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Pure Inductive Logic


Part of Perspectives in Logic

  • Date Published: April 2015
  • availability: Available
  • format: Hardback
  • isbn: 9781107042308

$ 120.00

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About the Authors
  • 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.

    • The first book to comprehensively treat inductive logic as a branch of mathematical logic, with many new existing results collected together into one unified presentation
    • A self-contained introduction to the field that takes the reader from the basics right through to the forefront of current research
    • Can also be used as an accessible work of reference for philosophers and computer scientists, as well as mathematical logic
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    Reviews & endorsements

    'The monograph should prove an invaluable reference for researchers keen to embark on working in this area …' Eric A. Martin, MathSciNet (

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    Product details

    • Date Published: April 2015
    • format: Hardback
    • isbn: 9781107042308
    • length: 354 pages
    • dimensions: 229 x 152 x 21 mm
    • weight: 0.64kg
    • contains: 1 b/w illus.
    • availability: Available
  • 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

  • Authors

    Jeffrey Paris, University of Manchester
    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, University of Manchester
    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.

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