A Logical Introduction to Probability and Induction starts with elementary logic and uses it as basis for a philosophical discussion of probability and induction. Throughout the book results are carefully proved using the inference rules introduced at the beginning. The textbook is suitable for undergraduate courses in philosophy and logic.
A Logical Introduction to Probability and Induction starts with elementary logic and uses it as basis for a philosophical discussion of probability and induction. Throughout the book results are carefully proved using the inference rules introduced at the beginning. The textbook is suitable for undergraduate courses in philosophy and logic.
Franz Huber is Associate Professor in the Department of Philosophy, and affiliate of the Institute for the History and Philosophy of Science and Technology, at the University of Toronto. Huber works in formal epistemology, general philosophy of science, and philosophical logic and previously held positions at Konstanz University and the California Institute of Technology.
Inhaltsangabe
1. Logic 1.1 Propositional logic 1.2 Predicate logic 1.3 Exercises 1.4 Readings 2. Set theory 2.1 Elementary postulates 2.2 2.3 Readings 3. Induction 3.1 Confirmation and induction 3.2 The problem of induction 3.3 Hume's argument 3.4 Readings 4. Deductive approaches to confirmation 4.1 Analysis and explication 4.2 The ravens paradox 4.3 The prediction criterion 4.4 The logic of confirmation 4.5 The satisfaction criterion 4.6 Falsificationism 4.7 Hypothetico-deductive confirmation 4.8 Exercises 4.9 Readings 5. Probability 5.1 The probability calculus 5.2 Examples 5.3 Conditional probability 5.4 Elementary consequences 5.5 Probabilities on languages 5.6 Exercises 5.7 Readings 6. The classical interpretation of probability 6.1 The principle of indifference 6.2 Bertrand's paradox 6.3 The paradox of water and wine 6.4 Reading 7. The logical interpretation of probability 7.1 State descriptions and structure descriptions 7.2 Absolute confirmation and incremental confirmation 7.3 Carnap on Hempel 7.4 The justification of logic 7.5 The new riddle of induction 7.6 Exercises 7.7 Readings 8. The subjective interpretation of probability 8.1 Degrees of belief 8.2 The Dutch book argument 8.3 The gradational accuracy argument 8.4 Bayesian confirmation theory 8.5 Updating 8.6 Bayesian decision theory 8.7 Exercises 8.8 Readings 9. The chance interpretation of probability 9.1 Chances 9.2 Probability in physics 9.3 The principal principle 9.4 Readings 10. The (limiting) relative frequency interpretation of probability 10.1 The justification of induction 10.2 The straight(-forward) rule 10.3 Random variables 10.4 Independent and identically distributed random variables 10.5 The strong law of large numbers 10.6 Degrees of belief, chances, and relative frequencies 10.7 Descriptive statistics 10.8 The central limit theorem 10.9 Inferential statistics 10.10 Exercises 10.11 Reading 11. Alternative approaches to induction 11.1 Formal learning theory 11.2 Putnam's argument 11.3 Readings
1. Logic 1.1 Propositional logic 1.2 Predicate logic 1.3 Exercises 1.4 Readings 2. Set theory 2.1 Elementary postulates 2.2 2.3 Readings 3. Induction 3.1 Confirmation and induction 3.2 The problem of induction 3.3 Hume's argument 3.4 Readings 4. Deductive approaches to confirmation 4.1 Analysis and explication 4.2 The ravens paradox 4.3 The prediction criterion 4.4 The logic of confirmation 4.5 The satisfaction criterion 4.6 Falsificationism 4.7 Hypothetico-deductive confirmation 4.8 Exercises 4.9 Readings 5. Probability 5.1 The probability calculus 5.2 Examples 5.3 Conditional probability 5.4 Elementary consequences 5.5 Probabilities on languages 5.6 Exercises 5.7 Readings 6. The classical interpretation of probability 6.1 The principle of indifference 6.2 Bertrand's paradox 6.3 The paradox of water and wine 6.4 Reading 7. The logical interpretation of probability 7.1 State descriptions and structure descriptions 7.2 Absolute confirmation and incremental confirmation 7.3 Carnap on Hempel 7.4 The justification of logic 7.5 The new riddle of induction 7.6 Exercises 7.7 Readings 8. The subjective interpretation of probability 8.1 Degrees of belief 8.2 The Dutch book argument 8.3 The gradational accuracy argument 8.4 Bayesian confirmation theory 8.5 Updating 8.6 Bayesian decision theory 8.7 Exercises 8.8 Readings 9. The chance interpretation of probability 9.1 Chances 9.2 Probability in physics 9.3 The principal principle 9.4 Readings 10. The (limiting) relative frequency interpretation of probability 10.1 The justification of induction 10.2 The straight(-forward) rule 10.3 Random variables 10.4 Independent and identically distributed random variables 10.5 The strong law of large numbers 10.6 Degrees of belief, chances, and relative frequencies 10.7 Descriptive statistics 10.8 The central limit theorem 10.9 Inferential statistics 10.10 Exercises 10.11 Reading 11. Alternative approaches to induction 11.1 Formal learning theory 11.2 Putnam's argument 11.3 Readings
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