This reissue of D. A. Gillies highly influential work, first published in 1973, is a philosophical theory of probability which seeks to develop von Mises' views on the subject. In agreement with von Mises, the author regards probability theory as a mathematical science like mechanics or electrodynamics, and probability as an objective, measurable concept like force, mass or charge. On the other hand, Dr Gillies rejects von Mises' definition of probability in terms of limiting frequency and claims that probability should be taken as a primitive or undefined term in accordance with modern axiomatic approaches. This of course raises the problem of how the abstract calculus of probability should be connected with the 'actual world of experiments'. It is suggested that this link should be established, not by a definition of probability, but by an application of Popper's concept of falsifiability. In addition to formulating his own interesting theory, Dr Gillies gives a detailed criticism of the generally accepted Neyman Pearson theory of testing, as well as of alternative philosophical approaches to probability theory. The reissue will be of interest both to philosophers with no previous knowledge of probability theory and to mathematicians interested in the foundations of probability theory and statistics.

Part One: The Special Sciences in General 1. Von Mises' Philosophy of Science: Its Machian Origins 2. Force and Mass 3. Conceptual Innovation in the Exact Sciences Part Two: The Axiomatic Superstructure 4. Probability and Frequency 5. Repeatability and Independence 6. Deduction of the Law of Excluded Gambling Systems: The Role of Randomness in Probability Theory 7. Probabilities of Single Events: Popper's Propensity Theory Part Three: A Falsifying Rule for Probability Statements 8. The Falsification Problem for Probability Statements 9. Formulation of a Falsifying Rule 10. Evaluation of the Falsifying Rule 11. The Neyman-Pearson Theory