This book contains seminal discussions of central issues in the philosophy of language, mathematics, mind, religion and time. Is common language conceptually prior to idiolectics? What is a theory of meaning? Does constructivism provide a satisfactory account of mathematics? What are indefinitely extensible concepts? Can we change the past? These are only some of the very important questions addressed here. Both the papers written by the contributors and Dummett's replies provide a great wealth of stimulating ideas for those who currently (...) do research in the respective areas touched upon without making the reading exceedingly tedious. This feature, common to most of the papers in this book, makes it possible to use the material presented in undergraduate courses at university level. (shrink)

This book grew out of lectures. It is intended as an introduction to classical two-valued predicate logic. The restriction to classical logic is not meant to imply that this logic is intrinsically better than other, non-classical logics; however, classical logic is a good introduction to logic because of its simplicity, and a good basis for applications because it is the foundation of classical mathematics, and thus of the exact sciences which are based on it. The book is meant primarily for (...) mathematics students who are already acquainted with some of the fundamental concepts of mathematics, such as that of a group. It should help the reader to see for himself the advantages of a formalisation. The step from the everyday language to a formalised language, which usually creates difficulties, is dis cussed and practised thoroughly. The analysis of the way in which basic mathematical structures are approached in mathematics leads in a natural way to the semantic notion of consequence. One of the substantial achievements of modern logic has been to show that the notion of consequence can be replaced by a provably equivalent notion of derivability which is defined by means of a calculus. Today we know of many calculi which have this property. (shrink)

general, abstract situation. On the other side, I know that graduate students and all mathematicians sometimes falter because their intuitive, ..

Such a conception, says Dummett, will form "a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base ...

The tenor of much recent work in the philosophy of mathematics has been dictated by the popular assumption that Platonism is defunct. Some embrace that assumption and look for alternatives, others deny it and attempt to revive Platonism, but either way it is the starting point. The fate of Platonism took center stage with the appearance of Paul Benacerraf’s “Mathematical truth”, but a decade has passed since then, and the philosophical climate has changed. Most important, the quarter from which Platonism (...) was to receive its mortal wound—epistemology—has developed considerably; the epistemological theory presupposed by Benacerraf is no longer popular. This makes it difficult to assess the value of work in the philosophy of mathematics done under the influence of Benacerraf’s formulation. (shrink)