Normal view MARC view ISBD view

# Pure inductive logic / Jeffrey Paris, University of Manchester; Alena Vencovská, University of Manchester.

Material type: TextSeries: Perspectives in logic.Publisher: New York : Cambridge University Press, 2015Description: x, 342 pages; UKP 82.00 23 cms.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781107042308 (hardback).Subject(s): Induction (Logic) | MATHEMATICS / LogicDDC classification: 161 Other classification: MAT018000 Online resources: Cover image
Contents:
Machine generated contents note: 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.
Summary: "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"-- Provided by publisher.
List(s) this item appears in: 2018-07-27
Item type Current location Call number Status Date due Barcode Item holds
Book Chennai Mathematical Institute
General Stacks
161 PAR (Browse shelf) Available 10407
Total holds: 0
##### Browsing Chennai Mathematical Institute Shelves , Shelving location: General Stacks Close shelf browser
 No cover image available No cover image available 153.83 ARI Predictably irrational : the hidden forces that shape our decisions / 155.5 VAR The effectiveness of counselling on adolescents in relation to psychological stress, self-concept, adjustment, and educational aspirations / 158.1 PET 12 rules for life : an antidote to chaos / 161 PAR Pure inductive logic / 162 IND Natural deduction, hybrid systems and modal logics / 165 PEN The emperor's new mind : concerning computers, minds, and the laws of physics / 165 PEN Shadows of the mind : a search for the missing science of consciousness /

Includes bibliographical references and index.

Machine generated contents note: 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.

"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"-- Provided by publisher.