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.
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