Pure inductive logic /
Pure inductive logic is the study of rational probability treated as a branch of mathematical logic. This monograph, the first devoted to this approach, brings together the key results from the past seventy years plus the main contributions of the authors and their collaborators over the last decade...
| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge ; New York :
Cambridge University Press,
2015.
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| Series: | Perspectives in logic.
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| Subjects: |
Table of Contents:
- Part I. The Basics: 1. Introduction to pure inductive logic; 2. Context; 3. Probability functions; 4. Conditional probability; 5. The Dutch book argument; 6. Some basic principles; 7. Specifying probability functions; Part II. Unary Inductive Logic: 8. Introduction to unary pure inductive logic; 9. de Finetti's representation theorem; 10. Regularity and universal certainty; 11. Relevance; 12. Asymptotic conditional probabilities; 13. The conditionalization theorem; 14. Atom exchangeability; 15. Carnap's continuum of inductive methods; 16. Irrelevance; 17. Another continuum of inductive methods; 18. The NP-continuum; 19. The weak irrelevance principle; 20. Equalities and inequalities; 21. Principles of analogy; 22. Unary symmetry; Part III. Polyadic Inductive Logic: 23. Introduction to polyadic pure inductive logic; 24. Polyadic constant exchangeability; 25. Polyadic regularity; 26. Spectrum exchangeability; 27. Conformity; 28. The probability functions $u^{ overline{p},L}$; 29. The homogeneous/heterogeneous divide; 30. Representation theorems for Sx; 31. Language invariance with Sx; 32. Sx without language invariance; 33. A general representation theorem for Sx; 34. The Carnap-Stegmüller principle; 35. Instantial relevance and Sx; 36. Equality; 37. The polyadic Johnson's sufficientness postulate; 38. Polyadic symmetry; 39. Nathanial's invariance principle, NIP; 40. NIP and atom exchangeability; 41. The functions $u_{ overline{E}}^{ overline{p},L}$; 42. The state of play; Bibliography; Index; Glossary.