Paradoxes in Probability Theory

By: William Eckhardt

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Paperback | 27 September 2012

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96 Pages

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Paradoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.

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Non-Fiction Philosophy Philosophy & Logic Mathematics Probability & Statistics Science Science in General Philosophy of Science

Seven Paradoxes	p. 1
The Doomsday Argument	p. 1
The Betting Crowd	p. 2
The Simulation Argument	p. 2
Newcomb's Problem	p. 2
The Open Box Game	p. 3
The Hardon Collider Card Experiment	p. 3
The Two-Envelopes Paradox	p. 3
References	p. 4
Anthropic Fallacies
Doomsday!	p. 7
Randomness in Reference Class	p. 8
Retrocausality	p. 9
References	p. 10
The Betting Crowd	p. 11
Randomness and Reference Class	p. 12
Retrocausality	p. 13
Reference	p. 13
The Simulation Argument	p. 15
Randomness and Reference Class	p. 15
Retrocausality	p. 16
Summary	p. 17
References	p. 17
Dilemmas of Cooperation
Newcomb's Problem	p. 21
Preliminaries	p. 21
Three Problems, Four Theories	p. 22
Correlation	p. 25
Advisors	p. 26
Coherence	p. 30
The Perils of Incoherence	p. 33
References	p. 34
The Open Box Game	p. 35
The Hadron Collider Card Experiment	p. 39
Another Open Box Game	p. 40
References	p. 44
Mystifying Envelopes
The Two-Envelopes Problem	p. 47
Opening the Envelope	p. 48
How to Play	p. 55
Summary	p. 58
References	p. 58
Odds and Ends	p. 59
Doomsday	p. 59
The Betting Crowd	p. 61
Sims	p. 61
Newcomb's Problem	p. 62
Alternatives to Advisors	p. 62
The Consequence of Randomization	p. 63
Liebnitzian Lethargy	p. 64
Coherence Implies Stability	p. 65
Is the Card Game at all Feasible?	p. 66
Two Envelopes	p. 67
Additional Approaches?	p. 67
Causal Structure	p. 70
The Finite Two-Envelopes Game	p. 71
Ross's Theorem	p. 72
References	p. 73
Epilogue: Anthropic Eden	p. 75
Index	p. 77
Table of Contents provided by Ingram. All Rights Reserved.

Paradoxes in Probability Theory

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