§ 1. Old Theological objection to Chance. 2-4. Scientific version of the same. 5. Statistics in reference to Free-will. 6-8. Inconclusiveness of the common arguments here. 9, 10. _Chance as opposed to Physical Causation._ 11. _Chance as opposed to Design in the case of numerical constants._ 12-14. _Theoretic solution between Chance and Design._ 15. _Illustration from the dimensions of the Pyramid._ 16, 17. _Discussion of certain difficulties here._ 18, 19. _Illustration from Psychical Phenomena._ 20. Arbuthnott's Problem of the proportion of the sexes. 21-23. Random or designed distribution of the stars. (_Note on the proportion of the sexes_.) CHAPTER XI. MATERIAL AND FORMAL LOGIC. §§ 1, 2. _Broad distinction between these views;_ 2, 3. _Difficulty of adhering consistently to the objective view;_ 4. _Especially in the case of Hypotheses._ 5. The doubtful stage of our facts is only occasional in Inductive Logic. 6-9. But normal and permanent in Probability. 10, 11. Consequent difficulty of avoiding Conceptualist phraseology. CHAPTER XII. CONSEQUENCES OF THE DISTINCTIONS OF THE PREVIOUS CHAPTER. §§ 1, 2. Probability has no relation to time. 3, 4. Butler and Mill on Probability before and after the event. 5. Other attempts at explaining the difficulty. 6-8. What is really meant by the distinction. 9. Origin of the common mistake. 10-12. Examples in illustration of this view, 13. Is Probability relative? 14. What is really meant by this expression. 15. Objections to terming Probability relative. 16, 17. In suitable examples the difficulty scarcely presents itself. CHAPTER XIII. ON MODALITY. § 1. Various senses of Modality; 2. Having mostly some relation to Probability. 3. Modality must be recognized. 4. Sometimes relegated to the predicate, 5, 6. Sometimes incorrectly rejected altogether. 7, 8. Common practical recognition of it. 9-11. Modal propositions in Logic and in Probability. 12. Aristotelian view of the Modals; 13, 14. Founded on extinct philosophical views; 15. But long and widely maintained. 16. Kant's general view. 17-19. The number of modal divisions admitted by various logicians. 20. Influence of the theory of Probability. 21, 22. Modal syllogisms. 23. Popular modal phraseology. 24-26. Probable and Dialectic syllogisms. 27, 28. Modal difficulties occur in Jurisprudence. 29, 30. Proposed standards of legal certainty. 31. Rejected formally in English Law, but possibly recognized practically. 32. How, if so, it might be determined. CHAPTER XIV. FALLACIES.