Pure Inductive Logic

Pure Inductive Logic

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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.
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Product details

  • Hardback | 354 pages
  • 152 x 229 x 21mm | 640g
  • Cambridge, United Kingdom
  • English
  • 1 Line drawings, unspecified
  • 1107042305
  • 9781107042308
  • 2,827,584

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-Stegmuller 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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Review quote

'The monograph should prove an invaluable reference for researchers keen to embark on working in this area ...' Eric A. Martin, MathSciNet (www.ams.org/mathscinet)
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About Jeffrey Paris

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 Vencovska 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.
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