Is truth objective or relative? What exists independently of our minds? This book is about these two questions. The essays in its pages variously defend and critique answers to each, grapple over the proper methodology for addressing them, and wonder whether either question is worth pursuing. In so doing, they carry on a long and esteemed tradition - for our two questions are among the oldest of philosophical issues, and have vexed almost every major philosopher, from Plato, to Kant to Wittgenstein. Fifteen eminent contributors bring fresh perspectives, renewed energy and original answers to debates which have been the focus of a tremendous amount of interest in the last three decades both within philosophy and the culture at large.

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed development of higher-order logic, including a comprehensive discussion of its semantics. Professor Shapiro demonstrates the prevalence of second-order notions in mathematics is practised, and also the extent to which mathematical concepts can be formulated in second-order languages . He shows how first-order languages are insufficient to codify many concepts in contemporary mathematics, and thus that higher-order logic is needed to fully reflect current mathematics. Throughout, the emphasis is on discussing the philosophical and historical issues associated with this subject, and the implications that they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic as might be gained from a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in this subject.

Are people rational? This question was central to Greek thought; and has been at the heart of psychology and philosophy for millennia. This book provides a radical and controversial reappraisal of conventional wisdom in the psychology of reasoning, proposing that the Western conception of the mind as a logical system is flawed at the very outset. It argues that cognition should be understood in terms of probability theory, the calculus of uncertain reasoning, rather than in terms of logic, the calculus of certain reasoning.

Colin Howson offers a solution to one of the central, unsolved problems of Western philosophy, the problem of induction. In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth or probable truth of the predicting theory. Howson claims that Hume's argument is correct, and examines what follows about the relation between science and its empirical base.

This book was designed primarily as a textbook; though the author hopes that it will prove to be of interests to others beside logic students. Part I of this book covers the fundamentals of the subject the propositional calculus and the theory of quantification. Part II deals with the traditional formal logic and with the developments which have taken that as their starting-point. Part III deals with modal, three-valued, and extensional systems.

In Contradiction advocates and defends the view that there are true contradictions (dialetheism), a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in
1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author's reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion volume, Doubt Truth to be a Liar, also published by
Oxford University Press in 2006.

The book sets out a new logic of rules, developed to demonstrate how such a logic can contribute to the clarification of historical questions about social rules. The authors illustrate applications of this new logic in their extensive treatments of a variety of accounts of social changes, analysing in these examples the content of particular social rules and the course of changes in them.