Pure inductive logic:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2015
|
| Edition: | 1. publ. |
| Series: | Perspectives in logic
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | X, 342 S. |
| ISBN: | 9781107042308 |
Staff View
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Record in the Search Index
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| adam_text | 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.
Jeffrey 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.
CONTENTS f!
Preface.................................................. ix
Part 1. The Basics
Chapter 1. Introduction to Pure Inductive Logic.......... 3
Chapter 2. Context....................................... 9
Chapter 3. Probability Functions........................ 11
Chapter 4. Conditional Probability...................... 21
Chapter 5. The Dutch Book Argument...................... 25
Chapter 6. Some Basíc Principles........................ 33
Chapter 7. Specifying Probability Functions............. 39
Part 2. Unary Pure Inductive Logic
Chapter 8. Introduction to Unary Pure Inductive Logic... 49
Chapter 9. de Finetti’s Representation Theorem.......... 55
Chapter 10. Regularity and Universal Certainty ......... 61
Chapter 11. Relevance................................... 69
Chapter 12. Asymptotic Conditional Probabilities........ 73
Chapter 13. The Conditionalization Theorem.............. 81
Chapter 14. Atom Exchangeability........................ 87
Chapter 15. Reichenbach s Axiom......................... 93
Chapter 16. Carnap’s Continuum of Inductive Methods..... 99
Chapter 17. Irrelevance.................................103
v
vi Contents
Chapter 18. Anothhr Continuum of Inductive TvIethods...... 125
Chapter 19. The NP-Continuum..............................135
Chapter 20. The Weak Irrelevance Principle................143
Chapter 21. Equalities and Inequalities...................155
Chapter 22. Principles of Analogy.........................165
Chapter 23. Unary Symmetry................................171
Part 3. Polvadic Pure Inductive Logic
Chapter 24. Introduction to Polyadic Pure Inductive Logic . 181
Chapter 25. Polyadic Constant Exchangeability.............183
Chapter 26. Polyadic Regularity...........................189
Chapter 27. Spectrum Exchangeability......................193
Chapter 28. Conformity....................................199
Chapter 29. The Probability Functions up L................205
Chapter 30. The Homogeneous/Heterogeneous Divide..........213
Chapter 31. Representation Theorems for Sx................223
Chapter 32. Language Invariance with Sx...................239
Chapter 33. Sx without Language Invariance................247
Chapter 34. A General Representation Theorem for Sx.......257
Chapter 35. The Carnap-Stegmùller Principle...............267
Chapter 36. Instantial Relevance and Sx...................269
Chapter 37. Equality......................................275
Chapter 38. The Polyadic Johnson’s Sufficientness Postulate . 285
Chapter 39. Polyadic Symmetry.............................291
Chapter 40. Similarity....................................303
Chapter 4L PIP and Atom Exchangeability..................311
Chapter 42. The Functions u^ l............................317
Contents vii
Chapter 43. Less Well Travelled Roads....................323
Bibliography.............................................327
Index....................................................337
Symbols and Abbreviations................................341
|
| any_adam_object | 1 |
| author | Paris, Jeff B. Vencovská, Alena |
| author_GND | (DE-588)1071099108 (DE-588)1071691422 |
| author_facet | Paris, Jeff B. Vencovská, Alena |
| author_role | aut aut |
| author_sort | Paris, Jeff B. |
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| dewey-full | 161 |
| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 161 - Induction |
| dewey-raw | 161 |
| dewey-search | 161 |
| dewey-sort | 3161 |
| dewey-tens | 160 - Philosophical logic |
| discipline | Informatik Mathematik Philosophie |
| edition | 1. publ. |
| format | Book |
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| isbn | 9781107042308 |
| language | English |
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| physical | X, 342 S. |
| publishDate | 2015 |
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| series2 | Perspectives in logic |
| spelling | Paris, Jeff B. Verfasser (DE-588)1071099108 aut Pure inductive logic Jeffrey Paris ; Alena Vencovská 1. publ. Cambridge Cambridge Univ. Press 2015 X, 342 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in logic Induktive Logik (DE-588)4161594-3 gnd rswk-swf Induktive Logik (DE-588)4161594-3 s DE-604 Vencovská, Alena Verfasser (DE-588)1071691422 aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027595462&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027595462&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Paris, Jeff B. Vencovská, Alena Pure inductive logic Induktive Logik (DE-588)4161594-3 gnd |
| subject_GND | (DE-588)4161594-3 |
| title | Pure inductive logic |
| title_auth | Pure inductive logic |
| title_exact_search | Pure inductive logic |
| title_full | Pure inductive logic Jeffrey Paris ; Alena Vencovská |
| title_fullStr | Pure inductive logic Jeffrey Paris ; Alena Vencovská |
| title_full_unstemmed | Pure inductive logic Jeffrey Paris ; Alena Vencovská |
| title_short | Pure inductive logic |
| title_sort | pure inductive logic |
| topic | Induktive Logik (DE-588)4161594-3 gnd |
| topic_facet | Induktive Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027595462&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027595462&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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