§§ 1, 2. Preliminary remarks. 3, 4. Are we accurately conscious of gradations of belief? 5. Probability only concerned with part of this enquiry. 6. Difficulty of measuring our belief; 7. Owing to intrusion of emotions, 8. And complexity of the evidence. 9. And when measured, is it always correct? 10, 11. Distinction between logical and psychological views. 12-16. Analogy of Formal Logic fails to show that we can thus detach and measure our belief. 17. Apparent evidence of popular language to the contrary. 18. How is full belief justified in inductive enquiry? 19-23. Attempt to show how partial belief may be similarly justified. 24-28. Extension of this explanation to cases which cannot be repeated in experience. 29. Can other emotions besides belief be thus measured? 30. Errors thus arising in connection with the Petersburg Problem. 31, 32. The emotion of surprise is a partial exception. 33, 34. Objective and subjective phraseology. 35. The definition of probability, 36. Introduces the notion of a 'limit', 37. And implies, vaguely, some degree of belief. CHAPTER VII. THE RULES OF INFERENCE IN PROBABILITY. § 1. Nature of these inferences. 2. Inferences by addition and subtraction. 3. Inferences by multiplication and division. 4-6. Rule for independent events. 7. Other rules sometimes introduced. 8. All the above rules may be interpreted subjectively, i.e. in terms of belief. 9-11. Rules of so-called Inverse Probability. 12, 13. Nature of the assumption involved in them: 14-16. Arbitrary character of this assumption. 17, 18. _Physical illustrations._ CHAPTER VIII. THE RULE OF SUCCESSION. § 1. Reasons for desiring some such rule: 2. Though it could scarcely belong to Probability. 3. Distinction between Probability and Induction. 4, 5. Impossibility of reducing the various rules of the latter under one head. 6. Statement of the Rule of Succession; 7. _Proof offered for it._ 8. _Is it a strict rule of inference?_ 9. _Or is it a psychological principle?_ CHAPTER IX. INDUCTION. §§ 1-5. Statement of the Inductive problem, and origin of the Inductive inference. 6. Relation of Probability to Induction. 7-9. The two are sometimes merged into one. 10. Extent to which causation is needed in Probability. 11-13. Difficulty of referring an individual to a class: 14. This difficulty but slight in Logic, 15, 16. But leads to perplexity in Probability: 17-21. Mild form of this perplexity; 22, 23. Serious form. 24-27. Illustration from Life Insurance. 28, 29. Meaning of 'the value of a life'. 30, 31. Successive specialization of the classes to which objects are referred. 32. Summary of results. CHAPTER X. CHANGE, CAUSATION AND DESIGN.