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E-raamat: Pure Inductive Logic

(University of Manchester), (University of Manchester)
  • Formaat: EPUB+DRM
  • Sari: Perspectives in Logic
  • Ilmumisaeg: 02-Apr-2015
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316392805
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Pure Inductive LogicSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Perspectives in Logic
  • Ilmumisaeg: 02-Apr-2015
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316392805
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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.

Arvustused

'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)

Muu info

A self-contained guide to pure inductive logic, the study of rational probability treated as a branch of mathematical logic.
Preface ix
Part 1 The Basics
Chapter 1 Introduction to Pure Inductive Logic
3(6)
Chapter 2 Context
9(2)
Chapter 3 Probability Functions
11(10)
Chapter 4 Conditional Probability
21(4)
Chapter 5 The Dutch Book Argument
25(8)
Chapter 6 Some Basic Principles
33(6)
Chapter 7 Specifying Probability Functions
39(10)
Part 2 Unary Pure Inductive Logic
Chapter 8 Introduction to Unary Pure Inductive Logic
49(6)
Chapter 9 De Finetti's Representation Theorem
55(6)
Chapter 10 Regularity and Universal Certainty
61(8)
Chapter 11 Relevance
69(4)
Chapter 12 Asymptotic Conditional Probabilities
73(8)
Chapter 13 The Conditionalization Theorem
81(6)
Chapter 14 Atom Exchangeability
87(6)
Chapter 15 Reichenbach's Axiom
93(6)
Chapter 16 Carnap's Continuum of Inductive Methods
99(4)
Chapter 17 Irrelevance
103(22)
Chapter 18 Another Continuum of Inductive Methods
125(10)
Chapter 19 The NP-Continuum
135(8)
Chapter 20 The Weak Irrelevance Principle
143(12)
Chapter 21 Equalities and Inequalities
155(10)
Chapter 22 Principles of Analogy
165(6)
Chapter 23 Unary Symmetry
171(10)
Part 3 Polyadic Pure Inductive Logic
Chapter 24 Introduction to Polyadic Pure Inductive Logic
181(2)
Chapter 25 Polyadic Constant Exchangeability
183(6)
Chapter 26 Polyadic Regularity
189(4)
Chapter 27 Spectrum Exchangeability
193(6)
Chapter 28 Conformity
199(6)
Chapter 29 The Probability Functions up, L
205(8)
Chapter 30 The Homogeneous/Heterogeneous Divide
213(10)
Chapter 31 Representation Theorems for Sx
223(16)
Chapter 32 Language Invariance with Sx
239(8)
Chapter 33 Sx without Language Invariance
247(10)
Chapter 34 A General Representation Theorem for Sx
257(10)
Chapter 35 The Carnap-Stegmuller Principle
267(2)
Chapter 36 Instantial Relevance and Sx
269(6)
Chapter 37 Equality
275(10)
Chapter 38 The Polyadic Johnson's Sufficientness Postulate
285(6)
Chapter 39 Polyadic Symmetry
291(12)
Chapter 40 Similarity
303(8)
Chapter 41 PIP and Atom Exchangeability
311(6)
Chapter 42 The Functions p.LE
317(6)
Chapter 43 Less Well Travelled Roads
323(4)
Bibliography 327(10)
Index 337(4)
Symbols and Abbreviations 341
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 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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