Symmetry and its Discontents

This volume brings together a collection of essays on the history and philosophy of probability and statistics by one of the eminent scholars in these subjects. Written over the last fifteen years, they fall into three broad categories. The first deals with the use of symmetry arguments in inductive probability, in particular, their use in deriving rules of succession (Carnap’s ‘continuum of inductive methods’). The second group deals with four outstanding individuals who made lasting contributions to probability and statistics in very different ways: Frank Ramsey, R. A. Fisher, Alan Turing, and Abraham de Moivre. The last group of essays deals with the problem of ‘predicting the unpredictable’ - making predictions when the range of possible outcomes is unknown in advance. The essays weave together the history and philosophy of these subjects and document the fascination that they have exercised for more than three centuries.

• Interweaving of history, philosophy and mathematics • Focus on important Cambridge personalities: Ramsey, Fisher, and Turing • Explains the origins of modern subjective probability

Part I. Probability: 1. Symmetry and its discontents; 2. The rule of succession; 3. Buffon, Price, and Laplace: scientific attribution in the eighteenth century; 4. W. E. Johnson’s sufficientness postulate. Part II. Personalities: 5 Abraham De Moivre and the birth of the Central Limit Theorem; 6 Ramsey, truth, and probability; 7. R. A. Fisher on the history of inverse probability; 8. R. A. Fisher and the fiducial argument; 9. Alan Turing and the Central Limit Theorem; Part III. Prediction: 10. Predicting the unpredictable; 11. The continuum of inductive methods revised.