In Defence of Objective Bayesianism

by Williamson, Jon

• ISBN13: 9780199228003
• ISBN10: 0199228000
• Format: Hardcover
• Copyright: 2010-07-01
• Publisher: Oxford University Press

Summary

How strongly should you believe the various propositions that you can express?That is the key question facing Bayesian epistemology. Subjective Bayesians hold that it is largely (though not entirely) up to the agent as to which degrees of belief to adopt. Objective Bayesians, on the other hand, maintain that appropriate degrees of belief are largely (though not entirely)determined by the agent's evidence. This book states and defends a version of objective Bayesian epistemology. According to this version, objective Bayesianism is characterized by three norms: * Probability - degrees of belief should be probabilities* Calibration - they should be calibrated with evidence* Equivocation - they should otherwise equivocate between basic outcomesObjective Bayesianism has been challenged on a number of different fronts. For example, some claim it is poorly motivated, or fails to handle qualitative evidence, or yields counter-intuitive degrees of belief after updating, or suffers from a failure to learn from experience. It has also beenaccused of being computationally intractable, susceptible to paradox, language dependent, and of not being objective enough.Especially suitable for graduates or researchers in philosophy of science, foundations of statistics and artificial intelligence, the book argues that these criticisms can be met and that objective Bayesianism is a promising theory with an exciting agenda for further research.

Author Biography

Jon Williamson is Professor of Reasoning, Inference and Scientific Method in the philosophy department at the University of Kent and is Editor of the Reasoner, an interdisciplinary monthly digest highlighting exciting new research on reasoning, inference, and method.

Table of Contents

Introduction	p. 1
Objective Bayesianism outlined	p. l
Objective Bayesian theory	p. 2
Criticisms of objective Bayesianism	p. 3
Evidence, Language, and rationality	p. 4
Objective Bayesianism	p. 10
Desiderata for a theory of probability	p. 10
From Jakob Bernoulli to Edwin Jaynes	p. 12
A characterization of objective Bayesianism	p. 26
Motivation	p. 31
Beliefs and bets	p. 31
Probability	p. 33
Calibration	p. 39
Equivocation	p. 49
Radical subjectivism	p. 72
Updating	p. 75
Objective and subjective Bayesian updating	p. 75
Four kinds of incompatibility	p. 78
Criticisms of conditionalization	p. 82
A Dutch book for conditionalization?	p. 85
Conditionalization from conservativity?	p. 88
Summary	p. 89
Predicate Languages	p. 90
The framework	p. 90
The Probability norm	p. 92
Properties of the closer relation	p. 95
Closure	p. 96
Characterizing Equivocation	p. 98
Order invariance	p. 101
Equidistance	p. 103
Objective Bayesian Nets	p. 108
Probabilistic networks	p. 108
Representing objective Bayesian probability	p. 112
Application to cancer prognosis	p. 116
Probabilistic Logic	p. 121
A formal framework for probabilistic logics	p. 121
A range of semantics	p. 123
Objective Bayesian semantics	p. 129
A calculus for the objective Bayesian semantics	p. 133
Judgement Aggregation	p. 136
Aggregating judgements	p. 136
Belief revision and merging	p. 137
Merging evidence	p. 139
From merged evidence to judgements	p. 142
Discussion	p. 144
Languages and Relativity	p. 148
Richer languages	p. 148
Language relativity	p. 155
Objectivity	p. 157
Objective Bayesianism in Perspective	p. 163
The state of play	p. 163
Statistics	p. 165
Confirmation and science	p. 169
Epistemic metaphysics	p. 170
References	p. 173
Index	p. 183
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