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Sleights of Reason: Norm, Bisexuality, Development

Demonstrates the dramatic interplay of elements that comprise the concepts of norm, bisexuality, and development
Jahr: 2011
Verlag: State University of New York Press
Sprache: english
Seiten: 162
ISBN 10: 1438434324
ISBN 13: 9781438434322
Series: SUNY series in gender theory
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“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


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


new york press

mary beth mader

mader hc.indd 1

12/3/10 7:30:42 AM

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SUNY series in Gender Theory
Tina Chanter, editor

Norm, Bisexuality, Development


State University of New York Press



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
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prior permission in writing of the publisher.
For information, contact
State University of New York Press, Albany, NY
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

10 9 8 7 6 5 4 3 2 1








The Sleight of Reason


Sleights of the Norm


Sleights of Bisexuality


Sleights of Development










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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



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.


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



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.



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

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



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.

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 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



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.

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



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

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



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.’

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



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.



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-



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

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



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,



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



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



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



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
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



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 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:



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



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-



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-



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.

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



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



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.
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



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.

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 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



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



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



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.



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,



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.



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



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