# Pure Inductive Logic

## £89.99

Part of Perspectives in Logic

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

## £89.99 Hardback

### Looking for an inspection copy?

This title is not currently available on inspection

Description
Product filter button
Description
Contents
Resources
Courses
• 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

## Reviews & endorsements

'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)

## Customer reviews

### Not yet reviewed

Be the first to review

Review was not posted due to profanity

×

## , create a review

(If you're not , sign out)

Your review must be a minimum of 12 words.

×

## 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

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
23. Introduction to polyadic pure inductive logic
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
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.

• ## 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.

Not already registered? Create an account now. ×

### Sorry, this resource is locked

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.

×