Lectures on inductive logic:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2017
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| Edition: | First edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xiii, 201 Seiten Illustrationen, Diagramme |
| ISBN: | 9780199666478 |
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| 245 | 1 | 0 | |a Lectures on inductive logic |c Jon Williamson (Professor of Reasoning, Inference and Scientific Method, University of Kent) |
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Record in the Search Index
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| adam_text | 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
* The starred sections contain material which is less central to the main thrust of the argument and which can be
more technical.
xii | CONTENTS
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
* The starred sections contain material which is less central to the main thrust of the argument and which can be
more technical.
CONTENTS | xiii
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 Minimax 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
References 193
Index 199
* The starred sections contain material which is less central to the main thrust of the argument and which can be
more technical.
|
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| author_facet | Williamson, Jon |
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| dewey-hundreds | 100 - Philosophy & psychology |
| dewey-ones | 161 - Induction |
| dewey-raw | 161 |
| dewey-search | 161 |
| dewey-sort | 3161 |
| dewey-tens | 160 - Philosophical logic |
| discipline | Mathematik Philosophie |
| edition | First edition |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T07:40:17Z |
| institution | BVB |
| isbn | 9780199666478 |
| language | English |
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| physical | xiii, 201 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Oxford University Press |
| record_format | marc |
| spelling | Williamson, Jon Verfasser aut Lectures on inductive logic Jon Williamson (Professor of Reasoning, Inference and Scientific Method, University of Kent) First edition Oxford Oxford University Press 2017 xiii, 201 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Induktive Logik (DE-588)4161594-3 gnd rswk-swf Induktive Logik (DE-588)4161594-3 s DE-604 Digitalisierung BSB Muenchen - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029389755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Williamson, Jon Lectures on inductive logic Induktive Logik (DE-588)4161594-3 gnd |
| subject_GND | (DE-588)4161594-3 |
| title | Lectures on inductive logic |
| title_auth | Lectures on inductive logic |
| title_exact_search | Lectures on inductive logic |
| title_full | Lectures on inductive logic Jon Williamson (Professor of Reasoning, Inference and Scientific Method, University of Kent) |
| title_fullStr | Lectures on inductive logic Jon Williamson (Professor of Reasoning, Inference and Scientific Method, University of Kent) |
| title_full_unstemmed | Lectures on inductive logic Jon Williamson (Professor of Reasoning, Inference and Scientific Method, University of Kent) |
| title_short | Lectures on inductive logic |
| title_sort | lectures on 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=029389755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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