Space, Geometry and Aesthetics Through Kant and Towards Deleuze Peg Rawes Space, Geometry and Aesthetics 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd ii 44//33//22000088 33::3344::1133 PPMM Renewing Philosophy General Editor: Gary Banham Titles include: Peg Rawes SPACE, GEOMETRY AND AESTHETICS: Through Kant and Towards Deleuze Simon O’Sullivan ART ENCOUNTERS DELEUZE AND GUATTARI: Thought Beyond Representation Jean-Paul Martinon ON FUTURITY: Malabou, Nancy & Derrida Vasiliki Tsakiri KIERKEGAARD: Anxiety, Repetition and Contemporaneity Alberto Toscano PHILOSOPHY AND INDIVIDUATION BETWEEN KANT AND DELEUZE: The Theatre of Production Philip Walsh SKEPTICISM, MODERNITY AND CRITICAL THEORY Celine Surprenant FREUD’S MASS PSYCHOLOGY Keekok Lee PHILOSOPHY AND REVOLUTIONS IN GENETICS: Deep Science and Deep Technology Kyriaki Goudeli CHALLENGES TO GERMAN IDEALISM: Schelling, Fichte and Kant Martin Weatherston HEIDEGGER’S INTERPRETATION OF KANT: Categories, Imagination and Temporality Jill Marsden AFTER NIETZSCHE 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd iiii 44//33//22000088 33::3344::1133 PPMM Space, Geometry and Aesthetics Through Kant and Towards Deleuze Peg Rawes University College London 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd iiiiii 44//33//22000088 33::3344::1133 PPMM © Peg Rawes 2008 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, 90 Tottenham Court Road, London W1T 4LP. Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The author has asserted her right to be identified as the author of this work in accordance with the Copyright, Designs and Patents Act 1988. First published in 2008 by PALGRAVE MACMILLAN Houndmills, Basingstoke, Hampshire RG21 6XS and 175 Fifth Avenue, New York, N.Y. 10010 Companies and representatives throughout the world. PALGRAVE MACMILLAN is the global academic imprint of the Palgrave Macmillan division of St. Martin’s Press, LLC and of Palgrave Macmillan Ltd. Macmillan® is a registered trademark in the United States, United Kingdom and other countries. Palgrave is a registered trademark in the European Union and other countries. ISBN-13: 978–0–230–55291–3 hardback ISBN-10: 0–230–55291–9 hardback This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin. A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Rawes, Peg. Space, geometry, and aesthetics through Kant and towards Deleuze / Peg Rawes. p. cm.—(Renewing philosophy) Includes bibliographical references and index. ISBN 0–230–55291–9 (alk. paper) 1. Space. 2. Geometry – Foundations. 3. Geometry – Philosophy. 4. Aesthetics. 5. Kant, Immanuel, 1724–1804. 6. Deleuze, Gilles, 1925–1995. I. Title. BD621.R39 2008 114—dc22 2008011821 10 9 8 7 6 5 4 3 2 1 17 16 15 14 13 12 11 10 09 08 Printed and bound in Great Britain by CPI Antony Rowe, Chippenham and Eastbourne 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd iivv 44//33//22000088 33::3344::1144 PPMM For Clare and James 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd vv 44//33//22000088 33::3344::1144 PPMM This page intentionally left blank Contents Acknowledgements ix Series Editor’s Preface x Preface xiii Introduction 1 Space 2 Geometry 3 Aesthetic geometric figure-subjects 4 1 Drawing Figures 9 Part I: Embodied Figures 9 Forms of pure intuition 11 Synthetic and analytic relations 13 Space and time 15 External and internal differentiations of space 17 Part II: Drawing Figures 19 Acts of construction 19 Reflective judgment 20 The imagination 22 Drawing a line 29 Summary 31 2 Folding-Unfolding 34 Discursive geometry 37 Soul 41 Imagination 44 Limit and unlimit 48 Imagination, limit and unlimit 51 Discursivity of the elements 54 Figure 57 Summary 60 3 Passages 62 Geometric methods after Descartes 62 Geometric method in the Ethics 65 vii 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd vviiii 44//33//22000088 33::3344::1144 PPMM viii Contents Substance 68 Passage I: attributes, modes, affects and common notions 72 Passage II: reading the text 82 Passage III: modes of geometric thinking 84 Summary 89 4 Plenums 91 The transition from synthetic to analytic geometry 94 Corporeal magnitude 99 Incorporeal magnitude 103 Sufficient reason 109 The plenum 113 Summary 119 5 Envelopes 121 Limit and unlimit 123 Extensity 126 Body-image and perception 128 Memory 132 The envelope 135 Space and time 136 Intuition 141 Envelope I: intuition as duration 143 Envelope II: intuitive philosophy 145 Envelope III: natural geometry and intuitive construction 146 Summary 151 6 Horizons 154 Geometric reason and ‘Teleological-historical reflection’ 156 Geometric sense-ideas and sense-intuitions 161 Explication 165 Retrieving sense-intuition from Descartes and Kant 169 Geometric self-evidence 173 Horizons 175 Horizon I: intersubjectivity 178 Horizon II: we-horizons and future-horizons 180 Summary 182 Notes 184 Bibliography 202 Index 207 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd vviiiiii 44//33//22000088 33::3344::1144 PPMM Acknowledgements Numerous people have helped me at various times in writing this book. I owe special thanks to Howard Caygill’s supportive advice, and Gary Banham’s encouragement of the project has been invaluable. Fiona Candlin, Uriel Orlow, Joanne Morra and Jane Rendell have generously given feedback on drafts at various stages of the project. Thanks also to Laura Allen and Mark Smout for permission to use their drawing on the front cover, and colleagues at The Bartlett School of Architecture, UCL, have supported me with financial assistance from the Architectural Research Fund. Finally, I would like to thank my family, Tom and my parents, James and Clare, especially, for their constant support. ix 99778800223300__555522991133__0011__pprreexxvviiiiii..iinndddd iixx 44//33//22000088 33::3344::1144 PPMM