Lectures on inductive logic / Jon Williamson.

Format:

Book

Author/Creator:

Williamson, Jon, author.

Language:

English

Subjects (All):

Induction (Logic).

Physical Description:

xiii, 201 pages ; 24 cm

Edition:

First edition.

Place of Publication:

Oxford : Oxford University Press, 2017.

Summary:

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premisses of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this book, Jon Williamson embarks on a quest to find a general, reasonable, applicable inductive logic (GRAIL), examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task. Along the way he presents a general framework for the field, and reaches a new inductive logic, which builds upon recent developments in Bayesian epistemology (a theory about how strongly one should believe the various propositions that one can express). The book explores this logic in detail, discusses some key criticisms and considers how it might be justified. Is this truly the GRAIL? Although the book presents new research, this material is well suited to being delivered as a series of lectures to students of philosophy, mathematics or computing and doubles as an introduction to the field of inductive logic. Book jacket.

Contents:

1 Classical Inductive Logic 1

1.1 From Deductive to Inductive Logic 1

1.2 Patterns of Partial Entailment and Support 3

1.2.1 The Fundamental Inductive Pattern 3

1.2.2 Diminishing Returns 5

1.2.3 Examining a Possible Ground 6

1.2.4 Analogy 7

1.3 Why Inductive Logic? 8

1.3.1 Decision Making 8

1.3.2 Artificial Intelligence 10

1.3.3 The GRAIL Quest 11

1.4 Learning from Experience 11

1.5 Inductive Entailment and Logical Entailment 13

2 Logic and Probability 16

2.1 Propositional Logic 16

2.2 Predicate Logic 17

2.3 Probability over Logical Languages 18

2.3.1 Axioms of Probability 18

2.3.2 Properties of Probability 19

2.3.3 Truth Tables and Probability 21

2.3.4 Conditional Probability and Inductive Logic 22

2.4 Entropy, Divergence and Score 25

2.5 Interpretations of Probability 31

2.6 *Probability over Fields of Sets 32

2.6.1 Fields of Sets 32

2.6.2 Axioms of Probability 33

2.6.3 The Valuation Space 34

3 Combining Probability and Logic 40

3.1 Entailment 40

3.2 Support and Consistency 45

3.3 The Languages of Inductive Logic 46

3.4 Inductive Qualities 47

3.5 Probabilistic Logics 49

3.6 *More Examples of Inductive Logics 55

4 Carnap's Programme 59

4.1 Conditionalizing on a Blank Slate 59

4.2 Pure and Applied Inductive Logic 61

4.3 Conditionalization 63

4.4 The Permutation Postulate 65

4.5 The Principle of Indifference 68

4.6 Which Value in the Continuum? 71

4.7 Which Continuum of Inductive Methods? 72

4.8 Capturing Logical Entailment 72

4.9 Summary 74

5 From Objective Bayesian Epistemology to Inductive Logic 75

5.1 Objective Bayesian Epistemology 75

5.2 *Objective versus Subjective Bayesian Epistemology 77

5.3 Objective Bayesian Inductive Logic 81

5.4 *Language Invariance 85

5.5 *Finitely Generated Evidence Sets 91

5.6 Updating, Expansion and Revision 94

5.6.1 Maxent and Conditionalization 96

5.6.2 Maxent and KL-updating 101

5.7 Summary 103

6 Logical Entailment 105

6.1 Truth Tables with Probabilities 105

6.2 Logical Irrelevance Revisited 108

6.3 Context and Chance Constraints 111

6.4 Constraints on Conditional Probabilities 115

6.5 Revision Under Constraints 118

6.6 Lottery and Preface Paradoxes Revisited 120

6.7 The Fundamental Inductive Pattern Revisited 122

6.7.1 A Surprising Consequence 122

6.7.2 An Otherwise Surprising Consequence 123

6.7.3 A Plausible Consequence 124

6.8 *Inferences in Predicate Inductive Logic 126

7 Inductive Entailment 134

7.1 Syntactic Relevance 134

7.2 The Calibration Norm 135

7.3 Extended Example 138

7.4 Is this Application of Confidence Intervals Legitimate? 142

7.5 Uniqueness of the Interval 145

7.6 Loss of Information 146

7.7 Generalization 147

8 Criticisms of Inductive Logic 151

8.1 Language Invariance Revisited 151

8.2 Goodman's New Problem of Induction 154

8.3 The Principle of Indifference Revisited 159

8.4 Universal Hypotheses 162

8.5 Summary 166

9 Justification 167

9.1 Two Problems of Induction 167

9.2 Two Principles of Rationality 168

9.3 Minimal Worst-Case Expected Loss 175

9.4 *Robustness of the Minim ax Theorem 180

9.4.1 Key Assumptions 180

9.4.2 Rationality Principles 182

10 Conclusion 187

10.1 Have we Found the GRAIL? 187

10.2 Open Questions 189

10.2.1 Knowledge Engineering 189

10.2.2 Other Questions 191.

Notes:

Includes bibliographical references and index.

ISBN:

0199666474

9780199666478

OCLC:

960837974