The Chinese Room
•
Brains and Milk
•
Reactions
•
Chinese the Hard Way
•
Dr. Jekyll and Mr. Hyde
•
The Systems Reply
•
A Page from the Instructions
•
A Conversation with Einstein’s Brain
12.
Omniscience: Newcomb’s Paradox
The Paradox of Omniscience
•
The Prisoner’s Dilemma
•
Newcomb’s Paradox
•
Reactions
•
Glass Boxes
•
Nozick’s Two Principles of Choice
•
Must It Be a Hoax?
•
Two Types of Prediction
•
Chaos
•
Free Will vs. Determinism
•
Prediction and Infinite Regress
•
Newcomb’s Paradox 3000
A.D
.
B
LUE SKY, sunshine, déjà vu glazed with dread. Something horrible is going to happen about now. It is a perfect summer day in a meadow of tall grass. J.V. is following her brothers, lagging lazily behind. A shadow falls on the ground; something rustles the grass. J.V. turns—she cannot help it, it is what happens next—and sees a strange man. He has no face, like a minor character in a dream. The man holds something writhing and indistinct. He asks, “How would you like to get into this bag with the snakes?”
J.V.’s encounter is an unlikely milestone of twentieth-century thought. J.V., a fourteen-year-old girl, was not in a summer field but on an operating table in the Montreal Neurological Institute. Her physician, Wilder Penfield, was attempting an experimental operation to relieve her violent epileptic seizures. The operating
team had removed the side of J.V.’s skull to expose the temporal lobe of the brain. In order to locate the site of the attacks, Penfield probed the brain with an electrode connected to an EEG machine. The surgery was a collaboration between physician and patient. J.V. had to remain conscious throughout and help locate the site of the seizures. When Penfield touched the probe to a certain spot on J.V.’s temporal lobe, she again found herself in the field of grass …
J.V.’s experience with the strange man had occurred seven years earlier, in Canada, in what we call the real world. She reported seeing herself as she was then, a seven-year-old girl. J.V. had been frightened but not physically harmed, and ran crying home to her mother. These few moments of terror were to haunt her over and over. The man with the bag of snakes entered her dreams, made them nightmares. The trauma became interwoven with her epileptic seizures. Like a madeleine, a fleeting recollection would trigger the whole memory, then an attack.
Under the EEG probe, J.V. not merely recalled but
relived
the encounter. All the richness of detail, all the lucid horror of the original experience, came back. Penfield’s probe caused the brain to replay past experiences like a movie. With bits of lettered or numbered paper, Penfield kept track of the sites on the cerebral cortex associated with the recollection. Touching nearby points produced different sensations. When the probe touched one point, J.V. recalled people scolding her for doing something wrong. Other sites produced only a phantasmagoria of colored stars.
Penfield’s classic brain experiments of the 1930s inspired a certain famous riddle, long since dubbed “brains in vats” by philosophy students. It goes like this: You think you’re sitting there reading this book. Actually, you could be a disembodied brain in a laboratory somewhere, soaking in a vat of nutrients. Electrodes are attached to the brain, and a mad scientist is feeding it a stream of electrical impulses that exactly
simulates
the experience of reading this book!
Let’s expand a little on the anecdote to see the full force of this. At some indistinct past time, while you were sleeping, your brain was removed from your body. Every nerve was severed by skilled surgeons and attached to a microscopic electrode. Each of these millions of electrodes is hooked to a machine that produces tiny electrical pulses just as the original nerves did.
When you turn the page, it
feels
like a page because the electrodes send your brain exactly the same nerve impulses that would have come from real fingers grasping a real page. But the page and the fingers are illusion. Bringing the book closer to your face makes it look bigger; holding it at arm’s length makes it look smaller … 3-D perspective is simulated by judiciously adjusting the voltages of the electrodes attached to the stump of the optic nerve. If, right this instant, you can smell spaghetti cooking and hear dulcimer music in the background, that is part of the illusion too. You can pinch yourself and receive the expected sensation, but it will prove nothing. In fact,
there’s no way you can prove that this isn’t so
. How, then, can you justify your belief that the external world exists?