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 to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts,…mehr
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 to present a comprehensive account of the discipline within a single unified context. The exposition is structured around the traditional bases of rationality, such as avoiding Dutch Books, respecting symmetry and ignoring irrelevant information. The authors uncover further rationality concepts, both in the unary and in the newly emerging polyadic languages, such as conformity, spectrum exchangeability, similarity and language invariance. For logicians with a mathematical grounding, this book provides a complete self-contained course on the subject, taking the reader from the basics up to the most recent developments. It is also a useful reference for a wider audience from philosophy and computer science.
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).
Inhaltsangabe
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.
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.
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