メイン Sleights of Reason: Norm, Bisexuality, Development
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03 December 2019 (21:30)
PHILOSOPHY / GENDER STUDIES “Somewhere between mere errors and dialectical illusions, Mader’s ‘sleights of reason’ are biases that derive from the ability of concepts to refer to themselves. Tendentious concepts such as ‘norm,’ ‘bisexuality,’ and ‘development’ purport to refer to actual objects, but actually refer only to their own ability to structure experience. Like Jacquemarts, they hammer home a way of thinking, repeatedly striking us as self-evident features of the world. By showing in detail how the three sleights of her subtitle came to govern modern conceptions of sexuality, Mader frees us from their conceptual bell tower.” — Andrew Cutrofello, author of The Owl at Dawn: A Sequel to Hegel’s Phenomenology of Spirit Mary Beth Mader is Associate Professor of Philosophy at the University of Memphis. She is the translator of The Forgetting of Air in Martin Heidegger by Luce Irigaray. sleights of reason sleights of reason “In addition to creating her own philosophical concept, Mary Beth Mader pulls off something no one else has even attempted, to my knowledge—namely, to bring Gilles Deleuze’s rigorous analyses of the nature of the concepts in What Is Philosophy? to bear on the concept of sexuality. The result is an injection of conceptual rigor into debates that hitherto have been more focused on historical considerations. This is a superb book.” — Daniel W. Smith, coeditor of Gilles Deleuze: Image and Text mader A brilliant and original reimagining of sexuality, Sleights of Reason examines how concepts lend themselves to power/knowledge formations. Many contemporary French philosophers make incidental use of the notion of a ruse. Its names are legion: “duplicity,” “concealment,” “forgetting,” and “subterfuge,” among others. Mary Beth Mader employs Gilles Deleuze’s philosophy of the concept to describe three specifically conceptual ruses, or sleights, that make up part of the conceptual support for the concept of sex. These are the sleights associated with the concepts of norm, bisexuality, and dev; elopment. Mader argues that concepts can trick us, and shows how they can effect conceptual sleights, or what she calls sleights of reason. She concludes by offering a robust synthesis of insights from Foucault and Deleuze to extend those into a proposal for a conceptual next step for imagining the structures of sexuality as eros. n o r m , b i s e x u a l i t y, d e v e l o p m e n t A volume in the SUNY series in Gender Theory Tina Chanter, editor SUNY P R E S S new york press mary beth mader mader hc.indd 1 12/3/10 7:30:42 AM This page intentionally left blank. SLEIGHTS OF REASON SUNY series in Gender Theory ———— Tina Chanter, editor SLEIGHTS OF REASON Norm, Bisexuality, Development MARY BETH MADER State University of New York Press iv ACKNOWLEDGMENTS Published by State University of New York Press, Albany © 2011 State University of New York All rights reserved Printed in the United States of America No part of this book may be used or reproduced in any manner whatsoever without written permission. No part of this book may be stored in a retrieval system or transmitted in any form or by any means including electronic, electrostatic, magnetic tape, mechanical, photocopying, recording, or otherwise without the prior permission in writing of the publisher. For information, contact State University of New York Press, Albany, NY www.sunypress.edu Production, Laurie Searl Marketing, Anne M. Valentine Library of Congress Cataloging-in-Publication Data Mader, Mary Beth. Sleights of reason : norm, bisexuality, development / Mary Beth Mader. p. cm. — (SUNY series in gender theory) Includes bibliographical references and index. ISBN 978-1-4384-3431-5 (hardcover : alk. paper) 1. Women—Sexual behavior. 2. Sex. 3. Feminism. I. Title. HQ29.M327 2011 306.7082—dc22 2010016007 10 9 8 7 6 5 4 3 2 1 ACKNOWLEDGMENTS v CONTENTS PREFACE vii ACKNOWLEDGMENTS ix CHAPTER ONE The Sleight of Reason 1 CHAPTER TWO Sleights of the Norm 43 CHAPTER THREE Sleights of Bisexuality 71 CHAPTER FOUR Sleights of Development 87 CHAPTER FIVE Conclusion 107 NOTES 123 BIBLIOGRAPHY 137 INDEX 143 This page intentionally left blank. PREFACE The work of many contemporary French philosophers of note makes incidental use of the notion of a ruse. Its names are legion: duplicity, concealment, forgetting, and subterfuge, among others. This book employs Gilles Deleuze’s philosophy of the concept to describe three specifically conceptual ruses, or sleights, that make up part of the conceptual support for the concept of ‘sex.’ These are the sleights associated with the concepts of ‘norm,’ ‘bisexuality,’ and ‘development.’ This book aims to identify the oft-obscured workings of these three concepts and to display the subtle collaborations of their components. For these components can work together to constitute sleights. Such sleights could also be called “conceptual Jacquemarts.” In the Jacquemart, we have a single machine whose internal differentiation permits its self-reference and whose self-reference permits trickery. A first component allows that a second component carries out chiming work that it does not; it mimes a chime. Other parts of the machine actually effect the chiming. The machine as a whole refers to itself precisely through the dissimulation of the source of the chime. The machine’s trickery requires self-reference. Similarly, concepts are ideal mechanisms that necessarily have the conceptual equivalent of this capacity for internal ventriloquism. This book attempts to draft the conceptual equivalents of horological technical figures for several complex conceptual Jacquemarts relating to the concept of ‘sex.’ Chapter 1 presents a general account of the sleight of reason. Chapter 2, on sleights of the norm, scrutinizes several basic moves found in certain elementary social statistical concepts through a reading of Foucault’s work on normalization and biopower. First, the conversion of discrete into continuous quantities that is effected with the statistical norm is examined so as to demonstrate the role of apparently simple tools of statistical measure in the constitution of social homogeneities. Second, an account of this conversion and similar operations is offered in terms of the concept of the ‘average’ or ‘mean’ in social statistics. Third, the existential function of these statistical orderings is sketched in an account of what is here termed “statistical panopticism.” Chapter 3 is devoted to sleights of bisexuality. The examination focuses on two interrelated sleights found in the Freudian construal of bisexuality vii viii PREFACE as the universal, coconstitution of each sex by both sexes. These are, first, the sleight of pure and impure sexes and, second, the sleight of what are termed here “microsex” and “macrosex.” Sleights of development are the topic of chapter 4. First, it exposes a sleight that pertains to the concept of ‘societal development’ according to which societies can be progressive or regressive. This sleight is relevant to the question of the relation between the concepts of ‘sexuality,’ ‘primitivity,’ and ‘societal evolution.’ It operates through a covert switching between two kinds of contemporaneity, temporal and normative. Second, Freud’s developmental accounts of sexuation and sexuality exemplify some sleights of sexual development. The section exposes duplicities in Freud’s cultural version of Ernst Haeckel’s biogenetic law and examines a proleptic fallacy in Freud’s teleological account of infantile eroticism in the context of his evolutionary thought. Identification and discussion of these three kinds of sleights of reason,1 then, occupy the bulk of this text. The book concludes with a chapter that attempts a synthesis of insights from Foucault and Deleuze to extend those, jointly, into a proposal for a conceptual next step for imagining the structures of sexuality as eros. ACKNOWLEDGMENTS For making me fortunate, I have many people to thank. Among them are my generous current and former colleagues in the University of Memphis Philosophy Department, whose gift to me was to let me go on my merry philosophical way. You can see, and so can they, the result of that liberty now. Should it occasion any regrets, their gravity would be utterly alleviated by that rare gift of freedom. So thanks galore to my colleagues, Robert Bernasconi, Nancy Simco, Leonard Lawlor, Tom Nenon, John Tienson, and Gene James. Robert Bernasconi, in particular, has been hors catégorie as a colleague, mentor, and friend. Other colleagues have my heartfelt thanks as well: from the old days, Sara Beardsworth, David Henderson, Alan Kim, and Ron Sundstrom; from the new days, Stephan Blatti, Pleshette DeArmitt, Bill Lawson, Sarah Miller, and Kas Saghafi. No one could be more grateful to our department chair, Deborah Tollefsen, than I. From historic days, I have my teachers—my supervisor, the late Bob Solomon, Kelly Oliver, Kathy Higgins, and Doug Kellner—to thank for their unwavering support. From prehistoric days, although they had no way of knowing this, I will always treasure the examples of Kathryn Pyne Addelson, John Connelly, Murray Kiteley, and Eric Reeves, all of Smith College. I am grateful to Dean Linda Bennett and the University of Memphis for sabbatical and travel support in the form of a professional development assignment in 2005–2006. The Society for Phenomenology and Existential Philosophy (SPEP) has been an invaluable forum for the presentation of portions of the work of this book, and member philosophers have been uniquely enthusiastic interlocutors. Ellen Armour, Debra Berghoffen, Andrew Cutrofello, Penelope Deutscher, Laura Hengehold, Lynne Huffer, Pierre Lamarche, Noëlle McAfee, Mary Rawlinson, Peg Simons, Alison Stone, Shannon Winnubst, and Ewa Ziarek have been delightful discussants. Catherine Mills, Kelly Oliver, Diane Perpich, Fanny Söderbäck, Tony Steinbock, and Elizabeth Weed have my gratitude for their editorial interest in my work. The Société Américaine de Philosophie de Langue Française, the Society for the Study of Difference, the Foucault Circle, and the Society for the Philosophy of History kindly invited work included in this book. The philosophical talent and curiosity of the University of Memphis Philosophy Department graduate students have been an inspiration to my ix x ACKNOWLEDGMENTS own thinking. I am grateful to them all, and especially to Bryan Bannon, Gabriella Beckles, Michael Burroughs, Cheri Carr, Jon Dodds, Kristie Dotson, Nico Garréra, Peter Giannopoulos, Erinn Gilson, Kathryn Gines, Kristin Gissberg, David Gougelet, Tamara Haywood, Marda Kaiser, Stacy Keltner, Anika Mann, Donna Marcano, Valentine Moulard-Leonard, Matthew Lexow, Arsalan Memon, Ann Murphy, Maia Nahele, John Nale, Jacob Neal, Carolyn O’Mara, Camisha Russell, Kris Sealey, and Cigdem Yazici. Special thanks to Amit Sen for unflagging solidarity. Cathy Wilhelm, Connie Diffee, and the late Lisa Andrews supplied administrative support without which . . . Friends have encouraged my work despite its evident menace to the time of our friendship. My deep thanks for this and for wisdom, patience, and emergency housing, to Gilberte de Poncheville and Patrick Maury. Mille mercis to dear friends in Paris for asking me the most skeptical questions. I am grateful to Roger Gathman for his generous and impossible erudition. I owe Carrie Laing Pickett a great debt for spontaneous rallying cries, philosophical curiosity, and proofreading. Many thanks for years of every kind of generous support to C. Roger Mader and Martine Mader. Thank goodness for Madeleine Mader, who always asked, and listened, about the book. Deepest personal thanks to Kyoo Eun Lee de New York. Responsible for a whopping share of my luck is the model editor Jane Bunker, editor-in-chief of State University of New York Press. She has my inescapable gratitude for her interest in and publication of this book and my utmost respect for her leading role in the cultivation of contemporary intellectual life in the United States. Anonymous reviewers of the manuscript have my awe and thanks for their insightful recommendations and comments and for the time and attention they devoted to the text. Were it not for the vision, care, and isotropic smarts of Tina Chanter, editor of the State University of New York Press series in Gender Theory, this book would not be. For being the grandest vector of my good fortune, thank you, Tina Chanter. ONE THE SLEIGHT OF REASON What happens to a diseased truth? .... Does it copulate with a lie And beget history? Is it a good mixer? Or does it sit silent at parties? —Burns Singer, Collected Poems “A GOOD MIXER”: FOUCAULT AND THE “FICTITIOUS UNITY OF SEX” Thought daily encounters motive to investigate further the operative ontologies of the social category of sex. Certainly, the social category of sex, as an attribute said to qualify human bodies, is an instrument central to the history of human domination. But whether or not to affirm the category, or which versions to affirm, continues to puzzle many. In fact, a number of disagreements in specifically feminist thought can be traced to divergent views about the nature of the social category of sex. Despite much exemplary work on the topic, there is still a great deal of confusion about the very sense of this category that is taken, from lived social experience, to be so basic to feminist inquiry and action. On a Foucaultian reading of the category, this confusion is a constitutive aspect of the kind of thing the category is, namely, a “fictitious unity.” He writes: “First, the notion of ‘sex’ made it possible to group together, in an artificial unity, anatomical elements, biological functions, conducts, sensations, and pleasures, and it enabled one to make use of this fictitious unity as a causal principle, an omnipresent meaning, a secret to be discovered 1 2 SLEIGHTS OF REASON everywhere: sex was thus able to function as a unique signifier and as a universal signified.”1 As many important works have done already, this book affirms Foucault’s claim about the category and seeks to amplify our understanding of the nature and operation of its unity. Of course, the inherent confusion of the notion of sex implies that there is an intrinsic limit to the degree of precision or clarity an account of the category could achieve. Indeed, it is difficult to know which strand of the practico-conceptual tangle of the category of sex to grasp first in attempting such an account. THREE CRUCIAL ELEMENTS: NORM, BISEXUALITY, DEVELOPMENT This work is motivated by the sense that this fictive category is a busy, gregarious one that operates with a loyal crowd of conceptual friends. Moreover, it seems that this cohort of supporting terms often works with a smooth and subtle power whose sources are obscure and often dimly identified. This book examines the question of how several of these supporting terms collaborate with the category of sex, seeking to press that question into what further exactitude is possible. Though there are many candidates from among these allies, only a few are examined in detail in this work: the notions of norm, bisexuality, and development. Moreover, only certain specific versions of these notions are the object of its study. It does not treat all, or even all of the most current versions, of these notions. But the notions chosen, and the versions of the notions chosen, are selected for two reasons: they are of great social and intellectual influence and prominence, and they are crucial to certain conceptual sleights that form and maintain the fictive unity of sex. It is in large part their fictions that comprise the operative unity of the category of sex. This book aims to expose the specific mechanisms of these conceptual sleights at work in the selected versions of the notions of the norm, bisexuality, and development. Plainly, many scholars, thinkers, and activists have had much of great value to say about these notions already. The proposals offered here have benefited greatly from existing work. The wager of this text is that despite this important existing body of thought, it is possible to locate and explicate the specific operations of these notions further still. One might locate its effort in relation to a summative characterization of his work in History of Sexuality, Volume I, that Foucault offers: “It is apparent that the deployment of sexuality, with its different strategies, was what established this notion of ‘sex’; and in the four major forms of hysteria, onanism, fetishism and interrupted coition, it showed this sex to be governed by the interplay of whole and part, principle and lack, absence and presence, excess and deficiency, by the function of instinct, finality, and meaning, of reality and pleasure.”2 In much thinking on the nature of social categories it is precisely this notion of an interplay of concepts, categories, or terms that seems both to be glimpsed and to remain in an obscurity that matches the notion’s apparent utility. THE SLEIGHT OF REASON 3 THE CONCEPTUAL SLEIGHT: COLLABORATION OF THE INCOMPATIBLE? The aim of this book is to present the dramatic “interplay” of elements that comprise the concepts of ‘norm,’ ‘bisexuality,’ and ‘development.’ Its claim is that certain such conceptual interplays should be recognized as “sleights,” that is, as conceptual collaborations that function as switches or ruses important to the continuing centrality and pertinence of the social category of sex. Like the concepts that compose them, such sleights are not authored by individuals but are marked by a quasi-independence and impersonality. They are not independent of practices, but their specific mutations, combinations, fragmentations, and collaborations cannot be laid at the feet of any particular author or set of authors. The theoretical account of the relation of concepts to each other that is best suited to the purposes of this work is that of Gilles Deleuze. Although the text cannot elaborate a genuinely complete theory of the concept, Deleuze’s thought on the concept provides a minimal framework within which we can understand the relevant kind of conceptual interaction.3 That said, however, the work to which the thought of both Foucault and Deleuze will be put in the course of this inquiry is not universally faithful to their own results, as will be evident. For the moment, let us ask: What is the importance of the enumerated terms in the quoted passage? What would be wrong with sex being “governed” by their “interplay”? After all, they are all standard philosophical terms, with a venerated history in Western philosophical discourse. Why should they be the objects of Foucault’s sustained genealogical argument against their governing role in this case? Why would they not be sage and trustworthy governors? The three concepts examined in this book can be linked to these suspect governing terms, though their senses are not exhausted by these terms. The concept of a norm depends on the notions of excess, deficiency, and in some cases, finality. This book argues that it also relies on the interplay between the notions of discrete and continuous quantity and between quality and quantity. The concept of bisexuality examined here relies on the interplay between whole and part. The concept of development treated here relies on the notions of principle and lack, absence and presence, as well as that of finality. The general problem with the conceptual relations that operate to make up the notions of norm, bisexuality, and development is that in the cases examined here they amount to sleights or to elaborate forms of equivocation. The book can be characterized, then, as an attempt to display the movements that make up these sleights of reason or conceptual switches. Playing-card trickery, an ancient form of entertainment and swindling, includes confidence games known as “card switches” in which one or more cards, or even whole packs of cards, are surreptitiously “switched out” or exchanged for others. Conceptual switches are equally convincing and difficult to detect. Like the hand movements of a card-switching specialist, these conceptual sleights most 4 SLEIGHTS OF REASON often are not perceived. This book does not identify or shackle an invisible hand at work behind these sleights—especially since they have no identifiable authors. It seeks instead to trace the conceptual equivalent of the obscured paths of the cards. In the cases examined, then, the “interplay” between the component concepts is not an innocent dialectic of some sort, but a collaboration (or colludication, since it is an interplay). It seems that existing work on the conceptual problems associated with the social category of sex can be enriched by close attention to the workings of the interplays or sleights permitted by the concepts of norm, bisexuality, and development. The main form of the sleights identified is switching between two or more different terms or concepts unknowingly. One main reason this sleight is unwitting is that we often ignore the fact that the sense of a concept depends on those with which it is “mixing.” Concepts combine by necessity with other concepts, but through these combinations they do not retain the same sense. The company a concept keeps is critical to its practico-semantic function. Yet too often we are duped by a verbal continuity or identity into missing changes in sense that depend on change in conceptual combination. Some would argue that the importance of these notions that are here claimed to constitute sleights has today waned into insignificance. But even if many of these sleights seem to characterize nineteenth-century thought more than contemporary thought, they still survive and operate today. It would take another book to extend the critique offered here to focus more completely on solely contemporary thought, but this could be done. For example, sleights of the norm can be found in some contemporary social scientific reasoning; sleights of sexuation persist in certain conceptualizations of sexuality, transsexuality, and gender in some work in the fields of psychology and medicine; and sleights of development persist in some work in economics, psychology, and sociobiology. The book does not argue that there are or could be no legitimate uses for the three elements that are its focus; there may well be. It aims, rather, to present what appear to be missteps in their conceptualization. Thinkers who have devised versions of or uses for these notions that are not part of the sleights outlined in this work therefore simply do not figure among its objects of study. THE CONCEPTUAL JACQUEMART This work employs Gilles Deleuze’s philosophy of the concept to identify and describe three specifically conceptual ruses, or sleights, that comprise part of the conceptual support for the concept of sex. These are the concepts of norm, bisexuality, and development. It aims to identify the often-obscured workings of these three concepts and to display the subtle collaborations of their components. The difficulty is that these components can work together THE SLEIGHT OF REASON 5 to constitute sleights. In addition to the figure of the card switch, such sleights may also be described by reference to the device called a “Jacquemart.” Also called “Jack.” Strictly, the model figure or automaton which strikes or appears to strike a bell at the hours or quarters. In watches, the term is generally applied to repeating watches where figures appear to strike bells but where, in fact, normal repeating work causes hammers to strike gongs. Such watches were popular in France and Switzerland during the early 19th century. Some, not strictly speaking Jacquemarts, depict unedifying subjects.4 JACQUEMART. The sleights at issue, then, could be called “conceptual Jacquemarts.” Several features of the concept as described by Deleuze are important for the book’s account. According to his philosophy of the concept, the concept contains heterogeneous components that are ordinally related or characterized by a position in relation to each other, and are necessarily posited by the concept to go together, in fact, to be inseparable. Further, the concept itself “has no reference”5 but is self-referential. I would add the point that these features are related: the internal fragmentation of the concept, its composite nature, permits its self-reference. This book develops this account to show how these features of the concept permit the sleights that are the book’s focus. The multiple, heterogeneous nature of the concept permits its self-reference, and its self-reference permits the sleights of the reason that employs these concepts. These sleights take the form of switching emphasis among components and of diversions that obscure components’ conditioning by the components with which they are in relation. The relation of components to concept is such that though the concept has no reference, components refer to each other; it is the reference of the components that permits the self-reference of the concepts. However, since each component itself has no self-reference, components need not be conveyed in all of their interrelations at any one time and may assume an order within the concept that misleads not in reference to other concepts but with respect to their internal relations. Concepts are not self-referential by ostention, formal implication, comprehension, extension, intentionality, isomorphic mapping, or any number of other traditional construals of the reference of statements, propositions, judgments, or functions. They self-refer, rather, by ontological implication posited by the concept, which sets forth the internal consistency of the components of the concept in positing those components as inseparably united. How is the conceptual sleight like the Jacquemart? In the Jacquemart, we have a single machine whose internal differentiation makes possible its self-reference and whose self-reference makes trickery possible. A first component allows that a second component carries out the chiming work 6 SLEIGHTS OF REASON that the first component itself does. The machine as a whole refers to itself precisely through, or by means of, the dissimulation of the source of the chime. Concepts are ideal mechanisms that necessarily have the conceptual equivalent of this capacity for internal ventriloquism. This book attempts to draft the conceptual equivalents of horological technical figures for several complex conceptual Jacquemarts relating to the concept of ‘sex.’ DELEUZE’S CONCEPTUAL CONSTRUCTIVISM It is one thing to attempt to identify conceptual sleights and to trace the moves that compose them. But is quite another thing to try to offer a philosophy of what permits such sleights or, rather, to seek to describe in ontological terms what we mean when we say that sleights, ruses, or equivocations take place. How do they take place? How can we conceive of the conceptual sleights we will seek to identify? These questions take us somewhat beyond the specific content and contexts of the sleights, without removing our attention from them altogether. The proposal sketched here is that the philosophy of the concept, or the concept of the concept, that we find in the work of Gilles Deleuze can help to answer these questions. Deleuze offers a rich and complex theory of the concept, one whose intricacies and whose integral place in his own elaborate ontology are too grand to include in all its detail here. However, the wager here is that we can fruitfully and respectfully extract from that theory an account of the concept that may go some way to amplifying our understanding of the conceptual sleight. This application of Deleuze’s account to a meditation on the conceptual sleight will necessarily curtail the full reach of his thought and enter it into new theoretical contexts that will modify its functioning. Of course, the hope is that whatever torsion of the account thereby results will count as sufficiently illuminating to compensate for its possible departures from the exact uses to which Deleuze himself put it. The primary value of Deleuze’s theory for present purposes is its explicit construal of the concept as necessarily self-referential, and this in several ways. To understand the sleight that occurs on the conceptual level, and to attempt an ontological account of it, it is crucial to have the means to describe concepts as at least self-referential. One reason that this is crucial can be glimpsed in a preliminary manner by considering the language that philosophers so frequently use when discussing philosophical ruses. So often it is the concept itself that is thought to be misleading; the concept is often said to “purport,” “propose,” “suggest,” and not in an innocent way. Its observers lend it the ability to engage in trickery, subterfuge, or deception. If we do indeed accept the notion that the origins of such trickery can be sought in the concept itself, how should this capacity be understood? Ought it be located in the specific content of a given duplicitous concept? Or should it rather be sought in the very capacities and nature of the concept itself, as THE SLEIGHT OF REASON 7 a potential of what it is to be a concept? The hope of part of this book’s inquiry is that we might gain from considering the latter possibility. It arises from an affirmation and a hunch. The affirmation is of many philosophers’ identification of conceptual trickery; there is something important in their frequent plaints about such trickery and in their practically entomological zeal for tracking and classifying the ruses that have become old standbys. The hunch is that trickery in the concept depends centrally on its self-referential capacity. This suspicion is that the concept is internally multiple in the sense that it can take part of itself as an object, that integral to the concept is its having a component that indexes another of its components. It is this internal indexing that is essential to the nature of the concept, and ultimately, it is that which permits its subtle subterfuge. The concept conveys both a sense and an index—or value, status, rank, or level—linked to or about that given sense. But in every concept, not merely in concepts that participate in conceptual sleights, the sense of the concept is its evident face, while its self-indexical or self-referential capacity, although registered in any competent user of a concept, is operating smoothly in the wings. But this initial position on conceptual subterfuge will require refinement and modification, if we apply Deleuze’s account of the concept to it accurately. Deleuze’s reliance on the work of the philosopher Raymond Ruyer especially compels revision of this initial view. With respect to this revision, a point to keep in mind is that for Deleuze our insistence on conceiving of the concept as fundamentally referential obscures and ignores the singular nature of the concept that actually distinguishes it from things that refer. Note that the concept is self-referential, not referential, in Deleuze’s account. This focus on the singular nature of beings, on what a given kind of being can do that it alone can do—and that it can do alone—is characteristic of Deleuze’s philosophical style. It may be worth mentioning two other general points about Deleuze’s philosophical approach. First, he crafts extended criticisms of the Hegelian dialectic as a way of understanding difference. The central roles of negation and contradiction in the Hegelian dialectic come in for sustained attack in Deleuze’s writings.6 Here, then, we can expect that this “interplay” whose understanding we seek will not be, or be modeled on, the Hegelian dialectic, if we look to Deleuze for its illumination. Second, one implication of this is that the movement of the dialectic cannot be the sort of movement that a Deleuzian approach will contain. In the context of his account of the concept, this means that Deleuze’s discussion of a kind of movement in the concept cannot be conceived of on the dialectical model. The abandonment of this model and the retention of the notion of a kind of movement mean that Deleuze must look elsewhere for the type of movement sought. As we shall see, the work of Ruyer is one source for an allegedly nondialectical type of movement that Deleuze locates in the concept. 8 SLEIGHTS OF REASON CONCEPTUAL SLEIGHTS AND THE DELEUZIAN CONCEPT Self-reference in the concept permits a form of sleight specific to the concept and internal to it. The inseparable whole that is the concept is set up so its fragmentation into components allows the characterization of its components, that is, not just the affirmation of their existence, but their existence as x (and relative to other parts and to the whole). Self-reference means the relation between the components is characterized. Self-reference is what permits a status to be given to the relation between the components. What is the relation of self-reference to the conceptual sleight, as distinct from its relation to the concept per se? It is the self-reference of the concept that permits the conceptual sleight. This is so because a component of the concept can refer to other components, or to the whole, but not to itself. Recall that self-reference takes place on the level of the concept, not on the level of its components. In fact, it is the inability of a component to refer to itself that grounds its referential function. But what is it about conceptual self-reference that makes it the condition for the conceptual sleight? In its internal self-reference, the components of a concept can, in effect, misdirect, or misindicate which components are doing the purported work of the whole. For this reason, it may be noted, the ruse of the concept will not be any of the four illusions that Deleuze identifies as surrounding the plane of immanence.7 Nor will it be a matter of faulty reference per se, that is, a matter of reference to a nonexistent object. It is not that this cannot occur. But Deleuze would claim that the latter type of faulty reference has to occur with something that is referring, something discursive. For Deleuze, the concept is neither discursive nor referential: it is nonpropositional. Propositions, presumably, can refer falsely. But concepts, being fundamentally nonreferential, cannot refer in a way that opens them to the labels of true or false. Propositions can. Concepts refer to virtual events, not to actual states of affairs. The attempt of this book can be described as an effort to show how concepts, though nonreferential, still may be said to exhibit an intrinsic possibility for a kind of trumpery or error, if we start from Deleuze’s ontology of concepts. It is not an error of reference, or an illusion surrounding the plane of immanence, but a sleight of consistency, ordinality, connection, neighborhood, vicinity, and linkage. A conceptual component cannot refer to itself, but conceptual components are in a distinctive relation to each other, on Deleuze’s account. They are intensive parts of the concept and hence are described according to an ontology of intensities. This ontology constitutes a genuine historical alternative to ontologies of substance and form or form and instantiation that are canonical in Western philosophy.8 In Deleuze’s work, we see this alternative ontology progressively traced from medieval scholasticism to Spinoza to Bergson, Riemann, and Simondon. The ontology of intensities is developed throughout this history for the purpose of ontological descrip- THE SLEIGHT OF REASON 9 tion and classification of the variations found in qualities. Colors are more and less deep, sounds more or less loud, illumination more or less bright, temperatures more or less warm, altitudes more or less elevated, pressures more or less firm. The language of intensity aims to describe such variation and to situate it relative to other kinds of things. Obviously, it is most immediately related to the notion of quality or of a quality. Indeed, to understand Deleuze’s philosophy in general and his theory of the concept in particular, it is useful to keep in mind the philosophical question of the ontology of quality and the philosophical struggles over the relation between quality and quantity that have marked the history of Western philosophy. For the moment, it suffices to note that Deleuze’s philosophy of the concept explicitly and implicitly meets up with his general ontology of intensities. However, Deleuze will impart to this philosophy a distinctive twist; he gives an intensive and ordinal account of intensity instead of the extensive and cardinal account that he associates with Bergson. Deleuze’s intensive ontology is intensive “all the way down.”9 THE CHIEF FEATURES OF THE DELEUZIAN CONCEPT Description of the singularity of the philosophical concept is Deleuze’s aim in What Is Philosophy?10 There, the language of the philosophical concept is distinguished from the mathematico-scientific language of function, the logical language of propositions, and the aesthetic domain of percepts and affects. The characteristic features of the concept are that (1) it is interconceptually related; (2) it is of composite nature; it is constructed of components; (3) its components are variations; its components are distinct, inseparable, heterogeneous, and finite; (4) it is doubly consistent; (5) it is intensive; it is ordinal; (6) it is virtual; (7) it is in absolute self-survey, moving at infinite speed; (8) it is the point of coincidence of its components; and (9) it is self-referential and capable of saturation. Though these features themselves are related in many ways, their characters can be sketched somewhat independently. Interconceptual Relation Perhaps the most philosophically traditional feature of the concept, for Deleuze, is that every concept is related to other concepts. Its relation to other concepts is not just historical or genetic, but present; at any moment, the concept is always in relation to other concepts. This is a traditional characteristic in the sense that a number of other philosophers have included this feature in their thinking about concepts. Easy examples of this are Hegel and Frege. For Deleuze, this interrelation is also an infinite one; concepts can be blocked in their relation, but their unimpeded state is to “extend to infinity.”11 10 SLEIGHTS OF REASON Composite Nature Concepts likewise must be created—they are constructions—and this creation takes place from within this infinite network of concepts. Concepts are composed of components. The most important feature of this composition is that it posits the inseparability of the composed elements of the concept. Deleuze calls this posited inseparability the concept’s “consistency”: “[W]hat is distinctive about the concept is that it renders components inseparable within itself.”12 Hence, consistency in the context of his account of the concept does not mean a logical or formal compatibility with any other concept, component, object, state of affairs, referent, or logical law. It is rather the assertion of a linkage or togetherness, a con-existing or existing-with. It is the setting-together or posing-together of distinct elements. It is not the recognition that a given group of components ought to be together, but the positing of them (as) together. The togetherness in this case is conceived as a partially overlapping proximity. The partial overlaps create undecidable “zones of indiscernibility” but without blurring components into indistinction. In Deleuze’s words, “Components . . . are distinct, heterogeneous, and yet not separable. The point is that each partially overlaps, has a zone of neighborhood, or a threshold of indiscernibility, with another one.”13 As an example of this indiscernibility, Deleuze gives the example of the relation between the possible world and the face, two components of the concept of the other person. In his discussion of the relation between these two components, he suggests that each component requires the other. The component “face” expresses the component “possible world” since I grasp the existence of a possible world as it is expressed in or through the face of the other, and since I apprehend the face of the other as it expresses a possible world. This sort of example is perhaps conceptually more apt than the extensive language of set theory or Venn diagrams that Deleuze also employs to describe this undecidability: “There is an area ab that belongs to both a and b, where a and b ‘become’ indiscernible.”14 For, as will be seen later, Deleuze’s ontology of the concept breaks with extensive ontologies in favor of intensive descriptions. Components Are Variations Deleuze holds that “the concept’s components are neither constants nor variables but pure and simple variations ordered according to their neighborhood. They are processual, modular.”15 But how can the language of variations apply in the case of concepts? Deleuze’s first example of the application of this language of variations to the concept is the concept of the ‘cogito’ created by Descartes.16 This example shows the brilliance of Deleuze’s mature vision of the ontology of the concept. On this account Descartes’ ‘cogito’ is a concept with three components: doubting, thinking, THE SLEIGHT OF REASON 11 and being. As intensive ordinates, or elements ordered intensively, these three components are condensed in a point that at the same time circulates endlessly through them. The ontology here is that of an intensive quantity. For the concept “is immediately co-present to all its components or variations, at no distance from them, passing back and forth through them.”17 (This immediate pervasive, but mobile, presence should be understood on the basis of the concept of an absolute surface. This is discussed later in this chapter.) Deleuze argues that the ‘I’ of the cogito is the point of ‘condensation’ within the concept of the cogito; it is that which circulates, in a flash, among the component zones: doubting, thinking, and being. Deleuze calls these components “variations” or “phases of a variation,” specifying that doubt here is a phase of a variation, not a species of a genus. To be a variation on doubt is not the same thing as to be a species of the genus doubt. The phases of the variation on doubt can be “perceptual, scientific, obsessional doubt.” The same is the case for being and for thinking, which are likewise phases of a variation. Deleuze is trying to capture the sense that the concept includes elements, that these elements are given all at once, but that nonetheless there can be shifts of emphasis within that simultaneous givenness, depending on the ‘circulation’ of the concept’s internal point of condensation. This strange notion will require explication in terms that are presented later under the heading of “absolute surface.” In the case of the cogito, although we get the concept ‘I think, therefore, I am’ all at once, this unity and simultaneity are marked by an internal movement that takes place among the intensively related components. This internal movement, despite the interpenetration of all the components of the concept, that is, despite the fact that they constitute an intensive ordinate, is what ultimately constitutes the possibility for self-reference in the concept. For self-reference requires internal differentiation of some sort. In the concept’s self-survey, the internal differentiation of the concept occurs through the shifts in emphasis created by the internal ‘circulation’ of the point of condensation. Here, the ‘I’ passes through the zones of indiscernibility so: “The first zone is between doubting and thinking (myself who doubts, I cannot doubt that I think), and the second is between thinking and being (in order to think it is necessary to be).”18 The positing of these components or zones as together, or the positing-together of these components, is the concept’s reference to itself: its joining of these components together is its positing of itself as a concept. But I suggest below another potential of this internal form of self-reference, one that would make possible the conceptual sleight. Double Consistency The concept is also said to have an internal consistency, an endoconsistency. These zones of indiscernibility that create the inseparability of the 12 SLEIGHTS OF REASON components are the source of the concept’s internal consistency. The concept can have an external consistency, that is, a consistency in relation to other concepts, an exoconsistency. Intensity and Ordinality The concept is fundamentally and essentially compositional, intensive, ordinate. Relations in the concept are only ordinate. There are no relations of comprehension or extension. While the functions expressed in science include variables and constants, the concept’s components are pure variations. In fact, they are necessarily virtual variations rather than actual variables. What is an intensity, and how could a concept be one? First, on a traditional conception of it, an intensive quantity is linearly ordered but is not additive. A temperature is an example of an intensive quantity. As Justus Hartnack explains: In the number of an amount—the number expressing an amount of yards, feet, inches, and the like—the unit numbers are potentially extensive. They are absorbed into the number of the amount, but they can be recounted as extensive. However, if we talk about a degree, for instance a room temperature of 20 degrees C, then the degrees below the 20 degrees C never formed an extensive magnitude that was absorbed in the degree of temperature, in this case 20 degrees C. The degree cannot be verified by adding the degrees below 20 degrees C—as we can add the yards in order to verify the correctness of a length. In a room temperature of 20 degrees C, the degrees below 20 degrees simply are not there to be added up.19 But why is intensity ordinal? We can answer the question in Hegelian terms. In Science of Logic, Hegel writes: The determinateness of degree must, it is true, be expressed by a number, the completely determined form of quantum, but the number is not an amount but unitary, only a degree. When we speak of ten or twenty degrees, the quantum that has that number of degrees is the tenth or twentieth degree, not the amount and sum of them—as such, it would be an extensive quantum—but it is only one degree, the tenth or twentieth. It contains the determinateness implied in the amount ten or twenty, but does not contain it as a plurality but is number as a sublated amount, as a unitary determinateness.20 Here, the descriptor “unitary determinateness” is Hegel’s way of referring to what we would call, after Cantor, an “ordinal number.” It does not indicate the sum of an amount; hence it is not additive. It indicates a position, or pure THE SLEIGHT OF REASON 13 positionality; it is purely and fundamentally relational. But the relationality in question is ordered. On Lalande’s definition,21 ordinality is a transitive and asymmetrical relation. It is easy to see that ordinality is transitive: if first is prior to second and second is prior to third, then first is prior to third. It is likewise not hard to see that ordinality is asymmetrical: first is prior to second, but second is not prior to first. Though Deleuze certainly does not accept Hegel’s philosophy of quantity in its entirety, we can see in it some points of contact and thus use it to understand further the conversation on quantity to which Deleuze contributes. Consider Hegel’s description of the internal relations of an intensive quantity: “This relation of degree through itself to its other makes ascent and descent in the scale of degrees a continuous progress, a flux, which is an uninterrupted, indivisible alteration; none of the various distinct degrees is separate from the others but each is determined only through them.”22 Here, we can see several features that Deleuze holds are definitive features of an intensity and hence, of a concept: inseparability of components, or, here, degrees. It should be noted that one reason Deleuze does not use the language of degree with respect to an intensity or intensive quantity is that he rejects Hegel’s view that intensive quantity ultimately can be expressed as extension or with extensive language. Deleuze will not lend to “degree” an extensive sense.23 The substance of his disagreement with Hegel on the intensive nature of an intensive quantity is that Hegel holds that intensive quantities are divisible into extensive parts, while Deleuze insists that intensities are intensive “all the way down” or do not—without alteration—resolve into extensities or extensive parts. He does think that intensities are expressed in extensions or extended quantities, but not as themselves, if you will. Thus, the intensive quantity of heat can be expressed as an extensity in the spatial expansion of mercury in a thermometer, of course. But such an extensive expression is not the intensity that it expresses. Intensities are continuous quantities, but when divided they must change in kind, or their metric must change. In the description of intensity and intensive quantity, Deleuze uses the language of components—not even “parts”—to avoid language with extensive senses as much as possible. Deleuze holds that concepts are intensive ordinates, not that they resemble or are analogous to intensive ordinates. This means that the inseparability of the components of a concept is not merely analogous to the inseparability of the degrees of an intensive quantity. Though a concept is not identical to every intensive quantity, obviously, the inseparability of a concept’s components is identical to the inseparability of the degrees, parts, or components of any intensive quantity. If we remain with Hegel’s account, the inseparability of degrees in an intensive quantity is due to the continuous, scalar nature of the kind of quantity it is. Notably, although degrees are distinct from each other, they are not separable. Moreover, each is determined only through the others. Each degree of the 14 SLEIGHTS OF REASON twenty degrees of the air’s temperature is distinct, but each is determined only through all the others. And no degree is separable from the others. One could consider the intensive quantity of altitude as an example, as well. Though often defined as a distance, length, or height, this is not conceptually accurate, for our purposes. Clearly, altitude is not a distance, length, or height if by those measures we mean quantities that are symmetrical. For while a distance, length, or height can be measured from either end of the measured extension, this is not true for an altitude. This is because an altitude is a measure from or to a single reference point, a feature that renders it asymmetrical. We can see, then, that both temperature and altitude are intensive quantities and hence ordinal. How does the notion of succession relate to that of ordinality? In contemporary mathematical conceptions of ordinality, succession need not be a temporal succession. The notion of succession out of which the contemporary conception of ordinality grows implies a dynamic order unfolding over time. But contemporary understandings of ordinality retain the asymmetry and transitivity of the notion of temporal succession while subtracting the temporal priority and subsequence. This development is in part what Deleuze discusses and critiques in Difference and Repetition when he treats the history of the differential calculus: the progressive emergence of a static version of ordinality out of a temporal, successive version of ordinality. There the value of the discovery of the static notion of ordinality is contested; Deleuze agrees with the Bergsonian line of argumentation that charges that the singularity of the character of time is lost when it is spatialized through the notion of extensive quantity that is employed in modern static interpretation of the calculus. We can also distinguish Deleuze’s view of this development of the static ordinal interpretation of the calculus out of a dynamic, infinitesimal, fluxist interpretation from his valorization of the genetic power of virtual structures. Is the virtuality of ordinality to be attributed to its specific kind of gradational modality? That is, is the virtuality of ordinality a result of its particular potential or power to increase and decrease? If so, the increase and decrease are not best described numerically, for Deleuze. As Simon Duffy explains in The Logic of Expression, number expresses only by abstraction, and inadequately, the nature of intensive quantity.24 Deleuze holds this view because by “number,” here, he means “that which expresses extension.” An increase or decrease in an intensity may be represented numerically, but this would be to misconstrue the relation between degrees of that intensity and to deny the ontological nature of change in intensity. Change in intensity cannot be expressed adequately as a change in extension. Duffy explains this relative to Deleuze’s thought on Spinoza. He considers the Wilson scale of the hardness—an intensity—of minerals as an example of the differences between Deleuze and Hegel on this point. Differing degrees of hardness in a mineral are ordinally related. For Hegel these differences can be represented THE SLEIGHT OF REASON 15 as extensive differences. But, as Duffy puts it, Deleuze insists that “[i]n a scale of intensity, number lacks this quantitative significance, it rather indicates simply the position of any particular degrees in a linearly ordered series. Deleuze considers the immanent existence of singular modal essences, as different degrees of power, to be implicated in such a scale of intensity, and, therefore, that the relation between them should be considered to be ‘quantitative, rather than numerical.’ ”25 So it is clear that here Deleuze reserves “numerical” for that which does not include intensive quantity, but employs “quantitative” to include intensive quantity. One might think that this quantity is describable in terms of a variable, and of course this is done as a matter of convention today in the physical sciences. But in his treatment of intensive quantity, with respect to the ontology of quantities, Deleuze will reject the variable in favor of the variation. This position is clear in What Is Philosophy? as well as in Difference and Repetition. In both texts, Deleuze contends that the notion of variable is insufficient to grasp the modality of intensive quantities. This is because the variable carries the sense of ‘any one of a number of possible values’ while the variation does not imply this ultimately exclusive disjunction in which only a single value will, or may, replace the open variable; rather, the variation implies the ineliminable difference in intensive quantities. The relevant difference is between the term any one of and the term a, that is, between an ultimately definite particular and an indefinite singular. In his rejection of the variable as an apt descriptor of an intensive quantity, Deleuze shows his consistent preference for the singularity of the indefinite article over the particularity of the ‘no matter which one of.’ In the case of the indefinite article, singularity is precisely what one approaches in the mode of ‘a life,’ ‘a day,’ ‘a season,’ and not ‘any life,’ ‘any day,’ ‘any season.’ There is a substitutability implied in the sense of ‘any one of’ that is found in the notion of the variable. In the ‘any one’ it does not matter ‘which one’ is the one. This is exactly what Deleuze’s language of the indefinite means to deny or refuse. There is a singularity to what is expressed in the indefinite article, and this singularity is not the particularity that is expressed in the ‘any one of which.’ Deleuze constantly opposes particularity to generality and offers the language of the indefinite and singularity to avoid that opposition. The variable or the ‘any-one-of’ expresses the particular (chosen out) of the general, not the singular of the indefinite. THE COMPOSITION OF CONCEPTS The philosopher is a concept maker, hence, for Deleuze, essentially a composer. The concept must be created, but not out of nothing; it must be composed of components. But the specific kind of composition Deleuze has in mind must be specified. First, a word about what this kind of composition is not: 16 SLEIGHTS OF REASON it is not a partes extra partes composition, an assembling of parts whose full natures are external to each other. Deleuze does use the term modular to describe the relation of a concept’s components to each other. We will go astray, however, if we think of this term in the sense in which it is sometimes used in industry and commerce. For there it carries precisely the sense of an interchangeability of external parts, components that can be subtracted and added exactly without changing the remaining parts. Modularity in that industrial sense, that is, the sense of an indifferent substitution of equivalent parts (‘snap in, snap out’) is nearly the contrary sense of what Deleuze has in mind here. Second, then, what is the positive notion of modularity in effect here? It is the ideal of a continual variation, the sense of modulation that is closer to that used with respect to qualitative, or even intensive, variation. A sound that can be modulated with sound engineering technology is one susceptible to variation in a continuous manner.26 Consider a sound of a certain loudness, where that loudness is an ‘intensity’ of the sound. We may say that the whole of that sound is characterized by that certain intensity, its loudness. And on that basis we can compare it to other sounds, distinguishing some as of greater, lesser, or equal loudness. It may appear, then, that loudness comes in degrees, since we said “greater, lesser, or equal.” Or, at least, sounds seem comparable on the basis of loudness. But what kind of comparability is this, and what does it imply for the quantitative nature of what is being compared? Deleuze would argue that even if the loudnesses of the sounds, here conceived of as their intensities, can be described in terms of degrees, in order to understand these cases correctly, we must take seriously the relation of degrees to each other in intensive quantities or in ordinality. It is important to avoid the capital mistake of assimilating a degree to an extensive quantity or to its measure. For measures of extensive quantity—inches, meters, micrometers—measure parts that are external to each other and hence are additive, symmetric, and commutative. The term variation can be used to help avoid this error, instead of using the term degree. But in fact the history of discussion of intensity and intensive quantity includes frequent use of the language of degrees. The suggestion here is that attention be paid to whether or not an author’s use of this language of degree is meant to imply an extensive sense. In Deleuze’s work, it is clear that he does not mean it to do so. Part of the confusion on this issue can be attributed to the fact that intensive quantities can find extensive expression, though this expression must fundamentally differ in kind from that which it expresses; indeed Deleuze argues in Difference and Repetition that extensities are ultimately describable in terms of constituent intensities that have been annulled or canceled out in their extensive expression. Extensive expression of intensities certainly is a part of the physical descriptions of the world found in the THE SLEIGHT OF REASON 17 natural sciences. The sciences of intensities have their roots in philosophical accounts, in particular in ontologies like those developed in the philosophies of medieval European Christendom. But the ontology of intensities that Deleuze proposes departs significantly in a number of ways from contemporary scientific discourses on intensive quantity. For his position is that the expression of intensive quantities as extensive quantities must necessarily lose the essential features of intensive quantity in that expression. Hence, those expressions are effects or residues of their causes and contain their intensive causes in them implicitly. Qualities and extensities are the derelict residues of intensities. Of course, scientific and technical discourses on intensive quantity do not generally include this claim or worry that the intensive nature of intensive quantity itself is lost in its extensive expression, although Deleuze makes precisely that claim. But what do we mean by this notion of intensive quantity finding an extensive expression? Consider again the case of temperature. The registration of temperature in an analog thermometer is the spatial expansion of mercury. This extensive expression of an intensive quantity may suggest that the intensive parts or degrees of a temperature are additive, although they are not. A temperature of a body is not the result of adding separable degrees of temperature to each other but the result of successive registration of inseparable ‘parts’ of a varying quality. Described in traditional philosophical terms, temperature is a measure of the intensity of a quality, that is, its variation, rather than the extensity of a substance. The temperature of a body of ninety-eight degrees cannot correctly be described as the summing-together of ninety-eight separate degree units. Rather, the registration of temperature measures an ordered difference from a temperature, a zero point. In this regard, temperature is an intensive quantity like altitude. Despite the fact that many imprecise definitions of altitude class it as a distance, it is better described as a relational or relative distance. It requires a reference point and is a measure from that reference point. Moreover, and importantly, it is a measure from a single reference point, and hence is unidirectional. It is, then, fundamentally asymmetric. It is not the case that any two degrees of altitude bear the same relation to each other. This is another way of saying that altitude is an ordinal quantity. An intensive quantity, despite its somewhat deceptive expressions in extensive measures, cannot be measured from either of two ends for the reasons that it does not have two same kinds of ends and certainly does not have the kinds of ends that an extensive quantity has (namely, two of the same kind). We can measure a height or a distance from either end, but we cannot measure an altitude from either end.27 In fact, strictly speaking, an intensity in itself—Deleuze’s concern— should not be said to have ends. But its measure in the discourses of intensive quantity affirmed by Deleuze does imply that it has at least one ‘end’ of a kind. By this, I mean that ordinality when conceived geometrically and numeri- 18 SLEIGHTS OF REASON cally is often thought to require an ‘end’ as starting point (first, notably, in the series first, second, third . . . nth). And certainly at times in the history of Western metaphysics and mathematical philosophy, ordinality has been thought of as essentially successive, on the model of an enumeration or counting that unfolds over time. There, the idea of ordinality more likely carries with it the notion of temporal succession. Then, anything else conceived of as ordinal on this model will likely retain this notion of temporal succession and construe ordinality as temporal ranking. Then, temporal ranking lends itself to the conception of other kinds of ranking or hierarchy. Why, then, does Deleuze explicitly specify that his notion of ordinality with respect to the concept is not hierarchical? How does he arrive at that point? To see this we have to consider the concept in its virtuality.28 Deleuze stresses that the philosophical concept is a virtuality: “[T]he concept has the reality of the virtual.”29 The importance of the notion of the virtual in Deleuze, and the variety of its own conceptual incarnations throughout his writings, cannot be underestimated. Two of his formulations on this topic are instructive. First, the central dictum that captures his differential structuralist understanding of virtuality: “The reality of the virtual is structure.”30 Second, the formulation of Proustian inspiration to the effect that the virtual is “real without being actual, ideal without being abstract.”31 The Deleuzian concept of the virtual is the conceptual move that underwrites much of his theoretical constructions. It is essential to his doctrine of the univocity of being, for it grants to the creations of the Understanding,32 such as the philosophical concept, a reality that does not exile them to an unreachable transcendent realm of ideality. This is an ontological leveling, a dehierarchization, that Deleuze conceives of as an anti-Platonic move. Indeed, he traces the genealogy of his univocity to medieval philosophical sources and explicitly calls it an “anarchy.”33 It is not the concept of the orderless, but the concept of an ontological egalitarianism: all that is, insofar as it is, is in the same way. It is not that there is not difference in what is. On the contrary, true difference among beings is possible because though all beings are in the same way, they can differ in kind, quality, mode, intensity. Being is distributed in a radically egalitarian way. Differences, in other words, are not differences of being. But in addition to the concept not being hierarchical, an intensity, for Deleuze, is also, contrary to the customary contemporary scientific understandings, not ordered in a linear fashion, anyway. This stipulation is easy to miss in Deleuze’s work. For though he relies on the medieval and modern discourses on intensity from the history of philosophy that eventually became the customary contemporary scientific understandings of intensity, he rarely makes explicit exactly what notions of intensity he retains from the tradition and when he departs from it. In What Is Philosophy? we find hints of answers to this question. In a passage differentiating the concept from the proposition, Deleuze writes about propositions: “They imply opera- THE SLEIGHT OF REASON 19 tions by which abscissas or successive linearizations are formed that force intensive ordinates into spatiotemporal and energetic coordinates.”34 This statement provides a clue to his resistance to a linear conception of the order of components within concepts, despite the fact that he will use the language of intensive quantity to express that order. LATITUDE AND LONGIT UDE The confusion comes from the history of concepts of intensity. In The History of the Calculus and Its Conceptual Development, Carl B. Boyer presents a brief history of the mathematical and philosophical treatment of intensive quantity in its explicit stage of evolution in medieval Europe.35 His focus is on the fourteenth-century doctrine of the latitude of forms. After the work of Duns Scotus, the major thinker on this matter for Deleuze is Nicolas Oresme (1320–1382), a Norman cleric who became bishop of Lisieux. His best-known work on the theory of the latitude of forms is De configurationibus qualitatum et motuum, most likely written in the 1350s.36 Deleuze employs the language of latitude and longitude in much of his work. Since it is used in many different theories of intensity, and into the period of modern philosophy, as well, it is not easy to pinpoint his precise use of this language in every case. But we can at least say that, according to Boyer, in fourteenth-century medieval thought, the language of latitude and longitude was used to describe two different sorts of variation in forms. A form in this sense is a quality that can vary in intensity. The intensities at issue were such things as “velocity, acceleration, density,” as well as “illumination” and “thermal content.” Their variation was stated in terms of increase (intensio) and decrease (remissio). As Boyer conveys it: “In general, the latitude of a form was the degree to which the latter possessed a certain quality, and the discussion centered about the intensio and the remissio of the form, or the alterations by which this quality is acquired or lost.”37 But a second kind of variation accompanies latitude: the variation of longitude, which represents “divisions of a time or space interval.” Oresme eventually combines latitude and longitude into a single graphical representation, with a vertical line, representing the latitude of a quality, and a horizontal line, representing its longitude. Boyer explains, then, that the intensity of a velocity would be represented by its latitude, on the vertical line, and its time or duration represented by its longitude, on the horizontal line. About intensive quantities such as velocity, temperature, and acceleration, Boyer interjects to provide the contemporary outcome of the story of medieval thought on intensity: “These concepts are now expressed quantitatively in terms of limits of ratios—that is, simply as numbers—so that no need is now felt for a word to express the medieval idea of a form” (73). This is a point at which Deleuze diverges from science and contemporary scientific discourse on intensity. That is the meaning of the quote 20 SLEIGHTS OF REASON above, about propositions forcing intensive ordinates into spatiotemporal and energetic coordinates by abscissas. (“They imply operations by which abscissas or successive linearizations are formed that force intensive ordinates into spatiotemporal and energetic coordinates.”) Importantly, Deleuze does not accept Boyer’s reading of Oresme’s longitude as identical to a Cartesian coordinate. For Deleuze, the longitude in Oresme would indeed be extensive, but it does not coordinate as the Cartesian abscissa does; it does not make an intensity fully and reductively coordered to an extensity. Deleuze is not thinking of longitudes as fully developed “abscissas or successive linearizations.” Indeed, a careful reading of Oresme shows this: Oresme’s longitude is not a coordinate. It does not coorder but, surprisingly, composes intensities and extensities into a surface area. Boyer misses this aspect of Oresme’s graphic representation that is important to Deleuze and that Deleuze finds explained in Gilles Châtelet’s text, Les Enjeux du mobile. In fact, we could say that Boyer reads Oresme anachronistically on this matter: he takes the straight lines of Oresme’s configurations to be coordinates that produce points or lines as outputs. But Oresme’s configurations (with some qualifications) do not yield points or lines, as the Cartesian coordinate system does. For qualities that are represented along two straight lines, these lines yield an entire area, not points or lines. For example, the product of a given speed and a given quantity of time is represented by a linear length in the modern Cartesian coordinate system, while they are composed into and represented by a plane surface in Oresme’s diagrams. In Châtelet’s words, in the modern representation, “the relation L = VT (Length = Velocity x Time) makes this bit of the abscissa ‘correspond’ to this bit of the ordinate, thus atrophying the horizontality of the abscissa and the verticality of the ordinate.” Coordination is thus a form of reduction, while composition is not. Châtelet explains Oresme’s achievement, so foreign to both the modern and the contemporary ‘mechanician’ alike: “In representing length as an area, Oresme showed that he had succeeded in grasping intensities and extensions in one common intuition, without going beyond a tradition that carefully distinguished them.”38 Oresme’s diagrams allow qualities to be given a double expression, in both extensive and intensive terms. Deleuze approves of this duality and of preserving—while composing—the distinctive difference between intensity and extension. Hence, Boyer overlooks an important feature of Oresme’s thought that distinguishes it from Descartes’ coordinate system and from contemporary graphic representations of continuous change. Deleuze never abandons the language of either intensity or longitude and does not affirm the value of the historical transformations that converted intensive longitudes into extended quantities—along with the same conversion for intensive quantities, as Boyer describes it. In fact, Boyer shows that what happens historically is transformation of Oresme’s geometrical diagram into the coordinate system of analytic geometry; historically speaking, the THE SLEIGHT OF REASON 21 notions of longitude and latitude do become representations of extended quantities with the advent of the abscissa and the ordinate or the two axes of the familiar Cartesian coordinate system. The variations of latitude and longitude were conceived of as variations in continuous quantity, as Boyer (81) implies in his discussion of Oresme’s work on intensive change: “Oresme was led naturally to associate continuous change with a geometrical diagram.” However, with respect to philosophy, Deleuze refuses both the eventual conversion of those axes into representations of extended quantities and the reading of Oresme that casts Oresme’s notion of longitude as a version of a coordinate. How is this account of the medieval ontology of intensities pertinent to Deleuze’s theory of the concept? Deleuze is rejecting the idea that propositions are the same kinds of things as concepts. Propositions, on his view, are discursive and referential, whereas concepts are neither. Components of a concept are intensive ordinates, and propositions “force” them to be ordered extensively. Deleuze’s use of Oresme identifies a point at which the tradition attempted to conceive of intensity and extensity as composing together instead of to conceive of intensity as entirely converted or convertible into extension. In A Thousand Plateaus, Deleuze favors a conception of the composition of intensities rather than their translation into extensities. In What Is Philosophy?, Deleuze is concerned less with the composition of intensities and more with the issue of the neutralization of intensities as a feature that distinguishes science from philosophy. Virtuality For Deleuze, the virtual characterizes many different particular structures. In fact, Deleuze’s corpus could be read as a continual identification of the force of a great variety of structures. One way to grasp Deleuze’s notion of the virtual is to consider the structuralist insight into the generativity of structures, of the structure’s essential overdetermination and reserve. A structure necessarily “includes”39 unactualized relations between its terms, and its terms operate in virtue of their difference from all the other terms of the structure, in virtue of their differential position or location in the structure. It is not that everything is possible; it is that what is possible in the structure has a necessarily excessive possibility relative to that which becomes actualized in the structure. Language as a structure, or kinship as a structure, must always contain unrealized, or in Deleuzian terms, unactualized, statements or relational schemes. But Deleuze modifies his structuralist sources in at least two important ways. He attempts to avoid construal of the essential generativity of structures in terms of (1) possibility and (2) opposition or negation, and replaces these two notions with those of virtuality and difference. In fact, it is that “necessarily excessive possibility” that Deleuze will term “the virtual.” To be more 22 SLEIGHTS OF REASON precise, whether a differential relation between elements in the structure is never actualized or simply “pre”-actualized, it has the reality of the virtual. In a language structure, there must be both temporarily unuttered statements and a necessary “reserve” of virtual statements that are never uttered. This is the case because of the synagmatic and serial nature of language production. Among other reasons for this endlessness, well-formed statements of a language can always be extended by addition, just like an infinite number line, by the use of the linguistic operation of conjunction (. . . and . . . and . . . and . . .). Likewise, structuralist anthropological accounts of kinship posit that kinship systems often must include a permanently unrealizable kin relation, symbolized in the taboos and prohibitions of kinship. Following Bergson’s critique of the ontology of the possible and the real, Deleuze prefers to call this reality of the structure “virtual” rather than “possible.” For the possible, on his view, is a retrospective reconstruction of an allegedly potential ontological antechamber (customarily termed “the Possible”) derived after the fact from our actual experience (customarily termed “the Real”). Hence, this customary notion of the possible would completely ignore the singular character of the reality of the virtual itself. The crucial point is that the virtual must not be conceived as essentially pre-ex-post-facto. Yet this is precisely the error that conventional philosophical construals of the possible, and hence, of the essence of the structure as possible, commit. With respect to the distinction between opposition and difference, Deleuze rejects the common structuralist claim that the difference that disposes relations in a structure is fundamentally a kind of negation or opposition. Deleuze reads Saussure, for example, as proposing a structuralist theory of language in which phonemes are distinguished from each other by negation, by not occupying the place of other phonemes in the system. Saussure’s position, for Deleuze, implies that the difference of phonemes from each other as sounds or marks could be accurately described in terms of negation. To Deleuze, this is an intolerable reduction of the singular nature of linguistic difference and of the difference we find in any structure whose differential relations are generative. DIFFERENCE AND REPETITION We may also approach the question of the nature of the virtual through Deleuze’s thought in Difference and Repetition. There in several quick, rich pages, Deleuze explicates his concept of the ‘Idea’ as a qualitative multiplicity. As is well known, this crucial concept of a qualitative multiplicity is drawn from the work of Bergson, Husserl, and Riemann. Deleuze writes: “In all cases the multiplicity is intrinsically defined, without external reference or recourse to a uniform space in which it would be submerged.”40 The notion of a multiplicity here does not resemble in every respect his later concept of THE SLEIGHT OF REASON 23 the concept found in What Is Philosophy? But we can identify some of the same features that define the concept in What Is Philosophy? First, the multiplicity includes the necessary condition of intrinsic definition and lack of “external reference.” Deleuze also terms this feature of the Idea its “internal multiplicity.” The elements of the multiplicity enter the multiplicity undetermined but must be determined by “reciprocal relations which allow no independence whatsoever to subsist.”41 Second, the notion of the definition of the elements of the Idea in Difference and Repetition finds its correlate in the well-bounded contours of the concept in What Is Philosophy? There the concept is defined by being deinfinitized; it is cut out of the chaos of a possible virtual infinite chain of resonance with other concepts. That is, the individuation of concepts takes place on the ground of a serial linkage of concepts that possesses the potential for unlimited conjunction. By Deleuze’s stipulation, the definition of concepts halts the infinity of resonance between concepts. It does this by “locating” a sort of infinity within the concept, or perhaps by relocating an infinity said to obtain between concepts to a kind of infinity found within concepts. But this will be a special kind of infinity, namely, the infinity of the survey associated with the concept, and with an ontology of perception drawn in part from the philosophy of Raymond Ruyer. This notion is discussed further later in this chapter. Third, we can also detect in this section of Difference and Repetition the notion that the internal definition of the elements of the Idea—elements that are analogous to or, perhaps more accurately, that find their correlates or future roles in, the components of the concept as described in What Is Philosophy?—the notion of an inevitable dependence among elements: there is “no independence” among elements, which are reciprocally related. Technically, the aspect of reciprocal relation would seem to distinguish Deleuze’s thought in Difference and Repetition from that which we find in the later text. This is because the internal relations of the concept’s components in What Is Philosophy? are not reciprocally but ordinally related. Strictly speaking, then, the ordinality of the internal relations of the concept would differ from the reciprocity of the intrinsic relations of the elements of the Idea or multiplicity. But the noted lack of independence is a feature of the ordinality of the concept; ordinality means that the components of the concept are distinct but inseparable. Absolute Surface and Self-Survey Much of Deleuze’s treatment of the notion of the virtual in Difference and Repetition is rendered in the language of structure and multiplicity. But by the time of the publication of What Is Philosophy?, confessedly a work of “old age,” the idiom has changed, and one of his essential reference points becomes the work of French philosopher Raymond Ruyer. Indeed, drawn 24 SLEIGHTS OF REASON from the thought of Ruyer, the notion of an absolute surface or survey is perhaps the most difficult, unusual, and important notion for his argument in What Is Philosophy? Deleuze adopts this notion to characterize the concept: “The concept is defined by the inseparability of a finite number of heterogeneous components traversed by a point of absolute survey at infinite speed. Concepts are ‘absolute surfaces or volumes,’ forms whose only object is the inseparability of distinct variations.”42 What is an absolute surface? Ruyer’s identification of an absolute surface and its self-survey takes place in the context of his work in the philosophy of biology and psychology found in the book Néo-finalisme.43 An absolute surface is a surface that surveys itself without being of a different dimension than that which it surveys. It is allegedly a “mode of reality,” then, that differs ontologically from the world of spatiotemporal dimensions as we know them. Ruyer’s argument for this “mode of reality” is based on his nonphenomenological analysis of perception. He makes a crucial distinction between “perception as a physico-physiological event” and “visual sensation as a state of consciousness.”44 It is the latter, “visual sensation,” that will be the site of his identification of the self-survey that he holds characterizes an absolute surface. As opposed to visual sensation, the rule that governs perception is that for an observer fully to perceive within any given dimension, that observer must occupy a dimension beyond the dimension observed. An observer must occupy a third dimension in order to perceive both dimensions of a two-dimensional object. “One-dimensional beings could not see a line as a line, but only as a point. . . . In short, one always requires an observer situated in the n + 1 dimension to see at once all the constitutive points of a being of n dimensions.”45 That dimensional requirement is what characterizes “perception as a physico-physiological event.” But “visual sensation” is radically distinct from “perception” on this dimensional question. The thrust of Ruyer’s valorization of the special character of “visual sensation” is to expose what he claims is the capital error of construing visual sensation as perception. This is not an error of the theorist, scientist, or philosopher; it is a widespread, quotidian temptation that is “almost irresistible.”46 To grasp the alleged distinction between visual sensation and perception, Ruyer thus invites the reader to consider several concrete cases of visual experience. The point of doing so is for us to notice by attention to our own visual experience that the dimensional rule pertaining to perception does not hold with respect to visual sensation itself. Ruyer proposes that we consider the case of an observer, an eye or a camera, that takes in the whole of a physical surface, in his example, a checkerboard marquetry table surface. To take in the entirety of this surface composed of the partes extra partes squares of the checkerboard, the observer must be situated “at some distance, along a perpendicular dimension” to the table surface. Ruyer invites us to contrast to this perception our experience THE SLEIGHT OF REASON 25 of the “visual sensation itself.”47 If one “inspects” one’s visual sensation itself, one finds it comprises multiple parts, like the table or like a photograph of the table’s surface. But Ruyer holds that, unlike in my perception of the table’s surface, in this case: ‘I’ do not need to be outside of my sensation, in a perpendicular dimension, to consider, one apart from the other, all the details of the sensation. Even if, instead of fixing my attention on the table, ‘I inspect’ my sensation (to register my astigmatism or my myopia), I need not put myself outside of it in order to know it. If I observed the cortex of a being looking at the table, I would have to be outside of that cortex. But this is not the case if it is a matter of experiencing my own sensation. Luckily for me, for otherwise I would need a third eye to see what my first two eyes see, and then a fourth to see what the third one sees, etc.48 Ruyer lends “surface” to the visual sensation called the “seen-table,” in this case. The notion of this “surface” obtained in visual sensation, as opposed to in perception, prevents an infinite regress of observers. Ruyer describes the absolute surface so: “It does not obey the laws of physical geometry. It is a surface seized in all its details, without a third dimension. It is an ‘absolute surface’ that is not relative to any point of view external to itself, that knows itself without observing itself.”49 Thus, as far as the visual field itself goes, it is grasped as a unity. But at the same time, importantly, a kind of interior attention or “mental prospection” occurs in which the attention can move from one detail of the sensation to another, say from one checkerboard square to another, without any eye movement. There is a sort of moving attention point that must be somehow within the sensation. And this is so, crucially, despite the fact that we typically tend irresistibly to act as if there is another internal observer that accounts for that mobile attention to details of the sensation (and which is not the movement of the eyes). We wrongly presume that there is an eye behind the eye, in other words. Moreover, although they are distinct, the parts of the sensation are not really other each to the other, though they have relations between each other. They form an “absolute unity” that is given immediately in my visual sensation. Though in my sensation of the checkerboard I can distinguish ‘squares’ that are ‘nearer’ from those that are ‘farther,’ this is “not a true distance that would require physical means and energy to overcome.”50 But the only way to grasp Ruyer’s point about the nature of the absolute surface of visual sensation is to attend to one’s own visual experience. Ruyer proposes the example of me sitting at my table with a book and papers on it. According to Ruyer, if I attend to my visual field itself, I will find that I have given to me all at once part of my body (including a sort of “nasal 26 SLEIGHTS OF REASON penumbra,” as one might call it) and some objects observed in front of me. I will sense the parts of my body given in the sensation as being at a distance from the items on the table. This is a sensorial distance given in my sensation, but I will easily confuse it with the distance that an outside observer could measure between my body and those items on the table. That external measurement takes place segment by segment—centimeter by centimeter—over the course of time. But my sensorial distance is not this sort of distance. For I grasp all the details in the sensorial image at once. Ruyer writes that “they must be given in an immediate way in an absolute unity, because there is not in addition a third retina . . . to see this visual field from the outside, as does the observer who sees the man writing.”51 The important point is that I tend to think that my visual field is seen by something behind it. The reason that I tend to think that is because my sensation has the capacity for self-survey; ‘I’ can attend variously, without moving my eyes, of course, to different details of the sensation. So in the visual sensation I now have I can attend to different ‘quadrants’ of it or different locations on the computer screen I look at, and this has nothing to do with moving my eyes. (To accept this point, one need not claim that such changes in the point of the survey can take place without any physical correlative changes in the eye, although Ruyer seems inclined in that direction.) The point is that the “unity of consciousness is not at a distance from, in a dimension perpendicular to, the whole of the visual field, in the same way that my eyes, or my head of flesh, are at a distance from the sheet on which my hand writes.”52 Thus, Ruyer concludes that his “visual field sees itself necessarily by ‘absolute’ or ‘non-dimensional survey.’ ”53 There is no third eye; there is no eye behind the eye. Of course, Ruyer’s particular manner of ontologizing the results of his analysis of perception and sensation is contestable and has hardly met with universal assent. But Deleuze applies this notion of the absolute surface to many things, as does Ruyer, in fact. We find a separate application of it to an account of the brain, also heavily influenced by Ruyer’s philosophical biopsychology of the brain. There, Deleuze specifies his Ruyerian understanding of the survey of an absolute surface: It is a primary “true form” as Ruyer defined it: neither a Gestalt nor a perceived form but a form in itself that does not refer to any external point of view, any more than the retina or striated area of the cortex refers to another retina or cortical area; it is an absolute consistent form that surveys itself independently of any supplementary dimension, which does not appeal therefore to any transcendence, which has only a single side whatever the number of its dimensions, which remains co-present to all its determinations without proximity or distance, traverses them at infinite speed, without limit-speed, and which makes of them so many inseparable variations on which it confers an equipotentiality without confusion. THE SLEIGHT OF REASON 27 We have seen that this was the status of the concept as pure event or reality of the virtual.”54 Thus, one of the main aims of Deleuze’s use of the notion of an absolute surface derived from Ruyer is to explain the being of the concept as an intensive unity. It is a unitas multiplex55 that confounds the relations of part to whole with which we are familiar from ordinary extended substances. The notion of the concept’s consistency likewise finds a source in Ruyer and in the alternative part-whole relation that Ruyer identifies in the absolute surface. Here, Ruyer specifies the unique nature of consciousness as not only knowledge, but as a fundamentally compositional force: “Psychology and philosophy insist in an almost exclusive way on consciousness as knowing (connaissance). Consciousness is also essentially a force of binding (liaison).”56 The ontology of the absolute surface thus destabilizes traditional distinctions between being and having. Ruyer explains: “An absolute domain, a real form, being a unity in multiplicity, realizes the synthesis, otherwise inconceivable, of being and having. About the system ab, we can ask: Is it a and b, or has it a and b, as possessed parts? Does the surveying unity have the details over which it surveys, or since the survey is purely metaphorical, is it the whole of the surveyed details itself? The word ‘to be’ here signifies ‘to consist in’; ‘to be’ is opposed to ‘to have’ in this sense only.”57 Point of Coincidence On Deleuze’s account, the concept is also “the point of coincidence, condensation, or accumulation of its own components.” Further, “The conceptual point constantly traverses its components, rising and falling within them.”58 What does it mean for a point of an intensive ordinate to traverse its components? An answer could be given in many terms. In the terms of Ruyer’s analysis of sensation, the point of coincidence is that internal mobile prospection; I can attend successively to various different details, features, ‘areas,’ or parts of my visual sensation, and certainly not by moving my eyes. It is that internal change of ‘focus’ within the sensation that does not require any stepping back or recourse to an external or supplementary dimension that is paramount for Deleuze’s account of the self-survey, and hence the self-reference, that he finds in the concept. But note that my attending successively takes place in the context of a simultaneous feature of the absolute surface, namely, that the details in the sensorial image are “given in an immediate way in an absolute unity.” Self-Reference and Saturation It is clear that the self-reference of the concept is essentially a matter of its positing its components as inseparable components of itself. One consequence of that positing is that to extract a portion of the concept can, 28 SLEIGHTS OF REASON but need not, amount to changing its kind. Deleuze writes: “And this is really what the creation of concepts means: to connect internal, inseparable components to the point of closure or saturation so that we can no longer add or withdraw a component without changing the nature of the concept; to connect the concept with another in such a way that the nature of other connections will change. The plurivocity of the concept depends solely upon neighborhood (one concept can have several neighborhoods.)”59 The passage identifies two kinds of change for the two kinds of consistency, for well-created concepts: internal change in components and external change in connection to other concepts. For the first kind of change, every component matters for the consistency of the concept. Removing one changes the kind of concept. For the second kind of change, since concepts are necessarily interrelated, they can be connected in such a way that changing one can change connections with others. Deleuze is claiming that concepts behave like other kinds of intensities. Take a color of a given intensity and place it next to a new color, and it can change intensity. Change the neighborhood of an intensive magnitude, and you can change the intensity. Deleuze thinks that concepts that are fully “saturated” will, like intensive quantities, not survive division, or extraction of one of their components, without a change in kind. This would be a concept that is maximally comparable to the examples of intensive quantities given above: temperature, altitude. Something like this is also a commonplace of contemporary scientific discourse on intensive quantity: there are intensive quantities that when divided must yield two extensive quantities. This is easy to see with the examples of such intensive quantities as speed, which in these discourses is a ratio measured by distance relative to time. In the contemporary scientific discourse on intensive quantities, the division of the intensive quantity of speed produces two extensive quantities: distance and time. Now, it must be recalled that, strictly speaking, Deleuze develops notions of intensive distance, time, and speed. So he does not endorse this particular example of the division of intensive quantities. But it is not always possible to say what the division of an intensive quantity yields. In A Thousand Plateaus, Deleuze and Guattari provide the example of dividing a horse’s gallop.60 The point of the example of dividing a gallop is that such a division certainly does not yield simply a smaller set of gallops, or a lesser quantity of gallops, or even a lesser amount of degrees of a gallop. It yields a canter or a walk; hence, it changes in kind. So, in this case, we have names for the kinds generated. But in the case of the division of temperatures, or altitudes, the languages I know have few names to register many of these changes in intensity. They probably have more adjectives, in any case, than substantives: a warm evening or a low land, a cool pool or a lofty cloud. THE SLEIGHT OF REASON 29 ONTOLOGY OF THE SLEIGHT: VARIATION IN CONCEPTUAL SURVEY How may we describe the source of the concept’s potential for sleight? May we employ the features of the Deleuzian concept to describe the conceptual sleight? Let us investigate the possibility that although a concept is the kind of thing that is “intrinsically defined, without external reference” it can yet purport to refer externally, that is, extraconceptually. The proposal is simply that though a concept does not refer externally or extraconceptually it can purport to do so. More specifically, a concept can include within it a component that indexes the concept itself as something that refers to, rather than posits, an object. This component, then, would be a component that refers to the concept itself as referential, even though the concept itself cannot, on Deleuze’s view, refer. So, the suggestion is that a concept may contain a component that posits the concept as referring. This would be a disavowal of the primacy of the virtual intensive nature of the concept by a component of the concept itself. But what could “purporting” or “disavowal” mean in this context of an ontology of the concept and its capacity for sleight? We can look to Anselm’s ontological argument in order to display the workings of this strange form of purported reference. For his cleverly flawed argument beautifully exploits the concept’s capacity for sleight. How does it do so? Anselm creates a concept—necessarily existing being or, simply, necessary being—that is explicitly self-referential, since it posits the object of the concept as existing necessarily. That is, it posits that there exists an object to which it refers. This is a fine example of how the concept must be the kind of thing that can refer to itself. It may also help to demonstrate Deleuze’s point that the concept has the same compacted, vacillating, multiple virtuality of the absolute surface with its self-survey. Importantly, though, the kind of reference that Deleuze, following Ruyer, wishes to expose in his ontology of the concept, is a special kind of reference associated with intensity rather than extensity. We might say, then, that Deleuze’s account implies an intensive notion of reference, or the kind of internal or absolute reference that characterizes the relation of the degrees of an intensity to each other, or that marks the inseparability and the inevitable plenitude of the sections of an absolute surface. Thus, we can specify further in what the concept’s capacity for sleight consists: the concept can purport to refer extensively when it is in fact the sort of thing that “refers” only in the manner of an intensity, by its consistency, by its being an absolute surface whose ‘parts’ are related to each other precisely by being coposited. The concept is self-referential because it posits its components as inseparable components of itself. According to news reports, the temperature in Memphis, Tennessee, will reach 106 degrees today, breaking a 30 SLEIGHTS OF REASON record that local weathercasters find especially moving. How does the 106th degree relate to the other 105 degrees? Or more simply, how does an ordinal number greater than 1st relate to the ordinal number 1st? 105 degrees are not extensively contained in 106 degrees. For that matter, 105 degrees are not extensively contained in 105 degrees, either. First, 2nd, and 3rd are not extensively contained in 4th. They are, however, coposited or posited as together, in the very expression “105 degrees.” They are implicated in “105 degrees” and not contained extensively. Deleuze’s theory of the concept permits us to describe an additional possibility inherent in the nature of the concept. This is the possibility that the concept not posit the object of every component of the concept as existing. For the concept can have a component that refers to the other components. More precisely, in the case of Anselm’s concept of ‘God,’ it may have a component that is about the extraconceptual existence of the object of the other components, without being about itself (since components are not self-referential, but referential). Thus, in this case, not all of the concept’s components are posited as necessarily existing. This is so because one component—namely, the component of the-conceiving-of-god—is not posited as necessarily existing, even though it is a component of the concept. The necessary referential self-exemption of the concept’s components is a requirement for Anselm’s proof. Otherwise, it would posit the necessary existence of the conceiving of a necessary (because perfect) being, a result that would be repugnant to Anselm, since perfection, and hence necessary being, is allegedly unique. This account of the ontology of the concept implies that the concept can treat itself or characterize itself as an extensive quantity, as co