Subjects and Objects: Art, Essentialism, and Abstraction (Philosophy of History and Culture)

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Subjects and Objects

Philosophy of History and Culture Editor

Michael Krausz Bryn Mawr College Advisory Board

Annette Baier (University of Pittsburgh), Purushottama Bilimoria (Deakin University, Australia), Cora Diamond (University of Virginia), William Dray (University of Ottawa), Nancy Fraser (New School for Social Research), Cliﬀord Geertz (Institute for Advanced Study, Princeton), Peter Hacker (St. John’s College, Oxford), Rom Harré (Linacre College, Oxford), Bernard Harrison (University of Sussex), Martha Nussbaum (University of Chicago), Leon Pompa (University of Birmingham), Joseph Raz (Balliol College, Oxford), and Amélie Rorty (Brandeis University)

VOLUME 25

Subjects and Objects Art, Essentialism, and Abstraction

By

Jeﬀrey Strayer

LEIDEN • BOSTON 2007

Cover photograph, used by permission: Gehry Web, Chicago by John Gevers © 2005. www.newmediabrew.com. This book is printed on acid-free paper. Library of Congress Cataloging-in-Publication Data Szulakowska, Urszula. The sacriﬁcial body and the day of doom : alchemy and apocalyptic discourse in the Protestant Reformation / by Urszula Szulakowska. p. cm. — (Aries book series ; vol. 1) Includes bibliographical references and index. ISBN-13: 978-90-04-15025-6 ISBN-10: 90-04-15025-0 (hardback : alk. paper) 1. Alchemy—Religious aspects—Christianity—History. 2. Apocalyptic literature—History and criticism. 3. Reformation. I. Title. II. Series. BR115.A57S98 2006 540’.1120943—dc22 2006043990

ISSN 0922-6001 ISBN 978-90-04-15714-9 © Copyright 2007 by Koninklijke Brill NV, Leiden, The Netherlands. Koninklijke Brill NV incorporates the imprints Brill Hotei Publishing, IDC Publishers, Martinus Nijhoﬀ Publishers and VSP. All rights reserved. No part of this publication may be reproduced, translated, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission from the publisher. Authorization to photocopy items for internal or personal use is granted by Brill provided that the appropriate fees are paid directly to The Copyright Clearance Center, 222 Rosewood Drive, Suite 910, Danvers, MA 01923, USA. Fees are subject to change. printed in the netherlands

To Angela, to the memory of my father, and to the memory of Max

CONTENTS

Acknowledgements ......................................................................

xix

Introduction ................................................................................ 1. The subject matter of this work .......................................... 2. Artworks and subjects and objects ...................................... 3. Artworks and artistic complexes .......................................... 4. Essentialism and essential elements of artistic complexes .... 5. The format of this book ...................................................... 6. Concluding introductory remarks ........................................

1 1 2 3 4 8 8

PART ONE

PRELIMINARY ISSUES RELEVANT TO ESSENTIALIST ABSTRACTION 1. 2. 3. 4.

The terms ‘Abstract’ and ‘Abstraction’ .............................. The development of Abstraction in art history .................. Levels of Abstraction in art ................................................ The diﬀerent relation of philosophy and art to the question of the limits of Abstraction in art ........................ 4.1. The general diﬀerence of art and philosophy, and the diﬀerent relation of each to Essentialist Abstraction .................................................................... 4.2. Philosophy and Essentialist art .................................... 4.3. The non-hierarchical relation of art and philosophy ...................................................................... 4.4. The complementary relation of art and philosophy in the question of Abstract art’s limits ........................ 5. Modernism and Essentialist Abstraction .............................. 5.1. Modernism and Essentialism and identity and reﬂexivity ........................................................................

13 15 20 26

26 26 27 29 29 31

viii

contents PART TWO

ON SUBJECTS AND OBJECTS AND WORKS OF ART: GENERAL CONSIDERATIONS AND BASIC POINTS OF RELEVANCE TO ESSENTIALIST ABSTRACTION Introduction ................................................................................ Division I: Singling Something Out, Artistic Identity, and Intentional Actions .................................................................... 1. Singling something out ........................................................ 1.1. Creating, selecting, and specifying objects .................. 1.2. Artworks and objects .................................................... 1.3. Singling something out determinately ........................ 1.4. Singling something out indeterminately ...................... 1.5. Success and failure in singling something out ............ 1.6. Possible lack of clarity in singling something out ...... 1.7. Singling out more than one object, but not more than one artwork .......................................................... 1.8. Singling something out, the visual arts, and the arts in general ...................................................................... 2. Artworks and apprehensible objects .................................... 2.1. Phenomenal and noumenal objects ............................ 3. The notion of the identity of an artwork .......................... 3.1. The logical and epistemological aspects of an artwork’s identity .......................................................... 3.2. The identity of an artwork and phenomenal and noumenal objects .......................................................... 4. The minimal conceptual relation of artist to artwork ...... 4.1. No artwork without an identity .................................. 5. Two kinds of required intentional relation of an artist to an artwork ............................................................................ 5.1. The artist’s conscious understanding of each kind of relation .......................................................................... 5.2. Implicit and explicit claims that certain objects are artworks .......................................................................... 5.3. Time and intentional relations of an artist to an object meant to be a work of art .............................. 6. Artworks, aesthetic objects, and intentional actions .......... 6.1. Intentional actions and novel artworks ......................

35

39 39 40 53 59 61 64 66 66 68 69 69 74 76 77 78 79 80 81 81 81 82 82

contents 7. The liberal notion of the use of objects and the direct and indirect relation of an artist to an object used to make an artwork .................................................................. 7.1. Artworks and the products of accidental actions ...... 8. The dependence of artworks on artistic intentions and cultural contexts .................................................................... 8.1. Abstraction, lack of artistic action, and publicity ...... Division II: Artists, Objects, and Some Minimum Conditions of Artistic Identity ...................................................................... 1. The dependence of artworks on preexistent objects .......... 1.1. The minimum number of preexistent objects required to make artworks depends on the metaphysics of personhood .......................................... 1.2. Metaphysics, acts, and objects used in producing art 2. That an artwork must be something singled out does not dictate the nature of what is singled out ............................ 3. The history of an object with which an artwork is meant to be identiﬁed ...................................................................... 4. The dependence of an artwork not meant to be identiﬁed with some preexistent object on the artistic use of some preexistent object .................................................................. 5. An artwork has its particular identity in spite of any degree of similarity that it has to any other object .......... Division III: Artistic Identity, Subjects, and Apprehensible Objects ........................................................................................ 1. The dependence of the identity of an artwork on an apprehensible object .............................................................. 1.1. Speciﬁcation and objects that are meant to be artworks that cannot be apprehended ........................ 2. The dependence of knowledge of the identity of an artwork on an apprehensible object .................................... 3. Relevant apprehension of the apprehensible object on which knowledge of the identity of an artwork is dependent .............................................................................. 3.1. Relevant apprehension of an apprehensible artwork .......................................................................... 3.2. The dependence of an artwork that is meant to be identiﬁed with a non-apprehensible object on an apprehensible object ......................................................

ix

83 84 85 86

89 89

89 90 91 91

92 92

93 93 93 93

94 94

94

contents

x

4. 5.

6. 7.

8.

9. 10. 11.

3.3. Understanding the relation of an apprehensible object on which the identity of an artwork is dependent to that identity .......................................... The artistic identity of an artwork and its relevance to the ontology, meaning, and value of an artwork ............ The dependence of the identity and the apprehension of the identity of an artwork on a public perceptual object .................................................................................... 5.1. Privacy and publicity and phenomenal objects ........ 5.2. A public perceptual object is necessary but is not suﬃcient ...................................................................... 5.3. Apprehensible properties relevant to an artwork’s identity .......................................................................... 5.4. No a priori limitations on public perceptual objects 5.5. Art-historical objects and consciousness .................... Original and subsequent dependence of artworks on objects .................................................................................. Embodied artworks ............................................................ 7.1. Embodiment, identiﬁcation of artworks, and sophisticated notions of artworks .............................. 7.2. Diﬀerent kinds of appreciation of embodied artworks ........................................................................ 7.3. Ways of producing embodied artworks .................... Non-embodied artworks ...................................................... 8.1. Non-embodied artworks and speciﬁcation ................ 8.2. Non-embodied artworks and selection ...................... 8.3. Non-embodied artworks and perceptible objects ...... Awareness and agency and perceptual objects ................ Conceptual idealism and works of art .............................. An artist’s presentation of an object to the artworld as an artwork ..........................................................................

Division IV: Artworks and Kinds of Object .......................... 1. Artworks and times and places of apprehending them .... 2. An artist’s identiﬁcation of the same artwork with apprehensibly diﬀerent things ............................................ 3. An artist’s identiﬁcation of a number of works with a number of indistinguishable objects .................................. 4. The equal identiﬁcation of an artwork with diﬀerent objects at the same or diﬀerent times ..............................

95 95

96 98 100 100 100 101 102 103 104 106 107 107 108 108 110 110 111 112 115 115 116 116 117

contents 5. An artist’s identiﬁcation of an artwork with the same object with which another artwork is meant to be identiﬁed ................................................................................ 6. Temporal and atemporal objects ........................................ 7. Artworks and change ............................................................ 8. Artworks, artifacts, and physical objects ............................ Division V: Art and the Aesthetic .......................................... 1. The distinction between art and the aesthetic .................. 2. Diﬀerent sources of aesthetic experience and the possible heterogeneity of aesthetic experience .................................. 2.1. Perceptual and intellectual objects .............................. 2.2. The possibility of intellectual aesthetic experience of intellectual objects ........................................................ 2.3. Aesthetic experiences, thoughts, and feelings .............. 2.4. The possible heterogeneity of aesthetic experience .... 3. Art-historical artworks and kinds of appreciable artistic property .................................................................................. 3.1. The notion of an artistic property .............................. 3.2. Appreciation of an artistic property ............................ 3.3. The notion of an aesthetic property .......................... 3.4. Artworks and their appreciable properties .................. 3.5. The Intentional direction of events of appreciation .... 3.6. Artworks and judgements of artistic value .................. 3.7. Artistic interest and the possible expansion of the concept of the aesthetic ................................................ 3.8. Essentialism and the aesthetic ...................................... 4. Factors relevant to the aesthetic value of a work of art .... 4.1. The aesthetic value of artworks identiﬁed with artistically-independent objects .................................... 4.2. Aesthetic value and created artworks .......................... 4.3. Aesthetic value and participatory artworks ................

xi

118 118 118 119 121 121 122 122 123 126 127 128 128 129 130 131 131 134 134 139 139 140 144 145

xii

contents PART THREE

ON SUBJECTS AND OBJECTS AND ARTISTIC COMPLEXES: THE MATERIAL OF ESSENTIALISM Introduction ................................................................................

147

Division I: Subjects and Objects and Artistic Complexes .... Introduction ................................................................................ 1. The concept of an artistic complex .................................... 1.1. The notion of original dependence ........................ 1.2. Derived and acceptably derived objects .................. 1.3. Relevant objects ........................................................ 1.4. Appropriate apprehension ........................................ 1.5. Subjects, relevant objects, and artistic complexes .... 2. The nature of an object or objects on which a work of art is relevantly dependent .................................................. 2.1. A single spatio-temporally continuous perceptual object that can be apprehended in full from a single perspective ...................................................... 2.2. A single spatio-temporally continuous perceptual object that cannot be apprehended in full from a single perspective ...................................................... 2.3. A number of spatio-temporally continuous perceptual objects distributed in spatial proximity 2.4. A number of spatio-temporally continuous perceptual objects distributed over distances from one another ................................................................ 2.5–6. Temporally distributed objects ................................ 2.7. Possibilities for a plurality of objects on which the identity of an artwork is dependent ........................ 2.8. Artworks and tokens of a type ................................ 3. Artworks and reproductions or documentation .................. 4. Kinds of relevant object and their ﬁguring in artistic complexes .............................................................................. 4.1. A relevant object with which an artwork is meant to be identiﬁed .......................................................... 4.2. A relevant object through which an artwork is meant to be identiﬁed ..............................................

149 149 149 150 152 154 155 156 158

159

160 160

161 162 162 163 164 165 166 168

contents 4.3. A complex relevant object that has an aspect with which an artwork is meant to be identiﬁed and an aspect through which an artwork is meant to be identiﬁed .................................................................. 4.4. A relevant object through which and with which an artwork is meant to be identiﬁed ................................ 4.5. Relevant objects and artistic complexes ...................... Division II: Artistic Complexes and Subjects .......................... Introduction ................................................................................ 1. Any artwork is related to consciousness .............................. 1.1. Consciousness is a necessary condition of the identity of any artwork ................................................ 1.2. Consciousness is a necessary condition of responding to any artwork .............................................................. 2. Consciousness and traditional and Essentialist art ............ 3. Kinds of conscious event of interest to Essentialism ........ 4. Forms of conscious event of interest to Essentialism ........ 4.1. Any event of awareness is either Intentional or non-Intentional .............................................................. 4.2. Any event of awareness has or lacks structure .......... 4.3. The structure of Intentional events is reﬂexive or irreﬂexive ........................................................................ 4.4. Areﬂexive awareness ...................................................... 4.5. Any event of awareness is either monadic or polyadic .......................................................................... 4.6. First-order awareness .................................................... 4.7. Second-order awareness ................................................ 4.8. The ﬁve fundamental forms of conscious event ........ 5. Consciousness and Essentialist Abstraction ........................ 6. Language, consciousness, and Essentialism ........................ 7. Agency .................................................................................... 8. Awareness and agency .......................................................... 9. Knowing which, knowing that, and knowing what .......... 9.1. Knowing which ............................................................ 9.2. Knowing that ................................................................ 9.3. Knowing what ..............................................................

xiii

169 169 170 171 171 171 171 172 173 174 175 176 178 178 179 179 181 181 183 185 186 187 188 188 189 190 191

xiv

contents

Division III: Artistic Complexes and Objects ........................ Introduction ................................................................................ 1. Identity and diﬀerence .......................................................... 1.1. The primitive concepts of logical sameness and logical diﬀerence ............................................................ 1.2. Laws of identity and diﬀerence .................................. 2. Particular identity .................................................................. 2.1. Logical identity and particular identity ...................... 2.2. Particular identity is unique and singular .................. 2.3. Haecceity is a core logical property ............................ 2.4. The laws of objects ...................................................... 3. Identity and diﬀerence and Essentialism ............................ 4. Logical space ........................................................................ 5. Identity and diﬀerence and artistic complexes .................. 5.1. The delimitation of logical space by artworks and things of relevance to them ........................................ 5.2. Essentialism and the delimitation of logical space .... 6. Artworks, objects, and parts ................................................ 7. Compositional relations and works of art .......................... 7.1. Simple and complex embodied artworks .................... 7.2. Simple and complex speciﬁed and non-embodied artworks .......................................................................... 7.3. Essentialism and compositional relations of objects ............................................................................ 8. An object either is or is not dependent on awareness to be the object that it is .......................................................... 9. Kinds of dependence: identity dependence and type dependence ............................................................................ 9.1. The diﬀerence between identity and identity dependence .................................................................... 9.2. Actual and possible awareness of consciousnessdependent objects .......................................................... 9.3. The heterogeneity of dependent objects and the events on which they depend ...................................... 9.4. Possible logical and metaphysical equivalence of dependent objects and the events on which they depend ............................................................................ 9.5. The implicit relation of a conscious event to an object dependent on it ..................................................

193 193 194 194 195 197 197 198 198 198 198 200 200 200 201 202 203 203 204 205 206 206 207 208 209

209 211

contents 10. Identity dependence in general .......................................... 10.1. The implicit relation of an identity-dependent object to a particular time ...................................... 10.2. The timeless use of ‘is’ ............................................ 10.3. Type-A identity dependence .................................... 10.4. Type-B identity dependence .................................... 10.5. Identity dependence and simplicity and complexity 11. Type dependence in general .............................................. 11.1. Type-A type dependence .......................................... 11.2. Type-B type dependence .......................................... 11.3. Type dependence and simplicity and complexity .... 12. Singly-dependent objects .................................................... 13. Multiply-dependent objects ................................................ 13.1. Homogeneous multiply-dependent objects .............. 13.2. Heterogeneous multiply-dependent objects ............ 14. Artworks as wholly or partially dependent objects .......... 14.1. Wholly-dependent objects ........................................ 14.2. Partially-dependent objects ...................................... 15. Essentialism and kinds of dependent object .................... 16. Kinds of independent object .............................................. 16.1. Generic independence .............................................. 16.2. Particular independence ............................................ 16.3. Biographical independence ...................................... 16.4. Universal independence ............................................ 16.5. Necessary independence ............................................ 17. Essentialism and kinds of independent object .................. Division IV: Artistic Complexes and Subjects and Objects .... Introduction ................................................................................ 1. Medium and media ............................................................ 1.1. Two notions of a medium ...................................... 1.2. A medium as a means of eﬀecting artworks .......... 1.3. A medium as a means of conveying artworks ...... 1.4. The restrictive notion of a medium ........................ 1.5. Media and embodied artworks ................................ 1.6. Media and eﬀecting a non-embodied artwork that is selected .................................................................. 1.7. Language as a medium for eﬀecting artworks ...... 1.8. Non-perceptible events as media for eﬀecting objects meant to be artworks ..................................

xv 212 212 213 213 215 216 217 217 220 221 222 222 223 223 223 224 224 224 225 225 226 227 228 229 230 233 233 234 235 236 238 238 239 242 243 245

xvi

2.

3.

4.

5.

6. 7.

8.

contents

1.9. Documentation and reproductions as media for conveying artworks ...................................................... 1.10. Media and parts of artworks .................................... 1.11. Relevant objects as media for conveying artworks .... 1.12. The conceptual linkage of medium and singling something out .............................................................. 1.13. Language as a medium that both eﬀects and conveys the identity of an artwork ............................ Non-perceptible events as media for Essentialist Abstraction ............................................................................ 2.1. Consciousness, ideational objects, and comprehension of identity .......................................... 2.2. Ideational objects and ideational artworks ................ 2.3. The mixed media of Essentialism .............................. 2.4. Possible uses of consciousness as a medium ............ 2.5. Consciousness, art, and philosophy .......................... 2.6. Agency as a medium .................................................. Meaning and concipients ...................................................... 3.1. Meaning and artistic complexes ................................ 3.2. The concept of a concipient ...................................... 3.3. Essentialism and meaning .......................................... Kinds and forms of Intentional event and essential elements of artistic complexes .............................................. 4.1. Perception and conception ........................................ 4.2. Essentialism and forms of awareness ........................ 4.3. Things that are relevant to the nature of an Essentialist object ........................................................ Cause and eﬀect and change .............................................. 5.1. Change and perceptual objects on which embodied and speciﬁed artworks are dependent ...... 5.2. Change and temporal art forms ................................ 5.3. Artworks that intentionally incorporate change ........ 5.4. Artworks and Cambridge changes ............................ 5.5. Origination and termination and works of art ........ Artistic complexes and becoming ........................................ Indexicals ................................................................................ 7.1. Indexicals and awareness ............................................ 7.2. Indexicals and agency ................................................ 7.3. Indexicals and perceptual objects .............................. Phenomenality and noumenality ..........................................

250 250 250 251 251 253 254 257 259 260 261 261 262 262 263 264 265 265 266 267 267 267 269 270 271 272 273 274 274 277 277 277

contents

xvii

9. Apprehension and reapprehension .................................... 10. Space and time .................................................................... 11. Continuity, discontinuity, recurrence, and non-recurrence 11.1. Contiguous and noncontiguous times ...................... 11.2. Continuity .................................................................. 11.3. Discontinuity .............................................................. 11.4. Artworks and continuity and discontinuity ............ 11.5. Recurrence ................................................................ 11.6. Non-recurrence .......................................................... 11.7. Artworks and recurrence and non-recurrence ........ 12. Aesthetically essential properties ........................................

278 280 280 281 282 283 284 285 286 287 288

Division V: The Essential Elements of Artistic Complexes ....

291

PART FOUR

IDENTITY AND SUBJECTS, OBJECTS, AND LANGUAGE: CONCLUDING REMARKS AS A PREAMBLE TO AN ESSENTIALIST INVESTIGATION OF THE LIMITS OF ABSTRACTION Introduction ................................................................................ 1. Preliminary observations .................................................... 1.1. Abstraction and subjects .......................................... 1.2. Abstraction and objects: Everything and nothing .... 2. Précis of the principles of Essentialist Abstraction .......... 3. Identity and Essentialist Abstraction .................................. 3.1. The relation of artist and audience to an artwork’s identity ...................................................... 3.2. Identity and essential elements of artistic complexes .................................................................. 4. Ideational objects and Essentialist Abstraction ................ 5. Comprehension of identity, language, and Essentially Abstract artworks ................................................................ 5.1. Non-perceptible events, ideational objects, and speciﬁcation ................................................................ 5.2. Speciﬁcation and perceptual and non-perceptual ideational objects ...................................................... 5.3. Speciﬁcation and Essentialist Abstraction ................

295 295 295 297 298 300 300 301 301 303 304 307 308

xviii

contents

6. The relation of the identity of an Essentially Abstract artwork to things that are used to eﬀect that identity .... 7. Concluding remarks: Essentialism and its objects ............ 7.1. Essentialism and the essential elements of artistic complexes .................................................................... 7.2. Additional Essentialist considerations ........................

309 313 314 316

APPENDICES Appendix I On the Notions of Object, Property, Haecceity, and Diversity ........................................................ 1. Objects and Properties ........................................................ 2. Haecceity and Diversity .................................................... Appendix II Leibniz’s Law, the Laws of Identity and Diﬀerence, and the Identity of Indiscernibles .................... 1. Leibniz’s Law—A Conceptual Consideration .................. 2. The Laws of Identity and Diﬀerence ................................ 3. The Identity of Indiscernibles ............................................ Appendix III Distinction, Discrimination, and Distinguishability .................................................................... Appendix IV Impossible Objects ............................................ 1. Deﬁnition of impossible object .......................................... 2. Diﬀerent views of impossible objects ................................ 3. Impossible objects and the laws of thought—I ................ 4. Diﬀerent views of the relation of impossible objects to consciousness ........................................................................ 5. Impossible objects as Type-A type-dependent objects .... 6. Type dependence and sameness ........................................ 7. The relation of impossible objects to events of conceiving of them ................................................................................ 8. Impossible objects and the laws of thought—II .............. 9. Saying something and saying something true .................. 10. Impossible objects, the laws of objects, and Abstraction ..........................................................................

321 321 330 335 335 340 343 351 353 353 354 356 359 360 361 363 364 364 365

Works Cited in the Text and Selected Bibliography ............

367

Index ..........................................................................................

375

ACKNOWLEDGEMENTS

Several colleagues have kindly read all or part of one version or another of the present work; commented on papers excerpted from the work that have been presented at professional conferences and universities; or discussed ideas of the book with me in conversation, correspondence, or both. These include: Tom Adajian, the anonymous reader for Brill, John Brown, Clark Butler, Evan Cameron, David Fairchild, Rodney Farnsworth, Dan Flory, Jeﬀ Goodman, Jeﬀ Governale, Victor Haines, Steve Hoeltzel, Phil Jenkins, Michael Krausz, Earl Kumfer, Donald Kuspit, Keith Lehrer, Ken Long, Bill McBride, John MacKinnon, Duston Moore, Ira Newman, Bob Peters, Alan Sandstrom, Steve Sarratore, Roger Seamon, and Leon Surette. I am very grateful to the people who patiently and carefully read the entire manuscript for their diligence, and I thank all those named for their camaraderie and perspicacity. Whether I have added, deleted, or changed something in the text due to a thoughtful suggestion or an insightful query, this book has beneﬁtted greatly from my commerce with these individuals. They of course bear no responsibility for its ﬁnal form. I want to thank Indiana University-Purdue University Fort Wayne, and the Department of Philosophy, for support provided for research, travel, and technical aid; members of the department for discussion; Jan Hoagburg, Jennifer Caseldine-Bracht, and Deborah Hoile for repeated and often supererogatory assistance; and students from a graduate seminar against whose inquisitive minds an earlier version of this work was tested.

INTRODUCTION

1. The subject matter of this work The focus of this work is a philosophical consideration of a particular artistic issue: the limits of Abstraction in art.1 However, proper treatment of that issue requires that it occur within a broader examination of several things that are relevant both to making and apprehending works of art in general,2 and to the artistic and aesthetic properties of artworks. Because it is subjects who make and apprehend works of art; because both making and apprehending works of art depend on objects; because determining the limits of Abstraction must be based on investigating the subject-object relationship; and because consideration of the matter of Abstraction demands a wider reﬂection on art, it should be understood that this book contains a great deal of philosophy of subjects and objects and philosophy of art in addition to thinking that more speciﬁcally targets the particular artistic issue with which the work is concerned.

1 I capitalize the terms ‘Abstract’ and ‘Abstraction’ to distinguish their use as terms of art from ‘abstract’ and ‘abstraction’ as terms of common parlance and philosophy because the use of these terms in the latter areas lack certain things of relevance to their use in art that this work identiﬁes, and because Kit Fine has recently published a work called The Limits of Abstraction that diﬀers in subject and intent from the topic of this book. I sometimes use the terms ‘minimal’ and ‘reductive’ as synonyms of ‘Abstract,’ where ‘minimal’ is written in lower case to distinguish it from Minimal art, whose objects are, nevertheless, of great importance to the history of Abstraction. When I speak of Abstraction it is to be understood that I am talking about Abstraction in art. And when I speak of the limits of Abstraction, it is implicit that those limits are the limits of Abstraction in art. 2 It will be seen that speaking of “making and apprehending works of art,” both here and throughout, pertains to an artist’s eﬀecting the intended identiﬁcation of an artwork with some object, and a subject’s understanding of the intended identiﬁcation eﬀected. These are complex matters that involve a number of things. Part of understanding the complexity of making and apprehending works of art includes recognizing that an artist’s eﬀecting the identiﬁcation of an artwork with some object need not be limited to traditional kinds of artistic production, and that that which is apprehended may be the identity of an artwork rather than the object itself with which the work is meant to be identiﬁed.

2

introduction

The questions, ‘Does Abstract art have a limit?’ and ‘On what must the creative identiﬁcation of any such limit rest?’ can be understood to arise in relation to certain works of Suprematism, Dadaism, Nouveau Réalisme, Fluxus, Minimalism, Conceptualism, Light and Space art, Body art, Land art, and Performance art, and in relation to other less classiﬁed or classiﬁable works of individual artists. As will be seen in the course of this work, these questions are of philosophical interest not only because of the depth and complexity of the problems that they deﬁne, but due to the relation of those problems to topics in the philosophy of subjects and objects, and to some wider issues in philosophical aesthetics. The philosophical analysis of the framework in which artistic identiﬁcation of the limits of Abstraction must occur treats that identiﬁcation as an art-historical issue. Accordingly, publicity, or the possible understanding of a work’s identity by any number of subjects, is an essential aspect of the determination of Abstract art’s limits. This publicity is necessary to avoid the vapidity and critical and historical irrelevance of any artwork the knowledge of which would be conﬁned to a single individual. Given this art-historical interest, the artworld is recognized as a sociological institution in relation to which investigations of the limits of Abstraction would have to be conducted, and within which the results of such investigations would have to be recognized and critically assessed. However, the requirement of the artworld for the recognition and assessment of a work does not mean that any object meant to be an artwork has to be exhibited in a gallery, museum, or alternative space. It only means that the artworld must be aware of any object in which a limit of Abstraction is determined if the object is going to have any critical and historical signiﬁcance.

2. Artworks and subjects and objects Although a philosophical work, as philosophical, cannot produce works of art that are more Abstract than any that has yet appeared, it can identify certain things with which even the more Abstract artworks cannot dispense. That identiﬁcation includes recognizing that any artwork, including any of the more Abstract works, is an object of some kind of object; that each artwork has a particular identity; that the particular identity of an artwork indicates that it is logically

introduction

3

distinct and epistemologically distinguished from each object that lacks its particular identity; that the identity of an artwork depends on the intention of the artist whose work it is to eﬀect the identiﬁcation of the work with some object; that although artists may eﬀect the identiﬁcation of artworks with objects in a variety of ways, and notwithstanding the nature of the object that an artwork is meant to be, the artist’s determination of the identity of an artwork depends on the use of at least one public perceptual object; that an artwork may or may not be meant to be identiﬁed with all or part of a public perceptual object that is used to eﬀect the identity of that work; that understanding the intended identiﬁcation of an artwork with some object depends on at least one public perceptual object that the work may or may not be meant to be, but that is relevant to the identity of the work; and that such understanding is presupposed by any appreciation of the work, and any assessment of its critical, historical, or philosophical importance.

3. Artworks and artistic complexes It follows from the preceding points that an artist must be responsible for eﬀecting a public perceptual object on which the identity of an artwork is relevantly dependent, such that, appropriate apprehension of such an object is a presupposition of understanding with which object the work is meant to be identiﬁed. An event of appropriately apprehending a public perceptual object on which the identity of an artwork is relevantly dependent produces an ‘artistic complex’ of which that apprehension, that object, and the subject whose apprehension it is are constituents. Such apprehension is appropriate when it is required to understand what the work is meant to be, such as seeing rather than touching for painting, and reading rather than hearing for language. Certain things are indispensable to the existence of any artistic complex, and certain things are unavoidable given its existence. Things of either kind of thing are said to be ‘essential elements’ of an artistic complex. These include: the subject, the perceptual object, and the subject’s consciousness of the object that are constituents of the complex; certain properties of these things; certain relations that hold between them; conditions by which the subject, her consciousness, the object, their properties, and the relations that hold between them are constrained; and particular facts that

4

introduction

pertain to these things. It is part of the purpose of this work to identify these properties, relations, conditions, and facts, and to examine them to the extent required for the objective of this investigation. The identiﬁcation and examination of the essential elements of artistic complexes is important since identifying the limits of Abstraction in art is an art-historical undertaking. Accordingly, an artist must be responsible for the production of a public perceptual object on which comprehension of the intended identiﬁcation of an artwork with some object depends. Appropriate apprehension of such a perceptual object is required to comprehend the intended identiﬁcation of the work with some object. Such apprehension results in an artistic complex that has certain essential elements. As these elements are essential, how they might be used, in certain ways and combinations, as the most reductive ‘material’ there is for eﬀecting the identiﬁcation of artworks with the more Abstract objects would have to be artistically investigated. Although determining the limits of Abstraction in art must be an artistic and not a philosophical investigation, philosophy can state that any identiﬁcation of a limit of Abstraction in art will involve an artistic complex in which the limit identiﬁed is comprehended. And philosophy can state in advance of, or in addition to, any artistic investigation of the limits of Abstraction that the identity of any of the more Abstract artworks possible will reﬂect the use of certain essential elements of any artistic complex in which that identity is comprehended to eﬀect that identity. This is because the reﬂection in the identity of a work of any essential element that is used to eﬀect that identity removes any conceptual gap between the object that the work is meant to be and the element that is used to eﬀect it. As the most reductive material conceivable, use of essential elements of artistic complexes would not only allow the limits of Abstraction to be determined, but would determine the nature of the aesthetic of the more Abstract artworks that they could be employed to eﬀect.

4. Essentialism and essential elements of artistic complexes Because any creative determination of the limits of Abstraction in art would have to be based on working with essential elements of artistic complexes, and so would include a commitment to what Béla Bartok in another context called the “inexorable elimination of all

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5

inessentials,” 3 the language ‘Essentialist Abstraction’ or simply ‘Essentialism’ is used to refer to any creative investigation in which the limits of Abstraction would be identiﬁed. Thus the notion of essential in the use of the terms ‘Essentialist,’ ‘Essentialism,’ and ‘Essentially’ is meant to cover in a single concept any such investigation, and to underline to the importance of such an investigation the essential elements of artistic complexes. The notion of essential that the use of these terms reﬂect itself reﬂects the indispensability of certain things to the existence of an artistic complex, and the ineluctability of certain things given the existence of such a complex. The use of the notion of essential in regard to the elements of that entity does not permit the automatic extension of that notion to other areas of philosophical investigation. As will be seen in the book, I do maintain that certain things are essential to making art in addition to certain things being essential to artistic complexes, but it is not maintained universally that any kind of thing has an essence or essential property, other than the property that it has of obeying all of the laws of objects, which includes the law that any object has the property of being the object that it is. Therefore nothing of global metaphysical signiﬁcance can be inferred from the use of the term ‘Essentialism’ in this work. Rather, its employment should be understood to be restricted to the project of determining the limits of Abstraction in art in terms of the use and reﬂection of essential elements of artistic complexes. The terms ‘Essentialism’ and ‘Essentialist Abstraction’ are then used to pertain to any investigation that would occur of the limits of Abstraction in art—the limits whose creative identiﬁcation must be based on and reﬂect the use of essential elements of artistic complexes. These terms are capitalized to tie them speciﬁcally to the project of determining the limits of Abstraction, but I use ‘essential’ in lower case when talking about the essential elements of artistic complexes. To speak of the ‘Essentialist’ is to speak of anyone who would be involved in such a creative investigation. Such remarks as: “It would be a task for Essentialism . . .;” “Essentialism must investigate . . .;” “Essentialist Abstraction would have to consider . . .;” and

3 Bartok’s quote refers to what music has to gain from studying folk music. See Tamplin, Ronald (ed.) The Arts: A History of Expression in the 20th Century, Oxford: Grange Books (1991) p. 52.

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“The Essentialist would have to recognize . . .” that appear in this work refer to any creative eﬀort to determine the limits of Abstraction in art. And the terms ‘Essentialist’ and ‘Essentialism’ that occur in such remarks reﬂect the fact that any such determination would have to be based on and reﬂect essential elements of artistic complexes that are identiﬁed and considered in this work. Any artwork that is one of the more Abstract possible, in being based on and reﬂecting the use of essential elements of artistic complexes, is an ‘Essentially Abstract’ artwork. The notion of essential that pertains to my use of the terms ‘Essentialist,’ ‘Essentialism,’ and ‘Essentially,’ and to my speaking of the essential elements of artistic complexes, is intended to be consistent with any metaphysical view of the nature of the essential elements of such complexes. For instance, consciousness is an essential element of any artistic complex, and that remains the case whatever the metaphysical nature of consciousness is. Further, my use of the terms ‘Essentialist,’ ‘Essentialism,’ and ‘Essentially,’ in being speciﬁcally tied to determining the limits of Abstraction through the use of essential elements of artistic complexes, is meant to be distinct from any use of these terms in art-critical or art-historical writing that pertains to prior Abstract art.4 Determining the limits of Abstraction must be based on the use of essential elements of artistic complexes since anything that might be used to produce an artwork that is not such an essential element is dispensable. However, just as diﬀerent colors, lines, and shapes can be combined in diﬀerent ways to result in diﬀerent things that are more or less Abstract, that diﬀerent essential elements of artistic complexes may be combined or used in diﬀerent possible ways to result in diﬀerent objects in which diﬀerent limits of Abstraction are diﬀerently determined must be recognized. Such diﬀerent objects would diﬀerently reﬂect certain elements of artistic complexes that are used to produce them, and such reﬂection would be important

4 For instance, my use of ‘Essentialism’ diﬀers from Mark Cheetham’s use of ‘essentialism’ when he says: “By essentialism I mean the search for immutable essence or truth and the concomitant ontological division between reality and mere appearance,” and when he says that he employs ‘essentialism’ “to refer to the belief in and search for the immutable and universal core of reality . . .” Cheetham, Mark A. The Rhetoric of Purity: Essentialist Theory and the Advent of Abstract Painting, Cambridge: Cambridge Univ. Press (1991). First quote p. xi, and second quote p. 38. Noting that diﬀerence does not denigrate the interest or importance of Cheetham’s study.

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to the character of their aesthetic. In addition, because diﬀerent kinds and forms of conscious event may be used in an investigation of those limits, and because these diﬀerent kinds and forms of conscious event may be combined with agency to produce objects that are meant to be Abstract artworks, an Essentialist determination of a limit of Abstraction may involve a restructuring of certain relations between certain of the elements of an artistic complex. Any such restructuring would then form part of the aesthetic of any determination of any Abstract limit. As will be seen in the course of this book, any attempt to determine the limits of Abstraction would be a deep and complex undertaking that would involve a number of diﬀerent things. Accordingly, it should not be inferred from talk of the need to use essential elements of artistic complexes alone that any of the simpler objects that it is possible to eﬀect is for that reason one of the more Abstract objects that it is possible to eﬀect, or that there is a single standard means of equating the degree of Abstraction of an object with its simplicity or complexity, or that the notions of simplicity and complexity have absolute meanings apart from their application to diﬀerent kinds of object that are put to diﬀerent kinds of use in diﬀerent kinds of situation. And because elements of artistic complexes may be used and combined in myriad ways to eﬀect objects that artworks are meant to be, the nature of any limit of Abstraction, diﬀerent kinds of limit that it may be possible to eﬀect, and the degree of Abstraction of any limit, cannot be determined in advance of any creative utilization of such elements. The aesthetic of the creative determination of the limits of Abstraction also cannot be determined in advance of such a determination. However, it is clear that such an aesthetic would result from ways in which essential elements of artistic complexes are used. This may include novel uses of space, time, and language in addition to those things that have already been mentioned and those things that are identiﬁed and examined in this work. Creative investigation of the limits of Abstraction in art does not presuppose knowledge of the results of the philosophical inquiry into what must underlie such an investigation. However, even though that is the case, eﬀecting any of the more Abstract artworks possible would entail the conscious or unconscious use of essential elements of artistic complexes, and any identiﬁcation of an artwork that is eﬀected through the use of such elements would result in an

8

introduction

Essentialist artwork, or one that can be said to be Essentially Abstract, that would reﬂect the use of those elements.

5. The format of this book This book is divided into four parts. Part One deals with issues prefatory to the project of identifying the limits of Abstraction, such as consideration of the meanings of the terms ‘Abstract’ and ‘Abstraction,’ and the relation of Modernism to that identiﬁcation. Part Two is devoted to points that are essential to making and apprehending works of art in general, and so includes attending to things with which even the most Abstract artwork cannot dispense. The analysis of an artistic complex in Part Three includes the identiﬁcation of things that are essential to the existence of any artistic complex, and things that necessarily obtain given the existence of such a complex, as well as matters that are relevant to each. Because such essential elements of an artistic complex must ﬁgure in any creative determination of the limits of Abstraction, Part Three’s identiﬁcation and consideration of them completes the inquiry into the things on which such a determination would rest. Part Four concludes the body of the work with remarks on eﬀecting and comprehending the identity of an artwork as the focus of the creative determination of the limits of Abstraction, and on the indispensability of language to eﬀecting and comprehending that identity, as that identity is determined in relation to the comprehension of language that pertains to essential elements of artistic complexes. Topics in the philosophy of subjects and objects that pertain to certain matters of the text are considered or elaborated upon in specialized appendices that appear after Part Four of the work for those who are interested.

6. Concluding introductory remarks Many of the points made in this work may be required in, or may qualify, any conceivable world. However, I do not attempt to state the presuppositions of any possible reality that would permit subjects and objects and various relations to hold between them, but only attempt to identify what is required to make the most artistically

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Abstract objects possible given the nature of this reality. Some of these considerations concern features of the world that, although contingent, are nevertheless essential to the project of determining the limits of Abstraction in art. In addition, an attempt to explain how or why things are as they are is for the most part superﬂuous to the project of identifying those things that constitute the conceptual and aesthetic framework for determining the limits of Abstraction in art, and to examining them and things that are pertinent to them in relation to their relevance to that framework. I am not aware that anyone in the history of either art or philosophy has directly raised the question of whether or not Abstraction in art has a limit or limits; and, if it does, what that limit or those limits might be; how we could know or justify that any such limit is in fact a limit, and hence what that knowledge or justiﬁcation would presuppose; and how any Abstract limit might be determined or exhibited in a particular work of art. I have found in thinking about these things that the issue of Abstract art’s limits is profound and intricate and requires the kind of examination that I have attempted to provide in order for it to be adequately investigated. Although I believe that my consideration of the things noted is novel, thoughts of other thinkers in the worlds of both art and philosophy that are relevant to them are recognized at appropriate points in the text. Admittedly, relevance admits of degrees, and some of the references cited are more directly and others are more peripherally related to the issue of how the question of the limits of the Abstraction in art must be approached philosophically. Other works of still more general relevance are listed in the bibliography of the book, which is by no means exhaustive, but which reﬂects the complexity of the issues pertaining to Abstraction that this work addresses. This book might have been reduced to a number of basic assertions from which creative investigations of the limits of Abstraction might then proceed. However, the work would then have been composed of propositions bold for absence of argument and sparse for lack of elucidation, giving it the character of the kind of artistic manifesto that is narrow and imperious, rather than consisting of some core thoughts buttressed by an amount and depth of reasoning required to render it complete and philosophical. An artistic manifesto is narrow and imperious, and so unduly restricted, when it, as Danto puts it, “deﬁnes a certain kind of movement, and a certain

10

introduction

kind of style, which the manifesto more or less proclaims as the only kind of art that matters.”5 A manifesto in the disagreeable parochial sense “singles out the art it justiﬁes as the true and only art . . .”6 However, ‘manifesto’ can be used in a sense that is both wider and more tolerant than the preceding sense to describe writing about art or an artistic issue that delineates relevant conceptual and aesthetic aspects of a position as it considers carefully those things that are pertinent to the solution of an artistic problem, and does so while recognizing the creative and aesthetic legitimacy of other art forms and ways of making art to which it is neither superior nor inferior, but from which it simply diﬀers. In this sense the present work can be understood to be a manifesto that is devoted to identifying and examining those things that are germane to the artistic problem that it considers. This book is written for interested readers in the world of art in addition to the world of philosophy, and for sophisticated readers who may be intrigued by the subject matter of the book who are not members of either discipline. The concern for a broad heterogeneous audience having been noted, it must be admitted that much of the work is technical. However, the technical portions of the book are dictated by the complicated and recondite nature of much of its subject matter and cannot be avoided if that subject matter is to be treated thoroughly and properly. Some concepts, including novel concepts, that require deﬁnition or discussion are deﬁned or discussed in the text in the least technical way possible when it is possible to do so without sacriﬁcing either accuracy or clarity. Before proceeding with the body of the text, I want to reemphasize that this book contains a substantial amount of philosophy of art in general, so that it may be of interest to philosophers of art whether or not they are particularly interested in the issue of the limits of Abstraction in art. And I want to reemphasize that much of the book is devoted to topics in the philosophy of subjects and objects, including diﬀerent forms of conscious event, and diﬀerent kinds of dependent and independent object, the identiﬁcation of all of which, as far as I am aware, has not previously appeared in the

5 Danto, Arthur C. After the End of Art: Contemporary Art and the Pale of History, Princeton, NJ: Princeton Univ. Press (1997) p. 28. 6 Danto, After the End of Art, p. 28.

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literature. Although the things noted are included because they are germane to the subject matter of this work, I hope that the intrinsic interest of these things, and their signiﬁcance to diﬀerent parts of philosophy, will be thought to give their inclusion a value that supplements the value that they have because of their pertinence to that matter.

PART ONE

PRELIMINARY ISSUES RELEVANT TO ESSENTIALIST ABSTRACTION

1. The terms ‘Abstract’ and ‘Abstraction’ According to the Oxford English Dictionary, the verb ‘abstract’ means “to withdraw, take away; to separate in mental conception; to consider apart from the concrete.” The noun ‘abstraction’ is “the act of abstracting;” and hence is “the act of separating in thought;” but it is also “the result of abstracting; a mere idea.” The same dictionary deﬁnes the adjective ‘abstract’ as “separated from matter, practice, or particulars; ideal; abstruse.” The Tenth Edition of Merriam-Webster’s Collegiate Dictionary deﬁnes the verb ‘abstract’ as “remove, separate; to consider apart from application to or association with a particular instance;” and the noun ‘abstraction’ is “the act or process of abstracting;” and is “the state of being abstracted” as well. The adjective ‘abstract’ means “disassociated from any speciﬁc instance;” and “expressing a quality apart from an object.” The term ‘abstract’ comes from the Medieval Latin abstractus which is from the Latin past participle of the verb abstrahere meaning ‘to drag away.’ This etymology underlies the preceding deﬁnitions as well as thinking of abstraction as “In thought, leaving out, by not attending to, the apparently irrelevant distinguishing features (or even common features) of the several individuals falling within a class.”1 The term ‘abstract’ in philosophy is typically opposed to the term ‘concrete,’ and it is a contested issue in this discipline how these two terms are to be deﬁned, as it is a matter of dispute whether anything answers, ontologically speaking, to the ﬁrst of these words.2 In any

1 Flew, Antony (ed.) A Dictionary of Philosophy, New York: St. Martin’s Press (1979) p. 3. 2 Gary Rosenkrantz lists the property of squareness, the relation of betweenness, the proposition that there are horses, the null set, and the number seven as examples of abstract object; and he gives as examples of concrete object an event like a hurricane, times such as instants and seconds, places such as points and extended

14

part one

case, an object with which all or part of an artwork is meant to be identiﬁed may in fact be either concrete or abstract in the philosophical senses of those terms, and an artwork may be meant to be identiﬁed with either kind of object or with a combination of objects of each kind of object if so intended by the artist whose work it is. For instance, an artist could paint a number on a canvas and intend that her work be identiﬁed with that concrete representation of an abstract entity, or she could rather intend that the work be identiﬁed with the abstract referent of that concrete symbol, or she might intend that the work be understood to be a complex entity consisting of both the concrete representation of an abstract object and the abstract object represented.3 ‘Abstraction’ is used in visual art either typically to mean, as Harold Osborne puts it, “a mode of representing objects which reduces the amount or particularity of the detail depicted,” or concerns a work in which, as he also says, “neither the work itself nor any of its parts represents or symbolizes objects in the visible world.”4 Synonyms of ‘Abstract’ or ‘Abstraction’ in this second sense are ‘nonﬁgurative,’ ‘non-representational,’ and ‘non-objective,’ and it should be noted that something, such as the color red, that has been abstracted from something else, such as a geranium, is nevertheless concrete as it forms all or part of a perceptible work of abstract art. spaces, and collections such as the couple consisting of Earth and Mars, as well as others. See the entry titled “concrete/abstract” in Kim, Jaegwon and Sosa, Ernest (eds.) A Companion to Metaphysics, Oxford: Blackwell (1995) pp. 90–92. Relevant deﬁnitions of ‘concrete’ from the OED include: “4. Logic and Gram. Applied to a quality viewed concreted or adherent to a substance, viz. the adjective; thus white (paper, etc.) is the concrete quality as dist. from whiteness, the abstract quality. 5. Hence, gen. Embodied in matter, actual practice, or a particular example. Opp. to abstract;” and from Merriam-Webster’s, Tenth Edition: “1: naming a real thing or class of things 3. a: characterized by or belonging to immediate experience of actual things or events b: SPECIFIC, PARTICULAR c: REAL, TANGIBLE.” 3 If an artist intends that some abstract object be understood to be the whole or part of her work, and there are abstract objects, then that object comes to have the property of being all or part of that work in virtue of that intention. If an artist has the same intention, but there are no abstract objects, then that all or part of the work is meant to be identiﬁed with an abstract object can only be understood as an intention, or the thought of that intended identiﬁcation can only be entertained as if there were abstract objects. If there are no abstract objects, then an object that is entertained as abstract would be what I will later call a Type-A typedependent object. 4 Osborne, Harold (ed.) The Oxford Companion to Twentieth Century Art, Oxford: Oxford Univ. Press (1988) pp. 2–5.

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As terms of art, these words are not always used perspicuously, and they are not always used consistently to mean one rather than another of the above deﬁnitions given by Osborne. In addition, Abstraction develops along diﬀerent lines in the history of art, and hence can mean diﬀerent things as it is associated with one or another of these lines of development. The notion of abstraction that is key to determining the limits of Abstraction in art is the notion of dragging away, removing, or separating the relevant from the irrelevant, the essential from the inessential. What is dragged away, removed, separated, or abstracted in Essentialist Abstraction is what is essential to eﬀecting and comprehending the intended identiﬁcation of an artwork with some object. And what those things that are essential to this eﬀecting and comprehending are dragged away, removed, separated, or abstracted from are those things that are not essential to eﬀecting and comprehending the intended identiﬁcation of an artwork with some object.

2. The development of Abstraction in art history I am not saying in what follows that the history of art is only or even primarily concerned with the development of Abstraction. Nor am I saying that the works that are cited in this section as being illustrative of the evolution of Abstraction in art history only have meaning or importance in that connection. But as my interest in this book is limited to the question of what philosophically must underlie the creative search for the limits of Abstraction in art, I now consider a few representative works, styles, and movements that can be seen as part of the progression towards greater and greater Abstraction in art history in order to raise the question of what must form part of the conceptual foundation on which creative investigations into the limits of Abstraction would have to be based. I only focus on these works in their relation to this particular matter, and I recognize that the works mentioned are but a few of the works that form part of the history of Abstraction. In addition, even this partial listing of representative works of diﬀerent kinds of Abstraction indicates the complexity of Abstraction as an art-historical issue. I am also not maintaining that the particular course of development of Abstraction as it has happened in history is necessary rather than contingent, nor am I asserting the general aesthetic superiority of

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part one

works that are more Abstract to those works that are less Abstract or to those works that would not typically be regarded as Abstract works. Finally, I concentrate on certain works in the artistic tradition with which I am familiar, without however maintaining that any work from outside this tradition either is not or could not be relevant to points that are made in this book. In a traditional representational painting, such as Brueghel’s Hunters in the Snow, there is a clear distinction between ﬁgure and ground in the work. Each common object stands out clearly as the thing that it is apart from the space that surrounds it. The painting as an object in the real world also stands out as a thing distinct from the space of the environment in which it is located as the painting is marked oﬀ from the rest of the world by its frame or by the edge of its canvas. The subject matter of such a work is abstracted from civilization and nature, and its elimination of the third spatial dimension common to the objects that it represents is a kind of reduction that involves concentration on matters essential to picturing a scene two-dimensionally. In addition, the scene pictured includes a segment of an event that appears to have been cut from its position in world history and pasted representationally into a diﬀerent position in art history.5 Not only is a particular past occurrence apparently abstracted from its particular location in the set of the world’s events and represented as present to the viewing consciousness of the artist who has recorded it, but the depiction of that event as occurring can be understood to be a pictorial idealization of the segment of time in or at which any perception of the painting must occur, namely, the present. This focus on the immobile presentness of both the event reproduced and any event of its apprehension contrasts with the constant receding further into the past of both the time in history at which the represented event occurred and the time at 5 I say that an event that Hunters in the Snow represents “appears to have been cut from its position in world history . . .” This event so appears whether or not Hunters in the Snow is based on an actual event that Brueghel witnessed, and it so appears because of its resemblance to such an event. Thus whether Brueghel perceived or invented what he chose to paint, either wholly or partially, the painting is perceived by the viewer as a record of the sort of event of which history partially consists, and so, as so perceived, the remarks of this paragraph are applicable whatever the truth of the historical occurrence of the subject matter depicted. These remarks apply to representational art in general when it is not known whether a depicted event occurred, or when it is not known whether something depicted existed or obtained, such as a person or a state of aﬀairs.

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which the painting was completed, and the painted image contrasts as visually stable with the ongoing activity in the aesthetic history of which both that image and an artwork of this kind form part. The hard edge between ﬁgure and ground begins to soften in the mature paintings and watercolors of J. M. W. Turner. In such later works as Mercury Sent to Admonish Aeneas, Turner begins to integrate ﬁgure and ground into a larger aesthetic whole in which each has equal visual importance. The boundaries between painted objects and the space in which they are pictorially located are blurred, and the ground begins to push to the front and occupy a position of prominence rather than recession. Such experiments in the integration of represented objects and the spaces that surrounded them were continued by the Impressionists, and in the masterpieces of late Monet in particular. Van Gogh, in such paintings as Starry Night, and Gauguin, in works like Fe Tata Te Miti, began integrations of ﬁgure and ground that were, in van Gogh’s case, turbulent and expressive, and, in Gauguin’s, both primitive and poetic in his deliberate ﬂattening of space and arbitrary use of color. Experiments of this kind that concern the integration of the objects and spaces of landscapes can be thought of as being organic in their reﬂection of or indebtedness to the lush and sinuous character of nature. Such paintings would eventually lead to the breakdown of the clear distinction of ﬁgure and ground in the Abstract Expressionism of such a work as Willem de Kooning’s Excavation as well as in those of other painters. Before the integration of ﬁgure and ground came the elimination of representational imagery in works such as Abstract Watercolor by Kandinsky, and both the elimination of representation as artistically inessential, and the collapse of the rigid ﬁgure-ground distinction, mark stages in the history of art towards greater Abstraction.6 An approach to Abstraction that is geometric rather than organic is found in the work of the father of modern art, Paul Cézanne.

6

The pure Abstract painting of Kandinsky and others is preﬁgured by the oftquoted remark of Maurice Denis, made in 1890, that “It is well to remember that a picture—before being a battle horse, a nude woman, or some anecdote—is essentially a plane surface covered with colors assembled in a certain order.” This recognition of the priority of paint makes subject matter dispensable, and leads to the primacy of the object and its possible consideration as a purely formal entity. Chipp, Herschel B. (with contributions by Peter Selz and Joshua C. Taylor) Theories of Modern Art: A Source Book by Artists and Critics, Berkeley: Univ. of California Press (1968). Quote p. 94.

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part one

Cézanne’s analysis of nature into ﬂat geometrical areas leads to the geometric integration of ﬁgure and ground in the Cubism of Braque and Picasso, and then to the geometric Abstraction of Piet Mondrian and other artists. Cubism retained representational elements at the same time that it fractured the objects being represented by overlapping images and presenting diﬀerent perspectives of the same object simultaneously. Mondrian eliminated representation but kept color and a fair amount of complexity in his works. Kasimir Malevich, on the other hand, eliminated both represented objects and color in some of his Suprematist paintings in the early part of the last century, working only with geometrical ﬁgures painted in whites or black and white. From Malevich it was a short conceptual distance to eliminating all internal diﬀerentiation in a painting and simply exhibiting a blank or black canvas. The ﬁgure-ground distinction is now found in the object as ﬁgure and its surrounding space as ground. A blank or monochromatic canvas can be replaced with a transparent rectangle, thus eliminating opacity after color had been dispensed with. An example of such a work is Joseph Kosuth’s Any Five Foot Sheet of Glass to Lean Against Any Wall. In addition, Kosuth explicitly made this work into a token of a type of physical object or state of aﬀairs through the wording of the title of the piece, and thus removed from it the idea of uniqueness. We are aware of all visual objects in virtue of light, which cannot be eliminated if we are to see them, and the reduction of artworks to sources of light is found in the ﬂuorescent sculptures of Dan Flavin. With the idea of abstracting being a kind of removing, comes the idea, as Ursula Meyer has indicated, of reduction, or the idea of eliminating what it is possible to eliminate and working with what remains.7 To that end, the most Abstract perceptual object possible would seem to be a pure beam of white light projected across an empty white space for a duration required to make its perception possible, and such that, given the conditions of the monochromatic space in which it is projected, were the properties of the light further minimized, it would not be perceptible.8

7

Meyer, Ursula Conceptual Art, New York: E. P. Dutton (1972) p. xviii. In fact it will be seen that more Abstract perceptual objects than such a beam of light are possible when the identiﬁcation of artworks with them is eﬀected in relation to essential elements of artistic complexes. See Part Four, 4 on pp. 301–303 and 3.2 on pp. 307–308 below. 8

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A diﬀerent approach to Abstraction from that described above was taken by Marcel Duchamp with his readymades. A readymade is a preexistent artifact, such as a snow shovel, urinal, or bottle rack, that Duchamp had no part in making but that he merely selected and claimed to be his work by exhibiting it in a gallery or museum. This is a diﬀerent kind of Abstract object, and one that both the worlds of art and philosophy have rightly found to be revolutionary. Consistent with the idea of Abstraction as removal is taking away things that are unnecessary to either the artwork or to the process of making it, that, although unnecessary, have been traditionally associated with art objects and artistic practices. What Duchamp eliminated as inessential was the process of making an artwork with his own hands. Rather, he was able to produce art simply by placing a selected object in a context in which the object’s intended status as an artwork could be recognized and accepted. Duchamp also eliminated the perceptual diﬀerence between a common object exhibited as a work of art and any remaining member of the class of objects from which the selected object is taken that is not so selected and exhibited.9 The context utilized by Duchamp for the conceptual conversion of readymades itself became the work in Yves Klein’s exhibition of an empty white gallery as a work of art, and was diﬀerently addressed by Robert Barry’s work—repeated in diﬀerent places at diﬀerent times—that consisted of the closing of a particular gallery slated for exhibition of his work for the duration of the work’s scheduled exhibition. This represented a nulliﬁcation of a traditional space of exhibition as the work itself was the exhibition of that nulliﬁcation. On the other hand, earthworks such as Smithson’s Spiral Jetty and de Maria’s Lightening Field eliminate the context of the gallery space in being located outside of this artiﬁcial context in the natural world, as they yet retain a relation to the artworld and its practices in order to exist as works of art rather than as some other kind of artifact. 9 Certain Minimalist works by such ﬁgures as Robert Morris and Donald Judd combine a concern with formal or perceptual reduction with the Dadaist elimination of the need for an artist to produce his work through his own manual eﬀorts in that they were assembled in factories according to the artists’ designs. For James Meyer such works “ﬁgured the collision of . . . the modernist tradition of reﬂexivity and innovation and the dadaist challenge to this narrative . . .” Meyer, James Minimalism: art and polemics of the sixties, New Haven, CT: Yale Univ. Press (2001) pp. 85–86, quote p. 85.

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Conceptual artists, much inﬂuenced by Duchamp and the Minimal sculpture and painting that preceded them, attempted to get beyond the limits of perceptual Abstraction with an art of ideas, or with artworks that are meant to be identiﬁed with non-perceptual objects. Accordingly, any perceptual object that makes us aware of an artwork of this kind only exists as a means of making it comprehensible which object or idea the art is to be understood to be. A good example of Conceptual art is Robert Barry’s ALL THE THINGS I KNOW BUT OF WHICH I AM NOT AT THE MOMENT THINKING1:36 PM; JUNE 15, 1969.10 This language with its date only makes us aware of what the artist intends the work to be and is not the work of art itself. Here the work is not only not perceptual, but that which is indicated to be the work is a class of objects of knowledge that were excluded from the awareness of the artist at the time at which the work was produced. More will be said of this signiﬁcant work later in its relation to awareness and the philosophical requirements of making and apprehending works of art. All of the works referred to in this section, and other relevant examples too numerous to mention, speak to an evolution of Abstraction in the history of art at the same time that they form part of that evolution in diﬀerent ways. The question is, is it possible to take Abstraction further by making a new kind of object or objects out of essential elements alone that reﬂect basic conditions by which all artworks are constrained, or have the limits of Abstraction already been reached?

3. Levels of Abstraction in art Levels of Abstraction in art concern art forms and media and the sorts of object that a particular medium or combinations of media allows to be constructed. The least Abstract visual art form is architecture since it requires three dimensions of space in which to be realized. Not only does architecture require three dimensions but, because it concerns buildings, every architectural object must have

10 This important work will be referred to more than once in this work, and on occasion I will, for brevity, omit the time and date when repeating it, and will print it in lower case italics, either in full without the date, or as all the things I know . . .

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an inside and outside that will accommodate human beings and the objects and purposes for which the building is designed. And the aesthetic properties of an architectural masterpiece, such as a Gothic cathedral, are as much on the inside of the building as the outside, and the viewer must have access to both to appreciate fully the artistic value of the structure. It should not be inferred that the aesthetic of architecture or any other art form is less signiﬁcant or appealing than the aesthetic of Essentialism or that of any other Abstract artwork. They are simply diﬀerent, just as the art forms that diﬀerent aesthetics concern are diﬀerent. Traditional and much modern and contemporary sculpture is more Abstract than architecture because, although three-dimensional, it lacks an inside in any sense that is relevant to its being an artwork or an aesthetic object. Sculpture may have a material inside as a physical object but it typically has none at all as a work of art, and so while, as three-dimensional, it has to be walked around to be seen in its entirety, it is a kind of artwork that is seen from the outside only and so eliminates an internal perspective of the object. Traditional works of sculpture, such as Michelangelo’s Pietà, have no artistic inside, while certain contemporary works that might be classiﬁed as sculpture, such as Bruce Nauman’s Green Light Corridor or one of Richard Serra’s Torqued Ellipses, do have artistic insides in that internal as well as external perspectives of the three-dimensional works are possible. Painting is more Abstract than sculpture since it is only two-dimensional, and thinking of levels of Abstraction in terms of art forms and their media approximates Hegel’s thinking of diﬀerent levels of what he terms “ideality” within the “romantic” arts of painting, music, and poetry—art forms that are said by him to be progressions beyond the earlier and less ideal “symbolic” and “classical” stages of art history represented by architecture and sculpture. Hegel thought that the reduction of three dimensions of space to two made painting more “inward” and “subjective” than sculpture, and the progress of subjectivity was continued in music and poetry. Although the elimination of the third dimension of space from the ﬂatness of painting makes painting more Abstract than sculpture, nothing about the aesthetic value of painting versus sculpture follows simply or necessarily from that increased level of Abstraction. Thus one might agree with Donald Judd when he says that “Three dimensions are real space. That gets rid of the problem of illusionism and of literal

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space, space in and around marks and colors . . .,” and when he states that “Actual space is intrinsically more powerful and speciﬁc than paint on a ﬂat surface.”11 Of course one could also disagree with Judd, and insist that paint on a ﬂat surface is as real and speciﬁc as anything, and that a ﬂat, monochromatic surface, such as that in Brice Marden’s The Dylan Painting, in lacking marks and colors that may suggest illusion as they separate areas of the surface that they deﬁne, lacks space that surrounds marks and colors, and is actual space that is as powerful as any three-dimensional entity. Music for Hegel is more subjective than painting because it is not in space, at least not in the same way in which painting is, since we can neither see it nor touch it as we can paintings.12 Poetry is more subjective than music because its perceptible sounds are replaced by the quiet workings of language, language that conveys thought. Thought can occur apart from anything external to itself in the perceptual world and so poetry, which works with the ﬂow, imagery, and conceptual content of thought, is the most ideal art form in being the most subjective in Hegel’s sense of the term.13 Although 11 Judd, Donald “Speciﬁc Objects,” in Art in Theory 1900–1990: An Anthology of Changing Ideas, Harrison, Charles and Wood, Paul (eds.) Oxford: Blackwell (1992) pp. 809–813. Quotes from p. 813. 12 The sense in which touch is here relevant is to the perception of the physical object in which the artwork is embodied—paint and canvas can be felt with the ﬁngers. However, the sense of touch is not the one that acquaints us with the identity of the artwork, and is not the one of primary importance to an aesthetic response to the object. I say that it is not of primary importance since someone may assert that a visual object can have tactual properties that are of aesthetic signiﬁcance, as when we say that the pictured covering on the pictured table ‘feels’ like cloth. But such tactual properties of the aesthetic object would be secondary in that they depend on visual and not on tactual perception of the object. That tactual properties can be attributed to a visual object that does not literally have them as seen depends both on our native constitution as percipients, and on our prior history of perception including integrated tactual and visual perceptions. That a painting as an object of art may have properties that the painting as an object of physics does not has led some thinkers to see the artwork as one thing and the physical object in which it is embodied as another. See Ziﬀ, Paul “Art and the ‘Object of Art’” in Elton, William (ed. and introductory essay) Aesthetics and Language, Oxford: Basil Blackwell (1959) pp. 170–186. For what I mean by the identity of an artwork see Part Two, Division I, 3 on pp. 74–78 below. On an artwork’s embodiment in a perceptual object commonly regarded as physical see Part Two, Division III, 7 on pp. 103–107 below. 13 Hegel, G. W. F. Introductory Lectures on Aesthetics, (trans. by Bernard Bosanquet, edited with an introduction and commentary by Michael Inwood) London: Penguin Books (1993). On page 191 of the commentary to this book, Michael Inwood says that “. . . poetry [for Hegel] is almost wholly ideal, i.e. uses hardly any sensuous element, but appeals almost entirely to what exists in the mind.” (His italics.) See

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Hegel’s thinking of the arts and its relation to his larger philosophical system is much more sophisticated than here indicated, and focuses on diﬀerent concerns, his notion of one art form being more or less subjective or ideal than another closely resembles what I am talking about in diﬀerent art forms and their media existing at diﬀerent levels of Abstraction. Although any work of Conceptual art must have a relation to a publicly perceptible object to be known and appreciated, a work of Conceptual art that is meant to be an idea or a non-perceptible object that is generated by, or that is linked conceptually to, the thinking of the artist would more closely approximate poetry as Hegel’s ideal art form.14 Thus Conceptual art, as concerned with thought or language as the most Abstract medium, is akin to poetry for Hegel in being an art of the mind.15 Both within and across art forms and media there are various levels of Abstraction and various ways of approaching Abstraction. And although pure Abstraction is based upon the notion of the elimination of things that are not essential to eﬀecting and comprehending the intended identiﬁcation of an artwork with some object, it is not always possible to say of two diﬀerent works that one is more Abstract than the other since diﬀerent kinds of thing may have been eliminated from and others retained in diﬀerent objects, and both what is eliminated from and what is retained in diﬀerent objects can diﬀerently pertain to the issue of Abstraction. For example, Joseph Kosuth’s Any Five Foot Sheet of Glass to Lean Against Any Wall might be thought to be more Abstract than Malevich’s White on White since also Kaminsky, Jack Hegel on Art: An Interpretation of Hegel’s Aesthetics, Albany, NY: SUNY Press (1970). 14 An object is “non-perceptible” when a subject cannot be aware of the object through any of the senses. However, it may be that such an object can be apprehended in thought, imagination, or conception. An object is ‘imperceptible’ when a subject cannot be aware of the object in any kind of awareness of the kinds of awareness of which subjects are capable. As will be seen, objects with which artworks are meant to be identiﬁed may be non-perceptible or imperceptible or a combination thereof. 15 I am not maintaining that Conceptual art ﬁts easily into Hegel’s thinking about the arts, but am only drawing attention to the fact that Hegel’s notion that a degree of ideality that is exhibited in poetry is not exhibited, for instance, in sculpture is similar to saying that a certain level of Abstraction that is reached in Conceptual art is not reached, for instance, in ﬁgurative painting. For a consideration of Conceptual art from a Hegelian point of view see Fowkes, William “A Hegelian Critique of Found Art and Conceptual Art,” The Journal of Aesthetics and Art Criticism, 37 (1978) pp. 157–168.

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Kosuth’s object lacks its own color in being transparent, and further is more Abstract in being speciﬁcally stated to be a token of a type of physical object or state of aﬀairs, thus eliminating the traditional uniqueness of a particular artwork. On the other hand, White on White might be thought to be more Abstract in being restricted to a single two-dimensional surface; in relying on a single room surface for exhibition rather than two; and in not reﬂecting properties of the environment in which it is situated, and so eliminating demonstrated reference to things beyond itself, including to a percipient’s body reﬂected in the glass of the Kosuth—a visible reﬂection that might be thought to multiply entities further by drawing attention to the mind on which that perception is dependent. Such comparisons suggest that a deﬁnitive answer to the question of which of two artworks is the more Abstract may not be possible, since the works may be thought to address Abstraction in diﬀerent ways, just as a Pointillist and a Neo-Classicist address the human ﬁgure or any subject matter in diﬀerent ways. The heterogeneity found in just the works cited to this point also indicates that Mel Bochner’s view of Abstract art, stated in his opposition to the use of the term ‘de-materialization’ in relation to Conceptual art, is unduly simple and parochial in relating Abstraction ﬁrst to the view—shared by physical and philosophical atomism— that reality consists of ultimate simples, and second to the view that analysis is impossible and so results in a false picture of reality. According to Bochner, “All ‘abstract art’ is premised on the belief in ﬁrst-level reality composed of constituent and separate qualities. In order to arrive at a truer ‘reality,’ the abstract artist must take apart this composite structure. The act of disjointure [sic] was to result in an intensiﬁcation of the abstracted quality (color, shape, texture, etc.). This then became the material for further manipulation. The entire substructure of this concept is ﬂawed. It simply is not possible to break things down into classiﬁable components, at least not without destroying the essential unity that is their existence. The blue of my typewriter is inseparable from its smooth surface. The blue-smooth surface was not created by combining a blue with a ‘smooth.’ Abstraction is an analytical method and not a reversible equation.”16 16 Bochner, Mel “Excerpts from Speculation (1967–1970)” in Alberro, Alexander and Stimson, Blake (eds.) Conceptual Art: A Critical Anthology, Cambridge, MA: MIT Press (2000), p. 196.

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Implicit in the ﬁrst view concerning Abstract art is something commonly held to be the case for all art, namely that art is an attempt to reﬂect the truth through copying in some way a reality that is separate from it, and hence it is implicit in that view that the validity of its aesthetic is based on its success as a means of such imitation. However, it is not at all clear that this is the case either with all of the works cited, or with any work that has as a concern working with essentials only, and it is not clear that reﬂecting reality at a subperceptual level is the inevitable result of any work that is the product of such a concern. The second view seems to recognize that two or more things that are physically inseparable may nevertheless be conceptually separable, and that to talk of something as blue and smooth is to distinguish in thought properties of the object that are joined in perception. This is what is meant by speaking of Abstraction as an “analytical method.” Saying that Abstraction is not a “reversible equation” is apparently meant to recognize that reality does not come parceled into separable properties, such as blueness and smoothness, that an artist can combine to create an object, rather than consisting of things in which such properties are already instantiated. But this second view then suggests an implicit endorsement of the ﬁrst view that art must copy, or at least be faithful to, perceptible reality, rather than seeing art as a means of looking for possibilities other than imitation of, or ﬁdelity to, the world found in perceptual awareness. In addition, the second view fails to recognize that a property that is distinguishable in thought—such as a color—from something with which it is paired—such as a smooth surface—in a particular experience of something—such as a typewriter—if repeatable, can be reproduced in another object that lacks the property with which it is paired in the object from which the property is thoughtfully abstracted. Thus the blue of the typewriter could be reproduced on the rough surface of some wood or paper and no falsiﬁcation of the nature of the color would have occurred. The failure to see Abstraction as a “reversible equation” is accordingly the failure to see that, given the possibility of reproducing a quality abstracted from an object in a diﬀerent object, it is possible to apprehend that the property abstracted and reproduced is a property common to distinct objects, and with such recognition comes the understanding that an “essential unity” is really a contingent conjunction.

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part one 4. The diﬀerent relation of philosophy and art to the question of the limits of Abstraction in art

4.1. The general diﬀerence of art and philosophy, and the diﬀerent relation of each to Essentialist Abstraction It is a philosophical task to identify what is required to make and apprehend works of art, and it is an artistic task actually to determine the limits themselves in works of art that use, as they address and reﬂect, certain things of those things that are identiﬁed to be necessary. Work that has as its purpose stating the essential elements of making and apprehending works of art, and identifying both the bare conditions to which these elements must conform and certain inevitable facts that pertain to them, is philosophy, not art. And work that has as its aim an aesthetic investigation of certain minimalist principles concerning subjects and objects is art and not philosophy. It is necessary to recognize a diﬀerence of aims, means, possibilities, and objects of these two disciplines in their relation to an Essentialist investigation of the limits of Abstraction. Art can do things that philosophy cannot, and philosophy can yield results that it is beyond the power of art to produce. That each of these human practices can accomplish things and reach levels unobtainable by the other speaks to their diﬀerent forms, methods of engaging awareness, and goals, rather than to their competition or the ultimate value of one compared with that of the other. And the enrichment of culture follows from the various kinds of achievement that their diﬀerences allow. 4.2. Philosophy and Essentialist art I speak here of philosophy’s relation to Essentialist art rather than to art in a larger sense because I am quite willing to recognize a philosophical book, essay, or statement as an artwork that is claimed by its author to be a work of art in more than a metaphorical sense, and that can be oﬀered to and possibly accepted as such by the artworld.17 But a philosophical work, such as this book, cannot be 17 See Danto, Arthur C. “The Last Work of Art: Artworks and Real Things,” originally published in Theoria, XXXIX, 1973, pp. 1–17. Reprinted in Dickie, George, Sclafani, Richard, and Roblin, Robin (eds.) Aesthetics, A Critical Anthology, 2nd ed., New York: St. Martin’s Press (1989) pp. 551–562.

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oﬀered as an Essentialist artwork since it fails to exhibit, in form and content, the principles that it identiﬁes as indispensable to the Essentialist project. Such an exhibition of foundational principles forms an essential aspect of the Essentialist aesthetic, and I believe that the aesthetic experience of Essentialist artworks would be much richer for that than any aesthetic experience that might be provoked by elucidating these principles in prose. As indicated in the introduction, the limits of Essentialist Abstraction and the nature of its aesthetic can only be determined in objects that are speciﬁcally designed to address the essential elements of an artistic complex. The point about Essentialist Abstraction having a particular aesthetic is an important one, and when I talk about aesthetic of Essentialism, I am not limiting the notion of the aesthetic to the perceptual, which is of great importance, but include as of equal or greater importance the aesthetic of ideas or the conceptual.18 4.3. The non-hierarchical relation of art and philosophy I ﬁnd implausible an argument, such as Hegel’s, that puts philosophy above art because of art’s relation to sensation and philosophy’s greater conceptual grasp of the cosmos. I also think that we should look unfavorably on the notion that, if the meaning of an artwork can be clearly stated, then the artwork itself becomes superﬂuous.19 Such a view wrongly conceives of art as a kind of concealed language that would be more powerfully and insightfully expressed in a philosophical essay or proposition. The assumption here is that art 18

See Part Two, Division V, 2 on pp. 122–127 below. According to Clark Butler, “If we clearly state the meaning of art, it loses its fascination.” For Butler, art is only capable of “puzzling symbolizations” of truth that lack the “rigorous conceptual grasp of the cosmos” provided in their diﬀerent ways by philosophy and science. Because “truth may be grasped adequately in pure thought without images, by logical discourse or philosophy . . . a consequence is the death of art.” Butler thinks that once the conceptually impuissant imagistic language of art is decoded, art remains of cultural interest only insofar as “it oﬀers precious documents of a past struggle for truth.” Butler, Clark History, p. 9. See pp. 29–34 of the same volume for my responses to Butler’s position. In addition to problems with this view that are stated in the text, this position treats artworks as having merely instrumental value in being nothing more than inchoate vehicles of truth that are superseded in history by the advance of pure imageless thought. As such it clearly fails to recognize that much of the allure of art is its aesthetic value, and that the aesthetic value of a work can continue to be of the greatest importance whether or not its meaning or meanings can be clearly stated, and whether or not there are other, perhaps even better, means of conveying any idea that it conveys. 19

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and philosophy are attempting to do the same things, and that art is a kind of protolanguage that is much less developed than the language of philosophy. It is also a mistake to think that art is primarily if not exclusively a perceptual matter that is based on noncognitive feeling, and so is less important or powerful than philosophy, which is an intellectual matter based purely on cognitive ideas. This is a mistake because, although every artwork presupposes a relation to a perceptual object, not every artwork is meant to be identiﬁed with a perceptual object. It is also not the case that all art is based on feeling, and some artworks may incorporate thought in a way or ways that is not found and that is not possible to ﬁnd in other kinds of artifact—including texts of philosophy—and may stimulate thinking in ways that no other means of provoking ideas may produce.20 In addition, it seems that there can be no general justiﬁcation of the superiority of thought to feeling as each concerns such cultural products as works of philosophy and art. Rather, one must look at speciﬁc cases in order to attempt to judge the relative merits of each, and, even then, it would have to be asked by what criteria it could be determined that one is more signiﬁcant or greater in value than another. Are the thoughts (and feelings?) elicited by reading Kant’s Critique of Pure Reason of greater importance than the feelings (and thoughts?) that follow from hearing Mozart’s Requiem? It seems improper to place art and philosophy in cultural competition, placing one on a higher level than the other, rather than recognizing and being grateful for their diﬀerences. Much more than this could be said, and the previous remarks are oﬀered only as general comments. The point of importance for us is that philosophy can only state the presuppositions of Essentialist Abstraction, it cannot pro-

20 Cf. John Dewey: “Thinking directly in terms of colors, tones, images, is a diﬀerent operation technically from thinking in words. But only superstition will hold that, because the meaning of paintings and symphonies cannot be translated into words, or that of poetry into prose, therefore thought is monopolized by the latter.” Dewey also says that “the idea that the artist does not think as intently and as penetratingly as the scientiﬁc inquirer is absurd.” In fact he says: “To think eﬀectively in terms of relations of qualities is as severe a demand on thought as to think in terms of symbols, verbal and mathematical. Indeed, since words are easily manipulated in mechanical ways, the production of a work of genuine art probably demands more intelligence than does most of the so-called thinking that goes on among those who pride themselves on being ‘intellectuals.’” All quotes are from Dewey’s Art as Experience, New York: Capricorn Books (1958). The ﬁrst quote is on pp. 73–74, the second quote is on p. 45, and the ﬁnal quote is on p. 46.

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duce works in which the limits of Abstraction are Essentially identiﬁed. For that you need art. 4.4. The complementary relation of art and philosophy in the question of Abstract art’s limits The previous remarks are oﬀered in an attempt to establish the factual relation of art and philosophy to one another as they concern Essentialist Abstraction, not as a matter of temporal priority, which is not necessary, since either could come before the other, but as a matter of recognizing the sphere of interest of each. It is the job of philosophy to do one thing and it is the job of art to do another, and although neither can perform the task of the other, one can complement the other.

5. Modernism and Essentialist Abstraction The view of Essentialism described to this point, and to be further elaborated, has something in common with Greenbergian Modernism in that, for Greenberg, “The essence of Modernism lies, as I see it, in the use of the characteristic methods of a discipline to criticize the discipline itself—not in order to subvert it, but to entrench it more thoroughly in its area of competence.”21 This Modernist criticism of a discipline is the discipline’s criticism of itself, done “from the inside, through the procedures themselves of that which is being criticized.”22 This amounts to a discipline’s self-analysis of its intrinsic nature, and the aesthetic value of the objects produced by the discipline will follow from its focus on its inherent aspects. Such a self-critical procedure involves making “explicit . . . that which [is] unique and irreducible not only in art in general but also in each particular art.”23 Thus for painting that meant concentrating on that of which the “irreducible essence” of painting consists, its “ﬂatness and the delimitation of its ﬂatness.”24 Essentialism has in common

21 Greenberg, Clement “Modernist Painting” in Battcock, The New Art, pp. 100–110. Quote p. 101. 22 “Modernist Painting,” p. 101. 23 “Modernist Painting,” p. 102. 24 Greenberg, Clement “After Abstract Expressionism,” Art International, Vol. VI,

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with Modernism an emphasis on identifying the irreducible and ineliminable, and using that which is irreducible and ineliminable as both the means and the focus of artistic production. However, Essentialism diﬀers from this Modernist perspective in that, whereas it is a principle of Modernism that each art focus on what is alone “unique and exclusive to that art,”25 Essentialism concerns the characteristics, conditions, and relations of subjects and objects that are philosophically basic to eﬀecting the identiﬁcation of artworks with objects in general, and that are required of and involved in understanding with which objects works of art are meant to be identiﬁed, and so apart from considerations devoted to the nature of any particular medium. More particularly, this means that the limits of Abstraction are to be revealed in the kinds of reductive object that it is possible to construct given creative uses of essential elements of artistic complexes, artistic complexes that exist in any case of appropriately apprehending an object on which the identity of an artwork is relevantly dependent. Thus Essentialism diﬀers from the Modernist notion that each medium has to explore its own nature and eliminate anything from its creative explorations that is shared by other media. Essentialism does have in common with Modernism an interest in eliminating inessentials and working only with the possibilities allowed by what remains, and in the kind of aesthetic that a concern with such essentials can eﬀect, but Essentialism and Modernism diﬀer importantly in the range of the concern of each, and in the nature of the objects and their relation to subjects that each concern can produce. For example, for Essentialism neither temporality nor the historical and indexical context supplied by the observer’s consciousness and the relation of the object contemplated to his awareness and agency can be avoided. As these things cannot be avoided, they need to be addressed to the extent possible so that they can form part of the material of Essentialist Abstraction. Essentialism then diﬀers in an important sense from Modernism in viewing the subject as not artistically indiﬀerent to the object.26 For Essentialism, No. 8, October 25, 1962, p. 30. Reprinted in O’Brian, John (ed.) Clement Greenberg: The Collected Essays and Criticism, Vol. 4, Modernism with a Vengeance 1951–1969, Chicago: The Univ. of Chicago Press (1993) p. 131. 25 “Modernist Painting,” p. 103. 26 For a consideration of the change in the subject’s role from spectator in Modernism to participant in Conceptual art in general and in the work of Art and Language in particular, where the subject is treated as “a reader and potential inter-

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both the subject and the object are to be seen as constituents of a larger complex whole that includes basic properties of each, fundamental relations that hold between them, and certain facts that pertain to members of the complex and their properties and relations. 5.1. Modernism and Essentialism and identity and reﬂexivity Any artwork must have an identity. That is, an artist must determine through some means with which object or objects an artwork is meant to be identiﬁed, and it must be possible to understand with which object or objects an artwork is meant to be identiﬁed. An artist’s determining the identity of a Modernist painting, for Greenberg, depended on, as Jonathan Harris puts it, “stripping the medium down to the bare bones of its material conditions and means.”27 Such a stripping down means attending solely to the conditions of painting, and the intentional concentration on those conditions and means to the exclusion of anything else makes such painting more Abstract than painting in which the focus is on anything else. A subject who attends to a Modernist painting is, or can be, aware of the reduction of the medium to the basics of painting since a Modernist painting “draws attention to its formal conditions and means.”28 The use of the formal conditions and means of painting to draw attention to themselves as such conditions and means can be understood to constitute a reﬂexive state of aﬀairs: paint is used to turn back on or point to itself in declaring its identity as paint on a two-dimensional surface rather than pointing away from itself to something beyond that surface, as happens when paint is used to represent something in three-dimensional reality. But paint can only be understood to be reﬂexively directed to itself as part of the conditions and means of painting through or in virtue of the consciousness of someone who is attending to it. And so the Modernist implicitly relies on consciousness for the reﬂexive relation of paint to itself to be understood and appreciated. Any artwork relies on consciousness to be understood and appreciated as art, and the degree of Abstraction of

locutor,” see Harrison, Charles Essays on Art & Language, Cambridge, MA: MIT Press (2001). Quoted language taken from p. 67. 27 Harris, Jonathan Writing Back to Modern Art: After Greenberg, Fried, and Clark, London: Routledge (2005) p. 61. 28 Harris, Jonathan Writing Back to Modern Art, p. 66.

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an artwork depends in part on how it is directed to or is designed to engage consciousness. The Modernist’s use of the medium of painting to engage a conscious subject in the manner described is part of the degree of Abstraction of the Modernist project. This is because the subject’s attention is directed to the essential conditions and means of painting as reﬂexively asserting their essential nature, rather than her attention being directed away from them to something that is extraneous to them—and so to something that either occludes or is irrelevant to that assertion. A subject’s knowledge of the identity of any artwork involves the subject’s apprehension of a public perceptual object on which the identity of the work is relevantly dependent. The subject’s apprehension of such an object is cognitive when the subject is conscious of the relevance of the object to the identity of the artwork. A subject’s cognitive apprehension of a public perceptual object on which the identity of the work is relevantly dependent creates an artistic complex of which the subject, the object, and the consciousness linking them are constituents. These matters will be thoroughly examined in Part Three. As will be seen in that part, any artistic complex is not only dependent on the things mentioned, but it will have certain features. All of these things are unavoidable, or are philosophically necessary. As things they can be understood to be ‘elements’ of artistic complexes, and as unavoidable they can be considered to be ‘essential’ elements of artistic complexes. Any artwork that would be Essentialist would result from various kinds of creative use of essential elements of artistic complexes to result in objects with which artworks are meant to be identiﬁed. Subjects who attend to objects on which the identities of Essentialist artworks are dependent are, or can be, aware that the reductive nature of the works results from the use of essential elements of artistic complexes to result in objects that draw attention to as they are understood to reﬂect such essential elements. Such a use of such essentials can be understood to be a reﬂexive process in resulting in such objects. This use of these elements is more Abstract for being so reﬂexive than is any use of essential or inessential entities to result in objects that are meant to be artworks in which those things that are essential are neither emphasized by, nor in some way reﬂected in, those objects. Although Essentialism has in common with Greenbergian Modernism an interest in the use of essentials to result in objects that draw attention to, as they can be understood to reﬂect

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in themselves in certain ways, essential elements that are used to result in them, Essentialism’s use of essential elements of artistic complexes is more Abstract than Modernist paintings for dispensing with the dispensable medium of paint, and for directly utilizing, as a medium itself, the consciousness that is a necessary ingredient of any artistic complex.29 What I have said about both ‘Abstraction’ and ‘Essentialism’ to this point should be understood to be an adumbration of their meaning. The development of the terms, which includes making clear the dependence of the limits of Abstraction on Essentialist principles, and the more mature understanding that will follow from that development, lie ahead.

29 Of course in using consciousness as a medium, and so going beyond the use of paint to declare itself as paint on a ﬂat surface, Essentialist Abstraction is PostModern, or, as Steve Sarratore has characterized my thinking, it is Post-Post-Modern. On medium and media and consciousness as a medium see Part Three, Division IV, 1–2 on pp. 234–262 below. See Part Four for further on the reﬂexive nature of Essentialist Abstraction.

PART TWO

ON SUBJECTS AND OBJECTS AND WORKS OF ART: GENERAL CONSIDERATIONS AND BASIC POINTS OF RELEVANCE TO ESSENTIALIST ABSTRACTION

Introduction This part of the book states things that are required to make and apprehend works of art in an art-historical sense of the concept ‘artwork.’ The statement of these things includes consideration of several points that are fundamental to subjects and objects, and so are relevant to those requirements, since it is subjects who make and apprehend works of art, and it is objects with which artworks are meant to be identiﬁed. Speaking of the “art-historical sense” of ‘artwork’ means recognizing the relation of that term to art history and to the artworld. More particularly, it means recognizing the relation of the concept ‘artwork’ to the artworld at this point in art history. The ‘artworld’ is divisible into two broad aspects consisting of kinds of subject and kinds of object, each kind of which is required for the artworld’s existence. The subject aspect of the artworld includes, without being necessarily limited to: artists; art historians; art critics; art museum directors and curators; gallery directors; educated museum and gallery goers; and people who write about art in books and art periodicals, as well as the people who customarily read such books and periodicals. The object aspect of the artworld is composed of artworks in all forms in which it is possible for artworks to be produced; the public perceptual objects on which the identities of artworks are dependent; places in which such perceptual objects are routinely exhibited or novel locations in which they nevertheless can be apprehended; publications and other kinds of media in which the objects on which artworks are dependent are reproduced and/or discussed; and memories of artworld subjects of artworks and/or the objects on which artworks are dependent. How the artworld has arisen and continues to be the means by which certain objects are accorded the status of being art-historical objects is irrelevant to attempt to decide.

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For brevity, and germane to the concerns of this book, only the visual arts and works, such as works of Conceptual art, that stem from them are being considered. And although most of the points made in this section apply to objects that have entered art history, and all apply to any object meant by its producer to enter art history, as my concern is with the limits of Abstraction, and prior works have not shown the ends that it is possible here to reach, my remarks are meant more speciﬁcally to concern basic things that would have to be met by works in which those limits would be meant to be exhibited or through which they would be determined. Accordingly, I will focus on points that any such reductive object will presuppose, and I will not be concerned with additional points that it would be necessary to consider in attempting both to give a deﬁnition of art, and to explain how certain objects have entered art history, such as the cave paintings, that could not have been intended to be seen as art-historical objects by their creators. For the purposes of this inquiry into the limits of Abstraction in art, I will say that an object or objects meant by its producer to be a work of art that becomes part of art history at this point in history does so by the perceptual object or objects on which the identity of the artwork is dependent being displayed in a legitimate ﬁne-arts context, and/or by the artworld being otherwise aware of and recognizing the intended object as an artwork. A ‘legitimate ﬁne-arts context’ is a museum, gallery, alternative space, or a place of exhibition that is intentionally and understandably related to the artworld and its practices. A ‘place of exhibition’ could include any public space, or any place to which any number of diﬀerent subjects theoretically can have access. The awareness or recognition of an object as an artwork, beyond understanding it to be understood as such, would include its being talked about, written about, interpreted, evaluated, appreciated, reproduced, and recollected as such by the artworld, as all or part of such conditions apply to the kind of object that the work is meant to be. How many of the members of the artworld are required for such recognition concerns the range of knowledge of the artwork and is purposely not here addressed. Finally, no implication about remaining in art history for any length of time follows necessarily from an object’s having been part of art history. To talk in this way of the relation of certain objects to the artworld is not necessarily to endorse the institutional view of art as a deﬁnition of art, but is to recognize the indispensability of the art-

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world to an object’s entering art history and remaining there, at whatever level of importance for whatever length of time, in the time to come. I am using the term ‘artworld’ then in a sociological, not a philosophical sense to describe certain social practices of certain people that concern certain objects that are recognized to be culturally important by the people engaging in those practices. This sociological use of ‘artworld’ simply recognizes the fact of a number of contingent practices that are compatible with diﬀerent means of deﬁning art and are compatible too with the notion that art cannot be deﬁned. On the other hand, speaking of a philosophical sense of the term ‘artworld’ is meant to acknowledge that that term ﬁgures signiﬁcantly in philosophical theory that locates these practices within a conceptual framework by means of which art is distinguished philosophically from non-art.1 In what follows, the term ‘artwork’ is meant to reﬂect the points made in the preceding paragraphs, and so the relation of any referent of that term to the artworld at this point in art history is meant to be implicit. It does not follow that any object to which the following paragraphs do not apply is thereby not a work of art in a non-historical sense of artwork, since additional points necessary to categorizing any object as a work of art in such a sense are left undiscussed. I only maintain that all of the conditions mentioned in this section that are required of making art, and things canvassed that are pertinent to that enterprise, must be met by, and would apply to, any object that would enter art history at this point in art history, including any that would extend the levels of Abstraction previously exhibited to those that it is theoretically possible to reach. I further maintain that one or a combination of the possibilities of object making open to artists that this work identiﬁes must be utilized by anyone acting as an artist to produce an intended arthistorical object. Some of these possibilities rather than others will 1 George Dickie uses the notion ‘artworld’ in his institutional theory of art as a means of deﬁning art. See Dickie, George Art and the Aesthetic: An Institutional Analysis, Ithaca, NY: Cornell Univ. Press (1974), The Art Circle, New York: Haven (1984), and, recently, “The Institutional Theory of Art,” in Carroll, Noël (ed.) Theories of Art Today, Madison, WI: Univ. of Wisconsin Press (2000) pp. 93–108. Dickie provides a history of the institutional theory of art in his Art and Value, Oxford: Blackwell (2001). ‘Artworld’ is also a term that ﬁgures importantly in the work of Arthur Danto. See Danto, Arthur C. “The Artworld,” Journal of Philosophy, 61 (1964) pp. 571–584, and Transﬁguration of the Commonplace, Cambridge, MA: Harvard Univ. Press (1981).

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better lend themselves to Essentialist Abstraction, as will be seen in the course of the book. The following assertions are only meant to indicate things that are fundamental to determining the limits of Abstraction, and certain thoughts and theses of this section could and should be given a more thorough analysis were it my intention to consider larger issues in the philosophy of art to which they are relevant. Many of the points made in the remainder of this book could also be treated in greater depth. I have attempted for the most part to restrict my remarks to what needs to be said for the purposes of this project, and have elaborated on points only when that seems to be required, or when the intrinsic interest or novelty of the point expanded upon justiﬁes such elaboration. The interest in pertinence and brevity having been noted, the reader will see that laying the philosophical groundwork for answering artistically the question with which this project is concerned is no short and simple matter.

DIVISION I: SINGLING SOMETHING OUT, ARTISTIC IDENTITY, AND INTENTIONAL ACTIONS

1. Singling something out For an artist to eﬀect a work of art she must be responsible for the identiﬁcation of the work either with a particular object or objects, or with some object or objects of a delineated group of objects.1 This identiﬁcation must be understandable, and represents singling something out with which the artwork is meant to be identiﬁed, and whether that which is singled out is singled out determinately or indeterminately as ‘determinately’ and ‘indeterminately’ are deﬁned in sections 1.3 and 1.4 below.2

1 The use of ‘artist,’ here and throughout the book, can be understood to mean ‘artist or artists’ to recognize the possibility that, although artworks are typically produced by a single individual, two or more artists can act together to eﬀect a particular work of art, as in the case of Mike and Doug Starn. In addition, the use of ‘object’ in ‘particular object,’ ‘the object,’ ‘an object,’ ‘some object,’ etc.— as it pertains either to the identity of an artwork or to the dependence of that identity on an object—can be understood to mean ‘object or objects’ to accommodate the possibility that an artwork may be meant to be identiﬁed with, or may be dependent on, a number of objects rather than a single object. I will also use ‘an object’ or ‘any object’ to stand equally for ‘the object’ or ‘the objects,’ and whether a particular use of the term ‘object’ pertains to the object or objects with which an artwork is meant to be identiﬁed—and whether all or some of these objects are themselves apprehensible or not—or it pertains to the apprehensible object or objects on which recognition of the identity of an artwork is dependent. (I talk repeatedly of the identity of an artwork throughout, and the reason for doing so is stated in Part Two, Division I, 3 on pp. 74–78 below.) In addition, ‘object’ is meant to cover any simple or complex object of any kind of object when a particular object or kind of object is not identiﬁed, and it is to be understood that the parts of a complex object can have the kinds of relation to one another permitted by logic and reality when such relations are left unspeciﬁed. Finally, what is said both here and throughout about artworks should be understood to apply to parts of artworks when parts of artworks are not mentioned or speciﬁcally addressed. 2 “To make art is, basically, to isolate something (an object, an idea, . . .) . . .” Binkley, Timothy “Piece: Contra Aesthetics” The Journal of Aesthetics and Art Criticism, 35 (1970) pp. 265–277. Quote p. 273. Such isolation is both logical and epistemological, as indicated below. These two aspects of such isolation together constitute a conceptual delineation of that which is isolated.

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1.1. Creating, selecting, and specifying objects 1.1.1. Creation. An artist may intend an artwork to be identiﬁed either with an object that she is wholly or partly responsible for creating, or with an object that she is not in any way responsible for creating. In any case the artist must be responsible for identifying the artwork with some object. Created objects that are meant to be artworks include traditional and modern paintings and sculptures, such as Angelico’s Annunciation and Giacometti’s Suspended Ball, and works of such newer art forms such as ﬁlm, video, Performance art, Installation art, electronic art, Land art, Body art, Kinetic art, computer art, mixed-media art, and certain works of Conceptual art. Of course, an object that an artist is wholly or partly responsible for creating that is meant to be a work of art need not fall under an established art form, or be tied to any present technology, or no new art form or means of making art could ever arise. An object that an artist has no responsibility for creating may be selected or speciﬁed by that artist to be a work of art of that artist’s, depending on the nature of the object and its relation to the artist. The notions of selection and speciﬁcation are the subjects of the following sections. 1.1.2. Selection. An object with which an artwork is meant to be identiﬁed is ‘selected’ when the artist responsible for the work chooses or has had chosen in at least a single act of choosing at least one preexistent object that the artist intends that the work be understood to be. This intention, to be successful, must be made comprehensible, and the comprehensibility of the intention amounts to an understandable claim by the artist that a certain selected object is to be understood to be a work of art by that artist. This intention is typically made comprehensible by placing the selected object in a museum or gallery with the title of the work and the artist’s name, and so in accordance with standard practices of exhibiting more traditional works, as is the case with Duchamp’s unassisted readymades, such as Bottle Rack, that were selected by him with the intention that they be exhibited as works of art. However, the intention that some preexistent object or objects is meant to be a work of art can also be made comprehensible through a kind or kinds of documentation that is appropriate to the object supplemented by any information that is required for that comprehension. For instance, an object, such as

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a mountain, that cannot be removed from its location and relocated to an art museum might be photographed. The photograph of the mountain could then be displayed in a gallery or museum with language that makes it understandable that the mountain, as a selected object, and not the photograph that can be understood to picture the selected object, is what some artwork is meant to be. In such an instance we would not be looking at the photograph as a formal entity, or as a means of eﬀecting a visual narrative, or making a psychological, social, or environmental point, or of eliciting some kind of intellectual or emotional reaction, or possibly a combination of such things, but would be looking through the photograph to the selected object that it documents. Visual recording devices, such as still photographs, ﬁlm, or video, might also be used to document selected perceptible actions, such as visible movements of people at a particular place or places at a particular time or times. Or a tape recorder could be used to document sounds at a particular place or places at a particular time or times that are selected auditory phenomena that are meant to be a work of art. A selected artwork could itself then exist outside of the framework of the museum or gallery as long the artworld is apprised of the artist’s intention that a selected object be understood to be all or part of a work of art by that artist, and is so apprised through a kind or kinds of documentation appropriate to the nature of the object selected supplemented by any language required to make the intended selection of the object comprehensible. An artist cannot select and exhibit an object, such as his neighbor’s checkbook, that, given the moral constraints of the society within which he operates, and for not performing any action—such as purchasing the object—that would give him the right to select and exhibit the object as his work, and for not being given permission to select and exhibit the object as his work, he does not have the right to select and exhibit as his work of art. If it is possible to document the object though, then he could select the object through choosing to identify a work of art with the selected object and making that selection comprehensible through documentation appropriate to understanding that intention for the object. In the example, an artist could photograph his neighbor’s checkbook—with permission or perhaps surreptitiously if he had the chance—and then combine the photograph of the checkbook with language that would make the identiﬁcation of the work with the pictured object, rather

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than with the picture of the object, something that could be understood. He could also simply specify such an object to be his work of art since speciﬁcation is not limited by the moral constraints by which selection is limited.3 Any selected artwork is embodied in the perceptual object or objects that the artwork is meant to be in the sense that the artwork is meant to be identiﬁed with that perceptual object. And this is the case even though understanding the intended identiﬁcation of the selected artwork with a certain perceptual object may rest on apprehension of certain things in addition to that perceptual object. A non-perceptual object that an artwork is meant to be may be one that it is possible to select. However, any understanding of any selection of such an object and the intended identiﬁcation of an artwork with a non-perceptual object selected rests on at least one perceptible object. For instance, Robert Barry’s work Inert Gas Series (Helium): From a Measured Volume to Indeﬁnite Expansion is meant to be identiﬁed with two cubic feet of helium that Barry selected and released into the atmosphere on March 4, 1969 in the Mojave Desert. Here the identiﬁcation of the artwork with that object depended on the use of a perceptible cannister that contained the gas, and the art-historical understanding of the identiﬁcation of the artwork with that expanding non-perceptual entity rests on a photograph of the cannister in the desert and language that pertains to that intended identiﬁcation.4 Selected artworks in any case are preexistent objects of kinds of object that either lend themselves to selection and exhibition, or to selection and documentation, with the exhibition of the documentation and any language that is required to make it understandable that the selected object documented—and not the means of documentation itself—is that which the artwork is to be understood to be. Although a preexistent perceptual object that is selected to be a work of art is unchanged perceptually merely by the act of selecting it, it is categorially modiﬁed by the artist’s claim that it is his work of art. Similarly, a preexistent non-perceptual object that is selected to be a work of art is unchanged qua non-perceptual object 3

See 1.1.3 of this section of this division on pp. 43–48 below. An artwork that is meant to be identiﬁed with a non-perceptual object is said to be ‘non-embodied.’ See Part Two, Division III, 8 on pp. 107–110 below. See that same section and Part Three, Division IV, 1.6 on pp. 242–243 below on the relation of perceptible objects to selected non-perceptual objects that are meant to be identiﬁed with non-embodied artworks. 4

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merely by the act of selecting it, but it is categorially modiﬁed by the artist’s claim that it is his work of art. 1.1.3. Speciﬁcation. Speciﬁcation is linguistic, and language functions as a ‘speciﬁcation’ when it is used in some way that language can be used to single out objects to single out an object that is meant to be a work of art. Such language so functions whether it is used in singling something out determinately or indeterminately as these terms are deﬁned below. That which is singled out by a speciﬁcation is in any case logically and epistemologically diﬀerent from everything that is not the determinate or indeterminate object that is delineated by the speciﬁcation. A determinate or an indeterminate object that is singled out or conceptually delineated by a speciﬁcation can be termed the ‘referent’ of the speciﬁcation. It can be so termed however the language functions to make the singling out of one or the other kind of object comprehensible, and it can be so termed whatever the nature of that which is so delineated. Although the nature of the object indicated may ultimately be relevant to the critical and aesthetic importance of a speciﬁed artwork, and to its ontology, it is the understanding of that to which the speciﬁcation is meant to point that is important for the use of speciﬁcation as a means of identifying certain artworks with certain objects. An artist who uses speciﬁcation as a means of identifying an artwork with a certain determinate or indeterminate object must intend to use language to eﬀect that identiﬁcation, and that intention must be capable of being understood. Two tokens of the same language might be distinguished by one having and the other lacking the property of being a speciﬁcation, as when this here now is meant and understood to single out the referent of that language as an artwork, and when this here now is merely used to point to a particular thing in a particular place at a particular time.5 It is always implicit then

5 Examples of language that either are or could be used to specify objects meant to be works of art appear in various parts of the book, and any example of such language will appear in lower-case italics. Speciﬁcations that have been used by artists to single out objects that are meant to be artworks or parts of artworks are attributed to the artists whose speciﬁcations they are. Several speciﬁcations that I have written to illustrate various things appear throughout the book. The referents of these speciﬁcations are entities that could be meant to be artworks or parts of artworks. However, it should not be inferred from the use of any speciﬁcation that I have written that the referent of the speciﬁcation is intended to be all or part of a work of art rather than its being the case that it could be so intended.

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in speaking of language functioning as a speciﬁcation that it is intended to do so and that that intention is comprehensible. The referent of a speciﬁcation acquires the property of being the artwork that is meant to be identiﬁed with that referent in virtue of the artist’s intention that the artwork be so identiﬁed through that speciﬁcation and the understanding of that intention. Because determining the limits of Abstraction in art is an art-historical issue, the understanding of an artist’s intention that the referent of a speciﬁcation be understood to be a work of art is the understanding of the artworld. Any use of speciﬁcation to determine a limit of Abstraction must be capable of being understood by the artworld for such a limit to be recognized as determined. An artwork that is conceptually delineated by a speciﬁcation is a ‘speciﬁed’ object, and an artist ‘speciﬁes’ an object that an artwork is meant to be when she uses a speciﬁcation to eﬀect that identiﬁcation. A speciﬁcation results in the identiﬁcation of a speciﬁed artwork with the object speciﬁed by using language rather than creation or selection to single something out that an artwork is meant to be. And that which is singled out as an artwork could not be understood to be that artwork apart from the speciﬁcation that makes that understanding possible. Although language may be used to specify an object to be an artwork that would have the property of being that object apart from that speciﬁcation, it does not simply name a created or selected object that an artwork is meant to be, as is the case with the titling of an artwork, but is a means of eﬀecting the identiﬁcation of an artwork with an object as much as either creation or selection is a means of eﬀecting the identiﬁcation of an artwork with an object. As seen, the object speciﬁed to be a work of art then acquires the property of being that work of art in virtue of the production and understanding of that speciﬁcation. It should be more speciﬁcally indicated though that it is the meaning of a speciﬁcation that refers to an object that a speciﬁed artwork is meant to be. This is because diﬀerent expressions in diﬀerent languages can be used to refer to an object that an artwork is intended to be, as can any synonymous expression in the same language. It is the meaning that these diﬀerent expressions have in common that enables a subject who grasps that meaning to comprehend what an artist intends his artwork to be understood to be. Objects that are speciﬁed to be artworks may or may not be perceptual, and the limits of speciﬁcation are deﬁned by the capacity

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of language to single out objects that can be understood to be singled out, and so can be understood to have their particular identities and to be distinct from everything that lacks their particular identities. The language the visible space of this page singles out a perceptual object that could be meant to be a work of art, and the object referred to by that language would be so meant if the language were intended to be a speciﬁcation. The referent of Robert Barry’s language all the things I know but of which I am not at the moment thinking—1:36 PM; June 15, 1969 is an example of an object that is speciﬁed to be a work of art that is not perceptual. The referent of all the things I know . . . is also an example of a speciﬁed object that would have its particular identity apart from the language that speciﬁes it to be a work of art, even though the object would lack the property of being the artwork that is eﬀected by the production and understanding of the speciﬁcation apart from the production and understanding of that speciﬁcation. An artist can use language to specify an object to be a work of art which object would have its identity as that object apart from that speciﬁcation. This kind of object may be something that the artist employing the speciﬁcation has created, such as a pie or a mound of dirt, or it may be something that she has no role in creating, such as an oven or the dirt of the earth. An artist may also use language to result in an object that an artwork is meant to be which object she has a least some responsibility for creating, and where creation here indicates that no object would be the object that the artwork is meant to be apart from the artist’s producing the language that refers to that object. An example is the speciﬁcation anything of which you are now thinking and only thinking in virtue of reading this language. Speciﬁcation is a means of singling out an object that an artwork is meant to be, and unless the speciﬁcation singles itself out as the work of art, as in this language or this here now, the identity of the work of art and the speciﬁcation that makes that identity comprehensible are two diﬀerent things. As indicated above, an artist who uses speciﬁcation to eﬀect the identity of her work can specify anything to be a work of art that can be conceptually delineated by language. This appears to be at odds both with Jerrold Levinson’s “proprietary-right condition” that maintains that “you cannot ‘artify’ what you do not own and thus have no right to dispose of,” and his view, as suggested in the following quote, that it is a mistake to

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identify an artwork with an object that is singled out by language that is used in eﬀecting that identiﬁcation, rather than with both the object and the language by which the object is indicated. Thus Levinson says, “It might be thought that the proprietary-right condition would rule out varieties of conceptual art, but this is not so. One must avoid making the mistake of taking the art object in such cases to be simply and solely what the artist has described or pointed to (e.g. Marilyn Monroe, the Empire State Building, a slice of life of a family in Queens—things that the artist clearly has no proprietary right over), rather than a directed complex of the description and the object.”6 Were an artist to specify that his artwork is the Empire State Building, then, according to Levinson, that piece of architecture would not thereby acquire the property of being an artwork by the artist who speciﬁes it—would not be ‘artiﬁed’ by the speciﬁcation—but the “directed complex” that consisted of the speciﬁcation of the object and the object speciﬁed would be the work of art. The problem with this, in terms of the artist’s determination of the identity of her work, is that there is a clear distinction between an artist’s specifying some object to be a work of art—where it is the artist’s intention that the object speciﬁed to be the work is the work but not the object speciﬁed and the speciﬁcation together— and an artist’s specifying that both a speciﬁcation that speciﬁes something and the object speciﬁed are together the work of art, as they would be in Levinson’s “directed complex.” There is a clear diﬀerence of artistic intention between the intent to identify an artwork with the Empire State Building through the use of the speciﬁcation The Empire State Building, and the intent to identify an artwork with the complex object that consists of the Empire State Building and a speciﬁcation that singles out both that building and itself as a work of art, as in The Empire State Building and this speciﬁcation, or as in, more thoroughly, The directed complex that consists of The Empire State Building and this speciﬁcation that refers to the directed complex that consists of The Empire State Building and this speciﬁcation. Accordingly, it cannot simply be said in any case in which an artist uses speciﬁcation that the work consists of the speciﬁcation and the speciﬁed object rather than its being the case that the artwork as the speciﬁed object presupposes the speciﬁcation, at least not in the sense in which what I 6 Levinson, Jerrold “Deﬁning Art Historically” in his Music, Art, and Metaphysics, Ithaca, NY: Cornell Univ. Press (1990), p. 10.

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term the ‘artistic identity’ of a work is at issue as opposed to what might be termed the ‘philosophical identity’ of an artwork—an identity that may include things in addition to the artistic identity of a work. The artistic identity of an artwork is the object that the work is meant to be as determined by the artist whose work it is. The philosophical identity of an artwork must begin with the artistic identity of the work but it may not end there, as it often does not in writing on the ontology of art, and as Levinson indicates that it does not in the examples of the uses of speciﬁcation that he gives. Levinson might accept the distinction between the artistic and the philosophical identity of artworks and yet maintain that a directed complex is implicit philosophically in any use of speciﬁcation. In that case something like what is stated by the second or third speciﬁcation is implicit in the ﬁrst speciﬁcation, and the philosophical identity of the artwork is the directed complex of the building and the speciﬁcation. It might then be said that the directed complex that is implicit in the ﬁrst speciﬁcation is named by the second speciﬁcation and made explicit in the third speciﬁcation, so that artistic identity and philosophical identity coincide in either example. However Levinson might respond to this, I think that one must acknowledge that the relation of a speciﬁcation to the object that it speciﬁes is relevant to the philosophy of the artwork. This relation is also relevant to the aesthetic value of the artwork and to its critical assessment. However, these things presuppose the artistic identity of the artwork as determined by the artist whose work it is, and speciﬁcation can be used to determine that identity without its being the case that the speciﬁcation thereby becomes part of the artistic identity that it is used to determine. Because the limits of speciﬁcation in art are the limits of the capacity of language to single things out, and language can be used to refer to hideous things, such as someone’s cancer or someone’s death from cancer, and to ethically questionable entities, including immoral actions and events or things that result from immoral actions, it might be asserted that propriety and ethics each prohibit the referents of certain speciﬁcations from having aesthetic value, or even from being works of art, in spite of their speciﬁcation as such. This might be maintained in particular about entities that are linked speciﬁcally to actions that are prompted by language that refers to those actions and to things that result from them, such as any damage that is willfully done to any property not owned by anyone who engages in any action to destroy such property which action is provoked by reading this language.

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It might then be thought that there are social and moral constraints on the use of speciﬁcation, and not anything that language can be used to conceptually delineate can be meant to be a work of art, let alone have aesthetic value.7 However, it is not clear that this is the case, since to single something out as a work of art is simply to categorize it as a certain kind of entity. Nothing of value follows necessarily from an artist’s classifying a thing as a work of art, and it cannot be inferred from an artist’s specifying something ugly or immoral to be a work of art that the artist thereby ﬁnds pleasing or condones what he has speciﬁed, or that the speciﬁed entity acquires aesthetic value that is either unaﬀected by the ugliness or immorality of the speciﬁed entity or overrides its ugliness or immorality in virtue of that speciﬁcation. Dickie’s distinction between the classiﬁcatory and the evaluative sense of artwork would seem to be applicable here, so that an artwork in the classiﬁcatory sense, including a speciﬁed artwork, is a “value-neutral” object.8 Although anything that can be understood to be speciﬁed to be a work of art can be speciﬁed to be a work of art, there is an important diﬀerence between its being possible to specify something to be a work of art and its being artistically and aesthetically relevant to do so. The same points apply to creation and selection. That is, from the fact that it is possible to create or select an object that an artwork can be meant to be it does not follow that that which is created or selected will have artistic or aesthetic merit simply or primarily in virtue of that creation or selection. Rather, a number of other factors may and likely will be involved in the determination of an artwork’s value. And this is the case even though how the identity of an artwork is eﬀected may be, and typically will be, a factor in the assessment of its value. 1.1.4. Complex artworks. A complex artwork could consist in part of a created object or objects, in part of a selected object or objects, 7

Victor Haines has expressed this reservation about speciﬁcation to me in conversation. 8 Dickie, George Art and Value, Oxford: Blackwell (2001) pp. 56–57. Also see Binkley, Timothy “Piece: Contra Aesthetics.” The value-neutral status of the classiﬁcatory sense of artwork having been acknowledged, it might be argued that no artwork enters art history that is not in some way important or that lacks any value relevant to that history, so that no object that comes to form part of art history can be a value-neutral object. See Division V of this part below on art and the aesthetic.

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and in part of a speciﬁed object or objects. For instance, a complex installation could consist of a white square that an artist has painted on a gallery wall, a mirror that the artist has purchased and placed on the wall next to the painted square, and a speciﬁcation placed beneath them that reads any diﬀerence now apprehended between the square and the mirror above this language. A complex artwork could also be eﬀected partly through the use of a created object or objects, partly through the use of a selected object or objects, and partly through the use of a speciﬁcation or speciﬁcations. For instance, a complex performance could consist ﬁrst of an artist’s painting a black square on a gallery wall that she then paints over with white to match the gallery wall; second, her hanging a mirror of the same size of the painted square that the artist has purchased on the wall where the painted square previously existed; third, her subsequent removal of the mirror after an amount of time that equals the amount of time that it took to paint and paint over the black square; and, ﬁnally, the artist’s placing a speciﬁcation printed on paper equal in size to the mirror where both the painted square and the mirror had been that reads any recollection of any object that formerly occupied the space in which this language now appears. A complex artwork could partially consist of and partially result from the use of a created object or objects; partially consist of and partially result from the use of a selected object or objects; and partially consist of and partially result from the use of a speciﬁed object or objects. For instance, an artist could paint a square on canvas with a brush that he designs and makes, then cut the canvas with a purchased knife that is then fastened to the canvas beneath the square, and ﬁnally specify that the agent behind the idea of cutting the canvas, namely the artist herself, is part of the work. Of course more limited combinations of those things indicated are also possible. 1.1.5. Artworks and existence. The diﬀerent examples of the ﬁrst two paragraphs of the preceding section illustrate that parts of a complex artwork may or may not coexist. In fact, because it is possible to use speciﬁcation to intend to identify all or part of an artwork with something that did not, does not, and will not exist—such as my older brother or the second term of President Kennedy—the notion of existence cannot be assumed to apply to an artwork or any part of a complex artwork, and the notion of coexistence cannot be assumed

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to apply to every part of a complex artwork. I mean that the notions of existence and coexistence cannot be assumed to apply to an artwork as what the work is meant to be, since the work may be intended to be identiﬁed with a non-existential object, or to include a nonexistential object as a part. Questions of existence are admittedly diﬃcult. A logically possible object is characterized by logically compatible properties, as in the forest on top of the hill, and an impossible object is characterized by logically incompatible properties, as in the forest without trees. A logically possible object can be instantiated in a possible world, or a world such as ours that consists of logically possible objects. An impossible object cannot be instantiated in a possible world. Speciﬁcation can be used to single out either a possible or an impossible object in the sense in which what is conceptually delineated by the speciﬁcation can be understood, and it can be understood that one rather than the other kind of object might be instantiated in a possible world. What is important to the use of speciﬁcation in art and in Essentialist Abstraction is the possibility of singling out objects that can be understood to be singled out, whatever their nature and relation to the actual world and its properties. Thus speciﬁcation precedes ontology in the sense that any object that language can be used to single out for consciousness can be speciﬁed to be a work of art. This is the case because artistic intention and exploration may follow from what the relation of language to consciousness makes possible for the intended identiﬁcation of artworks with conceptually delineated objects, and so is the case regardless of a speciﬁed object’s having or lacking being, or perhaps being “beyond being and nonbeing,” as Meinong asserts to be the case for impossible objects. As indicated in section 1.2 below, the concept of object must be given the greatest possible latitude to accommodate the myriad possibilities that are available to artists, and one cannot determine prior to creative investigation what works of interest and value might result from the exploration of those possibilities. To assert dogmatically that an artwork must be meant to be identiﬁed with an actual or present existential object rather than, perhaps, with a possible or even an impossible object, may be to preclude works of interest and importance that are meant to be identiﬁed with either kind of object, and might be analogous to precluding Cubism by dogmatically asserting that any represented object must maintain its integrity as it is rendered clearly and accurately in Renaissance perspective. There

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may in fact be nothing to be gained by identifying an artwork with a possible or an impossible object rather than with an actual object. However, one is hesitant to state in advance of creative inquiry that there could be nothing of artistic or philosophical interest or importance in either kind of identiﬁcation. In particular, because the identiﬁcation of an artwork with either kind of object would depend on language and consciousness, an object of either kind of object intended to be a work may be less a matter of interest itself than how the identiﬁcation of the work with the object may be eﬀected in relation to language and consciousness. One may be reminded that it is not the snow shovel qua snow shovel that is of interest. Rather, it is the identiﬁcation of In Advance of the Broken Arm with the snow shovel that is of interest. And stating that there could be nothing of artistic or philosophical interest in the identiﬁcation of an artwork with anything but an actual object might be like stating before Duchamp that there could be nothing of artistic or philosophical interest or importance from identifying artworks with common manufactured objects. Existential and non-existential objects are distinguished in section 1.2.4 below. I treat impossible objects as a kind of type-dependent object, and therefore as a kind of object that is dependent on awareness to have its particular identity, and it may be the case that an object that is picked out by a speciﬁcation that is not an existential object is a type-dependent object.9 Problems of ontology would then be resolved in terms of existential acts whose objects are dependent on the actual occurrence of those acts, and hence have no being or identity apart from them. The identiﬁcation of artworks with such objects then becomes ontologically innocuous in that the identiﬁcation depends on events of apprehending language that refers to objects that are dependent on those events of apprehension. Still, one cannot decide prior to artistic investigation what artistic results might be achieved by identifying artworks with certain kinds of type-dependent object that are possible or impossible non-existential objects. More is said about these matters below, but what is important to art and Abstraction is the intended identiﬁcation of an artwork with some object and the understanding of the identity of the object intended. That is, what is initially important, and what makes talk 9 On type-dependent objects see Part Three, Division III, 11 on pp. 217–221 below. On impossible objects see Appendix Four on pp. 353–365 below.

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of the importance, value, and ontology of an artwork possible is the artistic identity of the artwork. Although the nature of a speciﬁed object and its relation to language and consciousness may be relevant to the artistic importance of the work that is meant to be identiﬁed with that object, and to the aesthetic value of the work and its ontology, any determination of that importance, value, or ontology presupposes understanding the identity of the intended object. And that understanding is possible for a speciﬁed object in virtue of understanding language that speciﬁes the object. 1.1.6. Making or producing art-historical artworks. An object is singled out with which an artwork is meant to be identiﬁed when an act or a combination of acts of intentionally delineating the object through creation, selection, speciﬁcation, or through a combination thereof either includes or is supplemented by an act of intending that such an object be understood to be a work of art by the artist who is responsible for the ﬁrst kind of act. I will speak of this singling out as ‘making’ or ‘producing’ a work of art. Such making or producing always includes the two kinds of intentional relation of artist to an object that an artwork is meant to be, and which are the subject of sections 4–8 below. And because I am concerned with the art-historical identiﬁcation of the limits of Abstraction, it is always implicit that the artworld either is or can be aware of an artist’s intended identiﬁcation of some artwork with some object. 1.1.7. The expansive notion of eﬀecting artworks. The use of selection and speciﬁcation in art require that the traditional notion of creating an object that an artwork is meant to be be supplanted by the more inclusive notion of eﬀecting a work of art through the intentional identiﬁcation of the work either with a particular object or objects, or with some object or objects of a delineated group of objects, as indicated in 1 above and to be elucidated below.10 A means of eﬀecting the identiﬁcation of an artwork with some object may include any means used to eﬀect any eﬀected object that the work is meant to be, and so may include traditional and novel forms of creation. However, eﬀecting an object that a work is meant to be need not be limited to creation in any standard sense of creation, as is amply 10 This observation aﬀects how the notion of a medium in art must be analyzed. See Part Three, Division IV, 1 on pp. 234–253 below.

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illustrated in this work, and an object that a work is meant to be need not itself be eﬀected, rather than the work being what is eﬀected by eﬀecting the identiﬁcation of the work with the object that the work is meant to be, which is also illustrated. Although I will continue to speak of created artworks—or of creating objects that artworks are meant to be—in certain sections that are relevant to the use of such terminology, it should be understood that such talk does not exhaust but is included in the category of means of eﬀecting the identiﬁcation of an artwork with some object, and whether or not the artist who is responsible for eﬀecting that identiﬁcation is also responsible for in some way eﬀecting the object that the work is meant to be. 1.2. Artworks and objects All artworks are objects, where ‘object’ is used in the widest possible sense so that anything that is or can be experienced or apprehended in any kind or kinds of experience or apprehension is an object. Anything that can be mentioned, described, referred to, suggested, imagined, or conceived of is an object. This is the case whether that which is mentioned, described, referred to, suggested, imagined, or conceived of has or lacks a relation to actual or possible experience or apprehension; and is the case apart from the ontological status of that which is mentioned, described, referred to, suggested, imagined, or conceived of; and so is the case whatever nature or properties that which is mentioned, described, referred to, suggested, imagined, or conceived of has or is conceived of as having. Thus the concept of object, as it is used in this book, is meant to be both the most basic concept in the philosophical lexicon and the one with the broadest range of use, and such terms as ‘entity,’ ‘individual,’ ‘item,’ ‘particular,’ and ‘thing’ are to be understood to be synonyms of the term ‘object.’ That the concept of object has unrestricted application means that it includes, but is not necessarily limited to: spatial, temporal, and spatio-temporal entities—and any attributes of such things—such as mass and charge—and things that pertain to them—such as location and duration; abstract entities, including numbers and universals; acts, actions, events, and processes, and whether mental, physical, or neutral; states, conditions, and dispositions, and whether mental, physical, or neutral; states of aﬀairs, relations, and properties; aggregates, sets, and classes;

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causes and eﬀects; perceptible and imperceptible items; things that are comprehensible and things that are not; and actualities, possibilities, and impossibilities.11 That the concept of object is meant to apply to such impossible objects as the round square can be understood to mean either that the notion of conceivability referred to in the previous paragraph is to be given wide latitude (without, however, its being the case that any metaphysical or supra-metaphysical conclusion can be deduced from the recognition of such latitude) or that anything that is said or thought to be inconceivable is, for that saying or thinking, at least mentionable.12 1.2.1. The concept ‘object’ and awareness. The concept ‘object’ not only applies to anything of which subjects can be aware, but anything of which we think as not depending on awareness will also be an object. Putting the matter this way conceives of the notion of object in relation to awareness. This is as it must be in order for us to understand the concept, but I do not mean to use the concept in a way that would restrict its applicability to awareness and thus make the

11 Cf. Panayot Butchvarov: “An object is anything that can be referred to, singled out for attention, whether in perception, thought, or discourse; it is anything that may be classiﬁed, subjected to conceptualization.” Butchvarov, Panayot Being Qua Being: A Theory of Identity, Existence, and Predication, Bloomington, IN: Indiana Univ. Press (1979) p. 45. For the purpose of determining the limits of Abstraction in art, I will regard anything that is mentionable or conceivable—including logically impossible objects—as classiﬁable or subject to conceptualization, and therefore an object. Thus, a 45° right angle is something to which I have just referred or singled out through language as an object of thought, and it is classiﬁable as a kind of object, namely, an impossible or a self-contradictory one, about which it is possible to discourse. Impossible objects, and how they stand in relation to acts of conceiving of them, are considered in Appendix Four on pp. 353–365 below. 12 Dabney Townsend says that “an object is anything that can be referred to,” and that the concept ‘object’ can be used “to designate whatever someone is capable of thinking about.” However, Townsend restricts the use of ‘object’ to “at least logically possible combinations—something that can be referred to in some possible world, if not in this one,” and so his use of the concept ‘object’ is narrower than it is in this work. Townsend, Dabney An Introduction to Aesthetics, Oxford: Blackwell (1997). Quotes on pp. 136, 64, and 65. A wider use of the concept ‘object’ that appears to ﬁt my own wide use of the notion is Jerrold Levinson’s, since Levinson counts as an object “any thing whatsoever.” Thus, material objects are of course comprised, but also words, thoughts, structures, events, situations—whatever is in some way identiﬁable, indicatable, able to be picked out, at least in thought.” Levinson, Jerrold “Reﬁning Art Historically” in Music, Art, and Metaphysics, p. 39. (His italics.) Nothing should be inferred about the nature of an object to which my more liberal concept of object applies in virtue of that application, including its ontological status, and its being or failing to be mind-independent.

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existence or subsistence of an object apart from a relation to actual or possible awareness an unintelligible notion. I only mean to emphasize that anything of which a subject is aware is an object, and that anything that can be conceived to have or lack being independently of its being an object of awareness will be some kind of object, subject to the logical limitations of objects that are listed below. Further, concepts themselves are objects in being objects of understanding, in being things that we grasp and use in thought and language, and so the concept of object is itself an object.13 While it is true that any articulation of the concept ‘object’ will have a necessary relation to awareness, it does not follow from this that every kind of object is necessarily mental or that every kind of object has a necessary relation to awareness, as objects did for Berkeley. Rather, our conceiving of mind-independent objects only indicates that the concept of such an object must be one that we can understand, and to that extent consciousness enters the picture in the construction or apprehension of the concept. From this it does not follow that awareness is ontologically tied to every object of any kind, rather than being ontologically or epistemologically tied to particular objects of certain kinds. In fact, even if realism is false, its assertion of the intrinsic lack of connection of some objects to awareness must be understood by anyone wishing to dismiss the possibility of such an object. Thus, the idealist must comprehend what the realist asserts in order to deny the legitimacy of that assertion. On the other hand, although the possibility that certain objects have no necessary relation to awareness seems to be logically acceptable and readily comprehensible, any conception of the nature of such objects 13 Justus Buchler relates what he calls “discriminations” and “natural complexes.” According to Buchler, “. . . whatever is discriminated in any respect or in any degree is a natural complex . . .”, and “Anything identiﬁed or discovered or imagined or discerned or inferred or sensed or posited or encountered or apprehended or made or acted upon—no matter whether deliberately or not—is here said to be ‘discriminated.’” Buchler, Justus The Metaphysics of Natural Complexes, New York: Columbia Univ. Press (1966) p. 1. Buchler’s use of “natural complex” as that which is discriminated in the kinds of experience he lists would seem to be the same as my use of “object” as that of which we are aware in any form of awareness, since I would count the kinds of experience instanced as being species of discrimination as kinds of awareness that subjects have of objects, or at least as presupposing awareness in the cases of making and acting upon things. However, as indicated in the text, I am not using the concept ‘object’ to mean that, if something is an object, it must either be discriminated in fact or must be distinguishable in awareness from other objects.

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must be framed in terms that subjects can comprehend, and so will reﬂect thinking about the concept ‘object’ in general and the conditions by which the concept is regulated. This latter assertion does not imply, however, that our conceptual vocabulary necessarily has its source in the nature of awareness, since it is possible that that vocabulary is due at least in part to the nature of objects that awareness apprehends. 1.2.2. The ontological neutrality of the concept of object. That the concept of object is ontologically neutral or unlimited means that it may be the case that a thing is an object without its being the case that that thing exists, subsists, or has any kind of being conceivable. Thus nothing ontological can be inferred from the use of the terms ‘is,’ ‘has,’ and ‘being’ in either the assertion that a thing is an object or in the assertion that a thing has the property of being an object, and the unrestricted range of the concept ‘object’ is due in part to its lack of ontological commitment in addition to those things previously noted.14 Because language can be used to refer to items of experience, as well as to things that can be conceived of or mentioned, and because an artist could use language to specify that anything of any of these kinds of thing is to be understood to be a work of art, speaking generally of an object with which an artwork is meant to be identiﬁed requires recognizing the use of object in the widest possible sense. This wide construal of the concept ‘object’ is more speciﬁcally required for investigating the limits of Abstraction in art since it is unnecessary that an artwork be an artifact in the traditional sense, and the more Abstract objects are not objects in the sense in which the term ‘object’ is standardly used, and are not the sort of thing that we commonly associate with an art object. In addition, that some object 14 Cf. Reinhardt Grossman: “. . . being is not the most general notion under which things can be classiﬁed. Rather, it is the notion of an object of the mind or, for short, an object.” He also notes, in a Meinongian vein, that “To be an object of the mind implies neither existence nor any other kind of being.” The Existence of the World: An Introduction to Ontology, London: Routledge (1992) both quotes p. 93. (His italics.) According to Alexius Meinong: “. . . the totality of what exists, including what has existed and will exist, is inﬁnitely small in comparison with the totality of the Objects of knowledge.” “The Theory of Objects” (trans. by Isaac Levi, D. B. Terrell, and Roderick M. Chisholm) in Chisholm, Roderick M. (ed.) Realism and the Background of Phenomenology, Atascadero, CA: Ridgeview (1960) pp. 76–117. Quote on p. 79.

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has the property of being some work of art is, by itself, ontologically neutral. Accordingly, to assert that something is or has the property of being a particular artwork is merely to predicate the property of being that artwork of that thing. From knowing then that something has the property of being a particular artwork one cannot infer that it exists, since, although any object on which the identity of an artwork is originally or subsequently dependent must itself exist in virtue of that dependence, for any existential object on which a particular artwork is dependent, that object may or may not have the property of being that work. 1.2.3. Use of the terms ‘object,’ ‘thing,’ and ‘entity.’ I use the term ‘object’ in the manner indicated rather than either ‘thing’ or ‘entity,’ even though these are terms that are frequently used in a wider or more general sense than that in which ‘object’ is usually employed. I do so for the following reasons: First, we more naturally speak of art and its objects than we do of art and its things or of art and its entities, and it sounds odd to talk of an art thing, or an art entity rather than an art object. This, however, may merely reﬂect the fact that we commonly mean ‘physical object’ when we speak of objects, and that many people tend to equate, unreﬂectively, works of visual art and physical objects. Second, it is customary to speak of an object of awareness rather than a thing or entity of which we are aware, even though there is nothing to argue against either of these latter usages. And, as we will see, as all works of art depend on objects of which we can be aware, it seems more appropriate to use ‘object’ rather than ‘thing’ or ‘entity’ for this reason in addition to that which has already been stated. Third, both ‘entity’ and ‘thing’ are sometimes used ontologically as synonyms of ‘being,’ and I wish to avoid using terminology with ontological associations.15 For all of these reasons then, I use ‘object’ more frequently in this discourse than either ‘thing’ or ‘entity,’ but when either of the latter terms is used without qualiﬁcation, each is to be understood to be synonymous with 15 For instance, Gary Rosenkrantz says that ‘entity’ is the highest and most general of ontological categories. Rosenkrantz, Gary, Haecceity: An Ontological Essay, Dordrecht, The Netherlands: Kluwer (1993) p. 59. And E. J. Lowe writes: “‘Thing,’ in its most general sense, is interchangeable with ‘entity’ or ‘being’ and is applicable to any item whose existence is acknowledged by a system of ontology, whether that item be particular, universal, abstract, or concrete.” Honderich, Ted (ed.) The Oxford Companion to Philosophy, Oxford: Oxford Univ. Press (1995) p. 871.

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‘object,’ and thus is to be understood to lack any necessary relation to ontological being of any kind. 1.2.4. Existential and non-existential objects. The notion of kinds of being other than existence that may or may not be applicable to certain kinds of object is irrelevant to the concerns of this work. Although it is relevant to note the widest possible range of the use of the term ‘object,’ it is not similarly relevant to determine the range of the term ‘being.’ However, given the character of most artworks to this point in history and the concerns of this investigation, it is useful to distinguish terminologically between existential and non-existential objects. The term ‘existential’ refers to past, present, and future temporal and spatio-temporal objects, so that existential objects are past, present, or future. The term ‘non-existential’ refers to objects that are not existential. Non-existential objects include abstract types that can have existential instances, and impossible objects that, as impossible, cannot have existential instances. Any object that exists is existential, but an object ‘exists’ only if it is either a temporal or spatio-temporal object now, that is, if it is a present existential object, and is so whether or not it was also a past and/or will be a future existential object. Whether or not certain non-existential objects subsist or are “beyond being and non-being” is irrelevant. What is relevant is the conceptual demarcation of existential and non-existential objects, and the recognition that a non-existential object could be speciﬁed to be a work of art, and that any such speciﬁcation would itself be existential. 1.2.5. The logical limitation of objects according to the laws of objects. Although the concept ‘object’ has unrestricted application and is ontologically neutral or unlimited, anything to which the concept ‘object’ applies is logically limited according to ‘the laws of objects’ or ‘the logical conditions of objects.’ These laws state that each object is logically identical to itself, that no object is logically identical to any object but itself, and that each object is logically distinct from each object to which it is not logically identical. Further, each object has the property of being the particular object that it is, which is the haecceity of the object, and no other object can have the property of being that object. Thus any object x has the property of being x, no object y that is not x can have the property of being x, and so any object y that lacks the property of being x diﬀers logically from

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x if it diﬀers from x in no other respect. Accordingly, any object x is only logically identical to, or exactly the same as, an object that has the property of being x, which is x itself, and any object x is logically distinct or diﬀerent from everything to which it is not selfidentical, which is every other object. These remarks indicate that every object is logically particular. And this is the case whatever degree of complexity an object may have or lack; whether or not it consists of any number of parts that are distributed in space or time or space and time; and whether or not it can have any number of existential instances, that is, whether or not it is a type any number of tokens of which are equally tokens of the same type. That an object is logically particular means that it has a particular identity that everything else lacks.16 The logical being of an object is simply the object’s logically being the object that it is and not being any object that it is not. Whereas the ontological being of an object concerns some property such as being temporal or instantiable, the logical being of an object concerns the property that it has of being that object. 1.3. Singling something out determinately An object is singled out determinately as a particular work of art when some simple or complex object is the object that the work is meant to be. That the work is meant to be that object indicates that the artist intends that the work be identiﬁed with that object; that 16 If some object lacks a particular identity, then there is at least one object that lacks the property of being the object that it is, and it is distinguished as that object from all other objects that have particular identities. Assume that there is an object x that lacks its particular identity. In such a case x is an object that lacks the property of having its particular identity, and lacking the property of having its particular identity is said to characterize that object as that object, and so to distinguish it from any object that is not x. But if x lacks the property of having its particular identity, then x lacks the property of being x. And since an object’s being x is said to be that object’s lacking the property of being x, any object assumed to be x must lack the very property that is assumed to characterize that object as that object, namely, the property of lacking its particular identity. In that case any object assumed to be x cannot have the property of being x, and so no object can be such an object x that lacks its particular identity. To speak of any such object x then must either be to speak of nothing—no thing—in terms of a self-eliminating property, or to speak of some other object y that, as an object, has its particular identity, and so lacks the property of being an object that lacks its particular identity. Such an object y might be that which is conceived of in an event of conceiving of an object that lacks its particular identity.

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it is understood that the work is meant to be that object; and that it is understood that each object that lacks the property of being the object that the work is meant to be lacks the property of being the work. Such an artwork can be termed a ‘determinate’ artwork, and the object that such a work is meant to be can be termed a ‘determinate’ object in the sense in which it is linked determinately as indicated to that kind of work. All of the objects of all of the major art forms are determinate objects as deﬁned, whatever their ontology. A determinate artwork can be meant to be identiﬁed with a simple or complex object that the artist is responsible for creating, selecting, or specifying, or with a complex object that consists of some combination of objects that the artist is responsible for creating, selecting, or specifying. An object that is created, selected, or speciﬁed, or that is a complex of some combination of created, selected, or speciﬁed objects, is an object that has been ﬁrst singled out in that act of creation, selection, or speciﬁcation, or the appropriate combination thereof. Such an object is then singled out as a determinate artwork in virtue of being meant to be and being understood to be a particular work of art. A determinate artwork can also be meant to be identiﬁed with a simple or complex object that is causally and conceptually related to an object that the artist is responsible for producing, as when a composer conceives of a musical composition the written notation of which plays an essential role in the production of an auditory object that the work is meant to be, when Sol LeWitt writes a set of instructions for a wall drawing, or when an artist writes the speciﬁcation each eﬀect of any current apprehension of this information. An artist must in any case have an intentional causal and conceptual relation to any object meant to be a work of art by that artist, such an object is a determinate artwork when it ﬁts the criteria listed above, and an artist singles something out determinately when she has the required intentional causal and conceptual relation to a determinate object. The term ‘determinate’ can extend beyond existing objects that are works of art to past and future existential objects, to non-existential objects, and to abstract types and to existential tokens of the types any of which have the kind of determinate relation to artistic intention stated and to be considered below.

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1.4. Singling something out indeterminately An artist may intend that an artwork a be identiﬁed with one or the other of two or more numerically diﬀerent objects x and y but not speciﬁcally with either x or y. Or an artist may intend that an artwork a be identiﬁed with some n objects of a group of n+m objects—where n is *2 and where m is *1—and where it is understood of which objects group n+m consists, but where for any particular objects x, y . . . in the group that are numerically equivalent to n from that group, a is not determined to be x, y . . . rather than some other objects a, b . . . of which the group of n+m objects consists that equally are numerically equivalent to n. In this kind of case, two or more objects x, y . . . are singled out and are conceptually distinguished from every object that lacks the property of being x, y . . . at the same time that it is purposely left indeterminate which of x, y . . . is meant to be the work of art. This can be understood to be singling something out ‘indeterminately.’ For instance, an artist could paint two squares and say that the work is one or the other but not both, or an artist could select two or more objects—say an apple and a baking sheet—and let it be known that the work is neither deﬁnitely one nor the other object, but is at least one of these and is at most one of these. Similarly, an artist could specify that his work is either any thought that is provoked by reading this language or everything other than such a thought. In any of the examples given, the indeterminacy of artistic identity is part of the situation itself as designed by the artist, and is not simply a matter of a subject’s not knowing what the artist intended. However, any such indeterminacy must be intended by the artist who devises it, and must be a circumscribed indeterminacy as noted, since two or more objects must be singled out relative to which the indeterminacy can be understood to be eﬀected. The circumscription holds even if the artist writes something such as this or everything other than this, where the combination of those things named in the disjunction is all objects. This is because everything is conceptually distinct from everything that lacks its particular identity, which is each thing and each combination of things of which everything consists. A work of any of these kinds is diﬀerent from a work where the artist sets up a disjunction of objects—say either x or y—but then lets it be known that anyone who apprehends the disjunction determines through his choosing one or the other objects which object

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the work is meant to be, indexing the work to the decision of someone apprehending the disjunction, and so allowing for the possibility that the same disjunction of objects could allow for a number of diﬀerent works—diﬀerent works that are consistent with the possibilities of choosing objects from the group of objects disjoined. An artist could further index an artwork not just to the choosing of a particular person, but to the time at which any choice is made, so that each choice results in a numerically diﬀerent work, and does so even if the same objects are chosen by the same subject at diﬀerent times of choosing them. Yet another possibility is for an artist to maintain, not that some object or objects of some disjunction of objects is the work, but that the work itself is that disjunctive situation. For instance, an artist speciﬁes: this work is not either any thought that is provoked by reading this sentence or everything other than such a thought, but is the disjunctive state of aﬀairs that is represented by the language ‘either any thought that is provoked by reading this sentence or everything other than such a thought.’ It remains the case that, in order to provide for the possibility of speaking of and responding to a work of art, something has to be singled out in relation to which the identity of the work can possibly be determined, and if that is not the case, then there is no means of distinguishing any object that is not the work from any object that would be the work. Although this requirement is met by the examples considered, it is an interesting question to what we would be responding if an artist were to say: “My work is either x or y but not both.” Since this is something novel, what may provoke our interest—assuming perhaps that neither object has some property or properties that makes it intrinsically more interesting than the other— is that novelty, and the artist’s creativity in thinking of it. It could be like a Duchamp readymade then, in that it is not the selected object itself that provokes our interest—even though the artwork is meant to be identiﬁed with that object—but the novelty of producing art through simply choosing and displaying a preexistent artifact, and the creativity that Duchamp displayed in thinking of the possibility of that means of artistic production. We are simply used to artists singling out determinately single simple or complex objects that artworks are meant to be. And this is the case even if the complex object consists of a number of objects that are distributed in space or time or space and time, since, if that is the case, then any such object has the property of being part of

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the work, and the work is a single discontinuous object that is a complex of its parts. We are not used to an artist singling out two or more objects and then maintaining, not that each object has the property of being part of the same work, but that one object has the property of being the work and the other does not, and that the artist has not and cannot determine which is which, and neither can any observer of the work, unless the artist has so indicated. Although this conﬂicts with centuries of artistic practice, it does not seem to be a problem of the kind where we can say or write something that cannot be true—either due to logic or the nature of reality, as when I say that I am both older and younger than I am at the present moment, or when I say that I am in two places at once—or due to the very nature of the assertion, as in the case of “This is not a sentence,” or in the case of someone who says, audibly, “I am not now speaking aloud.” A case of saying something that could not artistically be true would result, for instance, if it were maintained of two or more objects that each is equally the same individual work at the same time that each object is said to be part of that work. I have been looking at singling something out indeterminately as a disjunction of objects where the term ‘or,’ in saying that an artwork a is an object x or y, is exclusive, so that a is either x or y but not both. Another possibility however is to treat ‘or’ as inclusive, so that an artist could maintain that an artwork a is x or y or x and y. Notice however, that such a situation remains indeterminate even in treating ‘or’ as inclusive. This is because that situation is itself a disjunction between x or y or both x and y, and does not become a determinate situation in which the artwork is meant to be x and y to the exclusion of the possibility that the artwork could be x and y or x or y. A ﬁnal artistic possibility in relation to indeterminate objects is to leave an indeterminate situation itself indeterminate, so that, of two or more objects x and y, it is indicated that a is meant to be x or y, but it is not made clear how ‘or’ is to be interpreted, and so it is not indicated that a is meant to be x or y but not both, and it is not indicated that a is meant to be x or y or x and y. To summarize the points of this section: An artist singles out some thing x or y or . . . indeterminately as an artwork a when some simple or complex object is x, some simple or complex object is y . . ., it is understood that a is meant to be x or y . . ., exclusively, inclusively, or exclusively or inclusively, and it is understood that, for any

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object o that is ~x, ~y, ~ . . ., o cannot have the property of being a. An artwork such as a can be termed an ‘indeterminate’ artwork, and a disjunction of objects x or y or . . . can be termed an ‘indeterminate’ object in the sense in which such a group of objects is linked indeterminately as indicated to a. Henceforth, talk of singling something out with which all or part of an artwork is meant to be identiﬁed will implicitly recognize that such singling out may be determinate or indeterminate, if one or the kind of singling out is not speciﬁcally mentioned. Similarly, general points that are made about artworks and objects can be understood to apply to indeterminate as well as to determinate artworks or objects when the nature of these things is not speciﬁcally indicated. 1.5. Success and failure in singling something out One may speak of ‘succeeding in singling something out’ and ‘failing to single something out’ to recognize a diﬀerence between successful and unsuccessful attempts to determine the identity of an artwork, or to mark a distinction between sense and nonsense in relation to such identity. Imagine that an artist were to write, for instance: “I intend my artwork to be identiﬁed with OPEIURERELKMOIET.”17 With what then is the artwork to be identiﬁed? There are two possibilities here: either the artist could intend that his work be identiﬁed with the visible string of capital letters as a perceptual object, or he could intend that his work be identiﬁed with something unknowable, unidentiﬁable, and unintelligible that is meant to be indicated by that meaningless string of letters. However, in the latter case no identity of the work has been determined. Because the string of letters is meaningless, it does not delineate anything with which the artist could intend the work to be identiﬁed. And it would 17 The example is Tom Adajian’s, and the quoted language was used in correspondence with me that raised the question of why an artwork must have a particular identity that must be capable of being understood, and must be capable of being so understood even if one cannot be aware of the object itself that an artwork is meant to be. Adajian says that “OPEIURERELKMOIET is intended to be gibberish. No one, including the artist, knows what it means.” That having been noted, Adajian asks why it could not be the case that this gibberish succeeds in eﬀecting the identiﬁcation of an artwork with something even though no one knows what the gibberish, as gibberish, means, and so no one knows with what object the artwork is meant to be identiﬁed, including the artist.

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have to be asked how a work that is meant to be identiﬁed with OPEIURERELKMOIET is diﬀerent from a work that is meant to be identiﬁed with OEUEEKOE, where neither work is meant to be identiﬁed with a visible string of capital letters as a perceptual object? Thus what if an artist were to write: “I intend my artwork Untitled 1 to be identiﬁed with OPEIURERELKMOIET,” and “I intend my artwork Untitled 2 to be identiﬁed with OEUEEKOE,” and he further maintains that Untitled 1 and Untitled 2 are diﬀerent works that are to be identiﬁed with the diﬀerent things indicated by “OPEIURERELKMOIET” and “OEUEEKOE?” How is one work to be distinguished from the other? What property or properties does one work have that the other work lacks? What property or properties does either work have or lack that any other work has or lacks— whether by the same or diﬀerent artists? What property or properties does either object have or lack that either work is meant to be that any other object has or lacks which either work is not meant to be? It is impossible to answer any of these questions since, by the nature of the case envisaged, we do not know what either string of letters signiﬁes. And if we do not know what either string of letters signiﬁes, then we have no basis for determining whether the letters single out diﬀerent objects that correspond to the diﬀerent titles meant to identify diﬀerent works, or are diﬀerent ways of singling out the same object, if in fact they are not diﬀerent ways of failing to single out any object. Even if we were to suppose that the diﬀerent strings of letters single out diﬀerent objects with which diﬀerent artworks are meant to be identiﬁed, still we have no way of knowing what properties either object has or lacks. And if we do not know what properties a putative work is supposed to have or lack, then how can we reﬂect on, evaluate, interpret, or respond to either work? How could we say that one work was more original or important than another? How then is either case not simply nonsense, where sense here pertains to the successful singling out of something that an artwork can be understood to be, and, as so delineated, is conceptually distinct from everything that lacks its identity? In fact there is no means by which one could distinguish the works, since there is no object that is conceptually delineated in either case. Each case is simply nonsense, since in neither case can it be supposed that any object corresponds to the sequence of letters, and so nothing can have the property of

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being the work of either title, and so no object can be distinguished from any object that lacks the identity of the work. 1.6. Possible lack of clarity in singling something out The distinction between successful and unsuccessful delineation of an object that an artwork can be meant to be having been made, it must also be recognized that there may be cases where it is not clear whether something has been clearly singled out, and there may be cases where it is not clear which of two or more things that may be singled out is meant to be the work, or if, rather, each is meant to be part of the work.18 Any attempt to single something out that an artwork is meant to be that is vague, obscure, ambiguous, recondite, paradoxical, or subject to interpretation19 may require knowledge of the artist’s intentions to understand the identity of the work, and such things as those mentioned that complicate the issue of identity may be used by an artist to investigate the notion of artistic identity and the relation of objects to subjects. 1.7. Singling out more than one object, but not more than one artwork It does not follow from the fact that an artist singles out an object that a work of art is meant to be that no other object or objects is

18

This may be the case, for instance, with one of On Kawara’s date paintings. Is the referent of such painted language as JUNE 2, 1971 to be understood to be an object that all or part of an artwork is meant to be, or is the visible token of that date, as a particular perceptual and semantic object, to be understood to be a feature of an artwork of which the referent of that token is not similarly a part? 19 The language every heap in Finland might be used to single out every heap in Finland as a work of art. And that language seems perfectly deﬁnite in one sense in singling out any object that has the property of being a heap and the property of being in Finland, but may be thought to be conceptually vague in the sense that it is not clear in every case whether an entity is or is not a heap, and it may not be clear in every case whether or not a heap is in Finland rather than in, say, Sweden. Further, even if what is meant by “heap” can be made clear, and it is clear, for any heap, whether or not it is in Finland, the language may still be thought to be vague in that it is not clear that there is a deﬁnite answer to the question “Every heap in Finland when?” Similarly, the language every tragedy of the last 100 years is ambiguous because it is not clear if “tragedy” refers to an event of human history or to a play. Accordingly, if that language were used to single out every tragedy of the last 100 years as a work of art, it would not be perfectly clear what the work would be meant to be. Similar considerations apply to the use of assertions that are paradoxical or apparently paradoxical, such as that to which language cannot refer, to single out objects with which artworks are meant to be identiﬁed.

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thereby also singled out. Whether or not an artist singles out a diﬀerent object in singling out the object that the work is meant to be depends either on whether the object that the work is meant to be is referential, and so points beyond itself to something that it singles out, or it depends on whether the identiﬁcation of the work with the object that it is meant to be depends on singling out an object or objects other than that object to eﬀect that identiﬁcation. In any case however, in virtue of the identiﬁcation of an artwork with some object, the work is not to be identiﬁed with any diﬀerent object in addition to or in lieu of the object that it is meant to be whatever its identiﬁcation with that object involves.20 For instance, David’s The Death of Socrates is meant to be identiﬁed with the painting of a particular historical event and not with the historical event itself to which the painting nevertheless can be understood to refer. On the other hand, the referent of Barry’s language all the things I know . . . is to be understood to be the object with which a particular artwork is meant to be identiﬁed, and the work is not meant to be the language that is nevertheless singled out by Barry as the particular means by which the referent of that language is singled out—the language whose meaning is also singled out in any event of comprehending that meaning.21 1.7.1. Understanding which object an artwork is meant to be. If in making a work of art an artist singles out more than one object, then it must be understood with which delineated object the work is meant to be identiﬁed. In many or most cases this will be understood in virtue of a convention or conventions that ﬁts the particular method used by an artist to single out an object that an artwork is to be understood to be—a convention that ﬁts not only the production but the exhibition of the object. Thus we learn as part of our artistic

20 I am indebted to Clark Butler for directing my attention to the possibility, considered in this section, that an artist’s singling out an object with which an artwork is meant to be identiﬁed may involve singling out an object or objects with which the artwork is not meant to be identiﬁed. 21 By saying that the language utilized by Barry to single out a particular object is itself singled out, I mean that a particular type or token of referential language is used as the particular means of singling out the object that the work is meant to be, as opposed to some other type or token of referential language. And saying that the meaning of that language is singled out in an event of comprehending that meaning means that that meaning, rather than something else, is the object of the event of comprehending it.

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education that a representational painting—such as David’s The Death of Socrates—is the object with which the artwork of that title is meant to be identiﬁed, and not some object, state of aﬀairs, or event that it represents. And we understand that even though such a painting as the David is understood to refer beyond itself, or to single out a particular event of history. For novel cases though, which may include novel forms of exhibition, we may need to know what the artist’s intention is if it is not obvious what the work is to be understood to be. I think that it is obvious in the case of Barry’s language all the things I know . . . but not obvious in one of On Kawara’s date paintings, or in one of Joseph Kosuth’s billboard or magazine works. 1.8. Singling something out, the visual arts, and the arts in general I remind the reader that the purpose of this work is to identify what is required to produce artworks in which the limits of Abstraction are identiﬁed, and that this issue is approached from the standpoint of the visual arts, to whose history the question of the limits of Abstraction in art is intimately indebted, and from contemporary art forms, including Conceptual art, that have originated from that tradition. Accordingly, the notion of eﬀecting the identiﬁcation of a particular artwork with a particular object, that is, singling something out with which an artwork is meant to be identiﬁed—which is fundamental and ineradicable in any case—is approached from the standpoint of works of visual art, and from certain non-perceptible works that are indebted to the visual arts, the Abstract progression of which they can be understood to extend. I say that singling something out is basic and indispensable to art in any kind of art since someone who produces a work in a diﬀerent art form, such as music or literature, nevertheless produces an object by which some object that the artwork is to be understood to be can be eﬀected, and so is responsible for eﬀecting the identiﬁcation of a particular artwork with a particular object—whatever the ontological nature of that object is, and however it is related to any particular means by which that identiﬁcation is eﬀected. In addition, anyone who wished to investigate the limits of Abstraction, but who came from something other than a visual arts background, would have to undertake the same kind of investigations required from someone who comes from or is working within the visual arts tradition. These investigations

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would include the use of speciﬁcation in the determination of the more Abstract objects.

2. Artworks and apprehensible objects Something must be singled out determinately or indeterminately that all or part of an artwork is meant to be. However, any object that all or part of an artwork is meant to be may or may not itself be apprehensible. Although it must be possible to be aware of the determinate or indeterminate singling out, for any object that all or part of an artwork is meant to be, it is either true or false that it is possible to be aware of the object, either in any way that is relevant to comprehending its relation to the work, or at all. 2.1. Phenomenal and noumenal objects Most artworks are meant to be identiﬁed with objects of awareness, typically with things that are seen or heard. However, it is possible to single out objects that are meant to be artworks of which it is not possible to be aware. And it may be possible for diﬀerent kinds of Abstract limit to be determined in or identiﬁed through diﬀerent objects of one or the other kind of object. For these reasons, it is useful to introduce the terms ‘phenomenal’ and ‘noumenal’ to qualify certain kinds of object that are of importance to this investigation. The concepts of phenomenal and noumenal objects are deﬁned in relation to acts or events of awareness.22 More particularly, an object is phenomenal or noumenal relative to a particular event of awareness of a particular subject at the time at which that event occurs. Consciousness is multifarious in that there are many diﬀerent

22 I am using the terms ‘act’ and ‘event,’ as they pertain to consciousness, as synonyms, and an act or event of consciousness actually rather than possibly occurs. An Intentional state may be a conscious event or something that has the potential to become a conscious event as that state is a property of or forms part of a mind or brain or a series of mental or physical events to which the mind or brain is causally related. The metaphysics of consciousness and Intentional states and events is irrelevant to the concerns of this work, since the relevance to Essentialist Abstraction of kinds and forms of conscious event remains unchanged on any view of the nature of consciousness and its relation to the mind or brain.

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kinds of conscious act or event.23 Kinds of conscious event include not only such things as perceiving, recollecting, anticipating, aﬃrming, denying, doubting, and thinking in which it is possible to be aware of or to be Intentionally24 related to things in diﬀerent temporal aspects of reality, but include as well such things as apprehending, comprehending, conceiving, imagining, entertaining, and supposing, that, in concerning or being directed to such things as abstract, counterfactual, possible, or impossible entities, extend the range of consciousness beyond the existential reality in which it occurs and by which it is nevertheless informed.25 Certain kinds of event, including kinds of aﬀective event such as pains and anxieties, that lack direction beyond themselves and so are simply unstructured occurrences, are also kinds of conscious event, and whether or not higherorder events are directed to them, and whatever their metaphysical nature. 2.1.1. Diﬀerent conceptions of the future. That certain conscious events are directed to the future accommodates diﬀerent conceptions of the future. On one conception, the future is as real as the past is real. In this sense of the future, statements made in the present concerning things in the future have truth values when made, as statements made in the present concerning things in the past have truth values when made. And the statements have truth values apart from our 23 There are also ﬁve basic forms of conscious event. These will be identiﬁed in Part Three, Division II, 4 on pp. 175–185 below. 24 I follow John Searle’s practice in his work Intentionality of capitalizing ‘Intentional’ to distinguish it from ‘intentional’ as that term concerns deliberate action. The terms ‘Intentionality’ and ‘Intentionally’ are also capitalized as they too pertain to a property of certain kinds of conscious event. The identiﬁcation of this property and the deﬁnition of ‘Intentional’ in terms of it, as well as the diﬀerence between Intentional and non-Intentional events of awareness, can be found in Part Three of the book below. Searle, John Intentionality: An essay in the philosophy of mind, Cambridge: Cambridge Univ. Press (1983). 25 An event of conceiving of an impossible object, such as the round square, is informed by reality in the sense that the incompatible properties combined in the conception of the object are individually apprehensible in events of a kind appropriate to their apprehension, such as seeing, and in the sense that one must have a conception of any property that forms part of a conjunction of incompatible properties of which an impossible object is conceived to consist in order for an event of conceiving of that object to occur. Any such conception would either reﬂect or be causally related to some aspect of reality, as in empiricist epistemology, or would itself be a constituent of reality that could be manifested in consciousness, as in an innate idea. For further on impossible objects, and a suggested solution of the problem of impossible objects, see Appendix Four on pp. 353–365 below.

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ignorance of which truth value a particular statement pertaining to something in the future or past has. On the other conception of the future, the future is not real as the past is real. In this sense of the future, statements made in the present concerning things in the future lack truth values when made. As such, they diﬀer from statements made in the present concerning things in the past that have truth values when made, and do have these values whether or not we know what they are in every case. These diﬀerent conceptions of the future I call, respectively, ‘closed’ and ‘open.’ 2.1.2. Deﬁnition of phenomenal object. An object is ‘phenomenal’ relative to a particular event of awareness of a particular subject’s when the subject is aware of the object in that event, or when the event of awareness lacks an object other than itself but is itself an object of awareness. Anything of which a subject is now aware in any conscious event, such as an event of seeing, hearing, thinking, recollecting, or imagining is phenomenal for that subject relative to that event. Any conscious event, such as an event of pain, that lacks an Intentional object, but is itself something of which, or perhaps in which, the subject is aware, is phenomenal for that subject in the event that is that awareness. A non-Intentional event of awareness is an object in the widest sense of object, and it is a phenomenal object relative to the conscious event that is that object. A nonIntentional event of awareness, such as a pain or anxiety, is phenomenal since it is nonsense to assert that the event is occurring but that the subject whose event it is is not aware of it. For instance, it is nonsense for me to say that I am in pain—where pain refers to a feeling and not, say, to a neurophysiological condition to which the feeling is causally related—but I am not aware of my pain. Similarly, pain admits of degrees, and I must be aware of any pain that I am prepared to qualify adjectively by a term such as ‘mild’ or ‘severe.’ Phenomenal objects and awareness. The examples indicate that phenomenal objects and the events of awareness relative to which they are phenomenal may or may not be distinct. For instance, a tree seen is distinct from the event of seeing it, whereas a pain felt is indistinct from the event of feeling it. Accordingly, a phenomenal object is phenomenal whether or not it is equivalent to the event relative to which it is phenomenal.

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Phenomenal equality. An object may be phenomenal relative to two or more of a subject’s conscious events at the same time, and such events are phenomenally equal in the sense that each is an event in virtue of which the subject is aware of the object. For instance, I am equally aware of my keyboard in an event of seeing it and an event of touching it. Such phenomenal equality simply pertains to the fact of awareness, and does not concern the separate issue of the kind or amount of information that a subject can get about an object in a particular event of awareness of the object. Two or more phenomenal objects are also equally phenomenal, and they are so whether they are phenomenal relative to the same event, diﬀerent events of the same type, or diﬀerent events of diﬀerent types. 2.1.3. Deﬁnition of noumenal object. An object is said to be ‘noumenal’ relative to a particular event of awareness of a particular subject’s when the subject is not aware of the object in that event, whatever the nature of the object, and whatever the nature of the event of awareness. Anything of which any conscious subject is not now in any way conscious is noumenal relative to each of her current events of consciousness, such as an event of seeing, an event of touching, an event of hearing, an event of thinking, or an event of recollecting. And anything of which a subject is not currently aware in some event of awareness, such as seeing, of which she is aware in some other current event of awareness, such as recollecting, is noumenal relative to the event in which she is not aware of that object in that event. ‘Noumenal’ is thus a term that is meant to be synonymous with ‘non-phenomenal.’ That nothing of a Kantian nature follows from the use of ‘noumenal’ in this work can be understood from the deﬁnition of that term and from the remarks of the two following sections. The term is used to mark the second part of the distinction between something that is and something that is not something of which a subject is aware in a particular event of awareness at the time that the event occurs. For any event of awareness and any object, that event either is or is not Intentional. If it is Intentional, then the object either is or is not the Intentional object of that event. If the object is the Intentional object of the event, then it is phenomenal relative to that event. If the object is not the Intentional object of the event, then it is noumenal relative to that event. If the event is not Intentional, then the object either is or is not itself that non-Intentional event of awareness. If the object is the non-Intentional

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event of awareness, then it is phenomenal relative to the event that it is. If the object is not the non-Intentional event of awareness, then it is noumenal relative to the event that it is not. Nothing beyond what is indicated by these facts follows simply from their recognition. I have been talking about the phenomenality and noumenality of an object relative to an event or events of awareness of a single subject, but the same object may be phenomenal or noumenal relative to events of awareness of diﬀerent subjects. If several people are looking at a painting at the same time, then that painting is phenomenal relative to each event of seeing it at the time that those events occur. The same painting would be noumenal relative to all events then occurring that are not events of seeing the painting, such as events of hearing sounds in the gallery in which the painting is exhibited.26 Any object of which no one is in any way now aware is noumenal relative to all events of awareness that are now occurring. 2.1.4. The possible phenomenality and noumenality of the same object at the same time. The preceding example indicates that the same object can be phenomenal relative to one event of awareness and noumenal relative to another event of awareness when both events are current events of awareness. This is the case whether the diverse events of awareness belong to the same or diﬀerent subjects. I now see my desk and feel the chair beneath me. The desk is phenomenal relative to the event of seeing it and noumenal relative to the concurrent event of feeling the chair, and the chair is phenomenal relative to the event of feeling it and noumenal relative to the event of seeing the page. My desk and my chair are each noumenal relative to your awareness of this sentence. 2.1.5. Phenomenality and noumenality and the present. The terms ‘phenomenal’ and ‘noumenal’ have meaning in relation to events of awareness, and since when any event of awareness occurs it occurs at a time that is then the present, the predication of phenomenality or noumenality of an object is to be understood to be relative to a time that was, is, or will be the present, and so to a time in 26 Since paintings are meant to be seen, paintings only exist as the phenomenal objects that they are intended to be when they are the Intentional objects of events of seeing them. Thus an event of touching the canvas in which a painting is embodied is not an event relative to which the painting is phenomenal, rather, it is an event relative to which the paint of the canvas is phenomenal.

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or at which any event relative to which the predication of phenomenality or noumenality is made occurs. This understanding that diﬀerent times in history name diﬀerent presents then does not preclude the acceptability of talking about an object that was phenomenal or noumenal relative to a particular event of awareness at a particular time in the past when that time was the present, and does not preclude the acceptability of talking about an object that will or may be phenomenal or noumenal relative to a particular event of awareness at a particular time in the future when that time will be the present. These remarks are consistent with either a punctiform or intervallic conception of the present.

3. The notion of the identity of an artwork Any artwork must be meant to be identiﬁed with some object or objects, and it must be possible to understand that the artwork is meant to be that object, or that the object is meant to have the property of being the work of art. However, because from the fact that a particular artwork is meant to be identiﬁed with a particular object it does not follow that it must be possible to be aware of the object, in the sense of being directly conscious of the object as opposed to being aware that the artwork is meant to be identiﬁed with the object, it is useful to speak of ‘the identity of an artwork,’ as I have been doing. To apprehend the identity of an artwork is to understand with which object the work is meant to be identiﬁed, and whether or not that object can itself be apprehended. Matisse’s Bathers by a River is an example of an artwork that is meant to be identiﬁed with a certain perceptible arrangement of shapes and colors. In such a case it is possible to be aware of the object itself that the work is meant to be. The object that is conceptually delineated by the language everything of which you have never been and are not now aware is an example of a noumenal object that an artwork that is dependent on that language could be meant to be. Although it is not possible to be aware of this object, it is possible to understand that the object that is singled out by that language is what is meant to be the work of art. Because this is the case, and because the linguistically delineated object could be meant to be a work of ﬁne art that is indebted to certain works and movements in the history of ﬁne arts preceding it, including those of

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Minimalism and Conceptualism, Richard Wollheim’s view that “. . . the identity of a work of ﬁne art resides in the actual stuﬀ of which it consists” is not true in every case.27 For Wollheim, a work of “ﬁne art,” such as a Rauschenberg combine, is to be identiﬁed with and not just through what we perceive in perceiving such an object. A work of ﬁne art contrasts with an artwork, such as a poem, that can be apprehended and interpreted in diﬀerent places and at diﬀerent times in virtue of the conforming of diﬀerent apprehensible objects to a common structure.28 These apprehensible objects are relevant to comprehending the identity of the work, e.g. one reads the words of a poem to know what the poem is, and diﬀerent words of diﬀerent poems enables us to distinguish the poems. The apprehensible objects of the second kind of artwork may be of diﬀerent kinds, such as written or spoken language, and diﬀerent objects of the same kind may have diﬀerent properties, as when the words of a poem are written by hand or typed, or are printed in black or red ink. In any case, this second kind of artwork does not reside in the material whose apprehension acquaints us with the work. Both the language of a poem and the lines of a drawing are marks on paper, but the latter and not the former work resides in the actual stuﬀ of which it consists. Accordingly, the latter but not the former is a work of ﬁne art in Wollheim’s sense. According to Wollheim’s view, an object that is conceptually delineated by a speciﬁcation, as in the preceding example, could be said to be like a poem in the sense that copies and reproductions of the language on which the identity of the artwork is dependent have a common conceptual structure that provides for possible apprehension of the identity of the work. However even if that were maintained, the earlier point that such a work is a counterexample to his assertion about the identity of any work of ﬁne art remains. It should also be understood that one might apprehend an apprehensible object with which an artwork is meant to be identiﬁed without understanding that the artwork is meant to be identiﬁed with that apprehensible object. Accordingly, apprehending an apprehensible object that an artwork is meant to be is not a suﬃcient condition of understanding that the artwork is meant to be that apprehensible 27 Wollheim, Richard “Minimal Art,” in Battcock, Gregory (ed.) Minimal Art: A Critical Anthology, New York: E. P. Dutton & Co. (1968). Quote p. 391. 28 Wollheim, Richard “Minimal Art,” pp. 390–391.

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object. For instance, one could apprehend a certain snow shovel and not be aware that an artwork called In Advance of the Broken Arm is meant to be identiﬁed with that object. One does not apprehend the identity of an artwork in apprehending any apprehensible object that the work is meant to be unless, when apprehending the object, one understands that the artwork is meant to be that object. Such understanding could be implicit, or something of which one is as conscious in attending to the apprehensible object as one is of that object. Apprehending an apprehensible object that an artwork is meant to be is also not a necessary condition of understanding that the artwork is meant to be that object if the understanding that the work is meant to be that object can be eﬀected apart from apprehending the object. This possibility will be discussed in Part Three. 3.1. The logical and epistemological aspects of an artwork’s identity The notion of the identity of an artwork has both a logical and an epistemological aspect. The logical aspect pertains to the artwork’s haecceity, which is the unique property that it has of being the particular object that it is. The epistemological aspect of the notion of the identity of an artwork pertains to understanding with which object or objects the artwork is meant to be identiﬁed, and whether or not any object that the work is to be understood to be is or can itself be apprehended in any way that is relevant to that understanding. When the identity of a particular artwork is apprehended, that identity is at least tacitly epistemologically distinguished from all objects that lack that identity, and so the identity of an artwork is singled out epistemologically in an event of apprehending that identity. The latter aspect implicitly involves the former aspect, and when the identity of an artwork is apprehended, the two aspects of its identity make the work conceptually distinct from all objects that lack that identity. An artwork’s identity has no necessary ontological aspect since an artist could specify an object to be an artwork that neither exists nor subsists.

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3.2. The identity of an artwork and phenomenal and noumenal objects The identity of an artwork is the object as intended to be that work of art by the artist whose work it is. Or the identity of an artwork is the object that the work of art is meant to be as meant by the artist whose work it is. These are equivalent ways of saying that an object can only have the property of being a particular work of art, or can only have the identity of a particular work of art, if the work is intended or meant to be that object by the artist whose work it is. That an artwork a is meant to be an object x by an artist s means that s intends a to be understood to be x and x to be understood to be a. To understand the identity of an artwork is to understand with which object the work is meant to be identiﬁed. Understanding the identity of an artwork is consistent with the possibility of being aware of the object itself that the artwork is meant to be, as in a painting or sculpture, not being aware of that object, or not being able to be aware of the object. Examples of the latter two kinds of object are given in the last paragraph of this section. It must in any case be possible to be aware of the identity of an artwork. When one is aware of the identity of an artwork one is aware that the work is meant to be identiﬁed with a particular object, and that is the case whether or not one is or can be aware of the object itself that the work is meant to be. A noumenon in the original sense of the term is something that is conceived of or apprehended in or by thought rather than something that appears in perception. Although something that is conceived of, or that is apprehended in or by thought, counts as phenomenal rather than as noumenal as these terms are used in this work, a reason that I have chosen to use ‘noumenal’ rather than ‘non-phenomenal,’ in addition to its brevity, is because of the fact that an artist can intend an artwork to be identiﬁed with an object of which a subject is not aware—a noumenal object—at the same time that it is possible to be aware that the work is meant to be that noumenal object. Use of the term ‘noumenal’ for noumenal artworks is meant to recognize that one is aware of the identity of a noumenal artwork—an artwork that is meant to be identiﬁed with a noumenal object—in an event of comprehending that identity, and that comprehension is intellectual. This apprehension of that identity in the thought or intellectual event that is the comprehension of that

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identity preserves something of the original meaning of the term. However, the novel use of ‘noumenal’ as equivalent to ‘non-phenomenal’ as deﬁned indicates that one cannot be aware of a noumenal object that an artwork is meant to be, but can only be aware that the work is meant to be that object, so that one does not apprehend in thought a noumenal object that a noumenal artwork is meant to be. Rather, one apprehends in thought the intended identiﬁcation of the noumenal artwork with a noumenal object. Artworks can be identiﬁed with diﬀerent kinds of noumenal object relative to phenomenal objects on which understanding the intended identiﬁcation of the works with the objects depends. An object that is noumenal relative to an event of comprehending the intended identiﬁcation of an artwork with that object may yet be phenomenal relative to some other event or events of awareness, either in the history of awareness of the subject who comprehends the intended identiﬁcation, as in something of which you are not now aware but of which you will later be aware, or in the history of awareness of some subject or subjects other than the subject who comprehends the intended identiﬁcation, as in anything of which you are not now aware of which someone else who is now aware is now aware. An object that is noumenal relative to any event of awareness, and so too to an event of comprehending the intended identiﬁcation of an artwork with that noumenal object, could also meant to be a work of art, as in anything of which no one who is ever aware is ever aware. These examples illustrate that, when one is aware of the identity of an artwork that is meant to be identiﬁed with a noumenal object, one is not thereby aware of the object itself that the work is meant to be. It remains noumenal. Instead, one is aware that, understands that, the work is meant to be identiﬁed with the noumenal object. What is then phenomenal for the subject who comprehends the intended identiﬁcation of an artwork with a noumenal object is the identity of the work. A noumenal object that an artwork is meant to be stands outside any ﬁeld of awareness that includes an event of comprehending the intended identiﬁcation of the artwork with that noumenal object.

4. The minimal conceptual relation of artist to artwork The minimal conceptual relation that an artist must have to her artwork is being responsible for eﬀecting the comprehensible identiﬁcation

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of the work with a determinate or an indeterminate object. Any such identiﬁcation eﬀected indicates that the artist has met the requirement of making it understandable which simple or complex object the artwork is to be understood to be, even if the singling out is indeterminate as deﬁned, and even if any object with which the artwork is meant to be identiﬁed cannot itself be apprehended, or is solely noumenal and never phenomenal, as the terms ‘noumenal’ and ‘phenomenal’ are used in this book. 4.1. No artwork without an identity That an artist must be responsible for singling something out, or for making it possible for an object to be singled out that an artwork is to be understood to be, reﬂects the fact that, before the content or meaning or value of a work of art can be considered; before the work can be judged or interpreted; before its precedents can be determined; before its place in history can be assessed; and before it can be responded to in any way made possible by or consistent with the nature of the work, it must ﬁrst be understood with which simple or complex object the work is meant to be identiﬁed. Thus an artist’s making it understandable which simple or complex object it is that an artwork is to be understood to be is philosophically fundamental and ineradicable, and constitutes an epistemological singling out of the identity of the artwork. Such an understanding pertains both to singling something out determinately and to singling something out indeterminately. Although it need not be possible to be aware of an object that an artwork is meant to be, it must be possible to be aware that the artwork is meant to be identiﬁed with that object, otherwise no identiﬁcation of the work has taken place, and so no object has the property of being the work. Here Quine’s “No entity without identity” can be adapted to our concerns by saying “No artwork without an identity.” Unless some object is conceptually delineated as some work of art—marked oﬀ logically and epistemologically from every other object—according to standard or novel means of production, then no talk or thought of the work would be possible, since there is nothing that any talk or thought could concern. Thus at the very minimum, an artist, in making a work of art, must be responsible for determining the identity of the work, that is, determining with what the artwork is meant to be identiﬁed.

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part two 5. Two kinds of required intentional relation of an artist to an artwork

An artist who means to make a work of art must be intentionally related in two senses to any object that she means all or part of the work to be. In the ﬁrst sense, the artist must intend that the object be singled out as a work of art. In the second sense, the artist must intend that the delineated object be understood to be an artwork by that artist.29 Although one can produce an object accidentally—including one of which no one is aware—one cannot single something out accidentally. Rather, one must mean for that which is singled out to be capable of being understood to be singled out—including by people other than the artist—otherwise—because the identity of an artwork is equivalent to some conceptually delineated object—one could not interpret, appreciate, or respond in any way to the artwork that presupposes that delineation. Singling something out thus presupposes the intent to discriminate something in such a way that that which is discriminated can be understood to be identiﬁed as a particular thing of a certain kind of thing.

29 To intend to do something is to mean to do it, and to do something intentionally is to do it deliberately. To speak of a subject’s agency is to speak of her intentionally doing the kinds of thing—such as choosing, deciding, and acting— that agents are typically thought to be capable of intentionally doing. Something that an agent does intentionally she does at a time that is then the present. When subjects act intentionally or act agentially, that is, as agents, they are said to be responsible for their actions. Subjects are also taken to be responsible for their choices and decisions since they are thought to make them freely. Whether things that agents are thought to do intentionally are free or not, in the sense in which “free” concerns the free will versus determinism debate, is of no relevance here since certain things that are required of making and apprehending works of art that are commonly called ‘intentional’ are required in any case. And it is worth keeping the terminology to diﬀerentiate things that are commonly called ‘intentional’ from things—such as those that are accidental or coerced—that are not in any way intentional. In addition, an agent apparently chooses, decides, and acts freely in the process of intentionally constructing a work for which he is responsible. And an agent seems to exercise her freedom in choosing to attend to a particular artwork or to an object on which apprehension of the identity of the work is dependent, in deciding to attend to it from a certain angle and distance, and in acting in accordance with such a choice and decisions. Accordingly, the manifest nature of such things would allow us to discriminate, within awareness, those things that are taken to be intentional from those things that are not, whatever the correct metaphysical picture of reality.

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5.1. The artist’s conscious understanding of each kind of relation Each kind of intentional relation of artist to an object meant to be an artwork noted presupposes the artist’s basic conscious understanding of the kind of thing to which each intentional relation is relevant, namely to intended discrimination of a certain sort of thing and to the particular identiﬁcation of such a thing discriminated. When an artist intends to produce a work of art she is conscious of that intent, and when she means for the object produced to be a work of art she is conscious of her intent that the object be so understood. Entities that lack consciousness cannot produce works of art, and entities that are conscious but are not continuously conscious can only produce works of art in periods of consciousness in which the production of works can be conceived of; and the intended identiﬁcation of things as ﬁnished works of art requires episodes of consciousness in which that classiﬁcation can be articulated. 5.2. Implicit and explicit claims that certain objects are artworks That an artist intends that an object to which she is intentionally related in the ﬁrst sense be understood to be an artwork by that artist constitutes a claim by the artist that that object is to be so recognized. This claim may be made implicitly or explicitly, depending on the novelty of the object and its relation to the artworld and its established practices, but the claim must be understandable for the object singled out to be understood to be a work of art by the artist claiming that status for the object. A claim that a painting is a work of art is made implicitly by hanging the painting on a wall of a gallery or museum and placing the title of the work and the name of its producer next to it. A claim that a remote and ephemeral earthwork is a work of art might be made explicitly through appropriate public presentation of written and photographic documentation of the work that includes its title and the name of the artist responsible for it. 5.3. Time and intentional relations of an artist to an object meant to be a work of art An artist’s intent to single out an object and her intent to identify a work of art with that object can characterize the artist at either

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the same or diﬀerent times, and so the two aspects of the intentional relation of an artist to an artwork may or may not be temporally separate.

6. Artworks, aesthetic objects, and intentional actions A person who means to make art must be intentionally related to an object in the two ways indicated. However, a stronger claim might be made that, for any artwork to be identiﬁed with some object, and whether or not any object was that object before the artwork is identiﬁed with it, the artist whose work it is must intend for the work to be understood to be that object. This second point precludes the possibility of an artifact becoming an artwork, rather than possibly an aesthetic object, if the producer of the artifact has not intended that it be understood to be a work of art.30 Such a position might be challenged. If the link between artistic intention and artifact is severed, then someone other than the artiﬁcer of an artifact can claim that the artifact should be understood to be a work of art by its original producer—and not to be a work of art that someone other than the original producer selects or speciﬁes to be her work of art—and so the consciousness and agency of some person or persons other than the artist becomes relevant to so classifying the artifact. This would complicate the possibilities of making art, and would require that we distinguish between objects that are produced with the intention that they be understood to be works of art and objects whose initiation was not preceded or accompanied by such an intention. The latter kind of object could then only come to be understood to be a work of art by a subsequent claim that it should be so regarded. 6.1. Intentional actions and novel artworks In any case it can be more generally asserted that any work that is meant and understood to challenge accepted notions of what con30 Here the use of “artifact” reﬂects its common meaning of being something humanly created for some purpose and, as such, to be distinguished from a natural object that is not the product of human intention. On artworks and artifacts in general see Part Two, Division IV, 8 on pp. 119–120 below. On the liberal use of objects to eﬀect artworks see the next section.

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stitutes an artwork—such as a readymade or a work of Conceptual art—depends on the artist whose work it is both to intend that a certain unconventional object be understood to be a work of art and to make it clear that this is the case. Had Duchamp purchased the original snow shovel that became In Advance of the Broken Arm but never made his intention known that he meant the snow shovel to be identiﬁed with the work of that title, then the work of that title never could have entered the history of art. And had Robert Barry written Everything in the unconscious perceived by the senses but not noted by the conscious mind during trips to Baltimore during the summer of 1967, but not made it clear that he intended the referent of that language to be understood to be a work of art, then one could not be certain of the relation of the language and its referent to a particular work of art.

7. The liberal notion of the use of objects and the direct and indirect relation of an artist to an object used to make an artwork Although an artist must in any case intend to produce an artwork; must use at least one preexistent object to produce an artwork; must act in some way with such an object so that something is singled out; and must take responsibility for identifying that which is delineated with a particular work of art; the idea of using an object, as it concerns making art, is supposed to have wide latitude, and to include the employment, application, and manipulation of an object in any way in which that object can be employed, applied, or manipulated to ﬁgure in the production of a work of art in a kind or kinds of production earlier identiﬁed. And that someone may act at an artist’s direction, or according to her plans or written instructions, to produce an artwork that complies with the intent and conception of the artist whose work it is, means that an artist’s relation to the use of an object that ﬁgures in the production of a work of art may be indirect, depending on the nature of the object and its relation to the work and the intent of the artist. Use of an object may constitute nothing more than choosing and exhibiting the object as that which an artwork is meant to be, which is what Duchamp did in producing his unassisted readymades. And the use of an object of this kind of use could be eﬀected by the artist whose intention it is to produce a work through this method,

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or it could be eﬀected by someone acting on behalf of the artist at the artist’s direction. An artist might say to his assistant, “I want you to go to the store and buy any ﬁve things,” and then intend that a work of his—the artist’s—consists of the objects purchased by his assistant. The ﬁrst use of choice to single out an object with which an artwork is meant to be identiﬁed is direct, and the second is indirect. However, in each instance the artist conceives of and initiates the use of choice to determine the artistic status of a particular selected object. Or an artist might use a pencil to make a single point at the center of a piece of paper, a single point that she means all or part of an artwork to be. And this is something that she may either do herself, or she could ask a studio assistant to do it for her at her direction. The ﬁrst use of the preexistent artifact is direct and the second is indirect, but in each instance the artist conceives of and initiates the use of the pencil and takes responsibility for the work to which the single point is relevant. And an artist may herself manipulate paint to create a non-objective ﬁeld of color or the image of a cloud, or may direct an assistant to do either of these things for her. The ﬁrst manipulation is direct and the second is indirect, but, again, the artist conceives of and initiates the manipulation of the paint and takes responsibility for the work of which either the ﬁeld or the image constitutes the whole or a part. 7.1. Artworks and the products of accidental actions Speaking of an artist’s direct or indirect use of or relation to an object on which the identity of an artwork is dependent speaks to the artist’s intention that such an object ﬁgure in the identiﬁcation of the work with some object. However, this does not preclude the possibility that an accidental eﬀect that results from the use of such an object is subsequently taken by the artist to constitute all or part of an artwork to which the use that results in the fortuitous eﬀect is historically related. An accidental eﬀect of any act meant to result in an object with which all or a part of a work of art is meant to be identiﬁed may itself become the object with which all or a part of a work is meant to be identiﬁed. However, if it does so it does so through a subsequent intention of the artist that this be understood to be the case. (It should be noted that there is a diﬀerence between doing something that is meant to produce unpredictable

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results, and doing something that is not meant to produce an unpredictable result but from which something unpredictable results.)

8. The dependence of artworks on artistic intentions and cultural contexts Artworks are extremely diverse, are frequently novel in form and content, and do not, as objects divorced from intentions and appropriate cultural contexts, form a recognizable kind. I mean that artworks are not discoverable natural or non-natural kinds, and the recognition of an object as an artwork requires a cultural tradition of singling out objects as artworks in relation to which a discriminated object meant to be so recognized can be so recognized, and where such singling out can be eﬀected either according to established or novel practices of artistic discrimination, but where, in any case, there must be a cultural framework within or in relation to which any intended discrimination can be recognized as intended. Artworks are objects that are meant to function culturally as artworks, and that cultural function cannot be deduced from a material description of any object on which the identity of an artwork is dependent. If a physicist could give a complete physical description of a sculpture, we could not deduce from that description that it is a work of art, any more than one can deduce from reading an economic appraisal of an object that the object appraised is a work of art.31 Even more telling, we cannot deduce from the perceptual properties of an object alone, no matter how aesthetically appealing they may be, that the object is a work of art in addition to being an aesthetic object. We must know that the object has intentionally been singled out as the object with which a particular artwork is meant to be identiﬁed, and we must know that the object is intended to be seen as a work of art before we can respond to it as a work of art. If Guernica had come into existence due to physical processes that had no relation to human intention, or had simply come into

31 Cf. John Searle: “[F]unctions [of objects] are never intrinsic to the physics of any phenomenon but are assigned from the outside by conscious observers and users. Functions, in short, are never intrinsic but are always observer relative.” (His italics.) Searle, John, The Construction of Social Reality, New York: The Free Press (1995) p. 14.

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existence ex nihilo then, although we might respond to it aesthetically, we would be prohibited from classifying it as a work of art since it would not have resulted from the kinds of intentional action necessary for such a classiﬁcation to be eﬀected.32 For an object to be an artwork in the art-historical sense, and so oﬀered to the artworld for consideration, both kinds of intention must be operative. If one wants to exhibit the limits of Abstraction in art one must intentionally produce artworks in which those limits are meant to be exhibited. As we are talking about artworks in the historical sense of that term, this will include the intention that any perceptual object on which the identity of any particular artwork is dependent be deliberately placed in a legitimate ﬁne-arts context or otherwise made public in such a way that the intended exhibition of those limits can be recognized by the artworld. 8.1. Abstraction, lack of artistic action, and publicity It is not possible for a person to determine a limit of Abstraction by both doing nothing and not intending that her doing nothing be understood to determine a limit of Abstraction—and where a person’s doing nothing represents her neither engaging in any kind of behavior personally, nor initiating any kind of behavior in another at her direction, that is meant to produce an object with which an

32 That works of art are objects that are intentionally produced is a widely accepted notion in philosophy of art. For instance, George Dickie says that “[A]rtmaking is an intentional activity: although elements of a work of art may have their origin in accidental circumstances which happen during the making of a work, a work as a whole is not accidental.” The Art Circle, p. 80. Richard Wollheim writes: “If we wanted to say something about art that we could be quite certain was true, we might settle for the assertion that art is intentional. And by this we mean that art is something we do, that works of art are things that human beings make.” “The Work of Art as Object,” in Harrison, Charles and Orton, Fred (eds.) Modernism, Criticism, Realism: Alternative Contexts for Art, London: Harper & Row (1984) pp. 9–17. Quote p. 10. Monroe Beardsley says that “To be a genuine work of art, an object or arrangement must be something for which some person or group of persons takes responsibility, stands behind. Without that we are back to nature.” And Randall Dipert maintains that “The attribution of some intentions to a creator of the object ﬁrmly separates regarding an object as an art work from regarding it as a nonartistic aesthetic object.” Both Beardsley and Dipert are quoted by Stephen Davies in his Deﬁnitions of Art, Ithaca, NY: Cornell Univ. Press (1991) p. 159. That there can be no artwork without a prior intention is true of all works, including those that are produced by the use of chance operations. See Tormey, Alan “Indeterminacy and Identity in Art,” The Monist 58 (1974) pp. 203–215.

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artwork is meant to be identiﬁed—since, barring a claim by the person who does nothing that her doing nothing is to be understood to constitute a work in which a limit of Abstraction is determined, her lack of artistic action cannot be so understood, and so could not be discriminated from any myriad number of other actions of other people that are not linked to artistic intentions. An artist could only claim that her doing nothing was to be understood to represent a work of art in which a limit of Abstraction is meant to be determined, but that claim—which itself is something, not nothing—then deﬁnes a comprehensible work in relation to a life in which any action meant to produce a diﬀerent kind of object with which an artwork could be identiﬁed is lacking, and what is so comprehended in comprehending the claim is also something, not nothing. A person also cannot produce something in which a limit of Abstraction is meant to be exhibited with the intent that the object in or through which the limit is exhibited never be made public. He might intend this for thinking that something like an idea conﬁned to a mind is more Abstract than either any public perceptual object in which an artwork is embodied or any artwork that is indebted for its identity to such an object. However, I am treating the issue of determining the limits of Abstraction in art as a project of cultural importance that forms part of the history of art, and since an artist’s producing something that is never known to anyone else is indistinguishable, for everyone but the artist, from the artist’s not producing anything at all, the thing produced—an idea, for instance— could not enter the history of art and could have no cultural signiﬁcance. Instead, an idea conﬁned to a mind in this way would be merely egocentric and insipid. To summarize: Because artworks presuppose the kinds of intentional action listed, one cannot reach a limit of Abstraction by doing or making something but not intending that the something done or made be regarded as a work of art; one cannot reach such a limit by simply doing nothing; and one cannot reach a limit of Abstraction in art by doing or making something intended to be art if it is not made publicly understandable to the appropriate audience that what is produced through doing or making is to be so understood.

DIVISION II: ARTISTS, OBJECTS, AND MINIMUM CONDITIONS OF ARTISTIC IDENTITY

1. The dependence of artworks on preexistent objects An artist must utilize at least one object that existed prior to his intention to produce a work of art in order to produce a work of art. Accordingly, no object can have or acquire the property of being a work of art that is not indebted to an object that existed prior to the identiﬁcation of the artwork with the object that it is meant to be. Any preexistent object that is utilized to produce the work is either an object, such as a camera or ﬁlm, that is utilized according to some practice relevant to the origination of an object of the kind of object dependent on the practice, or it is an object, such as the body or mind, on which the use and/or understanding of the use of an object to make art depends. The second kind of object must be paired with at least one object of the ﬁrst kind of object that is suited to the production of the kind of work intended if the second kind of object is either the mind or is the body, when the body is not directed to itself to eﬀect an object that an artwork is meant to be, as in the example of Body art given below. Further, any object that is used in a particular act of use to produce a particular work of art is that object before that act is that act. 1.1. The minimum number of preexistent objects required to make artworks depends on the metaphysics of personhood Whether or not a single preexistent object can be both the object used to produce an artwork and the means by which the use of that same object is conceived of and eﬀected depends on whether or not any monistic metaphysics is adequate to the concept of a person. If either a materialistic or an idealist metaphysics is defensible, then Vito Acconci, for instance, produced his work Rubbing Piece by using the same single existential entity on which the understanding of the use of that object depended, namely his body, including his brain. On the other hand, if some version of dualism is true, then he utilized his mind or mental properties in addition to his body to produce

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this work.1 The thesis of section 1 preceding is written to accommodate the possibility of taking a materialist or an immaterialist view of persons, so that a single entity might be used to eﬀect a work of Body art. If either dualism or neutral monism is the correct metaphysics of reality, then the ﬁrst line of that thesis should read: “An artist must utilize at least two objects that existed prior to his intention to produce a work of art in order to produce a work of art,” where at least one object would be the mind and at least one object would be the body of the artist. This is the case even on the assumption of the truth of neutral monism since the neutral entities of which minds and bodies consist are diﬀerently arranged to constitute the diﬀerent entities on which making art depends. I would say the same of the entities of panpsychism, that, diﬀerently combined, constitute bodies and minds. 1.2. Metaphysics, acts, and objects used in producing art Assuming a materialist or immaterialist metaphysics, any two or more entities that ﬁgure in the production of a particular artwork may be of the same or diﬀerent kind of physical or mental entity. If either of these monistic metaphysics is untenable, then at least two entities that ﬁgure in the production of a particular artwork must be of diﬀerent kinds since one must be mental and the other physical. Any two or more acts that ﬁgure in the production of the artwork may be of the same or diﬀerent kinds—an act of painting, an act of scraping, an act of gluing—and whether or not any act of any kind of act is mental, physical, or mental and physical. Henceforth it should be understood that two or more objects utilized in the production of an artwork may be of the same or diﬀerent kinds, as may be any two or more acts of a kind of act that can ﬁgure in the production of an artwork.

1 Carter Ratcliﬀ describes Acconci’s production of Rubbing Piece utilizing Acconci’s own language pertaining to the execution of the work: “In 1970, he presented Rubbing Piece on a Saturday afternoon at Max’s Kansas City: ‘Sitting alone in a booth, during the ordinary activity at the restaurant. With my right hand, rubbing my left arm, gradually producing a sore.’” Here Ratcliﬀ says that “Acconci the physical being was material for Acconci the artist.” Ratcliﬀ, Carter Out of the Box: The Reinvention of Art, 1965–1975, New York: Allworth Press (2000) p. 193.

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2. That an artwork must be something singled out does not dictate the nature of what is singled out We must be able to understand in any case with which object a work of art is meant to be identiﬁed, but that requirement places no limits deducible a priori on such things as an artwork’s existential status; its perceptual vagueness or ambiguity; its conceptual vagueness or ambiguity; its simplicity or complexity; any similarity or diversity of its parts if it is complex; a range of spaces or times that it may or may not occupy, and hence any spaces necessary to traverse or the lengths of time required to apprehend it; or the separation of its parts if its elements are disconnected in space or time or space and time. However, we must in any case be able to ascertain, and within a certain range of indeterminacy for certain kinds of object, what is and what is not a particular work of art and what is and what is not part of the work, if the work has parts. And by knowing with which object or objects an artwork is meant to be identiﬁed we know to what we are to pay attention and what we are to ignore.2

3. The history of an object with which an artwork is meant to be identiﬁed For any object that a work of art is meant to be—and whether or not that object is equivalent to any perceptual object on which apprehension of the identity of the work is relevantly dependent—it is either true or false that some object had the property of being the object that the work is meant to be before any object comes to have the property of being the work of art.

2 Given the preceding and earlier points it should be kept in mind that, where ‘object’ is used in the singular in what follows, it is to be understood to include an object of any kind and degree of complexity, and so to include, without being limited to, complex temporal or spatio-temporal objects whose parts are not temporally or spatio-temporally contiguous.

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If no object is the object that an artwork is meant to be before some object is that work of art, then the object that the work is meant to be depends on at least one preexistent object that is utilized in at least one act of use, and where such an act either characterizes the biography of the artist responsible for identifying the work with the object that it is meant to be, or characterizes the biography of a person or persons acting on behalf of and at the direction of the artist. This formula ﬁts traditional and many modern and contemporary works. Examples include Turner’s The Lake of Zug, Man Ray’s The Enigma of Isidore Ducasse, and Dennis Oppenheim’s Gallery Transplant. It also ﬁts an object speciﬁed to be an artwork that originates from an event of comprehending a speciﬁcation that refers to it. An example is anything that results from your current comprehension of this information.

5. An artwork has its particular identity in spite of any degree of similarity that it has to any other object The object that an artwork is meant to be may be similar, very similar, or qualitatively indistinguishable from some other object that the work is not meant to be, depending on the nature of the work of art. However, in any case only the object that the work is meant to be is and can be the work. Accordingly, notwithstanding any property or properties that an artwork has in common with any other object, only that artwork has and can have the property of being that particular work of art. For instance, at the time of the origination of Marcel Duchamp’s In Advance of the Broken Arm, the artwork of that title was perceptually indistinguishable from the object on which it was originally dependent, but that snow shovel, prior to Duchamp’s selecting and intending it to be a particular work of art, lacked the property of being the artwork of that title. And both prior to and subsequent to the time of the origination of the same work, other snow shovels were perceptually indistinguishable from the artwork, but lacked the property of being the work from which they could not be visually distinguished.

DIVISION III: ARTISTIC IDENTITY, SUBJECTS, AND APPREHENSIBLE OBJECTS

1. The dependence of the identity of an artwork on an apprehensible object An artist must be responsible for eﬀecting the identiﬁcation of an artwork with some object. Although the object itself that the work is meant to be need not be apprehensible, eﬀecting the identiﬁcation of the work with the object depends on the use of at least one apprehensible object. 1.1. Speciﬁcation and objects that are meant to be artworks that cannot be apprehended Artworks are typically meant to be identiﬁed with apprehensible objects, such as paintings and symphonies. Such works are not only meant to be apprehended, but depend on such apprehensible entities as paint and brushes to be eﬀected. However, it need not be the case that the object that a work is meant to be is itself apprehensible, rather than the intended identiﬁcation of the work with the object being apprehensible, as in that of which no one who is ever aware is ever aware. When this is the case, then eﬀecting the identiﬁcation of the artwork with the object depends on the use of an apprehensible speciﬁcation.

2. The dependence of knowledge of the identity of an artwork on an apprehensible object Although the object that an artwork is meant to be may or may not be apprehensible, it must be possible to understand the intended identiﬁcation of the work with the object. If the object that an artwork is meant to be cannot itself be apprehended, then it must be possible to apprehend some object through which the intended identiﬁcation of the artwork with the object is made comprehensible.

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3. Relevant apprehension of the apprehensible object on which knowledge of the identity of an artwork is dependent To apprehend the identity of an artwork, any currently apprehensible object with which the work is meant to be identiﬁed, or through or in relation to which apprehension of the identity of the work can occur, must be apprehended in any way relevant to the work’s identity as intended by the artist whose work it is. 3.1. Relevant apprehension of an apprehensible artwork If an artwork is meant to be identiﬁed with an apprehensible object when and only when that object is apprehended in any way relevant to the intended identiﬁcation of the work with the object, then it must be possible to apprehend the object in any way required to make comprehension of the identiﬁcation of the work with that object possible. Pollock’s Autumn Rhythm is an example of an artwork that is meant to be identiﬁed with a certain apprehensible object, and not with a set of mind-independent physical entities on which both the existence of that object and its perception are nevertheless dependent. Further, the apprehensible object with which Autumn Rhythm is meant to be identiﬁed is the perceived canvas of that title, and one can comprehend the identiﬁcation of the work with that object in virtue of apprehending it in the kind of awareness in which it is intended to be apprehended, namely sight, and not, for instance, touch. To comprehend the intended identiﬁcation of an artwork with the referent of the speciﬁcation anything that you are currently apprehending you must see and read the speciﬁcation that singles out that object. 3.2. The dependence of an artwork that is meant to be identiﬁed with a non-apprehensible object on an apprehensible object If an artwork is meant to be identiﬁed with an object of which it is not possible to be aware—either in any way in which its relevance to the work could be comprehended, or at all—then it must be possible to be aware of some object by which that intended identiﬁcation can be made comprehensible. For instance, in order to comprehend Robert Barry’s intended identiﬁcation of an artwork with the object delineated by the lan-

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guage all the things I know . . ., it must be possible to apprehend something, such as a token of Barry’s language, that will make the identity of the work comprehensible. 3.3. Understanding the relation of an apprehensible object on which the identity of an artwork is dependent to that identity Not only must it be possible to be aware of an object on which the understanding of the identity of an artwork is dependent, but it must be possible to understand the relevance of the object to that identity, or it must be possible to understand the dependence of the understanding of the identity of the artwork on the apprehension of the object. Thus it must be possible to understand the relevance of the perceptible image of Matisse’s The Piano Lesson to the artwork of that title, and it must be possible to understand the relevance of a token of Barry’s all the things I know . . . to the artwork meant to be identiﬁed with the delineated object of that language.

4. The artistic identity of an artwork and its relevance to the ontology, meaning, and value of an artwork An artist may eﬀect the identity of an artwork by intentionally creating, selecting, or specifying an object that the work is meant to be, or by doing a combination of these things, and then making it understandable that the work is meant to be that object. An artist may also eﬀect the identity of an artwork by instructing someone to create, select, or specify an object on her behalf, or by instructing someone to do a combination of these things on her behalf, and then making it understandable that the work is meant to be the object that is linked to her instruction. In any case, the artist is intentionally related to an object that an artwork is meant to be both in intending the object to be singled out and to be understood to be singled out as that work. As earlier indicated, the identity of an artwork as meant and determined by the artist whose work it is the artistic identity of the artwork, and any consideration of the ontology, meaning, and value of an artwork presupposes the artistic identity of the artwork. In particular, even if philosophy can establish that what the artwork is, ontologically speaking, is diﬀerent from

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what the artist intends the work to be, the artistic identity of an artwork remains the same. 5. The dependence of the identity and the apprehension of the identity of an artwork on a public perceptual object Any object on which the identity and the apprehension of the identity of any artwork is originally dependent must be a public perceptual object. However, an artwork may or may not be meant to be identiﬁed either with any such perceptual object or with a particular perceptual property or properties, whether of that or some other object. Certain things produced by Robert Irwin in the early 1970s, such as Retinal Replay Volume, were an attempt to get beyond objects, at least to get beyond the kind of relatively stable and enduring perceptual objects, such as paintings and sculptures, with which visual artworks have been traditionally identiﬁed. These were things that Jan Butterﬁeld said were “ephemeral and ‘invisible.’”1 As Butterﬁeld put it, “Irwin was faced with a problem of his own making: just how invisible was his work and what did that invisibility mean in terms of its public accessibility?”2 In regard to this pursuit of invisibility, this interest to make art without making traditional perceptual objects—which can be seen as an interest in investigating the limits of perceptual Abstraction—Butterﬁeld asked Irwin how he was “planning to transfer information without objects and without words?” Irwin replied that he did not know.3 If “to transfer information” means—as it must in any way relevant to making and apprehending works of art—to make it understandable with which object an artwork is meant to be identiﬁed, then an artist’s transferring information depends on an object or objects of some publicly apprehensible kind, a word or a series of words is a kind of publicly apprehensible object, and any information transferred from one subject to another would itself also be an object. Given the philosophical dependence of artworks on publicly perceptible objects, the answer 1 Butterﬁeld, Jan The Art of Light and Space, New York: Abbeville Press (1993) p. 29. 2 The Art of Light and Space, p. 29. 3 This interview of Buttterﬁeld’s of Irwin originally appeared in her article “Reshaping the Shape of Things: Part 2: The Myth of the Artist,” Arts Magazine 47 (September–October 1972) pp. 30–32. The above quote from this interview appears on p. 30 of The Art of Light and Space.

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to Butterﬁeld’s query is that the transference of information apart from an object or objects of some kind of object is impossible. And unless an artist makes it clear with which simple or complex object an artwork is meant to be identiﬁed, no understanding or appreciation of the work relevant to the artist’s intentions of what the work is meant to be can occur. The audience’s failure to apprehend Irwin’s Retinal Replay Volume is recounted in Butterﬁeld’s book The Art of Light and Space, and indicates how, although Irwin utilized objects, he did not utilize them in such a way that made it clear to anyone other than himself what he meant the work to be. As Butterﬁeld there puts it: “Irwin still talks about that piece. He loves it. Though he feels that it was extremely successful in relation to his own expectations for it, he does acknowledge that it was a failure on a cultural level. (‘Art,’ he notes, ‘is a matter of cultural agreement.’)”4 I think that art’s being a matter of cultural agreement is correct as that indicates that there must be a communal rather than a merely individual understanding of with which object or objects an artist intends his work to be identiﬁed. Such an understanding depends on the possibility of people in addition to the artist apprehending a public perceptual object in or through which the identity of a particular work of art is made theoretically comprehensible. That at least must be the beginning point, and hence the creative investigation of artistic identity, or the possibilities of singling out objects within an Essentialist framework— which constitutes the focal point of Essentialist Abstraction—cannot dispense with perceptual objects. Although the history of art has shown much of what is possible to eliminate from objects in order to make them progressively more Abstract, perceptual objects are indispensable to understanding with which object an artwork is meant to be identiﬁed. And this is the case even if the object that the artwork is to be understood to be is not itself perceptual. There is no object then meant to be a work of art whose identity as that work does not originally and subsequently depend on some perceptual object or objects, and there can be no object that would be a work of art whose identity would not depend on a perceptual object or objects.5

4

The Art of Light and Space, p. 29 (My italics.) It is typically the case that an artwork is both originally and continually dependent on the same public perceptual object. See 6 of this division of this part, and 5

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5.1. Privacy and publicity and phenomenal objects The notions of privacy and publicity are relevant to artworks in general since, as noted, eﬀecting and apprehending the identity of any artwork depends on a public perceptual object. These notions are also relevant to the issue of the limits of Abstraction since it may be possible for an Abstract object to be identiﬁed with a private object even though that identiﬁcation depends on a public object. ‘Privacy’ and ‘publicity’ are concepts that concern phenomenal objects. The deﬁnitions of privacy and publicity are given in the present tense since any object that is phenomenal relative to a particular event of awareness is phenomenal relative to that event at the time at which the event occurs, and, as consciousness occurs when it occurs at a time that is then the present, the time of the event’s occurrence, and hence the time at which the object is phenomenal relative to that event, is at a time that was, is, or will be the present. Given this understanding, it is perfectly acceptable to extend the notions of privacy and publicity to past and future objects of awareness, so that a past or future object of awareness that met or will meet the condition of privacy for phenomenal objects would have been or would be a private phenomenal object when a subject was or is later conscious of it in virtue of having met or later meeting that condition. And an object of past or future awareness that did not or will not meet the condition of privacy for phenomenal objects was or will be a public phenomenal object in virtue of not having met or in not later meeting that condition. 5.1.1. Deﬁnition of privacy. A phenomenal object is ‘private’ when a single subject who is aware of the object is aware of the object in a kind of awareness in which no other subject who either is or could be aware of the object is or could be aware of the object. Accordingly,

Part Three, Division I, 1.2–1.3, for consideration of the possibility that an artwork may be relevantly dependent on an object or objects other than the object or objects on which the artwork is originally dependent. However, this possibility presupposes a public perceptual object or objects on which the identity of a particular artwork was originally dependent, and presupposes a public perceptual object or objects on which the identity of a particular artwork is now dependent. Hence the remarks of this section and those that follow from it throughout the book remain unaﬀected by the possibility of the relevance of certain objects to certain artworks to be considered below.

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any event of awareness of such a kind of awareness that occurs only belongs, and only can belong, to the history of awareness of the subject who is so aware of the object. When a phenomenal object is private then, although more than one subject can be aware of the object at the same or diﬀerent times, only a single subject can be aware of the object in a particular kind of awareness at any time at which she is aware of it. As indicated, any such awareness can only belong to the history of awareness of the subject who is capable of being aware of the object in that kind of awareness. Although you could be aware of a pain in my foot by being told that I have a pain in my foot, because only I can be aware of the pain in the event of feeling that phenomenally is the pain, that object is private. You cannot be aware of my pain in an event of pain, and my awareness of my pain in the event that is the pain can only form part of my history of awareness. And although you can be made aware of what I am thinking by my telling you what I am thinking, my event of thinking something or thinking about something is private since only I can be aware of such an event in a higher-order event that takes the event of thinking as its Intentional object. And the occurrence of any such higher-order event that takes the event of thinking as its Intentional object can only form part of my history of awareness. 5.1.2. Deﬁnition of publicity. A phenomenal object that is not private is ‘public.’ 5.1.3. Privacy and publicity and works of art. An object is phenomenal if at least one subject is aware of the object. But given that an object is phenomenal, it is not how many subjects are or are not aware of the object that makes it private or public. That a single subject is the only one who is aware of an object does not make it private, and that several subjects are aware of the same object does not make it public. I might be the only one ever to see a particular mark that I make on a piece of paper, but as it does not meet the condition of privacy, it is a public phenomenal object. Accordingly, there is no objection to saying that history was such that one subject alone was aware of a particular public phenomenal object. And any number of subjects might be aware of the pain in my foot by being told that I have a pain in my foot, but the pain is nevertheless private in meeting the condition of privacy.

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Although an artwork may be a private object, and a limit or limits of Abstraction may be reached in a private object or objects, the identiﬁcation of any artwork with any public or private object depends on a public object. 5.2. A public perceptual object is necessary but is not suﬃcient A particular public perceptual object is a necessary but is not a suﬃcient condition of originally eﬀecting and comprehending the identity of the artwork dependent on it. For instance, both eﬀecting and comprehending that identity will depend in turn on cultural background information that will ﬁgure in the production of the object and that a perceiver of the object brings to an encounter with such an object. 5.3. Apprehensible properties relevant to an artwork’s identity A public perceptual object in or through which the identity of an artwork is both eﬀected and made comprehensible may have apprehensible properties in addition to purely perceptual ones that are relevant to the identity, and to apprehending the identity, of the artwork dependent on that perceptual object, such as the comprehensible semantic and syntactic properties of well-formed language. 5.4. No a priori limitations on public perceptual objects No a priori limitations are placed on a public perceptual object on which the identity of an artwork is dependent, so that such a perceptual object may be complex and consist of parts that are not continuous but are distributed in space or time or space and time, so that the parts must be apprehended successively, not simultaneously. I mean that there are no a priori limitations as described given the possibilities determined by the spatio-temporal framework within which artists are required to operate. However, even if a particular work is dependent on objects that are separated spatially, temporally, or spatially and temporally, it remains true that understanding, appreciating, interpreting, or responding to the work presupposes knowing which simple or complex object that work is meant to be, and any object on which such a cognitive event depends must be a public perceptual object.

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For brevity, I will typically talk of a public perceptual object in the singular, and so the preceding points should be kept in mind when that form of the word is used. 5.5. Art-historical objects and consciousness Art history depends on public perceptual objects, and any object that otherwise satisﬁes the requirements of artworks stated in this book that is meant to be an artwork, but that is either not itself perceptual, or is not related in an intentional and understandable way to a perceptual object that identiﬁes it as a particular artwork, is precluded from entering the history of art. Accordingly, Sol LeWitt’s remark that “A work of art may be understood as a conductor from the artist’s mind to the viewer’s” ﬁts acceptably with the points of this section if that which conducts is understood to be a public perceptual object, even if the artwork is not itself meant to be identiﬁed with that public object. But his following sentence, “But it may never reach the viewer, or it may never leave the artist’s mind,” does not. An artist may have an idea for a work that is never made public, but such an idea remains an idea for an artwork and cannot be considered an artwork itself, at least not in the art-historical sense with which we are here concerned, and this is the sense with which the identiﬁcation of the limits of Abstraction must be concerned. This does not mean that all or part of an artwork cannot be an idea or some kind of non-perceptual object. However, any understanding that such an object is meant to be all or part of a work of art depends on a public perceptual object, and this requirement makes it false that a work may fail to reach a conscious subject as suggested by LeWitt.6 When I use ‘perceptual object’ in what follows it is to be understood to be shorthand for ‘public perceptual object.’ In addition, ‘public perceptual object’ can be understood to be replaceable with ‘publicly perceptible object,’ and ‘perceptual object’ with ‘perceptible object’ to include, in either case, the possibility of being aware of any perceptual object on which the identity of a particular artwork is dependent. Further, that any object on which the identity 6 The two quotes reproduced here constitute both sentences of section 13 of LeWitt’s “Sentences on Conceptual Art,” which can be found in Harrison and Wood, Art in Theory, pp. 837–839. Quote on p. 838. (My italics.)

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of an artwork depends is public is implicit if the publicity of that object is not mentioned in relation to the dependence of the artwork on that object. Finally, what I have to say in this section about the identity of an artwork as a whole object also applies to the individual parts of which it is composed if the artwork is complex. That is, the identity of an object that is meant to be part of an artwork is linked conceptually to the possibility of being aware of any object on which the identity of the object as such a part is dependent.

6. Original and subsequent dependence of artworks on objects A work of art is originally dependent on a public perceptual object that it is meant to be or through or in relation to which its identity is made comprehensible. Comprehension of the identity of the work originally dependent on such an object can occur in virtue of apprehending that object as long as the object continues to exist, as can any response to the work that is consistent with its identity. Comprehension of the identity of a work of art, and any response to the work that is relevant to that identity, may be subsequently dependent on, or may occur in virtue of apprehending, an object of which each of the following things is true: a) any such object is so causally and historically linked to an object on which the work is originally dependent that, in virtue of this linkage, such a subsequent object may allow for the comprehension of the identity of the artwork and any relevant response to the work as much as the original; and b) any such object is recognized by the artist whose work it is to be as adequate to that comprehension and any such response as is any object on which the identity of the work was and may continue to be originally dependent. Such a derived object, as well as any object on which the work both was and continues to be originally dependent, is an object on which the work can be said to be ‘relevantly dependent’ and so can be called a ‘relevant object.’ For instance, Robert Barry may be willing to recognize any physical or mental token of all the things I know . . . that is causally linked to the original token of that language to be as acceptable to identifying a particular artwork with the object delineated by that language as is the original printed token of that language. And he may consider apprehension of such a token to be as acceptable a means of provoking any response to the work as is comprehension of the language on which the work originally depended.

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7. Embodied artworks A work of art is said to be ‘embodied’ in a particular public perceptual object when the work is meant to be identiﬁed with and not through that perceptual object. This identiﬁcation is originally determined by the artist whose work it is, at least for the art-historicallyintended works that are of interest to this work. It is important to understand that, as I am concerned in this book with Essentialism and the limits of Abstraction in relation to the visual arts, “public perceptual object” means “public visual object,” and ‘embodied’ in the sense explained is then a notion that is purposely linked to visual objects. These points having been made, it can nevertheless be recognized that the identity of an artwork in any medium depends on a public perceptual object or objects of a type that, given a background of cultural understandings, is the means by which that with which an artwork is meant to be identiﬁed is made intelligible. Thus, that with which a particular symphony is to be identiﬁed is made intelligible with the playing of certain sounds in a certain order, and the work is embodied in those sounds in the sense that we understand that the work is to be identiﬁed with the sounds heard in the order of their hearing. An example of a background understanding of a live symphonic performance is that, when a conductor instructs an orchestra to begin playing sounds, a particular work is unfolding perceptually. A complex artwork may be embodied in diﬀerent kinds of perceptual object that are equally relevant to comprehending the identity of the work, such as a play or an opera. Even an artwork that is displayed or occurs in a ﬁne arts context, such as an art museum, and so is related to the visual arts tradition, may have diﬀerent perceptual aspects, as a performance or an installation that consists of visual and auditory objects. Such works may also have conceptual aspects that are relevant to their identities. The embodiment of a work in a public perceptual object does not necessarily follow from the requirement that the identity of any artwork of any kind depends on a public perceptual object, since such an object may be a means through which the identity of the artwork is made comprehensible rather than being the thing itself that the work is meant to be. For instance, a novel is not perceptually embodied in the pages on which its identity is dependent, in that we do not understand the words of a novel to be a number of marks on paper that are meant to be attended to and appreciated visually.

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Instead we understand that the words of a novel are meant to be read, and so we understand that the linguistic properties of visible marks on paper are means by which the nature and identity of a particular work is made comprehensible. In addition, a background of cultural understandings for any art form is not immutable; artists can and do produce works that experiment with this background, and change of that background can be eﬀected according to the understanding and success of that experimentation. An object in which all or part of an artwork is embodied is an object on which all or part of the artwork is relevantly dependent. 7.1. Embodiment, identiﬁcation of artworks, and sophisticated notions of artworks Most works of art are embodied in perceptual objects, in the sense in which ‘embodiment’ is used here to talk about perceptual objects that certain artworks are meant to be by the artists who produce them. That an artwork, such as a Rothko painting, is an embodied artwork means that the work is meant to be identiﬁed with a certain perceptual object. It may be possible to talk about embodied artworks in more sophisticated philosophical, aesthetic, critical, and art-historical senses that pertain to such things as the emergence of the artwork from the perceptual object, and the extension of the work beyond the perceptual object through the meaning, value, and biography of the work as a cultural object.7 Any such talk presupposes the intended artistic identiﬁcation of an embodied artwork with a perceptual object, but the recognition of the legitimacy of speaking of an embodied artwork in any of these more sophisticated senses means that the thesis that the identiﬁcation of an embodied artwork with a perceptual object is not an implicit endorsement of what Gregory Currie refers to as “aesthetic empiricism.” That a painting, such as a Rothko, is embodied in a perceptual object means, for aesthetic empiricism, that “What is aesthetically

7 On the relation of artworks as cultural objects to the physical objects in which they are embodied see Margolis, Joseph “Works of Art as Physically Embodied and Culturally Emergent Entities” The British Journal of Aesthetics, 14 (1974) pp. 187–196, “The Ontological Peculiarity of Works of Art” The Journal of Aesthetics and Art Criticism, 36 (1977) pp. 45–50, and “The Deviant Ontology of Artworks” in Carroll, pp. 109–129.

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valuable in a painting can be detected merely by looking at it. Features that cannot be so detected are not properly aesthetic ones.” Accordingly, the view of aesthetic empiricism is that “aesthetics is concerned only with the surfaces of things.” For aesthetic empiricism, “the boundaries of the aesthetic are set by the boundaries of vision, hearing or verbal understanding, depending on which art form is in question.”8 No such inference can be drawn about the boundaries of, the nature of, or the factors that determine the aesthetic value of an embodied artwork, as embodiment is used in relation to the identity of an artwork in the most basic epistemological sense. That aesthetic empiricism and embodiment are two diﬀerent things is underlined by the fact that the aesthetic value of a selected object, such as a Duchamp readymade, may depend on non-perceptible properties of an artwork that is nevertheless embodied in a perceptual object. In addition, that such non-perceptible properties may be relevant to the identity of the artwork in an ontological sense, and perhaps also in a more sophisticated epistemological sense, is compatible with the notion of embodiment under consideration. A work that is embodied in a perceptual object is embodied in the object in the basic epistemological sense in which we know that we are to identify the work with a certain perceptual object, whatever the more sophisticated nature of the artwork that is dependent for its identity on that perceptual object. And apprehension and consideration of this more sophisticated nature of the work presupposes the perceptual object on which its identity is dependent, as do any properties of the work that may be relevant to its aesthetic appreciation that are not perceptual properties. Saying that we are to identify a particular embodied artwork, such as Kirchner’s Street, Dresden, with a particular perceptual object simply means that it must be possible to point to a particular perceptual object and say “This is Kirchner’s Street, Dresden.” Further, the ontological nature of an artwork that is embodied in a perceptual object, in the sense of embodiment being considered, is irrelevant to that sense of embodiment even though the embodiment of the work is relevant to consideration of its ontology. For instance, it may be that an embodied

8 Currie, Gregory An Ontology of Art, New York: St. Martin’s Press (1989). First two quotes p. 17, third quote p. 18. See also Davies, David Art as Performance, Oxford: Blackwell (2004).

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artwork, including a painting, is properly to be identiﬁed with a type rather than with any particular perceptual token of that type.9 However, even if this is the case, still that type is distinguished phenomenally from other objects, including other types, through any perceptible token of that type, and the artwork is identiﬁed as that artwork through such a token. 7.2. Diﬀerent kinds of appreciation of embodied artworks It is usually clear enough how we are to respond to objects created to be artworks that are embodied in public perceptual objects. We know that we are to respond to what we see principally in the way or ways in which such perceptual objects invite responses as aesthetic visual objects. However, in the case of a selected object, such as a Duchamp unassisted readymade, the case is diﬀerent in some important respects. Understanding, appreciating, interpreting, and responding to a selected artwork still depends on a public perceptual object with which the artwork is meant to be identiﬁed, but the point of the work is not that we should respond to such an object by attending to its perceptual qualities, as we would in responding to, say, a Color9 This is the view of P. F. Strawson. See pp. 183–184 of “Aesthetic Appraisal and Works of Art,” in Freedom and Resentment and Other Essays, London: Methuen (1974) pp. 178–188, and footnote 7 on p. 239 of Individuals: An Essay in Descriptive Metaphysics, Garden City, NY: Anchor Books (1963). Strawson maintains that “All works of art . . . are equally types and not particulars” and where it is characteristic of a type that it “can be embodied on diﬀerent occasions in diﬀerent particular physical phenomena.” (First quote p. 184, second quote p. 183.) Strawson is considering the possible embodiment of works, such as paintings, in any number of tokens of the same type of perceptual object, and does not consider the possibility of securing the particularity of an artwork through the use of language that speciﬁes an object with which an artwork is meant to be identiﬁed. However, it is easy to see that the particularity, uniqueness, or non-repeatability of an artwork can be ensured in this way by an artist’s specifying a time in history in relation to which the object speciﬁed to be the work is particularly determined, and since no other time in history can be the same time, the possible repetition or multiple instantiation of the work is precluded. Accordingly, the work cannot logically be said to be a type of which there could theoretically be any number of tokens. This is the case, for instance, with Barry’s all the things I know . . . It should be recognized that the particularity of a temporally-indexed speciﬁed work, such as Barry’s, is consistent with the existence of any number of tokens of a speciﬁcation that singles out the same temporally-indexed object. Even if Strawson were correct that artworks of all kinds are types, it could still be asked what type of type an artwork is. For an overview of recent thinking on the matter, plus a defense of a particular view, see Davies, David Art as Performance.

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Field painting. The importance to the history of art of the original selection of common objects as artworks concerns the aesthetic and philosophical questions that such objects raise.10 It is true that a person could not appreciate the revolutionary importance of a work like Duchamp’s Bottle Rack if she were unacquainted with the manner in which the artwork was produced: by a simple selection and exhibition of an object intended by its producer to be a work of art. And it is true that these historical actions are not themselves preserved in the exhibited object to whose nature and importance they are nevertheless crucial. However, these truths do not undermine the point that even artworks that are produced by an act of selection depend on public perceptual objects, and such selected artworks can be said to be embodied in such objects since we distinguish, for instance, between Fountain and Bottle Rack by distinguishing between the perceptual objects with which those artworks are supposed to be identiﬁed. And it does not undermine the point that any assessment of the artistic importance of a selected artwork depends, at least originally, on the object to which the actions of selection and exhibition are relevant. 7.3. Ways of producing embodied artworks A perceptual object with which an embodied artwork is meant to be identiﬁed may be created or selected, or it may be speciﬁed to be a work of art. A complex embodied artwork may consist of objects that are produced or singled out in a combination of these ways.

8. Non-embodied artworks An artwork that is meant to be identiﬁed with an object that is not perceptible is ‘non-embodied.’ The identiﬁcation of non-embodied artworks with non-perceptible objects may be eﬀected through speciﬁcation or selection, depending on the nature of the object. 10 I am not suggesting that this is the only importance of the readymades. Fountain, for instance, might be seen as an apt rebuﬃng of the pomposity of the traditional artworld, and, as it was produced in 1917 during World War I, as an embittered oﬀering to a civilization that treasures beauty and precious objects at the same time at which it engages in global conﬂict that threatens to extinguish much of itself and what it values.

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8.1. Non-embodied artworks and speciﬁcation A non-embodied artwork may be speciﬁed to be a non-perceptual object that either does or does not result from an event or events of comprehending language that refers to it. Robert Barry’s all the things I know but of which I am not at the moment thinking is a non-embodied artwork that is speciﬁed to be the nonperceptual referent of that speciﬁcation rather than with the linguistic perceptual object itself through which the identity of that work is speciﬁed. That is a key point for understanding the importance of the work to the history of Abstraction, replacing, as it does, the customary object of perceptual focus with a designated class of noumenal objects that are indexically related to the artist at a certain point in the history of his awareness. However, although the object meant to be the artwork is itself noumenal, and the work itself is not the same thing as the language that makes the identity of the work understandable, there would have been no art-historical possibility of understanding or in any way reacting to what Barry intends the work to be apart from the possibility of apprehending the kind of perceptual object on which the identity of this kind of work was originally dependent, and so an eﬀect of this work is to underline the dependence of the identity and assessment of art-historical artworks on perceptual objects in general. A speciﬁcation is an illustration of a public perceptual object that has an apprehensible property that is relevant to an artwork’s identity that is not perceptual, namely, the semantic property in virtue of which that language can be understood to refer to what it is meant to refer. However, apprehension of any such property presupposes apprehension of the perceptual object of which it is the property. The referent of the distinction between your current apprehension of this and everything other than your current apprehension of this speciﬁes a nonperceptual object to be a non-embodied work of art that results from an event of comprehending language that refers to that object. This example illustrates that a non-perceptible object may yet be phenomenal. 8.2. Non-embodied artworks and selection Certain kinds of non-perceptual object may be selected and meant to be identiﬁed with non-embodied artworks. Any such non-perceptual

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object must exist prior to its selection or there is nothing to select. The selection of the object must be eﬀected in relation to at least one perceptible object whose relevance to the identiﬁcation of the non-embodied artwork with the non-perceptual object is both comprehensible to the artist who intends to eﬀect that identiﬁcation, and can be made comprehensible to anyone who would understand the intended identiﬁcation. For instance, artworks from Robert Barry’s Inert Gas Series are meant to be identiﬁed with expanding non-perceptual gases, such as helium and argon, that go “from a measured volume” in a perceptible container “to indeﬁnite expansion” in being released from their containers into the earth’s atmosphere.11 The identiﬁcation of the artworks of this series with non-perceptually expanding non-perceptual gases depended on the use of the canisters that contained the gases prior to their release into the atmosphere. The works from Barry’s Inert Gas Series are selected artworks since he identiﬁes the works from this series with preexistent, albeit non-perceptual, entities. This shows their indebtedness to Duchamp as they represent a stage in the evolution of Abstraction in identifying artworks with non-perceptual objects. A speciﬁcation that singles out a non-perceptual object as a nonembodied artwork is a kind of sophisticated perceptual entity that is used not only to eﬀect the identiﬁcation of the work with the object, but to convey to others that intended identity. A perceptual object, such as a container, will not convey the intended identity of an artwork with a non-perceptual object to which that perceptual object is relevant. Although documentation of such a perceptual object may be helpful to understanding the relevance of the documented perceptual object to the identity of a non-embodied artwork, the documentation by itself cannot convey the intent of the artist that the work be identiﬁed with something that cannot be perceived. Thus Barry’s photographs of containers of gases in places where the gases that they contained were released could not by themselves indicate that the works from the Inert Gas Series are meant to be identiﬁed with non-perceptual entities rather than with either the photographs themselves, or with the containers that are pictured in the photographs. Understanding the intended identiﬁcation of a non-embodied

11 See Lippard, Lucy Six Years: The Dematerialization of the Art Object, 2nd ed. Berkeley: Univ. of California Press (1997) p. 95, and Wood, Paul Conceptual Art, New York: Delano Greenidge Editions (2002) pp. 36–37.

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artwork with a non-perceptual entity depends on information that pertains to the intended identiﬁcation.12 Such information is required whether or not it is supplemented by any photograph, map, or non-linguistic entity that may pertain to the identiﬁcation of a nonembodied artwork with a non-perceptual object. 8.3. Non-embodied artworks and perceptible objects The selection of a non-perceptual entity to be a non-embodied artwork depends on at least one perceptible entity, as noted. The identiﬁcation of an artwork with any non-perceptual entity that it may be possible to in some way eﬀect—so that no object was that non-perceptual entity before that intended identiﬁcation—must rest on at least one perceptible entity through which the intended identiﬁcation is made comprehensible. Any perceptual object on which a non-embodied artwork is relevantly dependent is diﬀerent, as perceptual, from any non-perceptual object that the non-embodied work is meant to be.

9. Awareness and agency and perceptual objects Objects on which works of art are dependent presuppose subjects to whom they are directed and concern both the awareness and the agency of subjects to whom they are directed. The perceptual object on which a work of art is dependent is implicitly directed towards awareness since the possibility of responding to the work critically, reﬂectively, and aesthetically presupposes being aware of an object that makes such responses possible. This is the case even if the artwork is not to be identiﬁed with the object on which its identity is dependent. In producing an object on which the identity of an artwork is dependent, an artist intends to engage directly the awareness of any

12 Information cited by Lippard that is relevant to the Inert Gas Series in general is: “The gases were released by the artist on the beach, in the desert, in the mountains, etc., around Los Angeles.” Lippard, Lucy Six Years, p. 95. Speciﬁc information that pertains to a particular work from the series quoted by Wood reads: “The text for Helium reads: ‘Sometime during the morning of March 4, 1969, 2 cubic feet of helium was returned to the atmosphere.’” Wood, Paul Conceptual Art, p. 36.

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subject who chooses to attend to the object, and that intention is implicit in the artist’s production of the object. By engaging awareness directly I mean that the artist intends that the subject should direct her attention to the object, that she should focus on it, and he does not intend that the subject should so situate herself in relation to the object that it becomes a peripheral or subsidiary element in her current ﬁeld of awareness. Such focused apprehension of the object on which the identity of a particular artwork is dependent will be a matter of choice, and so no object on which an artwork is dependent can escape a relation to agency. In addition to an initial decision to attend to such an object, a subject must also choose to look at the object from a certain angle and distance for a certain amount of time and with a certain degree of attention. Attention to the object may involve a certain amount of critical reﬂection if the subject is so educated to make such reﬂection possible, but any reﬂection that accompanies perception of the object will be a consequence of the person who is attending to the object deciding to reﬂect on the object to which she is attending. A subject must choose to read the language through which the identity of an artwork is speciﬁed, and comprehension of the language may or may not be followed by reﬂection on what the language indicates, but reﬂecting on such an indication will depend on a decision on the part of the person who has comprehended the language. Terminating any event of apprehending the object on which the identity of an artwork is dependent will also be a matter of choice. None of the agential relations mentioned, or any others of relevant kinds, need be conscious, but they are necessarily operative in the determination of the nature of the speciﬁc relation of the subject to the object on any particular occasion on which the object is attended to.

10. Conceptual idealism and works of art An artist’s eﬀecting the identiﬁcation of an artwork with some object depends both on her intended production or use of at least one perceptual object to eﬀect that identiﬁcation and her understanding of the intended relation of any such object to the identity of the artwork dependent on it. The dependence of the identity of an artwork on

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the intention and understanding of the artist is both conceptual and ideal. It is conceptual in pertaining to notions that are required of eﬀecting the intended identity, and it is ideal in that the required intention and understanding are conscious. A subject’s understanding of the intended identity of an artwork presupposes both her apprehension of some perceptual object on which the identity of the work is relevantly dependent and her understanding of the intended relation of that object to the identity of the artwork dependent on it. The presupposition of a subject’s understanding of an artwork’s identity of the apprehension and understanding noted is also both conceptual and ideal. It is conceptual in pertaining to notions that are required of comprehending the identity of an artwork, and it is ideal in requiring apprehension and understanding. Neither use of the word “ideal” either favors or eliminates any view of the kinds of act and state that are commonly called ‘mental.’ Similarly, use of the term “conceptual” is meant to reﬂect a required relation between notions that are indispensable to making, apprehending, interpreting, evaluating, discussing, and responding to works of art that is compatible with any metaphysics.13

11. An artist’s presentation of an object to the artworld as an artwork Any public perceptual object on which the identity of an artwork is wholly or partially dependent—either originally, subsequently, or both—must either be displayed or disseminated in such a way that its relevance to the artwork can be understood by the appropriate audience, or the relevance of such an object to the artwork must be made known to the artworld. That at least must be the case if the object with which the artwork is meant to be identiﬁed is to exhibit a limit of Abstraction that can be understood art-historically. Historically, the recognition and acceptance of an artist’s intention that an object be understood to be a work of art by people other than the artist depended upon making that intention known through embodied objects being placed in contexts that have been 13 The notion of conceptual idealism is borrowed from Nicholas Rescher, although he does not discuss works of art as conceptual idealistic objects. For his use of the term see his Conceptual Idealism, Oxford: Basil Blackwell (1973).

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and still are used for making such intentions public. A painting or sculpture being located in the customary way in a museum or gallery makes it implicit that the object is to be viewed as a work of art. This was and remains true, even when the public and the artworld ﬁnd the work shocking to the point that the typical response is, “You can’t be serious,” as was the case with the ﬁrst exhibition of paintings by the Fauves, for example. But it is possible for an artwork to be revolutionary enough that, although the object on which the work’s identity is dependent is exhibited in the proper context, the diﬀerence of the work from art-historical objects is suﬃcient to make the gesture of exhibiting that object as a work of art not immediately recognized or accepted as such, as was the case with the initial exhibition of Fountain. Such a revolutionary work can be recognized in virtue of the artist making his intentions known verbally or in writing or both, and may be accepted in virtue of the artist or someone else arguing for acceptance of the work in these ways, as was done by Duchamp.14 Many twentieth century works of art have been embodied in objects placed outside of museums, galleries, and contemporary alternative spaces or artists’ organizations in places that are truly alternative to traditional exhibition sites. Robert Smithson, Michael Heizer, Walter De Maria, Christo, Dennis Oppenheim, Richard Long, Hamish Fulton, and James Turrell are some of the artists who have produced works in rural and urban environments. Other artists, such as Joseph Kosuth and Dan Graham, have placed objects on which the identity of certain artworks are dependent on billboards and in magazines. For the works produced by these artists—some of which, in the case of Christo for example, no longer exist—to have entered art history, the objects on which the identity of the works depended had to be made known to the artworld in such a way that the identity of the work could be apprehended.

14

See Calvin Tomkins’ account of Duchamp’s response to the committee that rejected, or at least “indignantly refused to exhibit,” this work on page 39 of The World of Marcel Duchamp, New York: Time-Life Books (1966). Duchamp claims that the work was not rejected but “was simply suppressed.” See his account of the episode in Cabanne, Pierre, Dialogues with Marcel Duchamp, (trans. by Ron Padgett) New York: The Viking Press (1976) pp. 54–55. And see Duchamp’s argument that Fountain should have been accepted due to his intentional selection and intended exhibition of the object as a work of art in his “The Richard Mutt Case” in Harrison and Wood, Art in Theory, p. 248.

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For the concerns of this work, it is not necessary to consider marginal cases that may test what is being said in this section of the book—that a discovered artifact is determined to be a work of art and enters art history when the object was not intended to be seen as a work of art by its creator. For example, Jasper Johns might have painted a target on a substance that he meant for darts, died, and, because it was found in his studio, because of its resemblance to certain of his other works, because it was never marked from use as a dart board, and because of its perceived aesthetic value, it is mistakenly construed to be an object intended by Johns to be a work of art that he never chose to make public. My purpose is rather to consider what is indispensable to identifying the limits of Abstraction. Accordingly, it is necessary to consider the relation of Abstract artworks to those who could see them as such, and this means that publicity, as deﬁned above, is an essential aspect of Essentialist Abstraction. As earlier indicated, this prevents a limit of Abstraction from being reached in art history by conﬁning thoughts to a head, as Barry might have done in his work by simply thinking rather than writing down and exhibiting the language that acquaints us with the identity of the work, and, as also earlier noted, prevents a limit of Abstraction from being reached by a person’s simply doing nothing, since her doing nothing, without the intent that her doing nothing be understood to be a work of art, cannot constitute an advance the history of Abstraction in art.15 Instead, a person could only intend that her doing nothing be understood to be a work that is oﬀered as a contribution to art history. But that intention has to be made public to the artworld, and is in this way doing something, and is also, I believe, considerably less ambitious, interesting, and aesthetic than other possibilities that are available to Essentialist Abstraction.

15 Saying that publicity is an essential aspect of Essentialist Abstraction does not mean that there is no room for privacy in Essentialism, and does not mean that thoughts in heads cannot be meant to be objects with which either artworks or their parts are meant to be identiﬁed. This has already been brieﬂy indicated above. In addition, see Part Three, Division IV, 1–2 on pp. 234–262 below on the use of awareness as a medium for producing artworks.

DIVISION IV: ARTWORKS AND KINDS OF OBJECT

1. Artworks and times and places of apprehending them An artwork may be meant to be identiﬁed with a simple or complex object that can be apprehended at a single place at a single time—such as a performance; the same place at diﬀerent times— such as a painting; diﬀerent places at the same time—such as a print; or diﬀerent places at diﬀerent times—such as a ﬁlm. Or an artwork may be meant to be a simple or complex object that is not itself apprehensible. An example of the latter is an artist’s intended identiﬁcation of an artwork with the referent of the language everything of which everyone who is now aware is not now aware. Language that speciﬁes an object that cannot be apprehended to be a work of art may itself be apprehended at a single place at a single time—such as when the language is brieﬂy projected somewhere; the same place at diﬀerent times—as when the language is repeatedly projected on the same wall; diﬀerent places at the same time—as when tokens of the speciﬁcation are read simultaneously in any number of locations; or diﬀerent places at diﬀerent times—as when tokens of the speciﬁcation are read in any number of locations at diﬀerent points in history. The nature of an object that an artwork is meant to be, including its being a stable or labile temporal object or an atemporal entity, may or may not be aesthetically relevant in either a positive or a negative way to a work that is meant to be identiﬁed with the object. The relation to an actual or possible time and place of apprehending an apprehensible object on which the identity of an artwork is relevantly dependent may or may not be aesthetically relevant in either a positive or a negative way to the work that is dependent on the object. Any of the possibilities mentioned in this division to follow of the identiﬁcation of artworks with objects may or may not be aesthetically relevant in either a positive or a negative way to a work that utilizes them.

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An artist may mean for an artwork to be identiﬁed wholly with each object of two or more objects that are not only distinguishable as two, but are apprehensibly or understandably diﬀerent things of the same or diﬀerent kinds of thing. Whether or not of the same kind, such objects would not be perceived as two tokens of the same type, as would be the case with two tokens of the same print, for instance. And in such a case, the diﬀerent objects would not stand in the part-whole relation to the work, but would stand in the identity relation to the work, in that each object would equally be meant to be the work by the artist whose work it is. Two or more visually diﬀerent Sol LeWitt wall drawings generated from the same set of instructions could equally be considered to be the same work in virtue of their relation to the instructions from which they are derived, if so intended by LeWitt.1 A musical score for an aleatoric work may produce widely diﬀerent sound sequences each of which is equally meant to be the same work.2 In addition, an artist might select or specify two or more diﬀerent objects that he intends equally to be understood to be the same work of art, and not to be parts of a larger work that they together compose. And whether or not one or the other or both can be apprehended, their diﬀerence can be understood in virtue of understanding with which diﬀerent objects the artwork is meant to be identiﬁed.

3. An artist’s identiﬁcation of a number of works with a number of indistinguishable objects An artist may mean for two or more diﬀerent artworks of hers to be identiﬁed with two or more objects that, although numerically distinguishable, are qualitatively indistinguishable. And each of two

1 LeWitt is inconsistent on viewing such drawings as being instances of the same work in spite of their visible diﬀerences or diﬀerent works because of those diﬀerences. See pp. 369–370 of Pillow, Kirk “Did Goodman’s Distinction Survive LeWitt?” The Journal of Aesthetics and Art Criticism 61 (2003) pp. 365–379. 2 For an example see pp. 210–211 of Tormey, Alan “Indeterminacy and Identity in Art.”

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or more artists may intend that her artwork be identiﬁed with an object of two or more objects that are qualitatively indistinguishable from one another, and so any work from the group is distinguished numerically from any other member of the group and biographically in relation to the artists whose works they are. A serial Minimalist may maintain, for example, that two or more qualitatively indiscernible blank sheets of paper are two or more diﬀerent works of hers, and each of two or more Minimalists may maintain that a particular one of a number of two or more qualitatively indiscernible blank sheets of paper is a work of hers that diﬀers numerically and biographically from other works of the same perceptual kind.

4. The equal identiﬁcation of an artwork with diﬀerent objects at the same or diﬀerent times An artist may intend that a single artwork be identiﬁed with two or more numerically diﬀerent objects at the same or diﬀerent times, so that the work is to be identiﬁed wholly with two or more objects at a single time, or throughout the history of the work. Or an artist could intend that a single artwork be identiﬁed ﬁrst with some object or objects at one time or times, and then with a numerically diﬀerent object or objects at another time or times. In either case the numerically diﬀerent objects that the work is meant to be may or may not be qualitatively diﬀerent. For instance, an artist could hang two canvases next to one another on a wall and indicate that each is equally the same work of art and that neither is a part of a larger work that they together compose. And this could be intended to be the case if the canvases are or are not visually indistinguishable. An artist could also hang two canvases next to one another on a wall and indicate that, until some time t, her work is the canvas on the left, and that, after t, the work is the canvas on the right. Or she could indicate that, at any time during the ﬁrst 12 hours of each day that the canvases are seen that the work is the canvas on the left, and at any time during the second 12 hours of each day that the canvases are seen that the work is the canvas on the right. The latter possibilities could be intended no matter the nature of any properties the objects had in common or the nature of any properties by which they diﬀered.

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5. An artist’s identiﬁcation of an artwork with the same object with which another artwork is meant to be identiﬁed An artist may mean for an artwork of his to be identiﬁed with the same object as that with which another artwork is meant to be identiﬁed. For instance, a Conceptualist may specify that a work by another artist is also to be understood to be her work, as would be the case if, for instance, an artist wrote all the things that Robert Barry knew but of which he was not thinking at 1:36PM; June 15, 1969. Or a Conceptualist might specify that an object with which an artwork of his is meant to be identiﬁed is also the object with which a diﬀerent artwork of his is meant to be identiﬁed. Thus Barry might have produced a work titled One Day After: 1:36PM; June 16, 1969 that is meant to be identiﬁed with the object singled out by the speciﬁcation all the things I knew but of which I was not thinking at 1:36PM; June 15, 1969. And each artist of two or more artists may mean for her artwork to be identiﬁed with the same single object, and whether or not the intention of any such artist is known to any of the others. Thus each of a number of artists might specify independently of one another that that of which everyone who is conscious is conscious at a particular time is to be understood to be a particular artwork of hers.

6. Temporal and atemporal objects An object with which an artwork is meant to be identiﬁed may be relatively enduring or it may be relatively ephemeral if it is temporal, or it may be atemporal.

7. Artworks and change An object that an artwork is to be understood to be may undergo change. The identiﬁcation of an artwork with an object that changes may include an object of the kind of object that ceases to be that object in virtue of the change as well as an object of the kind of object that continues to be identiﬁed as the same object in spite of the change. If the former is the case, then the artist has the option of either maintaining that the artwork ceases to be when the object

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ceases to be, or that the artwork continues to be but is now to be identiﬁed with some or any succeeding object to which the expired object is causally connected. For instance, an artist could intend that an artwork be identiﬁed with a ﬁlm until the point at which the ﬁlm ends, and then to be identiﬁed with the memories of the ﬁlm.

8. Artworks, artifacts, and physical objects Every work of art must be an object that an artist intentionally singles out and identiﬁes as a work of art, however the singling out is eﬀected, and whether or not an object that is singled out would have existed or had its particular identity apart from the intent to so discriminate and identify it. If any object that is so intentionally discriminated and identiﬁed is to be classiﬁed as an artifact in virtue of such intentional discrimination and identiﬁcation—including those things that are singled out for awareness through selection or speciﬁcation—then every artwork is an artifact. But not every work of art is an artifact if the preceding ways of linking artifacts and intentional actions are rejected, and not every work of art is an artifact if ‘artifact’ means a physical object that has been brought into being by either the hand of the artist or by hands directed by the artist, and that exists in the common, physical, external world.3 Although a work of art need not itself be a physical object, under the standard concept of the physical in common and educated language, every work of art must be causally related to or dependent on a physical object in the external world in order that that which the artist intends his work to be, as a matter of identity, can be understood.4 This is because, as seen, any artwork of any kind of

3 For an overview and analysis of artifactuality as a necessary condition of an object’s being an artwork see Davies, Stephen Deﬁnitions of Art, Ithaca, NY: Cornell Univ. Press (1991) Chapter 5. 4 Cf. Robert Smithson’s comments on Conceptual art’s attempt to “escape from physicality:” “there is no evasion from physical limits;” “the idea that art doesn’t take a physical form is ridiculous;” and “there’s no escape from the physical.” The identity of every artwork is dependent on a public perceptual object, and in the metaphysics of science and common sense such objects are physical. Smithson’s remarks may have been meant merely to underline this dependence, and to recognize the commonly assumed physicality of public perceptual objects. However, the object with which all or part of a particular artwork is meant to be identiﬁed

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artwork is dependent on at least one public perceptual object, and such a perceptual object is both commonly and scientiﬁcally taken to be physical. Given the recent history of art and the concerns of this inquiry, we have seen the need to replace the traditional notion of an artwork as being the physical or perceptual bearer of traditional aesthetic properties with the notion of an artwork as an object that is in some understandable way indicated by the artist to be the work of art, and that, as so indicated, will be logically distinguished from every other object that is not so indicated to be the artwork. And that which is understandably indicated to be the work need not be physical, perceptible, or aesthetic in any traditional sense. All that is required is that the indication be the result of an intention of the artist, and be something that will be understandable to people other than the artist. Any work of art that is not meant to be identiﬁed with a perceptual object always rests on at least one perceptual object that is intended to be a means of conveying the intended identity of the work, and so is a means of making it possible to interpret, evaluate, and understand the artwork that is dependent on that object.

need not be physical, and to the extent that this is not recognized in what Smithson says he is incorrect. The ﬁrst two quotes are from page 208 and the last two from page 215 of Robert Smithson: The Collected Writings, Flam, Jack (ed.) Berkeley, CA: Univ. of California Press (1996).

DIVISION V: ART AND THE AESTHETIC

1. The distinction between art and the aesthetic Philosophy of art must recognize the distinction between art and the aesthetic: Not every aesthetic object is a work of art, and not every work of art is aesthetic—at least not in a circumscribed sense that would restrict use of that term to the perceptual beauty and emotional appeal of certain visual objects that are generally regarded as masterpieces of art history. Even important artworks may not be aesthetic objects if the concept of the aesthetic is not broadened beyond the narrow conﬁnes of traditional thinking of the aesthetic in ways that are suggested below. If objects that form part of art history can lack traditional aesthetic values, as many do, then ‘artwork’ is a conceptual classiﬁcation that is logically independent of such values.1 A work of art need have nothing to do with visual beauty or aﬀective experience in any traditional sense, as in a readymade by Duchamp, an installation by Haacke, or a performance by Acconci; and a natural object such as the Grand Canyon may be as aesthetic, in at least one sense of the aesthetic, as anything that we are likely to encounter in life without being a work of art in any but a metaphorical sense. That a certain object produces some kind of aesthetic experience in someone can be regarded as an experiential fact, but whether or not the object is a work of art, in the art-historical sense, is conceptually independent of such an experience. Accordingly, that apprehension of an object results in an aesthetic experience is not

1 The distinction between the classiﬁcation and evaluation of objects as works of art is recognized by many writers. See for instance, Binkley, Timothy “Piece: Contra Aesthetics.” Dickie says “Being a work of art does not guarantee any value or any degree of value. Another way of putting this is that a theory of art should not have the result of making the expression ‘good art’ redundant or the expression ‘bad art’ self-contradictory.” Dickie, George The Art Circle, p. 13. And further “It is important not to build into the deﬁnition of the classiﬁcatory sense of ‘work of art’ value properties such as actual appreciation; to do so would make it impossible to speak of unappreciated works of art and diﬃcult to speak of bad works of art, and this is clearly undesirable.” Dickie, George Introduction to Aesthetics: An Analytic Approach, Oxford: Oxford Univ. Press (1997) p. 84. (His italics).

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a suﬃcient condition of that object’s being a work of art, and it is not a necessary condition of an object’s being a work of art that either any apprehension of that object, or any understanding of the identiﬁcation of the artwork with the object, must result in an aesthetic experience of some kind of aesthetic experience.

2. Diﬀerent sources of aesthetic experience and the possible heterogeneity of aesthetic experience The objects to which it is possible to respond aesthetically may include some that are not perceptual, and as an artwork need not itself be a perceptual object, some artworks may elicit experiences that are not themselves perceptual that are nevertheless aesthetic. 2.1. Perceptual and intellectual objects There are diﬀerent sources of aesthetic experience, and one aesthetic experience may diﬀer from another in some important respects in virtue of a diﬀerence of the kinds of source of the experiences. Although there would be diﬀerences between the objects themselves that fall under these main kinds of source, one can broadly divide objects from which aesthetic experience can result into those that are perceptual and those that are intellectual, where an ‘intellectual’ object is a non-perceptual object that is grasped or constructed in an intellectual rather than a perceptual event, even though such an event may presuppose apprehension of a perceptual object, and even though any artwork that is meant to be identiﬁed with an intellectual object, or that has an intellectual dimension, will depend on a public perceptual object in which that identiﬁcation or that dimension is made comprehensible.2 Thus the notion of aesthetic experience

2

As seen above, it is not necessary in every case to be aware of an object that an artwork is meant to be rather than being aware that the work is meant to be a certain object. It may be possible to be aware of an intellectual object that an artwork is meant to be in an intellectual event, such as conceiving or comprehending, or it may only be possible to be aware that the artwork is meant to be an intellectual object in such an event. It is possible to be aware of what is speciﬁed by that of which you are now conscious as much as it is possible to be aware that what is singled out by that speciﬁcation is what a particular artwork is meant to be. It is not similarly possible to be aware of what is speciﬁed by all that of which you are

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that includes responding to intellectual objects is wider than the notion of aesthetic experience that is limited to the experience of perceptual beauty and to the occurrence of any emotion or feeling that is provoked by or that attends that experience. The diﬀerent sources of aesthetic experience is the subject of this second section of this division of this part of this book. 2.2. The possibility of intellectual aesthetic experience of intellectual objects Although Plato long ago asserted that the forms are beautiful, the thesis that aesthetic experience can have an intellectual as well as an emotional and perceptual dimension, that it can result from the experience of intellectual as well as from perceptual objects, is not one with which all thinkers would agree. For instance, Stephan Witasek said that “it is only intuitive presentations that come into consideration as the presupposition of aesthetic feelings. The shape of the ellipse is aesthetically pleasing to look at; the equation in which analytic geometry presents the same shape to the grasp of the intellect does not excite aesthetic feelings at all.” This quote is taken from Barry Smith’s book Austrian Philosophy: The Legacy of Franz Brentano,3 and the italics were provided by Smith due, it would seem, to the controversial nature of the comment. The terms that are ﬁrst most deserving of emphasis here are “intuitive presentations.” As Smith explains: “A presentation is an act or state of mental directedness towards an object conceived in abstraction from any associated judgments or emotional attitudes”—hence the reason for the use of the term ‘presupposition’—and presentations can be either outer or inner, and intuitive or intellectual. The latter sort of presentation, the one that would seem to be appropriate to things like mathematical objects, Smith says, “occurs, for example, when I present to myself an object purely in the sense that I run through a description of the object in my mind.”4

unaware in virtue of being conscious of that of which you are now conscious. However, you could still understand that that which is singled out by that speciﬁcation is what a certain work of art is meant to be, and that which is singled out is an intellectual object the understanding of the identity of which can be grasped in a kind of intellectual event called comprehension. 3 Chicago and LaSalle, IL: Open Court (1996) p. 139. The following quotes by Smith are also from page 139 of the same book. 4 This diﬀerence between intuitive and intellectual presentations is, of course,

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In addition to thinking of an intellectual object like an equation by thinking of a description of it, the equation can also be comprehended through seeing it written out on paper. Still, in this case, even though the mathematical language in which the equation is written is intuitively presented, the equation apprehended through the symbols is not similarly intuitively presented; rather, it is intellectually presented, since the intellect and not the senses comprehends the equation that the symbols represent. As the equation is not intuitively presented, it is barred by Witasek from being a source of aesthetic feeling. It would be possible to have an aesthetic reaction to the marks on paper themselves treated purely as visual rather than as symbolic objects, since then they would be isolated perceptually from their informative function and seen only as intuitive presentations. But then we are talking about something else, and are not addressing Witasek’s point about the aesthetic ineﬃcacy of intellectual presentations. A problem for Witasek’s view is that, even if the equation for the ellipse is not thought to be aesthetically pleasing, it does not follow that an object’s being intellectual necessarily precludes someone’s responding aesthetically to its apprehension. And although apprehension of any intellectual object with which all or part of an artwork is meant to be identiﬁed would depend on apprehension of a perceptual object in which that identiﬁcation is made comprehensible, still an aesthetic reaction to that intellectual object as intellectual may be possible, or it may be possible to predicate an aesthetic property or properties of the object as intellectual, and so intellectual apprehension of an intellectual object could be a presupposition of aesthetic experience or the predication of any aesthetic property of that kind of object. It does not follow then that one must restrict aesthetic experience to that which is tied to a perceptual source as perceptual.5 We cannot make such an assertion about the presupposi-

very much like Russell’s distinction between knowledge by acquaintance and knowledge by description, the former of which would be Witasek’s presupposition of aesthetic feeling. See Russell, Bertrand The Problems of Philosophy, Chapter V, pp. 46–59, and “Knowledge by Acquaintance and Knowledge by Description” in Mysticism and Logic, New York: W. W. Norton & Co. (1929) pp. 209–232. 5 This sentence not only ﬁnishes the thought of the previous sentence, and underlines what we have seen—that any identiﬁcation of any artwork with any object depends on at least one perceptual object—but its emphasized language indicates that that dependence does not restrict aesthetic value of a work to the perceptual

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tional nature of intuitive presentations for aesthetic experience a priori, but must examine individual reactions to individual objects of diﬀerent kinds to ascertain the nature of the responses to such objects, and to determine thereby whether or not any of these can be properly classiﬁed as aesthetic. If aesthetic reactions are to be restricted to perceptual objects alone, as perceptual, then what are we to call the sort of reaction that might otherwise be called aesthetic that can be had to some intellectual objects? If application of the term ‘aesthetic’ to intellectual objects is prohibited, then one wonders what to make of the talk of mathematicians and physicists about the aesthetic value and importance of their work, for instance, Paul Dirac’s remark that “It is more important to have beauty in one’s equations than to have them ﬁt experiment.”6 The preceding remarks can be seen to support the view that, adapting language of Francis Sparshott’s, some art is meant to be thought about rather than perceived. Some art that is meant to be thought about rather than perceived may be non-embodied art, or art that is meant to be identiﬁed with objects that cannot be perceived. And thinking about such work may provoke a response that deserves to be called aesthetic that is an intellectual or conceptual rather than a perceptual aesthetic. Sparshott’s remark that “some aesthetic objects exist to be thought about rather than perceived” can be understood to apply, for instance, to certain works of Dadaist and Conceptual art. That thought, and my own insistence that art need not be perceptible, is opposed to Marcia Muelder Eaton’s view that “art must be perceptual . . . if it is to generate artistic discussion.”7 While any

properties of a perceptual object. Although intellectual artworks whose point is to address the intellect as a ﬁeld of possible artistic investigation depend on perceptual objects to which they are not equivalent, such artworks may have appreciable properties that are properties of non-perceptual or intellectual objects that all or parts of the works are meant to be. And they may have such properties in addition to or in lieu of any appreciable properties that may characterize the perceptual objects on which they are dependent. 6 Dirac is quoted by Timothy Ferris in The Whole Shebang: A State of the Universe(s) Report, New York: Touchstone Books, Simon and Schuster (1998) p. 210. In his Dreams of a Final Theory: The Search for the Fundamental Laws of Nature, Steven Weinberg devotes chapter VI to “Beautiful Theories,” New York: Pantheon Books (1992). 7 Eaton, Marcia Muelder “Art and the Aesthetic” in Kivy, Peter (ed.) The Blackwell Guide to Aesthetics, Oxford: Blackwell (2004) pp. 63–77. Sparshott is quoted by Roger Seamon on p. 139 of Seamon’s “The Conceptual Dimension in Art and the Modern Theory of Artistic Value,” The Journal of Aesthetics and Art Criticism, vol. 59, no. 2, spring 2001, pp. 139–151.

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perceptual or non-perceptual artwork depends on a perceptual object in or through which the intended identity of the work can be made comprehensible, this requirement is consistent with the work itself having no perceptual dimension. Yet at the same time a nonperceptual artwork can be discussed artistically, and aesthetic properties of an intellectual sort may be attributable to it in virtue of apprehending a perceptual object on which understanding the intended identiﬁcation of the work with the non-perceptual object depends. Eaton’s assertion that, “If a thing has no perceptual dimension . . . then there is no basis for calling it art . . .,”8 must either be understood to be shorthand for a more complicated situation or incorrect. It is shorthand if it is taken to mean that eﬀecting and comprehending the intended identiﬁcation of any artwork with any object depends on a perceptual object. In that case the perceptual dimension noted would pertain to the perceptual object on which comprehension of the identity of any artwork is dependent, including a non-embodied artwork. However, that understanding is consistent with the object that the work is meant to be itself lacking a perceptual dimension. Eaton’s view is incorrect if it intends to assert that any object that any artwork is meant to be itself must have a perceptual dimension. That not only contradicts the acceptance of non-perceptual objects into the art history of the recent past, but, more importantly, such a limited view would unduly restrict the investigation of future artistic and aesthetic possibilities that, although dependent on perception, are not limited to it. 2.3. Aesthetic experiences, thoughts, and feelings Witasek’s quote regarding intuitive presentations and aesthetic feelings provokes the following questions: Is any aesthetic experience a feeling? Are all aesthetic feelings the same kind of feeling? Can no event be thought to be a feeling if it is a cerebral experience that is an eﬀect of an intellectual presentation? The possibilities for the intellect, feeling, and aesthetic experience are these: An intellectual presentation results in a cerebral experience that is: 1. neither aesthetic nor a feeling; 2. a feeling, but one that is not aesthetic; 3.

8

Eaton, “Art and the Aesthetic.” Both quotes from pp. 70–71.

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aesthetic, but one that is not a feeling; 4. an aesthetic feeling, although the feeling may diﬀer, and perhaps substantially, from any aesthetic feeling that results from an intuitive presentation. In addition, aesthetic reactions or aesthetic feelings that result from intellectual presentations may behave diﬀerently from those that result from intuitive presentations, and they may do so either in general or in particular cases relative to particular subjects. For instance, it may be that an aesthetic response to a perceptual object as perceptual may be sustained over a relatively protracted event of perceiving the object, and may be of the same or nearly the same strength on repeated occasions of perceiving the object. Yet it is possible that neither of these things holds true of aesthetic responses to intellectual objects. Rather, it may be the case that intellectual objects in most instances elicit aesthetic reactions, if they elicit them at all, on a single occasion, and that the reaction is of a short rather than a sustained duration. Whatever the case, such considerations are not enough to disqualify an intellectual object or an event of responding to it from being aesthetic. That an aesthetic response to an object is ephemeral and unrepeatable simply signiﬁes that the object has a diﬀerent historical relation to the subject who apprehends it than does one that provokes an aesthetic reaction on more than a single occasion. 2.4. The possible heterogeneity of aesthetic experience I am not attempting to decide whether aesthetic experience is itself heterogenous, that is, whether there are distinct kinds of feeling or non-aﬀective experience that deserve to be called aesthetic in spite of their intrinsic diﬀerences; or that there is a single type of aesthetic feeling or response to things that nevertheless can have as its cause the experience of diverse kinds of object in diverse kinds of awareness, such as seeing, hearing, or comprehension. This is a matter for other kinds of investigation. I only wish here to indicate the complexity of the matter and the viability of recognizing a wider application of the term than thinkers of Witasek’s ilk would seem to ﬁnd legitimate, and I conclude that aesthetic experience can have its proximate source in intellectual rather than perceptual apprehension, and even if it be true that the character of aesthetic experience is the same for diﬀerent sources of that kind of experience, the diversity of the kinds of source of this experience should be recognized.

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part two 3. Art-historical artworks and kinds of appreciable artistic property

Any artwork that is thought to have art-historical signiﬁcance must have some appreciable artistic property or properties in virtue of which it is thought to have that signiﬁcance. Any such property may or may not be perceptual. Although Dickie makes a clear distinction between the classiﬁcatory and evaluative senses of artwork, in the earlier version of his institutional theory of art he speaks of an artwork as being a “candidate for appreciation,” and one would imagine that any property of the work that is actually appreciated would be an artistic property in virtue of being a property of a work of art. Even though the language “candidate for appreciation” disappears from the later version of this theory, Dickie talks about works that are not presented to the artworld by their producers because those producers consider them to be “unworthy of presentation.”9 Accordingly, it seems that an object that is thought to be worthy of presentation is thought to be so because of a property or properties that is thought to be appreciable, and is thought to be appreciable in an at least an artistic sense of that term since the object is being oﬀered as an artwork to the artworld, and is not being oﬀered as some other kind of thing to any of the other ‘worlds’ into which society might be divided, and thus not as something to which judging it from an a non-artistic perspective would be appropriate. Such a property might also be said to be an aesthetic property in virtue of being a property of appreciation of a work of art, although it may be said to be so in an extended sense of the aesthetic. If an appreciable artistic property were said not to be an aesthetic property, then it may be said not to be aesthetic in that appreciation of the property is either not itself an aesthetic experience or it fails to result in an aesthetic experience. A way to widen the concept of an aesthetic property is given in 3.3 below. 3.1. The notion of an artistic property An ‘artistic property’ is a property that an artwork has as a work of art. Accordingly, an artistic property is not simply any property 9 Introduction to Aesthetics, p. 83 and p. 89. See also Dickie’s “The Institutional Theory of Art” in Carroll, Noël (ed.) Theories of Art Today, Madison, WI: The Univ. of Wisconsin Press (2000) pp. 93–108.

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that any object that the work is meant to be has or might have apart from, or in addition to, its being the object that the work of art is meant to be. Only artistic properties are relevant to appreciating works of art as works of art. It does not follow from this however that any artistic property is relevant to art appreciation, since a property that an artwork has as a work of art that is not determinative of, or an essential aspect of, its nature or identity—such as, for some kinds of artwork, being in a particular place at a particular time, or being owned by someone, or having a particular economic value—may be irrelevant to its artistic appreciation. A property that an object would have whether or not the artwork that is meant to be identiﬁed with the object were identiﬁed with that object may be an artistic property of the artwork, and so may be relevant to the work’s appreciation. However, any property that the object has as that object that is irrelevant to the identiﬁcation of the artwork with the object is not an artistic property of the work, and so is irrelevant to its appreciation. For instance, the object that Duchamp’s Fountain is meant to be would have the property of being a urinal whether or not Fountain were meant to be identiﬁed with that urinal, but the property that the urinal has of being a urinal is relevant to that work of art as a work of art. However, the property that the urinal has of weighing a particular number of ounces—x ounces rather that x +1 or x–1 ounces—is irrelevant to Fountain, and hence is irrelevant to its artistic appreciation. 3.2. Appreciation of an artistic property Artistic properties are apprehended by taking an ‘artistic perspective’ in the apprehension of the property. To apprehend an artistic property from an artistic perspective is to apprehend the property as a property of a work of art qua work of art, and it is to do so even if the property so apprehended could also be apprehended as a nonartistic property from a non-artistic perspective; that is, by apprehending the property, but not apprehending it as a property of a work of art qua work of art. Any appreciation of an artistic property occurs as a result of apprehending the property from an artistic perspective. For instance, if the property that Fountain has of being a urinal is appreciated as an artistic property, it is because that property is attended to as a property of a work of art qua work of art, and the

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property is not attended to as a property of a quotidian object with which the artwork is meant to be identiﬁed that the common object has apart from that artistic identiﬁcation. 3.3. The notion of an aesthetic property Any artistic property in virtue of which an artwork is appreciated as a work of art can be said to be an ‘aesthetic property’ in virtue of being a property of appreciation of that kind of object. And any artistic property in virtue of which an artwork is thought to be arthistorically important can be called an ‘aesthetic property’ in virtue of that importance. Either kind of aesthetic property may be said to be aesthetic in an expanded sense of the aesthetic. The ﬁrst sentence of point 3.3 taken together with 3.2 results in a view that is similar to P. F. Strawson’s thinking that: “[T]he concepts ‘work of art’ and ‘aesthetic assessment’ are logically coupled and move together, in the sense that it would be self-contradictory to speak of judging something as a work of art, but not from the aesthetic point of view.”10 While I maintain that a work of art could lack aesthetic value, and so recognize Dickie’s distinction between the classiﬁcatory and evaluative senses of ‘artwork,’ I think that judging something as a work of art, rather than judging something to be a work of art—which only entails recognition of its classiﬁcation as a certain kind of, possibly valueless, object—means attending to it from an artistic perspective in an eﬀort to ascertain if the work has any appreciable artistic properties. Presumably Strawson’s talk of the “aesthetic assessment” of works of art means that we would be making a kind of category mistake if we judged such an artwork as a sculpture from a physical point of view by, for instance, basing our appreciation of the object on how much it weighs, or if we judged it from an economic point of view by basing our appreciation of the work on its market value. I maintain that appreciative judgement of an artwork is approached from the artistic perspective to exclude other kinds of irrelevant property that might be apprehended from a perspective that is not germane to apprehending the object as a work of art, and this seems

10 Strawson, P. F., “Aesthetic Appraisal and Works of Art” in Freedom and Resentment and Other Essays, London: Methuen (1974) p. 183. (His italics.)

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to ﬁt both Strawson’s view that artworks are judged as art from an aesthetic point of view, and Dickie’s view that artworks are subject to evaluation without necessarily being excellent or even good.11 As noted, I also maintain that anything of value that emerges from taking this perspective is an aesthetic property in virtue of being a property of the work that is found within that perspective. 3.4. Artworks and their appreciable properties It does not follow from the fact that an artwork has an appreciable property that it must be possible to be aware of the artwork itself as opposed to being aware of the identity of the work. However, any appreciable property of an artwork is a property of the work and is not a property of any object on which apprehension of the identity of the work is dependent when the work is not meant to be any apprehensible object on which apprehension of its identity depends. For instance, any appreciable property of Barry’s all the things I know . . . is a property of the work, and is not a property of any token of that speciﬁcation. This is because the work is the referent of the speciﬁcation and not the speciﬁcation that makes comprehension of the identity of the work possible. 3.4.1. Appreciable properties are apprehensible. That a property of an artwork is appreciable presupposes understanding that the property is attributable to the work, even if the work rather than its identity is not apprehensible. A property’s being attributable to an artwork in turn presupposes the possibility either of apprehending any apprehensible object that the work is meant to be, or of apprehending some object on which apprehension of the identity of the work is dependent if the work itself is not an apprehensible object. 3.5. The Intentional direction of events of appreciation An event of appreciating an artistic property of a work of art is directed towards the work that has that property in virtue of its being the case that the appreciated property is a property of that

11 See the chapter on art and value in Dickie’s Art and Value, Oxford: Blackwell (2001).

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work. Such an event has this direction whether or not the object that the work is meant to be can itself be apprehended. A noumenal object that is meant to be a work of art depends on a speciﬁcation to eﬀect the identiﬁcation of the artwork with that object. More particularly, it depends on the meaning of the speciﬁcation to single out a noumenal object that is meant to be a work of art since it is the meaning of a speciﬁcation that is comprehended when an apprehended speciﬁcation is understood to refer to some object. But when a speciﬁcation singles out a noumenal object as the object that an artwork is meant to be, it is not the speciﬁcation or its meaning to which artistic and aesthetic values are to be attributed. Rather, it is that to which the meaning of the speciﬁcation refers to which such properties are to be attributed since the object to which the meaning refers is the work of art and artistic properties are attributable to works of art. The comprehended meaning is merely the means by which appreciation of a property or properties of the artwork to which the meaning refers can result. One cannot simply assume in any case that artistic and aesthetic properties are to be attributed to a speciﬁcation or its meaning, or to a speciﬁcation and its meaning. This is because it is possible to use a speciﬁcation to refer to something other than itself in addition to referring to itself or to its meaning. And if it is possible for speciﬁcation to have this variety of reference, then it cannot be assumed that one view ﬁts all. For instance, all the things of which you are not now aware, the language ‘all the things of which you are not now aware,’ and the meaning of ‘all the things of which you are not now aware’ are equally legitimate but diﬀerent speciﬁcations that single out diﬀerent objects, and the diﬀerent referents could be understood to be meant to be diﬀerent works of art. Because it is possible to single out a linguistic token of a speciﬁcation or the meaning of a speciﬁcation that refers to an object as much as it is possible to use a speciﬁcation to single out something other than itself or its meaning, and because these can be, and typically are, diﬀerent objects, appreciation of a property of one is not necessarily the same thing as appreciation of a property of the other.12

12 This token of this language is an example of a speciﬁcation that singles itself out, and although it depends on its meaning to identify itself with its referent, still this token of this language and the meaning of ‘this token of this language’ are two diﬀerent things. The meaning of this is an example of a speciﬁcation whose meaning singles out the

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Whereas no artwork that is meant to be identiﬁed with a noumenal object can have an appreciable property apart from comprehending a speciﬁcation that makes appreciating such a property of such an artwork possible, still an event of appreciating an artistic property of a noumenal artwork is directed to the artwork that has that property rather than to the phenomenal object that makes that appreciation possible. It does not follow from this that when a subject appreciates an artistic property of a noumenal artwork that she is aware of the object to which the property that she appreciates is attributed. Rather, she is aware that her appreciation is directed to that object as she appreciates a property or properties that she understands to be a property of the work. Appreciation then has a direction in any case. It is Intentional. Appreciation is always appreciation of something. And so, whether a particular appreciated object is phenomenal or noumenal, appreciation of that object is directed to that object. If appreciation of a particular object were not directed to the object of appreciation, then it would not be possible to speak of the appreciation of an artwork that is meant to be a noumenal object. Every event of appreciation depends on a phenomenal object in virtue of which the direction of appreciation can be eﬀected. However, in some cases, an event of appreciation, although it presupposes a phenomenal object to give it its direction, can be directed towards an object of which the subject whose appreciation it is is not aware. And once again, in such a case, a subject appreciating the noumenal object is not aware of the object that she appreciates, but she is aware that her appreciation is directed to that object. That of which the subject is aware in such an event of appreciation is the phenomenal object responsible for giving the event its particular direction. And, in apprehending the directing phenomenal object, the subject is aware too of the

meaning by which that reference is eﬀected, and so the speciﬁcation’s meaning and the referent of that meaning are the same thing. It would seem that the meaning of ‘the meaning of this’ and the meaning of this have the same referent, and thinking that the ﬁrst speciﬁcation adds nothing to the second might be thought to be analogous to saying that ‘it is true that it is true’ adds nothing to ‘it is true.’ If this is correct, then the meaning and referent of a speciﬁcation are the same whenever adding ‘the meaning of ’ to ‘the meaning of x’—and where x represents the remaining language of an original speciﬁcation—is superﬂuous in the sense of not changing the referent of the original speciﬁcation to which the language ‘the meaning of ’ is added.

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direction of appreciation given by that object, and in virtue of that direction, the subject is aware that her appreciation is directed towards a particular noumenal object. 3.6. Artworks and judgements of artistic value Even though judging anything to be important about an artwork would depend on a subject who could make that judgement, any artistically important property that a work is judged to have would be a property of the work in virtue of which it is judged to be important, and not instead merely a property of the subject who judges the work to be important, since judgement presupposes something that is judged, and it is the object that the subject judges to be important rather than the subject judging herself to be the thing of importance in her judgement of the object. This is true even if the artwork is meant to be identiﬁed with an object, such as a thought, that is a property of a subject attending to a public perceptual object by means of the apprehension of which the object that the work is meant to be is produced—in this case a thought. This is because it is the thought as the artwork, and not merely the thought as a property of the subject whose thought it is, that is judged to have aesthetic signiﬁcance, if it is so judged. An aesthetic property of an artwork is a relational property in presupposing a relation to a subject who can be conscious of the identity of the work to which the property is attributed, and can be aware that the property is attributed to the work. However, the relational property is an aesthetic property of the artwork as an object—any appreciable property of which depends on a subject—and the aesthetic property is not an aesthetic property of a subject that depends on the object that the artwork is meant to be, even when, as noted, the object is a property of the subject. A subject can judge such an object to have aesthetic value, but it is the object as an artwork and not merely as a property of the judging subject as so judging that has aesthetic value. 3.7. Artistic interest and the possible expansion of the concept of the aesthetic in relation to artistic interest Perhaps talk of the aesthetic diﬀerence between many older and newer artworks, and the diﬀerence between contemporary and tra-

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ditional artistic attitudes about an artwork’s value, could be summarized in Donald Judd’s statement that “A work needs only to be interesting” if the notion of interest were taken in an unrestricted sense.13 Talk of artistic interest in an unrestricted sense would recognize a number of kinds and a diversity of sources of artistic value, and it may be thought that the aesthetic merit of a work should be equated with any interest that is a consequence of apprehending a property or properties of the work that is a source of such interest; with any valuable experience of which such interest is the proximate cause; with any property in virtue of which such interest and any valuable experience that may result from it may materialize; or with all three. If the aesthetic merit of a work is equated with interest that results from apprehending a source or sources of that interest, then that interest is a kind of experience or conscious event, and the work has aesthetic merit in terms of the interest that it provokes. In such a case the experience of interest may or may not itself be an aesthetic experience, depending on what the nature of aesthetic experience is understood to be, but it would in any case be valuable in that interest is something that is valuable. If it is not itself an aesthetic experience, then it may yet be the proximate cause of an aesthetic experience, or it may be the proximate cause of some other valuable experience or experiences if any experience that it causes is not an aesthetic experience. 13 Judd, Donald “Speciﬁc Objects,” pp. 809–813. Quote on p. 813. Michael Fried says that “The interest of a given work resides, in Judd’s view, both in its character as a whole and in the sheer speciﬁcity of the materials of which it is made.” Fried, Michael “Art and Objecthood,” in Battcock, (ed.) Minimal Art, pp. 116–147. Quote p. 142. (His italics.) Such interest is restricted in eliminating any interest in or generated by any work that lacks the properties in virtue of which work has interest for Judd according to Fried, for instance, immaterial art. See also Raskin, David “Judd’s Moral Art,” in Serota, Nicholas (ed.) Donald Judd, New York: Distributed Art Publishers, Inc. (2004) pp. 79–95. Karsten Harries says that “Modern art has realized the aesthetic potential of the interesting,” and he maintains that “it is possible to understand the interesting as a species of the beautiful.” Harries, Karsten The Meaning of Modern Art: A Philosophical Interpretation, Evanston, IL: Northwestern Univ. Press (1968) p. 58. See also Jacquette, Dale “Intention, Meaning, and Substance in the Phenomenology of Abstract Painting,” The British Journal of Aesthetics, Vol. 46, No. 1, January 2006, pp. 38–58. Whether or not Harries is correct in thinking of the interesting as a species of the beautiful, it is nevertheless valuable. And the value of any interest that we have in a property or properties of an artwork that provokes that interest may be enough for us to value the artwork to which such a property is attributable. And we may so value it whether or not we are willing to call the property of interest, or the interest itself, beautiful.

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If the aesthetic merit of a work is equated rather with any property or set of properties in virtue of which interest in the work can arise, then the aesthetic value of the work is equated with some property or properties of the work in virtue of or in relation to which interest can occur, rather than either with any experience of interest in such properties, or with any experiential result of such an experience of interest, as I have suggested above to be the case. Thus although knowledge, understanding, and appreciation of any such property presupposes the possibility of being aware that the property is a property of the work, the aesthetic merit of an artwork is said in this third case to be equivalent to an interesting property or properties of the work rather than either to any experience of interest itself—whatever the nature of that experience—or to any valuable experience that may follow from interest in that property.14 In this third case then it is any property of a work that can provoke interest in that property in virtue of which the work that has that property is said to be aesthetic, rather than its being the case that the work is said to be aesthetic in virtue of the experience of interest in that property or any experience of value that follows from that interest. An advantage of this third point of view, in addition to points that have already been stated, is that a work could have an appreciable property or properties that has yet to be appreciated for lack of understanding such a property of potential interest—by, for instance, failing to see its relevance to past and future works; failing to see its relevance to other aspects of culture, including philosophy; and failing to see its relevance to solving or provoking an artistic problem. On either of the ﬁrst two views though, an advanced work that is not in fact appreciated would have to be said to lack aesthetic value in virtue of no interest being taken in it. In the ﬁrst two cases an artwork is said to be aesthetic in virtue of the occurrence of actual experiences that certain of its properties can produce, and in the third case an artwork is said to be aesthetic in virtue of properties that can result in the kinds of experience noted. It might be observed however that these cases are not in fact mutually exclusive, given both the potential properties of interest of the work and the actual experience of interest in those properties.

14 This third kind of case is how Judd is using the notion of interest according to Fried.

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An artwork may then be recognized to be aesthetic in a primary or fundamental sense in virtue of some property or properties of potential interest, and to be aesthetic too in a secondary or derivative sense in virtue of any valuable experience that results from understanding any such property to be a property of the work: the experience derives from or presupposes some potential property of interest of the work. Calling such experiences “secondary” is not to diminish their importance, and calling properties of potential interest of a work “primary” is not to deny their required relation to understanding that such properties are properties of the work. Any potential property of interest of an artwork and the experience of interest in such a property are interrelated, in that a property of interest presupposes a possible relation to understanding that the property is a property of the work, and any valuable experience that results from such understanding presupposes the interesting property that is so understood. It is in any case implicit that any property in virtue of which a work is thought to be interesting is a property in virtue of which an artwork may be possibly deemed to be important, and that such a property is a property of the work and is not, as noted, a property of an event of apprehension on which the interest depends. This is the case even on the view that the experience of interest of an interesting property is itself an aesthetic experience or the proximate cause of an aesthetic experience. 3.7.1. Possible sources of artistic interest. An artwork might be thought to be interesting, and hence important, in full or in part because it requires us to revise our ideas of what an artwork is or can be and how artworks can be produced, and hence enables us to extend the now broadened notion of artwork to objects that would have been excluded from being artworks prior to the work’s appearance. All or part of such a work’s aesthetic value might either be said to be equivalent to the intellectual interest that we have in having to extend or revise concepts in virtue of a property or properties of a work that provokes recognition of the need for such extension or revision, or to any property of the work in relation to which that extension or revision becomes both necessary and interesting. Of course, any apprehension of such a value as characteristic of the work would depend on attending to the work as a work of art, and any aesthetic experience of the work related to this property of the work

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would be dependent on the apprehension of that property. Examples of such works are Marcel Duchamp’s In Advance of the Broken Arm and Robert Rauschenberg’s Erased de Kooning Drawing. In addition to an artwork’s importance deriving from such traditional properties as form and color, an artwork’s importance might be said to rest on such things as the novelty of its meaning; its conceptual validity; the thoughts it provokes; the questions it raises; the way or ways in which it addresses or engages awareness; its use of novel materials; or its elimination of things once thought to be necessary to artworks. These things are neither exhaustive nor mutually exclusive. A complicated artwork can derive whatever importance it is thought to have from a number of factors, including ones that are intellectual or perceptual. Chris Burden’s early performance works such as Shoot, where the artist was shot in the arm by an assistant with a riﬂe, and Bed Piece, where the artist lay in a bed in the center of a gallery for the duration of the exhibition, are examples of works that have little if anything to do with traditional aesthetic qualities. Rather, the importance and validity of these works consists in their capacity to, in Burden’s own words, “raise questions”—and the questions raised would concern such things as the empathy of the viewer, the psychological relation of the artist to the work of which he formed part, and the relation between ethics and aesthetics. Works such as these can be seen to be interesting and important in, for instance, being part of the development of Abstraction in eliminating as unnecessary traditional aesthetic qualities; in eliminating the customary physical and emotional distance between the artist and the artwork in Burden’s use of his own body as the object on or through which the artwork is produced; and in his using his own mental and emotional makeup as a ﬁeld for investigation in which certain of his mental and emotional attitudes are examined and tested, rather than using such attitudes as partial means to create objects in which they are expressed. Works of this nature helped forge the institutional theory of art since, if such works were accepted by the artworld as serious art, then philosophical theories that attempted to explain art as representation, expression, or form could not be correct. And although works such as Burden’s may lack traditional aesthetic value, they can be seen to be interesting in, for example, having such properties as those that have been noted. Such properties of interest may be thought to be aesthetic values in an expanded sense of that term because

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they are properties that can be attributed to works of art, and so are properties the understanding of which arises from consideration of the objects to which they are attributed as works of art, and hence from an artistic point of view.15 3.8. Essentialism and the aesthetic Because Essentialism is concerned with the art-historical identiﬁcation of the limits of Abstraction in art, and because any art-historically important artwork must have some appreciable perceptual and/or non-perceptual artistic property or properties in virtue of which it is said to be important, a concern of Essentialism will be to produce artworks with properties that are suﬃciently interesting to be thought to be art-historically signiﬁcant, as such properties of interest are determined in relation to ineliminable properties of artistic complexes to be identiﬁed and considered in Part Three.

4. Factors relevant to the aesthetic value of a work of art The nature and degree of any aesthetic value of any artwork that has such value will depend on a number of factors. This includes whether or not any object would have the property of being the object that the work is meant to be whether or not the identiﬁcation of the work with the object is eﬀected. The aesthetic value of a work will also depend on one or a number of things that depends in turn on which of the possibilities of the preceding sentence characterizes the relation of the artwork to that which the work is meant to be. A complex artwork that consists of a number of objects of one or more of the kinds of object that are considered in sections 4.1–4.3 below may have aesthetic value in relation to the diﬀerent kinds of object considered of which it consists.

15 On Burden’s work see Loeﬄer, Carl E. and Tong, Darlene (eds.) Performance Anthology: Source Book for a Decade of California Performance Art, San Francisco: Contemporary Arts Press (1980), and Burden’s self-published artist’s book Chris Burden 74–77 which documents performances by the artist from 1974 to 1977.

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4.1. The aesthetic value of artworks identiﬁed with artistically-independent objects An artwork may be meant to be identiﬁed with an object that would have its particular identity as that object, rather than as that artwork, apart from the intended identiﬁcation of the work with the object. In such a case no object is the work of art apart from the intent of the artist whose work it is to identify the work with the object, but some object is that object apart from the intent to eﬀect that identiﬁcation.16 Such an object may have its particular identity before, at, after, or independently of the time at which the intended identiﬁcation of the work with the object is eﬀected, and may or may not be perceptible or in some way apprehensible. In addition, the object may or may not depend on an intentional action or actions of the artist whose work is meant to be identiﬁed with the object for the object simply to be that object, rather than that artwork. However, if the object that the work is meant to be depends on an intentional action or actions of the artist who identiﬁes the work with that object to be the object that it is, then the intent to identify the work with that object must come after any intentional action on which the object itself depends to be that object. Accordingly, the intent to identify the artwork with the object cannot inform any intentional action on which that object depends to be that object, and so the nature of the object is not determined by any later intent to eﬀect that identiﬁcation. For instance, an artist may build a bookcase without the intention that it be understood to be a work of art, and then subsequently decide that she intends it to be so understood. Any intentional action of the artist that was relevant to the existence of the bookcase is not informed by the later intent to identify an 16 These remarks employ a timeless and ontologically neutral sense of ‘is’ and pertain to existential and non-existential objects. The timeless use of ‘is’ simply refers to the conservation of the truth value of a statement about something at any time at which the statement is made. The statement is made in the present tense and is not indexed to the time at which the statement is made. For instance, the statements ‘2+2=4’ and ‘2–2=5’ are, respectively, true and false at any time at which they are made, as are the statements ‘Cubism is a 20th century art movement’ and ‘Dadaism precedes Impressionism in the history of art.’ As earlier indicated, either statements made in any present that pertain to things in or related to any future present have truth values when made or they do not. This situation results in a conception, on the one hand, that the future is closed, in the sense that present statements about the future now have truth values and, on the other hand, that it is open, in the sense that present statements about the future now lack truth values.

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artwork with that particular artifact since that later intent comes after the appearance of the bookcase. Finally, an object that would have its particular identity as that object apart from the intended identiﬁcation of the work with the object may be a kind of dependent or independent object of a kind of dependent or independent object to be identiﬁed in Part Three, Division III below. However, in virtue of the object’s being in any case separate from the intent to identify the artwork with the object, in the sense that something is that object whether or not anything is the work, the object as that object can be said to be ‘artistically independent’ of the intent to eﬀect that identiﬁcation. Because the object as the object that it is is separate as indicated from any intent to identify an artwork with it, if the work has any aesthetic value, it may have value in virtue of such things as the way or ways in which the identiﬁcation of the work with the object is eﬀected; any problem of interest that is raised or solved by the nature of any means of eﬀecting the identiﬁcation; any matter of interest that is identiﬁed by or that arises in relation to the nature of any means of eﬀecting the identiﬁcation; the time in history at which the identiﬁcation is eﬀected; any signiﬁcant relation of the artwork to preceding and succeeding artworks in art history; and any signiﬁcant relation of the work to things of prior or subsequent importance in intellectual or world history, as all such things are complex relational properties of the work. Kinds of interest and relation include, but are not necessarily limited to, those that are art critical, art historical, and philosophical. The kind of artwork being considered may also have aesthetic value in virtue of some property or properties that the object has independently of the intended identiﬁcation of the artwork with it, but which property is signiﬁcant for the way in which it ﬁts with the preceding points. However, an artwork of this kind may not have aesthetic value merely because of any property that the object has apart from the intended identiﬁcation of the work with it, if that sort of property is not relevant to the preceding points. And if this is the case then it is the case whether or not such a property is a property in virtue of which the object is thought to have aesthetic value as an artistically-independent object. Any way in which the identiﬁcation of an artwork with such an artistically-independent object is eﬀected may concern the relation of the object as the work to any subject who could understand that

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relation, and the nature of this relation may be of importance to any aesthetic value of the work. Any relevance of the time in history at which the identiﬁcation of the work with the object is eﬀected would include consideration of the nature of any means utilized to eﬀect that identiﬁcation, and both this and the preceding point recognize the possible importance to the value of the work of the novelty of any means used to result in the identiﬁcation considered. The points about any signiﬁcant relation to preceding and succeeding artworks in art history of the kind of artwork now being considered, and any signiﬁcant relation of such a work to things of prior or subsequent importance in intellectual or world history, speak both to the work’s creative and intelligent response to prior objects and events in any relevant history, and to its subsequent creative and intellectual inﬂuence in any sphere of interest. Accordingly, although the artwork is meant to be a particular object, and talk of the value of the work must be talk of the value of the work as that object, the work has no value as that object except in relation to the things noted. Further, any appreciation of the object as the object that it is is separate from any appreciation of the artwork as that object, and so any appreciation of the object as that object would occur apart from consideration of the factors relevant to the appreciation of the work as the object that have been noted. The points of the preceding paragraphs of this section ﬁt such artworks as Marcel Duchamp’s readymades that depend on the selection of preexistent perceptible objects with which the works are meant to be identiﬁed, and artworks such as Robert Barry’s all the things I know . . . that are dependent on the use of language to single out objects that would have their particular identity apart from their being meant to be works of art. The same points would ﬁt an artist’s claim that something that she earlier intentionally produced, but without the intention that it be understood to be a work of art— such as a pile of leaves that resulted from her raking—is to be understood to be a work of art, and would ﬁt the intended identiﬁcation of a particular work of art with another previously identiﬁed work of art, and whether by the same or a diﬀerent artist, as was indicated to be possible earlier in the book. It should also be recognized that an artwork may be meant to be identiﬁed with a particular object when it is the case that some object is that object before the identiﬁcation is eﬀected, as in the examples noted, but where the identiﬁcation is eﬀected speciﬁcally because of

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some property or properties of value that the object would have independently of that identiﬁcation. For instance, an artist might accidentally spill a bucket of paint on a piece of canvas tacked to the ﬂoor of her studio, and, after contemplating the eﬀect of this event, decide to display the canvas as her work in virtue of the beauty of the resultant conﬁguration, and without letting anyone know how it was produced. However, although this possibility is consistent with the remarks of this section, these remarks have been written primarily to address the possible attribution of aesthetic value to such selected objects as Duchamp’s readymades, and to such speciﬁed artworks as Barry’s, while recognizing that certain of the things in virtue of which works of this kind may be thought to be aesthetic may also apply to works of other kinds to be noted below. 4.1.1. The aesthetic value of an artwork versus the aesthetic value of the idea for the work. It is usually maintained in one form or another that Conceptual art is an art of ideas,17 and it might be maintained, in a case where an artwork is meant to be identiﬁed with something other than the idea for the work, that, given the essentially ideational basis and focus of Conceptual art, it is nevertheless the idea for the work rather than the work itself that is of interest and importance. Thus it might be said that Barry’s idea to identify an artwork with the object delineated by his personally and temporally-indexed language all the things I know . . . is more interesting and important than

17 For instance Lucy Lippard writes that “Conceptual art, for me, means work in which the idea is paramount and the material form is secondary, lightweight, ephemeral, cheap, unpretentious, and/or ‘dematerialized.’” Six Years: The Dematerialization of the Art Object, 2nd ed. Berkeley: Univ. of California Press (1997) p. vii. And Tony Godfrey states that “Conceptual art is not about forms or materials, but about ideas and meanings.” Godfrey, Tony Conceptual Art, London: Phaidon (1998) p. 4. Marcia Muelder Eaton’s view, expressed in “Art and the Aesthetic,” that “conceptual art is not art” rests on the mistaken view that every artwork must have a perceptual dimension. Quote p. 70. The fact that any understanding of the identity of any artwork must be tied to a perceptual object accommodates the possibility of identifying an artwork with an object that is not itself perceptible, and so is consistent with the recognition of any work of Conceptual art or any other kind of art that is meant to be identiﬁed with such an object. The view that Conceptual art is not the only art that is concerned with ideas and meanings, but that a conceptual dimension “was already present in some art” that “Conceptual art strongly emphasizes” without its being the case that Conceptual art forces “us to rethink completely the nature of art” is defended by Roger Seamon in “The Conceptual Dimension.” Quotes excerpted from pp. 139 and 140.

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the factual identiﬁcation of the work with that linguistically delineated object. However, even when the idea for a work is thought to be more valuable than the work that results from the idea, the remarks of the previous section hold, since if an artwork and the idea for the artwork are two diﬀerent things, then the attribution of some value property to the work is not, in that act of attribution, the attribution of that property to the idea for the work. From this it does not follow that a work and the idea for it could not have certain value properties in common, such as being interesting, and it does not follow that an idea for an artwork might be thought to be more important, more interesting, or in some way more aesthetically valuable than the artwork that resulted from it. These points having been recognized, it must also be recognized that any appreciation of an idea for a work presupposes either knowledge of the work that makes recognition of the value of that idea possible, or presupposes understanding the actual or intended nature of the work in virtue of understanding the idea for it, so that the relation of the idea for the work to the work can be understood, and the idea can be appreciated in virtue of comprehending that relation. Even if the idea for an artwork is what is thought to be valuable, rather than the work generated by the idea for it, still, any aesthetic or critical value that is attributable to this idea is attributable to it in virtue of its relation to the actual or theorized work that makes talk of the idea for that work possible. Accordingly, understanding such a schematic relation of an object x that is meant to be a particular artwork a to that work as so meant that is indicated by ‘x as a as intended by the artist whose work a is’ is presupposed not only by any critical evaluation or appreciation of the artwork, but by any consideration of the idea that pertains to the work that is structurally described by that schema. 4.2. Aesthetic value and created artworks An artwork may be meant to be identiﬁed with a particular object where it is not only the case that the identiﬁcation of the work with the object depends on the intention of the artist to eﬀect that identiﬁcation, but where it is the case that the object itself depends on at least one intentional action from or in relation to which it is meant to result, such that, if nothing is such an intentional action, then nothing is that object—and so no identiﬁcation of the work with the

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object can be eﬀected—and the intentional action is part of the history of agency of the artist who is responsible for the work. Further, the artist’s intent to produce the work, or to eﬀect the identiﬁcation of the work with some object, would inform any intentional action in virtue of which some object is the object with which the work comes to be identiﬁed, and would do so whether or not the artist has a clear vision of what he intends the object to be at or before the occurrence of any such action apart from which no object is that object. The preceding points pertain to a created artwork, such as a painting, and if such a work has aesthetic value, then it either has value according to some condition or conditions of the aesthetic value of artworks named in 4.1 above that is relevant to any kind of object noted that an artwork can be meant to be, or it has value in relation to some apprehensible property or properties of the created object as determined by some practice or practices that is the means by which the object results, or both. The determination of the nature of the object according to some novel or established practice, or a combination thereof, may have a bearing on any value that the artwork has as that object in addition to any value that that object may have the appreciation of which is not tied directly to knowledge of how the object was or is eﬀected. 4.3. Aesthetic value and participatory artworks An artwork may be meant to be identiﬁed with a particular object, where the following things are the case: i.) the identiﬁcation of the work with the object depends on the intention of the artist to eﬀect that identiﬁcation; ii.) the object depends on at least one intentional act of the artist who is responsible for the work, and from or in relation to which the object as the work is meant to result, such that, if nothing is that intentional act, then nothing is that object, and so no identiﬁcation of the work with the object can be eﬀected; iii.) the object that the work is meant to be depends on at least one additional intentional act from or in relation to which the object is meant to result, such that, if nothing is that additional intentional act, then nothing is that object—and so no identiﬁcation of the work with the object can be eﬀected—and the additional intentional act is an act of a subject who is appropriately attending to a public perceptual object on which the identity of the artwork is relevantly

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dependent. Such a subject may or may not be the artist who is responsible for the work, and so an additional intentional act of the second sort may form part of the history of agency of the artist or of some other subject. The preceding points pertain to a ‘participatory artwork,’ or an artwork whose identiﬁcation with a particular object depends on the participation of a subject. Such a work may or may not be perceptible or in any way apprehensible. If such a work has aesthetic value, then it either has value according to some condition or conditions of the aesthetic value of artworks named in 4.1 above that is relevant to any kind of object noted that an artwork can be meant to be, or it has value in relation to some comprehensible property or properties of the object as determined by some practice or practices that is the means by which the object results, or both. The determination of the nature of the object according to some novel or established practice, or a combination thereof, may have a bearing on any value that the work has as that object in addition to any value that the object may have the appreciation of which is not tied directly to knowledge of how the object was or is eﬀected. An example of a participatory artwork is the referent of any eﬀect of your decision to reﬂect on your comprehending this to be any eﬀect of your decision to reﬂect on that comprehension. 4.3.1. Essentialism and participatory artworks. Both the understanding of the identity of an artwork and any appreciation of any property of interest of a work depend on a conscious agent. Essentialism seeks to utilize as it addresses things on which such understanding and appreciation depend in the determination of its objects. Investigating the limits of Abstraction would include exploring ways of utilizing the participation of a subject in the determination of an object that a work of art is meant to be. The nature and properties of interest of any participatory artwork would be shaped by essential elements of artistic complexes that are used to result in the object, and so would shape the aesthetic of this kind of Essentialist object.18 18 A participatory artwork is one of two kinds of ideational artwork that are identiﬁed below and that are relevant both to Essentialist Abstraction and its aesthetic. For the deﬁnition of ideational object and ideational artwork see Part Three, Division IV, 2.2 on p. 257 below. The importance of ideational artworks to Essentialist Abstraction appears at various points in the remainder of the book following that section, and in Part Four in particular.

PART THREE

ON SUBJECTS AND OBJECTS AND ARTISTIC COMPLEXES: THE MATERIAL OF ESSENTIALISM

Introduction It is the purpose of Part Three of this book to identify those things with which, given all of the preceding considerations, even the most Abstract artwork cannot dispense, and which, with respect to what has been seen, will therefore form the basis for investigating the limits of Abstraction in art within an Essentialist framework. Because works of art are speciﬁcally addressed to subjects and cannot exist apart from objects, what is possible in Essentialist Abstraction will be determined by basic characteristics of subjects and objects; fundamental relations of objects to objects, and the most basic relations of objects to subjects and subjects to objects; laws or conditions that pertain to subjects and objects and their properties and relations; and certain facts that concern these things. An artist must be responsible for eﬀecting the identiﬁcation of an artwork with some object, and it must be possible for people in addition to the artist to understand that intended identiﬁcation. Thus the artistic eﬀecting of the identiﬁcation of an artwork with some object must take into consideration the possible comprehension of the intended identiﬁcation. To that end, an artist must be responsible for a public perceptible object on which comprehension of the identity of an artwork is relevantly dependent. Apprehension of such a perceptual object creates an artistic complex of which the object, the apprehension, and the subject whose apprehension it is are constituents. These constituents have certain properties that pertain to their being constituents of an artistic complex; certain relations hold between them; and certain facts pertain to them. Whatever the metaphysical nature of the constituents of an artistic complex, and the properties, relations, and facts that pertain to them, they are philosophically coterminous in the sense that they all feature in or apply to the complex in their diﬀerent ways, and they do so unavoidably. It is in this sense that these properties, relations, and facts, together with the constituents

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to which they pertain, are said to be essential elements of artistic complexes. Because an artist must make the intended identiﬁcation of an artwork with some object comprehensible, and comprehension of the identity of an artwork occurs in an artistic complex that has certain essential elements, possible uses of these philosophically basic elements as the fundamental material of Essentialist Abstraction would have to be creatively investigated. That is, Essentialism would have to explore the possible uses of things that are essential to comprehending the identity of an artwork to eﬀect that identity. Those things that are essentially involved with the comprehension of the identity of an artwork are the essential elements of artistic complexes, and everything else is superﬂuous and hence inessential to determining the limits of Abstraction. Hence the importance of the identiﬁcation of the essential elements of artistic complexes to the Essentialist project. Not only are the essential elements of artistic complexes identiﬁed and considered in the pages of Part Three, but a considerable portion of this part of the book consists of attention to things that pertain to these essential elements and their possible use in determining the limits of Abstraction. Were this not the case, then the identiﬁcation and consideration of those elements would be incomplete.

DIVISION I: SUBJECTS AND OBJECTS AND ARTISTIC COMPLEXES

Introduction The examination of an artistic complex is initiated in this ﬁrst division of the ﬁnal part of this book. This division considers original and derived objects in relation to which artistic complexes can be eﬀected according to artistic intentions; diﬀerent natures that such objects may have; what it means to apprehend any such object appropriately; the relation of a subject to two or more objects that form part of an artistic complex at the same time; the relevance of reproductions and documentation to artworks; and how diﬀerent kinds of relevant object and their parts can ﬁgure as objects in artistic complexes.

1. The concept of an artistic complex When a subject intentionally singles out in awareness an object on which comprehension of all or part of the identity of an artwork is dependent, and attends to such an object in awareness that is appropriate to comprehending that identity, then a complex results of which the subject and the isolated object of awareness are constituents. The subject’s attentive apprehension of such an object, in a way or ways that is appropriate to the object, is the relation that unites the subject and the object in a complex of which each is a constituent, and of which the uniting relation is also a constituent. When the object singled out in such awareness is either all or part of a public perceptual object on which all or part of the identity of a particular artwork is originally dependent, or is all or part of a public perceptual object that is acceptably derived from an object on which all or part of the identity of an artwork is originally dependent, then the complex that includes the object, the subject, and the subject’s awareness of the object is an artistic complex. The event of attentive apprehension that is a constituent of an artistic complex is a constituent of the complex in the sense that the complex is as much dependent on mindful apprehension appropriate

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to comprehending the identity of the artwork as it is dependent on the object apprehended and the subject whose apprehension it is. Attentive apprehension of such an object is appropriate when one apprehends the object in any way intended by the artist whose work is dependent on the object, such as seeing for painting, and seeing and linguistic comprehension for apprehended language. It is attentive when the object is that which is focused on in any ﬁeld or aspect of awareness of which it forms part. Such appropriate attentive apprehension is cognitive when the subject whose apprehension it is comprehends the relevance of the object apprehended to the identity of the artwork that is dependent on that object. A subject and her consciousness are essential elements of artistic complexes, and unless the subject understands the relevance of the object of which she is conscious to the identity of an artwork, her consciousness of the object does not result in an artistic complex of which she is a constituent. For ease in talking about artistic complexes and their essential elements, and to avoid the irrelevant issue of whether the subject’s comprehension of the relevance of an apprehended object to an artwork is distinct from, but coexists with, the event that apprehends the object, it will be assumed that such comprehension is a property of such an event of apprehension. Thus when a subject is perceiving the object in which an artwork is meant to be embodied, and she understands that the work is meant to be identiﬁed with it, then her perception of that object is said to be cognitive in virtue of that understanding, and that understanding will be assumed to characterize that event of perception. And when a subject comprehends a speciﬁcation that singles out an object that an artwork is meant to be, and she understands that the work is meant to be identiﬁed with the speciﬁed object, then her comprehension of the speciﬁcation is said to be cognitive in virtue of that understanding, and that understanding will be assumed to characterize that event of comprehension. The vertical line in Diagram One on the following page represents an Intentional event of cognitive awareness of a conscious subject of a public perceptual object on which the identity of an artwork is relevantly dependent. That event links the subject and the object and is a constituent of the complex that is dependent on it. 1.1. The notion of original dependence An object on which a certain artwork is ‘originally dependent’ is an object in which all or part of the artwork is ﬁrst embodied, through

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Public Perceptual Object on which all or part of an artwork is relevantly dependent

Conscious Subject who is appropriately attending to a relevant object

An Artistic Complex Diagram 1.

which all or part of the artwork is ﬁrst speciﬁed, or in which all or part of the artwork is ﬁrst partially embodied and through which that whole or part is ﬁrst partially speciﬁed. It is implicit in the idea of original dependence that an artwork is considered to be ‘complete’ by the artist whose work it is in relation to the completion of an object on which the work is originally dependent. For instance, a painting is a ﬁnished artwork when the artist considers the perceptual object in which the identity of the painting is ﬁrst, and typically only, embodied to be complete.1 An artwork that is meant to be identiﬁed with a speciﬁed object is or becomes complete in relation to language for which the artist is responsible that ﬁrst, and perhaps only, speciﬁes that object as a

1 There is nothing that would logically prevent an artist from painting a painting x and then painting a second painting y that is visually indiscernible from x. It would then be open to the artist to consider x and y to be parts of a work that consists of them; to be diﬀerent tokens of the same painting A; or to be two diﬀerent works A and B that could not be told apart, which is something Rauschenberg experimented with in painting Factum I and Factum II. The artist who produced x and y could also destroy either x or y and identify an artwork A or B with the painting that is not destroyed. And if the artist who painted the paintings x and y were a Conceptualist, then she might destroy one or the other painting, and then state that an artwork A or B is to be understood to be identiﬁed with the painting that was destroyed, and further state that the remaining painting is simply to be seen as a visual illustration of an object that has ceased to exist.

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work of art. Any initial object of the kinds mentioned is also typically, but is not necessarily, the means by which the artwork is ﬁrst made public to the artworld, since, for instance, an original object may cease to exist for some reason, and may then be replaced by the artist by a duplicate of the original. An object on which an artwork is originally dependent is also referred to as an ‘original’ object. 1.2. Derived and acceptably derived objects A ‘derived’ object is an object that is so causally and historically linked to an object on which the identity of an artwork is or was originally dependent that apprehension of the derived object can eﬀect an understanding of the identity of that work of art. Understanding the identity of an artwork through apprehension of the derived object is consistent with apprehension of the identity of the artwork through apprehension of the object on which the identity of the artwork is originally dependent, where such consistency indicates that apprehension of the derived object would not lead someone who subsequently apprehends the object on which the identity of the work is originally dependent to associate the original object apprehended with a diﬀerent artwork. A derived object is also so causally and historically linked to an object on which the identity of a particular artwork is or was originally dependent that at least some of the aesthetic value of the artwork can be appreciated through apprehension of the derived object. A photographic reproduction of a painting is an example of a derived object, as is a spoken or written instance of the original language of a speciﬁcation. An object may also be derived from an original part of an original artwork such that the derived object is so causally and historically linked to the object on which the identity of that part of the particular artwork is or was originally dependent that apprehension of the derived object similarly eﬀects an understanding of the identity of that part of the artwork, and at least some of the aesthetic value of that part of the artwork can be appreciated through apprehension of the derived object. A photographic detail of an original painting is an example, as is a recording of a movement of a piano concerto. For a derived object of either kind to form part of an artistic complex, and not just a complex of which the subject and the derived object are constituents, the artist whose work it is must consider the

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derived object to be consistent with his original intentions, and so to be not only as suitable to apprehending the identity of the whole or the part of the artwork, but to be as suitable to the possibility of appreciating any aesthetic value of the whole or the part as the original object from which either kind of secondary object derives. Either of these latter kinds of derived object is an ‘acceptably derived’ object. The diﬀerence between a derived and an acceptably derived object is the acceptance of the legitimacy of the latter kind of object by the artist from whose work the derived object originates, and that acceptance is taken to be contingent on the artist’s recognition that no less an aesthetic appreciation of the artwork can result from apprehension of the derived object than can result from apprehension of the original object from which the derived object results, even though proper or full aesthetic appreciation of the artwork in which either apprehension of the original or derived object ﬁgures may depend on knowledge of things in addition to either object. That aesthetic appreciation of an artwork may depend on knowledge of things in addition to knowledge of either an original or derived object is the reason for speaking in the previous paragraph of the suitability of either kind of object to the possibility of appreciating any aesthetic value of the artwork to which either object is relevant. Speaking of appreciation of the aesthetic value of an artwork as possible recognizes both that a derived object ﬁgures as acceptably in that appreciation as the original from which it is derived if it is said to by the artist whose work it is, and that things in addition to an original or derived object may be required to appreciate an artwork fully. Were Rauschenberg willing to count a photograph of Erased de Kooning Drawing as being as suitable a means of comprehending the intended identiﬁcation of the artwork of that title with the drawing paper photographed, and to be as suited to appreciating the aesthetic value of Erased de Kooning Drawing as perception of the original paper, then the photograph would be an acceptably derived object. And he may do this at the same time that he insists that proper appreciation of the artwork depends on knowledge of its genesis in addition to perception of either the original or the derived object. Were Barry willing to count any token of all the things I know . . . as being as good as the original for both comprehending the identity of the artwork dependent on that speciﬁcation and for appreciating any aesthetic value of that work, then any such token would be an acceptably derived object.

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1.3. Relevant objects Both any original and any acceptably derived object on which all or part of the identity of a particular artwork is dependent is what I have termed a ‘relevant object,’ since either kind of object is an object on which all or part of the identity of a particular artwork has been said to be ‘relevantly dependent,’ in being implicitly or explicitly recognized by the artist whose work it is to be relevant not only to understanding which object all or part of that work is meant to be, but to be relevant too to appreciating all or part of the artwork in virtue of that understanding. A relevant object is perceptible. However, it may have an apprehensible property that is not perceptible that is required to comprehend the identity of the artwork that is dependent on the relevant object, and that is required to appreciate any aesthetic value of the artwork that is intellectual rather than perceptual. An artistic complex holds between a conscious subject and all or part of a relevant object whenever the subject is attending to all or part of the relevant object in a way or ways appropriate to apprehending the identity of all or part of the artwork dependent on that object, and so in a way or ways that makes appreciation of all or part of the artwork dependent on the apprehension of that identity possible. Because the points made about the appropriate apprehension of an object relevant to the identity of a particular artwork apply as well to attending appropriately to any part of any relevant object that is singled out in awareness, when, for simplicity and ease of exposition, I refer only to wholes, it should be understood that what I say applies as well to parts. A relevant object is a necessary condition of any artistic complex, as is a conscious subject, and the subject’s appropriate consciousness of the relevant object. It may be observed that this consciousness of that object is a suﬃcient condition of the subject whose consciousness it is, and that the event of consciousness, in being one of appropriate attention to the relevant object, is a suﬃcient condition of that object’s being a constituent of an artistic complex. In addition, because an artistic complex exists in virtue of a conscious subject’s appropriately apprehending a relevant object, that sort of apprehension of that sort of object is a suﬃcient condition of the existence of the complex. A subject’s appropriate consciousness of a relevant object is then both a necessary and a suﬃcient condition of the existence of an artistic complex.

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When a subject is aware of a relevant object then her awareness is cognitive in that in being aware of the relevant object she is aware of the identity of the whole or a part of an artwork that is dependent on the object, and where, once again, being aware of the identity of all or part of an artwork is equivalent to being aware that the whole or a part of the work is meant to be identiﬁed with a particular object. Any relevant object is phenomenal, and the identity of an artwork is phenomenal as it is comprehended since one is then aware that all or part of the work is meant to be identiﬁed with some object. This is the case whether that object itself is phenomenal or noumenal. For the purposes of this work, a subject’s knowledge of the identity of all or part of a particular artwork is taken to be based on, in each instance, her apprehension of an object on which the identity of all or part of the work is deemed by the artist to be relevantly dependent, and this is the case to avoid irrelevant epistemological issues concerning knowledge of the identity of a work apart from apprehension of such an object; to avoid consideration of the degree to which one can appreciate the aesthetic value of an artwork in virtue of apprehending an object derived from it but not acceptably derived from it; and to determine the ineliminable features of artistic complexes that will form the foundation of Essentialist Abstraction. In addition, I have tied the notion of relevant dependence to the artist’s recognition of such relevant dependence, and, although it is at least theoretically possible that a derived object’s relevance to the identity and aesthetic appreciation of all or part of a particular artwork might be recognized by people other than the artist when the artist herself has not recognized the relevance of such an object, I am disregarding this possibility since it is irrelevant to the aims of Essentialist Abstraction. When I speak in what follows of an object that forms part of an artistic complex, or of an object on which the identity of an artwork is dependent, and the term ‘relevant’ is not used to qualify the term ‘object’ in either case, then it is to be understood that the object that is talked about in either case is a relevant object. 1.4. Appropriate apprehension As we are concerned with visually based artworks—including nonembodied artworks that rely on visible entities that may include nonvisible properties that are relevant to the identiﬁcation of non-embodied

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artworks with non-perceptual objects—‘appropriately apprehending’ an object means looking at the object if the artwork is embodied in that object, as in a painting of a black square; comprehending visual language if the artwork is speciﬁed through that language, as in everything you know but of which you are not now aware; and doing a combination of these things if, on the one hand, the artwork is partially embodied in and partially speciﬁed through public perceptual objects, as in an artwork that consists of a painting of a black square and the language printed beneath it this square and everything other than this square; or if, on the other hand, the language is both that through which and that with which the artwork is meant to be identiﬁed, as in this here now. Appropriate apprehension also includes apprehension of an object, such as a photograph or text, of a kind required to comprehend the intended identiﬁcation of an artwork with an object, as in works from Barry’s Inert Gas Series cited above. Appropriately apprehending an object on which the identity of an artwork is relevantly dependent is not the same thing as understanding or being able to interpret or appreciate fully the artwork, which seems likely always to involve things that may be available to subjects in addition to the relevant object, such as the artist’s oral or written thoughts about the work and/or other works of his that are material to the work; criticism of the work and other works that are similar to or related to the work—whether by the same or diﬀerent artists; art history; and any theorizing other than art criticism and art history that is pertinent to the work and other works of the same or similar type. For instance, although one appropriately apprehends a selected artwork that is embodied in a perceptual object simply by looking at the object, one does not understand, nor can one properly interpret or appreciate, a selected artwork such as Bottle Rack if one merely looks. 1.5. Subjects, relevant objects, and artistic complexes If x is an object on which an artwork a is relevantly dependent, and a subject is appropriately conscious of x, then an artistic complex exists of which the subject and the relevant object are constituents that pertains to the identity and appreciation of a. If two or more objects x and y are relevant to the identity of an artwork a, and it is possible for the same subject to appropriately attend to x and y at the same time—and whether or not the attention that is appro-

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priate to attending to y is the same kind of attention that is appropriate to attending to x—then a single artistic complex exists that pertains to the identity and appreciation of a of which complex the subject and the relevant objects are constituents. It is not the case that the subject is simultaneously a constituent of two artistic complexes that equally pertain to a. Thus if x is the speciﬁcation in Diagram Two below, y is the perceptual space to which the speciﬁcation refers, and x and y are being appropriately attended to by the same subject at the same time, then an artistic complex exists of which the subject and each relevant object is a constituent that pertains to the identity and appreciation of a.

all the space within this rectangle other than the space occupied by this language

Diagram 2.

The point that artistic complexes are not multiplied in relation to a single subject who appropriately attends at a single time to two or more objects that are relevant to the identity and appreciation of the same work may be thought to be arbitrary in stipulating that a single artistic complex exists of which the subject and the relevant objects are constituents, rather than its being the case that the subject is simultaneously a constituent of two artistic complexes that equally pertain to the same work. However, that artistic complexes are not multiplied at a time in relation to the same subject’s apprehension at the same time of two or more objects that are relevant to the identity and appreciation of the same work can be maintained for economy. And this is possible because it does not seem that there is a substantial philosophical or aesthetic diﬀerence between maintaining that the same subject’s simultaneous apprehension of two or more relevant objects results in one or more than one artistic complex, at least not as far as Essentialist Abstraction is concerned. Thus, although relevant objects may diﬀer in some of their properties— including in ways that are important to apprehending the identity of an artwork and to any aesthetic appreciation of the work—because

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such things as subjects, consciousness, and objects that are indispensable to artistic complexes in general will characterize any artistic complex, one artistic complex will not be distinguished philosophically from another in terms of those things that are necessary for the existence of any artistic complex. And in eﬀecting or using any objects on which the identity of an artwork is relevantly dependent, the Essentialist would have to consider any relations that are relevant to Essentialist Abstraction that might hold between such simultaneously apprehended objects and the subject who apprehends them, and would have to consider any relations that are relevant to Essentialist Abstraction that might hold between the simultaneously apprehended objects themselves. The consideration of such relations would be unaﬀected by whether the simultaneously apprehended objects formed part of a single or a number of artistic complexes that pertain to the same work at the same time.2

2. The nature of an object or objects on which a work of art is relevantly dependent An object on which the identity of any work of art is relevantly dependent can have any nature consistent with the possibilities of making and apprehending works of art within the kind of sociohistorical matrix indicated in this book to be germane to the continuation and progress of art history, and to be the cultural context within which the limits of Abstraction are determined. Any object on which any work of art is relevantly dependent is a public perceptual object. Although an artist may utilize a perceptual object other than a visual object in producing a work of art, as Acconci does in the use of recorded sounds in some of his works, for instance, the relevant object of an artistic complex will be assumed to be a visual object that may or may not be linguistic. This is because the issue of the limits of Abstraction is being approached from the visual arts tradition, for reasons that were earlier stated. Use of the term ‘object’ in what follows—as it pertains to an object on which the identity of an artwork is relevantly dependent—should

2 I am grateful to Keith Lehrer for a conversation that led to the assertions and observations of this section.

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then be understood to be qualiﬁed by the terms ‘public visual,’ and it should be understood that the terms ‘relevant object’ refer to a publicly visible object on which the identity of an artwork is relevantly dependent. As visual, objects relevant to artworks are spatial, and it may or may not be the case that any two or more objects of any plurality of objects relevant to an artwork’s identity are qualiﬁed by the same spatial properties or relations. For instance, some two or any two objects of a number of objects mounted on a wall may or may not be of the same size, located at the same height, and separated by a distance equal to their width, and some two or any two pages of the pages of an artist’s book may or may not be of the same shape and size and have a common binding. A single relevant object, or any number of relevant objects, may be internally simple or complex. Finally, relevant dependence should be understood to be implicit in talk of the dependence of the identity of an artwork on an object or objects. Kinds of relevant object include the following. 2.1. A single spatio-temporally continuous perceptual object that can be apprehended in full from a single perspective The identity of an artwork may depend in whole or in part on a single object that can be apprehended in full from a single perspective. The size of such an object may demand that it be scanned, and any complexity of such an object may mean that its various features have to be individually considered, taking, in either case, a period of time. However, any feature of such an object that dictates that it must be attended to over a period of time to be apprehended properly is a property of the same single object, and so is not a property of a number of diﬀerent things that are disconnected in space or time or space and time. An example of such an object is a painting, such as Cy Twombly’s The Italians. The kind of apprehension relevant to paintings is seeing, but the notion of apprehending a relevant object in full from a single perspective can concern certain speciﬁcations too. Thus the identity of an artwork may be dependent in whole or in part on a single speciﬁcation that is either itself a single perceptual object, or that is contained in or forms part of a single perceptual object, and where the language that is that object, or that is contained in or forms part of that object, is of such a length and size that it can be

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comprehended in its entirety without a subject attending to the language having to change his position in space relative to the object in order for comprehension of the language to occur. And this language, as constituting a single speciﬁcation of the nature indicated, need not itself, as opposed perhaps to its words, be apprehended sequentially over time. An example is Barry’s all the things I know . . . 2.2. A single spatio-temporally continuous perceptual object that cannot be apprehended in full from a single perspective The identity of an artwork may depend in whole or in part on a single object that cannot be apprehended in full from a single perspective, but must be apprehended from diﬀerent perspectives to apprehend the object in its entirety, such as Bruce Nauman’s Green Light Corridor, or an uninterrupted speciﬁcation that begins on one wall, proceeds around the corner, and ends on the wall on the opposite side. A single object that must be apprehended from diﬀerent perspectives may be situated in a single place, as when the Nauman is placed in the center of a gallery, or may, although continuous from one end to the other, have its parts situated in diﬀerent places, as in the example of the speciﬁcation, part of which is stenciled on the wall of one gallery, and another part of which is stenciled on the wall of a contiguous gallery. 2.3. A number of spatio-temporally continuous perceptual objects distributed in spatial proximity The identity of an artwork may depend in whole or in part on a number of separate objects that are contiguous—as in the ﬁrebricks of Carl Andre’s Equivalent VIII—or that exist in spatial proximity to one another, so that, whether contiguous or not, these objects may either be apprehended together in full from a single perspective— as in two rectangles painted on or brieﬂy projected onto a wall that are in contact or are a short distance apart—or, although they may be apprehended together from any one of a number of perspectives, no single perspective of this number exhausts the information of these objects—as in Equivalent VIII, one of Judd’s Untitled works consisting of stacked boxes, or Robert Morris’s Untitled (Four Mirrored Cubes). Although the identity of an artwork may depend in whole or in part on a number of separate or diﬀerent objects, as indicated in

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this and following sections, it must be recognized both that a single relevant object, if complex, can itself be understood to consist of a number of diﬀerent objects, and that any artwork that is dependent on a number of diﬀerent objects is nevertheless itself a single complex object. I hope that the examples cited in relation to each kind of object will facilitate understanding what is meant by speaking of each kind of object and the diﬀerences between them. 2.4. A number of spatio-temporally continuous perceptual objects distributed over distances from one another The identity of an artwork may depend in whole or in part on a number of separate objects that, although they exist at the same time, cannot be apprehended at a single time but must be apprehended over time, and whether the objects are connected or disconnected, and, if disconnected, whether or not they are spatially proximate. Relevant coexistent objects that must be apprehended over time may exist in one or in a number of places. Relevant objects that must be apprehended over time may have to be apprehended in a particular order—as in Victor Burgin’s Idea Structures Project 3 or an artist’s book—or in no particular order—as in Walter de Maria’s Lightening Field or an opaque cube that can be lifted and rotated manually, each side of which contains an individual image or speciﬁcation. Parts of points 2.2–2.4 indicate that, when the identity of all or part of an artwork depends on an object or objects that is designed not to be taken in from a single perspective, apprehension of such an object or objects must occur either sequentially over a series of connected times that are devoted to attending to the object or objects, or episodically over a number of disconnected times during which attention to the relevant object or objects is interrupted. This is true when any such relevant object embodies, speciﬁes, or embodies and speciﬁes all or part of the identity of a particular work of art.

3 See Lippard, Lucy R. Six Years, pp. 171–172. This work appears without a title in the text, but is given the name “‘Idea Structures’ project” in the index under Burgin’s name. For this reason I give the work that title here.

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2.5. Temporally distributed objects—I The identity of all or part of an artwork may wholly or partially depend on a number of diﬀerent objects that, taken individually, can be apprehended from a single perspective pertaining to the same space in the same place, but cannot be apprehended at the same time. Accordingly, as temporally distributed, such relevant objects must be apprehended over a period of time, as in the projection of a series of slides in which all or part of the identity of an artwork is embodied, through which it is speciﬁed, or in which it is partially embodied and through which it is partially speciﬁed. Robert Barry’s work Again and Again is an example of a work the identity of which is dependent on the projection of a number of diﬀerent slides at diﬀerent times onto the same space in the same place.5 2.6. Temporally distributed objects—II The identity of all or part of an artwork may depend on objects that do not exist at the same time and must either be apprehended in diﬀerent spaces in the same place at diﬀerent times or in diﬀerent places at diﬀerent times. An example of the ﬁrst kind of work would be one that consisted of a number of slides projected at diﬀerent times onto diﬀerent walls of the same room, and the projection of diﬀerent slides in diﬀerent cities at diﬀerent times would represent an example of the second kind of work. 2.7. Possibilities for a plurality of objects on which the identity of an artwork is dependent From points 2.3–2.6 it can be seen that, if the identity of all or part of an artwork is dependent on a number of diﬀerent objects, then those objects may exist in the same place at the same time; the same place at diﬀerent times; diﬀerent places at the same time; or diﬀerent places at diﬀerent times. Further, objects on which all or part of the identity of an artwork depends can be separated spatially, temporally, or spatially and temporally at the same or diﬀerent distances and

5 See Denizot, René and Barry, Robert Word for Word: It’s about time, Paris: Yvon Lambert (1980), pp. 142–165.

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intervals, and for any distance or interval or distance and interval that would make apprehension of all of the objects on which the work depends possible. A particular kind of separation of relevant objects utilized by an artist for a particular work will dictate the subject’s relation to those objects, and will determine whether they can be apprehended from a single perspective, or must be apprehended from a number of diﬀerent perspectives. 2.8. Artworks and tokens of a type The identity of all or part of an artwork may not depend on a single object—as a painting typically depends on a single object—and may not depend on a number of diﬀerent objects that combine to form a larger work of which each separate object is a part—as an installation typically depends on a number of diﬀerent objects—but may instead be embodied in and/or speciﬁed through each member of a set of any plurality of indiscernible tokens of the same type, and where the dependence of the identity of all or part of the work on each such member of the set further means that that identity is not dependent on any particular token or tokens of the set, and is not dependent on every member of the set. The preceding statement recognizes that the very same identity of a work can be embodied in, speciﬁed through, or embodied in and speciﬁed through a number of visually indiscernible objects, so the point here is repetition of identity, not the dependence of the identity of a work on a number of diﬀerent objects. Thus the particularity indicated by “the object” relevant to the identity of all or part of a particular artwork can give way to the multiplicity sanctioned by ‘an object’ relevant to the identity of all or part of a work to accommodate multiple works such as prints and mass produced and distributed speciﬁcations. Because each token of a number of tokens of the same type can embody or specify or embody and specify the identity of the same artwork or the same part of the same artwork, an artistic complex results whenever a subject is appropriately conscious of any such relevant object, and where being appropriately conscious of a relevant object of any of these kinds means attending to the object in a way that is suitable to understanding the identity of all or part of the work that is dependent on the object, and in a way that is suitable to appreciating all or part of the artwork that is dependent on that object.

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The preceding examples having been given, it is in any case true that all or part of an artwork’s dependence on one or more than one relevant perceptual object, as well as the nature of that dependence, is determined by the artist whose artwork it is, either at the time of its original conception and production or thereafter. However, that determination must be made by the artist at some time during her lifetime. It would be a task for Essentialism to consider the relation of an object with which an artwork is meant to be identiﬁed to any object on which the identity of that work is relevantly dependent, as well as the relation of each kind of object to a subject who can comprehend that identity.

3. Artworks and reproductions or documentation When a reproduction or documentation of the object on which an artwork is originally dependent is considered by the artist whose work it is to be as good as the original object for apprehending the identity of the work and appreciating the work’s aesthetic value, then apprehension by a subject of such a relevant object would constitute an artistic complex. For instance, an artist might state that any reproduction of any original language that speciﬁes an object that an artwork of his is meant to be is as good as the original, both for making it understood what the artwork is to be understood to be, and for appreciating its aesthetic value. And because tokens of the same type of object as the object on which a particular artwork was originally dependent can be perceptually indistinguishable from the original object, an artist could regard such tokens as being as good as that original, as Duchamp did with replacements of lost readymades. Such precise tokens could then be thought to derive from the artist’s original concept in a manner that appropriately ﬁts the aesthetic value of the original. A performance that is documented on ﬁlm, videotape, or still photographs might be accepted by the artist whose work it is as being as acceptable as the original performance, both as a means of making it understood what the work is meant to be, and for making it possible to appreciate any aesthetic value of the work. The acceptably derived objects of the previous examples would count philosophically and artistically as much as any original for

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apprehending the identity of the work and appreciating the work’s aesthetic value, and so apprehension by a subject of such a relevant object would constitute an artistic complex. When this is not the case however, or when a reproduction or documentation is not regarded by the artist as being as legitimate a means both for apprehending the identity of the work and for appreciating the artwork in the manner that he originally intended, then the reproduction or documentation is of no relevance to the notion of artistic complex, as that notion is used to determine the ‘materials’ of Essentialist Abstraction.6 And this is the case even though it may remain true, as an epistemological matter, that we can as much understand with which object an artwork is meant to be identiﬁed in apprehending the reproduction or documentation as we do in apprehending the object on which the identity of the artwork originally depended, and even though it may be true that we can have an aesthetic reaction to either kind of secondary object as much as we can have to the original. 4. Kinds of relevant object and their ﬁguring in artistic complexes An object on which the identity of an artwork is relevantly dependent may be an object with which the work is meant to be identiﬁed, or it may be an object through which the work is meant to be identiﬁed. An object on which the identity of an artwork is relevantly dependent may be complex. As such, it may have an aspect with which the work is meant to be identiﬁed, and an aspect through which the work is meant to be identiﬁed. Finally, an object on which the identity of an artwork is relevantly dependent may be an object through which and with which the work is meant to be identiﬁed. 6 It would be possible for an artist to specify that any reproduction of any object relevant to the identity of a particular work of another artist’s is to be understood to be her work. In such a case any object derived from any object relevant to the identity of the ﬁrst artist’s work becomes relevant to the second artist’s work rather than merely to the work to which any original object produced by the ﬁrst artist is relevant. An artistic complex would result from a subject’s appropriately apprehending such a derived object relevant to the second artist’s work if that derived object is understood by the subject attending to it to be relevant to the second artist’s work, and such a complex would thus result as much as would an artistic complex result from a subject’s apprehending the speciﬁcation through which that identiﬁcation is eﬀected.

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The kinds of relevant object noted in the previous paragraph are objects on which the identities of objects are originally dependent. An object that is acceptably derived from any such original relevant object is itself a relevant object. Any kind of object on which the identity of an artwork is relevantly dependent is a constituent of an artistic complex when it is attended to in an event of awareness that is appropriate to apprehending its relevance to the identity of the artwork dependent on it, and so is appropriate too to appreciating any aesthetic value that the artwork may have. The previous and the following remarks pertain to artworks as wholes. However, remarks that pertain to objects with which artworks are meant to be identiﬁed pertain as well to objects with which parts of artworks are meant to be identiﬁed. And a subject’s apprehension of an object that is relevant to the identity and appreciation of part of an artwork also forms an artistic complex of which the subject, her apprehension, and the relevant object are constituents. 4.1. A relevant object with which an artwork is meant to be identiﬁed A relevant object with which an artwork is meant to be identiﬁed is an object in which the artwork is embodied. Artworks that are meant to be identiﬁed with original perceptual objects, including such things as paintings, sculptures, prints, photographs, and installations, are objects in which artworks are meant to be embodied. A created relevant object that an artwork is meant to be—such as Matisse’s Bathers by a River—forms part of an artistic complex of which a subject who is appropriately attending to it is also a part when it is being perceived. Selected objects are also embodied works, and as a selected object—such as Duchamp’s Bottle Rack—is attended to, the selected object forms part of an artistic complex of which the subject attending to it is also a part. Relevant objects with which parts of an artwork are meant to be identiﬁed may include some that are created and others that are selected, as in a Rauschenberg combine painting. Whether an object that is derived from the original created, selected, or partially created and partially selected object with which an artwork is meant to be identiﬁed counts as a relevant object must be determined by the artist whose work it is. Although a derived object

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is a constituent of a complex of which a subject who is apprehending it is also a constituent, only a relevant object can form part of a complex that is artistic. For instance, a complex exists when someone looks at an object, such as a photograph, slide, or poster, that is derived from Bathers by a River, but it is not an artistic complex. This is because only the original object in which the work is embodied counts for Matisse as relevant. Many of the objects on which Duchamp’s readymade artworks, such as Bottle Rack, were originally dependent were lost, and were replaced by certain derived objects that are visually indiscernible from the objects in which the identities of readymade artworks, such as Bottle Rack, were originally embodied. Because these derived objects were licensed by Duchamp to be relevant to the identities of those works, apprehension of such a derived object would form an artistic complex of which the apprehending subject and the relevant object apprehended are constituents. A derived object that the artist has not recognized to be relevant is diﬀerent from a derived object that the artist has recognized to be relevant. This is the case even if a derived object will enable a person who apprehends it both to comprehend the identity of a particular work and to appreciate its value. For instance, a photograph of Bottle Rack is derived from Bottle Rack, and it must be admitted that one can understand what a work such as Bottle Rack is meant to be, and can appreciate its value, by viewing a picture of it in connection with reading about it. This is worth mentioning in this context since it must be admitted that part of the importance of Duchamp’s readymades is to have made viewing the readymades themselves dispensable. This means that one only needs to know what Duchamp did to understand and appreciate the importance of the readymades, and this dispensability of perceptual appreciation of an object in favor of conceptual appreciation of an idea, makes Duchamp the progenitor of Conceptual art. These points having been noted, a photograph of Bottle Rack could not count as a relevant object unless Duchamp so recognized it. As far as I know, this is something that he never did. Although apprehension of a photograph of Bottle Rack is a constituent of a complex of which the apprehending subject and apprehended photograph are constituents, it is not an artistic complex if the photograph is not a relevant object.

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4.2. A relevant object through which an artwork is meant to be identiﬁed A speciﬁcation is an example of a relevant object through which an artwork is meant to be identiﬁed. The original speciﬁcational language that is relevant to the identity of an artwork is singled out perceptually as a certain visual object, and the meaning of the language is singled out in comprehension as indicating a particular object with which all or part of an artwork is meant to be identiﬁed. When an original speciﬁcation is phenomenally isolated or attended to in these ways, it forms part of an artistic complex of which the subject apprehending it is also a part. Whenever the meaning of a speciﬁcation comprehended points to a noumenal object, then the meaning itself and not that to which the meaning points is a phenomenally isolated constituent of an artistic complex. An example of an object singled out in awareness through which an artwork is meant to be identiﬁed is the perceptible language and the meaning of the language that speciﬁes the object with which Robert Barry’s work all the things . . . is meant to be identiﬁed. When that language is perceived and comprehended by a subject attending to the original object in which Barry placed it, it forms part of an artistic complex of which the subject is also a part. Were an artist, such as Barry, to accept an object that is derived from his original speciﬁcation as a relevant object, such as a photograph of it, or a newly typed or written token of the speciﬁcation that is produced from knowledge of the original, then an artistic complex would exist that included the relevant object and a subject who is appropriately attending to it. Original photographs, documentation, and writing that pertains to the relation of the photographs and documentation to an artwork may be relevant objects through which an artwork is meant to be identiﬁed. The original photographs and informative language that pertain to a work from Barry’s Inert Gas Series are examples of such a relevant object. Were Barry to recognize things that are derived from these originals, such as photographs and language that appear in books, as being acceptably derived from them, then they too would be relevant objects through which an artwork from that series is identiﬁed, or through which the intended identiﬁcation of an artwork with an object can be understood.

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4.3. A complex relevant object that has an aspect with which an artwork is meant to be identiﬁed and an aspect through which an artwork is meant to be identiﬁed A relevant object that combines both of the points of 4.1 and 4.2 has an aspect with which a part of the artwork is meant to be identiﬁed, and another aspect through which a diﬀerent part of the artwork is meant to be identiﬁed. Thus not only could an artist consider an object that is singled out by a speciﬁcation to be a part of an artwork, but she could consider the perceptual object that includes the speciﬁcation to be a part of the same complex work. In such a case the relevant object would consist of perceptual and linguistic media, and the artwork would consist partially of an embodied and partially of a speciﬁed object. An example may be one of Roman Opalka’s number paintings. Each canvas full of painted integers would be an object with which part of the work is meant to be identiﬁed, and the painted numbers could be understood to function as speciﬁcations through which the referents of these symbols— perhaps thought of as abstract entities—are understood to form part of the work as much as the embodied objects that specify them. When all or any part of an object relevant to the identity of such a work is attended to in a way or ways appropriate to apprehending the identity of the artwork, then the relevant object being attended to forms part of an artistic complex of which the attending subject is also a part. An object that is acceptably derived from such a relevant object would form part of an artistic complex of which a subject who is attending to it is also a part. 4.4. A relevant object through which and with which an artwork is meant to be identiﬁed A relevant object through which and with which an artwork is meant to be identiﬁed is a certain kind of speciﬁcation. The meaning of a speciﬁcation that singles out the object that an artwork is meant to be need not be directed away from the language whose meaning it is. It can be directed instead to that very language. In such a case the perceived language becomes self-referring, and becomes both that which singles out and that which is singled out. The speciﬁcation this here now is an example of an artwork whose identity is understood

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to be embodied in the very perceptual language the comprehension of which makes that understanding possible. As the speciﬁcation this here now is perceived and comprehended it is a phenomenally isolated constituent of an artistic complex of which the subject apprehending it is also a constituent. The points made in section 4.2 above about the acceptable derivation of an object from an original speciﬁcation apply here. And an artistic complex would exist that included the relevant object and a subject who is appropriately attending to it. 4.5. Relevant objects and artistic complexes Although there are diﬀerent kinds of relevant object as noted, any artistic complex in which a relevant object of any kind ﬁgures will have certain features. These features will include properties of the subject, properties of the relevant object, and relations holding between the subject and the object in addition to the uniting relation of awareness in virtue of which they are constituents of a particular complex at a particular time—the uniting relation that itself will have a speciﬁc character determined in relation to the nature of the object that it apprehends. In addition, certain facts will pertain to these things. It is the purpose of the remaining divisions of this part of this volume to identify these features, things that they logically presuppose or entail, or in any signiﬁcant way involve, or on which they are otherwise dependent, as well as to consider issues of relevance to them. The results of these considerations will form the ‘material’ that Essentialism will use, in various forms and measures, in its investigation into the limits of Abstraction.

DIVISION II: ARTISTIC COMPLEXES AND SUBJECTS

Introduction A subject is a presupposition of eﬀecting and apprehending the identity of any work of art. Such a subject is a conscious agent. Any object on which all or part of an artwork is relevantly dependent is implicitly directed to subjects who could attend to it. Certain properties of subjects are required of the existence of any artistic complex, such as consciousness and agency, and certain things will characterize a subject who forms part of an artistic complex, such as attending to the object that forms part of the complex, and knowing that that object is relevant to the identity of a particular work of art. Kinds of conscious event that are of interest to Essentialist Abstraction are identiﬁed in this division, and diﬀerent forms of conscious event are enumerated, as are certain structured forms of conscious event that may be utilized by an Essentialist investigation of the limits of Abstraction. Kinds of epistemological event that pertain to artistic complexes are considered in this division before the pertinence of agency and the relation of awareness and agency are also considered.

1. Any artwork is related to consciousness It is not possible to conceive of an artwork that would not have a relation to consciousness. Consciousness is both a necessary condition of an artist’s eﬀecting the identity of an artwork and of a subject’s understanding of that intended identity. This is the case even when it is not possible to be aware of an object that an artwork is meant to be, since, in such a case, it must be possible to be aware that the work is meant to be identiﬁed with that object. 1.1. Consciousness is a necessary condition of the identity of any artwork Two points of relevance to the project of this book need to be recognized about consciousness and the identity of any work of art: i.) For

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any work of any kind to enter art history, it must be possible to understand with which object or objects the artwork is meant to be identiﬁed. Accordingly, any kind of object meant to be an artwork presupposes a relation to an object in or through which the intended identiﬁcation of the work with the object can be made comprehensible. Such an object must be a public perceptual object of some kind that is suited to understanding the identity of the artwork. This does not entail that the artwork must itself be a perceptual object, or some kind of phenomenal object that has a perceptual dimension, but only that the identity of each artwork depends on an object of which subjects can theoretically be aware. Thus even a noumenal artwork, such as that which is speciﬁed by everything of which you are not now aware, is dependent on awareness of the language by which that object is delineated. ii.) One is prohibited logically from conceiving of the identity of an artwork that would lack a relation to consciousness since, in conceiving of the work, the conceiver would be made aware of the identity of the work in that conception, and conceiving is a kind of conscious event that relates a subject to an object. Not even the most Abstract artwork can then dispense with a relation to consciousness. 1.2. Consciousness is a necessary condition of responding to any artwork Any simple or complex object on which the identity of an artwork is relevantly dependent is implicitly directed towards awareness in that no responses of any kind that such an object can be designed to elicit can occur apart from being aware of the object.1 Responses to any object on which the identity of an artwork is relevantly dependent could include experiences that are aesthetic, 1 Use of the term ‘any,’ in speaking of any object on which the identity of a particular work of art is relevantly dependent, does not necessarily imply plurality, or does not mean that the identity of the work is either dependent on or equally instantiated in two or more objects. Rather, use of the term ‘any’ is meant to include the possibility of the exclusivity implied by the use of the word ‘the’ in addition to the possibility of plurality. This is true too for the use of the words ‘a’ and ‘an’ as either pertains to an object relevant to the identity of an artwork. Accordingly, when I speak of ‘any relevant object,’ ‘a relevant object,’ or ‘any object,’ or ‘an object,’ on which the identity of an artwork is dependent, it cannot be inferred from any of these uses how many objects are relevant to the identity of the work, but it may only be one. And again, remarks that pertain to any object on which the whole of an artwork is relevantly dependent apply to an object on which any part of the artwork is relevantly dependent.

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emotional, intellectual, or a combination thereof, in addition to such basic responses as comprehending the identity of the work and apprehending at least certain aspects of the nature of the work in virtue of apprehending such a relevant object. However, any such response presupposes being aware of a relevant object that provides for the possibility of its occurrence.

2. Consciousness and traditional and Essentialist art Although artworks are usually meant to be objects that are intentionally directed to awareness, in the sense that they are meant to be seen, heard, or in some way apprehended, awareness has typically been taken for granted as something that knowledge and any appreciation of works of art presuppose. This taking of awareness for granted means that it has been customary for artists to treat awareness merely epistemologically, or transparently as it were, or in tacit fashion, rather than engaging it intentionally either as a means of producing certain kinds of object—including private phenomenal objects—that artworks are meant to be, or as a means by which the identiﬁcation of artworks with certain kinds of object can be eﬀected in virtue of the occurrence of certain events of awareness on which those objects depend.2

2 By treating “awareness merely epistemologically” I mean that we know, for instance, that we are to identify a painting with a certain circumscribed object of awareness in a ﬁeld of awareness of which it forms part; or that we know that we are to identify a string quartet with a certain sequence of apprehensible sounds; or that we know that we are to identify a novel with what is apprehended in reading it—typically a story with its characters, setting, plot, dialogue, and relevant relations between such things—and that the kind or kinds of awareness relevant to such knowledge is a presupposition of that knowledge. And it might be argued that so treating awareness epistemologically represents “engaging it intentionally . . . as a means of producing certain kinds of object . . . that [an] artwork [is] meant to be,” where that indicates that awareness is a necessary condition of the being or existence of the work. Although that may be the case, the argumentative point is ontological and, as such, is not determinative of the identity of the work in the active sense that I mean to recognize in this section and in the section on kinds of media in Division IV of this part of the book below. As earlier indicated, Victor Burgin’s Idea Structures Project, 1970, makes partial use of awareness to determine objects with which parts of the work of that title are meant to be identiﬁed. See Lippard, Lucy R. Six Years pp. 171–172. Because that work is too long to reproduce here, and because it may be unfamiliar to the reader, that which is delineated by the following

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Since it is possible to engage awareness actively as noted, and awareness is indispensable to originally eﬀecting and subsequently comprehending the identity of artworks, the Essentialist must ask what possibilities there are for working with awareness itself, in its various kinds and forms, in his pursuit of the limits of Abstraction. If awareness can be used as a means of producing certain kinds of object, and as something on which certain other kinds of object are dependent, then an Essentialist relation will be established between the identity of an object and a property of the subject on which that identity is dependent.

3. Kinds of conscious event of interest to Essentialism Because the determination of the limits of Abstraction in art is an art-historical issue, that determination depends on public perceptual objects whose apprehension will allow the identities of the works in which those limits are determined to be comprehended. And because the determination of Abstract art’s limits depends on the use of visual language, the public perceptual objects utilized by Essentialism will be both visual and linguistic.3 Thus both visual perception and linguistic comprehension are kinds of conscious event that must be utilized by Essentialism. A limit of Abstraction might be determined in a noumenal object as well as a phenomenal object. However, it must be possible in any case to comprehend the identity of either kind of object. Accordingly, the identiﬁcation and understanding of the determination of any limit of Abstraction will depend on comprehending the identity of the work in which such a limit is determined. The identity of an artwork may be made to rest on interpreting apprehensible material that is relevant to the determination of that identity, and so acts of interpretation are relevant to Essentialist Abstraction. The identity of an artwork may also be meant to depend on a judgement or judgements that follows from the comprehension of apprehensible material—including language and aspects of the visual object

speciﬁcation is an example of an object that could be meant to be an artwork and that is actively dependent on consciousness in the manner considered in these ﬁnal sections: anything of which you are now thinking in virtue of thinking of anything of which you are now thinking. 3 See 6 of this division on pp. 186–187 below, and Part Four.

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in which that language is embedded—and so a judgement of identity by which the identity is determined is of interest to Essentialism. Essentialism will also have to explore the possibility of using diﬀerent kinds of thought to determine the identities of works in which Abstract limits are determined. These include thinking of, thinking about, and deductive thinking. Because any subject who apprehends any visual linguistic object that is used by the Essentialist will have a sense of the past and the future in addition to the present, and because both memory and anticipation might be utilized in the determination of an object that an artwork is meant to be, the Essentialist will have to consider the relevance of memory and anticipation to the determination of the limits of Abstraction in addition to kinds of conscious event that are directed towards as they occur in the present. Kinds of conscious event of interest to Essentialist Abstraction thus include: visual perception; linguistic comprehension; comprehension of identity; interpretation of apprehensible material, as the interpretation is involved in the determination of identity; judgements of identity, as apprehensible material in relation to which the judgement is eﬀected allows for the possible determination of diﬀerent identities; species of thinking: including thinking of, thinking about, and deductive thinking; recollection; and anticipation. Because consciousness cannot be eliminated from eﬀecting and comprehending the identity of even the most Abstract artwork; because determining the limits of Abstraction must eliminate what can be eliminated and must investigate ways of working with things that cannot be eliminated; and because there are diﬀerent kinds of conscious event that must be considered as useful to the determination of the limits of Abstraction, the kinds of conscious event listed can be understood to be part of the ‘material’ of Essentialism, as much as kinds of color are part of the material of polychromatic painting. All of these kinds of conscious event are of interest to the Essentialist not just as means that can be used in some combination to eﬀect the identity of an Abstract artwork, but they are of interest to the Essentialist as means of shaping if not determining the aesthetic of the artwork eﬀected.

4. Forms of conscious event of interest to Essentialism There are diﬀerent forms in addition to diﬀerent kinds of conscious event, and as at least certain of these forms may be relevant to kinds

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of conscious event and object utilized by Essentialism, the fundamental forms of awareness and their relations to diﬀerent kinds of object must be identiﬁed and considered to the extent to which they are material to those aims. 4.1. Any event of awareness is either Intentional or non-Intentional 4.1.1. Intentional awareness. A conscious event is ‘Intentional’ when it is directed to, represents, or is about something.4 Any Intentional event of awareness has at least one object, and an object of an Intentional event of awareness is an ‘Intentional object.’ An Intentional object of an Intentional event of awareness may or may not itself be an event of awareness. For instance, a painting is the Intentional object of an event of perceiving it, but the painting is not itself an event of perception. On the other hand, my event of perceiving a painting can itself be the Intentional object of an event of awareness since I can be aware of my awareness of the painting. Further, the Intentional object of an event of awareness that itself is an event of awareness may or may not itself be an Intentional event with its own Intentional object. My being aware of my awareness of a painting takes as its Intentional object an event of awareness with its own Intentional object, while my reﬂecting on my anxiety takes an event of awareness—anxiety—that is non-Intentional. Artworks, artistic complexes, and Intentional awareness. Any artistic complex presupposes Intentional awareness since any event that links any conscious subject and a public perceptual object on which the identity

4 I follow John Searle in denying that all conscious events or states are Intentional. Searle observes that “not all, only some, mental states and events have Intentionality,” and so “the class of conscious states and the class of Intentional mental states overlap but they are not identical, nor is one included in the other.” According to Searle, it is also false that all Intentional mental states are conscious. This is because unconscious mental states, such as beliefs that have not been brought to consciousness, but that could be brought to consciousness, are about something. Searle’s ﬁrst quote is taken from page 1 and the second from page 3 of his Intentionality: An essay in the philosophy of mind, Cambridge: Cambridge Univ. Press (1983). Searle also distinguishes between ‘intrinsic’ Intentionality, that characterizes certain conscious and mental states, and ‘derived’ Intentionality, that can be attributed to such things as maps, portraits, and meaningful language, although derived Intentionality is dependent on “the Intentionality of human agents.” See both Intentionality and Searle’s The Rediscovery of the Mind, Cambridge, MA: MIT Press (1995) pp. 78–80.

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of an artwork is relevantly dependent is Intentional. Any visual awareness of such a relevant object is Intentional; any understanding of the relevance of such an object to the identity of an artwork that is dependent on it is Intentional; any comprehension of any language on which understanding the identity of an artwork is dependent is Intentional; and any understanding of that identity is Intentional. The Intentionality of these kinds of Intentional event is as indispensable to Essentialist Abstraction as are the kinds of event that are Intentional. 4.1.2. Non-Intentional awareness. A ‘non-Intentional’ event of awareness lacks the act-object properties of an Intentional event of awareness, and, in not being directed to, representing, or being about anything, whether itself or something else, it is an object that is simply a structureless occurrence. For the person whose pain it is, an event of feeling pain is an example of a event of awareness that is non-Intentional.5 Although an event of non-Intentional awareness may be conceptually or causally connected to other things in a ﬁeld or history of awareness in which it is situated, such a connection is extrinsic and

5 Speaking of an event of feeling pain might be thought to suggest that the pain is one thing and the event of feeling is another thing that, so to speak, grasps the pain as an event of comprehending something might be said to grasp what is comprehended, in which case the event of feeling would be Intentional. However there is no distinction between a pain as an object felt and the event of feeling pain for the person whose pain it is. Accordingly, saying that I am aware of my pain in non-Intentional awareness can be understood to be properly stated as “I am aware in my pain” to reﬂect the equivalence of a non-Intentional event of awareness to a painful experience. Cf. Searle’s discussion of conscious states, such as elation and anxiety, that, although conscious, lack Intentionality. Searle, John R. Intentionality, p. 2. Conceiving of such non-Intentional events of awareness as pains as events of awareness does not preclude talking of them in any other respect. For instance, a pain might be conceived of either as a neurophysiological condition of which we are not conscious but which is the cause of the conscious experience we call pain when we are awake, or a pain might be conceived of as a kind of temporally extended entity of which the person whose pain it is can be conscious at some time or times and unconscious at others, so that a pain of which a person is now conscious may be the same pain of which she was earlier and may yet later be unconscious. These possibilities are irrelevant however to the consideration of the nature of such events as pains when they are events of experience, and that nature includes their being non-Intentional events of awareness in addition to their having other characteristics, to be described below, as events of awareness. On the possibility of speaking of unconscious pains as an alternative to “the Cartesian notion that for something to be a genuine pain, it has to be conscious” see Searle, John The Rediscovery of the Mind, pp. 164–167.

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not an inherent property of the event qua event, or as an item of experience. 4.2. Any event of awareness has or lacks structure Any Intentional event of awareness has structure, in having, being directed to, representing, or being about an object. And any nonIntentional event of awareness, in lacking any such characteristic, lacks structure.6 4.3. The structure of Intentional events is reﬂexive or irreﬂexive Any Intentional event of awareness is either reﬂexive or irreﬂexive, and reﬂexivity and irreﬂexivity are the types of structure possible for Intentional events. 4.3.1. Reﬂexive awareness. Any reﬂexive event of awareness is Intentional, and in an event of ‘reﬂexive’ awareness an object is directed to, linked to, or turned back on itself in or through that event as the event takes that object as its Intentional object. Examples of reﬂexive awareness include: an event of my thinking of myself; an event of consciousness that takes itself as its Intentional object; and an event of comprehending the perceptible language this here now. The examples illustrate that ‘reﬂexive’ describes the structure of Intentional awareness whose Intentional object is linked to itself in or through that awareness. Such an Intentional object is a ‘reﬂexive object.’

6 The view that a non-Intentional conscious event, such as a pain, lacks structure in the sense indicated is compatible with an event of this kind having a natural or metaphysical structure that links it to the brain, but which natural or metaphysical structure is not an apparent part of the event as a conscious occurrence. Cf. Colin McGinn: “. . . consciousness must have a hidden structure, intrinsic and essential to it.” The reason that consciousness must have such a hidden structure according to McGinn is that “the unknown properties that link it to the brain must be internal to consciousness.” (His italics.) “Experiences have a ‘deep structure’ in somewhat the way that sentences do—or indeed natural substances like gold and water,” and this is true of all conscious events, including those that are non-Intentional. McGinn, Colin The Character of Mind: An Introduction to the Philosophy of Mind, Second Edition, Oxford: Oxford Univ. Press (1996). All quotes are on p. 44.

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4.3.2. Irreﬂexive awareness. Any ‘irreﬂexive’ Intentional event of awareness takes an object other than itself as its object of awareness, and, in doing so, it neither turns back on itself, nor is the object directed to or turned back on itself in or through the event as the event takes that object as its Intentional object. The Intentional object of an irreﬂexive Intentional event may or may not itself be an event of awareness, but since the event is irreﬂexive, its Intentional object is in any case something other than the Intentional event of which the Intentional object is the object. Such an object is ‘irreﬂexive.’ Looking at a painting, reading a book, listening to opera, and my awareness of my listening to opera are kinds of irreﬂexive Intentional event with diﬀerent kinds of Intentional object, the last of which is itself an event of awareness. 4.4. Areﬂexive awareness Any non-Intentional event, as non-Intentional, lacks structure. In lacking the kinds of structure possible for Intentional events, a nonIntentional event of awareness is said to be ‘areﬂexive,’ where an event’s being areﬂexive indicates that it is neither reﬂexive nor irreﬂexive. Any non-Intentional event, in lacking structure, can neither be an event in which the identity of an artwork is comprehended, nor can it be the kind of event in or through which an object that an artwork is meant to be is both eﬀected and reﬂects in itself essential elements of artistic complexes. This is the case even though an artwork could be meant to be identiﬁed with an event of areﬂexive awareness. Because determining the limits of Abstraction in art requires using diﬀerent kinds and forms of structured awareness that implicitly or explicitly address, as they utilize, essential elements of artistic complexes to result in objects that depend on structured awareness, I will say nothing about non-Intentional awareness except where it is relevant to the deﬁnition of something following, but will concentrate instead on Intentional awareness. 4.5. Any event of awareness is either monadic or polyadic 4.5.1. Monadic awareness. An event of awareness is ‘monadic’ when it is a self-contained unit, in the sense that, although it may be

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self-directed, it is not directed to or about anything other than itself. A monadic event may be Intentional or non-Intentional. A nonIntentional event of awareness, in lacking structure, lacks direction, representation, or aboutness, and so, considered simply as an occurrence, is a self-contained event. A pain is an example of a monadic non-Intentional event. An Intentional event is monadic when it takes itself as its object, as in an event of my consciousness of my consciousness.7 Although such a reﬂexive event has direction, it is directed solely to itself. Accordingly it too is a self-contained unit, and so is monadic as that term is deﬁned. 4.5.2. Polyadic awareness. Any event of awareness that is directed to, about, or represents an object other than itself is ‘polyadic.’ Seeing a painting, thinking about Surrealism, recollecting an interior, imagining the room being a diﬀerent color, and devising a plan for a work are all polyadic. These are all examples of polyadic awareness that are irreﬂexive. Both an event of my thinking of myself, and an event of comprehending the perceptible language this here now are examples of polyadic events that are reﬂexive. A polyadic event that is ‘dyadic’ is directed to a single Intentional object. Thus my thinking about something is dyadic in being directed to a single Intentional object. A polyadic event that is ‘triadic’ is directed to two Intentional objects, one of which points beyond itself to the other. The two Intentional objects of a triadic event are Intentionally linked in being conceptually or referentially connected in the same Intentional event, and they do not simply coexist in the same event, as may happen with two or more objects in a dyadic event. My thinking about my thinking about something is triadic in being directed to an Intentional object that points beyond itself to a second Intentional object that is conceptually or referentially linked to the other Intentional object of that event. The designation of any more complicated Intentional event would be determined by adding

7 Although an event of my consciousness can take itself as its Intentional object, and so be monadic, it is important to recognize that the object of such an event is the event itself and not some sort of substantial self that may underlie and make possible diﬀerent events of the same kind. If the latter were the case, then the event would not be reﬂexive and monadic, but would be reﬂexive and polyadic. Further, such a reﬂexive monadic event as that considered is possible on either a Humean or non-Humean view of the self, as is a polyadic reﬂexive event of thinking of myself.

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the awareness of a number of Intentional objects to the number of objects of which the Intentional event is aware when these objects are Intentionally linked as indicated. 4.6. First-order awareness A subject s’s event of awareness e of an object x is ‘ﬁrst-order’ awareness either when e is non-Intentional, and so e and x are diﬀerent ways of naming the same unstructured entity, or when e is Intentional, but its Intentional object x is not an event of awareness f of s’s that occurs when e occurs. Thus a subject’s event of awareness of an object is ﬁrst-order awareness either when the awareness is a structureless occurrence, or when the awareness has an Intentional object, but where that object of awareness is not itself the subject’s simultaneous awareness of an object. Feeling pain, a pain felt, or being in pain are diﬀerent ways of talking about an unstructured event of awareness that itself is an object, and, as unstructured, feeling pain is neither the awareness of an object other than that awareness, nor is feeling pain the awareness of the awareness that is the pain.8 Each of the following is an example of a subject’s event of awareness of an object of awareness: sensing a color, perceiving a tree, thinking about Mars, imagining being on a beach, and recollecting an encounter. However, as each is the subject’s Intentional event of awareness of an Intentional object, and none is the subject’s Intentional awareness of either an Intentional or a non-Intentional event of awareness of that same subject’s that occurs when the event that takes it as its Intentional object occurs, they are examples of ﬁrst-order awareness. Jane’s awareness of John’s awareness of her is ﬁrst order since, although the Intentional object of Jane’s awareness is an event of awareness, that event of awareness is John’s and not Jane’s. 4.7. Second-order awareness A subject s’s event of awareness e of an object x is ‘second-order’ awareness when e is Intentional, and x is both the Intentional object 8 This of course does not preclude the possibility of my being aware of the ﬁrstorder event of being in pain in a second-order event that has the ﬁrst-order event as its Intentional object.

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of e and is itself an event of awareness of s’s that occurs when e occurs. In such a case x and e could be diﬀerent ways of talking about an Intentional event that is reﬂexive and monadic, in which case e is directed to itself as x. Or x could be an event of awareness f of s’s that occurs when e occurs that is the Intentional object of e. In the latter case f could be Intentional or non-Intentional. If f is non-Intentional, then it is areﬂexive, and monadic. If f is Intentional then it is polyadic, although it could be either reﬂexive or irreﬂexive. In either of the latter cases, where f is the Intentional object of e, e has an object other than itself as its object. A subject’s event of awareness exists then at a second level either when it takes itself as its object of awareness, or when its object is a ﬁrst-order event of awareness that forms part of that same subject’s history of awareness at the same time that it does, and which ﬁrst-order event is either monadic or polyadic. Jane can be aware of a painting in an event of seeing that is a ﬁrst-order Intentional event that belongs to Jane’s history of awareness. And Jane can be aware of her awareness of the painting when she is aware of the painting. Since both Jane’s awareness of the painting and her awareness of her awareness of the painting form part of Jane’s history of awareness at the same time, and the second Intentional event takes the ﬁrst Intentional event as its Intentional object, it is second order. If Jane were aware of the painting at some time t1 and were then aware of her earlier awareness of the painting at t1 at some later time t2, then Jane’s later awareness at t2 of her earlier awareness of the painting at t1 would be ﬁrst order, since although the later event of awareness takes an event of awareness of the same subject’s as its Intentional object, the events do not occur at the same time, but are temporally separate. The order of any possible event of awareness higher than secondorder awareness would be determined by adding the awareness that is aware of awarenesses to the number of awarenesses of which it is aware. For instance, a subject’s event of awareness of his awareness of an awareness of his would be a ‘third-order’ awareness. Levels of awareness beyond ﬁrst-order awareness can be grouped together under the rubric of ‘higher-order’ awareness, while ﬁrst-order awareness can be called ‘lowest-order’ awareness to contrast with awarenesses of higher order. Any higher-order awareness beyond second-order awareness would be Intentional, irreﬂexive, and polyadic.

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4.8. The ﬁve fundamental forms of conscious event Any event of awareness is either Intentional or non-Intentional. Any non-Intentional event is areﬂexive, monadic, and ﬁrst order. An Intentional event can be either reﬂexive or irreﬂexive. A reﬂexive event is either monadic and second order, or is polyadic and ﬁrst order. Any irreﬂexive Intentional event is polyadic, but such an event can be either ﬁrst order or higher order. Thus there are ﬁve fundamental forms of conscious event as seen in Diagram Three below. Events of awareness

Intentional

Reﬂexive

Monadic

Second order

Polyadic

Non-Intentional

Irreﬂexive

Areﬂexive

Polyadic

Monadic

First order Higher order

First order

First order

Diagram 3.

4.8.1. Any monadic reﬂexive event is second order. Monadic reﬂexive events can only be second order since, although such an event as an event of my consciousness of my consciousness of my consciousness is a third-order event, the event that takes my consciousness of my consciousness as its Intentional object is directed away from itself and so lacks the structure that makes a reﬂexive Intentional event monadic. (And in failing to reﬂexively relate its Intentional object to that object, it also lacks the property required for an Intentional event to be reﬂexive.) 4.8.2. Any polyadic reﬂexive event is ﬁrst order. For an event of polyadic reﬂexive awareness e to be higher order, its Intentional object would have to be a ﬁrst-order or higher-order event of awareness f that occurs when the polyadic awareness in or through which that object

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is directed to or turned back on itself occurs, and where both e and f are events of awareness of the same subject. However, it is not clear to me that there are such events with such objects. Thus the Intentional object of a subject’s event of thinking about thinking is either the event turned reﬂexively on itself, in which case it would be monadic rather than polyadic, or, as seems more accurate, the Intentional object of such an event is not itself an event of awareness of the subject who is thinking of that object, but is a kind of general intellectual activity about which the subject is thinking. And if that is the case, then the Intentional event, although polyadic, is irreﬂexive. And an event of thinking about thinking about thinking is simply a higher-order event that takes the other event as its Intentional object without its being an event in or through which that object is directed to or turned back on itself. As such, the Intentional event is irreﬂexive. It might be thought that the reﬂexive monadic event that is named by the speciﬁcation an event of your awareness of your awareness that occurs in virtue of understanding the relevance of this information to provoking an event of your awareness of your awareness is the Intentional object of the event of understanding the speciﬁcation that is named by the speciﬁcation. If that thinking is correct, then the monadic event that is named by an event of your awareness of your awareness would be reﬂexively linked to itself in polyadic reﬂexive awareness that is higher order in occurring when the monadic event occurs and taking that second-order reﬂexive event as its Intentional object. It would then be incorrect that all polyadic reﬂexive events are ﬁrst order. However, it is not clear to me that this is the case. The existence of the event that is named by your awareness of your awareness is provoked by the polyadic event of awareness that is the event of understanding the speciﬁcation that is named by the speciﬁcation. If the Intentional object of your awareness of your awareness is linked reﬂexively to itself in the monadic Intentional event that is named by that language, and that event is not also linked reﬂexively to itself through the polyadic event of understanding the speciﬁcation, then that event of understanding is ﬁrst-order and irreﬂexive. The coexistence of these monadic and polyadic events does not necessarily indicate that they are linked reﬂexively rather than being linked causally and conceptually as indicated by the speciﬁcation that names them. And although the Intentional event named by your awareness of your awareness may itself be the Intentional object of a higher-order event of irreﬂexive aware-

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ness that coincides with that monadic event and that is also provoked by the event of understanding the speciﬁcation, it does not seem to be the case that the referent of your current awareness of your current awareness is linked reﬂexively to itself through the event of comprehending the speciﬁcation. Rather, it seems to be reﬂexively linked to itself simply in the monadic reﬂexive event that is its own Intentional object. If that is correct, then the event of understanding the speciﬁcation is not an event of a higher-order event of polyadic reﬂexive awareness. If I am wrong about the examples considered, or examples that I have not considered would indicate that higher-order polyadic reﬂexive awareness should be recognized, then there are six fundamental forms of awareness rather than ﬁve, and the possible relevance of higher-order polyadic reﬂexive awareness to Essentialist Abstraction would have to be creatively investigated.

5. Consciousness and Essentialist Abstraction Any artistic complex depends on an Intentional event of perception of a public perceptual object on which the identity of an artwork is relevantly dependent. Any perceptual awareness of such a perceptual object is irreﬂexive, polyadic, and ﬁrst order. Any comprehension of the identity of any artwork is Intentional, although such an Intentional event may be reﬂexive or irreﬂexive. If it is reﬂexive it may be either second-order monadic awareness or ﬁrst-order polyadic awareness. If it is irreﬂexive it is polyadic, but it may be ﬁrst order or higher order. Because Intentional events may be either reﬂexive events that are monadic or polyadic, or irreﬂexive events of diﬀerent orders; because language can be directed to a subject comprehending it to result in an Intentional event that is either some order of irreﬂexive awareness, or that is reﬂexive and monadic, or that is reﬂexive and polyadic; and because the Intentional object of any of these kinds of Intentional event may be meant to be a work of art, the Essentialist investigation of the limits of Abstraction will have to include exploring the use of reﬂexive events that are either monadic or polyadic in addition to kinds and orders of irreﬂexive awareness in the determination of its objects. And given that diﬀerent kinds of object can be eﬀected in relation to these diﬀerent kinds of awareness, the Essentialist investigation cannot ignore the possibility that

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diﬀerent Abstract limits may be determined through the use of each kind of Intentional awareness. Although Essentialist Abstraction and the pursuit of simplicity are not the same thing, and the identiﬁcation of a limit of Abstraction may be quite complicated, and may involve an event or events or higher-order awareness as indicated, Essentialism seeks to avoid unnecessary complexity, and so would not utilize any higher-order awareness unless it could not be supplanted by a form of lower-order Intentional awareness in the determination of a limit of Abstraction.

6. Language, consciousness, and Essentialism Only language can be used to single out objects that cannot be perceived. Only language can be used to single out noumenal objects. Only language can be used to single out non-existential objects. Only language can be used to single out private objects. And only language can be used to refer to objects that, whether perceptual or non-perceptual, phenomenal or noumenal, existential or non-existential, or public or private, reﬂect in themselves essential elements of artistic complexes used to result in them. Because it may be possible for diﬀerent limits of Abstraction to be determined in objects of these diﬀerent kinds of object, any creative inquiry into the limits of Abstraction must investigate the use of speciﬁcations. And because events of comprehending speciﬁcations are required for the speciﬁcations to function, determining the limits of Abstraction will rely on events of comprehending speciﬁcations that single out objects in which the limits of Abstraction are determined. Investigating the limits of Abstraction will include consideration of the relevance and possible use of such events of comprehension in the determination of the limits of Abstraction. That in turn will involve exploring the use of language to engage diﬀerent forms that events of comprehending speciﬁcations can take to result in objects that are meant to be artworks to which the language that engages such acts refers. Any comprehension of any speciﬁcation will be Intentional. Such Intentional comprehension can be monadic or polyadic, depending on the nature of the speciﬁcation and its intended Intentional object. Monadic Intentional awareness is reﬂexive. Polyadic Intentional awareness may be either reﬂexive or irreﬂexive. Because of these facts, Essentialism will have to investigate the possible use of diﬀerent kinds

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of Intentional awareness in the determination of the limits of Abstraction, and will have to consider the relation of the Intentional objects of Intentional awareness to the events of which they are the Intentional objects, and the relation of any such Intentional object that is meant to be an artwork to the language that so speciﬁes it.

7. Agency Because a subject must choose to attend to an object on which the identity of an artwork is relevantly dependent, a subject will be agentially related to any such object to which he has decided to attend. Consciousness of and reﬂection on the perceptual object that forms part of an artistic complex are not independent of a subject’s volition. Comprehending the intended identity of an artwork is linked to the intention to comprehend that identity when a subject purposely attends to an object on which the identity of an artwork is relevantly dependent. Subjects are related to the objects on which artworks are dependent as decision-making agents, even when some or all of the decisions that they make when aware of such an object are made at an unconscious or a phenomenally transparent level so that the decisions, when occurring, are not themselves objects of conscious focus. The agential relation of subject to object will extend to any aspect of that object that calls for a decision on the part of the subject to attend to it in any manner required to understand its relation to the identity of the artwork dependent on it. As agency is an essential part of an artistic complex, the question is how it can be made a focus of, or can be made to form part of the material of, an Abstract investigation. If a subject’s agential relation to the perceptual object of an artistic complex can be extended beyond that complex to the artwork itself to which the complex pertains—in either relating directly to the origination of the artwork or in aﬀecting it in some way—then the customary separation between a work of art and the agency of a subject attending to it can be reduced or eliminated. And such reduction or elimination as intentionally addressed in either manner noted would ﬁt the purposes of Essentialism.

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A subject’s awareness and her agency are reciprocally involving when an object or objects of which she is or has been aware determines, at least in part, how she will choose to act, and when how the subject chooses to act determines, at least in part, the objects or the nature of the objects of which she is aware. The identity of an artwork depends on a perceptual object that is relevant to its identity, and no subject is aware of such a relevant object who is not agentially related to that object, and no subject is agentially related to the object who is not aware of that object insofar as both subject and object are constituents of the same artistic complex. Both awareness and agency are interdependent and ineliminable aspects of any artistic complex, and, as each I/intentional relation is ineliminable, each should be used or focused on as essential elements of Abstract investigations to the extent to which this is possible.

9. Knowing which, knowing that, and knowing what The identity of any artwork depends upon an object that can be singled out in awareness either at a time or over a series of times. When such an object is singled out, attention is focused on the object as this thing alone apart from all other objects on which attention is not so focused. An object singled out in awareness, in addition to being attended to as a particular phenomenal object, is also one that can be said to be identiﬁed at one or more levels of identiﬁcation. In this section I comment brieﬂy on the notions of singling out and identifying objects in relation to three fundamental kinds of epistemological relation of subjects to objects that are relevant to the interests of Essentialist Abstraction, and that I call ‘knowing which,’ ‘knowing that,’ and ‘knowing what.’ Before proceeding, however, the following points should be understood. I am here and throughout only concerned with kinds of awareness and knowledge that pertain to very sophisticated forms of intelligence, such as that of adult humans who make and apprehend works of art, since that is all that is relevant to this inquiry. Further, I use the term ‘knowing’ in this section in cases where it might be thought more appropriate to continue to use the terms ‘aware’ or ‘awareness.’ Thus, in lieu of saying that a subject ‘knows which’ I

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could say that he is ‘aware of which,’ and in lieu of ‘knowing that’ and ‘knowing what’ I could say that a subject is ‘aware that’ and ‘aware of what.’ But although these locutions are sometimes used, and are perfectly acceptable given the wide territory that the term ‘awareness’ is here allowed to cover, their consistent use would seem to make for more awkward exposition than the ones that I have chosen to illustrate the basic epistemological relations of subjects to objects relevant to this inquiry. The reason that it might be thought more appropriate to use ‘aware’ or ‘awareness’ rather than ‘know’ or ‘knowing’ is because of the philosophical uncertainty regarding what human beings can legitimately be said to know. But arguments that would contest the use of either of these words in these instances are not relevant to this work, which is concerned with an Essentialist construction of objects and the limits of Abstraction in art and not with the foundations of knowledge. Accordingly, the kinds of awareness with which this section is concerned deserve to be called ‘epistemological’ and not simply ‘conscious’ in light of the concerns of this investigation. In addition, it is important to note that I concentrate on the epistemological relations of subjects to objects singled out in awareness rather than to phenomenal objects in general because, as noted above, in order for a particular subject to be aware of a particular artwork, the subject must be able to be aware of a particular perceptual object in which the artwork is embodied or on which the identity of a particular artwork is otherwise relevantly dependent. And the way or ways in which a subject is epistemologically related to any other object or objects of which he is aware when attending to such an object is irrelevant. 9.1. Knowing which ‘Knowing which’ is the epistemological counterpart of the metaphysical requirement that the identity of a particular artwork is dependent on an object that a subject must be able to single out in awareness. Knowing which is also a property of any subject who forms part of an artistic complex since, in deliberately attending to the object or any object on which the identity of an artwork is relevantly dependent, the subject knows which object it is on which the identity of the artwork is so dependent. A subject must know to which object she must attend in order to understand and appreciate

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a particular work of art. This must be a relevant perceptual object in which the identity of the artwork is embodied, through which it is speciﬁed, or in which it is partially embodied and through which it is partially speciﬁed. And a subject knows which object it is that she has singled out for attention in attending to such an object whether or not the subject apprehending the object understands or properly appreciates what she apprehends. Knowing which also applies to an artwork’s parts, in that a subject must be able to know with which object any part of a complex object is meant to be identiﬁed. And knowing which is a property of any subject who forms part of an artistic complex of which a part of a relevant perceptual object is part since, in attending to an object on which the identity of a part of the artwork is relevantly dependent, the subject knows which object it is on which the identity of that part is so dependent. Because knowing which is a property of any subject who forms part of an artistic complex, an artwork will be more Essentially Abstract to the extent to which it engages the epistemological event of knowing with which object it or one of its parts is meant to be identiﬁed in the determination of the object with which it or one of its parts is meant to be identiﬁed. 9.2. Knowing that An object that is singled out and attended to in an event of awareness is at the very least an object of which the subject is aware that he is aware, since a subject cannot attend to a particular object and not know that it is an object of which he is aware. Attending to an object is an Intentional event that, as Intentional, presupposes the object of the event. The Intentional object of an Intentional event is implicitly phenomenal, and no object can be an object of focus that the person who is focusing on the object is not aware. It is simply nonsense then for someone to maintain that he is attending to something but does not know to which object he is attending. Whether or not a person knows anything of a more sophisticated sort about the object to which he is attending, he knows that it is the object to which he is attending. Thus to the primitive intellectual act of singling out an object in awareness, the primitive epistemological relation of ‘knowing that’ the object is singled out corresponds.

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Accordingly, for any relevant perceptual object in which the identity of an artwork is fully or partially embodied, a subject attending to such an object will know that he is attending to that object even if he is uncertain how to explain or interpret that to which he is attending. And for the meaning of any language through which the identity of an artwork is fully or partially speciﬁed, a subject attending to such a meaning will know that he is attending to that meaning even if he is uncertain how to explain or interpret that to which the meaning points. Knowing which and knowing that are coexistent properties of the subject who forms part of an artistic complex, and whether the relevant object that is part of the complex pertains to the whole or part of the identity of the artwork. This is because, as a subject attends to the object to which he knows he must attend to apprehend the identity of all or part of an artwork, he is aware that he is attending to that object. Because knowing which and knowing that will be properties of any subject forming part of an artistic complex, and Essentialism depends on using the essential elements of artistic complexes to determine the limits of Abstraction, the possible use of knowing which and knowing that to determine those limits will have to be investigated. 9.3. Knowing what ‘Knowing what’ an object is, in the basic sense, means recognizing or being able to state what kind or kinds of thing the object is, and, in the more sophisticated sense, means understanding or being able to interpret the object. Thus knowing what is conceptual knowledge that concerns identiﬁcation and comprehension, and it presupposes but is not the same as singling something out. Just as knowing which involves knowing that, so it also involves at least a rudimentary form of identiﬁcation or knowing what. This is because any object to which a subject attends as an object on which all or part of the identity of an artwork is dependent can at least be classiﬁed or conceptualized as an object, and, more speciﬁcally, as a particular phenomenal object ‘this-(here)-now,’ or ‘this thing to which I am now attending’ as relevant to that particular work of art. I am not maintaining that the concepts under which an object falls are necessarily themselves objects to which a subject is attending,

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or are even concepts that a subject consciously brings to mind in identifying an object in either rudimentary or more sophisticated events of identiﬁcation. Thus, if someone singles out an object that falls under the concept ‘apple’ it does not mean, when he is aware of that particular object, that he says ‘apple’ to himself because he recognizes the kind of object it is to which he is attending, or that, in identifying an object, the concept under which the object falls is as much a focus of attention as the particular object. I only mean that when an object is identiﬁed by someone—when the person knows what it is to which he is attending—that the person would be able to respond correctly to the question ‘What kind of object is this?’ in one or more ways in which the question can be properly answered. Every knowing what something is, in being able to identify the object, includes knowing that it is, in knowing that the object identiﬁed is an object of awareness, while the converse is not the case if we are talking about more sophisticated levels of identiﬁcation. Knowledge of an object singled out for attention is usually more sophisticated than the kind of rudimentary classiﬁcation considered above that will apply to such an object, including a relevant object that is part of an artistic complex. A subject knows what a relevant object is at least minimally in understanding its relevance to the artwork whose identity is dependent on it. His knowledge of what such an object is is more sophisticated when he understands, or can interpret, or can appreciate the artwork that is embodied in or speciﬁed through the relevant object, where that understanding or interpretation or appreciation is consistent with any known intentions of the artist and that is supported by apprehensible properties of the object that pertain to the work. Whatever its level of sophistication, it is suﬃcient to note for Essentialism that knowing what will be a property of the subject who forms part of an artistic complex in addition to knowing which and knowing that. As it is unavoidable, the Essentialist must attempt to utilize concepts that, as an object that is singled out in awareness forms part of an artistic complex, any concept that would pertain to that object will engage a subject comprehending it in a way or ways in which his investigations will better be furthered. More speciﬁcally, knowing what will be more Essentialist to the extent to which it concerns knowing which, knowing that, and other aspects of artistic complexes that are ineliminable.

DIVISION III: ARTISTIC COMPLEXES AND OBJECTS

Introduction Any artwork of any kind of artwork is essentially an object of some kind of object. Any object of any kind of object is minimally logical in being logically circumscribed according to laws of objects to be identiﬁed below. Each object has a particular identity that no object other than itself has or can have. Each object is minimally logically related to each object that lacks its particular identity. This includes the minimal logical relation of an object to any act of awareness in which its identity is comprehended; the whole of an object to any part of it; any part of an object to the whole of which it is part; and the relation of either whole or part to every other object. Whatever properties can be eliminated from an object with which an artwork is meant to be identiﬁed, its logical properties cannot be eliminated. Whether or not such an object is related in any other way to any other object, it will be logically related to that object, and to all other objects. The logical relations that hold between objects can be understood to situate all objects—including objects that artworks are meant to be, and objects that form parts of artistic complexes—in ‘the logical space of objects.’ An object has a compositional relation to some other object if it is either a part of some other object or if some other object is part of it, and it lacks a compositional relation to some other object if neither of these things is the case. The part-whole relation will have to be considered for any complex object that an artwork is meant to be, and whether the artwork is embodied or non-embodied, or is a complex work that consists of embodied and non-embodied objects. An object is either dependent on consciousness to be the object that it is in the sense that, apart from an event of consciousness to which the object is either equivalent, or of which it is the Intentional object, no object is that object. Or an object is independent of consciousness in that consciousness of the object is not a necessary condition of its being the object that it is. However, there are diﬀerent kinds of dependent and independent object. The identiﬁcation of the

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diﬀerent kinds of dependent and independent object is not only of intrinsic philosophical interest, but is relevant to Essentialist Abstraction. Any artwork must have an identity, and any historical determination of any limit of Abstraction depends on comprehending the identity of an artwork. As indicated, such comprehension occurs in virtue of a subject’s forming part of an artistic complex of which a public perceptual object that is relevant to the comprehension of the work’s identity is also a constituent. Such an object is not only dependent on consciousness to be public and perceptual, but it is a certain kind of type-dependent object to be identiﬁed below. Although comprehending the identity of an artwork depends on consciousness of a certain kind of type-dependent object, the object that an artwork is meant to be need not itself be some kind of dependent object, and an artwork that is meant to be an independent object may be meant to be one or another of the kinds of independent object noted below that it is possible for an artwork to be. As all of the things mentioned in this introduction are unavoidable, and as the limits of Abstraction must be determined in objects whose identity results solely from the use of things that are minimally required of and pertain to eﬀecting and understanding the identity of a work of art, it is the purpose of this division of this part of this book to expatiate upon the preceding points, and to identify and comment on things of importance to them, and hence to Essentialism.

1. Identity and diﬀerence 1.1. The primitive concepts of logical sameness and logical diﬀerence The two concepts that are fundamental to the concept ‘object’ are ‘selfsameness,’ or ‘logical identity,’ and ‘logical diﬀerence.’ The concept of selfsameness or identity and the concept of diﬀerence are each primitive in that the concepts themselves must be employed in talking about them, and so any attempt to explain them through the use of more fundamental notions is not possible. Thus if we ask what is meant by saying that an object x is self-identical, we can say that x is x, or we can say that x is the same as itself. However, implicit in the repetition of symbols “x is x” is the understanding that the selfsame thing, and not either a completely diﬀerent thing

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or a diﬀerent token of the same type of thing is represented by the symbols on each side of the verb. If this were not the case, and one x were understood to represent some object other than the object that is represented by the other x then “x is x” would illustrate diﬀerence rather than sameness, and would do so in saying something contradictory, namely in saying that one thing is logically identical to another thing from which it is understood to be logically diﬀerent. The concept of selfsameness or strict identity is also explicitly used in saying that “x is the same as itself.” The concept of identity then ﬁgures in a visible illustration of sameness and in any talk of the notion of identity. Likewise, the notion of diﬀerence must be employed in talking about diﬀerence. We can say that diﬀerence is not selfsameness or strict identity, or we can say that ~x is not the same as x, and where “~x” represents any object y other than x. But in saying that diﬀerence is not identity, we are saying that diﬀerence is diﬀerent from identity. And in saying either that ~x is not x or that ~x represents any object y other than x, we are saying that ~x is diﬀerent from x. 1.2. Laws of identity and diﬀerence1 The laws of identity and diﬀerence are: i.) Each object is logically identical to itself; ii.) No object is logically identical to any object but itself; iii.) Each object is logically distinct or diﬀerent from every object to which it is not self-identical. 1.2.1. The interdependence of the notions of object, identity, and diﬀerence. The notions of object, identity, and diﬀerence are interdependent: the latter concepts have meaning in virtue of objects of which subjects can be aware, and can themselves be objects of awareness that are subject to the laws in which they ﬁgure in being self-identical and logically distinct from every other object. That is, identity is the same

1 These laws were identiﬁed earlier in the book in 1.2.5 of Division I of Part Two in reference to the logical limitations of objects according to the laws of objects. They are restated here not only because of their pertinence to material of this division concerning things at the foundation of our conceptual system, but because of the pertinence of their supremely elemental nature to the extreme reductionism of Essentialist Abstraction.

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as itself and is diﬀerent from diﬀerence, and diﬀerence is the same as itself and diﬀerent from identity. And there are no objects to which the concepts do not apply, and it requires objects to state and exemplify the concepts. 1.2.2. Identity and diﬀerence and number. The logical notions of identity and diﬀerence are inextricably bound up with the idea of number, and that of number with identity and diﬀerence. The idea of an object’s selfsameness and distinction from everything but itself is the idea of its oneness or its individuality.2 And for one object to diﬀer from another there must be at least two objects, and the notion of numerical diversity depends upon the notion of the logical diﬀerence of objects. That is, the possibility of counting objects rests on a distinction that the counting presupposes. Thus, there is no plurality without diﬀerence and there is no diﬀerence without plurality. (Number and diﬀerence, although intimately related in this fashion are not the same. For any collection of n number of objects greater than one, we can know, a priori, that each object in the collection is logically distinct from every other without knowing how many objects there are in the collection.) For any object x, x is logically identical to x, and for any object y, y is identical to y, and, if x is logically identical to y, then ‘x’ and ‘y’ must be two diﬀerent ways of referring to the same single thing. Any object is ‘metaphysically equivalent’ to itself, whatever its nature, and logical identity and metaphysical equivalence are diﬀerent ways of talking of an object’s selfsameness. The term ‘metaphysically’ is used here to qualify ‘equivalent’ to distinguish this kind of equivalence from logical equivalence, which is identiﬁed below. 1.2.3. Core logical properties of objects. The laws of identity and diﬀerence indicate that each object has the properties of being identical to 2 What I have said about the concept of ‘object’ to this point is very similar to what Russell calls a “term” in The Principles of Mathematics. There a term is said to be “the widest word in the philosophical vocabulary” and “the words unit, individual, and entity” are said to be “synonymous with it.” The words ‘unit’ and ‘individual’ are meant to “emphasize the fact that every term is one,” while the use of ‘entity’ “is derived from the fact that every term has being, i.e. is in some sense.” (Both italics his.) It is this last point from which my use of ‘object’ as being without ontological commitment diﬀers. Russell, as is well known, later abandoned the extreme realism of this early view. Bertrand Russell, The Principles of Mathematics, New York: W. W. Norton & Co. (1937) p. 43.

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itself, of being identical only to itself, and of being logically distinct or diﬀerent from every object to which it is not self-identical. These properties are ‘core’ logical properties of an object. Thus for any two objects x and y: x has the property of being identical to x and only to x; y has the property of being identical to y and only to y; and x has the property of being diﬀerent from y and y has the property of being diﬀerent from x. This diﬀerence of each object from the other is logical diﬀerence, and the logical diﬀerence of x from y and y from x indicates, at the most minimal level, that ‘x’ and ‘y’ are not two diﬀerent names of the same single thing. Accordingly, if x and y have every other property in common, only x has the property of being x—which is the haecceity of x—and only y has the property of being y—which is the haecceity of y—and x has the property of diﬀering from y, which y does not have, and y has the property of diﬀering from x, which x does not have.3

2. Particular identity As each object is logically identical to itself and no object is logically identical to any object but itself, and as each object is logically distinct or diﬀerent from every object to which it is not self-identical, each object has a particular identity that every object other than itself necessarily lacks. 2.1. Logical identity and particular identity It is possible to speak of two diﬀerent kinds of identity concerning objects in general: Logical identity or self-identity is universal in applying necessarily to every object, while the particular identity of any object, as unique and exclusive, necessarily pertains to that object alone. That any object x’s identity is particular means that x is x, x is only x, and only x is x, and so, given any other object y, x is not y and y is not x.

3 On the logic of the laws of identity and diﬀerence see Appendix Two on pp. 340–343 below.

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2.2. Particular identity is unique and singular It follows from the primitive concepts of identity and diﬀerence that no diverse objects can have the same particular identity. For two or more objects to have the same particular identity it would have to be both true that they are numerically distinct and true that they are numerically indistinct, which is a contradiction. In addition, no object can have more than one particular identity. For one object to have two or more particular identities it would have to be both true that it is a single object and false that it is a single object, which is a contradiction. 2.3. Haecceity is a core logical property The property that an object has of having its particular identity, that is, its haecceity, is also a core logical property of the object in addition to the other core properties of objects that have been noted.4 2.4. The laws of objects Here it is worth recalling that the laws of identity and diﬀerence that each object is logically identical to itself, that no object is logically identical to any object but itself, and that each object is logically distinct from each object to which it is not logically identical combine with the law that each object has the property of being the particular object that it is to form the basic laws of objects that were stated earlier in the book.5

3. Identity and diﬀerence and Essentialism The remarks of the ﬁrst two sections of this division are implicitly germane to the determination and identiﬁcation of artworks in general, since any artwork must be meant to be identiﬁed with some object, and that object is necessarily logically identical to itself and

4 For further on the notion of haecceity and the logical individuation of objects see 2 of Appendix One on pp. 330–334 below. 5 On impossible objects and the logical conditions of objects see Appendix Four on pp. 353–365 below.

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is necessarily logically distinct from everything that lacks its identity. The same remarks acquire explicit importance for the determination and identiﬁcation of Essentially Abstract artworks in particular, since no artwork can dispense with a particular identity, and, in virtue of an artwork’s being identiﬁed with some object, the work necessarily will be logically related in one way to itself and in a diﬀerent way to each object that lacks its particular identity. Just as a painter cannot avoid the relation of ﬁgure to ground in a work that is characterized by such a relation, so the Essentialist cannot avoid the identity-diﬀerence relation that holds between an object that an artwork is meant to be and every other object, including any object that a part of the work is meant to be. And just as a ﬁgure must have a property or set of properties in virtue of which it can ﬁgure in a ﬁgure-ground relation, so any object that an artwork is meant to be must have a property or set of properties in virtue of which it can ﬁgure in an identity-diﬀerence relation. An artist who produces a work that is characterized by a ﬁgureground relation must consider the properties of the ﬁgure and properties of the ground as they pertain to and aﬀect that relation. The Essentialist must consider the ‘non-core’ properties of the object that the work is meant to be—and where an object’s non-core properties are the properties that the object has in addition to its core logical properties—as those properties pertain to and aﬀect the identitydiﬀerence relation that holds between the work and those things that are not the work, including any parts of the work if the work is complex. Neither the properties of the ﬁgure nor the properties of the ground have to be minimized in any ﬁgure-ground painting—minimized so that properties that are not required to eﬀect a ﬁgure-ground relation are excluded, as, for instance, the property of being red and the property of being an image of a tree are excluded from each aspect of a ﬁgure-ground relation that is eﬀected by placing a white rectangle on a white rectangle. However, the Essentialist must consider, to the extent possible, the minimization of the properties of an object that an artwork is meant to be as the singling out of such an object eﬀects the identity-diﬀerence relation between that object and every other object. Creative investigation of the possibilities of such minimization would be based on restricting the properties of the object to properties that reﬂect essential elements of artistic complexes. This is equivalent to saying that the limits of Abstraction

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must be determined in objects whose particular identities are based on as they reﬂect essential elements of artistic complexes, and that the diﬀerence of such objects from objects in which those limits are not exhibited is that the former and not the latter are intentionally eﬀected to reﬂect essential elements of artistic complexes.6

4. Logical space ‘Logical space’ consists of all objects of all kinds of object as they stand in logical relation to one another. Logical space includes those objects that are phenomenal or noumenal, and is wholly relational in that there is no logical space of objects apart from the objects of which that space consists. As logical, this space is divisible according to the laws of objects. Any object of any kind of object has a particular identity, only one object can have that particular identity, and an object diﬀers necessarily from each object that lacks its particular identity. Speaking of the “space” of objects as logical recognizes the preceding requirements. Logical space is not restricted to objects of a particular kind, and objects that lack spatial or physical properties nevertheless ﬁgure as deﬁning elements of the logical space of objects in that that space will divide into a particular object with a particular identity and everything other than that object. Objects stand in logical relation to one another whatever their nonlogical nature and whatever their nonlogical relations to one another happen to be.

5. Identity and diﬀerence and artistic complexes 5.1. The delimitation of logical space by artworks and things of relevance to them When an artist produces a work of art she singles out a simple or complex object with which the work is meant to be identiﬁed. The object so singled out has a particular identity, no other object has

6

For further see 5.2 of this division below and Part Four.

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that particular identity, and the delineated object is logically distinct or diﬀerent from each object that lacks its particular identity. Thus the identity-diﬀerence relation that holds between any object and any other object also holds between any object that an artwork is meant to be and each object that lacks the identity of that work of art. The identity-diﬀerence relation also applies to the subject and any event in which he comprehends an artwork’s identity; to the artistic complex of which such a comprehending event is a constituent; to any part of a complex public perceptual object on which the identity of an artwork is dependent; to any part of a complex artwork; and to every element of any artistic complex, as each of the things noted stands in logical relation to the things that are not it. Because the logical space of objects includes objects of the kinds of object mentioned that are relevant to making and apprehending works of art, and because these objects stand in logical relation to one another as determined by the laws of objects, they eﬀect part of the delimitation of that logical space. 5.2. Essentialism and the delimitation of logical space As identity and diﬀerence cannot be eliminated from making and apprehending works of art, they must be ingredients in Essentialist Abstraction. The artist who wants to investigate the limits of Abstraction in art must directly investigate, to the extent possible, ways in which the identity-diﬀerence relation that holds between the object indicated to be the work of art and anything or everything other than that object can be used in pursuit of this aim. Thus the Essentialist project will include investigating ways of delimiting logical space relative to the object with which an artwork is meant to be identiﬁed, and where such a delimitation eﬀected will be eﬀected according to Essentialist principles, and so will rest on the utilization of things that are necessary constituents of artistic complexes. The Essentialist will also investigate the possibilities of using the identity-diﬀerence relation that holds between the parts of any complex object indicated to be a work of art, and the identity-diﬀerence relation that holds between the elements of any artistic complex, as each thing of each of these kinds of thing stands in turn in logical relation to the remaining class of objects in the logical space of objects. To pursue any of the investigations mentioned, the Essentialist must either use language in such a way that attention is drawn to

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the identity-diﬀerence relation as a concern or focus of the work, or he must use language explicitly to address that relation so that awareness will be directly focused on it as something essential to any object in or through which a limit of Abstraction is determined. Either approach recognizes that identity and diﬀerence are logically basic and correlated as indicated. As such, identity and diﬀerence must form part of the focus of investigating the limits of Abstraction in art. Essentialist Abstraction may also explore the relation of the bare logical distinction of objects that form part of an artistic complex to any apprehensible nonlogical diﬀerence between those objects. A relation of logical and nonlogical diﬀerence utilized will be more Essentialist to the extent to which any nonlogical diﬀerence between things that form part of an artistic complex are diﬀerences between things that are themselves essential to making and apprehending works of art—things such as an event of apprehending a public perceptual object on which the identity of an artwork is dependent and the perceptual object apprehended. Most fundamentally, a concern of Essentialist Abstraction will be to investigate ways of drawing conceptual distinctions, where distinctions to be drawn will involve or depend upon a subject’s event of comprehending the identity of the artwork, the identity which, in turn, will either depend upon or be equivalent to the distinction drawn.

6. Artworks, objects, and parts Any object x with which an artwork is meant to be identiﬁed is either simple or complex. If x is complex, then, for any object y other than x, y is either deﬁnitely part of x, is deﬁnitely not part of x, or is neither deﬁnitely part nor deﬁnitely not part of x. Thus, speaking of Spiral Jetty at the time of it completion, we would say that every object is either Spiral Jetty or not, and some objects, such as the rocks that were used to build it, are part of it, and some other objects, such as the sky above it, are not part of it. But we may not be able to say of some objects that they are deﬁnitely part of it or that they are deﬁnitely not part of it, such as a number of pebbles at an edge of the structure. Are they part of Spiral Jetty or part of the land from which the artwork protrudes? For the purpose of investigating the limits of Abstraction in art, it is not necessary to be able to perceive or state precisely where a

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particular artwork begins or ends, and it is not necessary to ascertain, of each object, whether it deﬁnitely is part of a particular work or is deﬁnitely not part of it for any complex artwork. It is enough that some objects are deﬁnitely part of the work and others are deﬁnitely not, so that the work as a complex object is marked oﬀ from every other object—including those that may or may not be part of it—and it can be understood with which complex object the artist intends a particular artwork to be identiﬁed. The logical point remains that any simple or complex artwork, in virtue of being an object, is logically delimited from everything but itself, including from each simple or complex object that is part of it if it is complex, and from each simple or complex object that is not part of it, and from each simple or complex object that may or may not be part of it.

7. Compositional relations and works of art For any objects x and y: If x is part of y or y is part of x then x and y are said to be ‘compositionally related’ to one another, in the ﬁrst instance as part to whole and in the second instance as whole to part from the perspective of x, and in the reverse order from the perspective of y. Thus, a compositional relation is either part to whole or whole to part. If, of any two objects, neither object is part of the other, then they lack a compositional relation to one another. But whether an object is compositionally related to another or not, it is in any case logically distinct from every object but itself, and so the identity-diﬀerence relation that holds between two or more objects is more fundamental than the part-whole relation, and the latter relation presupposes the former. 7.1. Simple and complex embodied artworks 7.1.1. Simple embodied artworks. For any simple work of art a and any object x that is not a, x does not and cannot form part of a in the sense in which we know that we are to identify the artwork with what we see. Thus, if an artist makes a pencil dot on a gallery wall and makes it known that that dot is a work of art, then it is irrelevant to the compositional consideration of the work that that simple perceptual point consists of a greater number of subperceptual objects.

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This is because we know that we are to identify the artwork with what we see, and not with physical entities that cannot be seen. We understand that they do not form part of the perceptual object that the work is meant to be, even if the perceptual object depends on them physically. 7.1.2. Complex embodied artworks. For any complex artwork a and any object x that is not a, either x deﬁnitely is or deﬁnitely is not part of a or x is neither deﬁnitely part of nor deﬁnitely not part of a, where determination of the presence or absence of the part-whole relation of x to a may not be possible, or may rest on subjective factors or arbitrary judgements. However, we have seen that it is necessary that it be understandable which simple or complex object an artist intends a work of art to be. If the object is complex, it is necessary that it be understandable that certain objects deﬁnitely are part of the work and that certain other objects are deﬁnitely not part of the work. If this is not the case, then no object has in fact been delineated for awareness, and the artist has not succeeded in making it clear with which object or objects he intends the work to be identiﬁed. We have also seen that it is suﬃcient for a person to understand the identity of a complex artwork if it is clear that some objects are deﬁnitely part of the work and others are deﬁnitely not, so that the work as a complex object is delineated for awareness and thus is conceptually distinguished from every other object, including from those objects that may or may not be part of it. Thus, that it is understandable that the artwork deﬁnitely consists of certain objects and deﬁnitely does not consist of certain others is enough to eﬀect the delineation of the artwork and to make its identity comprehensible. That certain other objects may or may not form part of the work does not then present a problem for identifying the artwork with a certain complex object. 7.2. Simple and complex speciﬁed and non-embodied artworks 7.2.1. Simple speciﬁed artworks. If a simple object x is singled out by speciﬁcation as the object that an artwork a is meant to be, then that object, as simple, excludes any other object y from being correctly identiﬁed as part of that work of art.

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7.2.2. Complex speciﬁed artworks. If a complex object x is singled out by speciﬁcation as the object that an artwork a is meant to be, then that speciﬁed object, as complex, includes as a part any object y to which the speciﬁcation refers and excludes as a part any other object z to which the speciﬁcation does not refer. Thus, all objects are excluded from being part of an object speciﬁed to be a work of art that do not answer to the speciﬁcation. The remarks of this and the following paragraph apply to a speciﬁed object, and do so whether the object speciﬁed is perceptual, non-perceptual, or a combination thereof. 7.2.3. Ambiguous speciﬁcations. If language that speciﬁes an object that an artwork is meant to be is written in such a way that it is not clear whether or not some particular object answers to the speciﬁcation, then it will not be clear whether or not that object can be said to form part of the object singled out by the speciﬁcation. But even so, for a speciﬁcation to succeed in singling out an object that an artwork is meant to be, it must be clear that a certain object or objects will answer to the speciﬁcation and certain others will not. An ambiguous or fuzzy speciﬁcation can be seen to be analogous to the kind of perceptual object considered earlier, all of whose parts may not be speciﬁcally determinable. A possible example here is all of the objects of your awareness in your immediate vicinity at the time at which you read this, since it is not clear for every object of your awareness when you read the speciﬁcation whether or not it is to be counted as being within or beyond your immediate vicinity, and the word ‘read’ can be pronounced in two diﬀerent ways—one of which refers to the present and the other of which refers to the past. 7.3. Essentialism and compositional relations of objects Because Essentialist Abstraction depends on the use of language; because the words of a speciﬁcation will have visible and semantic compositional relations to the speciﬁcation of which they form part; because the words of a speciﬁcation will have visible compositional relations to the perceptual object of which they form part; because language can be used to single out objects with which parts of an artwork are meant to be identiﬁed; and because the present segment of a subject’s history of awareness can be made to divide into objects

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that are meant to form part of a work and those that are not, Essentialism will have to investigate the whole-part relation to determine how use of that relation will best pertain to the pursuit of its aims, including its aesthetic. This will include consideration of the relation of the perceptual object and its parts to the object and its parts, if any, speciﬁed by the language that the perceptual object contains, where the objects of these diﬀerent kinds might be thought to be constituents of a kind of larger complex object that they together compose.

8. An object either is or is not dependent on awareness to be the object that it is Although an artwork must be meant to be identiﬁed with some object, an artwork may be meant to be an object that is in some way dependent on awareness or an object that is not in any way dependent on awareness. The situation is in fact more complicated since there are diﬀerent kinds of dependent object and diﬀerent kinds of independent object. And that diﬀerent limits of Abstraction might be determined in diﬀerent objects of these diﬀerent kinds of object must be recognized. The diﬀerent kinds of dependent and independent object are therefore the subject of the following sections.

9. Kinds of dependence: identity dependence and type dependence As a general matter it can be asserted that if an object is dependent on consciousness for its particular identity, then if nothing is an event of awareness then nothing is that object. More speciﬁcally, an object that is dependent on consciousness for its identity is dependent either on a particular event or events of awareness, or it is dependent on an event or events of awareness of a certain kind or kinds of awareness, or both. The ﬁrst kind of dependence is ‘identity dependence’ and the second kind of dependence is ‘type dependence.’ Identity dependence and type dependence will be considered in this order in 10 and 11 below. It is important to understand that I am considering kinds of dependence of objects on consciousness, and that that dependence does not necessarily preclude the dependence of such objects on kinds of

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non-conscious object, including any kind of non-conscious object on which a conscious event may itself depend. Nor does the dependence of an object of either kind of dependent object necessarily preclude the dependence of that object on some event or events of awareness in addition to some particular event or some event of a kind of event on which it is understood to be dependent. For instance, the object named by your comprehending this now is identity dependent on the occurrence of the event to which the object named by the language is equivalent, but that object would presuppose any event of awareness of the person responsible for the language that made the object a realized possibility. What makes the object identity dependent as deﬁned below is that no object named by the language is that object apart from the event that answers to its comprehension. And a particular type-dependent object may yet presuppose a particular event or events of awareness without which it would it would not be that type-dependent object. It is just that, if it is type dependent, then given any particular event without which no object would be that type-dependent object, still no object is that typedependent object apart from an event or events of awareness of the kind or kinds of awareness on which it is type dependent. For instance, no object could be a particular painting apart from any particular event of awareness on which its creation depended, but as any painting is meant to be seen, and is not meant to be the set of independent physical entities on which the painting as perceptual is physically dependent, no object is the painting apart from being the Intentional object of some event of seeing, and so a painting is a type-dependent object. 9.1. The diﬀerence between identity and identity dependence Identity and identity dependence are two diﬀerent things. Every object has an identity, where “identity” is short for ‘particular identity,’ and where an object’s particular identity is its being the particular object that it is and that no other object is or can be. In addition to the particular identity that each object has, some objects are identity dependent in the sense to be deﬁned and others are not.

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9.2. Actual and possible awareness of consciousness-dependent objects It does not follow from an object’s dependence on consciousness that it must be possible to be aware of the object, as opposed to possibly being aware that a particular object is so dependent. Thus it may be possible to be aware that some kind of dependent object has the particular identity of that object without its being possible to be aware of the object itself that is either identity dependent or type dependent on consciousness to be that particular object. For instance, a neurophysiological state in your brain that results from your current comprehension of this sentence is an object of which you are not aware that depends on the conscious event of comprehending this sentence. It may also be possible for an object of which no one is ever aware to be dependent on an event or events of consciousness, and it may be possible for an object of which no one can be aware, even in theory, to be dependent on an event or events of consciousness to be the object that it is. The referent of all the eﬀects of comprehending this of which no one is ever aware depends on comprehension of the speciﬁcation that refers to it, and so depends on consciousness to be that object.7 That referent is an example of something of which it is not possible to be aware, and yet it is possible to be aware that it is meant to be a work of art. Any object that answers to the speciﬁcation any eﬀect of any current event of comprehending this of which it is not possible to be aware is something of which, by the very nature of any object that answers to the speciﬁcation, no one can be aware, even theoretically, and yet that could be meant and understood to be a work of art. Artists may take advantage of and experiment with the distinction between awareness of an object that is dependent on consciousness, and awareness that an object is dependent on consciousness, by iden-

7 Speciﬁcational language—that is, language that can be used to single out an object that all or part of an artwork could be understood to be—will be frequently utilized throughout to illustrate kinds of dependence that are the subject of this division. Such language will be so utilized both because it can easily function as means of making certain deﬁnitions or assertions more comprehensible by serving as examples of things that are intended to clarify the deﬁnitions and assertions, and because the relevance of the speciﬁcation of kinds of identity-dependent and typedependent object to the limits of Abstraction would have to be investigated by Essentialism, although none of the examples given is intended to be part of that artistic enterprise.

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tifying an artwork with a consciousness-dependent object of which it is possible to be aware, or by identifying an artwork with a consciousness-dependent object of which it is not possible to be aware, although it is possible to be aware that it is meant to be a work of art. Such experimentation must characterize creative investigation of the limits of Abstraction. This is because both the determination and the understanding of the identities of artworks depend on consciousness; because artworks need not be phenomenal rather than noumenal objects; and because diﬀerent Abstract limits might be determined in diﬀerent objects as they stand in diﬀerent relation to conscious events on which they are dependent. 9.3. The heterogeneity of dependent objects and the events on which they depend There are diﬀerent kinds of identity-dependent object and there are diﬀerent kinds of type-dependent object. Events on which dependent objects of either kind of dependent object depend are also of diﬀerent kinds. Given the general heterogeneity of dependent objects and the events on which they depend, nothing can be inferred a priori about the nature of some dependent object merely from knowing that the object is a dependent object, and nothing can be so inferred about the nature of an event of awareness on which a dependent object depends simply from knowing that the event is one on which some object depends. 9.4. Possible logical and metaphysical equivalence of dependent objects and the events on which they depend A dependent object may or may not be logically equivalent to an event or events on which it depends. If a dependent object is logically equivalent to an event or events on which it depends it may or may not be metaphysically equivalent to that event or events. Two things x and y are ‘logically equivalent’ when: x if and only if y, and y if and only if x. Logical equivalence and metaphysical equivalence are two diﬀerent things. If x and y are logically equivalent they may name the same or numerically diﬀerent entities, but if x and y are metaphysically equivalent, then x and y must be two diﬀerent ways of referring to the same single entity, and x refers in one way—in the present instance ‘object’—to what y refers in

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another—in the same instance ‘event.’ As metaphysically equivalent, x and y are also logically equivalent, but x and y can be logically equivalent without being metaphysically equivalent, as they are not if they are numerically distinct. The notion of logical equivalence may be more typically taken to pertain to the relation of propositions that pertain to things rather than to the things to which the propositions pertain, so that propositions p and q that pertain to entities x and y are logically equivalent when p if and only if q, and q if and only if p. However, dependent objects and the events on which they depend can be understood to be connected in a relation of logical equivalence as much as can propositions that pertain to them. For instance, paintings are perceptual objects that are meant to be perceived, and a painting only exists as the entity that it is intended to be when it is being seen. Its being seen is a necessary and suﬃcient condition of its existing as the perceptual object that it is intended to be. But if a painting’s being seen is a necessary and suﬃcient condition of the painting’s existing as intended, as an object seen, then the painting as a perceived object is a suﬃcient and necessary condition of the event of perceiving it. A painting’s existence and an event of seeing it are numerically distinct things that are logically equivalent in that each is a necessary and suﬃcient condition of the other. These things can be understood to be the case as much as it can be understood that the truth of a proposition that pertains to a painting’s being seen is a necessary and suﬃcient condition of the truth of the statement that the painting exists as the perceptual object that it is intended to be, and that the truth of a statement about the existence of the painting as a perceptual object is a suﬃcient and necessary condition of the truth of a statement that pertains to the existence of the act of perceiving the painting. Because logical equivalence and metaphysical equivalence are diﬀerent things, the term ‘equivalent’ will be qualiﬁed adjectively if it is necessary to distinguish between these kinds of equivalence in a particular context. However, if unqualiﬁed, the term ‘equivalent’ is to be understood to mean metaphysically equivalent. Further, ‘metaphysical equivalence and ‘logical identity’ are synonymous expressions referring to an entity’s selfsameness.

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9.5. The implicit relation of a conscious event to an object dependent on it Diﬀerent kinds of dependent object will be deﬁned below in relation to an event or events on which they are dependent. Saying that a conscious event is an event on which a dependent object is dependent implicitly recognizes that any relation that is required to hold between the event and the object for the object to be that object so holds between the event and the object dependent on it. For instance, saying that Pegasus is a kind of object that is dependent on an event of conceiving implicitly recognizes that any such event of conceiving is an event of conceiving of Pegasus. Accordingly, the relation that is required to hold between an event of conceiving and Pegasus for some object to be that dependent object is the Intentional connection of the two. This can either be described as the Intentional direction of the former to the latter, or as the latter’s being the Intentional object of the former. The recognition of this relation is implicit since events of conceiving are always events of conceiving of something, and when events of conceiving are sorted into conceiving of diﬀerent things, they are so sorted according to their Intentional objects. Thus an event of conceiving of Pegasus is diﬀerent from an event of conceiving of the golden mountain because they have diﬀerent Intentional objects. It is understood then that Pegasus, as an object dependent on conceiving, is dependent on an event of the type of event called ‘conceiving of Pegasus,’ and so the implicit relation between an event of conceiving and Pegasus is the Intentional connection of the two as indicated. Similarly, any particular painting, as something meant to be seen, is dependent on an event of seeing. However, an event of seeing on which the painting depends is an event of seeing that takes that painting and not some other visual object as its Intentional object. This is implicit since seeing is Intentional and diﬀerent events of seeing diﬀerent things are distinguished by their diﬀerent Intentional objects, or the implicit required relation between an event of seeing and a particular painting seen is the Intentional connection of the two in the Intentional direction of the former to the latter, and, equivalently, in the latter’s being the Intentional object of the former.

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In general, a particular object is ‘identity dependent’ on a particular Intentional or non-Intentional event of awareness when, if nothing is that event, then nothing is that object. Although this is the case in general, two basic kinds of identity dependence will be identiﬁed in sections 10.3 and 10.4 below. 10.1. The implicit relation of an identity-dependent object to a particular time Since any event of awareness exists at a particular time, talk both here and throughout of a particular object’s identity dependence on a particular event of awareness implicitly links the being or identity of the identity-dependent object to a particular time, namely to the time at which the event on which it is dependent exists. Thus if an object x is in some way identity dependent on an event of awareness e, and e exists at t, then something is x relative to e’s existence at t. This is the case for the diﬀerent kinds of identity dependence to be identiﬁed below. It does not follow from this however that any identity-dependent object so linked to a time must exist at the time to which it is linked, or even that it is itself a temporal object. In addition, if the numerically same event e can exist at two or more diﬀerent noncontiguous times t and u, then it does not necessarily follow from the dependence of x on the existence e at t that x cannot be identity dependent on the existence of the identical event e at a diﬀerent earlier or later noncontiguous time u.8 Whether or not the numerically same event of awareness can exist at two or more separate times depends on whether or not separate times are taken to individuate events of awareness that exist at them. That is an issue that does not have to be resolved for the deﬁnition of identity dependence given, since it will hold on either view.

8 Speaking of times t and u as noncontiguous is meant to recognize the diﬀerence between the existence of the same event of awareness at a time or for a number of contiguous times, and the existence of the same event at times separated by at least one time at which the event did not exist. If the latter be possible, then an event of awareness that comes to exist at a time must have both ceased to exist at an earlier time and have failed to exist at or for at least one time that separates the times at which it earlier ceases and then later comes to exist.

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10.2. The timeless use of ‘is’ The term “is,” as it is used in the deﬁnition of and remarks on identity dependence and type dependence, and as it ﬁgures in remarks made throughout the book about the correlation of objects and events of awareness in any of the ways in which objects and events of awareness can be correlated, is used in the timeless sense to cover the facts of the past, present, and future existence of objects. The timeless correlation of objects with events on which they are identity dependent means that, if an object x is identity dependent on an event of awareness e at a time t, then it is not only true at t that x is identity dependent on e at t, but it is true at times other than t as well. For instance, if u is a time later than t, then that x is identity dependent on e at t is true at u, and this is the case whether or not x is identity dependent on e at u in addition to being identity dependent on e at t. Thus the timeless sense of truth being discussed is tenseless in that we say that, as much as it is true at t that x is identity dependent on e at t, so it is true at u that something at t is x in virtue of e’s occurrence at t. Thus speaking of facts as timeless simply recognizes a conservation of truth value for appropriate kinds of statement across time. Whether it is true at an earlier time s that x is identity dependent on e at t depends on whether statements that are or could be made at earlier times, such as at s, that pertain to things at later times have a truth value when made. 10.3. Type-A identity dependence An object is ‘Type-A identity dependent’ on a particular event of awareness when, if nothing is that event then nothing is that object, and if something is that event then something is that object. TypeA identity dependence is tied to a particular event of awareness rather than to one or another event of some kind of awareness. Thus in Type-A identity dependence a particular event of awareness is both a necessary and a suﬃcient condition of some object’s being the object that it is, and so the object and the event are logically equivalent whether or not they are metaphysically equivalent. The Intentional object of a particular second-order event of reﬂexive awareness, such as an event of consciousness that takes itself as its Intentional object, is metaphysically equivalent to the event on which it is Type-A identity dependent since the object is that event. Any

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particular eﬀect of such a particular event would be logically equivalent to the event on which it is Type-A identity dependent since such an object would be something other than the event on which it depends. 10.3.1. Events of awareness and Type-A identity dependence. Since an event of awareness is an object, and since an object is Type-A identity dependent on an event of awareness both when, if nothing is that event then nothing is that object, and when, if something is that event then something is that object, any event of awareness of any kind, Intentional or non-Intentional, and considered as an object that is the event of its occurrence, is itself a Type-A identity-dependent object. Here object and event are, and must be, simply diﬀerent ways of referring to the same single thing that is metaphysically equivalent to itself as object and event, and so the identity-dependence of any event of awareness on its own occurrence is trivial. 10.3.2. Identity-dependent objects and events of awareness. Although any event of awareness is trivially a Type-A identity-dependent object, it is not the case that any identity-dependent object of either kind of identity-dependent object is an event of awareness. 10.3.3. Intentional objects and Type-A identity-dependence. The Intentional object of an Intentional event may or may not be a Type-A identitydependent object. If the Intentional object of an Intentional event of awareness is a property of the event of which it is the object, then, as no such object could be a property of the event apart from the event of which it is the property, that object is Type-A identity dependent on the event of which it is the Intentional object. An example is the Intentional object of a second-order event of monadic awareness, as in an event of consciousness that takes itself as its Intentional object. If the Intentional object of an Intentional event of awareness is not a property of the event of which it is the object, then that object is not Type-A identity dependent on the event of which it is the Intentional object, although it might be Type-A identity dependent on some event other than the event of which it is the Intentional object. If, for instance, I am conscious of my consciousness, then the Intentional object of that conscious event is TypeA identity dependent on that reﬂexive monadic event. If I tell you that I am conscious of my consciousness, so that you are aware of

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that event, then your consciousness has as its Intentional object something that is not Type-A identity dependent on your event, but is so dependent on a diﬀerent event, namely on the event of mine of which you are conscious. 10.3.4. Type-A identity-dependence and phenomenal and noumenal objects and works of art. A Type-A identity-dependent object may be phenomenal or noumenal, or it may be a complex object that consists of phenomenal and noumenal objects. Any such object could be meant to be a work of art. The referent of your current apprehension of this speciﬁcation is a Type-A identity-dependent phenomenal object, whereas the referent of all the eﬀects of your current apprehension of this speciﬁcation of which you are never aware is a complex Type-A identity-dependent noumenal object that consists of such things as neurophysiological changes in your brain that result from the speciﬁed event of comprehension. The referent of both anything of which you are aware and anything of which you are not aware that is an eﬀect of your current comprehension of this information is a Type-A identity-dependent object that consists of phenomenal and noumenal entities. 10.4. Type-B identity dependence An object is ‘Type-B identity dependent’ if it consists of at least one object that is a Type-A identity-dependent object, and at least one other object that may or may not be a Type-A identity-dependent object. Accordingly, the event of awareness on which a Type-B identity-dependent object depends is a necessary condition of the object, but is not a suﬃcient condition of the object. The complex object named by the language your current event of comprehending this token of this language and any recollection you have of comprehending this token of this language is an example of a Type-B identitydependent object. It is Type-B in that no object has the property of being the object delineated by the language apart from the Intentional object of the event of comprehension named by the language, and that object depends in turn on that particular event of comprehension. Thus, that which is singled out by your current event of comprehending this token of this language is a Type-A identity-dependent object. However, nothing is the complex object named by the speciﬁcation apart from at least one recollection that is named by the language any recollection you have of comprehending this token of this

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language (which is a Type-A type-dependent object). Thus the complex object named by the speciﬁcation is a Type-B identity dependent object that consists of the objects that answer to the speciﬁcation. The referent of the speciﬁcation your current event of comprehending this token of this language and the space of the page surrounding it is also an example of a Type-B identity-dependent object. 10.4.1. Type-B identity-dependence and phenomenal and noumenal objects and works of art. A Type-B identity-dependent object may consist of phenomenal objects or it may consist of noumenal objects, or it may be a complex object that consists of phenomenal and noumenal objects. Any such object could be meant to be a work of art. The complex object named by the speciﬁcation your current event of comprehending this token of this language and any awareness that you have of having comprehended this token of this language is a Type-B identity-dependent object that is phenomenal. The complex object referred to by any eﬀect of which you are never aware that is caused by your current event of comprehending this token of this language and the subperceptual entities of which this token of this language consists is a Type-B identity-dependent object that is noumenal. The complex referent of the language your current event of comprehending this token of this language and any eﬀect of which you are never aware in virtue of now comprehending this token of this language is a Type-B identity-dependent object that is partly phenomenal and partly noumenal. 10.5. Identity dependence and simplicity and complexity A Type-A identity-dependent object may be simple, as is the referent of your current comprehension of this information, or it may be complex, as in all of the eﬀects of your current comprehension of this information. Any Type-B identity-dependent object is complex. One cannot determine prior to artistic investigation what Abstract limits might be determined in these diﬀerent kinds of identity-dependent object. Neither can it be determined how the aesthetic of a work might follow from or be shaped by its intended identiﬁcation with an identity-dependent object until the intended identiﬁcation is eﬀected.

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11. Type dependence in general An object is ‘type dependent’ on an Intentional or non-Intentional event or events of awareness of a certain kind or kinds of awareness when, if nothing is an event of awareness of that type, then nothing is that object. Some event or events of awareness of some kind or kinds of awareness then is a necessary condition of any typedependent object. Although this is the case in general, there are two basic kinds of type-dependent object. 11.1. Type-A type dependence An object is ‘Type-A type dependent’ on any event of awareness of a certain kind or kinds of awareness when, if nothing is such an event, then nothing is that object, and if something is such an event, then something is that object. In Type-A type dependence then, the occurrence of any event of awareness of a certain type or types of awareness on which a certain object is dependent is both a necessary and a suﬃcient condition of something’s being that object. Object and event are then logically equivalent in Type-A type dependence, but they are not metaphysically equivalent, and this is the case even if only a single event on which a Type-A type-dependent object depended occurs. They cannot be metaphysically equivalent since in no case in type dependence can talk of a dependent object and an event on which it depends be two diﬀerent ways of talking about the same thing, as can be the case in Type-A identity dependence. Object and event are correlated in Type-A type dependence, but they are not correlated properties of a single entity, as they can be in Type-A identity dependence, and no Intentional object that is type dependent on an Intentional event of awareness is a property of any event of the kind of event on which it depends. Pegasus is an example of a Type-A type-dependent object since no object is Pegasus apart from an act of conceiving of or imagining that object, and some object has the property of being that particular type-dependent object whenever it is conceived of or imagined. Thus conceiving of Pegasus or imagining Pegasus are kinds of event required for something to be Pegasus, and when any event of conceiving of or imagining Pegasus occurs, then some object has the property of being the object that is dependent on an event of that

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kind of event. Artworks, such as paintings, sculptures, and prints, that are meant to be identiﬁed with the perceived objects in which they are embodied are Type-A type-dependent objects. An embodied visual artwork is dependent on an event of seeing it to be the phenomenal object that it is meant to be, and it exists as the phenomenal entity that it is meant to be whenever it is the Intentional object of an event of seeing. An embodied auditory artwork is dependent on an event of hearing it to be the phenomenal object that it is meant to be, and it exists as the phenomenal entity that it is meant to be whenever it is the Intentional object of an event of hearing. 11.1.1. Type-A type-dependent objects and diﬀerent kinds of awareness. Although some object may be a particular Type-A type-dependent object whenever an event of some type of awareness, such as conceiving, occurs, or whenever an event of one or another type of awareness—such as conceiving or imagining—occurs, still any Type-A type-dependent object is a single object, as the example of Pegasus illustrates. Thus the same single Type-A type-dependent object can be tied to any number of diﬀerent events of a kind or kinds of event on which it is dependent. A painting is a single Type-A type-dependent object that has its particular identity as the visual entity that it is meant to be whenever it is the Intentional object of an event of seeing, and a string quartet is a single Type-A type-dependent object that has its particular identity as the auditory entity that it is meant to be whenever it is the Intentional object of an event of hearing. Type-A identity-dependent and Type-A type-dependent objects diﬀer then in that a Type-A identity-dependent object is speciﬁcally tied to a single particular event of awareness, and any diﬀerent event of awareness is not an event on which a Type-A identity-dependent object is or can be dependent. A Type-A type-dependent object, on the other hand, has its particular identity whenever an event of the kind of event on which it depends occurs. 11.1.2. Type-dependent Intentional objects. A Type-A type-dependent object that is the Intentional object of an Intentional event of the type of event on which it depends is not a property of that event. However, it does not follow that it is independent of any event of the type of event on which it is dependent for not being such a property. A painting is an example of a Type-A type-dependent object, and a

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painting, as something seen, as the Intentional object of an event of seeing, is not a property of that event. But neither is it, in being meant to be seen, independent of any event of the kind of event on which it depends to be what it is meant to be. (Here it is crucial to distinguish the painting as a cultural object, as something meant to be seen, and so dependent on events of visual perception, from the physical substrate that is a physical presupposition of the Intentional object of an event of seeing the painting.) It does not necessarily follow then from the fact that an object is the Intentional object of a certain Intentional event that either that object has to be a property of the event or independent of that event. By the law of excluded middle the object either is a property of the event or it is not. However, given that an Intentional object of an Intentional event is not a property of that event, it does not necessarily follow that the object is some kind of independent object that an event of that kind of event can apprehend. Instead, it can be a type-dependent object that is type dependent on some kind of Intentional event or events any occurrence of which takes the same object as its Intentional object. Type dependence is a third possibility for the relation of Intentional objects to Intentional events in addition to identity dependence and certain kinds of independence to be identiﬁed below. 11.1.3. Type-A type-dependent objects and events of awareness. It may seem that, in speaking of a Type-A type-dependent object on the one hand, and an event or events of awareness on which it depends on the other, that some object is that type-dependent object apart from its relation to any event of the type of event on which the object is said to be dependent. This is incorrect. Rather, the wording of the deﬁnition of Type-A type dependence is meant to indicate that, although a Type-A type-dependent object can be conceptually distinguished from any event of the type of event on which it is dependent, such an event is a presupposition or necessary condition of some object’s being that type-dependent object, and no object is that object apart from that necessary condition. This is a denial then that Type-A type-dependent objects are what I will call ‘generically-independent’ objects. In addition, a Type-A type-dependent object has its particular identity whenever an event of awareness of the kind of awareness on which it depends occurs. Accordingly, the occurrence of such an event of awareness is a suﬃcient condition of the

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object that is type dependent on it, and the relation of the object to any such event is not necessarily unique. 11.1.4. Type-A type-dependence and phenomenal and noumenal objects and works of art. A Type-A type-dependent object may be phenomenal or noumenal or it may be a complex object that consists of phenomenal and noumenal objects. Any such object could be meant to be a work of art. A painting is an example of a Type-A type-dependent phenomenal object since it depends, as visual, on perception to be an object that is meant to be seen. The referent of all the eﬀects of comprehending this of which no one is ever aware is a Type-A type-dependent noumenal object. The referent of any eﬀect of any event of comprehending this information of which anyone is aware and any eﬀect of any event of comprehending this information of which no one is aware is a Type-A type-dependent object that consists of phenomenal and noumenal entities. It is a Type-A type-dependent object since it depends on any event of comprehending the information to result in objects that are singled out by the comprehended speciﬁcation, and it is speciﬁed to consist of both phenomenal and noumenal objects that result from any such event of comprehension. 11.1.5. The dependence of artworks on Type-A type-dependent objects. Any public perceptual object on which all or part of the identity of an artwork is relevantly dependent is a Type-A type-dependent object. Any public perceptual object in which all or part of an artwork is embodied is a Type-A type-dependent object. And any speciﬁcation on which all or part of the identity of an artwork is dependent is a Type-A type-dependent object. 11.2. Type-B type dependence An object is ‘Type-B type dependent’ if it consists of at least one object that is a Type-A type-dependent object, and at least one other object that may or may not be a Type-A type-dependent object. Accordingly, any event or events of awareness of some kind or kinds of awareness on which a Type-B type-dependent object depends is a necessary condition of the object, but is not a suﬃcient condition of the object. The complex object named by the language any event of comprehending this language and any recollection that anyone has of comprehending this language is an example of a Type-B type-dependent object.

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It is type-dependent in that no object has the property of being the speciﬁed object apart from the occurrence of at least one event of each type of event named by the speciﬁcation, but any event of either kind of event is as relevant to the object as any other. It is Type-B in consisting of at least one object in addition to a Type-A type-dependent object, which happens to be, in this case, a second Type-A type-dependent object. The complex object named by the language any event of comprehending this language and all of the letters of which it consists is also an example of a Type-B type-dependent object. 11.2.1. Type-B type-dependence and phenomenal and noumenal objects and works of art. A Type-B type-dependent object may consist of phenomenal objects or it may consist of noumenal objects, or it may be a complex object that consists of phenomenal and noumenal objects. Any such object could be meant to be a work of art. The complex object named by the speciﬁcation any comprehension of this token of this language and any recollection that anyone has of comprehending this token of this language is a Type-B type-dependent object that is phenomenal. The complex object referred to by any eﬀect of which no one is ever aware that is caused by any event of comprehending this token of this language and the subperceptual entities of which this token of this language consists is a Type-B type-dependent object that is noumenal. The complex referent of the language any comprehension of this token of this language and any eﬀect of which no one is ever aware in virtue of any comprehension this token of this language is a Type-B type-dependent object that is partly phenomenal and partly noumenal. 11.3. Type dependence and simplicity and complexity A Type-A type-dependent object may be simple, as in the case of an artwork that is meant to be embodied in a pencil point on a wall, or it may be complex, as in an installation that consists of a number of diﬀerent objects in which it is embodied. Any Type-B type-dependent object is complex. As in identity dependence, it requires creative inquiry to determine the possibilities for Essentialist Abstraction of identifying artworks with kinds of type-dependent object, both in terms of determining the limits of Abstraction, and in terms of its aesthetic.

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A dependent object may depend either on no more than one particular event of awareness or on no more than one event of awareness of a certain kind of awareness to be the particular object that it is. Such a dependent object can be termed a ‘singly-dependent’ object in having its particular identity if something is either the event or an event on which it depends. Any singly-dependent object is either a Type-A identity-dependent object or a Type-A type-dependent object, and either kind of Type-A dependent object is singly dependent. The object that is singled out by the language your current event of comprehending this is singly identity dependent on a particular event of awareness named by the speciﬁcation to be relevant to the determination of the object to which the speciﬁcation refers. A painting is an example of a singly Type-A type-dependent object since it has its particular identity whenever it is the Intentional object of an event of seeing, and it would have its identity if it were only to be seen once.

13. Multiply-dependent objects A dependent object may depend on more than one particular event of awareness of a certain kind or kinds of awareness to be the particular object that it is. A dependent object may also depend on more than one event of awareness of a certain kind or kinds of awareness without, however, depending on any particular events of any kind or kinds of awareness on which it depends. A dependent object can be termed a ‘multiply-dependent’ object either when its particular identity depends on two or more particular events of awareness, or when it depends on any two or more events of one or more kinds of event of awareness. Any multiply-dependent object is either a Type-B identity-dependent object or a Type-B type-dependent object, where, in either case, at least one other object on which either kind of Type-B dependent object depends is itself dependent on awareness. However, either kind of Type-B dependent object may be, but is not necessarily, multiply dependent as deﬁned, since something on which this kind of dependent object may depend in addi-

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tion to some or any awareness on which it depends may be something other than some or any other awareness. The object that is singled out by the language your current event of comprehending this and your next event of recollecting having comprehended this is a Type-B identity-dependent object that might be speciﬁed to be a work of art and that is multiply identity dependent on particular events of awareness named by the speciﬁcation that refers to it. A traditional play is an example of a multiply Type-B type-dependent object. 13.1. Homogeneous multiply-dependent objects A multiply-dependent object that depends on one kind of awareness to be the particular object that it is is a ‘homogeneous’ multiplydependent object. An example is what is referred to by the speciﬁcation your current event of seeing this and your most recent event of seeing this prior to your current event of seeing this. 13.2. Heterogeneous multiply-dependent objects A multiply-dependent object that depends on events of awareness of more than one kind of awareness to be the particular object that it is is a ‘heterogeneous’ multiply-dependent object. An example is what is singled out by the language: your current event of comprehending this token of this language and your forthcoming event of recollecting having just comprehended this token of this language. As the examples illustrate, either a homogeneous or a heterogeneous multiply-dependent object can be meant to be a work of art.

14. Artworks as wholly or partially dependent objects An object with which an artwork is meant to be identiﬁed may be wholly or partially dependent on either a particular event or events of awareness of a certain kind or kinds of awareness, or on any event or events of awareness of a certain kind or kinds of awareness.

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224 14.1. Wholly-dependent objects

An object that an artwork is meant to be is said to be ‘wholly dependent’ when that object is some kind of dependent object. The referent of the speciﬁcation your current event of comprehending this token of this language is a wholly-dependent object, as is any event of comprehending this to be any event of comprehending this. 14.2. Partially-dependent objects A complex object that an artwork is meant to be is said to be ‘partially dependent’ when it consists of at least one dependent object of some kind of dependent object, and of at least one object that is not any kind of dependent object, as dependent objects have been deﬁned. The referent of the speciﬁcation your current event of comprehending this token of this language and the page on which this token of this language exists is a partially-dependent object, as is any event of comprehending this token of this language and the space other than the space occupied by this token of this language.

15. Essentialism and kinds of dependent object An artist must consider the use of diﬀerent kinds of dependent object and the possible identiﬁcation of artworks with diﬀerent kinds of dependent object both in the creative investigation of the limits of Abstraction and in the exploration of the aesthetic possibilities that form part of or follow from that investigation. This is because it cannot be assumed in advance of such creative inquiry how diﬀerent kinds of dependent object may be relevant both to the determination of certain Abstract limits, and to diﬀerent aesthetic possibilities that form part of or that follow from such a determination. Complex artworks, including complex Essentialist artworks, might be intended to be identiﬁed with diﬀerent possible combinations of Type-A identity-dependent, Type-B identity-dependent, Type-A type-dependent, and Type-B type-dependent objects. Parts of artworks might also be intended to be identiﬁed with a kind or kinds of dependent object. The relations of kinds of dependent object to one another that are meant to be parts of artworks, to the whole of which they form part, and to the subject on whom they depend may be relevant not only

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to an Essentialist determination of the limits of Abstraction but to the aesthetic of that determination.

16. Kinds of independent object Just as an investigation of the limits of Abstraction cannot discount the possible relevance of diﬀerent kinds of dependent object to that investigation, neither can it discount the possible relevance of diﬀerent kinds of independent object to that investigation. Objects that are independent of some or all events of consciousness can be talked about in the following ways. 16.1. Generic independence An object is ‘generically independent’ of consciousness when something would have the property of being that object whether or not anything had the property of being an event of awareness; whether or not any Intentional event has or had the object as its object; and, given the relevant contingent properties of the object and all conscious subjects, whether or not any Intentional event could have or could have had the object as its object. A stone at the bottom of an ocean that no being ever perceives is generically independent of awareness. So is a stone that someone does perceive in the Grand Canyon. 16.1.1. A generically-independent object may then be noumenal or phenomenal 16.1.2. Artworks and generically-independent objects. An artwork may be meant to be identiﬁed with a generically-independent object. A stone that someone selects and exhibits as her work of art eﬀects the identiﬁcation of an artwork with a generically-independent object. An artist who speciﬁes the center of the earth to be her work of art speciﬁes a generically-independent object to be that work. It might be thought that such uses of such generically-independent objects is part of the progression of Abstraction since such generically-independent objects selected or speciﬁed were not created, but were singled out through this diﬀerent means of delineating objects with which artworks are meant to be identiﬁed. Thus what has been

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removed as superﬂuous to the project of eﬀecting a work of art in either case is the need to ﬁrst create an object that an artwork is meant to be. 16.1.3. The form of awareness of a generically-independent object. Any awareness of any generically-independent object of which it is possible to be aware is Intentional, irreﬂexive, polyadic, and ﬁrst order. 16.2. Particular independence An object is ‘particularly independent’ of a particular event of awareness when the object is neither identity dependent nor type dependent on the event. If the event of awareness is an event of seeing and the object is a generically-independent object such as a tree, then the object is particularly independent of the event of awareness, and is so independent whether or not the object is the Intentional object of the event of awareness. However, if the event of awareness is an event of seeing and the object is a type-dependent object such as a painting, then the object is particularly independent of the event of awareness only if the object is not the Intentional object of that event of awareness. If the event of awareness is my seeing your body and the object is a pain in your foot, then the object is particularly independent of the event of awareness, since, although the object is an identity-dependent object, it is not dependent on that event of awareness. Such an object is also particularly independent of my awareness of your pain in virtue of something such as my understanding your words “I have a pain in my foot.” More generally, your pain is particularly independent of every event of awareness that is not the event of that pain itself. Any object that is generically independent of a particular event of awareness is also particularly independent of that event of awareness since, as generically independent of awareness, it cannot be dependent in either way on that event of awareness. However, it is not the case that an object that is particularly independent of a particular event of awareness is necessarily generically independent of any event of awareness. For instance, your pain is an object that is particularly independent of my awareness of your pain, but it is not an object that is generically independent of awareness, since there would be no object that is your pain apart from your event of awareness that is that pain.

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16.2.1. A particularly-independent object may be phenomenal or noumenal. An object that is particularly independent of an event of awareness my be phenomenal relative to that event. This page of this copy of this book, as a physical object, is particularly independent of the current event of perception relative to which it is phenomenal. An object that is particularly independent of an event of awareness may be noumenal relative to that event. An electron of which this page partially consists is noumenal relative to an event of perceiving this page. 16.2.2. Artworks and particularly-independent objects. An object with which an artwork is meant to be identiﬁed may be particularly independent of an event of awareness, including being particularly independent of an event of awareness in which the identiﬁcation of the work with such an object is apprehended. The referent of Barry’s all the things I know . . . is particularly independent of an event of comprehending the speciﬁcation that refers to it. 16.2.3. The form of awareness of a particularly-independent object. Any particular event of awareness of an object that is particularly independent of that event of awareness is Intentional, irreﬂexive, polyadic, and ﬁrst order. 16.3. Biographical independence An object is ‘biographically independent’ of an event of awareness both when the object is particularly independent of the event, and when the object is not the Intentional object of that event. For example, if the object is a pain in your foot, then that object is biographically independent of an event of awareness if, in addition to the event’s particular independence of the object because the event of awareness and the object are not diﬀerent ways of talking about the same thing, the event of awareness does not take the pain as its Intentional object. An object that is biographically independent of a particular event of awareness may or may not be generically independent of awareness, and an object that is generically independent of awareness may or may not be biographically independent of a particular event of awareness. An object that is biographically independent of an event of awareness is generically independent of awareness if the object is neither type dependent on a kind of awareness, nor is identity

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dependent on some particular event of awareness. Otherwise, although the object would be biographically independent of the event of awareness, the object would not be generically independent of awareness. A generically-independent object is biographically independent of any Intentional event that does not have the object as its Intentional object. Thus a stone in the Grand Canyon is biographically independent of my touching the Statue of Liberty, but is not biographically independent of someone who is examining the stone. In either case it is a generically-independent object. Although any object that is biographically independent of a particular event of awareness is particularly independent of that event of awareness, it is not the case that any particular object that is particularly independent of a particular event of awareness is also necessarily biographically independent of that event of awareness. For instance, the pain in your foot is particularly independent of my awareness of that pain but it is not biographically independent of that awareness. 16.3.1. Any biographically-independent object is noumenal. An object that is biographically independent of a particular event of awareness is noumenal relative to that event in being neither identity dependent nor type dependent on the event and in not being the Intentional object of the event. 16.3.2. Artworks and biographically-independent objects. An object that is biographically independent of an event of awareness may be meant to be identiﬁed with a work of art. Such an object could also be biographically independent of an event of comprehending the intended identiﬁcation of the artwork with that object. Some external-world object of which you have never been aware but of which you might have been aware singles out an indeterminate generically-independent object that could be meant to be a work of art that is biographically independent of any event in which you comprehend the intended identiﬁcation of the artwork with such an object. 16.4. Universal independence An object is ‘universally independent’ of awareness both when the object is generically independent, and when no event that forms part of the history of awareness of all conscious subjects—past, present,

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and future—has the object as its Intentional object. A stone in the Grand Canyon that no being has perceived, is perceiving, or will perceive in the universal history of awareness is universally independent of awareness. An object that is universally independent of awareness in this way is incessantly independent of awareness, but such lasting independence can be due to contingent features of the object and any subject who would be aware of it in the absence of such features. 16.4.1. Any universally-independent object is noumenal. Any universally-independent object is noumenal relative to each event of awareness in the history of awareness of each subject. 16.4.2. Artworks and universally-independent objects. A universally-independent object could be speciﬁed to be a work of art through such a speciﬁcation as an object of which no one who is ever aware is ever aware but of which it is possible to be aware. 16.5. Necessary independence An object is ‘necessarily independent’ of awareness both when the object is neither identity dependent nor type dependent on any event of awareness to be the object that it is, and when it is neither theoretically possible to be aware of the object, nor is it theoretically possible to be aware that some object is that object, or that some object has the identity of that object when it is not possible in theory to be aware of the object itself. By the very nature of the case, one cannot give an example of an object that is necessarily independent of consciousness without at least being made conscious that some object has that identity in virtue of that example, and so its ceasing to be the case that the object is necessarily independent of awareness. An object that is necessarily independent of awareness is also universally independent of awareness, but it is not the case that an object that is universally independent of awareness is also necessarily independent of awareness since, although no event in the history of awareness has that object as its Intentional object as a matter of contingent fact if it is universally independent of awareness, there may be nothing that makes it the case that the object cannot be the Intentional object of an event of awareness at any time in history

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rather than its being the case that the object is not the Intentional object of any event of awareness at any time in history. 16.5.1. Any necessarily-independent object is necessarily noumenal. Any object that has the properties of being necessarily independent as deﬁned is necessarily noumenal. 16.5.2. Artworks and necessarily-independent objects. Given the deﬁnition of necessary independence, it is necessarily impossible to know that any object is qualiﬁed by the properties required of an object for it to be necessarily independent. Accordingly, it is not possible to know if such language as any object that is in no way dependent on awareness and of which it is neither possible to be aware nor possible to know that some object is that object either singles something out with which an artwork could be meant to be identiﬁed, or that the language lacks a referent. In any case, such an object is of less interest to Essentialist Abstraction than is the sort of independent object that can either be creatively delineated in relation to essential elements of artistic complexes, or that can play a role in the delineation of an object that an artwork is meant to be which role is determined creatively in relation to essential elements of artistic complexes.

17. Essentialism and kinds of independent object Although it does not seem that an object that is necessarily independent of awareness can be meant or understood to be a work of art, the possible identiﬁcation of artworks with other kinds of independent object, and how that identiﬁcation could be eﬀected in relation to an event of awareness that forms part of an artistic complex, are open to creative investigation. And it cannot be discounted in advance of such an investigation that a limit or limits of Abstraction might be identiﬁed in one or another independent object, or that one or another kind of independent object may play a role in that investigation. However, any such identiﬁcation or determination of signiﬁcance would depend on at least one Type-A type-dependent object since any object on which the identity of an artwork is relevantly dependent is such an object. Given this dependence, the conceptual relation of an independent object meant to be an artwork

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to a dependent object that makes understanding that intended identiﬁcation possible would have to be considered, as would be the aesthetic relevance of an independent object to the determination of an artwork’s identity.

DIVISION IV: ARTISTIC COMPLEXES AND SUBJECTS AND OBJECTS

Introduction This division completes the philosophical examination of an artistic complex undertaken in this work. In doing so it continues the identiﬁcation of things that Essentialism would have to consider in its creative investigation of the limits of Abstraction. The ﬁrst section of this division reconsiders the notion of medium in relation to the fundamental requirements of making art of singling something out, and of making it possible to understand that what is singled out is meant to be a work of art. The possible use of consciousness as a medium is also considered, and so is such a use of agency. The kinds of media required of Essentialist Abstraction are identiﬁed in the second section, as is a kind of object that I call ‘ideational’ that is of interest to Essentialism. The relation of ideational objects to consciousness and language and the relevance of these things to the limits of Abstraction are further topics of the second section. The third section introduces the neologism ‘concipient’ and examines the relation of a concipient to the meaning of a speciﬁcation and to the production of an ideational object. Consciousness ﬁgures in one way or another in the ﬁrst three sections of this division, and section four lists kinds and forms of conscious event of interest to Essentialism as they pertain to essential elements of artistic complexes. Certain relations hold between the subject and perceptual object that are constituents of an artistic complex. In addition to the basic conscious, agential, and epistemological relations of the subject to the object that have already been considered, relevant relations here include the causal and indexical relations that are the subjects of sections ﬁve and seven. Section six’s recognition that both the coming and ceasing to be of an artistic complex and the coming and ceasing to be of the event of apprehension that is a constituent of the complex are unavoidable adds to points made in section ﬁve about causal relations that hold between the subject and the object of an artistic complex.

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As seen in section eight, all objects divide into those that are phenomenal and those that are noumenal relative to the conscious event that unites a subject and an object in an artistic complex. The relevant object of the complex is phenomenal, but the object that the work is meant to be may be phenomenal or noumenal, and, if phenomenal, may or may not be the relevant object of the complex. Section nine considers the possible relevance of apprehension and reapprehension of the object of an artistic complex and of the identity of an artwork to the identity of an artwork. As indicated in section 10, space and time are essential elements of artistic complexes in that the relevant object of a complex is spatial and the apprehension and agency that unite a subject and the object in a complex are temporal. Section 11 deﬁnes the notions of the continuity, discontinuity, recurrence, and non-recurrence of objects before examining the pertinence of each to artistic complexes, and to Essentialist Abstraction. Any creative determination of a limit of Abstraction will be subject to critical evaluation that will include the assessment of its aesthetic value. While that value can be considered in a wide sense, and so can be understood to include a conceptual in addition to a perceptual aesthetic, the aesthetic value of Essentialism is unavoidable. Section 12 distinguishes aesthetic properties that are essential from those that are inessential, and states that the focus of an Essentialist aesthetic must be those properties that are aesthetically essential.

1. Medium and media Because I spend some time in this section talking about the notion of a medium in general and the pertinence of that notion to created and selected artworks in addition to speciﬁed artworks, and because some media rather than others are more relevant to determining the limits of Abstraction, it might be thought that the consideration of medium might have occurred earlier in Part Two of the work as part of a more general examination of issues relevant to making and apprehending works of art, and that any consideration of media at this point would be limited to what is required of Essentialist Abstraction. I have delayed talking about the notion of a medium and media to this point both because certain concepts

division 1v: artistic complexes and subjects and objects 235 that are used in discussing ways of thinking of a medium and media do not appear in the work before this third part on artistic complexes, and because the general discussion of them both prefaces and permits a transition to the use of media in Essentialism. That having been noted, the remarks of this section of this division are both consistent with and follow from points made and elaborated upon earlier in the book. 1.1. Two notions of a medium A deﬁnition of the term ‘medium’ that is relevant to making and apprehending works of art is “a means of eﬀecting or conveying something.”1 1.1.1. A medium as eﬀecting something relevant to the identity of an artwork. For art, a medium can be understood to be a means of eﬀecting an object that an artwork is meant to be; or a medium can be understood to be a means of eﬀecting the identiﬁcation of an artwork with an object that the work is meant to be; or a medium can be understood to be a means of eﬀecting both of these things. 1.1.2. A medium as conveying the identity of an artwork. A medium can also be understood to be a means of conveying the identity of an artwork to an audience, where the conveying of the identity of an artwork to an audience indicates that the intended identiﬁcation of the artwork with a certain object is made comprehensible to people other than the artist whose work it is. 1.1.3. A medium as conveying the nature of an artwork. Since we typically apprehend the nature of an object that an artwork is meant to be in comprehending the intended identiﬁcation of an artwork with that object, the notion of a medium in this second sense of being something that conveys something can then also be understood to be a means of conveying the nature of an artwork when the nature of the object that an artwork is meant to be can be apprehended in comprehending the work’s identity. And by apprehending the nature of an object that an artwork is meant to be I

1

Merriam-Webster’s Collegiate Dictionary, Tenth Edition, s. v. “medium.”

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mean that we can at least to some extent categorize it as a particular kind of thing even if we know nothing more about it, and such apprehension is consistent with not understanding or not being able correctly to interpret the artwork in virtue of being aware of the identity and nature of the object that the work is meant to be. For instance, in knowing that an artwork by Chaim Soutine called House on Crete is to be identiﬁed with the painting of that title, we not only comprehend the intended identiﬁcation of the artwork with the painting, but we apprehend the nature of the object that the work is meant to be in seeing that it is a polychromatic landscape painting that includes a house, and do so whether or not we understand or can interpret the work. And in knowing that an artwork by Robert Rauschenberg called Monogram is to be identiﬁed with the combine painting of that title, we not only comprehend the intended identiﬁcation of the artwork with the combine painting, but we apprehend the nature of the object that the work is meant to be in seeing that it consists of a stuﬀed Angora goat with a rubber tire around its mid-section mounted in standing position on a platform that is marked by paint and collage, and that is supported by four casters that rest on the ﬂoor. And we so apprehend the nature of the object that the work is meant to be whether or not we understand or can interpret the work that is meant to be identiﬁed with that object. 1.2. A medium as a means of eﬀecting artworks An artistic medium, as it is conceived of both generally and restrictively in relation to means of eﬀecting artworks, must either be some kind of perceptible object or objects that is used in some way or ways to eﬀect the object that the artwork is meant to be; or it must be some kind of perceptible object or objects that is used in some way or ways to eﬀect the identiﬁcation of an artwork with some object; or it must be the comprehensible language of speciﬁcation that is used to eﬀect the identiﬁcation of an artwork with some object that may or may not have its identity apart from that identiﬁcation; or it must be a kind of non-perceptible event, such as an event of consciousness or an intentional event, that, in concert with language, and possibly other kinds of apprehensible object, is used to eﬀect the identiﬁcation of the artwork with the object that the artwork is meant to be; or it must be a kind of non-perceptible event, such as an event of consciousness or an intentional event, that, in concert

division 1v: artistic complexes and subjects and objects 237 with language, and possibly other kinds of apprehensible object, is used to eﬀect the object that the artwork is meant to be; or it must be some possible combination of these things.2 The perceptible objects noted may have apprehensible properties in addition to perceptible ones that are relevant to eﬀecting the identity of a work of art. The general notion of a medium or media as a means of eﬀecting artworks must be more speciﬁcally considered in relation to embodied and non-embodied artworks, and to the various means of eﬀecting them that have been identiﬁed, namely creation, selection, speciﬁcation, and combinations thereof. This will be done in sections 1.5.1, 1.5.3, 1.6, and 1.7–1.7.2 below. 1.2.1. The use of objects to determine the nature and structure of artworks in addition to eﬀecting artworks. Objects that may be means by which the identities of artworks can be eﬀected may also be used by artists to give their works a particular stable or changing nature and structure. For instance, an artist may mean for an artwork of hers to be identiﬁed with a number of visual objects that are situated in space in such a way that the perceptible spaces between them contribute to the nature and structure of the work, even though the work is meant to be identiﬁed with the objects and not with the spaces between them. An artist could also do the reverse and identify her work with the spaces between the displayed objects, in which case the placement and nature of the objects displayed would aﬀect the nature and structure of the work that is meant to be identiﬁed with the spaces between them. And an artwork that is meant to be identiﬁed with the images of a number of projected slides will be aﬀected in nature and structure by the apprehensible periods of time between the projection of the slides. The same would be true of a work that consisted of speciﬁed objects the speciﬁcations of which are projected on slides. The objects speciﬁed by such speciﬁcations might be the consciousness of things of which subjects who were conscious of the projected speciﬁcations were conscious between the projections, or the objects speciﬁed by such speciﬁcations might be the consciousness of the periods of time that occurred between the projections. The particular nature and structure of a work may be 2 As ‘object’ is used in the widest possible way in this work, perceptible objects include those actions, events, processes, states of aﬀairs, and so forth that are perceptible.

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subject to change, as in some of the previous examples, and an object that is used to eﬀect the identity of an artwork may also play a role in modifying the artwork. For instance, if an artwork is meant to be identiﬁed with a selected block of ice, and that ice is allowed to melt over a period of time at room temperature, then the same object that plays a role in eﬀecting the identity of the artwork, namely the ice, plays a role in changing the nature of the artwork that is meant to be identiﬁed with that object. 1.3. A medium as a means of conveying artworks Generally and restrictively, it can said that any medium that is a means of conveying the identity of any artwork to any subject must be a kind of public perceptual object that is a means by which understanding which object an artwork is meant to be can result. Such a perceptual object may have apprehensible features—such as containing or consisting of language—in addition to purely perceptual ones that are of importance to conveying the identity of an artwork. In any case, it must be the kind of object that is suited to making it comprehensible what the artwork is to be understood to be, given the nature and identity of the object that the artwork is meant to be. Accordingly, the notion of a medium as something that conveys the identity of an artwork to a subject would have to be more speciﬁcally considered in relation to embodied and non-embodied artworks, and what is required of a medium to convey the identity of a work of either kind to any subject who would comprehend that identity. 1.4. The restrictive notion of a medium Speaking of the notion of medium in either sense in a restrictive way is meant to recognize that eﬀecting and conveying the identities and properties of artworks depend in any case on things, such as consciousness and agency, in addition to those things mentioned as kinds of media relevant to works of art, which is the reason for speaking of a medium as a means of eﬀecting or conveying something, rather than as the means of eﬀecting or conveying something.3

3

Both consciousness and agency are considered as possible media both in 1.8.2

division 1v: artistic complexes and subjects and objects 239 1.5. Media and embodied artworks An object that an embodied artwork is meant to be may be created, selected, or speciﬁed, and a complex embodied artwork may consist partially of created objects, partially of selected objects, and partially of speciﬁed objects, and of limited combinations thereof. The sections of 1.5 look, in order, at created and selected embodied artworks in relation to a medium that is used to eﬀect each kind of embodied artwork, and then in relation to a medium that is used to convey the identity of each kind of embodied artwork. Section 1.7 considers speciﬁed embodied artworks, and, as speciﬁcation can be used to single out non-perceptual objects as works of art, speciﬁed non-embodied artworks are also a topic of that section. 1.5.1. Media and eﬀecting an embodied artwork that is created. A medium that is a means of eﬀecting a created object in which an artwork is meant to be embodied must be some kind of perceptible material, such as paint or stone, that can be used in some way or ways in concert with any object, such as a brush or chisel, that is either required of or that can be used with the material to eﬀect a perceptible object that the embodied artwork is meant to be, such as a painting or sculpture. Or it must be some kind of perceptible entity, such as a camera or photocopier, that can be used in some way or ways to eﬀect a perceptible object that the embodied artwork is meant to be, such as a photograph or photocopy, as that use involves any perceptible material, such as ﬁlm or paper, that is required to eﬀect an object of the kind of object that the perceptible entity can be used to eﬀect. Perceptible material and perceptible entities that are used to create artworks are typically distinct and are used in combination to eﬀect an object of the kind of object that their combined use can eﬀect. However, in the case of a work of Body art, such as Acconci’s Rubbing Piece that was cited earlier, the perceptible entity that is used to eﬀect a created object may be turned on itself and used as the perceptible material on which it

and 1.8.3 of this ﬁrst section, and in 2 of this division below. However, even when they are so used, other conscious and agential events are yet required of eﬀecting and conveying the identity of an artwork. And so they must still be considered to be a means rather than the means by which such an identity is eﬀected and conveyed.

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acts as a means of eﬀecting something that an artwork is meant to be. 1.5.2. Media and conveying the identity and nature of an embodied artwork that is created. Because an embodied artwork is meant to be identiﬁed with a certain perceptual object or objects, the perceptible object in which the artwork is embodied is itself a medium for conveying the identity of the work. This may be thought to be a nonstandard use of the notion of a medium, since any perceptual object in which an embodied artwork is meant to be embodied cannot function as a medium that can convey the identity of that work until that object exists as that perceptual object.4 But if an object that conveys the identity of an artwork is a medium in the second sense of medium cited, then a perceptual object in which an artwork is embodied is a medium in this second sense since it is a manifest means of conveying the identity of that artwork in being the object that the work is meant to be. No identity of any embodied artwork can be conveyed until some perceptible object is the perceptual object that the work is meant to be. But given that there is such an object, that object is a means of conveying the identiﬁcation of an embodied artwork with that object, and so it functions as a medium in the second sense of the term. Some other thing may be involved in conveying the identity of an artwork—such as a placard that includes the title of the work and the name of the artist whose work it is— and such a thing may also be considered to be a medium in the second sense of conveying the identity of the work. But when we perceive the entity in which Turner’s Rain, Steam, and Speed—The Great Western Railway is embodied next to a placard that reads: “Rain, Steam, and Speed—The Great Western Railway, J. M. W. Turner,” we know that that perceived entity is a means of conveying the identity of the artwork of that title by that artist since we understand that that entity is what that artwork is meant to be. As that understanding would not be possible apart from the perceptible entity that the work is meant to be, this example illustrates how the object in which an artwork is meant to be embodied can be understood to be a means 4 I say “until that object exists as that perceptual object.” It would also be unless that object exists as that perceptual object for any case in which the object in which the artwork is embodied is the only object that counts as relevant to the artwork for the artist whose work it is.

division 1v: artistic complexes and subjects and objects 241 of conveying the identity of that work. And, as seen, in such an object’s conveying the identity of the artwork it also conveys the nature of the artwork. 1.5.3. Media and eﬀecting an embodied artwork that is selected. A medium that is a means of eﬀecting the identiﬁcation of an artwork with a selected object in which the artwork is meant to be embodied must be some kind of perceptible object. This object must either be the selected object itself in which the selected artwork is to be understood to be embodied, such as a snow shovel, or it must be a perceptible object that is used in the process of singling out the selected object, such as a camera. A selected object, such as a bottle rack, that a selected artwork, such as Bottle Rack, is meant to be is a medium in the sense of being a means of eﬀecting the identiﬁcation of the artwork with the object since no object could be understood to be that artwork apart from that object. A camera that is used to single out a perceptible entity—such as a particular spouting of a particular geyser—is an object that is used in the process of singling out a selected entity that is singled out, and so counts as a means of eﬀecting the identiﬁcation of a selected artwork with a chosen object that the work is meant to be. In such an instance, it is the object itself that is photographed that is meant to be the selected artwork, and the work is not meant to be any photograph of that selected object. 1.5.4. Media and conveying the identity and nature of an embodied artwork that is selected. A selected object in which an artwork is meant to be embodied also functions as a medium in the second sense in being a means of conveying the identity of an artwork when the selected object is perceived and understood to be that artwork, since then it is understood that the artwork is meant to be identiﬁed with that perceptual object. For instance, the bottle rack that Bottle Rack is meant to be is a means of conveying the identity of that artwork to people in addition to the artist who has selected it since the artwork is meant to be identiﬁed with that selected object. At this point in history it is part of our artistic education that seeing a bottle rack next to a placard that says “Bottle Rack, Marcel Duchamp, 1914” indicates that that bottle rack is meant to be identiﬁed with the work of that title. Accordingly, the bottle rack that is Bottle Rack is a means of making it understandable that Bottle Rack is that bottle

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rack, and so it functions as a medium in the second sense of medium. A perceptible object, such as a photograph, that is derived from or causally related to an object, such as a camera, that is used in the process of singling out a selected object that an artwork is meant to be can also be understood to be a medium in the second sense of medium. This is the case when it is understood that the object photographed rather than the photograph itself is the object that the selected artwork is meant to be. This would depend on information in addition to the photograph for the photograph not to be mistaken for the work, but when the photograph so functions, then it is a means of conveying the identity of an artwork to others, and so functions as a medium in the second sense of medium. Either kind of perceptible object mentioned also conveys the nature of a selected object that a selected artwork is meant to be. It does so precisely in the selected object, and does so accurately in something such as a photograph on which the identity of the selected artwork is said to be relevantly dependent by the artist whose work it is. An entity, such as titular or informative language, that is also used to convey the identity of either kind of selected object may also be understood to be a medium in the second sense of medium. 1.6. Media and eﬀecting a non-embodied artwork that is selected A medium that is a means of eﬀecting the identiﬁcation of a nonembodied artwork with a selected non-perceptual object must be some kind of perceptible object. Such a perceptible object may have apprehensible properties in addition to perceptible ones that are required to eﬀect that identiﬁcation. The works from Barry’s Inert Gas Series will once again serve as examples here. Barry’s eﬀecting the identiﬁcation of works from this series with the non-perceptually expanding non-perceptual objects of the series depended minimally on the perceptible entities that contained the gases and from which the gases were released to expand, since gases can only be transported and released from such containers. And that gases can only be transported and released from such containers is an apprehensible property that is relevant to eﬀecting the identiﬁcation of a nonembodied artwork with a non-perceptual object of this kind that is not perceptible. It can also be observed that the photographic documentation of the works from this series depended on the percepti-

division 1v: artistic complexes and subjects and objects 243 ble entities that contained the selected gases with which the works of the series came to be identiﬁed—the photographic documentation that serves as a means of conveying the intended identities of the works from the series, and so that functions as media in the second sense of medium. 1.6.1. Media and conveying the identity and nature of a non-embodied artwork that is selected. A medium that is a means of conveying the identiﬁcation of a non-embodied artwork with a selected non-perceptual object must be some kind of perceptible object. As indicated above, one such object must be information that conveys the intended identiﬁcation. Although photographic documentation of a perceptual object that is used in the selection of the non-perceptual object may be understood to play a perceptible role in conveying that identiﬁcation, it will not by itself convey that identiﬁcation. Nor will any perceptual object that is used in the process of selecting the non-perceptual object. Accordingly, conveying the intended identiﬁcation of a selected non-perceptual object with a non-embodied artwork requires linguistic information, and such information functions as a medium in the second sense of medium. Linguistic information is also required to have some idea of the nature of a non-perceptual object that a non-embodied artwork is meant to be. 1.7. Language as a medium for eﬀecting artworks Language may be used as a means of eﬀecting the identiﬁcation of an artwork with an object that would have its identity apart from that identiﬁcation, or it may be used as a means of eﬀecting an object that an artwork is meant to be as it singles out the object as that work. Either kind of speciﬁed object may be perceptual or nonperceptual. As we are concerned with the art-historical production and identiﬁcation of artworks, language that is used to do any of these things must be perceptible. And as it is the semantic dimension of language that conceptually delineates objects, any language used is not simply perceptible but is also comprehensible. When language is used to single out an object that an artwork is meant to be which object would have its identity apart from that speciﬁcation, then the language so used is used as a means of eﬀecting the identiﬁcation of an artwork with an object, and so constitutes a medium in the ﬁrst sense of medium of eﬀecting something. Language

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that speciﬁes the center of the earth as an artwork is an example. Language also functions as a medium in this ﬁrst sense when it is used as a means of eﬀecting an object that an artwork is meant to be. An example is this language. In fact, because such language also singles out the eﬀected object as a work of art, it functions as a medium in the two senses of eﬀecting things that are relevant to works of art: eﬀecting an object that an artwork is meant to be, and eﬀecting the identiﬁcation of an artwork with some object. 1.7.1. Speciﬁcation and embodied artworks. A speciﬁed artwork may be meant to be embodied in an object, and such an object may or may not have its identity apart from that speciﬁcation. The speciﬁcation this page singles out an object in which an artwork could be meant to be embodied that would have its particular identity apart from that speciﬁcation, whereas this language singles out an object in which an artwork could be meant to be embodied that would have not its particular identity apart from that speciﬁcation. 1.7.2. Speciﬁcation and non-embodied artworks. An object that a nonembodied artwork is speciﬁed to be may or may not have its identity apart from that speciﬁcation. An example of an object that a non-embodied artwork could be speciﬁed to be that would have its particular identity apart from that speciﬁcation is the square root of two, whereas the referent of the distinction between this language and everything other than this language is an example of an object that a non-embodied artwork could be speciﬁed to be that would not have its particular identity apart from that speciﬁcation. The latter speciﬁcation is also an example of a speciﬁcation that is both a means of eﬀecting an object that an artwork is meant to be and a means of eﬀecting the identiﬁcation of the artwork with that object. 1.7.3. Language as a medium for conveying artworks. Any use of language to specify an object that an artwork is meant to be also functions as a medium in the second sense of medium in conveying the intended identity of the artwork to an audience, and in conveying too the nature of the objects speciﬁed to be works of art. The examples of the paragraphs of this section illustrate these things.

division 1v: artistic complexes and subjects and objects 245 1.8. Non-perceptible events as media for eﬀecting objects meant to be artworks Above I maintained that it is possible to think of the use of a kind of non-perceptible event as a medium either to eﬀect the identiﬁcation of an artwork with some object, or to eﬀect an object that an artwork is meant to be. I gave as examples of such events an event of consciousness and an intentional event. I also suggested that any use of some kind of non-perceptible event to eﬀect the identiﬁcation of an artwork with some object, or to eﬀect an object that an artwork is meant to be, would have to be coupled with language, and possibly other kinds of apprehensible object, to eﬀect such an identiﬁcation, or to eﬀect such an object. Whether or not eﬀecting the identiﬁcation of an artwork with some object that relies on the use of some kind of non-perceptible event to eﬀect that identiﬁcation requires some kind of apprehensible object in addition to language to eﬀect that identiﬁcation depends on the nature of the object. The speciﬁcation everything other than any awareness of any diﬀerence between this page and the space now surrounding it requires the page in addition to that language and the awareness that it names for the identiﬁcation of the artwork with the object to which the speciﬁcation refers to be eﬀected. And whether or not some kind of apprehensible object is required in addition to language to eﬀect an object that an artwork is meant to be that uses some kind of non-perceptible event to eﬀect that object depends on the nature of the object. For instance, the speciﬁcation any awareness of any similarity between this moment and the time preceding it requires the past in addition to that language and the awareness that it names for the object to which it refers to be eﬀected. Language is in any case a minimum condition of an object being eﬀected in relation to some non-perceptible event that an artwork is meant to be. This section identiﬁes a general principle for how consciousness can be used with language as a medium after it ﬁrst considers how consciousness is ordinarily thought to stand in relation to works of art. This section also includes a general assertion about any use of any kind of non-conscious, non-perceptible event as a means of eﬀecting an object that an artwork is meant to be, and an intentional event is used to illustrate that assertion. 1.8.1. The normal view of the relation of consciousness to artworks. Apart from the consciousness of the artist, consciousness is not usually thought to be a means of eﬀecting the identiﬁcation of an artwork

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with some object. Instead, it is seen as a presupposition of understanding the intended identiﬁcation. For instance, we do not normally think that an event of being conscious of Barnett Newman’s Cathedra in visual perception is a means of eﬀecting the identiﬁcation of the work of that title with the canvas that is the Intentional object of that event. Rather, we think that consciousness is a presupposition of being aware that Cathedra is meant to be identiﬁed with the Intentional object of an event or events of perceiving it.5 As we have seen, talk of medium here could see the completed canvas as a medium in being a means by which the identiﬁcation of Cathedra with that canvas is conveyed, since that canvas is what Cathedra is meant to be, and the canvas is for that reason also a means—in fact the most complete means—by which the nature of Cathedra is conveyed. When we think that consciousness is a presupposition of being aware that an artwork, such as Cathedra, is meant to be identiﬁed with the Intentional object of an event of perceiving the perceptible entity in which the artwork is embodied, we are thinking of consciousness in a general sense. And even if we are tacitly thinking of consciousness as being Intentional, we are not implicitly thinking of it as having any particular object as its Intentional object, rather than, possibly, supposing that it has a direction, and that it is directed to something other than itself. Therefore, to think of consciousness as a medium that may be a means of eﬀecting or conveying the identity of an artwork, we may have to particularize it to link it to a speciﬁc Intentional object, such as Cathedra, and say that consciousness of Cathedra is a medium by which the identiﬁcation of Cathedra with a particular canvas is eﬀected or conveyed. An artwork such as Cathedra is a Type-A type-dependent object that depends upon perception to have its particular identity, or, apart from events of perceiving the canvas that Cathedra is meant to be, nothing has the property of being Cathedra. Perhaps then the occur-

5 Identifying Cathedra with the Intentional object of an event of perceiving it can be understood to be equivalent to identifying that work with the Intentional object of an event of perceiving in its entirety the perceptual entity in which that work is understood to be embodied. Identifying Cathedra with the Intentional object of a number of events of perceiving it can be understood to be equivalent to identifying the work with a class of Intentional objects of a sequence of events of perceiving, from various angles and distances, the perceptual entity in which that work is understood to be embodied.

division 1v: artistic complexes and subjects and objects 247 rence of any such event of perception could be said to be a medium by which the identiﬁcation of Cathedra with a particular painting is eﬀected since nothing has the identity of that artwork apart from its being perceived. And it might be maintained that an Intentional event that has that painting as its Intentional object as much conveys the identity of Cathedra as does the painting, or perhaps only does, since the painting can only act as a medium that conveys the identity of the artwork that is meant to be that painting if it is seen. These points are well taken. However, they are more philosophical than what I have in mind for consideration of consciousness, and other kinds of event, as a medium that can be used as a means of eﬀecting the identity of an artwork. This is why I talked above more restrictively about consciousness being a means of eﬀecting an object that an artwork is meant to be, and did not talk more expansively about consciousness as a means of eﬀecting the identiﬁcation of an artwork with some object. 1.8.2. Language and consciousness. As noted above, consciousness must function with language in order for it to be either a means by which the identiﬁcation of an artwork with some object is eﬀected, or a means by which an object that an artwork can be meant to be can be eﬀected, and so in order for it to function in either way as a medium in the ﬁrst sense of medium. Language that is used in either way in relation to consciousness must be the language of speciﬁcation. For consciousness to be a means by which the identiﬁcation of an artwork with some object is eﬀected, it must be the comprehension of a speciﬁcation that singles out an object that a work is meant to be, such that comprehending the speciﬁcation is a condition of the identiﬁcation of the artwork with the object. Comprehension of a speciﬁcation that singles out an object that a work is meant to be is always a condition of the identiﬁcation of the artwork with the object in the sense of being a presupposition of understanding the intended identiﬁcation of the work with the object, as in the intended identiﬁcation of an artwork with the center of the earth that can be understood to be eﬀected in comprehending the speciﬁcation the center of the earth. Accordingly, it is not the case that any comprehension of a speciﬁcation is a medium for eﬀecting the identiﬁcation of an artwork with some object rather than being a presupposition of understanding the intended identiﬁcation of an artwork with some

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object, and the remarks of section 1.8.1 above could be adapted to ﬁt comprehension of a speciﬁcation as being a presupposition of understanding the intended identiﬁcation of an artwork with some object to preface the more restrictive sense in which consciousness is seen to be a means of eﬀecting the identiﬁcation of an artwork with some object or of eﬀecting an object that an artwork is meant to be in 2 of this division below. Speaking of the consciousness that is comprehension of a speciﬁcation as a medium indicates something stronger and more complicated, namely that the identiﬁcation of an artwork with a speciﬁed object is implicitly or explicitly indexed to comprehending the speciﬁcation that refers to the object, and that both the comprehension and the speciﬁcation have certain properties in virtue of which the comprehension functions as a medium in the ﬁrst sense of medium. In the previous example of eﬀecting the identiﬁcation of an artwork with the center of the earth, the medium used to eﬀect that identiﬁcation is language, and comprehension of that language is a presupposition of understanding the intended identiﬁcation, but the speciﬁcation the center of the earth is not indexed to its comprehension, as this here now is. And neither an event of comprehending the speciﬁcation nor the speciﬁcation itself have the properties required for consciousness to be a means of eﬀecting the identiﬁcation of an artwork with some object, and so to function as a medium in the ﬁrst sense of medium. For consciousness to be a means of eﬀecting an object that an artwork can be meant to be, it must be consciousness of a speciﬁcation that singles out an object of which consciousness of the speciﬁcation is a condition, so that, apart from an event that comprehends the speciﬁcation, nothing is the object to which the speciﬁcation refers. In this case both the object itself and the identiﬁcation of the artwork with the object are indexed to comprehending the speciﬁcation that refers to the object. Whereas in the ﬁrst case seen above, the object that the artwork is meant to be may or may not have its particular identity apart from the identiﬁcation of the artwork with the object, in the second case no object is the object that the artwork is meant to be apart from comprehension of a speciﬁcation that refers to the object of which that comprehension is a condition. This is because consciousness is a means of eﬀecting the object itself that the artwork is meant to be so that there is no object that the work is meant to be apart from the use of that means. Properties that are required of a speciﬁcation and an event of its

division 1v: artistic complexes and subjects and objects 249 comprehension for that comprehension to function as a medium in the ﬁrst sense of medium are identiﬁed in 2 of this division below. Kinds of indexical relation of comprehension of a speciﬁcation to an object that it singles out as an artwork are also listed in that section, as is the equivalence relation in which comprehension of a speciﬁcation stands to an object that it singles out as an artwork. These things are considered in that section in relation to the use of consciousness to eﬀect the identiﬁcation of an artwork either with an object that does or an object that does not have its particular identity apart from that identiﬁcation. 1.8.3. Non-conscious, non-perceptible events and language. The use of any non-conscious, non-perceptible event—such as an intentional event— as a means either of eﬀecting the identiﬁcation of an artwork with some object, or of eﬀecting an object that an artwork could be meant to be depends at least on language. More particularly, it depends on the use of language that is described in the following two principles: i.) For a non-perceptible, non-conscious event to be a means of eﬀecting the identiﬁcation of an artwork with some object that would have its particular identity apart from that identiﬁcation, it must be the case that a speciﬁcation singles out an object that would have its particular identity apart from the intended identiﬁcation of the artwork with that object, but which object cannot have the property of being the artwork apart from a non-perceptible event that is named by the speciﬁcation that refers to that object. ii.) For a nonperceptible, non-conscious event to be a means of eﬀecting an object that an artwork can be meant to be, it must be the case that a speciﬁcation singles out an object that an artwork is meant to be which object would not have its particular identity apart from a nonperceptible event that is named by the speciﬁcation that refers to that object. In each case the non-conscious, non-perceptible event functions as a medium in the ﬁrst sense of medium. An example of using an intentional event with language to eﬀect the identiﬁcation of an artwork with an object which identiﬁcation depends on that intentional event, and to which object the language that names the event can be understood to refer, but which object would have its particular identity apart from that identiﬁcation, is something other than anything that results from choosing to read this now. An example of using an intentional event with language to eﬀect an object that could be meant to be a work of art that the intentional

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event can be understood to have a role in eﬀecting, and to which the language that names the event can be understood to refer, is anything that results from any decision to attend to this at any time. In this case something that may result from deciding to attend to the speciﬁcation is understanding the relevance of deciding to attend to it to eﬀecting an object to which the speciﬁcation refers. Since such an understanding is itself eﬀected in virtue of deciding to attend to the speciﬁcation, it is referred to by the speciﬁcation that the decision to attend to is a means of eﬀecting. And so the decision functions as a medium in the ﬁrst sense of medium. 1.9. Documentation and reproductions as media for conveying artworks Any documentation or reproduction of any object on which the identity of an artwork is or was originally dependent that is considered to be a relevant object by the artist whose work it is may also be considered to be a medium, at least in the sense in which it can be understood to be a means of conveying the identity of an artwork to which it is said to be relevant. It would not be a medium in the sense of eﬀecting an object that an artwork is meant to be, and it would not be a medium in the sense of eﬀecting the identiﬁcation of an artwork with some object, since at least one other object from which the relevant object derives is a medium in either sense of being a means of eﬀecting something. 1.10. Media and parts of artworks The remarks on the diﬀerent senses of medium, and the diﬀerent possible uses of diﬀerent kinds of media in relation to diﬀerent kinds of artwork, and to the diﬀerent kinds of object with which the artworks can be meant to be identiﬁed, also apply to parts of artworks, and the diﬀerent kinds of object that parts of artworks can be meant to be. 1.11. Relevant objects as media for conveying artworks Any artistic complex includes as a constituent a public perceptual object on which the identity of an artwork is relevantly dependent. Such a relevant object may either be an original object in which all or part of the artwork is embodied, through which it is speciﬁed, or

division 1v: artistic complexes and subjects and objects 251 in which it is partially embodied and through which it is partially speciﬁed. Or it may be an object that is acceptably derived from any such original object. Any such relevant object is a medium in being a means of conveying the identity of the artwork to which that object is relevant. Accordingly, any artistic complex, in including a relevant object, includes an object that functions as a medium in the second sense of medium here employed. 1.12. The conceptual linkage of medium and singling something out These diﬀerent ways of thinking of how a medium or media relates to eﬀecting and conveying the identity of an artwork are speciﬁcally linked to the fundamental requirement of producing and apprehending the identity of any work of art of singling something out that the work is meant to be and can be understood to be meant to be. This conceptual linkage of medium and singling out pertains to the apprehension of the identity of a type-dependent object that all or part of a work is either to be understood to be, or on which it is dependent; to the apprehension of the identity of an identitydependent object with which all or part of a work is meant to be identiﬁed that is produced through engaging the subject directly in the production of that object; and to the apprehension of the identity of any kind of independent object that all or part of an artwork is meant to be; and to possible combinations thereof. Further, for simplicity, comments on the medium of a work are meant to pertain to any object on which the identity of a work is relevantly dependent, and not to any derived object not countenanced by the artist to be relevant to the identity of her work. And this is the case even though an object derived from an object on which a work is originally dependent may consist of the same substance, such as paint, or may be an indiscernible means of communicating identity, as in language. 1.13. Language as a medium that both eﬀects and conveys the identity of an artwork The notion of medium employed in this work is meant to avoid problems in the philosophy of art that arise from taking medium in the traditional sense and maintaining that works of art depend on and are to be identiﬁed with their physical medium, so that there

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can be no artwork apart from a physical medium in which the object that the work is meant to be has been crafted. Thus Dickie, contra Binkley, maintains that Robert Barry’s all the things I know but of which I am not at the moment thinking is not a work of art, or at least not a traditional work of art, since what is indicated by this language to be the artwork is not an object that has been executed in a medium. According to Dickie, Barry’s work “was not crafted with anything, it was just speciﬁed.” And the word “anything” in the preceding quote refers to things like “paint and canvas” in which objects like Albrecht Dürer’s Self-Portrait were and still are “crafted.” On the other hand, Dickie says that, if Binkley is right, and the work by Barry and others like it are art, then these are works that have “transcended the need for a medium.”6 It should be clear from what has been said in this book how Barry’s work and others like it succeed in being works of art. The identiﬁcation of Barry’s work with a certain object is eﬀected through the use of language that singles out the object that the work is meant to be. And that same language conveys to others the intended identity of the artwork with that speciﬁed object. Language is then a medium in both eﬀecting and conveying the identity of this work. If Barry were to regard any reproduction of the original token of his language as being as good as that original for understanding and appreciating what the work is to be understood to be, then each instance of that language would be a relevant object, and, as such, would qualify as a medium in the second sense. That is, it would qualify as a medium through which the identity of the work is made comprehensible. Language is no less a means of singling something out, and hence no less a means of making it clear with which object an artwork is supposed to be identiﬁed, than is a piece of crafted marble. It is here that my thinking about media and Dickie’s would appear to diﬀer. He seems to think that an artwork has to be identiﬁed with the medium or media itself on which its particular identity is dependent. And, as Barry’s speciﬁed object is something diﬀerent from the language in which its identity is speciﬁed, it cannot be a work of art. I think, on the other hand, that for an object to be a work of

6 See Dickie, George The Art Circle, pp. 59–61, from which the above quotes are taken, and Binkley, Timothy “Deciding about Art.”

division 1v: artistic complexes and subjects and objects 253 art it need only be intentionally singled out as a work of art and be capable of being understood as being so intentionally delineated. That is, an artist only needs to make it understood which object it is that his work of art is to be understood to be. And while the object on which that understanding is dependent is always a perceptual object of some kind or kinds—and this is an object that can be taken to be a medium of the work in virtue of being a means through which the identity of the work is conveyed, and is also a medium when it is a means by which the identiﬁcation of an artwork with an object is eﬀected—still an artwork need not be identiﬁed with any object on which apprehension of its identity is dependent. It is part of the philosophical and art-historical importance of Barry’s work to have been an illustration of this principle.

2. Non-perceptible events as media for Essentialist Abstraction Kinds of media identiﬁed in the ﬁrst section of this division above can be mixed in permissible combinations to produce complex objects, including Essentialist artworks, but it is the use of non-perceptible events as media that is the subject of sections 1.8.2. and 1.8.3. above that, in interaction with the language that the events require, must be the focus of any Essentialist treatment of artistic complexes in its investigation of Abstraction.7 Because of this required focus, it is the purpose of this section to expand on the use of consciousness as a medium for investigating the limits of Abstraction before brieﬂy noting the relevance of agency, as a non-perceptible, non-conscious medium, to such an investigation. When a conscious event is used either as a means of eﬀecting the identiﬁcation of all or part of an artwork with some object, or as a means of eﬀecting an object that all or part of an artwork is meant to be, then consciousness is being used as a medium rather than being simply tacitly accepted as a presupposition of comprehending the identity of an artwork, as is the case in traditional works of art. Although traditional visual artworks such as paintings and sculptures are implicitly directed toward consciousness, their relation to consciousness is passive rather than active, in that consciousness

7

See Part Four.

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discovers rather than creates an object meant to be all or part of a work of art.8 2.1. Consciousness, ideational objects, and comprehension of identity Consciousness can be understood to be a medium in the ﬁrst sense of medium when the identiﬁcation of an artwork with some object is implicitly or explicitly indexed to an event of comprehending a speciﬁcation that refers to that object, such that no object can have the property of being that work apart from that comprehension. Such an object may or may not have its particular identity apart from comprehension of a speciﬁcation, and when it does not, then comprehension of the speciﬁcation that refers to the object eﬀects the object as it eﬀects the identiﬁcation of all or part of an artwork with that object. There are several ways in which an object can be understood to be indexed to comprehension of a speciﬁcation that refers to it, and so for consciousness to be a medium in its being comprehension of a speciﬁcation that refers to an object that is indexed to that comprehension. In what follows I list a number of these ways to distinguish them from comprehension of a speciﬁcation as a mere presupposition of eﬀecting the identiﬁcation of an artwork with some object. However, this is not an exhaustive list of the ways in which an object can be understood to be indexed to comprehension of a speciﬁcation that refers to it, and so it is not an exhaustive list of

8

The relation of readers’ consciousness to literary artworks such as novels and poems can be debated. It might be argued that that relation is passive in the sense that such consciousness is a presupposition of understanding the identity and nature of the work without being a means by which that identity and nature are eﬀected. And this could be said to be the case either because the identity and nature of a literary work is said to be determined by the author, or because the work is taken to be an abstract type that has a timeless identity and nature as that type. Or it might be argued that that relation is active in the sense that there is nothing that a literary work can be apart from a reader’s consciousness of the author’s language, and that the nature of the work is determined in relation to properties of such consciousness—including its history and its location in history—in addition to properties of the language that that consciousness comprehends. The debate concerning the relation of consciousness to literary artworks pertains to the ontology of such works, and is in any case diﬀerent from the active relation of consciousness to speciﬁcations that are written to engage their comprehension to eﬀect the identiﬁcation of artworks with objects to which the speciﬁcations refer that is the subject of this section.

division 1v: artistic complexes and subjects and objects 255 the ways in which consciousness can be understood to be a medium. i.) An object is indexed to comprehension of a speciﬁcation that refers to the object if the object is reﬂexively linked to itself in polyadic or monadic awareness that is the same as, coincides with, or results from comprehending the speciﬁcation that refers to the object, as in this here now; your current consciousness of your current consciousness; and that which is thought of in thinking of this as being that which is thought of in thinking of this. ii.) An object x is indexed to comprehension of a speciﬁcation that refers to that object if x is delineated in negative, conjunctive, or disjunctive relation to an object y that is both reﬂexively linked to itself in polyadic or monadic awareness and is named by the speciﬁcation that refers to x. Examples include anything except your current consciousness of your current consciousness; this here now and something other than this here now; and this here now or everything other than this here now. iii.) An object x is indexed to comprehension of a speciﬁcation s that refers to x if x is conceptually and/or causally linked to an object y that is both reﬂexively linked to itself in polyadic or monadic awareness and that is named by s, as in anything that is similar to this here now; any eﬀect of your current consciousness of your current consciousness; and any diﬀerence between any eﬀect of your current consciousness of your current consciousness and anything other than any such eﬀect. iv.) An object x is indexed to comprehension of a speciﬁcation that refers to that object if x is deﬁned in negative, conjunctive, or disjunctive relation to an object y that is conceptually and/or causally linked to an object z that is both reﬂexively linked to itself in polyadic or monadic awareness and is named by the speciﬁcation that refers to x. Examples include anything other than anything that is similar to this here now and any eﬀect of your current consciousness of your current consciousness and something other than any such eﬀect. v.) An object is indexed to comprehension of a speciﬁcation that refers to the object if the object is the Intentional object of an irreﬂexive event that is named by the speciﬁcation that refers to that object, and which named event is the same as, coincides with, or results from comprehending the speciﬁcation. Examples include that which is comprehended in comprehending this information; anything you think of as you comprehend this information; and anything that is thought to be a possible eﬀect of thinking about the possible eﬀects of thoughts. vi.) An object x is indexed to comprehension of a speciﬁcation that refers to that object if x is delineated in negative, conjunctive, or disjunctive relation to an object y that is both is named by the speciﬁcation that refers to x and is the Intentional object of an

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irreﬂexive event that is named by the speciﬁcation that refers to x, and which irreﬂexive event is the same as, coincides with, or results from comprehending the speciﬁcation that refers to x. Anything other than that which is comprehended in comprehending this information; anything you think of as you comprehend this information and anything of which you do not think as you comprehend this information; and anything that is thought to be a possible eﬀect of thinking about the possible eﬀects of thoughts or something other any such possible eﬀect are examples. vii.) An object x is indexed to comprehension of a speciﬁcation that refers to that object if x is conceptually and/or causally linked to an object y that is the Intentional object of an irreﬂexive event that is named by the speciﬁcation that also names y, and which named event is the same as, coincides with, or results from comprehending the speciﬁcation. Examples include any eﬀect of that which is comprehended in comprehending this information; anything that is in some way related to anything you think of as you comprehend this information; and that which is in no way related to that which is thought of in thinking of that which is in no way related to any thought. viii.) An object that is deﬁned in negative, conjunctive, or disjunctive relation to the kind of indexed object described in vii.) can also be understood to be indexed to comprehension of a speciﬁcation that refers to that object, as in everything except any eﬀect of that which is comprehended in comprehending this information and any eﬀect of anything you think of as you comprehend this information or anything other than any such eﬀect. 2.1.1. Objects that are implicitly or explicitly indexed to events of comprehending speciﬁcations that refer to them. An object is implicitly indexed to comprehending the speciﬁcation that refers to it when no language in the speciﬁcation pertains to the comprehension required to eﬀect the identiﬁcation of the artwork with the object, as in this here now and something other than this here now. An object is explicitly indexed to comprehending the speciﬁcation that refers to it when language in the speciﬁcation pertains to the comprehension required to eﬀect the identiﬁcation of the artwork with the object, as in your current apprehension of that which is here and now apprehended and any apprehension of that which is here and now apprehended other than any current apprehension of that which is here and now apprehended. 2.1.2. Comprehension of a speciﬁcation is necessary and suﬃcient for an artwork dependent on that comprehension. Comprehending a speciﬁcation that refers to an object with which an artwork is meant to be identiﬁed

division 1v: artistic complexes and subjects and objects 257 is a necessary and suﬃcient condition of eﬀecting the identiﬁcation of the artwork with the object that is implicitly or explicitly indexed to comprehending the speciﬁcation that refers to it. It is necessary since no identiﬁcation of the artwork with the object to which the speciﬁcation refers can be the object that the work is meant to be apart from comprehending the speciﬁcation. And it is suﬃcient because the identiﬁcation of the artwork with the object that is indexed to comprehending the speciﬁcation is what is intended by the artist who has written the speciﬁcation to provide for the possibility of that identiﬁcation in virtue of the comprehension of the speciﬁcation. When comprehending a speciﬁcation that refers to an object that an artwork is meant to be eﬀects that object, then that comprehension is a necessary and suﬃcient condition of both eﬀecting the object and of eﬀecting the identiﬁcation of the artwork with the object—the object that is implicitly or explicitly indexed to comprehending the speciﬁcation that refers to it. It is necessary since no object can be the object that the work is meant to be apart from comprehending the speciﬁcation, and it is suﬃcient because the identiﬁcation of the artwork with the eﬀected object is what is intended by the artist who has written the speciﬁcation to provide for the possibility of eﬀecting the object that is eﬀected. 2.2. Ideational objects and ideational artworks An object with which an artwork is meant to be identiﬁed whose identity as that work is implicitly or explicitly indexed to an event of comprehending a speciﬁcation that refers to that object, such that no object can have the property of being that work apart from that comprehension, is an ‘ideational object.’ A speciﬁed object that a work is meant to be then becomes ideational, and is only ideational, in virtue of comprehension of a speciﬁcation that refers to it to which comprehension the object referred to is indexed. An ideational object that an artwork is meant to be may or may not have its particular identity apart from an event of comprehending a speciﬁcation to which the identiﬁcation of an artwork with that object is indexed. However, it can only be ideational as deﬁned in virtue of being indexed as indicated to comprehending a speciﬁcation that refers to it. An example of an ideational object that would have its particular identity apart from a speciﬁcation that refers to it is that of which you

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were most recently conscious before now being conscious of this. If no object is the object that an artwork is meant to be apart from comprehending a speciﬁcation that refers to that object, then the object is indexed to comprehending such a speciﬁcation, so that, apart from comprehension of the speciﬁcation, not only does no object have the property of being that work, but no object has the property of being that object. An example is your current consciousness of this. An artwork that is meant to be identiﬁed with an ideational object is an ‘ideational artwork.’ An ideational object that is itself eﬀected as the identiﬁcation of an ideational artwork with that object is eﬀected is a participatory artwork, as the notion of a participatory artwork was earlier deﬁned. This is because the ideational object that the work is meant to be depends on the a subject’s decision to attend to a speciﬁcation to whose comprehension the object is indexed, and so the subject participates in eﬀecting this kind of ideational artwork. And although Essentialism may investigate the use of either kind of ideational object in determining the limits of Abstraction, this second participatory kind of ideational object is the more Abstract since it is dependent on a conscious event of comprehension to have its particular identity, or to be the object that it is, in addition to having the property of being a work of art. And the event of comprehension presupposes a decision to attend to a speciﬁcation to which that event is indexed. Both consciousness and agency are ineliminable features of artistic complexes, and because an act of comprehending a speciﬁcation is a kind of conscious event, there is a conceptual reﬂection in the object of an essential ingredient of the artistic complex on which eﬀecting the object is dependent.9 The agency on which a participatory ideational artwork is dependent either implicitly or explicitly pertains or is related to a decision to attend to a speciﬁcation that singles out an eﬀected ideational object that is indexed to comprehending that speciﬁcation. It is implicit when the intentional act on which the eﬀected ideational object depends is not named by the speciﬁcation that refers to that ideational object, as in your current consciousness of this as being your current consciousness of this. It is explicit when the intentional act on which the eﬀected ideational

9

For more on this see Part Four 4–5 on pp. 301–308 below.

division 1v: artistic complexes and subjects and objects 259 object depends is named by the speciﬁcation that refers to that ideational object, as in your decision to reﬂect on your comprehending this to be your decision to reﬂect on that comprehension. 2.2.1. Speciﬁcation and ideational and non-ideational artworks. All ideational objects are speciﬁed objects but not all speciﬁed objects are ideational. An object that is speciﬁed to be a work of art that is not an ideational object is a ‘non-ideational’ object. A speciﬁed artwork that is meant to be identiﬁed with a non-ideational object is a ‘non-ideational artwork.’ The notions of ideational and non-ideational objects and ideational and non-ideational artworks are tied to speciﬁcations, and speciﬁed objects are sorted into these classiﬁcations according to whether or not they are indexed to events of comprehending the speciﬁcations that refer to them. The speciﬁcation your current consciousness of this singles out an ideational object since the property that the delineated object has of being a work of art is indexed to an event of comprehending the speciﬁcation that singles out the object, and so is an essential means by which the identiﬁcation of the artwork with the object is eﬀected. Barry’s speciﬁcation all the things I know . . . singles out a non-ideational object since, although the object is conceptually delineated by the speciﬁcation, it is not indexed to an event of comprehending the speciﬁcation that refers to it. Rather, it is indexed to Barry’s consciousness at the time named by the speciﬁcation. 2.3. The mixed media of Essentialism Given the prior considerations of subjects and objects, it follows that any of the more Abstract objects that it is possible to eﬀect can be eﬀected through the use of mixed media—through the use of a public, phenomenal, linguistic object that engages the intellectual process of apprehending its meaning as the remaining medium in which, in relation to which, through which, or from which the object that the artist intends the work to be originates. Thus the kind of conscious event utilized by Essentialism is that of semantic comprehension, and the meaning comprehended is that of language that speciﬁes an object with which all or part of an artwork is meant to be identiﬁed. This comprehension in any case eﬀects the identiﬁcation of an artwork with some object, and may eﬀect the object itself that the comprehended language singles out, in that no object has the identity

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of the speciﬁed object apart from comprehension of the language that refers to it. A speciﬁcation that is written to engage its comprehension in the production of an ideational object may be written to engage either a particular event—such as your current consciousness of this—or any event of a kind of event on which the ideational object is designed to depend—such as any consciousness of this.

2.4. Possible uses of consciousness as a medium Investigation of the use of consciousness to eﬀect an ideational object that an artwork is meant to be would include consideration of consciousness as a means in which, in relation to which, from which, or through which such an object could be eﬀected: in which, as when the object that the work is meant to be is the conscious event itself that apprehends that intended identity; in relation to which, as when the object that the work is meant to be is deﬁned in some relation to a conscious event on which identiﬁcation of the work with the object is dependent; from which, as when the object that the work is meant to be is a causal result of an event of comprehending a speciﬁcation that refers to the object; and through which, as when consciousness is required to deduce the identity of the object that the work is meant to be. Examples of consciousness being a means in which, in relation to which, and from which an object that all or part of an artwork is meant to be is eﬀected were seen in points i.)–viii.) of section 2.1 above. Consciousness can be a means through which an object that all or part of an artwork is meant to be is eﬀected either when a speciﬁcation is comprehended that singles out an object that must be deduced, or when a speciﬁcation must be completed by a term or terms that consciousness is required to deduce so that the completed speciﬁcation can then refer, or both, but where, in any case, apart from any deduction to which the speciﬁcation pertains, nothing is the object to which the speciﬁcation refers. An example of an incomplete speciﬁcation that depends on deducing a term that is required to complete it in order that it may refer is that which is understood to be required to ( ) in order to understand to what this refers, and where such a speciﬁcation is complemented by language that makes the deduction of the missing term possible. In this instance, the complementary language might be something like: “The missing

division 1v: artistic complexes and subjects and objects 261 term is a two-syllable word of six letters whose last letter follows its ﬁrst letter in the alphabet, and that refers to the very intellectual process that is required to understand the identity of that missing term.” One might then deduce that ‘deduce’ is the term that completes the speciﬁcation, and so then understand that the completed speciﬁcation refers to the understanding that that term must be deduced to complete the speciﬁcation that refers to that understanding. 2.5. Consciousness, art, and philosophy This section has looked at various ways in which consciousness could be used as a medium. How diﬀerent kinds and forms of conscious event could be used more speciﬁcally either to eﬀect the identiﬁcation of works of Essentialist art with Abstract objects or to eﬀect Abstract objects meant to be works of Essentialist art is up to the artist to determine. This is because philosophy cannot specify in advance of creative investigation how consciousness can be used artistically to eﬀect the identiﬁcation of Essentialist artworks with Abstract objects or to eﬀect Abstract objects that Essentialist artworks are meant to be. Rather, it is up to the artist to conceive of speciﬁcations that, in engaging conscious events to eﬀect the identiﬁcation of works of art with objects, or to determine objects to which the speciﬁcations refer, either eﬀect the identiﬁcation, or result in Abstract objects that are works of art and works of Essentialist art. Philosophy can state, however, that either kind of ideational object— one that does or one that does not have its particular identity apart from comprehension of a speciﬁcation that refers to it—is more Abstract to the extent that the identiﬁcation of the artwork with the object is eﬀected in relation to ineliminable elements of artistic complexes that the identiﬁcation of the artwork with the object reﬂects.10 2.6. Agency as a medium Because agency is an ineliminable feature of an artistic complex, the possible uses of agency as a medium to determine objects meant to be works of art would have to be considered. The use of an act of

10

See Part Four.

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agency to eﬀect an object that an artwork could be meant to be in this sense would depend on the use of language as indicated in the general principle for using non-perceptible, non-conscious events that appears in section 1.8.3 above. An object eﬀected by the use of agency according to this principle would be more Abstract to the extent to which it uses and reﬂects ineliminable elements of artistic complexes.

3. Meaning and concipients 3.1. Meaning and artistic complexes A subject is related to a speciﬁcation through diﬀerent kinds of awareness, through sight on the one hand, and through understanding on the other. Accordingly, when a subject attends to language of a relevant object that speciﬁes an object with which all or part of an artwork is meant to be identiﬁed, the meaning that is grasped through reading that language is part of an artistic complex of which the subject comprehending it is also part. This is because it is the meaning of a speciﬁcation that singles out and makes comprehensible with which object an artwork or one of its parts is meant to be identiﬁed rather than the speciﬁcation treated as a particular sequence of visible marks. The language of speciﬁcation, as visual, is non-referential. It is the semantic dimension of language through which it is made comprehensible what all or part of an artwork is to be understood to be. Thus in reading a speciﬁcation we grasp its meaning, and, in grasping that meaning, we understand to which object the meaning points. Although a speciﬁcation is not an essential element of any artistic complex, any artistic complex that includes the comprehended language of speciﬁcation as a constituent also includes the comprehended meaning of that language as a constituent since comprehension of language is not simply a matter of perception of the language. The comprehended meaning of a speciﬁcation is an essential element of any artistic complex in which the subject of the complex understands which object is singled out by the language that is a constituent of the complex. If determining the limits of Abstraction rests on the use of speciﬁcation, and the meaning of the speciﬁcation is an essential element of the complex of which a speciﬁcation that

division 1v: artistic complexes and subjects and objects 263 singles out an Abstract object is a constituent, then a creative inquiry into the limits of Abstraction would include investigating the relation of the meaning of a speciﬁcation to the subject who comprehends it. It would also include investigating the relation of that meaning to other elements of an artistic complex of which it forms part. A creative inquiry into the relation of these things would as much form part of an Essentialist investigation of the limits of Abstraction as a creative inquiry into the relation of colors, shapes, and surfaces forms part of an investigation of the possibilities of NonObjective painting. The things cited would have to be creatively investigated both for the pertinence of these things to Abstract objects that are delineated by the meaning comprehended, and to the nature of the aesthetic that would be determined in part by that investigation. This investigation would have to be creative rather than philosophical simply because philosophy can only state the need for the investigation to occur and cannot conduct the investigation itself. 3.2. The concept of a concipient The noun ‘concipient’ is here introduced as a neologism that is meant to be a kind of active conceptual counterpart to ‘percipient.’11 A subject acts as a concipient in comprehending a speciﬁcation either when the speciﬁcation comprehended refers to an object that cannot have the property of being all or part of a work of art apart from comprehension of that speciﬁcation, or when comprehension of the speciﬁcation produces an object that the speciﬁcation singles out as all or part of a work of art. In either case, a subject acts as a concipient in the role that she plays in eﬀecting the identiﬁcation of all or part of an artwork with an ideational object. A concipient does not conceive of the intended identiﬁcation of an ideational artwork with an ideational object of either kind of ideational object. Any intended identiﬁcation of an ideational artwork with an ideational object is originally conceived of by the artist prior to the concipient’s comprehension of language that singles out the object. ‘Conceiving’ or ‘conception’ in this context suggests the origination of the idea for the intended identiﬁcation of an ideational

11 The Oxford Universal English Dictionary deﬁnes the adjective ‘concipient’ as ‘that conceives, conceiving.’

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artwork with an ideational object, and the idea for the use of a speciﬁcation that is required to eﬀect the intended identiﬁcation. Accordingly, any conceiving that is applicable here must pertain to an act of the artist that precedes the subject’s involvement with the speciﬁcation that pertains to the work, namely, the act of conceiving of with which ideational object the whole or part of an artwork is meant to be identiﬁed. And the artist’s conceiving of her intended identiﬁcation of an artwork with an ideational object precedes or coincides with her writing a speciﬁcation that, when comprehended, singles out an ideational object that is indexed to that comprehension. This intended identiﬁcation of an artwork with an ideational object is conveyed to others through the language of speciﬁcation. The ideational object that an ideational artwork is meant to be may have its particular identity as that object, but not as that artwork, apart from comprehension of the speciﬁcation that refers to the object, as in that of which you were most recently conscious before being conscious of this. Or the ideational object that an ideational artwork is meant to be may itself be eﬀected in the concipient’s comprehension of the speciﬁcation that refers to the ideational object, as in your current comprehension of this information. In the latter case, the object neither has its particular identity as that object nor as that artwork apart from comprehension of the speciﬁcation that refers to the object. A concipient does have a role to play in eﬀecting the identiﬁcation of an artwork with an ideational object of either kind that the work is meant to be, since, apart from comprehension of a speciﬁcation that refers to the object, no object has the property of being the work that depends on comprehending the speciﬁcation that refers to that object. And so, although a concipient does not conceive of the speciﬁcation whose comprehension produces an ideational object to which the speciﬁcation refers, the concipient is partially responsible for the ideational object to which the comprehended speciﬁcation points. Still, in comprehending with which object the artist intends all or part of the artwork to be identiﬁed, a person is acting as a concipient and not as a conceiver. 3.3. Essentialism and meaning It is of no concern to the interests of Essentialist Abstraction where meaning is located, if in fact meaning is such a thing that can be properly said to have a location. Meaning is simply a necessary ele-

division 1v: artistic complexes and subjects and objects 265 ment of any Essentialist complex. This is because the language of speciﬁcation is required to reach the limits of Abstraction, and meaningless language cannot function as a speciﬁcation.12 Reaching the limits of Abstraction does not depend on meaning being abstract, and it is not impeded by meaning being some kind of existential object, if that is in fact the case. Awareness will be related to meaning in either case, and that is all that is necessary for Essentialism to recognize.13

4. Kinds and forms of Intentional event and essential elements of artistic complexes 4.1. Perception and conception As every artwork depends on a public perceptual object, perception is an indispensable element of any artistic complex. However, as the object that an artwork is meant to be need not itself be perceptual, an event of perception that forms part of an artistic complex need not be passively linked to the identiﬁcation of the work with a perceptual object, as is customarily the case with perceptual artworks. Rather, perception can either be made to play a supporting role as a presupposition of apprehending that a non-perceptual object is meant to be a work of art, or it may be meant to play a more constructive role in determining what the work is meant to be if what the work is meant to be is tied speciﬁcally either to a particular event of perception or to a kind of event of perception. If the former is the case, then conceptual or cognitive awareness may be used actively to produce as it understands what the work that is dependent on it is meant to be. An example is anything of which you think 12 On speciﬁcation and Essentialism see Part Four, and 3 of that part in particular. 13 Contemporary divergences of opinion on this issue are represented, for instance, by John Searle, who says that, “I think that meanings are precisely in the head— there is nowhere else for them to be;” and by Thomas Nagel, who writes, “The mystery of meaning is that it doesn’t seem to be located anywhere—not in the word, not in the mind, not in a separate concept or idea hovering between the word, the mind, and the things we are talking about.” Searle, John Intentionality: An essay in the philosophy of mind, Cambridge: Cambridge Univ. Press (1983) p. 200. Nagel, Thomas What Does It All Mean: A Very Short Introduction to Philosophy, Oxford: Oxford Univ. Press (1987) p. 43.

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in virtue of your current comprehension of this language since the comprehension on which the speciﬁed object depends itself depends on perception of the language comprehended. If the latter is the case, then perception must combine with conceptual or cognitive awareness in apprehending the identity of the work, as these diﬀerent kinds of awareness combine to produce the object that the work is meant to be. Examples of the latter include what is delineated by the language your current perception of this language and any perception of this language since the identiﬁcation of either object with the perception speciﬁed requires comprehension of that identiﬁcation. Either kind of use of perception and conception in the determination of limits of Abstraction would have to be creatively investigated. 4.2. Essentialism and forms of awareness Any event of apprehending any public perceptual object on which the identity of an artwork is dependent will be Intentional, irreﬂexive, ﬁrst-order awareness, and any event of comprehending the identity of an artwork will be Intentional. However, such a perceptual object can include language whose comprehension either is or causes an event with one of the basic forms of Intentional awareness earlier identiﬁed: is an event, as in your current comprehension of this information; or causes an event, as in your thinking of that of which this provokes you to think in virtue of your understanding that this is meant to be your thinking of that of which this provokes you to think in virtue of that understanding. Comprehension of a speciﬁcation may produce an event of higherorder awareness that includes one of the basic forms of awareness and any of its Intentional objects as its Intentional object. Such a comprehending event with some Intentional form can be directed to or can result in an object that is meant to be an a work of art, as in your current awareness of your current awareness of this, or it can be causally related to an event or events with some Intentional form that can be directed to or can result in such an object, as in anything that results from your current awareness of your current awareness of this. The use to Essentialist Abstraction of reﬂexive awareness to consciously connect objects to themselves, as both the objects and events of awareness that reﬂexively link them reﬂect essential elements of artistic complexes, would have to be investigated. Examples of such ideational objects that are eﬀected through the use of reﬂexive awareness include: this here now and an event of your awareness of your aware-

division 1v: artistic complexes and subjects and objects 267 ness that occurs in virtue of understanding the relevance of this information to provoking an event of your awareness of your awareness. 4.3. Things that are relevant to the nature of an Essentialist object The nature of any Essentialist object will depend on the kind and form of the event of which it is the Intentional object; the kind and form of any event of awareness that the event of which it is the Intentional object presupposes, or to which the latter event is conceptually and/or causally linked; and the kind and nature of any object that the Essentialist object presupposes or to which it is conceptually and/or causally linked. The nature of an Essentialist object will further be determined in relation to certain essential elements of artistic complexes that are utilized in the determination of that object and that may be referenced by the language that the Intentional event comprehends. It would be up to an artist to investigate how any such event can be used in relation to essential elements of an artistic complex to eﬀect an artwork in which a limit of Abstraction is determined. Kinds and forms of conscious event of interest to Essentialist Abstraction are of interest to it not only in the determination of its objects but in the determination of its aesthetic. 5. Cause and eﬀect and change Causal relations that hold between subjects and objects are of three broad sorts pertaining to the notions of modiﬁcation, origination, or termination. Either an object in some way changes a subject, a subject in some way changes an object, or an object originates or results from an action or actions of a subject, or is terminated due to an action or actions of a subject. Any time in or at which the modiﬁcation, origination, or termination of objects by subjects or of subjects by objects occurs is a time that is then the present. 5.1. Change and perceptual objects on which embodied and speciﬁed artworks are dependent Works of art that are embodied in public perceptual objects and that are considered to be ﬁnished works are not normally designed

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to change. Rather, an artist usually designs an object to have a certain stable visual appearance with which she intends that the artwork be permanently identiﬁed, as permanence pertains to and is limited by the nature of reality and things in reality by which the intended permanence may be aﬀected. Thus when an artist creates a work of art by painting a painting, she intends for it to remain the same shape and size; she intends any visible parts of the painting to retain the same relative spatial relations to one another; she intends colors of the painting to remain the same as when painted; and she intends individual painted areas to retain their integrity and not to crack in some anticipated aesthetic evolution of the object. Selected artworks that are embodied in perceptual objects are also typically not intended to change, but are meant to continue to provide the same visual information as when they were selected, so that the observer will not only know which object was originally selected to be this particular work of art, but will be able to apprehend how the object looked when it was originally selected. A block of ice is an example of a preexistent object that could be selected by someone and intended to be exhibited as a work of art, but it could only be exhibited as a block of ice for a time, at least at normal gallery temperature, and the object meant to be the work of art could no longer be identiﬁed perceptually as that work after ceasing to exist as that kind of perceptual object. If someone or something were to have split the urinal in which Fountain was originally embodied, and were it the case that the damaged object was then retained by Duchamp and purposely exhibited in that state, then the information that most likely would be derived simply from viewing that object would be that that was the way in which the object was originally designed and meant to be exhibited by Duchamp. In fact, a person has to know about the history of Duchamp’s Large Glass to know whether or not its cracks were an originally intended feature of the object. Language that speciﬁes an object with which an artwork is meant to be identiﬁed is not usually designed to change conceptually through the rearrangement of its words in a diﬀerent order, or through the replacement of individual words in the speciﬁcation with other words, or both. Speciﬁcations are also not meant to change perceptually by, say, taking on diﬀerent colors or sizes at diﬀerent times, or by gradually fading from sight.

division 1v: artistic complexes and subjects and objects 269 In general, the public perceptual objects on which the identities of artworks are relevantly dependent are typically not meant to change, and changes that occur in these objects are due to the laws of physics, and to other things, such as vandalism, over which the artist has no control. Every eﬀort is usually made to prevent such changes from occurring, and to restore the work to its original condition if damage is done to it by any changes that do occur. 5.2. Change and temporal art forms Temporal art forms, such as ﬁlm and most forms of theater, are also not supposed to change as the whole objects that the people who have produced them have designed. Although the frames of a ﬁlm come and cease to be projected at particular times, the frames do not change their order relative to one another, and so any two showings of a ﬁlm will feature the same perceptual data in the same order.14 There can be, and usually is, a diﬀerence between successive images that are part of the same ﬁlm, but the ﬁlm itself, as a complex object composed of a number of frames in a certain order, does not change. There is only a diﬀerence between some of the elements of which the ﬁlm is composed, diﬀerences from which changes in perception associated with the same artwork follow. And although there can be diﬀerent versions of the same play, and diﬀerent performances of the same play can diﬀer, still the diﬀerent versions and performances are versions and performances of the same play, the basic structure and nature of which has been determined by its author. That basic structure and nature, which includes certain characters speaking certain dialogue in a certain order, is not designed to change from one version or performance to another, and diﬀerences in versions and performances are typically diﬀerences that can be eﬀected by such people as the director, set designer, and actors, and that are allowed for by the playwright. Such diﬀerences, although they may be aesthetically signiﬁcant, are secondary. A change to the basic structure and nature of a play, and so a change that would

14 When I speak of “the same perceptual data” I am ignoring as irrelevant to the point of this section any diﬀerences between perceptual data that follow from seeing the data from diﬀerent angles and distances and that may be aﬀected by things that intervene between the perceiving subject and the data perceived.

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constitute a diﬀerence from the playwright’s original script and intentions, would be primary. It is not clear, incidentally, that a playwright could intend a particular play of his to be able to undergo a primary change from one performance to another, rather than to permit some number and kind of secondary changes that would allow the performance to be understood to be a performance of a particular work. This is because, even if he allowed for the possibility of change within some speciﬁed range of such things as characters, settings, and dialogue, such changes would be consistent with his original intention for the work and so such changes, as planned for and permitted, become secondary rather than primary changes to the work that anticipates and allows for them. 5.3. Artworks that intentionally incorporate change Although most embodied artworks are intended to be as immutable as physics and other forms of interference permit, and changes to the work of art have usually been treated as aesthetically oﬀensive interferences with an object that is intended to remain stable over a period of time, there have been some works of art that were speciﬁcally designed to include changes to the object due to things in its environment. These changes were then embraced as determinants of the way in which the work would be perceived or apprehended at any particular time. Works of art that have involved the use of mirrors, such as those of Robert Smithson, Robert Morris, and Michelangelo Pistoletto are examples of works that are immediately and continually aﬀected perceptually by the data in their environment. As that data comes to include an observer so situated that his image will be one of those reﬂected, then at least some of the images of the perceptual object will be due to the presence of the subject, the subject who in turn perceives the images for which he is partly responsible. Alexander Calder’s mobiles are artworks that reﬂect in themselves changes in their environment due to movement in the air surrounding them or due to human touch, and Hans Haacke’s Proposal: Poll of MOMA Visitors changed according to observer participation in Haacke’s request for information from people observing this work. And anyone who has seen photographs of Walter de Maria’s Lightening Field in sunlight and when hit by lightening during a storm can appreciate the dramatic diﬀerence in perception of the work that diﬀerent states of the environment in which it is located

division 1v: artistic complexes and subjects and objects 271 can produce. Artworks that address change as part of their design are not limited to embodied artworks or only to those works that are intended to be perceived rather than apprehended by thought. Victor Burgin’s artworks, such as his Idea Structures Project, that result from the use of language to single out as parts of the work phenomena of the site in which they are exhibited, and that call for subject participation to determine portions of the work through reading, comprehending, recollecting, and thinking about a certain ordered set of information, are examples of speciﬁed artworks that were constructed to incorporate or reﬂect certain changes in the environment in which they are placed.15 5.4. Artworks and Cambridge changes When a subject s perceives a fully or partially embodied artwork a at a particular time t, s has the property of perceiving a at t, or it is true of s that he is perceptually aware of a at t. The same fact of the subject’s perception of an artwork can also be stated as a property of the artwork, so that, in the previous instance, a has the property of being perceived by s at t, or it is true of a that it is perceived by s at t. And for any particular speciﬁcation, a particular subject who comprehends the speciﬁcation, and a particular time, the subject would have the property of comprehending the speciﬁcation at that time, and the speciﬁcation would have the property of being comprehended by the subject at that time. Regarding a subject s, an object x, the relation of awareness, and diﬀerent times t1 and t2, there is a change of both s and x either when it is true that s is aware of x at t1 and false that s is aware of x at t2, or when it is false that s is aware of x at t1 and true that s is aware of x at t2. This statement of change of subject and object in relation to a diﬀerence of the truth value of statements regarding the subject’s awareness of the object utilizes Bertrand Russell’s deﬁnition of change, and this deﬁnition of change would appear to be the most minimal kind of change conceivable.16

15 Burgin’s All Criteria is another work that embraces change through the use of speciﬁcations that are indexed to as subject comprehending them. It is reproduced in Schlatter, Christian Conceptual Art Conceptual Forms, exh.cat., Gallerie 1900D2000, Paris (1990), p. 185. 16 “Change is the diﬀerence, in respect of truth or falsehood, between a proposition

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Artistic complexes of which subjects and objects are constituents both come to exist and cease to exist in time, or it is true that the relation of awareness comes to hold between the subject and the object at a particular time which relation did not hold at some earlier time, and the same relation will cease to hold at some later time that held at some earlier time. Accordingly, the coming to exist of an artistic complex will constitute a change of both the subject and the object that are constituents of the complex. This is because, at some time te earlier than the time at which the complex comes to exist, it is false that the subject is then aware of the object. And the ceasing to exist of an artistic complex will constitute a change of both the subject and the object that are constituents of the complex because, at some time tl later than the time at which the complex comes to exist, it is false that the subject is then aware of the object. That is, it is not the case that a subject is always a constituent of a particular artistic complex, or it is not the case that, for any event of awareness that forms part of a subject’s history of awareness, that event of awareness is a constituent of a particular artistic complex. The importance of these points for Essentialism is that the becoming of a particular artistic complex silently and unconsciously modiﬁes both the subject and the object that are constituents of that complex. This minimal undetected change is nevertheless an ineliminable feature or consequence of any artistic complex, and can be an object of understanding. As change to the subject and the object involved in any artistic complex is unavoidable, Essentialism needs to investigate ways in which change can be explicitly addressed or implicitly embraced in a reductive manner in partial determination of objects with which artworks or their parts are meant to be identiﬁed. 5.5. Origination and termination and works of art An artist may intend a work to be identiﬁed with the origination or termination of some object rather than with the object itself that concerning an entity and a time T and a proposition concerning the entity and another time T ', provided that the two propositions diﬀer only by the fact that T occurs in the one where T ' occurs in the other.” Russell, Bertrand The Principles of Mathematics, p. 469. This is what P. T. Geach has referred to as a “Cambridge change.” If every property of an object is relevant to the object’s being the particular object that it is, then no object can continue to exist unchanged on a Cambridge conception of change. This is because an object that exists at more than one time will at least have the property of being older than it was at the earlier time, even if it has changed in no other respect.

division 1v: artistic complexes and subjects and objects 273 comes or ceases to be. Such intended origination or termination of an object might be linked to the action or actions of a subject or subjects. For instance, an artist might place a blackboard and a piece of chalk in an exhibition space next to language that indicates that the work is to be identiﬁed, not with the marks that are made on the board, but with the coming to be of each mark. Or an artist might place language next to a number of lighted candles that indicates that the work is meant to be identiﬁed, not with the burning candles, but with the ceasing to be of the last ﬂame to go out of these candles, and whether or not it is blown out or goes out on its own. Or an artist might place a blackboard and a piece of chalk in an exhibition space and invite people to make and erase marks on the board and identify an artwork with the ceasing to be of each mark that is erased from the board. It may be that a limit of Abstraction could be determined in the identiﬁcation of a work with the origination of something, as the coming to be of the thing that originates is eﬀected in relation to essential elements of artistic complexes. Thus a speciﬁcation might be written so that its comprehension eﬀects the existence of something at the same time that the speciﬁcation singles out the origination of that thing as the work, as in the coming to be of any current comprehension of language that refers to the coming to be of any current comprehension of that language. And it may be that another limit of Abstraction could be determined in the identiﬁcation of a work with the cessation of something, as the ceasing to be of the thing that ceases is eﬀected in relation to essential elements of artistic complexes. In this instance a speciﬁcation might be so written that its comprehension can result in an ephemeral entity the cessation of which the speciﬁcation singles out as a work of art, as in the ceasing to be of the next thought of the ceasing to be of the next thought that comprehension of this information provokes.

6. Artistic complexes and becoming A particular artistic complex comes to exist at a particular time in virtue of a particular subject coming to attend in appropriate awareness at that time to all or part of a public perceptual object on which the identity of an artwork is relevantly dependent. That particular artistic complex exists for the duration during which the relevant object is continuously the Intentional object of the same subject

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who attends to it in the kind of apprehension appropriate to the object. This apprehension is minimally seeing, but may include apprehension that is relevant to the identiﬁcation of the artwork, such as linguistic comprehension. That same artistic complex ceases to exist at the point at which the subject’s period of continuous apprehension appropriate to the relevant object ceases. Because the identiﬁcation of any limit of Abstraction depends on an artistic complex; because every artistic complex depends on the fact of attentive apprehension; and because all apprehensions both come and cease to exist in time, the coming and ceasing to exist of both artistic complexes and the events of apprehension on which artistic complexes are dependent cannot be avoided. Given that these things are unavoidable, their possible use in the creative investigation of the limits of Abstraction would have to be considered as much as any other ineliminable element of an artistic complex. The facts of the coming and ceasing to be of artistic complexes and the events of perception on which they depend extend the points made about causality in the previous section, and the relevance of causality and agency both to the becoming of an artistic complex and to an event of comprehending the identity of an artwork must be recognized. An Essentialist investigation of the limits of Abstraction would then include exploring how the origination and/or termination of certain objects, and how the coming and/or ceasing to exist of certain apprehensions of certain objects, can be made either to be a work of art, or can ﬁgure in determining what the artist intends the work to be, as either kind of origination or termination is linked to an action or actions of a subject forming part of an artistic complex in which either kind of becoming is identiﬁed by that subject.

7. Indexicals 7.1. Indexicals and awareness A word is indexical when the meaning of the word is constant for language users across places and times, but the object to which the word refers on a particular occasion can diﬀer depending on the context of the word’s use. The context of use for any indexical term is provided by the subject using it, so that indexicals are subject-relative. Thus, the term ‘I’ always has the same meaning in English,

division 1v: artistic complexes and subjects and objects 275 but the person to whom the word refers will diﬀer depending upon which person it is who is using the term. For Essentialist Abstraction, the most important indexicals are ‘this,’ ‘here,’ and ‘now.’ Each of these words is indexical because nothing can answer to either ‘this,’ ‘here,’ or ‘now’ apart from the relation of the referent of one of the terms used to the awareness of a particular subject using it. For instance, of two stones one cannot be this, here, or now for the other, as a stone can be this thing here and now for consciousness. Because stones are neither conscious nor language users, a stone is not the sort of thing that can provide the context or understanding necessary for the use of these terms. It is the particular awareness of particular subjects that gives these indexicals their particular reference, and the deﬁnition of each term must be given in terms of awareness. The constant meaning of ‘this’ is ‘the simple or complex object that is singled out in a particular event of awareness,’ or ‘that which is being attended to in a particular event of awareness;’ ‘here’ means ‘the place at which a particular event of awareness occurs,’ or ‘the place at which a subject exists when a particular event of awareness of hers occurs;’ and ‘now’ means ‘the time of particular event of awareness.’ Since ‘this’ pertains to the object that is singled out in a particular event of awareness, it can only refer to one object on any occasion of its use, and excludes every other object but that particular object. But this constant meaning can refer to diﬀerent objects on diﬀerent occasions, and it may be possible for two or more users to use ‘this’ to specify the same object of attention at the same time in the same place. That although the meaning of ‘this’ is constant the referent of ‘this’ is dependent on the context supplied by the consciousness of the subject using it, makes ‘this’ indexical. Just as with ‘this,’ the meaning of both ‘here’ and ‘now’ is constant, but ‘here’ can refer to a diﬀerent place and ‘now’ can refer to a diﬀerent time depending on the relation of either word to the awareness of the user of either term, and so each is indexical. However, whenever ‘here’ is used it can only refer to a single place relative to the subject using it, and ‘now’ can only refer to one time when it is used by a particular subject on a particular occasion. Accordingly, ‘here’ excludes all other places and ‘now’ excludes all other times on any occasion of their use relative to the consciousness of the subject then using them. The importance of these three words to this investigation comes from the fact that every work of art is dependent on a public

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perceptual object that, as such an object is singled out in awareness, is this-here-now for the subject who has consciously isolated it for attention. An object is also this-here-now for the person attending to it that is one of a number of objects on which the identity of an artwork is dependent, and which objects must be apprehended successively and cannot be apprehended simultaneously. For example, one could not have viewed but a part of Christo’s Running Fence at any time at which the work was extant, since it covered a distance of several miles. And to understand Victor Burgin’s Idea Structures Project one has to read a number of speciﬁcations in a certain order over a period of time required to digest them. It is of course also possible to attend to a part rather than to the whole of any perceptual object whose design permits attention to a part rather than to the whole, even if the whole is such that it can be taken in in its entirety in a single event of awareness, as in an average-size canvas. In this case the object would be apprehended over a number of connected or interrupted times in a number of events of awareness that are directed towards that object. But whether the parts that compose the whole of an object can be taken in simultaneously, must be apprehended over time, or are in fact apprehended over time, in attending to a part of such an object, the terms ‘this,’ ‘here,’ and ‘now’ apply to the part of that object given the attention to that part by the subject who has chosen to single it out. Although works of art depend upon public perceptual objects in which their identity is embodied or speciﬁed or embodied and speciﬁed, as artworks need not themselves be embodied in public perceptual objects, there may be no direct spatial relation of a subject to an object that an artist intends to be a particular work of art. However, ‘this’ will apply to a speciﬁcation’s meaning as that meaning is singled out in awareness as the object that itself singles out the object with which the artwork is meant to be identiﬁed. I mean that ‘this’ applies to a meaning comprehended, not in the sense that one can point to the meaning as one can point to the visible language whose meaning it is that is comprehended. Rather, I mean that ‘this’ applies to the meaning in the sense that it is this and not some other meaning that is comprehended. As the speciﬁcation’s meaning is comprehended, it will be an object that is comprehended in the present, and so ‘now’ will apply to the time of comprehending it. Accordingly, as the identity of a speciﬁed art-

division 1v: artistic complexes and subjects and objects 277 work is apprehended, an object will be this-now on which apprehension of that identity is dependent. 7.2. Indexicals and agency The relevance of indexicals to a subject’s agential relation(s) to the perceptual object to which the identity of a particular artwork is intentionally related can also be recognized. Subjects can only act in the present, and so, as a subject deliberately directs her attention to all or part of such a perceptual object, the whole or part of that object is an object to which she intentionally directs her attention now. And the object to which attention is deliberately directed is this particular object to which attention is deliberately directed, and it is an object that is here in relation to the subject who chooses to attend to it. In addition, comprehending the meaning of a speciﬁcation results from choosing to read the speciﬁcation, and the meaning comprehended is this-now as a result of the choice that led to its comprehension. 7.3. Indexicals and perceptual objects Because a public perceptual object is a requirement of any artwork, whether embodied or not, and because the principal indexicals ‘this,’ ‘here,’ and ‘now’ will apply to such an object as it is singled out in attention, a concern of Essentialist Abstraction would be to investigate how that which is indicated by these terms—taken individually, collectively, or in combination—can be used as partial means to determine which object it is with which all or part of a particular artwork is meant to be identiﬁed.

8. Phenomenality and noumenality It is unavoidable that an object is phenomenal or noumenal relative to any event of awareness of a particular conscious subject at any particular time. The relevant object of any artistic complex is phenomenal relative to the awareness that is a constituent of the same complex. As a subject forms part of an artistic complex, all objects will divide into those of which he is then aware and those of which

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he is not then aware, and an object of either of these classes will or will not be an object with which an artwork or one of its parts is meant to be identiﬁed. This too is unavoidable. Accordingly, the phenomenal and noumenal relation of objects to the awareness that is a constituent of an artistic complex is something that the artist must explore in his pursuit of the limits of Abstraction in art. These objects include most speciﬁcally those that are elements of the artistic complex of which the awareness relative to which they are phenomenal or noumenal is a constituent, the object that that awareness understands the artwork to be meant to be, and the objects that are parts of that work if the work is complex. To the extent to which noumenal objects can ﬁgure in the search for the limits of Abstraction, their so ﬁguring has to be made understandable. They must be related to phenomenal objects that can make the subject understand their intended relation to the work, as is the case with the speciﬁed work by Barry frequently cited in these pages. Noumenal objects that do not or cannot have such a comprehensible relation to an object of awareness cannot constitute a limit of Abstraction since they are indistinguishable from any number of other objects that have no designated relation to an artistic intention, or have no designated relation to a subject’s awareness of an object as meant to be a work of art or part of a work of art.

9. Apprehension and reapprehension When a particular subject ﬁrst apprehends the identity of a particular artwork through confrontation with an object on which the identity of the artwork is relevantly dependent, that apprehension occurs at a particular point in her history of awareness. The subject can again apprehend the identity of the artwork through apprehension of a relevant object if both the subject and such an object later exist, and nothing would prevent the subject from again being aware of such a relevant object. Because identifying the limits of Abstraction depends on apprehension of an object on which the identity of a particular artwork is relevantly dependent, and because more than one apprehension of a relevant object must be theoretically possible for the historical understanding and assessment of that identiﬁcation, Essentialist Abstraction needs to recognize as ineliminable the history of actual

division 1v: artistic complexes and subjects and objects 279 apprehensions and the possibility of subsequent apprehensions of such an object as such apprehensions concern either the history of awareness of a single individual or any number of individuals. Given this relation of the identity of a particular artwork to one or a number of apprehensions of one or a number of individuals of an object relevant to that identity, Essentialism must investigate ways in which a subject’s or subjects’ event or events of apprehending a relevant object can be utilized in its investigation of the limits of Abstraction according to its principles. More speciﬁcally, Essentialism must consider ways in which an object or objects with which a particular artwork is meant to be identiﬁed can be made to originate or can be modiﬁed by making a subject aware of how an initial or subsequent event of his apprehending an object relevant to the work’s identity can itself either produce or modify that which all or part of the artwork to which the apprehended object is relevant is to be understood to be. An event or events of apprehension utilized of the kind described would thus be coupled with causation, and such a pairing of one ineliminable element of an artistic complex with another, rather than pairing apprehension with a non-essential element such as color, better ﬁts the program and aesthetic of Essentialism in its pursuit of the limits of Abstraction. The implicit connection of awareness and agency would be an implicit aspect of the connection of any initial or subsequent apprehension and causation that is used in the origination or modiﬁcation of an object that an artwork is meant to be. The referent of any eﬀect of your next reﬂection on your current understanding that this is meant to be any eﬀect of your next reﬂection on what you have just understood combines apprehension, agency, and causation in the determination of an object that an artwork could be meant to be. Awareness, agency, and causation are all essential elements of artistic complexes, and their use to determine an object that an artwork is meant to be represents the determination of the identity of a work that is eﬀected through the use of such elements. However, it does not follow simply from the fact that such elements are used in eﬀecting an object that an artwork could be meant to be that it is one of the more Abstract possible. This is because the use of the same elements, as addressed and engaged by a diﬀerent speciﬁcation, might result in an entity that is more Abstract than the one in the example. The use of such events of apprehension and reapprehension to determine Abstract artworks would involve other things of relevance

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to them. This would include the temporal relation of such events to one another; their similarity to one another; and the nature of the object that they apprehend and the similarity of that object at one time to the object at another in addition to any causal relation holding between them. Recognition of any of these things that can be recognized depends in each case on memory. And recognition of the relation of reapprehension in the present either to original apprehension or any subsequent past apprehension, as well as recognition of the things of relevance to them, allows for anticipation, or the possibility of reapprehending in a future present what is apprehended now or has been earlier apprehended. Accordingly, Essentialism must consider the use of recollection and anticipation of the kinds of thing noted in the production of its objects.

10. Space and time Although the object meant to be a particular work of art may not itself be temporal or spatio-temporal, the Essentialist will have to take both space and time into consideration in producing Essentialist objects that are intended to reside at the limits of Abstraction. This follows from the fact that the identity of any artwork is dependent on a public visual object, and such visual objects are spatial objects that are situated in a surrounding space, and the fact that every artistic complex must involve the awareness and agency of a subject, and acts of awareness and agency are temporal entities that are situated in history. As the Essentialist is concerned to work with ineliminable features of artistic complexes formed by a subject and a relevant visual object, he will have to consider how best to use space and time as partial means by which the more Abstract objects possible can be constructed; how such objects stand in perceptual and/or conceptual relation to other objects relevant to their delineation; and how each of these things can aﬀect the aesthetic of Essentialism.

11. Continuity, discontinuity, recurrence, and non-recurrence The notions of continuity, discontinuity, recurrence, and non-recurrence are pertinent to objects on which artworks are relevantly dependent; certain objects with which artworks may be meant to be

division 1v: artistic complexes and subjects and objects 281 identiﬁed; and events of awareness that are relevant to comprehending and perhaps eﬀecting the identities of artworks. The pertinence of possible relations of these things to one another to the determination of the limits of Abstraction would have to be considered, as would their pertinence to the aesthetic of Essentialism. Deﬁnitions of these notions follow the deﬁnitions of contiguous and noncontiguous times that pertain to them and precede consideration of their relevance to art and to Abstract art. 11.1. Contiguous and noncontiguous times Two times t1 and t2 of a set s of two or more times are ‘contiguous’ when t1 precedes t2 and t2 succeeds t1 (so that s is a set of linear times) and no time tx comes between t1 and t2 (so that no time that precedes t2 succeeds t1 and no time that succeeds t1 precedes t2) and whether or not tx is a member of s. Any time of a set of times could be a moment or an interval. A moment or an instant can be understood to lack duration, either purely mathematically or in relation to human consciousness. A mathematical moment in time is named by a number such that, any number that names a time in history that is either less than or greater than the number that names the moment in history, names a time that is neither that moment nor a time that falls within the time that is that moment. A human or phenomenal moment in time is named by a number that pertains to repeatable segments of the time line, such as a tenth of a second, that is a time of which we can commonly be conscious, but of which we cannot be conscious as being divisible into smaller amounts of apprehensible times. Perhaps more accurately, consciousness of time pertains to phenomenal occurrences, such as seeing the momentary coincidence of the second hand and the minute hand on a clock, of which we are conscious as temporal. Such occurrences that lack temporal parts then constitute phenomenal moments. Since no two numbers are next to one another, a mathematical interval of time in history results from subtracting the smaller of two numbers that name times in history from the larger of those two numbers. A human or phenomenal interval is any apprehensible amount of time that is greater than a phenomenal instant. A set of times is a set of ‘contiguous times’ when the set has at least two members; when any member of the set is contiguous with

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at least one other member of the set; when no time that is not contiguous with at least one member of the set is a member of the set; and when any time that comes between any two times that are members of the set is a member of the set. Two times that are not contiguous are ‘noncontiguous.’ 11.2. Continuity An object x is said to be ‘continuous’ in relation to a set s of contiguous times of two or more times t1 and t2 either when: i.) some existential object is x at each t of s, and where x is either an event of awareness or an independent existential object; or when ii.) x is identity dependent or type dependent on an event or events of awareness e at each t of s, but x is not metaphysically equivalent to e, although it may be logically equivalent to e. Although any such e is existential, x may or may not be existential; and although x is continuous as deﬁned in virtue of the existence of e at each of the contiguous times of s, it need not be the case that any existential part of x, if x is complex, exists at a time that is contiguous with at least one time at which another existential part of x exists; nor do such parts have to exist only at the times of s, and hence at the times of e on which x is dependent. Pains and trees are examples of the ﬁrst kind of continuous object, and paintings and what is referred to by the eﬀects of your attending to this for the next six seconds are examples of the second kind of continuous object. The latter example indicates that not all parts of a continuous object, as ‘continuous’ is deﬁned, need be existential; that it is not necessarily the case that any existential part of any such complex continuous object is temporally contiguous with at least one other existential part of such an object; and that it is not necessarily the case that an existential object that is continuous in the second sense is conﬁned to the time at which any event or events on which it depends exists. For instance, one eﬀect of attending to the language may occur at one time and another at another noncontiguous time, and no eﬀect occurs at any time between them, and either or both eﬀects may not occur at or within the time of awareness in virtue of which they are parts of the same continuous object. That an object of the second kind of continuous object could be purely non-existential can be seen in the case of the referent of the distinction between the eﬀects of your attending to this for the next six seconds

division 1v: artistic complexes and subjects and objects 283 and everything other than the eﬀects of your attending to this for the next six seconds. 11.3. Discontinuity An object x is said to be ‘discontinuous’ either when: i.) some existential object is x at some time t and there is at least one time u preceding or following t at which nothing is x; or when ii.) x is identity dependent on the existence of a particular event or events of awareness e at t and it is either the case that no event is e at any time other than t, or there is at least one time u preceding or following t at which nothing is e;17 or when iii.) x is type dependent on an event or events of awareness e of a kind or kinds of awareness at t, and there is at least one time u preceding or following t at which nothing is such an e. In both the second and the third kind of discontinuity, x and e are diﬀerent things. In each kind of discontinuity, t could theoretically be a moment or an interval. An existential object of the ﬁrst kind of discontinuous object could be an event of awareness, such as seeing a stone, or an existential object that is generically independent of awareness, such as a stone seen. An object of either the second or the third kind of discontinuous object could be any kind of dependent object that is not metaphysically equivalent to any event on which it is dependent (although it may be logically equivalent to such an event) and such a dependent object could be an existential or a non-existential object. Any kind of discontinuous object noted could be continuous if t is an interval of contiguous times rather than a moment, that, as a moment, is not divisible into contiguous times. This is because the terms ‘continuous’ and ‘discontinuous’ are not incompatible as deﬁned. And any kind of discontinuous object noted could be discontinuous without being continuous in virtue of its being discontinuous as deﬁned relative to a single indivisible time.

17 This diﬀerent wording reﬂects ﬁrst the uniqueness of each event of awareness as indexed to the time at which it occurs, and then the possible occurrence of the same event at diﬀerent times where such times do not guarantee the uniqueness of any event that occurs at them. The deﬁnition of identity dependence does not itself decide between these possibilities, as was indicated above. See also paragraph two of section 11.5 of this section below.

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11.4. Artworks and continuity and discontinuity An object, including an object with which an artwork is meant to be identiﬁed, may be neither continuous nor discontinuous. Any nonexistential object, such as a number, that does not depend for its identity on consciousness is neither continuous nor discontinuous as these terms are deﬁned. Yet such an object could be singled out through speciﬁcation as a work of art. A public perceptual object on which all or part of an artwork is relevantly dependent is a continuous Type-A type-dependent object for any set of contiguous times at which it is phenomenal, relative to the same or diﬀerent subjects. Since such a continuous object is type-dependent it will also be discontinuous. Paintings are this kind of Type-A type-dependent object. A public perceptual object on which all or part of an artwork is relevantly dependent could be a discontinuous Type-A type-dependent object that is not also continuous if there is no set of contiguous times at each time of which it is phenomenal, and so whether or not the object is discontinuous at one or more times. For instance, an artwork may be meant to be identiﬁed with the momentary projected image of a slide, say a blank slide that results in rectangle of light on a white wall, but in any case so that nothing was that projected image preceding or following the moment at which the image appears. In this case the artwork is meant to be embodied in the image on which the identity of the artwork is relevantly dependent. If the slide is projected a single instantaneous time then there is a single discontinuous Type-A type-dependent object that the work is meant to be. Here the notion of an instantaneous time, and hence a time that is not divisible into a set of contiguous times, can only be established in relation to the time of human consciousness, where an instant might be thought to be a point of human time that is a fraction of a second, but, as indicated, must be a point of human time that is not divisible into a set of smaller points of contiguous times. If the slide is projected at a number of non-contiguous instants, then there are a number of discontinuous Type-A type-dependent objects, each one of which could equally be meant to the work, or each of which could be meant to be a part of the work. Both kinds of discontinuous object are Type-A type-dependent objects that are Type-A type-dependent relative to the same or diﬀerent subjects. An object with which all or part of an artwork is meant to be identiﬁed may be some kind of dependent object that may be con-

division 1v: artistic complexes and subjects and objects 285 tinuous and discontinuous, or it may be simply discontinuous. And an object that all or part of an artwork is meant to be may be some kind of independent object that is simply continuous, simply discontinuous, or is continuous and discontinuous.18 Because continuity and discontinuity cannot be avoided for any relevant object that forms part of an artistic complex, a task for Essentialism would be to explore the possible relations between the continuity and discontinuity of any public perceptual object on which all or part of the work is relevantly dependent, and the continuity and/or discontinuity of a continuous and/or discontinuous object that all or part of a work is meant to be, as this exploration is undertaken in relation to essential elements of artistic complexes. For instance, the continuity and the discontinuity of the speciﬁcation this here now coincides with the continuity and discontinuity of the object that is singled out by that speciﬁcation as the work. This coincidence is deﬁned in relation to the essential indexical relation of the perceptible relevant object to the subject that is named by that relevant object. On the other hand, the continuity and the discontinuity of the speciﬁcation the ceasing to be of your recollection of your most recent apprehension of this precedes both the discontinuity of the object that is singled out by that speciﬁcation and the continuity of the recollection that its ending presupposes. In this case the relation between these things is eﬀected in relation to the apprehension of a relevant object that is an essential element of any artistic complex of which that relevant object is an element. Perhaps diﬀerent Abstract limits could be identiﬁed in diﬀerent kinds of continuous and discontinuous object as the relation of such objects to the continuity and discontinuity of the relevant objects on which they depend would help to determine the nature of the Essentialist aesthetic. 11.5. Recurrence The notion of recurrence concerns either an existential object or an object that has its particular identity in virtue of an existential object. An object x ‘recurs’ or is ‘recurrent’ either when, for any two or

18 Any artwork that is meant to be the whole of the universe, past, present, and future, would be simply continuous.

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more times t1 and t2: i.) some existential object is x at each time and there is at least one time between t1 and t2 at which nothing is x; or ii.) some existential or non-existential object is x in virtue of some existential thing or things y at each time, such as an event of awareness, and there is at least one time between t1 and t2 at which nothing is y. Nothing in the deﬁnition of recurrence logically prohibits an existential object (x) from being a generically independent object, and a type-dependent object (x) that is existential or non-existential may recur in virtue of the existence at noncontiguous times of events of the kind or kinds of event of awareness ( y) on which it is dependent. Any existential object ( y) on which a recurrent existential or non-existential object (x) depends will be a non-recurrent entity, unless such an entity y is itself recurrent as deﬁned in i.). An identity-dependent object may or may not be thought to be recurrent, depending on whether or not the event or events on which it depends is or is not thought itself to be capable of recurring. An identity-dependent object is indexed to a time at which any event on which it depends occurs, and it may be thought that no event that occurs at one time can be the same event that occurs at a diﬀerent non-contiguous time since such diﬀerent times are thought to be necessarily distinguishing properties.19 On the other hand, this may be denied, and it might be thought possible for the very same event of awareness to exist at diﬀerent times. If that is the case, then diﬀerent times do not necessarily distinguish objects of which they are predicated, and an identity-dependent object could theoretically recur. The deﬁnition of recurrence is just that, a deﬁnition. And if times are thought to distinguish existential entities so that no existential object at one time can be the same existential object at another time if there is a time between these times at which nothing is that existential object, then no object can recur in either sense of recurrence. 11.6. Non-recurrence The notion of non-recurrence also pertains either to an existential object or to an object that has its particular identity in virtue of an existential object. An object x ‘does not recur’ or is ‘non-recurrent’ 19 On necessarily distinguishing properties see Appendix Two on pp. 336–337 below.

division 1v: artistic complexes and subjects and objects 287 either when: i.) some existential object is x at a time t, and for any time s that is earlier than t, no existential object is x at that time, and for any time u that is later than t, nothing is x at that time; or ii.) some existential or non-existential object is x in virtue of some existential thing or things y, such as an event of awareness, at a time t, and for any time s that is earlier than t, nothing is y at that time, and for any time u that is later than t, nothing is y at that time. Neither the notion of recurrence nor the notion of non-recurrence applies to a non-existential object that is not type dependent. 11.7. Artworks and recurrence and non-recurrence Although any public perceptual object on which the identity of all or part of an artwork is relevantly dependent recurs for any two noncontiguous times at which it is apprehended relative either to the same or diﬀerent subjects, an object that all or part of an artwork is meant to be may or may not be recurrent. The speciﬁcation the present moment recurs for any two noncontiguous times at which it is apprehended, but it singles out a diﬀerent non-recurrent object each time that it is apprehended. And an object that all or part of a work is meant to be may be recurrent, but may not be any public perceptual object on which the whole or a part of the work is relevantly dependent, and hence in relation to which its possible recurrence can be understood. The speciﬁcation your current conception of this as being the same conception of this as each of your past conceptions of this as so conceived recurs for any two noncontiguous times at which it is apprehended. If conceptions that answer to the speciﬁcation are not necessarily distinguished as diﬀerent objects in relation to the times at which they occur, then the object that is singled out by the speciﬁcation is a recurrent object that diﬀers from the recurrent speciﬁcation that refers to it. Because the possibility of recurrence cannot be avoided for objects on which works or their parts are relevantly dependent, but because there are options for the possible recurrence or non-recurrence of an object that all or part of a work is meant to be, Essentialism must investigate the relation of the possible recurrence of a relevant object to the possible recurrence or non-recurrence of the whole or part of a work of art. And it must do so as it recognizes the diﬀerence between the recurrence of the same thing and diﬀerent tokens of the same type of thing.

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It is possible to talk of ‘aesthetically essential’ properties in a positive and in a negative sense. In the positive sense, a property P that qualiﬁes an artwork a is aesthetically essential to that work either if a is a better or more aesthetic object by being qualiﬁed by P rather than by any diﬀerent property Q of the same kind of property as P, or if, were a not qualiﬁed by P, a would not have the aesthetic value that it does have in virtue of being qualiﬁed by P, and so whether or not there is any diﬀerent property Q of the same kind of property as P by which a might theoretically be qualiﬁed. For instance, the red color of Matisse’s Red Studio is an aesthetically essential property of that work if the painting is a better or more aesthetic work for not being any other color, and the property of being visibly marked by paint is an aesthetically essential property of Rauschenberg’s Bed if that work would not have the aesthetic value that it does if it had not had paint applied to it. It may also be essential to the aesthetic value of a particular artwork a that it not be qualiﬁed in whole or in part either by a particular property P rather than a particular property Q of the same kind as P by which a is qualiﬁed, or by any property P of a particular kind of property rather than some diﬀerent property Q by which a is qualiﬁed. When either of these things is the case, then a’s being qualiﬁed by P would either lessen or destroy the aesthetic value of a—an aesthetic value that a has, at least in part, due to the absence of P. For instance, P might be the size-property of being large and Q might be the size-property of not being large in being small, and it may be essential to the aesthetic value of a particular artwork a that it not be large. (It does not necessarily follow from this that Q is an aesthetically essential property of a, since a diﬀerent size-property R of the kind Q of not being large, such as being of medium size, may serve a as well as does Q.) Or P might be the property that a work can have of having a three-dimensional object attached to its surface, and it may be that the aesthetic value of a particular work, such as a Color-Field painting, would be lessened or destroyed in virtue of being qualiﬁed by such a property, rather than being qualiﬁed by the diﬀerent property Q of being two-dimensional. This paragraph outlines what is meant by speaking of aesthetically essential properties in the negative sense, and if it is essential to the aesthetic value of an artwork a that it not be qualiﬁed by a

division 1v: artistic complexes and subjects and objects 289 certain property P, then a would have the negative property of not being qualiﬁed by P. It is not necessarily the case that every property that qualiﬁes a particular artwork, including every aesthetic property of the artwork, is an aesthetically essential property. Any property of an artwork that is not aesthetically essential to the work, including any property that is aesthetic but not aesthetically essential, is an ‘aesthetically inessential’ property. It is typically thought that it should be part of an artist’s aim in producing a work of art to attempt to maximize the aesthetically essential properties of the work and to attempt to minimize, and perhaps even to eliminate, aesthetically inessential properties. The elimination of the aesthetically inessential is part of the general elimination of the inessential that characterizes the more Abstract artworks. A goal of Essentialist Abstraction would then be to eliminate properties that are aesthetically inessential. Those properties that are aesthetically essential for Essentialism would have to be determined either in relation to the use of things that are themselves philosophically essential to artistic complexes, or they would have to be determined in relation to the use of things that, although they are themselves not philosophically essential to artistic complexes, aesthetically enhance an artwork in which they ﬁgure by the way or ways in which they complement, aﬀect, or interact with those elements of an artistic complex that are philosophically essential. However, as is the case with any artwork, this determination can only be made artistically, and must be judged as successful or not from within that perspective.

DIVISION V: THE ESSENTIAL ELEMENTS OF ARTISTIC COMPLEXES

As the material of Part Three is long and intricate, and contains much writing not only on artistic complexes and Essentialism, but on matters that are pertinent to them, this ﬁnal division of this part lists the essential elements of artistic complexes. An artistic complex exists in virtue of a subject attending to an object on which an artwork is relevantly dependent. The object, the subject, and the subject’s consciousness of the object are constituents of the complex that are required for the existence of the complex. Certain relations hold between the subject and the object in addition to the conscious relation that holds between the subject and the object; certain properties qualify the constituents of the complex; certain conditions constrain the constituents, relations and properties; and certain facts pertain to these things. These relations, properties, conditions, and facts are philosophically coterminous and unavoidable given the existence of the complex. As such, they are lumped together under the rubric of ‘essential elements’ of the complex. Remarks that follow certain of these listings are limited to things that are pertinent to the elements and artworks that are worth recalling. The essential elements of artistic complexes are numbered. However, the numbering does not follow the order in which these things were considered in Part Three; the brevity of the numbered entries means that they are typically written diﬀerently from how they earlier appeared; and the subject matter of some of the numbers, here conﬁned to the space of a single entry, is spread amongst some diﬀerent earlier sections of Part Three. Remarks that follow an element that pertain to that element or artworks are unnumbered. Elements that are not essential to any artistic complex, but are essential to a kind of artistic complex, given the artistically-intended nature of the relevant object of the complex, are preceded by an asterisk. An artistic complex includes as an essential element: 1. A public perceptual object on which all or part of an artwork is relevantly dependent. This object is minimally visible and spatial but it may have apprehensible properties, such as linguistic properties, that are relevant to

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comprehending the identity of an artwork. *The meaning of any language of a relevant object is itself an element of an artistic complex in which the meaning is apprehended by the subject of the complex. The relevant object of an artistic complex is a Type-A type-dependent object. This is the case whether or not it has apprehensible properties in addition to perceptual ones that are relevant to comprehending the identity of the artwork that is dependent on the relevant object. The object that the artwork is meant to be may be either kind of type-dependent object, either kind of identity-dependent object, or some kind of independent object of those that are possible for artworks. A complex artwork may be a suitable combination of diﬀerent kinds of dependent and independent object. The relevant object may be simple or complex and the object that an artwork is meant to be may be simple or complex. Compositional relations that hold between the parts of a complex object cannot be avoided for either kind of complex object. *Compositional relations of the parts of a complex relevant object are then an essential element of any artistic complex the relevant object of which is not simple. 2. A subject who is appropriately attending to the relevant object. 3. The consciousness of the subject of the relevant object. This consciousness is appropriate to comprehending the intended identity of the artwork and is minimally perceptual. It may be conceptual as well as perceptual if the object is linguistic in addition to being visual. In any case the subject’s awareness of the object is cognitive in understanding the relevance of the object to the identity of an artwork. Perceptual consciousness of the relevant object as visual is Intentional, irreﬂexive, polyadic, and ﬁrst order. *Conceptual consciousness of any language that forms part of the relevant object is Intentional, but a speciﬁcation may be written to result in an event of comprehending it that is reﬂexive, and either polyadic and ﬁrst order, or monadic and second order. When this is the case, the particular structure of the conceptual consciousness is essential to that consciousness ﬁguring as an essential element of an artistic complex in which the speciﬁcation that it comprehends is an element. 4. The subject’s agential relation to the relevant object. 5. The subject’s epistemological relation to the relevant object. 6. The subject’s indexical relation to the relevant object.

division v: the essential elements of artistic complexes 293 7. The causal relation of the subject to the relevant object that minimally eﬀects a Cambridge change in the object, and the causal relation of the object to the subject that minimally eﬀects a Cambridge change in the subject. 8. The subject’s historical relation to the relevant object—where this historical relation pertains both to the subject’s history of awareness and her history of agency—and the historical relation of the relevant object to all subjects who have apprehended it—where this historical relation pertains both to the subjects’ history of awareness and their history of agency. These things pertain both to individual and collective apprehension and reapprehension, and to individual and collective choices as these things pertain to the relevant object of an artistic complex. 9. The phenomenality of the relevant object, and the phenomenality or noumenality of the object that the work is meant to be— or the partial phenomenality and the partial noumenality of the complex object that the work is meant to be if a complex work is meant to consist in part of phenomenal and in part of noumenal objects—relative to the subject’s apprehension of the relevant object. 10. The space of the relevant object and the time of the event of apprehending it, and hence the time of the existence of the complex of which the subject and the object are constituents. 11. The fact of the coming to be and the ceasing to be of the complex and the coming to be and the ceasing to be of the event of apprehension on which the complex depends. 12. The property that the relevant object has of being continuous, discontinuous, recurrent, or non-recurrent. 13. Aesthetic properties that are dictated by the nature of the relevant object of the complex, its relation to the object that the work is meant to be, and the relation of each to the subject of the complex. 14. The identity-diﬀerence relation in which all of the preceding elements of an artistic complex stand to one another and to all other objects in the logical space of objects. Recognition of this identity-diﬀerence relation implicitly includes recognition of the laws of objects by which the preceding elements of the complex are constrained, and so recognizes the property that each object, including each element of an artistic complex, has of conforming to the logical conditions of objects.

PART FOUR

IDENTITY AND SUBJECTS, OBJECTS, AND LANGUAGE: CONCLUDING REMARKS AS A PREAMBLE TO AN ESSENTIALIST INVESTIGATION OF THE LIMITS OF ABSTRACTION

Introduction

1. Preliminary observations 1.1. Abstraction and subjects Abstraction to this point in art history has for the most part concentrated on the properties of the object to the virtual exclusion of the properties of the subject, and by this I mean that the subject’s relevance to the object has largely been viewed as an implicit relationship. As a result, the whole formed by the conscious subject and the object of consciousness has not been directly investigated. The previous assertion may sound hyperbolic and incorrect as it stands since the nature of the object—the way it is designed at the time at which it is designed—is purposely constructed by the artist in a certain way to engage the observer epistemologically and not just aesthetically. That is, the object is constructed and presented in such a way that the observer knows what the object is in understanding that it is to be understood to be a work of art, and, in knowing what the object is in this way, he is epistemologically related to it. He is also epistemologically related to the object in knowing which object it is that is to be understood to be this particular work of art. In addition, it is certainly not true that artworks in general have merely concentrated on the properties of the visual object or have only been concerned to investigate the formal possibilities of perceptual surfaces. Thus if we look at Las Meninas purely formally, attending to the presence of “signiﬁcant form” within it, then we miss much of the cerebral character that Velásquez intended the work to have. And Goya’s The Third of May, 1808 and Picasso’s

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Guernica are examples of works that concern the observer’s knowledge of history in addition to his appreciation of composition and color. Even more ostensibly formal objects such as the paintings that form Richard Diebenkorn’s Ocean Park series concern the subject’s understanding of art history and how Diebenkorn’s work relates to earlier paintings by Matisse, for instance; and seeing the paintings in a certain way depends on knowing that Diebenkorn saw himself, temperamentally at least, as a landscape painter. Thus what we see when we look at art is not determined solely by the visual properties of the object that our developed aesthetic sensibility can appreciate, but includes knowledge that we bring to the work, and which knowledge the work may directly or indirectly address in certain ways. I am not maintaining then that artists have always focused on the properties of the object to the neglect of the properties of the subject and things beyond the surface of the canvas. I only maintain that the properties of subjects and objects and the relations that hold between them in an artistic complex have not previously been addressed in an Essentialist manner, and hence have not been used to investigate the limits of Abstraction in art.1 Investigations of ways in which the subject could be relevant to the object occurred with works of Minimalism and Conceptualism, and forms the basis of Modernist arguments against what Michael Fried calls “theatricality.”2 The purpose of painting for Fried is to “defeat theater,” but such a victory can only be had by ignoring certain fundamental aspects of the subject’s relation to any object on which an artwork is relevantly dependent. It is to concentrate on one side of the complex epistemo-aesthetic whole of which subject

1 On Diebenkorn’s thinking of himself as being a certain kind of artist see Robert T. Buck, Jr.’s essay “The Ocean Park Paintings” in Richard Diebenkorn: Paintings and Drawings, 1943–1980, New York: Rizzoli and Albright-Knox Art Gallery (1980) p. 42. 2 See Fried, Michael “Art and Objecthood.” Minimalism as decried by Fried actually reﬂects to a greater, though incomplete, extent elements of Essentialism than does Modernism in the way in which Minimalist objects relate the subjects who apprehend them to the space in which that apprehension occurs, and, in doing so, draw attention to the subject’s relation to the object. See Robert Morris’s “Notes on Sculpture,” pp. 222–235 in the same volume. Although Minimalist sculpture is important in drawing attention to the apprehension of its objects, and apprehension is an ineliminable element of an artistic complex, it is not as Abstract as other objects that are possible to make since space can be eliminated from an artwork, or from being a property of an object that is meant to be a work of art.

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and object are constituents to the exclusion of the other. But a subject is always present in any awareness of the identity of any artwork, and, as there is no art apart from consciousness, the artist who would investigate the limits of Abstraction must focus on both aspects of the complex whole that includes a subject’s awareness of the identity of an artwork, and he must concern himself with basic matters that the presence of the subject makes relevant to the complex. The recognition of the roles that the subject’s agency and awareness play in artistic wholes, and the potential to use both consciousness and agency in the production of objects, will allow the production of objects in which the limits of Abstraction are reached. 1.2. Abstraction and objects: Everything and nothing As art depends necessarily on objects, and as there is no object without there being a distinction between that object and everything other than that object, one might suppose that one limit of Abstraction is reached in art by “specifying everything to be art,” as Timothy Binkley once did,3 or by simply declaring a particular work of art to be everything. Specifying everything to be art and specifying a particular work of art to be everything are not the same thing. If it is to be understood that each member of the class of all objects is being speciﬁed to be its own work of art, then there is not a single work consisting of all objects, but a number of works equal to the number of objects in the class, one of which would be the language that makes that claim. On the other hand, if the class of all objects is taken to be the work of art speciﬁed, then that is specifying everything to be a particular work of art, a work that would include all members of the class of all objects as its parts, including the speciﬁcation of that artwork’s identity. A concern of Abstraction is to eliminate what it is possible to eliminate, and what has been eliminated by declaring everything to be art is the distinction between objects that are works of art and those that are not. On the other hand, if everything is speciﬁed to be a particular work of art, then the distinction between those objects that are part of the work and those that are not is erased. If one 3 Binkley, Timothy “Deciding about Art,” p. 109. Binkley says “I hereby create a prodigious class of pieces by specifying everything to be art, (x) (x is a piece).” p. 109.

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speciﬁes everything past, present, and future to be a particular artwork, then one also eliminates the possibility of specifying an object to be a work of art that either is not already an object that is included in everything, or that will become an object that is included in everything, and one eliminates the possibility of otherwise producing an object by any means that would not become part of the object identiﬁed by specifying everything, including every future thing, to be part of the particular work. It might be thought that another limit of Abstraction is reached by specifying nothing to be an artwork, either in the sense in which ‘nothing’ has a referent, or in the sense in which ‘nothing’ lacks a referent. However, I think that it is possible to produce objects that are more Essentially Abstract than what is referred to by ‘everything’ and whatever is indicated by ‘nothing,’ and the speciﬁcation of each of these objects to be works of art is, I believe, considerably less interesting, less challenging, and less aesthetically valuable for failing to reﬂect in themselves fundamental aspects of subjects and objects and their relations that are relevant to works of art and that are identiﬁed in this work.4 And by failing to do so they lack the creative interaction between subject and object that characterizes part of the aesthetic of the objects of Essentialist Abstraction.

2. Précis of the principles of Essentialist Abstraction Any artwork must have an identity. The identity of an artwork is the object with which the work is meant to be identiﬁed. The identity of any artwork is distinguished logically from every object that lacks the identity of the artwork. The object with which the work is meant to be identiﬁed has the identity of that work, or the property of being that work, in virtue of the artist’s intention that the work be understood to be that object. An artist eﬀects the identiﬁca-

4 A way to use speciﬁcation to single out nothing as a work of art that makes nothing an ideational object, and so links its speciﬁcation as an artwork to essential elements of artistic complexes, can be seen on p. 307 below. Singling out nothing in such a way that it becomes ideational, and is not what is singled out by nothing, may be artistically valid and interesting. The same may be true of singling out everything in such a way that it is ideational, and so that the identiﬁcation of an artwork with everything is eﬀected in relation to essential elements of an artistic complex of which understanding the intended identiﬁcation is itself such an element.

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tion of an artwork with some object by intentionally singling out the object that the work is meant to be in a way that the intended identiﬁcation of the work with that object can be understood. This may or may not involve the artist’s creation of the object that the work is meant to be. Comprehending the identity of an artwork is understanding with which object the work is meant to be identiﬁed. This is the case whether or not it is possible to be aware of that object in addition to being aware that the work is meant to be that object. The identity of an artwork must be comprehensible. When a subject understands with which object an artwork is meant to be identiﬁed, then the identity of the work is distinguished epistemologically for that subject from every object that lacks the identity of the artwork. Comprehending the identity of any artwork depends on apprehension of a public perceptual object on which the identity of the work is relevantly dependent. An artwork may or may not be meant to be identiﬁed with any object on which it is relevantly dependent. Apprehension of a relevant object creates an artistic complex of which that apprehension, that object, and the subject whose apprehension it is are constituents. Such a complex has essential elements that are identiﬁed in this book in addition to the constituents of the complex just mentioned. When the identiﬁcation of an artwork with an object is eﬀected in relation to essential elements of an artistic complex to the neglect or minimization of those things that are not essential, a work whose identiﬁcation with an object is so eﬀected is more Abstract than an artwork whose identiﬁcation with an object is not so eﬀected. Comprehension of a speciﬁcation that eﬀects the identiﬁcation of an artwork with an object which identiﬁcation is indexed to that comprehension identiﬁes the artwork with an ideational object. Such comprehension of a speciﬁcation understands the relevance of the speciﬁcation to the identity of the artwork, and so that comprehension is the kind of cognitive conscious event on which artistic complexes depend. Accordingly, this kind of identiﬁcation of an artwork with this kind of object utilizes an essential element of artistic complexes to eﬀect that identiﬁcation. A speciﬁcation may be written to implicitly or explicitly utilize essential elements of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object. An artwork whose identiﬁcation with such an object is so eﬀected is more Abstract than is one whose identiﬁcation with an object is diﬀerently eﬀected. Eliminating those things that are superﬂuous to the identiﬁcation of artworks with

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objects makes the identiﬁcation of an artwork with an ideational object stand in reﬂexive relation to anything that is used to eﬀect the identiﬁcation of the work with that object, in that something that is used to eﬀect the identiﬁcation is reﬂected in that identiﬁcation. The use of an essential element of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object may be implicitly or explicitly reﬂected in the identiﬁcation eﬀected. Any artwork in which an ineliminable feature of an artistic complex is implicitly or explicitly reﬂected in eﬀecting the identiﬁcation of the artwork with an ideational object will be more Abstract for that reason than any artwork in which such reﬂection is absent. The ﬁnal part of this book ampliﬁes and adds to the previous remarks, repeating where necessary in that ampliﬁcation and addition, as it looks at the individual and interconnected relevance of identity, objects, subjects, and language to the analytical deﬁnition of the project of Essentialist Abstraction. What is said in the following concluding pages represents the remainder of what I think can be said philosophically about the conceptual and aesthetic aspects of identifying the limits of Abstraction in art, and so what can be said apart from any artistic attempt to identify those limits. This ﬁnal part of the book thus can be understood either to complete the rational groundwork on which the artistic ediﬁce of Essentialism must be erected in setting up theoretically the creative investigations of the limits of Abstraction of which this work functions as philosophical foundation, or to establish the requirements of identifying, recognizing, and assessing those limits were they to be identiﬁed apart from knowledge of the philosophy that pertains to them.

3. Identity and Essentialist Abstraction 3.1. The relation of artist and audience to an artwork’s identity An artist’s determination of which object of all objects a work is meant to be is fundamental to both making and apprehending art. From the artist’s perspective of eﬀecting the identiﬁcation of an artwork with some object, the identity of a work that is speciﬁcally based upon indicating which object the work is meant to be is more basic in focusing on that indication as an area of investigation than any work in which this requirement is assumed but is not explored.

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From the subject’s perspective of understanding which object a work is meant to be, an artwork that consists of or is based upon such understanding is more basic in focusing directly on that understanding than is any work in which understanding the work’s identity does not ﬁgure in the determination of that identity. 3.2. Identity and essential elements of artistic complexes Because any artwork must have an identity, and because it must be possible to understand with which object or objects an artwork is meant to be identiﬁed, any of the more Abstract objects must be eﬀected in relation to things that are required of and involved in its having an identity, and its being possible to comprehend that identity, as both that identity and its comprehension implicitly or explicitly reﬂect some thing or things that is required of and involved in the determination and apprehension of the identity of the object, namely an essential element or elements of artistic complexes. The determination of the more Abstract objects possible must be predicated on the use of essential elements of artistic complexes in such a way that, when the intended use of such elements is understood in an artistic complex in which they ﬁgure, the identiﬁcation of the artwork with the object that the work is meant to be is thereby eﬀected.

4. Ideational objects and Essentialist Abstraction As indicated earlier in the book, an ideational object is an object with which an artwork is meant to be identiﬁed that is implicitly or explicitly indexed to comprehension of a speciﬁcation that refers to that object, such that, apart from such comprehension, no object has the property of being the work of art. An ideational object may or may not have its particular identity apart from the identiﬁcation of an artwork with the object, but the object cannot have the property of being the artwork apart from comprehension of a speciﬁcation that singles out the object. Ideational objects, in being indexed to comprehension of a speciﬁcation that refers to them, are Essentialist objects, or are more Essentially Abstract than traditional art objects, since they depend on something essential to the identiﬁcation of artworks with objects,

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namely, comprehension of identity. And given that making and apprehending artworks in general depends on consciousness, and given that comprehension of identity is a kind of conscious event, ideational objects are further Essentialist in underlining the necessity to art of consciousness. An ideational object may be perceptual or non-perceptual. Apart from the relation of either a perceptual or a non-perceptual object that an artwork is meant to be to essential elements of artistic complexes—which can complicate the issue of which of two objects of these two kinds of object is the more Abstract—it can be generally asserted that a non-perceptual object that an artwork is meant to be is more Abstract than a perceptual object that an artwork is meant to be because an object need not have perceptual properties to be a work of art. Although this is the case, it cannot be discounted prior to creative inquiry that a limit of Abstraction might be determined in an ideational object that is perceptual. This is because the identiﬁcation of an artwork with an Essentialist perceptual object would depend on the use of an essential element or elements of an artistic complex to eﬀect the identiﬁcation, and that identiﬁcation may so reﬂect the use of such an element that a perceptual limit of Abstraction is determined in the identiﬁcation.5 It also cannot be stated prior to artistic investigation what diﬀerent kinds of Abstract limit might be determined in diﬀerent kinds of perceptual and non-perceptual Essentialist object. And because the perceptual or non-perceptual objects in which the diﬀerent limits are identiﬁed may utilize and be related to diﬀerent elements of artistic complexes in diﬀerent ways, it cannot be known prior to eﬀecting Essentialist objects in which Abstract limits are determined which of two or more kinds of Abstract limit is the more Abstract. Indeed, because of their utilization of and relation to such diﬀerent elements, it may not be possible to say which of two or more Essentialist artworks is the more Abstract even after the eﬀecting of the identiﬁcation of the diﬀerent artworks with their diﬀerent objects allows for their

5 An Essentialist perceptual object would be diﬀerent from a typical perceptual object in being ideational, and so in being indexed to comprehension of a speciﬁcation that singles out the perceptual object. The nature of an Essentialist perceptual object would be determined in part by the comprehensible semantic properties of the language that refers to it. See section 5.2 on pp. 307–308 below.

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comparison. The remarks of this paragraph indicate why it is necessary to speak of the limits rather than the limit of Abstraction.

5. Comprehension of identity, language, and Essentially Abstract artworks The kind of awareness on which the more reductive types of object can be based is comprehending the identity of an object. To approach the limits of Abstraction, language must be used that implicitly or explicitly directs the subject to understand that, in comprehending with which object the work is meant to be identiﬁed, the identiﬁcation of the artwork with that object is dependent on that comprehension. The object with which an artwork is meant to be identiﬁed may itself be constructed in, or through, or result from an act or acts of comprehending the intended identiﬁcation of the artwork with that object, but where, in any case, no object is the object that the work is meant to be apart from comprehension of that intended identiﬁcation. Or the object may have its particular identity apart from the identiﬁcation of an artwork with it. Either kind of object is ideational. The identiﬁcation of an artwork with either kind of ideational object requires the use of language since only language can speciﬁcally engage the comprehension of the identiﬁcation of an artwork with an object so that that comprehension is reﬂected in that identiﬁcation. That such an identiﬁcation reﬂects such a comprehension makes the work so identiﬁed more Abstract for the use of such consciousness as a medium than is any artwork of which consciousness of its identity is a mere presupposition, as is the case with non-ideational works of art. Thus any of the more Abstract artworks possible will depend on mixing the medium of publicly perceptible language that speciﬁes the identity of the artwork and the medium of awareness in which the identity of the artwork is not only comprehended, but is a necessary means by which the identiﬁcation of the artwork with some object is eﬀected. Such a use of awareness eliminates the traditional gap between awareness and non-ideational artworks. As seen, language can not only be used as a means of eﬀecting the identiﬁcation of an artwork with some object, but language can be directed to a subject comprehending it to result in an object with which an artwork is meant to be identiﬁed that, as so resulting, would lack its identity apart from that comprehension. An object whose identity

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depends on, and that may existentially coincide with, an event of comprehending its identity is more Abstract than an object that an artwork is meant to be that, in having its identity both prior and subsequent to any event of apprehending it, lacks such dependence and coincidence. The object that is singled out by any diﬀerence between any current comprehension of this and any comprehension of this other than any current comprehension of this depends on an event of comprehending the identity of that object, whereas your current consciousness of this refers to an object that existentially coincides with an event of comprehending the identity of that speciﬁed object.6 The more reductive kinds of object possible include those in which the opposition between an event of awareness and the object of that event is either found within, pertains to, or results from comprehending the identity of the object that the artist intends the work to be. The possibility that the opposition noted might be eliminated, or at least restructured, in an event of reﬂexive, monadic, secondorder awareness, and so thereby determine another kind of supremely reductive object, would have to be investigated. The more Abstract kinds of object possible will presuppose perceptual awareness, but they cannot merely be non-ideational perceptual objects since such a perceptual object is something that can be dispensed with as being the artwork itself. It is possible to get beyond a perceptual object in which the identity of an artwork is embodied by using language that speciﬁes a certain object or objects to be a work of art, as has been done by Barry and Burgin for example. And it is possible to get beyond a speciﬁed non-ideational Conceptual object with which an artwork is meant to be identiﬁed by using language that engages an event of comprehending that language to result in an ideational object that the work is meant to be. 5.1. Non-perceptible events, ideational objects, and speciﬁcation The Essentialist artist must use the language of speciﬁcation to engage a subject’s comprehension of the speciﬁcation as a means of eﬀecting the identiﬁcation of an artwork with an ideational object which 6 Your current consciousness of this refers to ﬁrst-order Intentional awareness of that speciﬁcation. That awareness is the Intentional object of an existentially-coinciding second-order event that understands the ﬁrst-order event, with its correlated Intentional object, to be what is singled out by the speciﬁcation.

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identiﬁcation results from the subject’s comprehension of the speciﬁcation that singles out the ideational object. That the identiﬁcation of an artwork with an ideational object is Essentialist indicates that the identiﬁcation is eﬀected in relation to essential elements of artistic complexes and reﬂects any essential element that is used to eﬀect it. In fact, an object’s being ideational is a suﬃcient condition of its being Essentialist since a suﬃcient condition of an object’s being ideational is its being indexed to comprehension of a speciﬁcation that refers to that object. That comprehension is a cognitive event that includes understanding the relevance of the speciﬁcation to the identity of the work, and so is an essential element of any artistic complex. And the identiﬁcation of an artwork with an ideational object would implicitly or explicitly reﬂect the comprehension on which that identiﬁcation is dependent. An event of comprehending a speciﬁcation that singles out an ideational object that an artwork is to be understood to be can either be used artistically as a necessary and suﬃcient means of eﬀecting the identiﬁcation of an artwork with an object that would have its particular identity apart from such an event of understanding, or an event of comprehending a speciﬁcation that singles out an ideational object that an artwork is meant to be to be can be a necessary and suﬃcient means of eﬀecting the object itself that the artwork is to be understood to be as it is a necessary and suﬃcient means of eﬀecting the identiﬁcation of the artwork with the eﬀected object. These things were stated earlier in the book. They are repeated here to stress the active relation of a subject to an ideational object. In the ﬁrst case the subject becomes an active participant in eﬀecting the identiﬁcation of the artwork with an object through her understanding a speciﬁcation on which identiﬁcation of the artwork with the object depends. And this is the case because the identiﬁcation of the artwork with the object is indexed to that understanding, and so no object has the property of being the work apart from such an event of understanding, and so the object is ideational. In the second case the subject becomes an active participant in the production of the object that the work is meant to be in virtue of comprehending language the understanding of which results in an object to which the comprehended language refers. Such an object is also ideational, and since the object is produced in the way indicated, the artwork that is meant to be identiﬁed with the ideational object is a participatory artwork.

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The active relation of a subject to an ideational object is important because a condition for comprehending the identity of any artwork, namely consciousness, is a condition for eﬀecting the identiﬁcation of an artwork with an ideational object, since comprehension of a speciﬁcation to which an ideational object is indexed is a kind of conscious event. And the use of consciousness to eﬀect the identiﬁcation of an artwork with an ideational object means that that object, in being ideational, will implicitly or explicitly reﬂect the consciousness on which it is dependent, depending on the nature of the ideational object—implicitly as in this here now, and explicitly as in your current consciousness of this.7 The identiﬁcation of any artwork with some object depends on consciousness for that identiﬁcation to be eﬀected and understood. However, it is not the case that any identiﬁcation of an artwork with an object is indexed to comprehension of a speciﬁcation that eﬀects that identiﬁcation. And it is not the case that any object that an artwork is meant to be depends on consciousness to have the property of being the object that it is rather than depending on consciousness to have the property of being that work of art. The use of consciousness to eﬀect the identiﬁcation of an artwork with some object can be understood to be a medium that is more reductive for being indispensable to such an identiﬁcation than a dispensable medium such as paint, and a medium that is more reductive for being nonperceptible than a perceptible medium such as paper or stone. Although speciﬁcations may be diﬀerently written to diﬀerently engage their comprehension to eﬀect the identiﬁcation of artworks with objects to which they refer, speciﬁcation is a requirement of Essentialist art since nothing but the language of speciﬁcation can be used to address the Essentialist elements of artistic complexes in the way required to reach the limits of Abstraction. The kind of speciﬁcational language used to produce objects at the limits of Abstraction must be language that implicitly or explicitly employs awareness in concert with other ineliminable features of artistic complexes to eﬀect the identiﬁcation of an artwork with an ideational object that the artist intends the work to be. The identiﬁcation of 7 Consciousness is an essential element of an artistic complex that is reﬂected in the identiﬁcation of an artwork with an ideational object. For further on the reﬂection of consciousness in such objects that artworks are meant to be, as well as the reﬂection of essential elements of artistic complexes in ideational objects in general, see 6 on pp. 309–313 below.

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an Abstract artwork with an ideational object may involve diﬀerent elements of artistic complexes that are relevant to comprehending the language, and so that are relevant to the identiﬁcation of the work with the object to which the comprehended language refers. There may be a variety of ways in which this can be done, but, however it is done, an object that is designed to engage the awareness of a subject to produce an ideational object that all or part of a particular artwork is meant to be is more Abstract than traditional works in which awareness is passively rather than actively engaged. And this is because the customary conscious and conceptual separation of the subject and the object of her awareness has either been eliminated or redeﬁned in relation to Essentialist considerations. 5.2. Speciﬁcation and perceptual and non-perceptual ideational objects Any Essentialist perceptual object that an artwork is meant to be will be phenomenal as it is perceived, but the phenomenal nature of the perceptual object will be determined in part by the comprehensible semantic properties of the speciﬁcation on which identiﬁcation of the artwork with that object is dependent. And these comprehensible semantic properties will in turn reﬂect the meanings of the names of essential elements that are used to eﬀect the perceptual object, as in this here now. A non-perceptual object with which an artwork is meant to be identiﬁed may be phenomenal or noumenal. For a limit of Abstraction to be determined in an object of either kind of non-perceptual object, the object must be ideational, and so must be indexed to comprehension of a speciﬁcation that refers to the object. In depending on some element or elements of artistic complexes in relation to which it is eﬀected, the nature of the identiﬁcation of an artwork with some non-perceptual ideational object will also be determined in part by the comprehensible semantic properties of the speciﬁcation that refers to the object in addition to relevant properties of the comprehension of that speciﬁcation, as in any undetectable diﬀerence between this here now and something other than this here now. It does not follow from this however, that the nature of any non-perceptual ideational object itself that an artwork is meant to be will also be determined in part by the comprehensible semantic properties of the speciﬁcation that refers to the object. For instance, the speciﬁcation anything other than anything that is either this here now or something other than this here now refers to

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nothing. And although the identiﬁcation of an artwork with nothing that is eﬀected through that speciﬁcation is determined in part by the comprehensible semantic properties of the speciﬁcation that refers to nothing—and makes nothing ideational in relation to comprehension of the speciﬁcation that refers to it—nothing—as the Intentional object of not only the speciﬁcation that refers to it, but of any event of thinking of it, and so whatever its nature—is not itself determined in part by the comprehensible semantic properties of the speciﬁcation that refers to it. On the other hand, the identity of the non-perceptual ideational object that is singled out by the speciﬁcation the distinction between any apprehension of this and everything other than any apprehension of this is determined in part by the comprehensible semantic properties of the speciﬁcation that refers to that non-perceptual object. Because the nature of a non-perceptual ideational object that an artwork is meant to be may or may not be determined in part by the comprehensible semantic properties of the speciﬁcation on which identiﬁcation of the artwork with that object is dependent, there is no general formula for describing the relation of the comprehensible semantic properties of a speciﬁcation that singles out a non-perceptual ideational object that an artwork is meant to be to the nature of the non-perceptual object delineated. 5.3. Speciﬁcation and Essentialist Abstraction For reasons in addition to those that have been stated that will be seen in the remaining sections, speciﬁcation assumes particular importance in relation to the project of determining the limits of Abstraction in art. Although some illustrations have been provided of how language can be used to address a subject’s comprehension of it as a means of eﬀecting the identiﬁcation of an artwork with an ideational object to which the language refers, and how language can be directed to awareness to result in ideational objects that reﬂect in their apprehension indispensable elements of artistic complexes, how language can be used in aesthetically eﬀective ways to single out aesthetic ideational objects in which the limits of Abstraction are identiﬁed are things that must be determined artistically and cannot be stated philosophically.8 8 On matters that the Essentialist use of language would have to consider, both for the identiﬁcation of the limits of Abstraction, and the aesthetic of Essentialism, see 7 below.

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6. The relation of the identity of an Essentially Abstract artwork to things that are used to eﬀect that identity The limits of Abstraction must be determined in ideational objects. An ideational object is indexed to comprehension of a speciﬁcation in which the identiﬁcation of an artwork with the object is understood. The identiﬁcation of an artwork with an ideational object will implicitly reﬂect, in being understood to depend on, any essential element of an artistic complex that is used to eﬀect the identiﬁcation of the work with the ideational object that is not named by the speciﬁcation whose comprehension eﬀects the identiﬁcation of the artwork with the ideational object. For instance, this here now implicitly reﬂects the event of comprehension that is used to eﬀect the identiﬁcation of an artwork with that ideational object—the comprehension that is not named by the speciﬁcation that singles out the object that is indexed to that comprehension. The identiﬁcation of an artwork with an ideational object will explicitly reﬂect any essential element of an artistic complex that is used to eﬀect the identiﬁcation of the work with the ideational object that is named by the speciﬁcation whose comprehension eﬀects the identiﬁcation of the artwork with the ideational object. The speciﬁcation this here now explicitly reﬂects the indexical relations of the subject to the ideational object to which the speciﬁcation refers since the indexical relations in virtue of which the ideational object is that ideational object are named by the speciﬁcation that singles out that object. Because an ideational object is indexed to comprehension of a speciﬁcation that refers to the object, any identiﬁcation of an artwork with an ideational object will implicitly or explicitly reﬂect the conscious event of comprehension on which it is dependent, and will do so apart from or in addition to its reﬂection of any other essential element that is used to eﬀect that identiﬁcation. The identiﬁcation of an artwork with an ideational object that would have the property of being that object apart from the property of being that work of art, in depending on consciousness for that identiﬁcation to be eﬀected, results from and reﬂects in that identiﬁcation the consciousness that is presupposed in any case by eﬀecting the identiﬁcation of an artwork with some object; the consciousness that is presupposed by understanding with which object an artwork is meant to be identiﬁed; and the consciousness that is presupposed by the artistic complex on which understanding the identity of an artwork depends. And any ideational object that an artwork is meant to be

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that depends on consciousness to be that object, and not just that artwork, results from and reﬂects in itself the consciousness on which it depends and on which understanding the identiﬁcation of an artwork with that object depends. The use of an essential element of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object presupposes the existence of an artistic complex in which the implicit or explicit use of the element to eﬀect the identiﬁcation can be understood. Any such element that is so used will, as essential, form part of an artistic complex in which its use can be understood, and will do so whether or not it is speciﬁcally named by the speciﬁcation whose comprehension eﬀects the identiﬁcation of an artwork with an ideational object in which the essential element ﬁgures. Thus the use of consciousness to eﬀect the identiﬁcation of an artwork with an ideational object cannot be divorced from, but must itself be a constituent of, any complex in which its relevance to that identiﬁcation can be understood, and whether the relevant consciousness is named, as in any comprehension of this, or is not, but is implicit, as in this here now. And the indexical relation of the ideational object named by this here now to the subject who is a constituent of a complex of which that speciﬁcation is a constituent is an essential element of the complex in which the identity of that ideational object is comprehended. There is then a logical relation between an essential element’s use to eﬀect the identiﬁcation of an artwork with an ideational object, and the property that that element has of being an element of an artistic complex in which its relevance to that identiﬁcation can be understood, in that the latter is a necessary condition of the former and the former is a suﬃcient condition of the latter. Although any ideational object that an artwork is meant to be need not itself be a constituent of an artistic complex in which the identiﬁcation of the work with the ideational object is understood, the use of any essential element to eﬀect the identiﬁcation of an artwork with an ideational object must be logically tied as indicated to the artistic complex in which that identiﬁcation is understood. The required relation between an essential element’s use to eﬀect the identiﬁcation of an artwork with an ideational object, and the property that that element has of being an element of an artistic complex in which its relevance to that identiﬁcation can be understood, can be understood to be ‘insular’ in being a logical circumscription on ideational objects, and ‘hermetic’ in pertaining particularly and ineluctably to an artistic complex

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in which the relation is eﬀected. And just as the reﬂection in the identiﬁcation of an artwork with an ideational object of an essential element that forms part of an artistic complex in which that identiﬁcation is comprehended is part of the reﬂexive nature of Essentialism, the relation between an essential element’s use to eﬀect the identiﬁcation of an artwork with an ideational object and the property that that element has of being an element of an artistic complex in which its relevance to that identiﬁcation can be understood is part of the insular and hermetic nature of Essentialist Abstraction. And the reﬂexive, insular, and hermetic nature of Essentialism as indicated is partially determinative of the nature of its aesthetic. The use of an essential element of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object and the reﬂection of that use in that identiﬁcation contrasts with the nonuse of such an element, so that, although it is an implicit element of an artistic complex in which the identity of an artwork is comprehended, the essential element is not used to eﬀect the identiﬁcation of the artwork with the object that it is meant to be. The use of an essential element of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object also contrasts with any use of such an essential element to eﬀect the identiﬁcation of an artwork with a non-ideational object. Thus a public perceptual object is an essential element of an artistic complex, but the use of such an object, such as a white canvas, to identify an artwork with that object uses the element to eﬀect the identiﬁcation of the artwork with a nonideational object, and does so even though the canvas is an essential element of any artistic complex in which the artwork is understood to be embodied in that canvas. The object that the work is meant to be is non-ideational since it is not indexed to comprehension of a speciﬁcation that refers to that object. And although comprehension of the identity of such an artwork will be a constituent of any artistic complex of which the white canvas is a constituent, the identity of the artwork is not indexed to comprehension of a speciﬁcation that eﬀects the identiﬁcation of the artwork with an object, such that the identiﬁcation of the artwork with the object reﬂects the relevance of that comprehension to that identiﬁcation. The identity of an artwork that is meant to be identiﬁed with an all-white canvas does not reﬂect the comprehension of its identity, rather than its possibly being understood to reﬂect, in its bold assertion of its bare perceptual

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being, the requirement of a public perceptual object on which comprehension of identity depends. And although consciousness is an essential element of an artistic complex, and although Robert Barry can be understood to have used his consciousness of things at 1:36 PM, June 15, 1969 as that in relation to which the work speciﬁed by all the things I know . . . was delineated, as the object speciﬁed was indexed to Barry’s consciousness, and not to any conscious event of comprehending the speciﬁcation, it is a non-ideational object whose identity does not reﬂect the comprehension of its identity. Barry’s all the things I know . . . is non-ideational, whereas all the things you know but of which you are not at the moment conscious is ideational in being indexed to comprehension of the speciﬁcation that singles out that complex epistemological object. That an essential element of an artistic complex is a necessary condition of eﬀecting the identiﬁcation of an artwork with an ideational object as it is an essential element of an artistic complex in which its relevance to that identiﬁcation is understood makes the ideational object dependent on that element more Essentially Abstract than any object in which that relation between object and element is lacking. This is simply because the identity of the artwork is tied to an artistic complex in which its identity is understood, and the general indispensability of an artistic complex to comprehension of artistic identity is underlined in any case in which the identity of an artwork is dependent on an essential element or elements of the artistic complex in which that identity is comprehended. Thus the reﬂexive nature of Essentialist Abstraction consists in using essential elements of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object, such that comprehension of the identiﬁcation is relevant to eﬀecting the identiﬁcation comprehended, and that comprehension is implicitly or explicitly reﬂected in the identiﬁcation eﬀected. The implicit or explicit reﬂection in an object with which an artwork is meant to be identiﬁed of some thing that is required of and involved in the determination and apprehension of an artwork’s identity makes the work more Abstract than any work in which any such reﬂection is not found in the object that the work is meant to be. This is because such a reﬂection represents a turning of the work towards rather than away from some thing or things that is required of an artwork’s having and being known to have a particular identity. The turning of a work towards some thing or things that is

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required of the determination and apprehension of the identity of an artwork fails to involve the determination and apprehension of that identity with things that are not required of such determination and apprehension. In doing so it eliminates any conceptual gap between the work and things that are required of the work to have its particular identity, and it eliminates any epistemological gap between apprehension of the identity of the work and apprehension of anything that is not required of, or does not directly pertain to, such an apprehension, and so makes the work more Abstract for these reasons. The relation of the identity of an ideational artwork to a subject’s comprehension of that identity is part of the hermetic and insular nature of Essentialist Abstraction in that the identity of an ideational object is and only can be eﬀected in relation to essential elements of an artistic complex in which its identity is comprehended. A task for Essentialist Abstraction would be to investigate the implicit or explicit use of essential elements of artistic complexes to eﬀect the identiﬁcation of an artwork with an ideational object in which a limit of Abstraction is exhibited, or through which it is determined, as that identiﬁcation involves the relation to one another of elements that are utilized to eﬀect the identiﬁcation, and the relation of such elements to the identiﬁcation that they are used to eﬀect. An ideational object in which a limit of Abstraction is identiﬁed may itself be eﬀected through the implicit or explicit use of essential elements of artistic complexes. Eﬀecting such an ideational object would involve the relation to one another of essential elements that are utilized to eﬀect the object, and the relation of such elements to the ideational object that they are used to eﬀect. Not only is the relation to one another of essential elements that are utilized to eﬀect the identiﬁcation of an artwork with an ideational object, and the relation of such elements to the identiﬁcation that they are used to eﬀect important to determining the limits of Abstraction, but the relation of these things to one another would play an important role in determining the aesthetic of Essentialism.

7. Concluding remarks: Essentialism and its objects Although singling something out with which an artwork is meant to be identiﬁed is fundamental, Essentialism must determine which objects are to be singled out, and how they are to be singled out.

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Each of these things will depend in turn on both addressing certain features explicitly, and utilizing other features implicitly, of artistic complexes that are essential to such complexes. 7.1. Essentialism and the essential elements of artistic complexes An Essentialist investigation of the limits of Abstraction would include consideration of the following things that pertain to the essential elements of artistic complexes: The relation of conceptual and perceptual awareness in the apprehension of the identity of an ideational object, and the relation of these kinds of awareness to one another and to an ideational object that they may be responsible in part for eﬀecting. Forms of conceptual awareness that a speciﬁcation may be used to engage, including ﬁrst-order polyadic reﬂexive awareness and second-order monadic reﬂexive awareness in addition to diﬀerent orders of irreﬂexive Intentional awareness. The use of speciﬁcations to engage the consciousness of them to eﬀect the identiﬁcation of artworks with ideational objects that are diﬀerent kinds of type-dependent object, or perhaps a combination of diﬀerent kinds of type-dependent object if the ideational object is complex. The relation of any such dependent object to the type dependence of the relevant object of the artistic complex. The use of the type-dependent relevant object of an artistic complex to eﬀect the identiﬁcation of an artwork with an ideational object of some possible kind of independent object. The relation of an ideational object to the history of awareness of the subject whose comprehension of the intended identiﬁcation of an artwork with the ideational object is a necessary and suﬃcient condition of that identiﬁcation. The possible relevance of such an ideational object to the history of awareness of other subjects, as in every eﬀect of each comprehension of this information.9 9 When I concentrate in what follows on a single subject as she forms part of an artistic complex, the possible relevance of other subjects to eﬀecting the identiﬁcation of an artwork with an ideational object should be understood where the things that are said are germane to such possible relevance.

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The agential relation of the concipient to the conceptual and perceptual aspects of the speciﬁcation that she comprehends, and to the public perceptual object of which the speciﬁcation forms part, if the speciﬁcation is not itself that perceptual object. The interrelation of awareness and agency in comprehending and possibly eﬀecting the identity of an ideational object. The becoming of the artistic complex of which comprehension of the identity of an ideational object is a constituent, as the coming and ceasing to be of that complex has, or might have, a bearing on the identity of that ideational object. The ﬁguring of any such becoming in the history of awareness of the subject who is a constituent of the complex, and the historical relation of that becoming to that awareness that may be used to eﬀect or aﬀect the ideational object that the work is meant to be. The becoming of an event of comprehending a speciﬁcation that singles out an ideational object that an artwork is meant to be, as the coming and ceasing to be of that comprehension has, or might have, a bearing on the identity of that ideational object. The ﬁguring of any such becoming in the history of awareness of the subject who comprehends the speciﬁcation, and the historical relation of that becoming to that awareness that may be used to eﬀect or aﬀect the ideational object that the work is meant to be. The bearing of the indexical relation of the subject to the perceptual object and to the meaning of the speciﬁcation that she comprehends on the identity of the object singled out by the speciﬁcation. The relevance of the epistemological relations—knowing which, knowing that, and knowing what—of the subject to the perceptual object of the complex, its parts, and to the perceptual and conceptual aspects of the speciﬁcation, to the determination of the identiﬁcation of an artwork with an ideational object, including the determination of the identity of such an object that is eﬀected in comprehending the speciﬁcation that refers to it. The relations of identity and diﬀerence that hold between the perceptual object, the perceptual and conceptual aspects of the speciﬁcation, the ideational object to which the speciﬁcation refers, any comprehension of the speciﬁcation, and any other comprehension of the speciﬁcation—whether by the same or diﬀerent subjects— as all of these things are logically and epistemologically related to themselves, to one another, and to things that they are not.

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The degree of apprehensible similarity or diﬀerence between these things. The historical relation of the subject to the perceptual object, the speciﬁcation, and the ideational object to which the speciﬁcation refers. Any part-whole relation that characterizes the perceptual object, the speciﬁcation, its meaning, an event or events of apprehending the speciﬁcation, and the ideational object to which the speciﬁcation refers, as any of these things can be made to stand in mereological relation to one another in such a way that the identity of the ideational object to which the speciﬁcation refers follows from or is aﬀected by that relation. Consideration of continuity and discontinuity and recurrence and non-recurrence as these things pertain to the perceptual object, the subject’s awareness of that object, the concipient’s comprehension of the speciﬁcation, the meaning of the speciﬁcation comprehended, and the ideational object to which the speciﬁcation refers. 7.2. Additional Essentialist considerations In addition to what was stated in section 7.1, the Essentialist would have to consider: The speciﬁcation as a perceptual entity, including its font, color, and the uniform or varied treatment of its individual words and their letters. The relation of the speciﬁcation as a perceptual entity to any bounded space—such as framed paper—in which it is perceived, including its size in relation to that space, its orientation in relation to that space, and its perceptible value in relation to that space. The speciﬁcation as a conceptual entity, including its semantic length or brevity, the simplicity or complexity with which its meaning is conveyed, and the presence or absence of precise semantic repetition in its conceptual parts, and the degree of semantic similarity and diﬀerence between its conceptual parts. The relation of the meaning of the speciﬁcation as a semantic entity to the speciﬁcation as a perceptual entity. The relation of the semantic and perceptual aspects of the speciﬁcation to an event of comprehending it as the speciﬁcation engages its comprehension to single out an ideational object that is indexed to that comprehension.

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The relation of the semantic and perceptual aspects of the speciﬁcation to the ideational object that is indexed to comprehension of the speciﬁcation. The possibility of writing a speciﬁcation so to engage its concipient that it may have more than one possible referent, and so calls for interpretation and judgement on the part of the concipient to decide to what it refers on a particular occasion of comprehending it. The relation of an event of comprehending a speciﬁcation to the subject’s history of awareness and perhaps to the history of awareness of others as well. The relation of an event of comprehending a speciﬁcation to the subject’s history of agency and perhaps to the history of agency of others as well. The possibility of writing a comprehensible speciﬁcation in more than one way, such as in a circle in addition to a straight line, such that the relation of the identity of an ideational object to the comprehension of the speciﬁcation that refers to it is dependent on or follows from the way that the speciﬁcation is written to engage its comprehension, and so that at least some of the aesthetic value of the work that is dependent on the speciﬁcation is tied to the way in which the speciﬁcation is written. The single or multiple use of a token of the speciﬁcation, and, if multiple, the relation of repeated tokens to those things that have been noted to which such repetition would be relevant. The perceptual and conceptual relations to one another of a multiplicity of tokens if a multiplicity is used, and the conceptual relation of such a multiplicity to their common meaning and to the ideational object to which each refers. Any conceptual importance and aesthetic validity that may follow from limiting a speciﬁcation to a single token, or repeating a token a number of times. Whether or not a token or tokens might be given a temporal dimension that is utilized in addition to a spatial one to determine an Abstract object, to shape its aesthetic, or both, as the relation of the speciﬁcation to the object that it delineates is aﬀected by the speciﬁcation’s having a temporal dimension. The preceding remarks are not meant to be exhaustive, and other matters—including possibilities in addition to problems—may surface as relevant and interesting to Essentialist Abstraction and its aesthetic in the course of the artistic investigation of its subject.

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However, enough has been said to indicate both that identifying the limits of Abstraction in art will be no simple and straightforward matter for anyone interested in undertaking such an identiﬁcation, and that diﬀerent kinds of object in which diﬀerent limits of Abstraction are exhibited may have diﬀerent kinds and degrees of conceptual and aesthetic complexity. The observations of section 7.2 also indicate that the aesthetic of Essentialism is not merely instrumental. That is, it is not solely determined by any value that attaches to identifying the limits of Abstraction, but is determined in addition by any value that pertains to those things that have been noted that are involved in the enterprise of identifying those limits. Certain limits of Abstraction may be revealed through identifying artworks with ideational objects that, in being indexed to comprehending speciﬁcations that refer to them, utilize essential elements of artistic complexes to eﬀect that identiﬁcation. Other more Abstract limits may be identiﬁed in ideational objects that are eﬀected by or in relation to events of comprehending speciﬁcations to which events they are indexed, such that, apart from such events of comprehension, no objects are the objects with which the artworks are meant to be identiﬁed. The problem for the Essentialist is not only to conceive of speciﬁcations whose comprehension will result in ideational objects in which, in being based on and reﬂecting essential elements of artistic complexes, the limits of Abstraction are identiﬁed, but to conceive of how the aesthetic value of Essentially Abstract objects can result from the use of speciﬁcations to engage their comprehension to result in such objects.

APPENDICES

The following appendices pertain to the notions of object, identity, and diﬀerence and things that are relevant to them and their interrelation. These notions are fundamental to our general conceptual scheme, to making and apprehending works of art, and to establishing the limits of Abstraction. Various sections of the appendices amplify, clarify, or supplement points that appear in the text. Others introduce novel material.

APPENDIX I

ON THE NOTIONS OF OBJECT, PROPERTY, HAECCEITY, AND DIVERSITY

1. Objects and Properties 1.1. The concept of object is basic and undeﬁnable The term ‘object,’ as used in the widest possible sense, names a basic concept in our conceptual scheme. A concept is basic or undeﬁnable when any attempted deﬁnition of the concept must either use a term that names the concept itself that is to be deﬁned, or must employ a term that refers to a concept synonymous with the concept that is to be deﬁned, so that, in either case, the deﬁnition utilizes the concept itself of which it is meant to be the deﬁnition, and no meaning of the concept is thereby provided. One might attempt to deﬁne ‘object’ by saying that “An object is anything of any sort of which a property or properties can be predicated.” But since ‘thing’ in “anything” is a synonymous means of indicating what is meant by ‘object’ in the most basic sense of that term, the concept is not here deﬁned, but something is merely said about it that may or may not be true.1 Or if it be said that “An object is whatever can be presented in any way to consciousness” we would have to inquire into the meaning of the term ‘whatever,’ and in doing so would discover that it means ‘anything or everything that,’ and so we would be utilizing once again a synonym of our basic undeﬁnable notion. 1.2. Objects and properties Colin McGinn says that the concepts ‘object’ and ‘property’ “are woven inextricably together” since “a property is something that objects have or instantiate” and “an object is what has or instantiates properties.”2 One might attempt to defend the position that 1

See section 1.2 of this appendix below. McGinn, Colin Logical Properties: Identity, Existence, Predication, Necessity, Truth, Oxford: Oxford Univ. Press (2000) p. 15. 2

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every object has at least one property by saying that the object of which no property can be predicated has at least that property—the property that no (other) property can be predicated of it. Thus in saying of an object x that no property P can be predicated of it, and where P represents any standard property, such as being blue, x comes to have the non-standard property Q that no standard property can be predicated of it. It is not clear, however, that in addition to having property Q , x would not also have the basic logical properties of being self-identical and being diﬀerent from everything to which it is not self-identical, and would not also have the property of being conceivable, and the property of being the referent of a particular linguistic description. Accordingly, the object of which no property can be predicated is an impossible object, and although it is true that one can say or write ‘the object of which no property can be predicated,’ it is not true that some object has the property of being the object of which no property can be predicated.3 1.3. The concept of property is basic and undeﬁnable The foregoing remarks suggest that the concept ‘property’ is as fundamental a part of our conceptual scheme as is the concept of object. And McGinn’s assertion that the concepts ‘object’ and ‘property’ are interrelated notions seems to be correct on any metaphysics of objects; that is on a substance-attribute or bundle theory, since, even on the latter view of objects, a property is a property of the bundle that it partially composes, and that bundle is an object even if there is no object apart from the properties of which the bundle consists. McGinn also maintains that “the notion of a property . . . is not altogether clear.”4 He says that we might say that a property is “what is instantiated by an object in a way analogous to the way in which (say) redness is instantiated by an object: that is, choose a paradigm property and declare a property to be anything that resembles this paradigm.”5 This way of thinking of the concept of property may work well for thinking of any perceptible property, but such non-

3 On impossible objects see Appendix Four on pp. 353–365 below. The property of having no properties is an example of a non-predicable property. See 1.4.4 on pp. 329–330 below. 4 Logical Properties, p. 15. 5 Logical Properties, pp. 15–16.

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perceptible properties as ‘being owned by Smith,’ ‘having existed at some time in the past,’ or ‘obeying the law of identity’ may not be thought to have the requisite resemblance to a perceptible existential property to ﬁt the paradigm. It may not even be thought to be correct to call them existential properties. But even if so, it would not seem that they would come under the heading of physical theory in the way that redness or any perceptible property analogous to redness would. If properties are heterogeneous in this way, then the selection of a particular property to serve as a paradigm property would exclude recognition of certain properties as properties for their failure to resemble the paradigm property selected. However all of this may be, the concept ‘property’ seems to be an essential aspect of our conceptual scheme, and I cannot think of a way in which the notion of property can be deﬁned in terms of a more fundamental notion that either does not presuppose or is not equivalent to the notion being deﬁned. For instance, saying that a property is something that an object has or instantiates is to speak of a property as an attribute of, or something that characterizes, or qualiﬁes, an object. However, these are just diﬀerent ways of talking of the notion that is expressed by the term ‘property,’ and are not more fundamental notions that can be used to deﬁne the concept conveyed by the use of that term. Similarly, to say that ‘x has the property P ’ means that ‘it is true that x is P ’ either must be understood to say the same basic thing in two diﬀerent ways—in which case the ﬁrst assertion is of equivalent signiﬁcance to the second—or to see the former as the ground of the latter—in which case the notion of property is the more fundamental notion. To attempt to dispense with the notion of property would either entail giving up thinking that certain things that are conceived of as properties, such as whiteness, are in fact related to other things that are conceived of as that of which properties are predicated, such as snow, or it would entail describing the relation of the former to the latter in some way that is not equivalent to the notion of property. The problem with the former approach is that our thinking and talking about reality would not reﬂect what awareness presents to us as fact, and the problem with the latter approach is that it does not seem to be possible. Similar considerations would apply to thinking of the relation of non-perceptible properties to the perceptible or non-perceptible objects of which they are predicated. Accordingly, I think that the concept of property has to be treated as an essential

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and primitive part of our conceptual scheme, as does the notion of object to which it is fundamentally related.6 Given that everything is an object, any property of any kind of property is also an object. Any particular property is a certain kind of object, namely, the kind of object that is or can be predicated of some other object, including some other property in addition to some other kind or kinds of object. Anything of which a subject can be aware in any kind of awareness is an object, and properties such as ‘roundness,’ ‘greater than,’ and ‘similarity’ are things of which subjects can be aware, and in fact we speak of certain properties as being objects of thought or perception. If it is false, as it is customarily thought to be, that for any object x there is some other object y that has some property P such that P is x, then, although every property is an object, not every object is a property. Thus not all objects are the same kind of thing, nor do all objects have the same kinds of property. 1.4. Some basic kinds of property and their relevance to art and Essentialist Abstraction Several kinds of property that are not considered in this section are possible to identify. Those that are discussed are discussed because of their pertinence to the fundamental aspects of our conceptual scheme, and hence to the issues of art and the limits of Abstract art. The discussion of logical and nonlogical properties, which is pertinent to art and Abstraction, is delayed until section 2 on haecceity and diversity to follow. 1.4.1. Properties are either particular or repeatable. A property P of an object x is ‘particular’ if P is and only can be predicated of x and not of any other object y. The property that this sentence has of being read by you at this particular time is, in virtue of concerning

6 According to Dale Jacquette: “Nothing is meaningful, true or false at all, except by virtue of a property being truly or falsely predicated of an object or objects.” “The logical possibility of combining objects with properties . . . is the foundation of every system of logic.” And he says that: “To the extent that logic represents the structure of reasoning, it [“the logical possibility of combining objects with properties”] equally underlies the possibility of thought, and . . . of reality in so far as it is thinkable.” Jacquette, Dale Ontology, Montreal: McGill-Queen’s Univ. Press (2002). All quotes p. 48.

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a particular statement and being indexed to a particular person at a particular time, a particular property. The property X that x has of being x is a particular property because X can only be predicated of x. A property that is not particular is ‘repeatable,’ or a property P of an object x is repeatable if P is or can be predicated of some object y other than x. For instance, the property of being white that characterizes this page is a repeatable property if white can characterize an object in addition to this page. Two kinds of repeatable property can be recognized: restricted and universal. A repeatable property is ‘restricted’ when it applies to at least two objects but not to all objects. The property of being a work of art is an example. A repeatable property is ‘universal’ when it applies to all objects, or nothing can be an object if it lacks the repeatable property. The property of being an object is an example. Particular and repeatable properties are relevant to art and Abstraction since every artwork must be meant to be identiﬁed with some object or objects, and any object that an artwork is meant to be will have the property of being that work of art. The property of being a certain work of art is repeatable when, for any number of numerically distinct objects, each of those objects has the property of being the same work of art. This can be understood to be the case for artworks that are multiples, such as prints, but can also be understood to be the case for the diﬀerent referents of each event of comprehending this information, each of which is a diﬀerent object, if each event is equally meant to have the property of being the work of art that is speciﬁed by that object, rather than being parts of an evolving work. Essentialist Abstraction would have to consider the relevance both to determining the limits of Abstraction and to the aesthetic of Essentialism of identifying an artwork with a single object, and so making the property of being that work of art particular, or of identifying an artwork with a number of objects, and so making the property of being that work of art repeatable. Before proceeding, I want to note that the remarks of this appendix on some basic kinds of property pertain to the nomenclature of properties, or the conceptual conditions for distinguishing diﬀerent kinds of property. And in speaking of the nomenclature of properties, or the conceptual conditions for distinguishing diﬀerent kinds of property, I mean to emphasize the conceptually basic and comprehensible nature of the remarks. As so basic and comprehensible, the

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remarks are apt to the conceptual delineation of kinds of property, and remain so even if it be maintained, for instance, that no properties are repeatable, since the concept and the comprehension of the concept of a repeatable property are required of the denial that any property is repeatable. And that is the reason for the use of the term “notions” in the title of this appendix. 1.4.2. Properties are either relational or non-relational. There are two kinds of relational property. A property P of an object x is ‘relational’ if the predication of P of x characterizes a way in which x stands in regard to itself, in which case the predication of P of x presupposes x. For instance, P may be the property that x has of being logically identical to itself, and as P characterizes a way in which x stands in regard to itself, it is a relational property. This ﬁrst kind of relational property, in pertaining to a single object, can be termed ‘monadic’ or ‘insular.’ An event of reﬂexive Intentional awareness has the property of taking itself as its object, and the predication of that property of that monadic event characterizes the way in which that event stands to itself as it presupposes the event of which that property is predicated. A property P of an object x is also relational if the predication of P of x presupposes at least one other object y in addition to x such that P characterizes a way in which x stands in regard to y. For instance, x may have the property P of being larger than y. The predication of P presupposes y since x cannot be larger than y apart from y. And P ’s characterization of x is the way in which x stands to y, namely that x is larger than y. Or x may have the property P of being intended to be a work of art a by an artist s. The predication of P presupposes s since x cannot be a apart from the intention of s that a is meant to be x. P then characterizes the way in which x stands to s, namely that x is intended to be a by s. The second kind of relational property, in pertaining to two or more objects, can be termed ‘polyadic’ or ‘non-insular.’ A common Intentional event, such as your comprehension of this language, has the relational property of being Intentionally directed to that language. And the predication of that property of that polyadic event of comprehension characterizes the way in which that event stands to that language as the event presupposes the language that it comprehends. A ‘non-relational’ property is one that is not relational as deﬁned, and in being non-relational the property neither presupposes the par-

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ticular object of which it is the property nor does it presuppose another object to which the object of which it is the property is related. The property P that an object x has of being an object is non-relational since P is a general property that can be predicated of any object, and not just x. Its predication then does not presuppose x rather than some other object.7 In addition, the predication of P of x does not presuppose some other object y such that P characterizes a way in which x stands in regard to y. (The particular property X that an object x has of being x is a relational property, since Xx, or that x has the property X of being x, is equivalent to saying that x is x, or that x stands in the relation of being logically identical to itself to itself, which presupposes the object of which that particular property is the property).8 Any artwork has the monadic relational property of being that artwork, and any object that an artwork is meant to be has the polyadic relational property of being intended to be that work of art by the artist whose work it is. An object on which an artwork is relevantly dependent has the polyadic relational property of being so relevant due to the intention of the artist who is responsible for the relevant object. And a relevant object of an artistic complex has the polyadic relational property of being apprehended by the subject who is a constituent of the complex. Each of the particular objects mentioned in each of the examples are trivially qualiﬁed by the non-relational property of being an object, and each is qualiﬁed by the monadic relational property of being the object that it is, or of having its haecceity. All of the properties that the constituents of an artistic complex have as those constituents are either monadic or polyadic relational properties. The same is true of all elements of an artistic complex insofar as they are elements of that complex. Even a property of something that is an essential element of an artistic complex which property is itself an essential element of an artistic complex is a relational property. For instance, the phenomenality of the relevant object of an artistic complex is an essential element of 7 This point is yet consistent with its being the case that, if some object is x, then the property P that x has of being an object is a necessary property of that object. See the next paragraph on non-reciprocal necessary properties. 8 I am grateful to Evan Wm. Cameron for his commentary on a paper that I presented at the 2006 Annual Conference of the Canadian Society for Aesthetics that provoked the remarks of these paragraphs on relational and non-relational properties.

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an artistic complex. And the property that the relevant object has of being phenomenal is a polyadic relational property in presupposing the subject who is a constituent of the complex. As the creative investigation of the limits of Abstraction must focus on the essential elements of artistic complexes, and as the properties of these elements in virtue of which they are essential elements of artistic complexes are relational, it is relational properties that are of interest to Essentialism. Or, things that are of interest to Essentialism in eﬀecting the more Abstract artworks possible are of interest in virtue of their relational properties. 1.4.3. Properties are either necessary or contingent. A property P of an object x is ‘necessary’ if, given x then P, or it cannot be the case that some object is x and no property is P. This connection of x and P is conceptual, and the necessity of a necessary property as deﬁned is consistent with the contingency of the object of which it is the necessary property. There are two kinds of necessary property: reciprocal and non-reciprocal. A necessary property is ‘reciprocal’ when given x then P and when given P then x, or not only can it not be the case that some object is x and no property is P, but it cannot be the case that some property is P and no object is x. The property X that an object x has of being x is a necessary property that is reciprocal, since it cannot be the case that some object is x and that no property is X, and it cannot be the case that some property is X and no object is x. A necessary property is ‘non-reciprocal’ when, given that some object is x then some property is P, but it is not the case that, given that some property is P then some object is x rather than some other object y. For instance, given that x is an object and P is the property of being an object—rather than being the property of being a particular object or a haecceity—then P is a necessary property of x, as that concept has been deﬁned, since no object can be an object without having the property of being an object. However, given P it does not follow that some object is x as opposed to some other object y. A property that is ‘contingent’ is not necessary, or, if P is a contingent property of an object x, then some object could be x if no property is P. For instance if x is this page and P is the property of being looked at by you, then P is a contingent property of x since something could be this page whether or not it was viewed by you.

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An object on which the identity of an artwork is relevantly dependent that has the property of being apprehended by a particular person at a particular time has that property contingently. And, typically at least, the object that an artwork is meant to be does not have the property of being that artwork in virtue of some particular event of apprehending the relevant object on which comprehension of that identity depends. It is not typically the case then that, if some object is some artwork, then the object has the property of being that work in virtue of that event of apprehension. That is, the Type-A type-dependent object on which comprehension of the identity of an artwork is dependent is typically itself the object that the work is meant to be. And as a type-dependent object it is contingently qualiﬁed by the relational property of being apprehended in a particular event of apprehending it. It does not then depend on that particular event of apprehension to be that work rather than on an event of a certain type of apprehension. However, if an artwork is meant to be identiﬁed with a Type-A identity dependent object, as in your event of apprehending this now, then if some object is the referent of that speciﬁcation, then that object is qualiﬁed by the relational property of having its particular identity due to the event of apprehension named by the speciﬁcation. And this polyadic relational property is necessary and reciprocal since no object can be that object apart from the property, and if some property is that property then some object is that object. The importance to Essentialism of investigating the use and relation to one another of diﬀerent kinds of dependent object was noted in the text of the book. The ﬁguring of contingent and necessary properties in Essentialist Abstraction follows from the importance of dependent objects to that investigation. 1.4.4. Two kinds of non-predicable property: individual and universal. It is typically supposed that a property is a property of something, and hence, that it is predicable. However, certain things might be conceived of as being properties that cannot be predicated either of certain objects or of any object. Something that is conceived of as a property, but is such that it cannot be predicated is a ‘non-predicable’ property. If the notion of a non-predicable property is allowed, then two kinds of non-predicable property can be distinguished: individual and universal. A non-predicable property that cannot be predicated of a particular object is an ‘individual non-predicable property,’

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and a non-predicable property that cannot be predicated of any object is a ‘universal non-predicable property.’ Whereas an artwork might legitimately be said to have the property of being more arthistorically signiﬁcant than some other artwork, no artwork could have the property of being more art-historically signiﬁcant than itself, or no artwork a could have the property P of being more art-historically signiﬁcant than a. In this case P is an example of an individual non-predicable property. No object can have the property of not being an object, and the property Q of not being an object is an example of a universal non-predicable property. It might be maintained that such properties as P and Q are not really properties for not being predicable. They are nevertheless objects in the widest sense, and are things that we can conceive of and understand even if, in conceiving of them, we understand them to be impossible. Impossible objects are the subject of Appendix Four below. The relevance of predicable and non-predicable properties to art and Abstraction is that objects on which making and apprehending even the more Abstract artworks depend are qualiﬁed by predicable properties. And no object that would be one of the more Abstract possible could, by the very nature of the case, be qualiﬁed by a nonpredicable property, such as being more Abstract than itself.

2. Haecceity and Diversity 2.1. Properties are logical or nonlogical A property truthfully predicated of an object characterizes the object of which the property is predicated. In addition to the kinds of property that have been listed, it can be noted that a property of an object is either logical or nonlogical. 2.2. Deﬁnition of ‘logical property’ In the most basic sense applicable to the identity and diﬀerence of objects, a ‘logical property’ of an object is either the property the object has of obeying a law of the laws of objects—such as being identical to itself—or it is the property that the object has of being the particular object that it is. The property that a particular object has of being the particular object that it is, or the property that each

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object has of having its particular identity, follows from the laws of identity and diﬀerence, and is the object’s haecceity. Each logical property of an object is a core property of the object. For any object x, x has the property X of being x, and for any object y, y has the property Y of being y. The haecceity of x is X and the haecceity of y is Y. For instance, the haecceity of the law of identity is the property it has of being the law of identity, and the haecceity of the Empire State Building is the property it has of being that particular piece of architecture. If ‘x’ is a name, description, or means of singling out an object, and the same is true of ‘y,’ then, by the law of excluded middle, either ‘x ’ and ‘y ’ refer to the same object or they refer to diﬀerent objects. If it is true that ‘x ’ and ‘y’ are names or means of referring to diﬀerent objects, then their diﬀerent haecceities X and Y are properties of two objects and not one object. On the other hand, if it is false that ‘x’ and ‘y’ are names or means of referring to diﬀerent objects, but are names or means of referring to the same single object o, then ‘X ’ and ‘Y ’ are names of the same single property O that o has of being that particular object. 2.2.1. The diﬀerence and relation between haecceity and the ﬁrst law of identity and diﬀerence. An object’s haecceity is the property that it has of being that particular object. An object x has the property X of being that object, and no other object y can be characterized by X. An object’s haecceity is then a particular property. The ﬁrst law of objects says that an object is logically identical to itself. This is a repeatable property. If P is the property of being self- identical, then P characterizes any object y in addition to any object x, and P is not a property that will distinguish y from x, as X will distinguish these two objects in that the ﬁrst must lack it and the second must have it. An object’s haecceity is a monadic relational property that is a reciprocal necessary property. Given an object x, the predication of X of x presupposes x, and as X characterizes a way in which x stands to itself, X is a relational property that is monadic. It cannot be the case that some object is x and no property is X, and it cannot be the case that some property is X and no object is x, which is why X is a necessary property that is reciprocal. The property that an object has of obeying the ﬁrst law of identity and diﬀerence of being identical to itself is a non-reciprocal necessary

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property. This is the case since, given an object x, it is necessary that that object has the property P of being self-identical, but, given P, it is not necessary that some object is x rather than some other object y that is characterized by P. Although it is the case that if some property is X then some property is P, and P qualiﬁes the object that X qualiﬁes, X and P can be understood to be diﬀerent properties for the reasons stated as each forms part of the laws of objects. 2.3. Deﬁnition of ‘nonlogical property’ A ‘nonlogical property’ of an object, such as being red or round or Intentional, while conforming to the laws of objects and having a haecceity, is not itself a logical property. Each nonlogical property of an object is a non-core property of the object. 2.4. Individuation of objects according to properties Depending on the nature of the property, and other things to be noted presently, a particular property of a particular object may serve to individuate the object or to mark it oﬀ logically from every other object. A property P serves to individuate two objects x and y either if P is a property of x but is not a property of y, or P is a property of y but is not a property of x. It does not follow that, if P is individuating relative to x and y, there is no other property Q that one object has but that the other object lacks, so that x and y are also individuated relative to Q, only that, if P serves to individuate x and y, then P is a property in virtue of which ‘x’ and ‘y ’ must name two diﬀerent objects rather than naming the same single object. For any two objects x and y, and any property P, if it is false that P characterizes one but not the other object, but it is rather true either that P fails to characterize either object, or that P is shared by each object of that particular plurality of objects, then that property is non-individuating relative to those particular objects. For x and y to be two objects and not the same single object, it is necessary either that x has a property that y lacks or that x lacks a property that y has, and a single property that either x lacks and that y has or that x has and that y lacks is suﬃcient to individuate them. The preceding statement gives logical conditions that are necessary and suﬃcient for the diversity of objects, but, given the laws

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of objects, the nature of a property or properties necessary and suﬃcient for individuation is a matter of metaphysical disagreement called ‘the identity of indiscernibles,’ which will be considered in Appendix Two below. 2.5. Haecceity as the minimal condition of diversity The property that each object has of conforming to the laws of objects entails that each object in a plurality of objects will have a haecceity, that no two objects will have the same haecceity, and that each object will have the property of diﬀering from each object that lacks its haecceity. These properties that each object in a plurality of objects has of having a unique haecceity and of diﬀering from each object that lacks its haecceity are logically connected, in that we know, just from the logic of objects, and without knowledge of any properties of objects other than those properties that are guaranteed by the laws of objects, that if ‘x’ and ‘y ’ name two objects rather than a single object, then it follows that x will have the property X of being x—or it follows that x has the property of being identical to x, which is the same property X—and y will have the property Y of being y, or the property of being identical to y. Because x can only have the property of being identical to itself, and cannot have the property of being identical to a diﬀerent object y, x cannot have the property Y of being y, and so x will have the property P of diﬀering from y. Likewise, y cannot have the property X of being x, and so y will have the property Q of diﬀering from x. And we know that, given x and y, it cannot be true that x has the property X without P or the property P without X, and it cannot be true that y has the property Y without Q or the property Q without Y. Then given that some object is x and some other object is y, we can infer P and Q, and can do so simply based on X and Y, and so apart from any knowledge of any nonlogical property that x may have and that y may lack or that y may have and that x may lack. 2.6. Haecceity and Essentialist Abstraction The focus in Essentialist Abstraction is on eﬀecting the identity of an artwork, and doing so by using essential elements of artistic complexes. Another way to talk about Essentialism’s emphasis on identity, or on singling out a particular object that is conceptually delineated

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in relation to essential elements of artistic complexes, is to talk about the thisness of that object and the thisness of the artwork that is meant to be identiﬁed with that object: that it is this particular object and not another that this artwork and not another is meant to be. And that is the case whether this particular object that this particular artwork is meant to be can itself be apprehended, or it can only be apprehended that it is this object that this artwork is meant to be. The term ‘haecceity’ comes from the Latin haecceitas for ‘thisness.’ An object on which a particular artwork is relevantly dependent that is being attended to is this object on which this artwork is relevantly dependent. A speciﬁcation to which an ideational object is indexed is this speciﬁcation to which this object is indexed. An event of comprehending a speciﬁcation to which an ideational object is indexed is this comprehension of this speciﬁcation to which this ideational object is indexed. The property that an object has of being the particular object that it is that no other object is recognizes the thisness of the object, that it is this particular thing and not another and that nothing that is not this thing is this particular thing. Essentialism’s focus on the particular identity of an object can be understood to be equivalent to focusing on the thisness of an object. As so equivalent, its focus on the thisness of an object is the focus on that thisness as it is eﬀected in relation to essential elements of artistic complexes, and the haecceity of an object that an Essentialist artwork is meant to be would reﬂect that concern.

APPENDIX II

LEIBNIZ’S LAW, THE LAWS OF IDENTITY AND DIFFERENCE, AND THE IDENTITY OF INDISCERNIBLES

1. Leibniz’s Law—A Conceptual Consideration 1.1. Haecceities and Leibniz’s law The criterion of the exact sameness or strict identity of objects is stated in terms of the sameness of properties of objects and is called ‘Leibniz’s law,’ or ‘the indiscernibility of the identical.’ Leibniz’s law says that if one object x were to be strictly identical to another object y, then x and y would have to have precisely the same properties. However, entertaining the possible identity of diverse objects means implicitly recognizing the individual identities of the objects supposed to be the same. And because x and y are diverse individual objects, x has the property X of being x, and y has the property Y of being y. Each such property is the haecceity of the object whose property it is, and is a unique property particular to the object of which it is the property. It follows from the diﬀerence of X and Y that x has the property P of diﬀering from y, which y cannot have, and that y has the property Q of diﬀering from x, which x cannot have. No two objects x and y can then be strictly identical in virtue of their individual identities. And to assert that x and y have every property in common—including haecceity—and thus to assert that each object lacks any property that would diﬀerentiate it from the other—including each object’s property of diﬀering from the other that is due to their diﬀering haecceities—is either to assert something impossible, or it is to assert that ‘x’ and ‘y’ do not refer to diverse individual objects, but refer instead to the same single object z by diﬀerent names.1

1 This sentence is a statement of the logical version of the identity of indiscernibles. See 3.2 of this appendix on p. 344 below.

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1.2. Necessarily distinguishing properties Whereas it follows from Leibniz’s law that a diﬀerence of objects minimally requires a diﬀerence of properties of the kinds noted, it does not necessarily follow that a diﬀerence of properties requires a diﬀerence of objects in every case: it depends on the kinds of property and the object or objects of which the properties are predicated. Two or more diﬀerent properties P and Q are ‘necessarily distinguishing’ properties if they cannot be co-predicated of the selfsame object x, and are not necessarily distinguishing if this is not the case, and where the ‘co-predication’ of two or more diﬀerent properties P and Q of the selfsame object x indicates that, if it is true that P is predicated of x then it is true that Q is predicated of x, and vice versa, and where “is predicated” is or is not temporally indexed to a particular time, depending on the natures of P, Q, and x—that is, whether any or all is existential or non-existential. If P and Q are necessarily distinguishing properties, then it follows from any use of them that they must be predicated of diﬀerent objects, and so they are suﬃcient to distinguish that of which they are predicated. For instance, if P is the property that an object p has of being p—the haecceity of p—and Q is the property that an object q has of being q—the haecceity of q—then P and Q cannot be predicated of the same thing r, or ‘p’ and ‘q’ cannot be diﬀerent names of the same thing r, but ‘p’ and ‘q’ must designate diﬀerent things p and q. Two properties P and Q are also necessarily distinguishing if they are not co-predicable of the same thing x because one contradicts what the other asserts, so that either Q is the predication of ~P of x—which is logically incompatible with the co-predication of P of x—or P is the predication of ~Q of x—which is logically incompatible with the co-predication of Q of x. If x is an existential object, such as a table, P is the property of being round, Q is the property of being square, and both P and Q are predicated at a time t, then, as the predication of ~Q is implicit in the predication of P, if P qualiﬁes x at t then Q cannot qualify x at t, and, as the predication of ~P is implicit in the predication of Q, if Q qualiﬁes x at t then P cannot qualify x at t. If x is a non-existential object, such as a number, P is the property of being an even prime, Q is the property of being an odd prime, and both P and Q are predicated, then, as the predication of ~Q is implicit in the predication of P, if P qualiﬁes x then Q cannot qualify x, and, as the predication of ~P is

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implicit in the predication of Q, if Q qualiﬁes x then P cannot qualify x. If P and Q are not necessarily distinguishing properties, then a diﬀerence of objects cannot be deduced from knowing that the properties are predicated but not knowing of what they are predicated, since they may be predicated of the same single object. For instance, if P is the property red and Q is the property round, then P and Q can be predicated of the same or diﬀerent objects. It is a task for metaphysics to determine which co-predicated properties, if any, other than haecceity, and logically incompatible properties of the kind noted, are necessarily distinguishing.2 1.2.1. Art, Essentialism, and necessarily distinguishing properties. It is of interest to philosophy of art in general which properties will necessarily distinguish a work of art from all things that are not that work of art, including from all other works of art. One wants to know then what properties can be co-predicated of the same work of art, and what properties can be co-predicated of an object or objects that an artwork is meant to be. As earlier seen, one artwork will not necessarily be distinguished from another by being identiﬁed with the same object. For instance, a Conceptualist who writes all the things that Robert Barry knew but of which he was not thinking at 1:36 PM; June 15, 1969 identiﬁes a work that is eﬀected through the use of that speciﬁcation with the same object that was singled out by Barry’s speciﬁcation all the things I know but of which I am not at the moment thinking—1:36 PM; June 15, 1969. Thus the property that an object x has of being meant to be an artwork a and the property that x has of being meant to be an artwork b are properties that can qualify the same object that diﬀerent artworks are meant to be. And so the property P that an artwork a has of being meant to be identiﬁed with an object x will not necessarily distinguish a from an artwork b that is meant to be identiﬁed with x and so is qualiﬁed by the same property P. It may be of interest to Essentialist Abstraction to investigate the use of a speciﬁcation or speciﬁcations to identify diﬀerent artworks with the same thing. However, the identiﬁcation of diﬀerent artworks with the same thing would have to be eﬀected through the use of 2 For further see section 3 of this Appendix on the identity of indiscernibles on pp. 343–350 below.

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essential elements of artistic complexes which use is reﬂected in each identiﬁcation of a diﬀerent work with the same thing. If the use of these elements to eﬀect that identiﬁcation is either limited or unfeasible, then such identiﬁcation would be of limited or no interest to Essentialism. Not only can two or more artworks be meant to be identiﬁed with the same object, but the same artwork can be meant to be identiﬁed with two or more objects. The question that pertains to the latter possibility is: If an artwork is meant equally to be identiﬁed with each object of a plurality of objects that, as plural, have some property or properties in virtue of which they are, and can be known to be, distinguished, then what property or properties would prohibit the equal identiﬁcation of the same work with these objects? If an artist can assert that an artwork of his is to be identiﬁed equally with some objects of a plurality of objects, such that each object is the work and not part of the work, then it is either the case that properties in virtue of which these objects can be distinguished as plural are properties that are co-predicable of the same work of art, or the same work of art can be meant to be identiﬁed with two or more objects that are distinguishable as those objects in virtue of some property or properties other than the property that they equally have of being the same work of art. For instance, two or more copies of the same print are distinguishable as those copies in virtue of spatio-temporal properties. Either such properties can be understood to be co-predicable of the same artwork, or to characterize objects that are equally meant to have the identity of the same work of art. In either case the spatio-temporal properties are not necessarily distinguishing properties. That is, it is not asserted that two copies of the same print cannot have the identity of the same artwork because they came into existence at diﬀerent times and exist in diﬀerent places. Even a philosopher who identiﬁed the artwork with an abstract type, and so objected to the idea that diﬀering spatio-temporal properties could be co-predicable of the same artwork, would recognize that tokens of the print that are themselves distinguished by diﬀering spatio-temporal properties are yet qualiﬁed by the same property of being a token of the same work. If an artist can assert that an artwork of his is to be identiﬁed equally with some objects of a plurality of objects, such that each object is the work and not part of the work, then it is either the case that each object of the plurality is qualitatively indistinguishable

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or ostensibly the same, as in copies of a print, or each object is distinguishable qualitatively and not simply numerically. An artist who selects a rock and a toaster and identiﬁes an artwork equally and wholly with these two objects, such that each is intended to have the property of being the same single work of art and not the property of being part of the work, identiﬁes an artwork with objects whose properties enables them to be distinguished as diﬀerent physical objects, but whose properties can qualify the same work of art, as much as the properties of being white and being square can characterize the same white painting. Thus the property of being a rock and the property of being a toaster can be predicated of the same work of art. They are not then necessarily distinguishing properties of artworks, such that, if an artwork has the property of being meant to be wholly identiﬁed with a rock, it cannot also be meant to be wholly and equally identiﬁed with a toaster, or they are not then necessarily distinguishing properties of artworks in the sense that an artwork that is identiﬁed with a rock and an artwork that is identiﬁed with a toaster must be diﬀerent works of art. The rock and the toaster are distinguished by their diﬀering spatio-temporal properties as much as are instances of a print. The diﬀerence between the print and the selected artwork of this example is that the copies of the print are assumed to look the same, whereas rocks and toasters are visually distinguishable. However, it would not seem that one could logically prohibit the attribution of the property of being an artwork to things that diﬀer visually simply on account of that visual diﬀerence. Essentialist Abstraction cannot discount the possible relevance to its determination of the limits of Abstraction, and to its aesthetic, of the identiﬁcation of the same artwork equally with a number of ideational objects that, although indexed to comprehension of the same speciﬁcation or tokens of the same speciﬁcation, have properties that distinguish them as diﬀerent ideational objects. Exploration of this possible relevance would entail investigating how both the diﬀerence of such ideational objects from one another, and their identiﬁcation with the same work of art, could be eﬀected in relation to the use of essential elements of artistic complexes. 1.3. Haecceities and existential objects Haecceities are properties that necessarily distinguish existential objects across times in this sense: if the property X that an object x has of

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being x is predicated at a time t, then some object is x at t; and if X is not predicated at an earlier or later time u, then any object at u has the property P of diﬀering from x. For any property P that is predicated of an existential object at a time t, and any diﬀerent property Q that is predicated of an existential object at any earlier or later time u—and where neither P nor Q is a haecceity—unless P is the property of diﬀering from any object at u, and Q is the property of diﬀering from any object at t, it cannot be determined a priori that any object of which P is predicated at t must diﬀer from any object of which Q is predicated at u, and that any object of which Q is predicated at u must diﬀer from any object of which P is predicated at t. Whether or not any property or properties other than haecceity and the distinguishing properties noted will necessarily distinguish existential objects across times must be determined by metaphysics, which is why this appendix is a “conceptual consideration” of Leibniz’s law.

2. The Laws of Identity and Diﬀerence 2.1. Each object is logically identical to itself Each object is logically identical to itself, since for an object not to be identical to itself it would have to be diﬀerent from itself. It follows from Leibniz’s law that an object that is not strictly identical to itself would have to have at least one property that it lacks, or lack a property that it has, or both, in order for the diﬀerence from itself to be eﬀected. However that an object x has a property P that it lacks means that x both does not and does have P, and that an object x lacks a property Q that it has means that x both does and does not have Q. In either case the law of contradiction is violated, as it is as well if it is maintained both that x does not and does have P and does and does not have Q. That an object is identical to itself then means that it must have the properties that it has and lack the properties that it lacks. 2.2. No object is logically identical to any object but itself No object is logically identical to any object but itself since speaking of an object x that is identical to some other object y means

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that x and y must diﬀer by at least a single property in order for ‘x ’ and ‘y ’ to refer to distinct objects and not to the same single object. But then, by Leibniz’s law, they cannot be the same since, in diﬀering by at least a single property, they do not have exactly the same properties, and, by the law of contradiction, no property in virtue of which two objects are logically distinct can at the same time be a property relative to which the objects lack logical distinction. No object x can be logically identical to a diﬀerent object y without x having any property P that y has but that x lacks and in virtue of which the distinction of x from y is logically eﬀected. But then x must have a property P that it has already been said to lack and relative to which it is distinct from y. And so x must both lack and have P, and must be both distinct from y in lacking P, and indistinct from y relative to the property P that it is also said to have. In addition, no object x can be logically identical to a diﬀerent object y without x lacking any property Q that y lacks but which x has and on which x ’s diﬀerence from y is conceptually grounded. However, this indicates that x must lack a property Q it has ﬁrst been seen to have and relative to which its distinction from y is made meaningful. And so x must both have and lack Q , and must be both distinct from y in having Q and indistinct from y relative to the property Q that it is conceived to lack. Either of these positions maintains that both distinction and indistinction are simultaneously eﬀected in relation to the same property, which is to assert something contradictory. These points then illustrate that, that an object can be both x and ~x; that a property can both be and fail to be a property in virtue of which objects are diﬀerent; and that a property can both fail to be and be a property relative to which objects are the same, is each an idea that cannot be held consistently. To maintain that these ideas could be held in spite of contradiction would appear to require that the concepts ‘identity’ and ‘diﬀerence’—which are notions key to the concepts ‘object’ and ‘a plurality of objects’—and which themselves form part of the foundation of our conceptual structure—be relinquished. And if the concepts of identity and diﬀerence and their lawful relation are relinquished, then it would seem that the delimitations demanded both of the logical genesis of concepts and their consistent use would be erased, and, with that removal, all thought and intelligent discourse would apparently end.

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2.3. Each object is logically distinct from each object to which it is not logically identical Each object is logically distinct or diﬀerent from every object to which it is not self-identical since, if an object x is not identical to an object y, then, by Leibniz’s law that sameness of object requires sameness of properties, either x must have some property P that y lacks, or x must lack some property Q that y has, or both of these things may be the case. But then by the same law x and y cannot be the same thing. If P is a property that x has then, by the law of contradiction, P cannot also be a property that x lacks, and if Q is a property that x lacks then, by the same law, Q cannot also be a property that x has. Then if P is a property that y lacks, but that x has, then x and y are diﬀerent objects relative to P, and it is not the case that they are also the same object relative to P. In the same way, if Q is a property that x lacks, but that y has, then x and y are diﬀerent objects relative to Q , and it is not the case that they are also the same object relative to Q. In addition, no object x can acquire any property Q that y has but that x lacks, and so in relation to which x and y are diﬀerent, without x and y failing to be distinct relative to such a property. And no object x can come to lack any property P that y lacks but that x has, and relative to which x and y are thereby distinct, without x and y failing to be distinct in relation to such a property. 2.4. Leibniz’s law, the law of contradiction, and the laws of identity and diﬀerence Leibniz’s law combines with the law of contradiction to reinforce the notions that each object is logically identical to itself; that no object is logically identical to any object but itself; and that each object is logically distinct or diﬀerent from every object to which it is not self-identical. On the other hand, that each object is logically identical to itself; that no object is logically identical to any object but itself; and that each object is logically distinct or diﬀerent from every object to which it is not self-identical are notions that sustain Leibniz’s law and the law of contradiction which have been seen to reinforce these notions. Thus the points of sections 2.1 through 2.3 are interwoven and mutually supporting, and illustrate how the notions

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of identity and diﬀerence, which underlie the points, are fundamental to conceiving of the relation of an object to itself, and are fundamental to conceiving of the relations of objects in a plurality of objects.

3. The Identity of Indiscernibles 3.1. The identity of indiscernibles in general The identity of indiscernibles pertains, generally, to the issue of what property or properties the distinction between any two objects of a certain kind of object must minimally rest upon, such that, apart from any property on which that distinction must minimally rest, to refer to, talk about, or conceive of two objects that are indiscernible for lacking any such required distinguishing property, is in fact to refer to, talk about, or conceive of the same single object by using diﬀerent names or descriptions. Another way to think of the applicability of the general form of the identity of indiscernibles to objects is to ask if, given an object x, there could be an exact copy y of x, such that, for any property P that is a property of x, P is also a property of y, and for any property Q that is not a property of x, Q is also not a property of y. This would include determining what kind of property P could or could not be and what kind of property Q could or could not be, and would mean that, if such precise repetition is possible, then the identity of indiscernibles is false, and if it is impossible, then the identity of indiscernibles is true. The identity of indiscernibles can be understood more speciﬁcally to have a logical and a metaphysical formulation, and these diﬀerent formulations concern diﬀerent kinds of object and diﬀerent kinds of property required to distinguish them. However, the identity of indiscernibles indicates in any case that no two objects can have all of their properties in common without ceasing to be two. And so, whereas Leibniz’s law says that sameness of object dictates sameness of properties, the identity of indiscernibles says that sameness of properties dictates sameness of object.

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3.2. The logical version of the identity of indiscernibles The logical formulation of the identity of indiscernibles says that, for any two objects x and y, x has the property X of being x, y has the property Y of being y, X and Y are diﬀerent properties, and for any property E that x and y have in common, E is neither, nor can it be, X or Y. According to the logical version of the identity of indiscernibles, if x and y are distinct but otherwise identical objects, then the property P that x has of diﬀering from y and the property Q that y has of diﬀering from x presuppose the diﬀerent haecceities X and Y, and where “otherwise identical” means that any property F other than X that qualiﬁes x, and relative to which x could have the property P of diﬀering from y, also qualiﬁes y, so that F is irrelevant to P, and also means that any property G other than Y that qualiﬁes y, and relative to which y could have the property Q of diﬀering from x, also qualiﬁes x, so that G is irrelevant to Q. Here it should be understood that, since x and y have all logical properties other than haecceity in common, any such property as F or G relative to which x and y could be but are not distinct must be nonlogical. Another way to talk of the logical version of the identity of indiscernibles is to say that, if any logical or nonlogical property E, including haecceity, that qualiﬁes an object x also qualiﬁes y, then x and y are and must be the same single object o that, for illustration, has been diﬀerently referred to as ‘x ’ or ‘y’, and that has the single property O of being that particular object. And for any object n that diﬀers from o, n cannot have the property O of being o. 3.3. The metaphysical version of the identity of indiscernibles Relative to the logic of objects, the metaphysical version of the identity of indiscernibles says that the mutually entailing properties P and Q that are logically connected to haecceities X and Y of objects x and y entail at least one property R that is neither X nor Y, but is either a nonlogical property that x has and that y lacks, or is a nonlogical property that x lacks and that y has. Thus, according to the metaphysical formulation of the identity of indiscernibles, distinct objects are not and cannot be distinguished according to their diﬀering haecceities alone, and cannot be distinguished according to logical properties—such as being self-identical—that all objects have in common, but their diﬀering haecceities presuppose at least one nonlog-

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ical property that one object has and that the other object lacks. According to this formulation of the principle then, although there may be an object x or an object y apart from a property such as R, there are no two objects x and y apart from such a property as R, and so, although there may be a property X or a property Y, there are no two properties X and Y by which the supposed objects x and y could even theoretically be distinguished. Or, if the metaphysical version of the identity of indiscernibles is true, and there is no nonlogical property R relative to which x and y could be distinguished, then it is either the case that there are no two things x and y, or there is a single thing that is equally referred to as ‘x’ or ‘y.’ As all objects conform to the laws of objects, all logical properties other than haecceity, or the property that an object has of having its particular identity, are non-individuating relative to particular objects of a plurality of objects. This is the case for either formulation of the principle of the identity of indiscernibles, and is the reason then for speaking of a nonlogical property that would be required to individuate x and y if the metaphysical version of the identity of indiscernibles is true, or if properties P and Q of x and y are not eﬀected merely in relation to X and Y, but rather in relation to some nonlogical property of diﬀerence R in addition to X and Y. If the metaphysical version of the identity of indiscernibles is false, then two objects x and y may have all of their properties in common— logical and nonlogical—except their haecceities X and Y and their mutually entailing properties of diﬀerence P and Q that are logically connected to these haecceities. This latter assertion recognizes the logical version of the identity of indiscernibles, and is the equivalent, in terms of the kinds of property noted, of objects diﬀering “solo numero.” 3.4. The possible application of these diﬀerent versions to diﬀerent objects It may be that the metaphysical version of the identity of indiscernibles applies to objects that cannot be distinguished by a nonlogical property or properties, even in theory, and it may be that the logical version of the identity of indiscernibles applies to objects that could be distinguished by a nonlogical property or properties but that are not so distinguished.

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3.4.1. An argument for the application of the metaphysical version. An argument that the metaphysical version of the identity of indiscernibles applies to objects that cannot be distinguished by a nonlogical property or properties might proceed as follows. A property is a kind of object, since, depending on the kind of property, a property can be the object of thought or perception, and a property is something that can be referred to or talked about. The property that an object x has of diﬀering from another object y is itself an object, and although there may be any number of diﬀerences between two objects x and y, x is a single object with a single haecceity X; x has a single property P of diﬀering from a diﬀerent object y; y is a single object with a single haecceity Y; and y has a single property Q of diﬀering from x. For instance, let x be a red square and let y be a green circle. Then x and y diﬀer not only in color but in shape. However, in spite of these diﬀerences of properties of x and y, x diﬀers from y by the single property P, and y diﬀers from x by the single property Q. Similarly, x ’s single property of being square has the single property A of diﬀering as that shape from y’s single property of being circular, and y’s single property of being circular has the single property B of diﬀering as that shape from x’s single property of being square. And x’s single property of being red has the single property C of diﬀering as that color from y’s single property of being green, and y’s single property of being green has the single property D of diﬀering as that color from x ’s single property of being red. The previous statements assume the truth of the metaphysical version of the identity of indiscernibles. In the ﬁrst instance, this version of the identity of indiscernibles is assumed when it is said that x diﬀers from y by a single property P, which is x’s diﬀering from y, and that y diﬀers from x by a single property Q , which is y’s diﬀering from x. If x were said to have a second property O that had in common with P being x’s diﬀering from y, then O and P would equally be properties that are minimally logically correlated with the haecceities of x and y as indicated above, at the same time that nothing, save the properties pertaining to the individuality of each property—namely, the haecceities of O and P—would distinguish the two properties O and P that are said equally to be x ’s property of diﬀering from y. Likewise, if y were said to have a second property R that had in common with Q being y’s diﬀering from

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x, then Q and R would equally be properties that are minimally logically correlated with the haecceities of y and x at the same time that nothing other than the properties relevant to the numerical diﬀerence of each such correlated property would distinguish them. The metaphysical version of the identity of indiscernibles is also assumed in talking of x’s single property of being square and its single property of being red, and is assumed again in talking of y’s single property of being circular and its single property of being green. Further, the property that each of these things has of diﬀering from any other of them is also singular. Whether or not a number of properties that are diﬀerent instances of the same property, such as P and O, is possible depends on the applicability of the metaphysical version of the identity of indiscernibles to objects that could not be distinguished by any nonlogical property, even in theory. What nonlogical property could distinguish two properties, such as P and O, that are equally said to be the property that an object x has of diﬀering from another object y? It might be maintained that x could be conceived to have a second property O of diﬀering from y, and that any thought of O would be a nonlogical property of O that would distinguish it from another property P of x ’s that also would be the property that x has of diﬀering from y. However, it might be maintained that nothing would determine that the property O that is entertained is not simply the same property P that is conceived of by a diﬀerent name. A second possible response to this position is to note that, although there is a distinction between an act of thinking of such a property as O and the object of such an event of thought, it is possible that nothing answers to such an act apart from the occurrence of an act of that kind of act. If this is the case, then the object of the event of thought is not a generically-independent object, but is rather an object that is type dependent on an event of thinking of the object. Hence one could conceive of a second property O that an object x has of diﬀering from another object y, but that event of conception does not in itself establish that some object of all objects has the property of being O, as opposed to making it the case that O is the Intentional object of an event of conceiving of the applicability of that property to a certain object, each of which—object and property—is conceived to be generically independent of consciousness in general, and so to be independent of any event of the kind of event in which that status

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of each entity is entertained. The same points would apply to the supposition that y has a second property R of diﬀering from x, that x has a second property of being square, and so forth. To suppose that the metaphysical version of the identity of indiscernibles is false, and fails to apply to things such as the properties considered, is to suppose that the diﬀering haecceities of such diﬀerent properties of diﬀerence is suﬃcient to distinguish them. However, a consequence of this supposition is that there is no theoretical end to the number of properties that one object could have of diﬀering from another, no theoretical end to the number of properties that an object has of being square, red, and so forth. And if the metaphysical version of the identity of indiscernibles is not recognized to be applicable here, then arguments would have to be advanced to explain how the fact that, for instance, some object has the property of being x and the fact that another object has the property of being y could result in each object’s having more than a single property of diﬀering from the other. Arguments would also have to be provided to explain why additional properties should be recognized even if they could be recognized when a single property of one object’s diﬀering from another will meet the requirements of the laws of objects. Further, if the same two particular objects can generate any number of properties of each object diﬀering from the other—which properties are themselves individuated relative to their haecceities only—and if, for instance, the same circular object could have any number of properties of being round—properties that are only individuated relative to their haecceities—one might wonder if a particular object can have more than one property of being that particular object, or any number of haecceities, haecceities that are themselves individuated according to their haecceities. However, any haecceity of a supposed number of haecceities of an object could itself have any number of haecceities, any of which also has any number of haecceities. The inﬁnite and prodigal proliferation of such properties then suggests that economy would favor application of the metaphysical version of the principle to such objects. Because multiplying instances of the same property predicated of an object is both superﬂuous and objectionable; because the proliferation of such instances cannot be halted on the assumption that the diﬀering haecceities of diﬀerent objects of these kinds of object

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are suﬃcient to distinguish them; and because properties are as much objects as are the diﬀerent kinds of object to which they pertain, the metaphysical version of the identity of indiscernibles is applicable to objects of this kind of object. Thus it can be generally asserted that, for any property E that qualiﬁes an object x, x cannot be qualiﬁed by any additional property or properties En, where any property En is not the same kind of property as E—such as a color— but, apart from its haecceity, or apart from the property that any property En has of being the particular property that it is, En is precisely the same property as E and qualiﬁes x at the same time that E qualiﬁes x. The metaphysical version of the identity of indiscernibles also applies to the basic notions of object, identity, and diﬀerence, in that each concept is unique and individual. 3.4.2. Application of the logical version. If two objects x and y that could be distinguished by a nonlogical property or properties are not so distinguished—so that these objects have all of their relational and nonrelational nonlogical properties in common—then, according to the laws of objects, x and y must be distinguished according to their diﬀerent haecceities X and Y. For instance, Max Black’s radially symmetrical spheres are objects that could be distinguished by a nonlogical property or properties but are supposed not to be so distinguished.3 And his example, if credible, is an illustration of the applicability of the logical version of the identity of indiscernibles to such objects. The view that predicates diversity on the bare numerical diﬀerence of objects that are taken to be distinct is equivalent to diversity predicated on or recognized in the diﬀerence of the haecceities of the distinct objects. In opposition to this view, it might be argued that it takes advantage of the fact that language can be used to state certain things that cannot possibly be true, and that, concealed in the statement of the bare numerical diﬀerence of otherwise identical objects, is the assumption that the diversity of such objects need not be predicated on anything other than the diversity recognized in that statement. And if that is correct, then the logical formulation of the identity of indiscernibles, although reﬂecting the laws of objects in the statement 3 Black, Max “The Identity of Indiscernibles,” in Universals and Particulars: Readings in Ontology, Loux, Michael (ed.) Garden City, NY: Anchor Books (1970) pp. 203–216.

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of the example, cannot distinguish any kind of object.4 However, a defender of the theory that objects can have all of their properties in common, except their diﬀerent haecceities, may maintain that an opponent of this way of thinking simply assumes that two objects cannot have all of their properties in common other than the property that each object has of being that particular object, and uses that assumed position to eﬀect the points of the previous argument. For my part, I do not think that the possibility can be discounted a priori that two objects that could in theory be distinguished by any nonlogical property or properties by which they are not in fact distinguished are instead distinguished by their haecceities. I conclude then that the metaphysical version of the identity of indiscernibles applies to objects that cannot, even theoretically, be distinguished by a diﬀerence of any nonlogical property, and that the logical version of the identity of indiscernibles applies to objects that can, in theory, be so distinguished. This recognition means that, although the concepts of object, identity, and diﬀerence, and the basic laws of objects that regulate their interrelation must apply to and underline any talk of, reference to, or thought of or about objects of any kind of object, diﬀerent kinds of object require diﬀerent versions of the identity of indiscernibles that pertain to the possibility or the impossibility of the bare numerical diversity of any two objects of the same kind of object.

4 Cf. A. J. Ayer: “Being accustomed to speak of objects in the plural without further qualiﬁcation, we come to think that this alone is enough to diﬀerentiate them.” However, Ayer says that this may be “an illegitimate extension of the concept of number,” since it may be that “only where there is discernibility”—or diﬀerence of objects predicated on the diﬀerence of at least one nonlogical property—is there any possibility of talking about “a plurality of objects.” Although Ayer admits that he does not ﬁnd this argument “altogether convincing,” he nevertheless takes what I am calling the metaphysical version of the identity of indiscernibles to be true because he “cannot see how asserting that an individual exists can be to assert anything more than some predicate, or set of predicates, is instantiated.” “The Identity of Indiscernibles,” in his Philosophical Essays, London: St. Martin’s Press (1963) pp. 26–35. Quotes on pp. 34–35.

APPENDIX III

DISTINCTION, DISCRIMINATION, AND DISTINGUISHABILITY

The distinction of objects is symmetrical: if x is distinct from y then y is distinct from x, and this symmetrical relation of distinct entities is implicit in speaking of either the distinction between x and y or the distinction between y and x, which is to say the same thing in two diﬀerent ways. The phenomenal counterpart of the distinction of objects is discrimination, and we can apprehend that diverse objects are distinct if they are distinguishable and cannot if they are not. As diverse objects are distinct whether or not they are distinguished, distinction and discrimination are two diﬀerent things. Given the relevance of discriminatory consciousness and the distinguishability of distinct properties of objects to Essentialist Abstraction, it is worth noting that it cannot be maintained a priori as a matter of logical necessity that, if x is distinguishable from y that y is distinguishable from x, and so, unlike the distinction of objects, distinguishability is not necessarily symmetrical in every case. A thing x can be distinguished from another thing y if x has at least one property P that y lacks that is suﬃcient to distinguish it from y. And this could be the case at the same time that y has no property Q that would enable it to be distinguished from x, even though y must have at least one property that x lacks or lack at least one property that x has in order for the two objects to be distinct. For instance, x and y could each be kinds of event of awareness that form part of the history of awareness of the same subject, and while that subject can distinguish x from y he cannot distinguish y from x. Suppose that y is an event of coherent dreaming that, as coherent, is indistinguishable for the person dreaming y from a similar event x that characterizes the person’s history of awareness when he is awake. However, when the person is awake he can distinguish such an event as x from the similar dream event y if x has some property that y does not that is suﬃcient to make it known to the person that it is an event that occurs when he is awake and not asleep. It would seem that the higher-order aspect of second-order awareness is an example

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of such a property. Thus you might dream that you are now reading this, and, in doing so, not be able to tell that you are not awake as it in fact appears to you that you are awake, but you cannot be aware of that kind of ﬁrst-order awareness in an event of secondorder awareness if you are asleep, as you can if you are awake. Thus the event of reading, if dreamt, can only be ﬁrst-order, but if the event of reading is an event that occurs when you are awake, then that event can form the ﬁrst-order aspect of a second-order event of awareness that includes that ﬁrst-order event as its Intentional object. Because such a second-order event can characterize a period of awareness that occurs when a person is awake but not when she is asleep, while dreamt reading can be indistinguishable from reading when awake, an event of reading when awake can be distinguished from dreamt reading if it is the object of a second-order event of awareness rather than being a ﬁrst-order event of awareness.1 This example pertains to things that form part of a subject’s history of awareness at diﬀerent times in his history of awareness. If x and y are phenomenal objects that form part of a subject’s history of awareness at the same time t, then, as phenomenally distinct objects at the same time, each is distinguishable from the other.

1 Cf. Anthony Kenny: “The judgement ‘I am awake’ cannot be mistaken.” and “It is impossible falsely to believe that one is awake, because one cannot entertain beliefs in sleep.” Kenny, Anthony Descartes: A Study of His Philosophy, New York: Random House (1968) p. 31.

APPENDIX IV

IMPOSSIBLE OBJECTS

1. Deﬁnition of impossible object An object is ‘impossible’ when it is said to have a property, such as being round, that it cannot have in virtue of having another property, such as being square. An example of an impossible object that beﬁts basic logical properties of objects is ‘the object that has the property of being distinct from every object to which it is not selfidentical and the property of being indistinct from every object to which it is not self-identical.’ A property, which itself is a kind of object, is impossible either when it is said to have incompatible properties, as when a property P is said both to have the property of being P and to have the property of not being P, or a property is impossible when it is said to be predicated of an object that cannot have that property in virtue of having another property that logically excludes predication of the property. For instance, an artwork a cannot have the property P of being more art-historically signiﬁcant than a since the predication of one work’s being more art-historically signiﬁcant than another requires a work from which the more signiﬁcant work diﬀers. Accordingly, the predication of P of a is logically incompatible with the property that a has of being indistinct from itself. And ‘the artwork that is more art-historically signiﬁcant than itself ’ is an impossible object as much as is the property P of the previous sentence. Because impossible objects may be seen to test certain assertions made about the basic properties of objects and the logical relation of an object to itself and to other objects, and because conceiving of certain objects with certain incompatible properties may be of interest to Essentialism in addition to its interest in eﬀecting logical relations between things in relation to essential ingredients of artistic complexes, impossible objects are the focus of this appendix.

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appendices 2. Diﬀerent views of impossible objects

Some philosophers, such as Alexius Meinong, maintain that an impossible object, such as the round square, in fact has the properties in virtue of which it is that particular object, while other philosophers, such as Reinhardt Grossman, maintain that no object of all objects has the property of being both round and square, but that, in thinking of the round square, we conceive of something that we conceive to be round and square. For Meinong, the round square is what I have called a ‘generically-independent, non-existential’ object, and it is the kind of nonexistential object that is also non-subsistential in that it cannot have existential instances. However, Meinong insists that although an impossible object such as the round square does not exist, subsist, or have any kind of being, it nevertheless has the properties in virtue of which it is that particular object. That there are objects that lack being of any kind is a point on which Meinong is often misunderstood, since, in talking about impossible objects, he was given to saying things such as “There are objects of which it is true that there are no such objects.” But Meinong oﬀers this statement for “those who like paradoxical modes of expression.”1 And this is paradoxical if the word “are” is interpreted in the same way in each of its uses in the sentence. But what he meant is that there are objects that are inherently contradictory, and so have no ontological status whatever, and thus are not objects that can be instantiated in space-time, and yet they are objects that can be apprehended by thought. Although the round square does not exist or subsist, it would not be the round square unless it had the contradictory properties in virtue of which it is that particular object. Ernst Mally, a pupil of Meinong’s, says that, whereas it is impossible for a square to be round or for a circle to be square, it is necessary that the round square is both round and square, since, presumably, if it were not, it would not be that particular object—the particular object that is not a circle, not a square, and not a triangular square nor any object but the round square.2 However, Mally, with Meinong, insists that 1

Meinong, Alexius “The Theory of Objects,” both quotes p. 83. See Russell, Bertrand “Review of: A. Meinong, Untersuchungen zur Gegenstandtheorie und Psychologie” reprinted from Mind, 14 (October, 1905) in Essays in Analysis (Douglas Lackey, ed.) pp. 79–80. 2

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such impossible objects as the round square do not exist or subsist but are “beyond being and non-being.”3 Roderick Chisholm paraphrases the view shared by Meinong and Mally thus: “An object may have a set of characteristics whether or not it exists and whether or not it has any other kind of being.”4 Chisholm also says that the common view that Meinong’s theory of nonexistent objects was “demolished by Russell’s theory of descriptions . . . is false”5 because Russell’s theory does not provide a way of paraphrasing either such an analytically true statement as “The golden mountain is golden,” or the Intentional statement “The mountain I am thinking of is golden.” Russell’s paraphrase of “The golden mountain is golden,” according to his theory of descriptions, “implies ‘There exists an x such that x is both golden and a mountain’ and is therefore false.” But Chisholm asks: “How can a false statement be a paraphrase of a true one?”6 Trying to paraphrase the true Intentional statement for someone who is thinking of a golden mountain according to “Russell’s procedure would [also] provide us with a statement that is false” since the paraphrase of “The mountain I am thinking of is golden” is “There exists an x such that x is a mountain I am thinking of and x is golden, and, for every y, if y is a mountain I am thinking of, then y is identical with x.”7 And this is false since no golden mountain exists, and yet it is true that I am thinking of a golden mountain. According to Chisholm, that statements

3 “The Theory of Objects,” p. 86. Meinong uses the term ‘absistence’ to refer to “objects that do not exist or subsist.” The term ‘absistence’ refers to “a third something” that is “beyond existing and subsisting.” Meinong says that this third realm of objects lacks a “being-determination,” and remarks that absistence has no negative counterpart, as existence has non-existence, and subsistence has non-subsistence, and that this is “a situation which is altogether unparalleled.” Meinong, Alexius On Assumptions (edited and translated, and with an introduction by, James Heanue) Berkeley: Univ. of California Press (1983) p. 62. That, for Meinong, there are objects that lack being makes ‘object’ a concept that is more philosophically fundamental and wider ranging than ‘being’ in pertaining to all things, including certain things to which being does not. 4 Chisholm, Roderick “Beyond Being and Nonbeing,” in Brentano and Meinong Studies, Atlantic Highlands, NJ: Humanities Press (1982) pp. 53–67, quote p. 53. 5 “Beyond Being and Nonbeing,” pp. 53–54. For Russell’s theory of descriptions see his article “On Denoting” in Logic and Knowledge: Essays 1901–1950, Marsh, Robert C. (ed.) New York: Capricorn Books (1968) pp. 41–56, and chapter XVI of his Introduction to Mathematical Philosophy, New York: Touchstone Simon and Schuster (1967). 6 “Beyond Being and Nonbeing,” both quotes p. 61. (His italics.) 7 “Beyond Being and Nonbeing,” both quotes p. 64. (His italics.)

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about nonexistent Intentional objects cannot be adequately paraphrased so as to eliminate reference to nonexistent objects provides the best case for Meinong’s view that there are beingless objects in a sense of “are” that implies neither existence nor subsistence, and where ‘subsistence’ might be thought to apply to logically well-formed abstract or non-existential objects, such as numbers, that, as logically well-formed, can have existential instances.

3. Impossible objects and the laws of thought—I Because Meinong maintains that impossible objects have the properties in virtue of which they are impossible, his view, if correct, means that not all objects obey all of the laws of logic. For instance, Meinong says that the law of contradiction does not apply to such an impossible object as the round square, since, as Mally indicated, the round square would not be the round square if it did not combine in itself those incompatible properties. However, Meinong seems to be objecting to applying the law of contradiction to the relation of the mutually excluding properties in virtue of which the round square is that particular impossible object, rather than objecting to applying the law to the relation of the impossible object that has those properties to all other objects. And it seems to be one thing to say that an object that is both round and square violates the law of contradiction by being both square and not square and by being both round and not round, and it seems yet another to say that it violates it by both being and not being the round square. Whatever the case regarding the law of contradiction, an impossible object such as the round square might seem to obey the law of identity in that the object that has the properties of being round and square is the object itself that has those properties. However, according to Russell, the round square cannot even be said to obey the law of identity since, for him, the law of identity can only be applied to objects that exist. He says that “propositions of the form ‘the so-and-so is the so-and-so’ are not always true: it is necessary that the so-and-so should exist.” Accordingly, “It is false that the present King of France is the present King of France, or that the round square is the round square.”8 If, following Hume and Kant, it is 8

Russell, Bertrand Introduction to Mathematical Philosophy, p. 176. (His italics.)

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said that existence, in virtue of being redundant and so non-discriminatory, is not a ﬁrst-order property that can be predicated of an object, as the ﬁrst-order property ‘red’ can be predicated of an object, but ‘exists’ is taken instead to name a second-order property that is predicated of an object only in virtue of a distinguishing, instantiable property or properties that is predicated of the object— as is the case for Frege and Russell—and if no object can have the property of being round as it is square and the property of being square as it is round—or these mutually excluding properties cannot be simultaneously instantiated in some object—then no existent object can have the property of being the round square. And if the round square cannot exist, then for Russell, there is no entity by that name that can be said to conform to the law of identity. On the other hand, a defender of the view of impossible objects advocated by Meinong and Mally might reject the Russellian view as unduly and presumptively restrictive to existential objects, and might instead suggest that impossible objects such as the round square obey all of the laws of thought in the following manner: The round square is the round square in its being —in a non-ontological or absistential sense—the object that is determined by the conjunction of those particular incompatible properties; nothing is both the round square and not the round square, in that the round square does not both have and lack the properties in virtue of which it is the particular object that it absistentially is; and everything is either the round square or not the round square, in that the class of all objects— existential and non-existential combined—divides into two subclasses, those that have and those that lack the property of being the round square, and the ﬁrst class has a single member. In fact, the defender of the view that impossible objects are generically independent of awareness might maintain that any impossible object must obey the laws of thought in the preceding sense since each object, including any impossible object, has a particular identity, the particular identity that, for an impossible object, is determined by the conjunction of a certain set of incompatible properties that fail to characterize any other object. Given its particular identity, each object, including each impossible object, is conceptually delimited from every object that lacks its particular identity, which is every object other than itself, and this delimitation is regulated by the laws of objects. Hence if an impossible object did not obey the laws of objects in relation to all other

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objects—in being self-identical and in being distinct from everything to which it is not self-identical—then it would not be conceptually delimited from each object that lacks its particular identity, and so it could not be referred to or apprehended as the particular object that it is. In fact, there would be no “it” or “object” in any sense of object, including an absistential one, and so failure of reference and apprehension would be necessary, not contingent. The views of this paragraph underline the thinking that an impossible object is an object, and, as an object, it “is what it is and not another thing,” and so, were it not to obey the laws of objects in the manner indicated, it would not be the object that it is, in an absistential sense of “be” and “is.” It would seem though that there are diﬃculties with such a view for impossible objects given such an impossible object as ‘the object that is not itself.’ This is because, if the object that is not itself conforms to the laws of objects, then it must be itself. But its being itself, or its conforming to the laws that an object is logically identical to itself and has the property of being the object that it is, is ruled out by its being the object that is not itself, since if the object that is not itself did not have the property of not being itself it would not be the object that is not itself. Accordingly, the object that is not itself cannot be itself. However, not only does this contravene the laws of objects, but to say that the object that is not itself is not itself is to say that it is false that it is that particular object. But if the object that is not itself is not itself then it must lack the particular identity of that object, and so, on the laws of objects, cannot be described as ‘the object that is not itself.’ Further, on the laws of objects, if the object that is not itself does not have the particular identity of that object, then it could not be distinguished logically nor discriminated consciously from any object that lacked the property of being the object that is not itself. Therefore the object that is not itself must be itself. However, if it is itself then, as we have seen, it cannot be itself. Therefore it seems that the object that is not itself cannot be itself and cannot not be itself, and so it must be both itself and not itself. However, this is not to conform to the laws of objects but to violate them.

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4. Diﬀerent views of the relation of impossible objects to consciousness Because impossible objects are generically independent on Meinong’s theory, objects such as the round square are apprehended, not constructed, by thought. And because any two or more people can apprehend the same impossible object through the same kind of awareness, an impossible object would be a public object for anyone who is aware of it. According to Grossman on the other hand, impossible objects such as the round square are not apprehended by thought but are constructed by thought. Grossman says: “The round square is neither round nor square, it is merely thought of as round and square or, perhaps better, we conceive there to be something which we conceive to be both round and square. In a nutshell, while Meinong holds that imagined entities have properties, we maintain that imagined entities are imagined to have properties.”9 Although Grossman talks here of imagining impossible objects in addition to thinking of or conceiving of them, clearly he does not mean to suggest that such imagining is anything but imageless, since no image could combine in itself the contradictory properties of being both round and square. Another philosopher who argues against Meinong’s treatment of impossible objects as generically independent of awareness is J. N. Findlay. Findlay says that “What [Meinong’s] researches really indicate is . . . a deep inseparability between our conscious approaches and the features we discern in the world, the senselessness of trying to deal with the one without bringing in the other. They call, that is, for a certain reinfusion of that idealism from which his early study of Kant had made Meinong so adverse, a reinfusion which Husserl

9 Grossman, Reinhardt Meinong, London: Routledge and Kegan Paul (1974) p. 164. See also Grossman’s “Meinong’s Doctrine of the Aussersein of the Pure Object,” Noûs, 8, 1974, pp. 67–82. Grossman’s argument against treating impossible objects as generically-independent entities is similar to Richard Taylor’s argument against treating mental images as entities. For Taylor, imagining is something that human beings as physical objects do, or is perhaps a state of the brain, but “we can say all we want to say about men’s powers of imagination without ever introducing the substantive ‘an image.’” And it seems that, for Grossman, we can say all we want to say about impossible objects without using such substantives as ‘the round square,’ substantives that only seem to single out generically-independent objects rather than pertaining to certain events of conceiving of them. Taylor, Richard “How to Bury the Mind-Body Problem” American Philosophical Quarterly 6 (April 1969) pp. 136–143.

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admitted so fully as virtually to be an idealist.”10 Such idealism is particularly relevant for Findlay to the problem of impossible objects since “objects which combine contradictions, can . . . only be objects in the sense that there can be considerations of them, signiﬁcant references to them, and not in the sense that they can be made independent subjects of assertions . . .”11

5. Impossible objects as Type-A type-dependent objects For Grossman, and Findlay before him, an impossible object such as the round square is what I have referred to as a Type-A typedependent object. It is such an object since no object has the property of being the round square unless it is conceived of, and some object has the property of being that object whenever it is conceived of. Such an impossible object is public since it is possible for two or more people to conceive of the same impossible object and to understand that they conceive of the same impossible object through a mutual understanding of the concept of conjunction coupled with the recognition of the common meaning of the words ‘round’ and ‘square.’ Not only does such a type-dependent impossible object as the round square have no existence apart from the occurrence of an event of the kind of event on which its particular identity is dependent, but neither an event of conceiving of the round square nor the object of that event of conception has the incompatible properties that the object is conceived of as having. Thus an event of conceiving of the round square is not itself round and square, nor is the Intentional object of that event of conception. That is, that Intentional object is not apprehended to have incompatible properties but is rather conceived of as having them. A type-dependent object may be passively found by consciousness, such as a painting, or it may be actively created by consciousness, and where that creation can either be provoked by the volition of the person whose conscious creation it is, or the creation can result from the apprehension of spoken or written symbols—such as ‘round 10 Findlay, J. N. Meinong’s Theory of Objects and Values, Oxford: Clarendon Press (1963) p. 340. (My italics.) 11 Meinong’s Theory of Objects and Values, p. 341. (My italics.)

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square’—that provoke a person apprehending those symbols to conceive of the object that is conceived of as having these properties. Thus conceiving of something may or may not be reactive to symbolic entities that provoke events of conceiving of the thing to which the symbol is taken to point. And acts of conceiving of a type-dependent impossible object in either kind of creation can pertain to the same public type-dependent object, and this is the case whenever the acts have in common conceiving of the conjunction of the same incompatible properties, and so where the acts have in common a kind of doing rather than an apprehending of something independent of the activity of conceiving, which apprehending would amount to a kind of conscious receiving.

6. Type dependence and sameness Any impossible object, such as the round square, is a created, typedependent object, and any event of conceiving of the round square has in common with any other event of conceiving of the round square conceiving of an object conceived to have the same incompatible properties. Accordingly, we can speak of the same type-dependent object being entertained by any number of events of conceiving of that object even though there is no object generically independent of events of conception of the kind of conception on which the particular impossible object is dependent. What is meant by speaking of “the same type-dependent object” then is that diﬀerent events of conceiving have in common conceiving of the conjunction of the same incompatible properties as constituting a particular object that is logically prohibited from having the properties it is conceived of as having. It does not follow from what such acts of conceiving have in common that there is an object that is generically independent of those acts of conception. And, although any event of conceiving of a particular type-dependent object is, as a particular event of conception, itself numerically distinct from any other event of conceiving of that same type-dependent object, it does not follow from that fact that the concept of sameness cannot be understood to apply to that which is conceived of by any number of diﬀerent events of conception of a certain kind of conception. In fact this is how type-dependent objects, such as the round square, are understood. We understand a particular type-dependent object to be the same type-dependent

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object conceived of in diﬀerent acts of conceiving of it because certain properties qualify particular acts of conception of the kind of conception on which the particular object conceived of is dependent. For instance, each event of conceiving of the round square is qualiﬁed by the property of conceiving of something that is conceived to be square that is simultaneously conceived to be round. There would seem to be no a priori logical basis for thinking that, if a particular object is phenomenal relative to two or more events of awareness at the same or diﬀerent times, then that object must be generically independent of awareness. And if talk of diﬀerent events of awareness that pertain to a particular object does not require that the object is generically independent, then when any two or more events of awareness of the kind of awareness on which a particular type-dependent object is dependent occur, they can be understood to pertain to the same object. It is simply that a particular object that is said to be the same object in these diﬀerent cases of generic independence and type dependence is conceived of in diﬀerent ways. On the one hand, a particular generically-independent object is conceived of as not only being the same object apprehended by two diﬀerent events of apprehending it, but it is conceived of as being the same object whether it is apprehended or not. The independence of a generically-independent object indicates that, if such an object is apprehended, it is discovered rather than created. On the other hand, a particular type-dependent object is conceived of as being the same object conceived of in two or more events of the type of event on which it is dependent, or diﬀerent acts of conceiving of a particular type-dependent object are conceived of as conceiving of the same type-dependent object, and no object is conceived of as being the same object as a particular type-dependent object apart from the occurrence of any event of the type of event on which that particular type-dependent object is dependent. Therefore, conceiving of a particular object of the kind of object type dependent on conception creates the object conceived of. Although a generically-independent object, as generically independent, has a relation to consciousness that is diﬀerent from the relation to consciousness of a type-dependent object, we can as much speak of the same type-dependent object being apprehended by diﬀerent events of awareness as we can speak of the same generically-independent object being apprehended by diﬀerent events of awareness. Any number of events of perceiving a painting perceive

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the same type-dependent object, and they do so even though there is no painting, as the phenomenal object that it is intended to be— the thing that is meant to be seen, responded to, and interpreted as a phenomenal object—apart from an event of perception to which it is intentionally directed. And any number of events of conceiving of a particular type-dependent object conceive of the same typedependent object, whether at the same or diﬀerent times, and this is the case even though no object has the property of being a particular type-dependent object apart from any event of conception of the kind of conception on which it is dependent. For instance, any number of events of conceiving of the round square conceive of the same impossible object, and do so even though there is no such object apart from such events of conception. Thus the diﬀerence of generically-independent and type-dependent objects and the relation of each to awareness does not prohibit us from understanding and using the concept of sameness to apply to objects of each kind of object.

7. The relation of impossible objects to events of conceiving of them Any event of conceiving of an impossible object is Intentional in being about something; it is irreﬂexive in not being about itself, or in not taking itself as its Intentional object; it is for that reason also not monadic, but polyadic; and, as seen, diﬀerent events of conceiving of the same impossible object, such as the round square, can be understood to concern the same type-dependent object in virtue of doing the same thing, or in virtue of conceiving of an object as consisting of the same incompatible properties. We can also speak of the same type-dependent object being entertained by diﬀerent events of conception in virtue of the fact that no event of conceiving of the object excludes in virtue of the event’s occurrence the possibility of conceiving of the conjunction of the properties of which the object is conceived to consist in another event of conception of the kind of conception on which that object is dependent. As indicated earlier in the text, from the fact that an object is the Intentional object of a certain Intentional event it does not necessarily follow that either that object has to be a property of the event or independent of that event. Instead, it can be a type-dependent object. A type-dependent object is not a property of any event of

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the type of event on which it is dependent, but neither is it for that reason independent of an event of the type of event on which it is dependent. The preceding points indicate that a type-dependent object that is impossible, such as the round square, is, as both typedependent and impossible, sui generis, and, as such, it cannot be modeled on any diﬀerent kind of object of awareness.12

8. Impossible objects and the laws of thought—II As seen, for Meinong the law of contradiction does not apply to impossible objects such as the round square, whereas, for Findlay and Grossman, as there is no generically-independent object that combines in itself such contradictory properties, there is no such object to which the law can be said to fail to apply. And because, on their view, a particular event of conceiving of an impossible object would have the particular identity of that event, nothing would both have and lack the identity of that event, and everything would either have or lack the identity of that event, we can speak of an event of conceiving of an impossible object as obeying the laws of logic even if the object conceived of is conceived of as violating them.

9. Saying something and saying something true The view of Grossman and Findlay would also support recognizing a distinction between ‘saying something’ and ‘saying something true,’ and where “saying” can pertain to spoken or written language. For instance, if I say audibly to you, “I am not now speaking aloud,” it is true that I say, “I am not now speaking aloud.” But, by the very nature of the assertion, I contradict myself in making the assertion, and so cannot be saying something true. On this view I could say or write: “Some object of all generically-independent objects is the round square,” without saying something true. And I could say or

12 Whereas logically well-formed concepts, such as ‘red,’ ‘pencil,’ or ‘unicorn,’ depend as concepts on events of conceiving of them, and so have this in common with impossible objects, logically well-formed concepts can and often do point beyond themselves to generically-independent objects that fall under the concepts conceived of.

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write: “Some object both has and lacks the property of being distinct from every object to which it is not self-identical,” without saying something true. A distinction could also be recognized between ‘conceiving of something’ and ‘it being true that that of which one conceives is not dependent on any act of conceiving of it.’ For instance, it could be asserted that one can conceive of an impossible object, but that, as a certain kind of type-dependent object, it is not true that the object conceived of has its particular identity apart from events of conception of that kind of conception.

10. Impossible objects, the laws of objects, and Abstraction I have considered impossible objects because making and apprehending any work of art depends fundamentally on singling something out with which the work is meant to be identiﬁed, and any object singled out will be understandably logically distinct from every object that is not so singled out, and it is just this identity-diﬀerence conjunction that singling out involves and to which the laws of objects apply. This at least must be the conceptual foundation on which investigating the limits of Abstraction is based and from which it proceeds. And it would seem that solving the problem of impossible objects depends on the recognition of ‘object,’ ‘identity,’ and ‘diﬀerence’ as concepts fundamental to our conceptual scheme, at least provisionally and perhaps unconditionally. If the basic notions of object, identity, and diﬀerence prove to be provisional, then they will nevertheless constitute rungs of the ladder that is used “to climb up beyond them.” If they are unconditional, then they must be conceptually retained, and the designation in language or the construction by consciousness of impossible objects does nothing to alter the basic notions on which all thought and discourse are dependent.

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——, Individuals: An Essay in Descriptive Metaphysics, Garden City, NY: Anchor Books (1963). Strayer, Jeﬀrey, “On the ‘Death of Art,’” in Butler, Clark, pp. 29–34. ——, “Consciousness, Art, and the Limits of Abstraction in Art,” in Meyer-Dinkgräfe (ed.) Consciousness, Theatre, Literature, and the Arts, Newcastle, UK: Cambridge Scholars Press (2006) pp. 278–295. Strickland, Edward, Minimalism: Origins, Bloomington, IN: Indiana Univ. Press (1993). Tamplin, Ronald (ed.), The Arts: A History of Expression in the 20th Century, Oxford: Grange Books (1991). Taylor, Richard, “How to Bury the Mind-Body Problem,” American Philosophical Quarterly 6 (1969) pp. 136–143. Tomkins, Calvin, The World of Marcel Duchamp, New York: Time-Life Books (1966). Tormey, Alan, “Indeterminacy and Identity in Art,” The Monist 58 (1974) pp. 203–215. Townsend, Dabney, An Introduction to Aesthetics, Oxford: Blackwell (1997). Twardowski, Kasimir, On the Content and Object of Presentations: A Psychological Investigation (translated with an introduction by Reinhardt Grossman) The Hague: Martinus Nijhoﬀ (1977). Varnedoe, Kirk, Pictures of Nothing: Abstract Art since Pollock, Princeton, NJ: Princeton Univ. Press (2006). Walther, Ingo F., Art of the 20th Century, Cologne: Taschen (2000). Weinberg, Steven, Dreams of a Final Theory: The Search for the Fundamental Laws of Nature, New York: Pantheon Books (1992). Weitz, Morris, “The Role of Theory in Aesthetics,” The Journal of Aesthetics and Art Criticism 15 (1956) pp. 27–35. Wölﬄin, Heinrich, Principles of Art History: The Problem of the Development of Style in Later Art, (Hottinger, M. D. trans.) New York: Dover (1950). Wolfram, Sybil, Philosophical Logic: An Introduction, London: Routledge (1989). Wollheim, Richard, “Minimal Art,” in Battcock, Minimal Art, pp. 387–399. ——, “The Work of Art as Object,” in Harrison and Orton, Modernism, Criticism, Realism, pp. 9–17. Wood, Paul, Conceptual Art, New York: Delano Greenidge Editions (2002). Yanal, Robert J. (ed.), Institutions of Art: Reconsiderations of George Dickie’s Philosophy, University Park, PA: The Pennsylvania State Univ. Press (1994). Ziﬀ, Paul, “Art and the ‘Object of Art,’” in Elton, William (ed. and introductory essay) Aesthetics and Language, Oxford: Basil Blackwell (1959).

INDEX

abstract/Abstract 1 n. 1, 2, 4, 6–9, 13–14, 14 n. 2, 16–18, 18 n. 8, 19–21, 23–25, 31–33, 56, 57 n. 15, 58, 60, 68–70, 87, 97–98, 114, 147, 169, 172, 174–75, 186–88, 190, 209, 216, 224, 254 n. 8, 258–59, 261–63, 265, 279–81, 285, 289, 296 n. 2, 299–304, 307, 312–13, 317–18, 324, 328, 330, 338, 356 meanings and uses of the terms 1 n. 1, 8 ‘minimal’ and ‘reductive’ as synonyms of ‘Abstract’ 1 n. 1 Abstract art (Abstraction) 1 n. 1, 8, 13–30 art and 9, 19, 26–29 and artistic action 86–87 as an art-historical issue 2, 174 Essentialist (see Essentialism/ Essentialist Abstraction) and everything (see everything) history of 15–20 levels of 20–25 limits of 26–29 material of 30, 148, 175 and nothing (see nothing) and objects 1–2, 8, 10, 26, 30, 35, 147, 259, 267, 272, 296, 298 and philosophy 9, 19, 26, 28–29 and publicity 2, 86, 98–99, 114 and subjects 1–2, 8, 10, 26, 30, 35, 147, 259, 267, 272, 296, 298 acceptably derived objects. See relevant object(s) Acconci, Vito 89, 90 n. 1, 121, 158 Rubbing Piece 239 Adajian, Thomas xix, 64 n. 17 aesthetic empiricism 104–105 and embodied artworks (see embodied artworks) aesthetic experience 27, 121–28, 135, 137 and feelings 123, 126–27 the possible heterogeneity of 122, 126 and conceptual or intellectual objects 125, 280, 292, 304, 314–15, 317

and perceptual objects 125, 280, 292, 314–15, 317 as secondary 22 n. 12, 137, 153, 165, 269 and thoughts 126–27 aesthetic property 124, 128, 130–31, 134, 289 and artistic properties 132 the appreciation of 128–29 deﬁned 130 essential 234, 288–89 inessential 234, 289 as primary 137 as a property of interest 137, 146 agency 30, 82, 110–11, 171, 187–88, 233–34, 238, 238 n. 3, 253, 258, 261–62, 274, 277, 279–80, 297, 315 and artistic complexes 171, 187, 261, 274 and artworks 7 and awareness 30, 110, 171, 188, 279–80, 297, 315 and Essentialism 30, 187 history of agency 145–46, 293, 317 Andre, Carl 139 n. 15, 160 Equivalent VIII 160 Angelico, Fra 40 Annunciation 40 appreciable properties of artworks. See art and the aesthetic apprehension and reapprehension 234, 279, 293 art and the aesthetic 121–46 aesthetic property (see aesthetic property) aesthetic value and created artworks (see creation/created artworks) aesthetic value and participatory artworks (see participatory artworks) the aesthetic value of the idea for an artwork 121, 153, 155, 288 appreciable properties of art 128, 131, 133–34, 136 the apprehensibility of 131, 145, 154 art, the aesthetic, and the interesting 136–39, 144

376

index

artistic perspective 129–30 artistic property (see artistic property) and conceptual or intellectual objects 125 the distinction between 121 and Essentialism (see Essentialism) events of art appreciation 129 the Intentional direction of 131 and perceptual objects 122 the possible extension of the notion of the aesthetic 122–23 possible sources of artistic interest 137 art appreciation. See art and the aesthetic art and philosophy in relation to Abstraction 26 artistic complex(es) 3, 30, 149–50, 155–58, 165, 170–71, 176, 192–93, 200–201, 234–35, 253, 258, 261–62, 272–74, 280, 291, 299, 306, 353 and artistic identity 312 appropriate apprehension of 3, 155 and becoming 272–74, 315 and consciousness 233 as cognitive 265–66 conception 265 perception 265 deﬁned 3, 149 diagram of 150–51, 157, 183 essential elements of 4–8, 30, 32–33, 146, 148, 150, 179, 186, 191, 199–200, 230, 233–34, 265–67, 273, 279, 285, 291, 301–302, 305, 313–14, 318, 328, 333–34, 338–39 and metaphysics 89–90, 112, 322, 337, 340 as philosophically coterminous 147, 291 and Essentialism 4, 291 and ideational objects 233 and relevant objects 156 and subjects 156 artistic identity. See identity of an artwork artistically-independent objects 140–41 the aesthetic value of 141 artistic property 129–31, 133, 139 and aesthetic properties 1, 21, 120, 126, 132, 234, 293 the appreciation of 129 deﬁned 128 artist(s). See artwork(s)

artist’s identiﬁcation of an artwork. (See identity of an artwork) artwork(s) 35, 37, 121 and accidental actions (see intentions/intentional relations of an artist to an artwork) and aesthetic properties (see aesthetic property and see art and the aesthetic) and appropriate apprehension of 3–4, 154–56 art-historical sense of 35, 86, 101, 104, 121 and artifacts 82 n. 30, 119–20 and artistic properties (see artistic property and see art and the aesthetic) and artists 2–3, 18, 20, 35, 37, 50, 62, 100, 104, 113, 117–118, 156, 173, 208, 237, 296 the minimal conceptual relation of artist to artwork 78 and the artworld 35 atemporal (see time(s)) and change (see causality and change) and conceptual idealism (see conceptual idealism) as conceptually delineated objects 50, 80 and cultural contexts 85, 158 dependence on consciousness 208 determinate (see determinate artworks/objects) and documentation 149, 164, 168 eﬀecting the identity of 171, 238, 247, 333 embodied (see embodied artworks) and everything 297 and existence (see existence/existential objects) and existential objects (see existence/existential objects) ideational (see ideational artworks) identity of (see identity of an artwork) identity dependence (see identity-dependent objects/identity dependence) indeterminate (see indeterminate artworks/objects) and intentions (see intentions/ intentional relations of an artist to an artwork) judgements of value of 134 kinds of 118

index temporal and atemporal (see time(s)) making or producing 52, 90 the expansive notion of eﬀecting artworks 53 and media (see medium/media) and metaphysics 90 non-embodied (see non-embodied artworks) and non-existential objects (see non-existential objects) and nothing 297 and objects 2, 53 apprehensible 69 kinds of 115 non-apprehensible 94–95 physical 119 public perceptual (see publicity/public objects) wide use of (see object(s)) and ontology 95 participatory (see participatory objects) and parts (see compositional relations) possible nature of 91, 158 and preexistent objects 89 and the metaphysics of personhood 89 and public perceptual objects (see publicity/public objects) and relevant objects (see relevant objects) and reproduction 164 and subjects 2 temporal (see time(s)) and tokens of a type 163 and type dependence (see type dependent objects/type dependence) artworld 2, 19, 26, 35–37, 37 n. 1, 41, 44, 52, 81, 86, 112–14, 128, 138, 152 as a sociological institution 2, 37 deﬁned 35 Essentialism and 36 institutional theory and 37 n. 1, 128, 138 object aspect of 35 subject aspect of 35 Ayer, A. J. 350 n. 4 awareness of and awareness that 74, 77–79, 122 n. 2, 133–34, 136, 155, 171, 208, 229, 246, 299 See also the identity of an artwork

377

Barry, Robert 19, 42, 67, 67 n. 21, 94–95, 114, 162 n. 5, 252, 278, 304 Again and Again 162 all the things I know but of which I am not at the moment thinking-1:36 PM; June 15, 1969 20, 45, 67–68, 95, 102, 106 n. 9, 108, 118, 131, 142–43, 153, 160, 168, 227, 252–53, 312, 337 as a speciﬁed noumenal artwork 172 Everything in the unconscious perceived by the senses but not noted by the conscious mind during trips to Baltimore during the summer of 1967 83 Inert Gas Series (Helium): From a Measured Volume to Indeﬁnite Expansion 42, 109, 156, 168, 242 as selected non-embodied artworks 242 Bartok, Béla 4 Beardsley, Monroe 86 n. 32 Binkley, Timothy 39 n. 2, 48 n. 8, 121 n. 1, 252, 252 n. 6, 297, 297 n. 3 Black, Max 349 n. 3 Bochner, Mel 24, 24 n. 16 Braque, George 18 Brueghel, Pieter 16, 16 n. 5 Hunters in the Snow 16, 16 n. 5 Buchler, Justus 55 n. 13 Burden, Chris 138, 139 n. 15 Bed Piece 138 Shoot 138 Burgin, Victor 161 n. 3, 304 All Criteria 271 n. 15 Idea Structures Project 161, 173 n. 2, 271, 276 Butchvarov, Panayot 54 n. 11 Butler, Clark xix, 27 n. 19, 67 n. 20 Butterﬁeld, Jan 96, 96 n. 1, 97 Calder, Alexander 270 causality and artworks 274 and artistic complexes 234 and Essentialism 258–59, 264–65, 265 n. 12, 266, 272, 279–81, 285, 287 modiﬁcation 267, 279 artworks that incorporate change 270 Cambridge change 271, 272 n. 16, 293 origination 267, 272–74, 279

378

index

and relevant objects 234, 250–52, 262, 273–74, 277–79, 285, 287 and temporal art forms 269 termination 267, 272–74 Cézanne, Paul 17–18 Cheetham, Mark 6 n. 4 Chisholm, Roderick 56 n. 14, 355, 355 n. 4 Christo 113 Running Fence 276 compositional relations 203, 205, 292 and ambiguous speciﬁcations 205 and embodied artworks 203 complex 204 simple 203 and Essentialism 205 and speciﬁed non-embodied artworks 204 complex 205 simple 204 Conceptual art 20, 23, 23 n. 15, 24, 30 n. 26, 36, 40, 46, 68, 83, 125, 143, 143 n. 17, 167 and Abstract art 24–25 and de-materialization 24 and Essentialism 30 conceptual idealism 111, 112 n. 13 concipient 233, 258, 262–63, 263 n. 11, 264, 315–17 and artistic complexes 233 deﬁned 263 and Essentialism 258 and ideational objects 233, 254–57, 261, 263–64 and meaning (see speciﬁcation/speciﬁed artworks) and speciﬁcations (see speciﬁcation/speciﬁed artworks) consciousness (conscious acts/events) (awareness) areﬂexive 179, 182–83 and art 171 Essentialist 173 Traditional 252–53, 301 and art-historical objects 35–36, 101, 113 and artistic complexes (see artistic complex(es)) conceptual 292 the conceptually primitive nature of 194, 198 and Essentialism (see Essentialism/ Essentialist Abstraction)

and dependent objects (see dependent objects, see identity-dependent objects, and see type-dependent objects) ﬁrst order/lowest order 181–85, 226–27, 266, 292, 314, 352 deﬁned 181 the ﬁve fundamental forms of 183 diagram of 183 higher order 182–86 deﬁned 183–86 history of awareness 272, 278–79, 293, 314–15, 317, 351–52 apprehension and reapprehension 278 Intentional (see Intentionality/ Intentional events) irreﬂexive (see irreﬂexive consciousness/awareness) kinds of 115 memory 175, 280 monadic (see monadic consciousness) multifarious nature of 69 non-Intentional 71–73, 176–83, 212 perceptual 122 polyadic (see polyadic consciousness) as a necessary condition of apprehending the identity of an artwork 157, 169 as a necessary condition of making art 171–72 reﬂexive (see reﬂexive consciousness/awareness) second order 181–85, 213–14, 292, 314, 351–52 deﬁned 181–82 structure of (see Intentionality/Intentional events) and traditional art 301 contiguous and noncontiguous times (see time(s)) continuous objects/continuity 282, 284 and artworks 282, 284–85 deﬁned 282, 284–85 and Essentialism 282, 284–85 and relevant objects 282, 284–85 creation/created artworks 144–45 and aesthetic value 144–45 Cubism 18, 50, 140 Currie, Gregory 104, 105 n. 8

index Dadaism 2 and Abstract art 2 Danto, Arthur C. 9, 10 nn. 5–6, 26 n. 17, 37 n. 1 David, Jacques-Louis 67–68 The Death of Socrates 67–68 Davies, David 105 n. 8, 106 n. 9 de Kooning, Willem 17 Excavation 17 de Maria, Walter 19, 161, 270 Lightening Field 19, 161, 270 Denis, Maurice 17 n. 6 dependent objects/dependence 206–208 and the acts on which they depend 209–10 possible logical equivalence of 209–10 possible metaphysical equivalence of 209–10 actual and possible awareness of 208 and artworks 202, 223 wholly-dependent objects 223–24 partially-dependent objects 223–24 and Essentialism 224 the heterogeneity of 209 in general 209 identity-dependent objects (see identity-dependent objects) the implicit relation to consciousness of 211 multiply 222 deﬁned 222 heterogeneous 223 homogeneous 223 original 102, 150, 152 and artistic intentions 150, 153 partially-dependent objects 223–24 and relevant objects 192 and artistic intentions 192 singly 222 and subjects 192 subsequent 102 type-dependent objects (see type-dependent objects) wholly-dependent objects 223–24 derived object(s). See relevant object(s) determinate artworks/objects 60 deﬁned 60 Dewey, John 28 n. 20 Dickie, George 26 n. 17, 37 n. 1, 48,

379

48 n. 8, 86 n. 32, 121 n. 1, 128, 128 n. 9, 130–31, 131 n. 11, 252, 252 n. 6 Diebenkorn, Richard Ocean Park series 296 Dipart, Randall 86 n. 32 Dirac, Paul 125, 125 n. 6 direct and indirect relation of an artist to an object used to make an artwork 83 discontinuous objects/discontinuity 283 and artworks 284 deﬁned 283 and Essentialism 285 and relevant objects 285 distinction, discrimination, and distinguishability 351 Duchamp, Marcel 19–20, 40, 51, 62, 83, 92, 105–107, 109, 113, 113 n. 14, 121, 129, 138, 142–43, 164, 166–67, 241, 268 unassisted readymades 40, 62, 83, 105–106 121, 142–43, 167 Bottle Rack 107, 166–67, 241 Fountain 113 n. 14, 129, 268 In Advance of the Broken Arm 83, 92, 138 Large Glass (The Bride Stripped Bare by Her Bachelors, Even) 268 Eaton, Marcia Muelder 125, 125 n. 7, 126, 126 n. 8, 143 n. 17 embodied artworks 103–104 and aesthetic empiricism 104–105 and creation 237 deﬁned 103–104 diﬀerent kinds of appreciation of 106 and Essentialism 103, 114 n. 15 and perceptual objects 103–112 and relevant objects 102 and selection (see selection) and speciﬁcation (see speciﬁcation) ways of producing 107 equivalence 209–10 logical 209–10 metaphysical 209–10 essential elements of artistic complexes. See artistic complex(es) Essentialism/Essentialist Abstraction 4–6, 29–33, 103, 139, 146, 148, 164, 174–76, 186–87, 191–92, 194, 198, 201, 205–206, 224, 230,

380

index

233–35, 258–59, 264–66, 272, 279–80, 285, 287, 289, 291, 300, 311, 313–14, 328–29, 334, 337–38, 353 the aesthetic of 21, 27 and art 26 art criticism and art history and 156 and conception 13 and dependent objects (see dependent objects/dependence) and forms of awareness 266 and ideational objects (see ideational artwork(s)/object(s)) and identity (see identity) and independent objects (see independent objects/independence) insular and hermetic nature of 311, 313 and kinds of awareness 314 and language (see speciﬁcation/ speciﬁed artworks) the material of 30, 147, 175 and meaning (see speciﬁcation/ speciﬁed artworks) and media (see medium/media) and metaphysics 337 and Modernism 29–32 and identity (see Modernism) and reﬂexivity (see reﬂexivity) and its objects 26, 30, 35 and participatory artworks (see participatory artworks) and perception 185 the principles of 26–27, 33, 201, 298 the notion of 5–6 and philosophy 26 and reﬂexivity (see reﬂexivity) and simplicity and complexity 7 and speciﬁcation (see speciﬁcation/speciﬁed artworks) things for the Essentialist to consider 5 things relevant to the nature of an Essentialist object 267 everything 297 and Binkley 297 and Essentialism 297 existence/existential objects 58 and artistic complexes 3–5, 8, 154, 158, 171, 310 and artworks 58 current 60 deﬁned 58

and Essentialism 4 future 58, 60, 98 past 58, 60, 98 Findlay, J. N. 359–60, 360 n. 10, 364 Flavin, Dan 18 forms of conscious event of interest to Essentialism. See Essentialism/ Essentialist Abstraction Fowkes, William 23 n. 15 Fried, Michael and Minimalism 296 n. 2 and theatricality 296 Fulton, Hamish 113 Future 71 closed conception of 71, 140 n. 16 open conception of 71, 140 n. 16 Gauguin, Paul 17 Fe Tata Te Miti 17 Geach, P. T. 272 n. 16 Giacometti, Alberto 40 Suspended Ball 40 Godfrey, Tony 143 n. 17 Gogh, Vincent van 17 Starry Night 17 Goya y Lucientes, Francisco José de The Third of May, 1808 295 Graham, Dan 113 Greenberg, Clement 29, 29 nn. 21, 24, 31 Grossman, Reinhardt 56 n. 14, 354, 359, 359 n. 9, 360, 364 Haacke, Hans 270 Proposal: Poll of MOMA Visitors 270 Haecceity 198, 321, 330–37, 340 and artworks 76 as a core logical property of objects 196–99 deﬁned 321 and Essentialism 333 and existential objects 339 and the ﬁrst law of identity and diﬀerence 195, 331 and the laws of objects 198 as the minimum condition of diversity 333 Haines, Victor Yelverton xix, 48 n. 7 Harries, Karsten 135 n. 13 Harris, Jonathan 31, 31 nn. 27–28 Harrison, Charles 22 n. 11, 31 n. 6, 86 n. 32, 101 n. 6, 113 n. 14

index Hegel, G. W. F. 21–22, 22 n. 13, 23, 23 nn. 13, 15, 27 Heizer, Michael 113 Hume, David 356 ideational artwork(s)/object(s) 257 deﬁned 257 and Essentialism 258–59 and participatory artworks 146 n. 18, 258, 305 and perceptual objects 250, 253, 265 relation to an essential element’s use to eﬀect it 310–11 and speciﬁcation (see speciﬁcation/speciﬁed artworks) and subjects 238, 259 and agency 238 and consciousness 238 two kinds of 146 n. 18, 302 identity 300–301 and artists 300 and artworks (see identity of an artwork) and audience 300 and comprehension 303 and diﬀerence (see identity and diﬀerence) and Essentialism 31, 313 and artists 313 and audience 313 and Essential elements of artistic complexes 314 and ideational objects 301, 304, 307 and its relation to things used to eﬀect it 309 logical 194 as primitive 194 particular 197–98 and speciﬁcation 205 strict 335 and Leibniz’s law (see Leibniz’s law) identity and diﬀerence 194–96 and artistic complexes 200 and Essentialism 198 laws of (see laws of identity and diﬀerence) logical diﬀerence as primitive 194 and number 196 identity-dependent objects/ identity-dependence 212–16 and artworks 202

381

and complexity 216, 221 and Essentialism 205 in general 212 relation to a time 212–213 and simplicity 216, 221 and subjects 206 Type-A 213 and artworks 220 deﬁned 213 and events of awareness 214, 219 and Intentional objects 214, 218 and phenomenal and noumenal objects 215, 220 Type-B 215 and artworks 216 deﬁned 215 and phenomenal and noumenal objects 216, 221 identity of an artwork 74 artistic versus philosophical 47 an artist’s eﬀecting 111 artistic 95 comprehension of 94, 102 deﬁned 74 dependence on an apprehensible object 93 epistemological aspect of 76 and Essentialism 198 as essential knowledge/understanding of 94 logical aspect of 76 and noumenal objects 69, 73, 77 the particularity of 92 and similarity 92 and perceptible objects 110 and phenomenal objects 69, 73, 77, 98 philosophical 47 relevance to the ontology, meaning, and value of the work 95 relevant objects and 102 identity of indiscernibles 343–50 application of diﬀerent versions to diﬀerent objects 345 in general 343 logical version 349 application of 349 metaphysical version 346 application of 346 impossible objects 353–65 and Abstraction 365 and art 353 and conceiving 363

382

index

deﬁned 353 diﬀerent views of 354, 359 Findlay on 359–60, 364 Grossman on 354, 359–60, 364 Meinong on 354–57, 359, 364 relation to consciousness 362 Russell on 357 and the laws of objects 365 and the laws of thought 356 as type-A type-dependent objects 360 and sameness (see type-dependent objects/type-dependence) independent objects/independence 225–31 biographical 227 and artworks 228 noumenal 228 and Essentialism 230 generic 225 and artworks 225 the form of awareness of 226 noumenal 225 phenomenal 225 necessary 229 and artworks 230 noumenal 230 particular 226 and artworks 227 the form of awareness of 227 noumenal 227 phenomenal 227 universal 228 and artworks 229 noumenal 229 indeterminate artworks/objects 43, 63–64, 79 deﬁned 43 indexicals 274–77 and agency 277 and artistic complexes 272 and awareness 274 deﬁned 274 and Essentialism 279–80, 285 and perceptual objects 277 Intentionality/Intentional events 176 and art 176 and artistic complexes 176 dyadic 180 and Essentialism 175, 186 irreﬂexive 178 reﬂexive 178 ﬁrst order (lowest order) 181 monadic (see monadic consciousness)

polyadic (see polyadic consciousness) and relevant objects 177 second and higher order 181 structure of 178 Intentional objects 176–187 deﬁned 176 irreﬂexive 179 reﬂexive 178 intentions/intentional relations of an artist to an artwork 80 and accidental actions 84 the artist’s conscious understanding of 81 and claims 81 explicit 81 implicit 81 as essential to artworks 60 two kinds 80 and novel artworks 82 and time 81 Inwood, Michael 22 n. 13 irreﬂexive consciousness/awareness 179 and Essentialism 186 polyadic 180 ﬁrst order 181 higher order 181 and relevant objects 179 Irwin, Robert 96–97 Retinal Replay Volume 96–97 Jacquette, Dale 135 n. 13, 324 n. 6 Johns, Jasper 114 Judd, Donald on actual space 22 Fried on 135 n. 13, 136 n. 14 and the interesting nature of artworks 135 Untitled 160 judging something as a work of art versus judging something to be a work of art 130 Kandinsky, Wassily 17 Abstract Watercolor 17 Kant, Immanuel 28, 356, 359 Kawara, On 66 n. 18, 68 kinds of conscious event of interest to Essentialism. See Essentialism/ Essentialist Abstraction Kirchner, Ernst Ludwig 105 Street, Dresden 105 Klein, Yves 19

index knowing that 188–92, 209, 236, 296, 315, 337 knowing what 188–89, 191–92, 295, 315 knowing which 188–92, 295, 315 Kosuth, Joseph 18, 23–24, 68, 113 Any Five Foot Sheet of Glass to Lean Against Any Wall 18, 23–24 language and art 243–44 information and non-embodied selected artworks 242–43 speciﬁcation (see speciﬁcation) laws of identity and diﬀerence 195–97, 340–43 and the law of contradiction 342 and Leibniz’s law (see Leibniz’s law) and objects 198 and number 196 statement of 195 laws of objects/logical conditions of objects 58 legitimate ﬁne-arts context 36, 86 Lehrer, Keith xix, 158 n. 2 Leibniz, G. W. 335–36, 340–43 Leibniz’s law 335–350 and haecceities 335 and the laws of objects 337 as regulating strict identity 335 Levinson, Jerrold 45–46, 46 n. 6, 47, 54 n. 12 LeWitt, Sol 60, 101, 101 n. 6, 116, 116 n. 1 Lippard, Lucy 109 n. 11, 110 n. 12, 143 n. 17, 161 n. 3, 173 n. 2 logical equivalence. See equivalence. logical space. See space Long, Richard 113 Lowe, E. J. 57 n. 15 Malevich, Kasimir 23 White on White 23 Mally, Ernst 354–57 Man Ray 92 The Enigma of Isidore Ducasse 92 Marden, Brice 22 The Dylan Painting 22 Margolis, Joseph 104 n. 7 Matisse, Henri 74, 95, 166–67, 288, 296 Bathers by a River 74, 166 The Piano Lesson 95 Red Studio 288 McGinn, Colin 178 n. 6, 321, 321 n. 2, 322

383

medium/media 234–53 agency as 261 consciousness as 247, 261 as conveying the nature of an artwork 235 and embodied artworks 239 created 239 selected (see selection/selected artworks) speciﬁed (see speciﬁcation/speciﬁed artworks) and Essentialism 259, 264 and ideational artworks 257 and language 243 and non-embodied artworks 242 and non-perceptual events 245 and objects 237 and parts of artworks 250 relevant objects as 250 the restrictive notion of 238 and singling something out 251 speciﬁcation (see speciﬁcation/ speciﬁed artworks) and non-embodied artworks (see speciﬁcation/speciﬁed artworks) two notions of that pertain to the identity of an artwork 235–36 conveying the identity of an artwork 235, 238 eﬀecting the identity of an artwork 236 Meinong, Alexius 50, 56 n. 14, 354, 354 nn. 1–2, 355, 355 n. 3, 356–57, 359, 364 metaphysical equivalence. See equivalence. Meyer, James 19 n. 9 Meyer, Ursula 18, 18 n. 7 Michelangelo 21 Pietà 21 Minimal art (Minimalism) 2, 296 and Abstract art 2 and Essentialism 4–8 Modernism 29–32 and Essentialism (see Essentialism/ Essentialist Abstraction) and identity 31 and reﬂexivity (see reﬂexivity) monadic consciousness 179 areﬂexive 179 deﬁned 180 ﬁrst order 181 Intentional 176 non-Intentional 177

384

index

reﬂexive 178 and Essentialism 186 second order 181 Mondrian, Piet 18 Monet, Claude 17 Morris, Robert 19 n. 9, 160, 270, 296 n. 2 Untitled (Four Mirrored Cubes) 160 multiply-dependent objects (see dependent objects/dependence) Nauman, Bruce 21, 160 Green Light Corridor 21, 160 Newman, Barnett 246 Cathedra 246 non-embodied artworks 107–10 deﬁned 107 dependence on perceptual objects 110 and documentation and information 109 and eﬀected objects 244 and Essentialism 103 and non-perceptible objects 107 and preexistent objects 40, 42, 83, 89, 92, 268 and relevant objects 102, 154–55 and selection (see selection) and speciﬁcation (see speciﬁcation) non-existential objects 58 and artworks 58 deﬁned 58 and Essentialism 186 non-ideational artwork(s)/object(s) 259 deﬁned 259 Essentialism and 259 speciﬁcation and 259 non-Intentional events of consciousness. See consciousness (conscious acts/ events)(awareness) non-recurrence 280–81 and artworks 280–81 deﬁned 280–81 and Essentialism 281 nothing 297–98 and Abstraction 297–98 and Essentialism 297–98 and intentions noumenality/noumenal objects 69, 72 and artworks 62, 77 and awareness 69–70 deﬁned 72 and Essentialism as non-phenomenal 73, 77–78

and phenomenality 73, 277 and the present 73 and speciﬁcation 70, 76 object(s) 147–70 and artistic complexes (see artistic complex(es)) artistically independent 140–41 and artworks 140, 153 original dependence 150–52 the conceptually primitive nature of 56 consciousness and the concept of object 321 and idealism 111, 112 n. 13 continuous (see continuous objects) the core logical properties of 196 dependent (see dependent objects) determinate (see determinate artworks/objects) as equivalent to thing or entity 57 and Essentialism (see Essentialism/ Essentialist Abstraction) existential (see existence/existential objects) discontinuous (see discontinuous objects) ideational (see ideational artwork(s)/object(s)) and identity and diﬀerence 195 interdependence of the notions of 195 impossible (see impossible objects) independent (see independent objects) indeterminate (see indeterminate artworks/objects) intellectual 122–25 Intentional (see Intentional object(s)) laws of (see laws of objects/logical conditions of objects) liberal notion/unrestricted application of 53, 58, 83 the logical particularity of 163 the logical conditions of/the logical limitations of (see laws of objects/logical conditions of objects) non-existential (see nonexistence/ non-existential objects) non-perceptual 20, 42, 101, 108–10, 122, 125 n. 5, 126, 156, 239, 242–43, 265, 302–303, 307 noumenal (see noumenality/noumenal objects)

index the ontologically neutral nature of 56 phenomenal (see phenomenality/ phenomenal objects) preferential use of ‘object’ 39 n. 1, 158, 196 n. 2 private (see privacy/private objects) and properties 324, 347 properties of (see properties) public (see publicity/public objects) relevant (see relevant objects) universal application of the notion of 53, 58, 83, 345 Opalka, Roman 169 Oppenheim, Dennis 92, 113 Gallery Transplant 92 original dependence. See relevant object(s) Osborne, Harold 14, 14 n. 4, 15 participatory artworks 145–47 and aesthetic value 145 and Essentialism 146 and ideational objects (see ideational artwork(s)/object(s)) parts and wholes. See compositional relations perceptual objects 96–114 and agency and awareness 110 a perceptual object as required for understanding the identity of an artwork (see identity of an artwork) and embodied artworks (see embodied artworks) and non-embodied artworks (see non-embodied artworks) the publicity of (see publicity/public objects) phenomenality/phenomenal objects 69, 71–73, 98–99, 133, 172–74, 188–89, 191, 215–16, 218, 220–21, 277–78, 352, 363 and artworks 71 and awareness 71 deﬁned 71 and Essentialism and noumenality 73 phenomenal equality 72 and the present 73 and privacy 98 and publicity 98 and relevant objects 102, 154–56 Picasso, Pablo 296 Guernica 296

385

Pillow, Kirk 116 n. 1 Pistoletto, Michelangelo 270 place of exhibition 36 Plato 123 Pollock, Jackson 94 Autumn Rhythm 94 polyadic consciousness 179–81 deﬁned 180 dyadic 180 ﬁrst order 181 Intentional 176 irreﬂexive (see irreﬂexive consciousness/awareness) non-Intentional 177 reﬂexive (see reﬂexive consciousness/awareness) second order 181 triadic 180 privacy/private objects 98–99 and artworks 98–99 deﬁned 98 and Essentialism 98–99 and phenomenality 98 properties 321–334 aesthetic (see aesthetic property) artistic (see artistic property) contingent 328 core 196, 198 haecceity (see haecceity) individuation of objects according to 332 logical 330 necessarily distinguishing 336 and art and Essentialism 336–37 and Leibniz’s law 335 necessary 328 non-reciprocal 327 n. 7, 328, 331 reciprocal 328–29, 331–32 non-core 199, 332 nonlogical 330 non-predicable 329 individual 329 universal 329 non-relational 326 particular 324 relational 326 monadic/insular 327, 331 polyadic/non-insular 327–29 repeatable 324 restricted 325 universal 325 publicity/public objects 98–100

386

index

apprehensible properties of which relevant to artistic identity 100 and art appreciation 129 and art-historical art 101 and artworks 99 deﬁned 99 and Essentialism as minimally perceptible 292, 101 as necessary but not suﬃcient 100 no a priori limitations on 100 and phenomenality 98 of relevant objects 100 Quine, W. V. O. 79 Ratcliﬀ, Carter 90 n. 1 Rauschenberg, Robert 75, 138, 151 n. 1, 153, 166, 236, 288 Bed 288 Erased de Kooning Drawing 138, 153 Factum I 151 n. 1 Factum II 151 n. 1 Monogram 236 readymades, unassisted. See Duchamp, Marcel. Also see selection/selected artworks recurrence 285 and artworks 287 deﬁned 285 and Essentialism 286 reﬂexive consciousness/awareness 178 and Essentialism 178 monadic 183 polyadic 183 reﬂexivity 19 n. 9, 31–32, 311–12 in Essentialism 31–32, 311–12 in Modernism 31 relevant object(s) (object(s) on which an artwork is relevantly dependent) 158 acceptably derived objects as 152 appropriate apprehension of 155 as cognitive 150 and artistic intentions 47, 50, 61, 82, 85, 88, 150, 229 artworks and 163–164 as a necessary condition of an artistic complex 154 deﬁned 154 derived objects and 152 diﬀerence from acceptably derived objects 153 documentation as 164

kinds of 165 the nature of 158 original dependence/original objects as 150 parts of artworks and 166 perception and 94, 111, 150, 185 as phenomenal 155 reproductions as 164 and tokens of a type 163 Rescher, Nicholas 112 n. 13 Rosenkrantz, Gary 13 n. 2, 57 n. 15 Rothko, Mark 104 Russell, Bertrand 124 n. 4, 196 n. 2, 271, 272 n. 16, 354 n. 2, 355, 355 n. 5, 356, 356 n. 8, 357 Sarratore, Steven xix, 33 n. 29 saying something and saying something true 364 Seamon, Roger xix, 125 n. 7, 143 n. 17 Searle, John 70 n. 24, 85 n. 31, 176 n. 4, 177 n. 5, 265 n. 13 selection/selected artworks 40–43 and categorial modiﬁcation 42 and documentation 42 embodied 241 non-embodied 108 and information 110 and intentions 39, 41–42, 44–45 moral constraints on 41–42 and non-perceptible objects 68 and perceptible objects 42 as preexistent 40, 42 unassisted readymades as 40, 83, 106 Serra, Richard 21 Torqued Ellipses 21 singling something out 39–69 and artistic conventions 67 and the arts in general 68 determinately 59 and Essentialism indeterminately 61 and intentions 66 one artwork but more than one object 66 possible lack of clarity in 66 as a requirement of any artwork 66 success and failure in 64 and the visual arts 68 singly-dependent objects. See dependent objects/dependence

index Smith, Barry 123, 123 n. 3, 323 Smithson, Robert 19, 113, 119 n. 4, 270 on art and physicality 119 n. 4 Spiral Jetty 19 space 200–201 and Essentialism 201 logical 200 the delimitation of by objects and artworks 201 Essentialism and the delimitation of logical space 201 Perceptual 201–202 physical 200 Sparshott, Francis 125, 125 n. 7 speciﬁcation/speciﬁed artworks 43–48 and artistic complexes 314 and artistic and aesthetic relevance 43 and artistic identity 95 and conceptual delineation 39 n. 2, 326 and concipients 233 deﬁned 43 and embodied artworks 244 and Essentialism 264 and ideational objects 259, 304 non-perceptual 307 perceptual 307 and intentions 43–44, 46 and language 43–52 and Levinson’s proprietary-right condition 45 the limits of 45, 47 as logically and epistemologically distinguishing 43 and meaning 362 as a medium 248, 250 and non-embodied artworks 108, 244 and non-perceptual objects 307 and philosophical identity 47 as preceding ontology 50 and propriety and morality 45 the referent of 43 and singling out 43 Strawson, P. F. 106 n. 9, 130, 130 n. 10, 131 subject(s) 35–38, 93–114, 147–70, 233, 295–318 and agency (see agency) and artistic complexes (see artistic complex(es))

387 and artworks 163–64 as conscious agents 146, 171 and consciousness (see consciousness) and Essentialism 30, 146–48, 164, 170, Part Three Division II passim, Part Three Division IV passim, Part Four passim and Intentionality (see Intentionality)

Taylor, Richard 359 n. 9 time(s) 157–58, 170, 234, 273, 280, 293 and artistic complexes 157–58, 170, 234, 273, 280, 293 and artworks 115 atemporal 115, 118 temporal 115, 118 contiguous 281 and Essentialism 6, 234, 271–74, 280, 284–85, 287, 317 instants and moments 281 intervals 281, 283 noncontiguous 281 the present 229, 267, 276–77, 285 n. 18, 298 timeless sense of ‘is’ 213 Tomkins, Calvin 113 n. 14 Tormey, Alan 86 n. 32, 116 n. 2 Townsend, Dabney 54 n. 12 Turner, J. M. W. 17, 92, 240 The Lake of Zug 92 Mercury Sent to Admonish Aeneas 17 Rain, Steam, and Speed—The Great Western Railway 240 Turrell, James 113 Twombly, Cy 159 The Italians 159 type-dependent objects/ type-dependence 51, 51 n. 9, 194, 207, 209, 216–24, 226, 230, 246, 251, 284, 286, 292, 314, 329, 360–65 and artworks 220–221 and complexity 221 and Essentialism 224 in general 217 and impossible objects 360 and non-existential objects 283, 287 and possible objects 50 and relevant objects 154 and sameness 361 and simplicity 221 and subjects

388

index

Type-A 14 n. 3, 213–22, 224, 230, 246, 284, 292, 329, 360 and artworks 220 deﬁned 217 and diﬀerent kinds of awareness 218 and events of awareness 219 and Intentional objects 218 and phenomenal and noumenal objects 220 Type-B 215–16, 220–24 and artworks 221 deﬁned 220 and phenomenal and noumenal objects 221

Velásquez, Diego 295 Las Meninas 295 Witasek, Stephan 123–24, 124 n. 4, 126–27 Wollheim, Richard 75, 75 nn. 27–28, 86 n. 32 Wood, Paul 22 n. 11, 101 n. 6, 109 n. 11, 110 n. 12, 113 n. 14 Ziﬀ, Paul 22 n. 12

Philosophy of History and Culture

1. HERTZBERG, L. and J. PIETARINEN (eds.). Perspectives on Human Conduct. 1988. ISBN 90 04 08937 3 2. DRAY, W.H. On History and Philosophers of History. 1989. ISBN 90 04 09000 2 3. ROTENSTREICH, N. Alienation. The Concept and its Reception. 1989. ISBN 90 04 09001 0 4. ORUKA, H.O. Sage Philosophy. Indigenous Thinkers and Modern Debate on African Philosophy. 1990. ISBN 90 04 09283 8 5. MERCER, R. Deep Words. Miura Baien’s System of Natural Philosophy. 1991. ISBN 90 04 09351 6 6. van der DUSSEN, W. J. and L. RUBINOFF (eds.). Objectivity, Method and Point of View. 1991. ISBN 90 04 09411 3 7. DASCAL, M. (ed.). Cultural Relativism and Philosophy. North and Latin American Perspectives. 1991. ISBN 90 04 09433 4 8. WHITE, F.C. On Schopenhauer’s Fourfold Root of the Principle of SuYcient Reason. 1992. ISBN 90 04 09543 8 9. ZEMACH, E.M. Types. Essays in Metaphysics. 1992. ISBN 90 04 09500 4 10. FLEISCHACKER, S. Integrity and Moral Relativism. 1992. ISBN 90 04 09526 8 11. von WRIGHT, G.H. The Tree of Knowledge and Other Essays. 1993. ISBN 90 04 09764 3 12. WU, Kuang-ming. On Chinese Body Thinking. A Cultural Hermeneu-tic. 1997. ISBN 90 04 10150 0 13. ANDERSSON, G. Criticism and the History of Science. Kuhn’s, Lakatos’s and Feyerabend’s Criticisms of Critical Rationalism. 1994. ISBN 90 04 10050 4 14. VADEN HOUSE, D. Without God or His Doubles. Realism, Relativism and Rorty. 1994. ISBN 90 04 10062 8 15. GOLDSTEIN, L.J. The What and the Why of History. Philosophical Essays. 1996. ISBN 90 04 10308 2 16. BARRY, D.K. Forms of Life and Following Rules. A Wittgensteinian Defence of Relativism. 1996. ISBN 90 04 10540 9 17. van DAMME, W. Beauty in Context. Towards an Anthropological Approach to Aesthetics. 1996. ISBN 90 04 10608 1 18. CHATTOPADHYAYA, D.P. Sociology, Ideology and Utopia. Socio-Political Philosophy of East and West. 1997. ISBN 90 04 10807 6

19. GUPTA, C. and D.P. CHATTOPADHYAYA (eds.). Cultural Other-ness and Beyond. 1998. ISBN 90 04 10026 1 20. WU, Kuang-ming. On the “Logic” of Togetherness. A Cultural Hermeneutic. 1998. ISBN 90 04 11000 3 21. DESJARDINS, Rosemary. Plato and the Good. Illuminating the Darkling Vision. 2004. ISBN 90 04 13573 1 22. MOFFITT, John F. “Inspiration”: Bacchus and the Cultural History of a Creation Myth. 2004. ISBN 90 04 14279 7 23. MOU, B. Davidson’s Philosophy and Chinese Philosophy. Constructive Engagement. 2005. ISBN 90 04 15048 X 24. BOULTING, N.E. On Interpretative Activity. A Peircian Approach to the Interpretation of Science, Technology and the Arts. 2006. ISBN-10: 90 04 15409 4; ISBN-13: 978 90 04 15409 4 25. STRAYER, J. Subjects and Objects. Art, Essentialism, and Abstraction. 2007. ISBN 978-90-04-15714-9