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.

An introductory 2001 textbook on probability and induction written by a foremost philosopher of science.

A thorough and practical introduction to inductive logic with a focus on arguments and the rules used for making inductive inferences. This textbook offers a thorough and practical introduction to inductive logic. The book covers a range of different types of inferences with an emphasis throughout on representing them as arguments. This allows the reader to see that, although the rules and guidelines for making each type of inference differ, the purpose is always to generate a probable conclusion. After explaining the basic features of an argument and the different standards for evaluating arguments, the book covers inferences that do not require precise probabilities or the probability calculus: the induction by confirmation, inference to the best explanation, and Mill's methods. The second half of the book presents arguments that do require the probability calculus, first explaining the rules of probability, and then the proportional syllogism, inductive generalization, and Bayes' rule. Each chapter ends with practice problems and their solutions. Appendixes offer additional material on deductive logic, odds, expected value, and (very briefly) the foundations of probability. Argument and Inference can be used in critical thinking courses. It provides these courses with a coherent theme while covering the type of reasoning that is most often used in day-to-day life and in the natural, social, and medical sciences. Argument and Inference is also suitable for inductive logic and informal logic courses, as well as philosophy of sciences courses that need an introductory text on scientific and inductive methods.

Two new philosophical problems surrounding the gradation of certainty began to emerge in the 17th century and are still very much alive today. One is concerned with the evaluation of inductive reasoning, whether in science, jurisprudence, or elsewhere; the other with the interpretation of the mathematical calculus of change. This book, aimed at non-specialists, investigates both problems and the extent to which they are connected. Cohen demonstrates the diversity of logical structures that are available for judgements of probability, and explores the rationale for their appropriateness in different contexts of application. Thus his study deals with the complexity of the underlying philosophical issues without simply cataloging alternative conceptions or espousing a particular "favorite" theory.

The Twentieth Century has seen a dramatic rise in the use of probability and statistics in almost all fields of research. This has stimulated many new philosophical ideas on probability. Philosophical Theories of Probability is the first book to present a clear, comprehensive and systematic account of these various theories and to explain how they relate to one another. Gillies also offers a distinctive version of the propensity theory of probability, and the intersubjective interpretation, which develops the subjective theory.

The implications for philosophy and cognitive science of developments in statistical learning theory. In Reliable Reasoning, Gilbert Harman and Sanjeev Kulkarni—a philosopher and an engineer—argue that philosophy and cognitive science can benefit from statistical learning theory (SLT), the theory that lies behind recent advances in machine learning. The philosophical problem of induction, for example, is in part about the reliability of inductive reasoning, where the reliability of a method is measured by its statistically expected percentage of errors—a central topic in SLT. After discussing philosophical attempts to evade the problem of induction, Harman and Kulkarni provide an admirably clear account of the basic framework of SLT and its implications for inductive reasoning. They explain the Vapnik-Chervonenkis (VC) dimension of a set of hypotheses and distinguish two kinds of inductive reasoning. The authors discuss various topics in machine learning, including nearest-neighbor methods, neural networks, and support vector machines. Finally, they describe transductive reasoning and suggest possible new models of human reasoning suggested by developments in SLT.

An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.

Originally published in 1973. This book presents a valid mode of reasoning that is different to mathematical probability. This inductive logic is investigated in terms of scientific investigation. The author presents his criteria of adequacy for analysing inductive support for hypotheses and discusses each of these criteria in depth. The chapters cover philosophical problems and paradoxes about experimental support, probability and justifiability, ending with a system of logical syntax of induction. Each section begins with a summary of its contents and there is a glossary of technical terms to aid the reader.