Labyrinths of Reason

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Authors: William Poundstone

BOOK: Labyrinths of Reason
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To William Hilliard, Jr.

Contents

P
ART
O
NE

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

2.
  
Induction: Hempel’s Raven

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?

P
ART
T
WO

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

8.
  
Infinity: The Thomson Lamp

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

P
ART
T
HREE

10.
  
Meaning: Twin Earth

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
.

Bibliography

About the Author

PART ONE

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.

Brains in Vats

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?

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