A Logical Introduction to Probability and Induction is a textbook on the mathematics of the probability calculus and its applications in philosophy.On the mathematical side, the textbook introduces these parts of logic and set theory that are needed for a precise formulation of the probability calculus. On the philosophical side, the main focus is on the problem of induction and its reception in epistemology and the philosophy of science. Particular emphasis is placed on the means-end approach to the justification of inductive inference rules.In addition, the book discusses the major interpretations of probability. These are philosophical accounts of the nature of probability that interpret the mathematical structure of the probability calculus. Besides the classical and logical interpretation, they include the interpretation of probability as chance, degree of belief, and relative frequency. The Bayesian interpretation of probability as degree of belief locates probability in a subject's mind. It raises the question why her degrees of belief ought to obey the probability calculus. In contrast to this, chance and relative frequency belong to the external world. While chance is postulated by theory, relative frequencies can be observed empirically.A Logical Introduction to Probability and Induction aims to equip students with the ability to successfully carry out arguments. It begins with elementary deductive logic and uses it as basis for the material on probability and induction. Throughout the textbook results are carefully proved using the inference rules introduced at the beginning, and students are asked to solve problems in the form of 50 exercises. An instructor's manual contains the solutions to these exercises as well as suggested exam questions.The book does not presuppose any background in mathematics, although sections 10.3-10.9 on statistics are technically sophisticated and optional. The textbook is suitable for lower level undergraduate courses in philosophy and logic.

1. Logic1.1 Propositional logic1.2 Predicate logic1.3 Exercises1.4 Readings2. Set theory2.1 Elementary postulates2.22.3 Readings3. Induction3.1 Confirmation and induction3.2 The problem of induction3.3 Hume's argument3.4 Readings4. Deductive approaches to confirmation4.1 Analysis and explication4.2 The ravens paradox4.3 The prediction criterion4.4 The logic of confirmation4.5 The satisfaction criterion4.6 Falsificationism4.7 Hypothetico-deductive confirmation4.8 Exercises4.9 Readings5. Probability5.1 The probability calculus5.2 Examples5.3 Conditional probability5.4 Elementary consequences5.5 Probabilities on languages5.6 Exercises5.7 Readings6. The classical interpretation of probability6.1 The principle of indifference6.2 Bertrand's paradox6.3 The paradox of water and wine6.4 Reading7. The logical interpretation of probability7.1 State descriptions and structure descriptions7.2 Absolute confirmation and incremental confirmation7.3 Carnap on Hempel7.4 The justification of logic7.5 The new riddle of induction7.6 Exercises7.7 Readings8. The subjective interpretation of probability8.1 Degrees of belief8.2 The Dutch book argument8.3 The gradational accuracy argument8.4 Bayesian confirmation theory8.5 Updating8.6 Bayesian decision theory8.7 Exercises8.8 Readings9. The chance interpretation of probability9.1 Chances9.2 Probability in physics9.3 The principal principle9.4 Readings10. The (limiting) relative frequency interpretation of probability10.1 The justification of induction10.2 The straight(-forward) rule10.3 Random variables10.4 Independent and identically distributed random variables10.5 The strong law of large numbers10.6 Degrees of belief, chances, and relative frequencies10.7 Descriptive statistics10.8 The central limit theorem10.9 Inferential statistics10.10 Exercises10.11 Reading11. Alternative approaches to induction11.1 Formal learning theory11.2 Putnam's argument11.3 Readings