Interpreting Probability: Controversies and Developments in the Early Twentieth Century David Howie Frontmatter More Information

Cambridge University Press 978-0-521-03754-9 - Interpreting Probability: Controversies and Developments in the Early Twentieth Century David Howie Frontmatter More information

Interpreting Probability

Interpreting Probability: Controversies and Developments in the Early Twen- tieth Century is a study of the two main types of probability: the “frequency interpretation,” in which a probability is a limiting ratio in a sequence of repeat- able events, and the “Bayesian interpretation,” in which probability is a mental construct representing uncertainty, and which applies not directly to events but to our knowledge of them. David Howie sketches the history of both types of probability and investi- gates how the Bayesian interpretation, despite being adopted at least implicitly by many scientists and statisticians in the eighteenth and nineteenth centuries, was discredited as the basis for a theory of scientific inference during the 1920s and 1930s. Through analysis of the work of two British scientists, Sir Harold Jeffreys and Sir Ronald Aylmer Fisher, and a close examination of a dispute between them in the early 1930s, Howie argues that a choice between the two interpretations of probability is not forced by pure logic or the mathematics of the situation, but rather depends on the experiences and aims of the individuals involved and their views of the correct form of scientific inquiry. Interpreting Probability will be read by academicians and students working in the history, philosophy, and sociology of science, particularly in probability and statistics, and by general readers interested in the development of the scientific method.

David Howie holds two doctorates, one in atomic physics from the University of Oxford and one in the history and sociology of science from the University of Pennsylvania. He lives in London.

© Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-03754-9 - Interpreting Probability: Controversies and Developments in the Early Twentieth Century David Howie Frontmatter More information

Cambridge Studies in Probability, Induction, and Decision Theory General editor: Brian Skyrms

Advisory editors: Ernest W. Adams, Ken Binmore, Jeremy Butterﬁeld, Persi Diaconis, William L. Harper, John Harsanyi, Richard C. Jeffrey, James M. Joyce, Wlodek Rabinowicz, Wolfgang Spohn, Patrick Suppes, Sandy Zabell

Ellery Eells, Probabilistic Causality Richard Jeffrey, Probability and the Art of Judgment Robert C. Koons, Paradoxes of Belief and Strategic Rationality Cristina Bicchieri and Maria Luisa Dalla Chiara (eds.), Knowledge, Belief, and Strategic Interactions Patrick Maher, Betting on Theories Cristina Bicchieri, Rationality and Coordination J. Howard Sobel, Taking Chances Jan von Plato, Creating Modern Probability: Its Mathematics, Physics, and Philosophy in Historical Perspective Ellery Eells and Brian Skyrms (eds.), Probability and Conditionals Cristina Bicchieri, Richard Jeffrey, and Brian Skyrms (eds.), The Dynamics of Norms Patrick Suppes and Mario Zanotti, Foundations of Probability with Applications Paul Weirich, Equilibrium and Rationality Daniel Hausman, Causal Asymmetries William A. Dembski, The Design Inference James M. Joyce, The Foundations of Causal Decision Theory Yair Guttmann, The Concept of Probability in Statistical Physics Joseph B. Kadane, Mark B. Schervish, and Teddy Seidenfeld (eds.), Rethinking the Foundations of Statistics Phil Dowe, Physical Causation Sven Ove Hansson, The Structure of Values and Norms Paul Weirich, Decision Space

Interpreting Probability Controversies and Developments in the Early Twentieth Century

DAVID HOWIE

CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

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First published 2002 This digitally printed version 2007

A catalogue record for this publication is available from the British Library

Library of Congress Cataloguing in Publication data Howie, David, 1970– Interpreting probability : controversies and developments in the early twentieth century / David Howie. p. cm. – (Cambridge studies in probability, induction, and decision theory) Includes bibliographical references and index. ISBN 0-521-81251-8 1. Probabilities. 2. Bayesian statistical decision theory. 3. Jeffreys, Harold, Sir, 1891–1989 4. Fisher, Ronald Aylmer, Sir, 1890–1962. I. Title. II. Series. QA273.A4 H69 2002 2001052430

ISBN 978-0-521-81251-1 hardback ISBN 978-0-521-03754-9 paperback

Contents

Acknowledgments page xi 1 Introduction 1 1.1 The meaning of probability 1 1.2 The history of probability 2 1.3 Scope of this book 4 1.4 Methods and argument 5 1.5 Synopsis and aims 11 2 Probability up to the Twentieth Century 14 2.1 Introduction 14 2.2 Early applications of the probability calculus 15 2.3 Resistance to the calculation of uncertainty 17 2.4 The doctrine of chances 19 2.5 Inverse probability 23 2.6 Laplacean probability 27 2.7 The eclipse of Laplacean probability 28 2.8 Social statistics 33 2.9 The rise of the frequency interpretation of probability 36 2.10 Opposition to social statistics and probabilistic methods 38 2.11 Probability theory in the sciences: evolution and biometrics 41 2.12 The interpretation of probability around the end of the nineteenth century 47 3 R.A. Fisher and Statistical Probability 52 3.1 R.A. Fisher’s early years 52 3.2 Evolution – the biometricians versus the Mendelians 53 3.3 Fisher’s early work 56 3.4 The clash with Pearson 59

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3.5 Fisher’s rejection of inverse probability 61 3.5.1 Fisher’s new version of probability 61 3.5.2 The papers of 1921 and 1922 62 3.5.3 The Pearson–Fisher feud 65 3.6 The move to Rothamsted: experimental design 70 3.7 The position in 1925 – Statistical Methods for Research Workers 72 3.8 The development of fiducial probability 75 3.9 Fisher’s position in 1932 79 4 Harold Jeffreys and Inverse Probability 81 4.1 Jeffreys’s background and early career 81 4.2 The Meteorological Office 83 4.3 Dorothy Wrinch 85 4.4 Broad’s 1918 paper 87 4.5 Wrinch and Jeffreys tackle probability 89 4.6 After the first paper 92 4.6.1 General relativity 92 4.6.2 The Oppau explosion 94 4.6.3 New work on probability – John Maynard Keynes 96 4.6.4 Other factors 101 4.7 Probability theory extended 103 4.7.1 The Simplicity Postulate 103 4.7.2 The papers of 1921 and 1923 107 4.8 The collaboration starts to crumble 109 4.9 Jeffreys becomes established 111 4.10 Probability and learning from experience – Scientific Inference 113 4.10.1 Science and probability 113 4.10.2 Scientific Inference 114 4.11 Jeffreys and prior probabilities 119 4.11.1 The status of prior probabilities 119 4.11.2 J.B.S. Haldane’s paper 121 4.12 Jeffreys’s position in 1932 126 5 The Fisher–Jeffreys Exchange, 1932–1934 128 5.1 Errors of observation and seismology 128 5.2 Fisher responds 133 5.3 Outline of the dispute 137

viii

5.4 The mathematics of the dispute 139 5.5 Probability and science 143 5.5.1 The status of prior probabilities 144 5.5.2 The Principle of Insufﬁcient Reason 148 5.5.3 The deﬁnition of probability 150 5.5.4 Logical versus epistemic probabilities 152 5.5.5 Role of science: inference and estimation 154 5.6 Conclusions 162 6 Probability During the 1930s 171 6.1 Introduction 171 6.2 Probability in statistics 172 6.2.1 The position of the discipline to 1930 172 6.2.2 Mathematical statistics 173 6.2.3 The Neyman–Fisher dispute 176 6.2.4 The Royal Statistical Society 180 6.2.5 The reading of Fisher’s 1935 paper 183 6.2.6 Statisticians and inverse probability 187 6.3 Probability in the social sciences 191 6.3.1 Statistics in the social sciences 191 6.3.2 Statistics reformed for the social sciences 194 6.3.3 The social sciences reformed for statistics 197 6.4 Probability in physics 199 6.4.1 General remarks 199 6.4.2 Probability and determinism: statistical physics 199 6.4.3 Probability at the turn of the century 202 6.4.4 The rejection of causality 204 6.4.5 The view in the 1930s 206 6.4.6 The interpretation of probability in physics 209 6.4.7 Quantum mechanics and inverse probability 211 6.5 Probability in biology 213 6.6 Probability in mathematics 216 6.6.1 Richard von Mises’s theory 216 6.6.2 Andrei Kolmogorov’s theory 219 6.7 Conclusions 220 7 Epilogue and Conclusions 222 7.1 Epilogue 222 7.2 Conclusions 226

Appendix 1 Sources for Chapter 2 231 Appendix 2 Bayesian Conditioning as a Model of Scientiﬁc Inference 235 Appendix 3 Abbreviations Used in the Footnotes 237 Bibliography 239 Index 253

Acknowledgments

This book grew out of a doctoral dissertation completed in the Department of the History and Sociology of Science at the University of Pennsylvania. I am indebted to my supervisor there, Professor Robert E. Kohler, both for his moral support and for his detailed and constructive criticism of my work. I am also grateful to Professor M. Norton Wise, then at Princeton and the second member of my committee, for his encouragement and advice. A number of statisticians were willing to answer my queries on the Jeffreys–Fisher debate, and to comment more generally on twentieth-century interpretations of probability. I am grateful here to Professors M.S. Bartlett and I.J. Good. It has been a particular privilege to have corresponded with Professor George Barnard during the last few years. He was also kind enough to read through the entire manuscript, and his insightful comments have helped me avoid many statistical and historical blunders, and have greatly enriched my understanding and feel for the thinking of the period. Professor Paul Forman of the Smithsonian Institution read through an earlier draft, too, as did a philosopher, Dr Matt Cavanagh. Their suggestions have much improved the final text. Thanks, too, for comments and suggestions from Professor John Forrester of Cambridge, and for the support and advice of Dr Elisa Becker of the American Bar Foundation. Ronald Cohen edited the manuscript judiciously. Special gratitude is due to Lady Jeffreys, for granting me access to her late husband’s papers, and for providing me with encouragement and conversation during the weeks I worked in her home researching this book. I deeply regret her passing away before it was completed. I spent my first two years in Philadelphia as a Fulbright Scholar; thereafter, I was funded by the University of Pennsylvania, first as a teaching assistant, then as a doctoral dissertation fellow. The American Institute of Physics supported a research trip to England in early 1997. I completed my research during the summer of 1998 as a research fellow at the Smithsonian Institution. Finally, I thank the directors and shareholders of Oxford Nanotechnology Plc for their generous support while I finished the manuscript.