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.

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