Table Of Contenti
Chance in the World
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OXFORD STUDIES IN PHILOSOPHY OF SCIENCE
General Editor:
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Chance in the World: A Humean
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Guide to Objective Chance
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Chance in the World
A Humean Guide to Objective Chance
CARL HOEFER
ICREA and University of Barcelona
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Contents
List of Boxes vii
Analytic Table of Contents ix
Preface xix
Acknowledgments xxv
1. Metaphysical Preliminaries 1
1.1. Humean Objective Chance (HOC): A First Sketch 1
1.2. The Humean Mosaic 6
1.3. The Dialectics of Primitive Chance 16
1.4. Chance as Hypothetical Infinite- Run
Frequency: Propensities Made Respectable? 35
1.5. Summing Up 42
2. From Lewisian Chance to Humean Chance 47
2.1. Principal Principle (PP) 47
2.2. Time and Chance 50
2.3. Lewis’s Best System Analysis (BSA) of Laws
and Chance 53
2.4. Chance and Determinism 57
2.5. Chance and Credence 59
2.6. Summing Up 62
3. Humean Objective Chance 63
3.1. The Basic Features 63
3.2. Examples 70
3.3. The Best System of Chances 80
3.4. More about the Contents of the Best System 87
3.5. Summing Up 95
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4. Deducing the Principal Principle 98
4.1. Deducing the Reasonableness of PP 99
4.2. PP and the Epistemology of HOC 125
4.3. Other Accounts and PP 129
4.4. Summing Up 137
5. Undermining 138
5.1. Undermining— What Is It? 139
5.2. Is the Contradiction Real? 140
5.3. The Lewis- Hall Solution 148
5.4. Independence for Humeans 152
5.5. The NP Solution Redeemed 155
5.6. Summing Up 158
6. Macro- Level and Micro- Level Chances 163
6.1. A Chance for All Setups? 163
6.2. Epistemology of Micro- Derived Chances 165
6.3. Micro-D erived Chances and PP 166
6.4. Summing Up 179
7. Humean Chance in Physics (coauthored
with Roman Frigg) 181
7.1. Introduction 181
7.2. Classical Statistical Mechanics 183
7.3. Quantum Chances 198
7.4. Summing Up 212
8. Chance and Causation 214
8.1. A Reductive Relation? 214
8.2. Bob’s Great Presentation 217
8.3. The Cause- Credence Principle 221
8.4. More on Causation 227
8.5. Summing Up 234
Concluding Remarks 237
Bibliography 241
Index 249
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Boxes
1.1 What Is Credence or Subjective Probability or Degree of Belief? 3
1.2 How to Think about a Growing Block World 10
1.3 A Further Attempt at the Modal Content of Chancy Laws 22
1.4 An IBE to Primitive Chances? 32
1.5 On Subjectivism 44
3.1 The Method of Arbitrary Functions Approach 75
3.2 Does PP Really Need an Admissibility Clause? 92
3.3 A Cosmic Dilemma for HOC? 95
4.1 Sleeping Beauty: A Counterexample to PP? 111
5.1 Does NP* Need a Separate Justification? 159
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Analytic Table of Contents
Chapter 1: Metaphysical Preliminaries
The chapter starts with a rough first approximation to the theory
of chance to be developed. Objective chance facts are grounded on
the existence of patterns in the events found in our world’s Humean
Mosaic; and the chance facts so grounded will later be seen to be apt
for guiding rational credences (subjective probabilities) in the way
captured by the Principal Principle (PP), which in one form can be
written:
PP: Cr(A|XE) = x,
where X is the proposition that the objective chance of A is x, and E is
background knowledge.
After laying out the basic idea, the rest of the chapter is dedicated to
exploring two issues. First, what is this Humean Mosaic (HM)? What
does it contain, and what does it leave out? What understanding of
time is presupposed? What sorts of properties and things make up
the events in the HM? Unlike Lewis and other Humeans, I do not
insist that the HM have only “occurrent properties” in it; I am happy
to allow ordinary dispositions, causal relations and/ or causal powers,
and suchlike things— as long as they are not probabilistic. I also adopt
an agnostic or ecumenical attitude concerning the laws of nature: they
may be Humean facts supervening on the HM, or primitives, or
even necessary truths of some sort— again, as long as they are not
probabilistic.
Second, the rest of the chapter gives an extended discussion of the
idea of considering objective chance facts to be primitives of some
sort, as most propensity views hold, or to be based on primitively
