Before his death in 2003, Bernard Williams planned to publish a collection of historical essays, focusing primarily on the ancient world. This posthumous volume brings together a much wider selection, written over some forty years. His legacy lives on in this masterful work, the first collection ever published of Williams' essays on the history of philosophy. The subjects range from the sixth century B.C. to the twentieth A.D., from Homer to Wittgenstein by way of Socrates, Plato, Aristotle, Descartes, Hume, Sidgwick, Collingwood, and Nietzsche. Often one would be hard put to say which part is history, which philosophy. Both are involved throughout, because this is the history of philosophy written philosophically.Historical exposition goes hand in hand with philosophical scrutiny. Insights into the past counteract blind acceptance of present assumptions. In his touching and illuminating introduction, Myles Burnyeat writes of these essays: 'They show a depth of commitment to the history of philosophy seldom to be found nowadays in a thinker so prominent on the contemporary philosophical scene.' The result celebrates the interest and importance to philosophy today of its near and distant past. "The Sense of the Past" is one of three collections of essays by Bernard Williams published by Princeton University Press since his death. "In the Beginning Was the Deed: Realism and Moralism in Political Argument", selected, edited, and with an introduction by Geoffrey Hawthorn, and "Philosophy as a Humanistic Discipline", selected, edited, and with an introduction by A. W. Moore, make up the trio.

T. M. Scanlon offers a qualified defense of normative cognitivism—the view that there are irreducibly normative truths about reasons for action. He responds to three familiar objections: that such truths would have troubling metaphysical implications; that we would have no way of knowing what they are; and that the role of reasons in motivating and explaining action could not be explained if accepting a conclusion about reasons for action were a kind of belief. Scanlon answers the first of these objections within a general account of ontological commitment, applying to mathematics as well as normative judgments. He argues that the method of reflective equilibrium, properly understood, provides an adequate account of how we come to know both normative truths and mathematical truths, and that the idea of a rational agent explains the link between an agent's normative beliefs and his or her actions. Whether every statement about reasons for action has a determinate truth value is a question to be answered by an overall account of reasons for action, in normative terms. Since it seems unlikely that there is such an account, the defense of normative cognitivism offered here is qualified: statements about reasons for action can have determinate truth values, but it is not clear that all of them do. Along the way, Scanlon offers an interpretation of the distinction between normative and non-normative claims, a new account of the supervenience of the normative on the non-normative, an interpretation of the idea of the relative strength of reasons, and a defense of the method of reflective equilibrium.

At the heart of the justification for the reasoning used in modern mathematics lies the completeness theorem for predicate calculus. This unique textbook covers two entirely different ways of looking at such reasoning. Topics include: the representation of mathematical statements by formulas in a formal language; the interpretation of formulas as true or false in a mathematical structure; logical consequence of one formula from others; formal proof; the soundness and completeness theorems connecting logical consequence and formal proof; the axiomatization of some mathematical theories using a formal language; the compactness theorem and an introduction to model theory. This book is designed for self-study by students, as well as for taught courses, using principles successfully developed by the Open University and used across the world. It includes exercises embedded within the text with full solutions to many of these. In addition there are a number of exercises without answers so that students studying under the guidance of a tutor may be assessed on the basis of what has been taught. Some experience of axiom-based mathematics is required but no previous experience of logic. Propositional and Predicate Calculus gives students the basis for further study of mathematical logic and the use of formal languages in other subjects. Derek Goldrei is Senior Lecturer and Staff Tutor at the Open University and part-time Lecturer in Mathematics at Mansfield College, Oxford, UK.

This book lays out foundations for a "science of morals." Binmore uses game theory as a systematic tool for investigating ethical matters. He reinterprets classical social contract ideas within a game-theory framework and generates new insights into the fundamental questions of social philosophy. In contrast to the previous writing in moral philosophy that relied on vague notion such as " societal well-being" and "moral duty," Binmore begins with individuals; rational decision-makers with the ability to emphasize with one another. Any social arrangement that prescribes them to act against their interests will become unstable and eventually will be replaced by another, until one is found that includes worthwhile actions for all individuals involved.