The Art Of The Intelligible

A compact survey, at the elementary level, of some of the most important concepts of mathematics. Attention is paid to their technical features, historical development and broader philosophical significance. Each of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics - such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics - are discussed in detail. Appendices outline from scratch the proofs of two of the most celebrated limitative results of mathematics: the insolubility of the problem of doubling the cube and trisecting an arbitrary angle, and the Gödel incompleteness theorems. Additional appendices contain brief accounts of smooth infinitesimal analysis - a new approach to the use of infinitesimals in the calculus - and of the philosophical thought of the great 20th century mathematician Hermann Weyl. Readership: Students and teachers of mathematics, science and philosophy. The greater part of the book can be read and enjoyed by anyone possessing a good high school mathematics background.

The field of Byzantine jewellery (4th-15th centuries) is a rapidly expanding one and a large amount of important research has been conducted within the last ten years, both by scholars on the continent and in America. The intention of the conference, and subsequently the volume, is to draw together the many strands involved in this research and to publish them in accessible form. This volume represents a rare opportunity to make this crucial work available to a much wider specialist and non-specialist audience in Britain (and beyond). In particular the topics to be addressed by foreign speakers are either not well-known in Britain or are published in largely inaccessible journals. Chris Entwistle has been the curator of the Late Roman and Byzantine Collections at the British Museum since 1985. Dr Nöel Adams is an independent scholar who has published widely on the metalwork and jewellery of the Early Middle Ages.

Delving into the intersections between artistic images and philosophical knowledge in Europe from the late sixteenth to the early eighteenth centuries, The Art of Philosophy shows that the making and study of visual art functioned as important methods of philosophical thinking and instruction. From frontispieces of books to monumental prints created by philosophers in collaboration with renowned artists, Susanna Berger examines visual representations of philosophy and overturns prevailing assumptions about the limited function of the visual in European intellectual history. Rather than merely illustrating already existing philosophical concepts, visual images generated new knowledge for both Aristotelian thinkers and anti-Aristotelians, such as Descartes and Hobbes. Printmaking and drawing played a decisive role in discoveries that led to a move away from the authority of Aristotle in the seventeenth century. Berger interprets visual art from printed books, student lecture notebooks, alba amicorum (friendship albums), broadsides, and paintings, and examines the work of such artists as Pietro Testa, Léonard Gaultier, Abraham Bosse, Dürer, and Rembrandt. In particular, she focuses on the rise and decline of the "plural image," a genre that was popular among early modern philosophers. Plural images brought multiple images together on the same page, often in order to visualize systems of logic, metaphysics, natural philosophy, or moral philosophy. Featuring previously unpublished prints and drawings from the early modern period and lavish gatefolds, The Art of Philosophy reveals the essential connections between visual commentary and philosophical thought.

First published in 2002. This is Volume XIV of seventeen in the Library of Philosophy series on Metaphysics. Written in 1929, this book is on metaphysics and value in the intelligible world, which states that there are only two kinds of philosophies: those that find the world ultimately meaningful and intelligible and those that do not. The present book claims to belong to the first of these, and as such to be apart, however modest, of the Great Tradition in philosophy.