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• Part I. Fundamental Ideas: 1. The meaning of probability; 2. Probability in relation to the theory of knowledge; 3. The measurement of probabilities; 4. The principle of indifference; 5. Other methods of determining probabilities; 6. The weight of arguments; 7. Historical retrospect; 8. The frequency theory of probability; 9. The constructive theory of Part I summarised; Part II. Fundamental Theories: 10. Introductory; 11. The theory of groups, with special inference, and logical priority; 12. The definitions and axioms of inference and probability; 13. The fundamental theorems of necessary inference; 14. The fundamental theorems of probable inference; 15. Numerical measurement and approximation of probabilities; 16. Observations on the theorems of Chapter 14 and their developments including testimony; 17. Some problems in inverse probability, including averages; Part III. Induction and Analogy: 18. Introduction; 19. The nature of argument by analogy; 20. The value of multiplication of instances, or pure induction; 21. The nature of inductive argument continued; 22. The justification of these methods; 23. Some historical notes on induction notes on Part III; Part IV. Some Philosophical Applications of Probability: 24. The meanings of objective chance, and of randomness; 25. Some problems arising out of the discussion of chance; 26. The application of probability to conduct; Part V. The Foundations of Statistical Inference: 27. The nature of statistical inference; 28. The law of great numbers; 29. The use of a priori probabilities for the prediction of statistical frequency - the theorems of Bernoulli, Poisson, and Tchebycheff; 30. The mathematical use of statistical frequencies for the determination of probability a posteriori - the methods of Laplace; 31. The inversion of Bernoulli's theorem; 32. The inductive use of statistical frequencies for the determination of probability a posteriori - the methods of Lexis; 33. Outline of a constructive theory.