THE PHILOSOPHY OF RIGHT AND LEFT

THE PHILOSOPHY OF RIGHT AND LEFT

THE UNIVERSITY OF WESTERN ONT ARlO SERIES IN PHILOSOPHY OF SCIENCE A SERIES OF BOOKS IN PHILOSOPHY OF SCIENCE, METHODOLOGY, EPISTEMOLOGY, LOGIC, HISTORY OF SCIENCE, AND RELATED FIELDS Managing Editor ROBERT E. BUITS Dept. of Philosophy, University of Western Ontario, Canada Editorial Board JEFFREY BUB, University of Mary/and L. JONATHAN COHEN, Queen's College, Oxford WILLIAM DEMOPOULOS, University of Western Ontario WILLIAM HARPER, University of Western Ontario JAAKKO HINTIKKA, Boston University CLIFFORD A. HOOKER, University of Newcastle HENRY E. KYBURG, JR., University of Rochester AUSONIO MARRAS, University of Western Ontario JiiRGEN MITTELSTRASS, Universitiit Konstanz JOHN M. NICHOLAS, University of Western Ontario GLENN A. PEARCE, University of Western Ontario BAS C. VAN FRAASSEN, Princeton University VOLUME 46

THE PHILOSOPHY OF RIGHT AND LEFT Incongruent Counterparts and the Nature of Space Edited by JAMES VAN CLEVE Brown University ROBERT E. FREDERICK Bentley College SPRINGER SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging-in-Publication Data The philosophy of right and left ineongruent eounterparts and the nature of spaee I edited by James Van Cleve, Robert Frederiek. p. em. -- (The University of Western Ontario series in ph il osophy of se i enee ; v. 46) Ine ludes bibllographiea 1 referenees and index. ISBN 978-94-010-5661-8 ISBN 978-94-011-3736-2 (ebook) DOI 10.1007/978-94-011-3736-2 1. Right and left (Phllosophy) 2. Spaee and time. 3. Kant, Immanuel,1724-1804. 1. Van Cleve. James. II. Frederiek, Robert. III. Series. B105.R54P45 1990 114--de20 90-38262 ISBN 978-94-010-5661-8 printed on acid free paper AII Rights Reserved 1991 by Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1991 Softcover reprint of the hardcover 1 st edition 1991 and copyrightholders as specified on appropriate pages within No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, includ ing photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner

TABLE OF CONTENTS PREFACE ROBERT E. FREDERICK I Introduction to the Argument of 1768 1 JAMES VAN CLEVE I Introduction to the Arguments of 1770 and 1783 15 IMMANUEL KANT IOn the First Ground of the Distinction of Regions in Space (1768) 27 IMMANUEL KANT I Selection from Section 15 of Dissertation on the Form and Principles of the Sensible and Intelligible World (1770) 35 IMMANUEL KANT I Selection from the Prolegomena to Any Future Metaphysics (1783) 37 AUGUST FERDINAND MOBIUS IOn Higher Space 39 NORMAN KEMP SMITH I The Paradox of Incongruous Counterparts 43 LUDWIG WITTGENSTEIN I Tractatus 6.36111 49 PETER REMNANT I Incongruent Counterparts and Absolute Space 51 MARTIN GARDNER I The Fourth Dimension 61 MARTIN GARDNER I The Ozma Problem and the Fall of Parity 75 JONATHAN BENNETT I The Difference Between Right and L ~ 97 JOHN EARMAN I Kant, Incongruous Counterparts, and the Nature of Space and Space-Time 131 GRAHAM NERLICH I Hands, Knees, and Absolute Space 151 vii

vi TABLE OF CONTENTS LA WRENCE SKLAR I Incongruous Counterparts, Intrinsic Features, and the Substantiviality of Space 173 RALPH WALKER I Incongruent Counterparts 187 MARTIN CURD I Showing and Telling: Can the Difference Between Right and Left Be Explained in Words? 195 JAMES VAN CLEVE I Right, Left, and the Fourth Dimension 203 JOHN EARMAN IOn the Other Hand... : A Reconsideration of Kant, Incongruent Counterparts, and Absolute Space 235 GRAHAM NERLICH I Replies to Sklar and Earman 257 WILLIAM HARPER I Kant on Incongruent Counterparts 263 JILL VANCE BUROKER I The Role of Incongruent Counterparts in Kant's Transcendental Idealism 315 JAMES VAN CLEVE I Incongruent Counterparts and Things in Themselves 341 BIBLIOGRAPHY 353 CONTEMPORAR Y CONTRIBUTORS 357 INDEX 359

JAMES VAN CLEVE AND ROBERT E. FREDERICK PREFACE Incongruent counterparts are objects that are perfectly similar except for being mirror images of each other, such as left and right human hands. Immanuel Kant was the first great thinker to point out the philosophical significance of such objects. He called them "counterparts" because they are similar in nearly every way, "incongruent" because, despite their similarity, one could never be put in the place of the other. Three important discussions of incongruent counterparts occur in Kant's writings. The first is an article published in 1768, 'On the First Ground of the Distinction of Regions in Space', in which Kant contended that incongruent counterparts furnish a refutation of Leibniz's relational theory of space and a proof of Newton's rival theory of absolute space. The second is a section of his Inaugural Dissertation, published two years later in 1770, in which he cited incongruent counterparts as showing that our knowledge of space must rest on intuitions. The third is a section of the Prolegomena to Any Future Metaphysics of 1783, in which he cited incongruent counterparts as a paradox resolvable only by his own theory of space as mind-dependent. A fourth mention in the Metaphysical Foundations of Natural Science of 1786 briefly repeats the Prolegomena point. Curiously, there is no mention of incongruent counterparts in either of the editions (1781 and 1787) of Kant's magnum opus, the Critique of Pure Reason. Kant's arguments, whatever the final verdict on them, are highly ingenious, and evaluation of them leads one into a number of fascinating topics. These include the possibility of "higher" dimensions of space and the physicist's principle, now known to have exceptions, of parity, or right-left indifference of the laws of nature. Interest in Kant's arguments has heightened during the last three decades. A succession of journal articles and discussions in books has appeared, some of them criticizing Kant, others defending him, and each nicely building on its predecessors. This volume brings together some of the best of this work, together with Kant's three main treatments of the topic. vii

viii JAMES VAN CLEVE AND ROBERT E. FREDERICK Also included in this volume are three items from the nineteenth and early twentieth centuries: Mobius's note connecting Kant's problem with higher dimensions (1827), Norman Kemp Smith's discussion of the place of the three uses of incongruent counterparts in Kant's philosophy (1918), and a brief but pregnant observation from Wittgenstein's Tractatus (1922). Most of the literature on incongruent counterparts focuses on Kant's argument of 1768. The issue here is whether space is an entity in its own right, as Newton believed, or merely a network of relations among material things, as Leibniz believed. Readers unfamiliar with this issue may wish to consult the locus classicus for the debate, which is the correspondence between Leibniz and Newton's disciple Samuel Clarke. Other background reading is listed in our bibliography. For the most part the selections in this volume are arranged chronologically. The selections devoted mainly to the 1768 argument (space as absolute) are the first article by Gardner, the first by Van Cleve, both by Earman, both by Nerlich, and the articles by Remnant, Sklar, Walker, and Harper. (The first of the articles by Earman does not represent his current views, but it is included because it helped to shape the debate.) The articles most germane to the 1770 argument (space as intuitive) are the second by Gardner and those by Bennett, Curd, Harper, and Buroker. Finally, the articles most germane to the 1783 argument (space as mind-dependent) are those of Kemp Smith and Buroker and the second by Van Cleve. The editors wish to thank Jonathan Bennett, John Earman, and Lewis White Beck for their advice on several points (including Bennett's suggestion for a less boring title than we had originally planned). We also wish to thank Eleanor Thurn for helping prepare the manuscript, Rex Welshon for preparing the index, and Sung-Ho Chung, Teresa Ferguson, Jean Chambers, Michael Ialacci, David Martens, and John Gibbons for assisting with the bibliography.

ACKNOWLEDGMENTS The contributions to this volume by Jill Vance Buroker and William Harper were written for the occasion, as was the second by Graham Nerlich. The other contributions are reprinted. We wish to thank the following authors and publishers for permission to reprint. Immanuel Kant, 'On the First Ground of the Distinction of Regions in Space: in John Handyside (trans.), Kant's Inaugural Dissertation and Early Writings on Space (Chicago: Open Court, 1929),pp. 19-29. Immanuel Kant, selection from Section 15 of 'Dissertation on the Form and Principles of the Sensible and Intelligible World: in Handyside, p. 60. Immanuel Kant, section 13 of the Prolegomena to Any Future Metaphysics, trans. by L. W. Beck (Indianapolis: Bobbs-Merrill, 1950), pp. 32-4; 1950 Macmillan Publishing Company. August Ferdinand Mobius, 'On Higher Space,' Der barycentrische Calcul (Leipzig: 1827), Part 2, Chapter 1. Norman Kemp Smith, 'The Paradox of Incongruous Counterparts,' from A Commentary on Kant's Critique of Pure Reason (London: Macmillan, 1918), pp. 161-66. Ludwig Wittgenstein, 'Tractatus 6.36111: from Tractatus Logico-Philosophicus, trans. by D. F. Pears and B. F. McGuinness (London: Routledge & Kegan Paul, 1961), pp. 141-2. Peter Remnant, 'Incongruent Counterparts and Absolute Space: Mind, 72 (1963), 393-99. Martin Gardner, 'The Fourth Dimension: Chapter 17 of The Ambidextrous Universe (3rd. ed.; San Francisco: W. H. Freeman, 1989); 1989 W. H. Freeman. Martin Gardner, 'The Ozma Problem and the Fall of Parity: selections from Chapters 18, 20, and 22 of The Ambidextrous Universe; 1989 W. H. Freeman. Jonathan Bennett, 'The Difference Between Right and Left: American Philosophical Quarterly, 7 (1970), 175-91. John Earman, 'Kant, Incongruous Counterparts, and the Nature of Space and Space Time: Ratio, 13 (1971), 1-18. ix

x ACKNOWLEDGMENTS Graham Nerlich, 'Hands, Knees, and Absolute Space,' Chapter 2 of The Shape of Space (Cambridge: Cambridge University Press, 1976). This is a revised version of the article of the same name that appeared in The Journal of Philosophy, 70 (1973), 337-51. Lawrence Sklar, 'Incongruous Counterparts, Intrinsic Features, and the Substantiviality of Space; The Journal of Philosophy, 71 (1974),277-90. Ralph Walker, 'Incongruent Counterparts; from Kant (London: Routledge & Kegan Paul, 1978), pp. 44-51; 1978 R. C. S. Walker. Martin Curd, 'Showing and Telling: Can the Difference Between Right and Left Be Explained in Words?; Ratio, 26 (1984),63-69. James Van Cleve, 'Right, Left and the Fourth Dimension; The Philosophical Review, 96 (1987), 33-68. John Earman, 'On the Other Hand.... : A Reconsideration of Kant, Incongruent Counterparts, and Absolute Space.' Except for minor changes this paper appears as Chapter 7 of Earman's book World and Space-Time Enough (Cambridge, Mass.: The MIT Press, 1989). James Van Cleve, 'Incongruent Counterparts and Things in Themselves; in Proceedings: Sixth International Kant Congress, ed. by G. Funke and Thomas M. Seebohm; 1988 The Center for Advanced Research in Phenomenology, Inc., co-publisher (Washington, D.C.: University Press of America, Inc., 1988).