TEN GREAT IDEAS ABOUT CHANCE T E N G R E AT I D E A S A B O U T C H A N C E PERSI DIACONIS BRIAN SKYRMS PRINCETON UNIVERSITY PRESS Princeton and Oxford Copyright © 2018 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TR press.princeton.edu Jacket image courtesy of Shutterstock All Rights Reserved ISBN 978- 0- 691- 17416- 7 Library of Congress Control Number 2017943311 British Library Cataloging- in- Publication Data is available This book has been composed in Sabon Next LT Pro text with Akzidenz Grotesk BQ Display Printed on acid- free paper. ∞ Printed in the United States of America 1 3 5 7 9 10 8 6 4 2 WE DEDICATE THIS BOOK TO THE MEMORY OF Richard “Diamond Jim” Jeffrey, good friend and true philosopher. CONTENTS Preface ix Acknowledgments xi 1. Measurement 1 2. Judgment 22 3. Psychology 48 4. Frequency 62 5. Mathematics 79 6. Inverse Inference 100 7. Unification 122 8. Algorithmic Randomness 145 9. Physical Chance 165 10. Induction 190 Appendix: Probability Tutorial 209 Notes 225 Annotated Select Bibliography 239 Image Credits 247 Index 249 PREFACE This book grew out of a course that we taught together at Stanford for about 10 years. This was a large, mixed course. There were under- graduates and graduates. There were participants from philosophy, statistics, and a number of other disciplines across the academic spectrum. As the course evolved over time, we came to believe that the story we are telling would be of interest to a larger audience. Our course had as a prerequisite exposure to one course in probability or statistics. Our book retains this level. But for the reader who may have had such a course a long time ago, we have included an appendix designed as a probability refresher. This is a history book, a probability book, and a philosophy book. We give the history of what we see as great ideas in the development of probability, but we also pursue the philosophical import of these ideas. One reader of an earlier version of this manuscript complained that at the end of the book, he still did not know our philosophical views about chance. We were, perhaps, too evenhanded. This prob- lem has now been fixed. You will see that we are thorough Bayesians, followers of Bayes, Laplace, Ramsey, and deFinetti. Bayesianism is sometimes thought to be opposed to frequencies. We insist that our view does not deny the importance of frequencies or the usefulness of talking about objective chances. Rather, it unifies these consider- ations within the framework of rational degrees of belief. At the beginning of this book we are thinking along with the pio- neers, and the tools involved are simple. By the end, we are up to the present, and some technicalities have to be at arm’s length. We try to ease the flow of exposition by putting some details in appendices,