Space, Number, and Geometry from Helmholtz to Cassirer

This book offers a reconstruction of the debate on non-Euclidean geometry in neo-Kantianism between the second half of the nineteenth century and the first decades of the twentieth century. Kant famously characterized space and time as a priori forms of i

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New Studies in the History and Philosophy of Science and Technology

Francesca Biagioli

Space, Number, and Geometry from Helmholtz to Cassirer

Space, Number, and Geometry from Helmholtz to Cassirer

Archimedes

NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY VOLUME 46

EDITOR JED Z. BUCHWALD, Dreyfuss Professor of History, California Institute of Technology, Pasadena, CA, USA.

ASSOCIATE EDITORS FOR MATHEMATICS AND PHYSICAL SCIENCES JEREMY GRAY, The Faculty of Mathematics and Computing, The Open University, Buckinghamshire, UK. TILMAN SAUER, California Institute of Technology

ASSOCIATE EDITORS FOR BIOLOGICAL SCIENCES SHARON KINGSLAND, Department of History of Science and Technology, Johns Hopkins University, Baltimore, MD, USA. MANFRED LAUBICHLER, Arizona State University

ADVISORY BOARD FOR MATHEMATICS, PHYSICAL SCIENCES AND TECHNOLOGY HENK BOS, University of Utrecht MORDECHAI FEINGOLD, California Institute of Technology ALLAN D. FRANKLIN, University of Colorado at Boulder KOSTAS GAVROGLU, National Technical University of Athens PAUL HOYNINGEN-HUENE, Leibniz University in Hannover TREVOR LEVERE, University of Toronto JESPER LÜTZEN, Copenhagen University WILLIAM NEWMAN, Indian University, Bloomington LAWRENCE PRINCIPE, The Johns Hopkins University JÜRGEN RENN, Max-Planck-Institut für Wissenschaftsgeschichte ALEX ROLAND, Duke University ALAN SHAPIRO, University of Minnesota NOEL SWERDLOW, California Institute of Technology

ADVISORY BOARD FOR BIOLOGY MICHAEL DIETRICH, Dartmouth College, USA MICHEL MORANGE, Centre Cavaillès, Ecole Normale Supérieure, Paris HANS-JÖRG RHEINBERGER, Max Planck Institute for the History of Science, Berlin NANCY SIRAISI, Hunter College of the City University of New York, USA

Archimedes has three fundamental goals; to further the integration of the histories of science and technology with one another: to investigate the technical, social and practical histories of specific developments in science and technology; and fi nally, where possible and desirable, to bring the histories of science and technology into closer contact with the philosophy of science. To these ends, each volume will have its own theme and title and will be planned by one or more members of the Advisory Board in consultation with the editor. Although the volumes have specific themes, the series itself will not be limited to one or even to a few particular areas. Its subjects include any of the sciences, ranging from biology through physics, all aspects of technology, broadly construed, as well as historically-engaged philosophy of science or technology. Taken as a whole, Archimedes will be of interest to historians, philosophers, and scientists, as well as to those in business and industry who seek to understand how science and industry have come to be so strongly linked. More information about this series at http://www.springer.com/series/5644

Francesca Biagioli

Space, Number, and Geometry from Helmholtz to Cassirer

Francesca Biagioli Zukunftskolleg University of Konstanz Konstanz, Germany

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