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.

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside _The Open Society and Its Enemies_ as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

Karl Popper equates simplicity with falsifiability. He develops his argument for this equation through a geometrical example. There is a flaw in his example, which undermines his claim that simplicity is falsifiability. I point out the flaw here.

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. This second edition contains three new chapters devoted to further development of the learning theory and SVM techniques. Written in a readable (...) and concise style, the book is intended for statisticians, mathematicians, physicists, and computer scientists. (shrink)

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, 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 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. (shrink)