Rudolf Carnap: Early Writings


Book Description

Rudolf Carnap (1891-1970) is generally acknowledged to have been one of the central figures of twentieth-century philosophy. He was the leading philosopher of the Vienna Circle, a group that was central to the international movement known as logical empiricism, which pursued the goal of making philosophy scientific and eliminating metaphysics that went beyond the limits of what humans can coherently comprehend. Carnap was not only well-versed in this area of thought but also contrary ideas; he interacted philosophically with Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein, Edmund Husserl, and Martin Heidegger, and in his formative years he was influenced by the positivists Mach and Ostwald, neo-Kantians such as Cassirer and Natorp, and Husserl's phenomenology. Interest in logical empiricism waned in the decades following Carnap's death but was revived towards the end of the twentieth century; the wave of new scholarship that resulted identified Carnap as far more subtle and interesting than was previously understood. The complete fourteen-volume edition of Carnap's published writings builds upon these more recent interpretations of his philosophy. This first book contains Carnap's early publications up until 1928, none of which have previously been translated from their original German. The introduction and notes place the text in the relevant scientific and historical contexts, in addition to explaining obscure references or outdated notation and terminology. Carnap's neo-Kantian origins are more obvious in these works than in his later writings, and the overall figure which emerges from this volume is a very different Carnap to the caricature that many philosophers will know.



















The Mathematics of the Heavens and the Earth


Book Description

The Mathematics of the Heavens and the Earth is the first major history in English of the origins and early development of trigonometry. Glen Van Brummelen identifies the earliest known trigonometric precursors in ancient Egypt, Babylon, and Greece, and he examines the revolutionary discoveries of Hipparchus, the Greek astronomer believed to have been the first to make systematic use of trigonometry in the second century BC while studying the motions of the stars. The book traces trigonometry's development into a full-fledged mathematical discipline in India and Islam; explores its applications to such areas as geography and seafaring navigation in the European Middle Ages and Renaissance; and shows how trigonometry retained its ancient roots at the same time that it became an important part of the foundation of modern mathematics. The Mathematics of the Heavens and the Earth looks at the controversies as well, including disputes over whether Hipparchus was indeed the father of trigonometry, whether Indian trigonometry is original or derived from the Greeks, and the extent to which Western science is indebted to Islamic trigonometry and astronomy. The book also features extended excerpts of translations of original texts, and detailed yet accessible explanations of the mathematics in them. No other book on trigonometry offers the historical breadth, analytical depth, and coverage of non-Western mathematics that readers will find in The Mathematics of the Heavens and the Earth.