WHOLES. SUMS AND UNITIES

WHOLES. SUMS AND UNITIES

PHILOSOPHICAL STUDIES SERIES VOLUME 97 Founded by Wilfrid S. Sellars and Keith Lehrer Editor Keith Lehrer, University of Arizona, Tucson Associate Editor Stewart Cohen, Arizona State University, Tempe Board of Consulting Editors Lynne Rudder Baker, University of Massachusetts at Amherst Radu Bogdan, Tulane University, New Orleans Marian David, University of Notre Dame Allan Gibbard, University of Michigan Denise Meyerson, Macquarie University Fran<;ois Recanati, Institut lean-nicod, EHESS, Paris Stuart Silvers, Clemson University Barry Smith, State University of New York at Buffalo Nicholas D. Smith, Lewis & Clark College The titles published in this series are listed at the end of this volume.

WHOLES, SUMS AND UNITIES by ARIEL MEIRAV University of Haifa, Israel... " SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6442-4 ISBN 978-94-017-0209-6 (ebook) DOI 10.1007/978-94-017-0209-6 Photograph pp. 23-24: Giuseppe Arcimboldo, L 'Ortolano. Museo Civico Ala Ponzone - Pinacoteca, Cremona, Italy. Printed on acid-free paper All Rights Reserved 2003 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2003 Softcover reprint of the hardcover 1st edition 2003 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

Table of Contents Preface Chapter 1 - Introduction I Plato's Challenge II Two Approaches to Wholes and Parts III lllustration of the Idea of a Three-Tiered Whole IV The Theoretical Context V Outline of the Argument vii 1 1 6 17 30 44 Part One: Wholes Chapter 2 - Concrete Comprising Entities I Preliminaries II Ways of Being One Appendix: Plural Quantification Chapter 3 - Types of Comprising Entities I Collective and Distributive Classes II Distributive Classes and Concreteness III Collections Chapter 4 - Theory and Pre-theory of Wholes I The Pre-theoretical Conception II Preliminaries to a Theoretical Conception 51 51 61 77 81 81 85 92 99 99 107 Part Two: Sums Chapter 5 - Classical and Neoclassical Mereology I Principles of Classical and Neoclassical Mereology II Limitations of the Notion of a Classical Sum III Flexibility of the Notion of a Neoclassical Sum Chapter 6 - Traditional Higher-grade Wholes as Sums I Organic Wholes and Gestalts II Features of Organic Wholes and Gestalts III Organic Wholes and Gestalts as Sums 117 117 122 130 141 143 150 161

VI TABLE OF CONTENTS Chapter 7 - Criticism of the Notion of a Neoclassical Sum 167 I Conditioned Sums 168 IT Non-unique Sums 173 ITI Mereologically Varying Sums 181 Chapter 8 - Sums, Collections and All the Parts 189 I Inherent Limitation in the Notion of a Sum 190 IT Classical Sums as Identical to their Parts 193 Part Three: Unities Chapter 9 - A Theory of Unities I Introduction IT Unities and Collections ITI Principles for a Theory of Unities Appendix: Proofs of Theorems Chapter 10 - Further Elaborations and Applications I Perspectives on the Theory of Unities IT Applying a Theory of Unities ITI The Paradox of Tibbles Bibliography Index 211 211 215 229 247 253 253 267 277 293 303

Preface The well-worn claim that a whole is greater than the sum of its parts means many things to many people. Nevertheless, it may be thought to express a particular widespread intuition about the nature of wholes. It indicates, however inadequately and vaguely, that wholes are in some way surprizing, different to what might be expected, non-trivial in their characteristics. Perhaps it hints at the impression that if a whole is composed of several parts, then to tell us all we may wish to know about each of these parts is still not to tell us something crucial about the whole itself. This book may be viewed as an attempt to justify and develop this intuition by focusing on what I take to be a neglected dimension in the nature of wholes. To attend to this dimension is to consider different ways in which parts, irrespective of their individual characters and of the relations between them, can compose a whole. My contention will be that contemporary metaphysical discussion by and large fails to notice this dimension, and that this may explain some of its more serious difficulties in treating questions about wholes and parts. I shall suggest that a study of this dimension may have far reaching philosophical consequences. The task of exploring this neglected dimension is reflected in the structure of the book as follows. In Part One I aim to show that the theoretical space within which a theory of wholes and parts might be devised is larger than is often assumed. This prepares us for the possibility of rejecting certain widely accepted assumptions about wholes. In Part Two I isolate assumptions shared by contemporary theories, showing how they stand in the way of considering the dimension I am referring to, and arguing that they lead to decisive theoretical weaknesses. Finally, in Part Three, I develop a theory - the theory of Unities - which rejects these assumptions, and demonstrate the explanatory power of this theory. Before proceeding to attend to these tasks, however, I devote an introductory chapter to explaining the significance of the project, the motivation for it, and the context in which it is undertaken. The book is based on and developed from my doctoral dissertation at the University of Edinburgh (1997). I wish to thank all those who have helped, inspired and criticised my work in this field both during the Edinburgh years and later as a member of the departments of philosophy at Tel-Aviv University and the University of Haifa. I would like to

viii PREFACE mention in particular Leora Bilsky, Pete Campbell, William Charlton, Paolo Crivelli, Fritz-Gregor Herrmann, Hagi Kenaan, Vered Lev Kenaan, E. J. Lowe, lise Mogensen, Gregory Owcarz, Jennifer Richards, David Robinson, Theodore Scaltsas, Eva Schiedrum, Traute Schiedrum, Barry Smith, Paul Suttie, Christopher Strachan, David Vila Domini, and Ruth Weintraub. I am greatly appreciative of the suggestions made by Kluwer Academic Publishers' anonymous reader in response to a draft of my manuscript. And finally, I would like to express a very special gratitude to Sharon Krishek for her unflinching, loving and wise support. Tel-Aviv, May 2003