Pure Inductive Logic

Jeff Paris is a Professor in the School of Mathematics at the University of Manchester. His research interests lie in mathematical logic, particularly set theory, models of arithmetic and non-standard logics. In 1983 he was awarded the London Mathematical Society's Junior Whitehead Prize and in 1999 was elected a Fellow of the British Academy in the Philosophy Section. He is the author of The Uncertain Reasoner's Companion (Cambridge University Press, 1995). Alena Vencovská received her PhD from Charles University, Prague. She has held a string of research and lecturing positions in the School of Mathematics at the University of Manchester. Her research interests include uncertain reasoning, nonstandard analysis, alternative set theory and the foundations of mathematics.

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.