An Introduction to the Philosophy of Induction and Probability

This book means to introduce the reader to philosophical issues and arguments about probability and induction, not to survey the past and present range of those issues and arguments. The text is therefore highly selective both in the topics and authors that it discusses and also in the points that it makes about them. It seeks to present a coherent and readily intelligible picture of the field, with due regard to the difficulty of the fundamental philosophical issues, rather than to aim at a more comprehensive and encyclopaedic type of treatment. It economizes as much as possible in the use of mathematical symbolism, the statement of mathematical results and the derivation of statistical algorithms, because its concern is with the philosophical issues rather than with the mathematical ones. A broadly historical approach is adopted in the first chapter, in order to show how the central problems developed. The other five chapters seek to impose a clarificatory structure on the consideration of those problems. In order to assist understanding, each section is preceded by a summary of its contents. – The origins of this book are in a course of lectures given for some years within the Sub-Faculty of Philosophy at Oxford. – I. «The origins of the problem» (An outline of the issues; The Baconian tradition in the philosophy of induction; The rise of Pascalian probability; The combination of Baconian and Pascalian themes). – II. «The controversy about the nature of Pascalian probability» (Some general considerations; Indifference theories; Frequency theories; Propensity theories; Personalist theories; Multi-valued logic theories; Logical relation theories). – III. «The foundations of pluralism in the analysis of probability» (Some logical distinctions exploited by differing analyses of Pascalian probability; The appropriateness of different conceptions of Pascalian probability to different purposes; The need to supplement Pascalian judgements by non-Pascalian ones; How are different conceptions of probability possible ?). – IV. «The Pascalian gradation of ampliative induction» (Inductive probability under a realist construal; Inductive probability under a range-theoretical construal; Pascalian gradation for variative induction; Inductive probability under a personalist construal). – V. «The Baconian gradation of ampliative induction» (Inductive support by the Method of Relevant Variables; The logical syntax of the Method of Relevant Variables; Some non-standard interpretations of Baconian logical syntax). – VI. «Four paradoxes about induction» (The classical problem of induction; The paradox of the ravens; The ‘grue’ paradox; The lottery paradox). M.-M. V.